Home

Installation - Total Resolution

1. Haya Pass Light 343 High Pass Medium 404 Hage Pass Haay 335 Hag Pass Light 5x5 High Pass Medes 535 Hays Pass Hansy 5x5 Laplacian 3x3 Laplacian 5x5 Invert Inverts the image Repeat Allow the current image to be repeated n by m times Extend image Repeat mage Unirs in X direction Lets in Y direction 2 Cancel REpent Transform Ch 6 Menus p 122 MacTempas User Manual Contains the following operations Scale Rotate Pad Flip Horizontal Flip Vertical Rotate Right Rotate Left Scale Scale the current image Seale image rale in Pixels Wedth Height Pixels Pixels ET 22 Seale in Percent Width 100 00 M Height 10000 X M Keen Aspect Ratio Cancel soie Rotate Rotate the current image Rotate Image Rotate Cd Deg C3 Anti Clockwise amp Clockwise Cancel SRY Ch 6 Menus p 123 MacTempas User Manual Pad Pad the current image New Image Sze of New image Hidth 256 Pixels Height 32 Pixels Typt ish aaa Real value lOG O Comos imag Value 0 00 Cancel Statistics Contains the following operations Min amp Max Mean amp Std Dev All The data is shown in the Info window Calibrate When a length have been marked by the Ruler tool the image Ch 6 Menus p 124 MacTempas User Manual can be calibrated If there is no line drawn the menu command Calibrate Distance Line
2. Lemgt iA 2522 j Pace Spacing 3 2140 Cakculater pdate Angles 7 Ch 6 Menus p 87 MacTempas User Manual Quantitative Menu Ch 6 Menus p 88 when the Calculate Update Angles button is clicked the angls between the family of reflections and the zone in which they occur will show to the right The length of the vectors and the corresponging plane spacing is updated live when typing in a new reflection The lattice parameters can be changed and invoked through the Update Lattice Parameter such that the calculator can be used for structures different from the one that is loaded This is the menu for quantitative comparison between experi mental images and exit wavefunctions with calculated data Structure refinement and imaging parameter refinement is also Quantitative Load Experimental image Load Mandard Deviation mage Compare Image with Simulatian Compare W Arnplitude with Simulation Compare Xw Phase with Simulation Refina Parameters Refine Mructure Sumenebry Transform Calculator Make Front image the Experimental Image invoked from this menu Operating The Routines All the routines except for the Symmetry Transform Calcula tor requires the presence of an image that is considered the experimental image The purpose of this package is to provide the user with tools that permit the following attempts Q Quantitative comparison of experimental images with those si
3. tus of the calculation If the simulation has already been carried out for the current set of parameters then no commands will be active If a change has been made or the file is a newly created structure file the commands showing which subprograms needs to be run are shown active Full Calculation Use this command if you would like the program to run the multislice calculation to its end starting from the point required by the last change made to the simulation parameters Projected Potential Only calculate the projected potential s Exit Wavefunctions s Only calculate the exit wave functions s Image s normal calculation Calculates the image by using using partial coherence envelope Ch 6 Menus p 77 MacTempas User Manual Ch 6 Menus p 78 functions and the lens contrast transfer function Image Plane Wavefunctions s Calculates the wave function at the image plane This would be equivalent to what would be reconstructed using holography Image s incoherent summation Calculates the image s but sums up incoherent images pro duced by electrons from different incoming directions and dif ferent energy ineho rent Surnmarion er Images Parce ns Humber of sampling points across beam spread radius 7 humber of sarnplang poini acrass energy spread 10 Cancel Image s frozen phonons Calculates the image by summing over images calculated from different atomic configurations cons
4. Focal Plane of Objective lens FN M st Intermediate RC N SU 4 DA di ji i 5s n Intermediate Lens w N Y 4 vu 4 NN 4 8 V 2 nd Intermediate W N YN Image S l Projecter Lu 3 NN Lens N y l l l Imaging Mode a Diffraction Mode b Figure 1 Geometrical optics representation of the TEM in imaging mode a and diffraction mode b Ch 1 Introduction to Image Simulation p 6 MacTempas User Manual Simplifying the Description of the Microscope Consideration of the description of the electron microscope in figure 1 shows that the projector lens and the intermediate lens or lenses merely magnify the original image I1 formed by the objective lens For the purposes of image simulation we can reduce the TEM to three essential components 1 an electron beam that passes through 2 a specimen and then through 3 an objective lens fig 2 Our next step in describing the electron microscope for image simulation is to move from the geometrical optics description of the TEM to a description based on wave optics In this descrip tion of the microscope we examine the amplitude of the elec tron wavefield on various planes within the TEM and attempt to determine how the wavefield at the viewing screen comes to contain an image of our specimen By treating the electrons as waves and considering our simpli fied electron microscope Figure 2 we see that there are thre
5. MacTempas User Manual Chapter I Installing the Hardware Protec tion Key Activating the Hardware Key and Personalizing the Program Changing Hard ware or Versions of the MacOS Installation The application MacTempas and its associated files are installed by double clicking on the installer package After authorizing the installer with the administrator password the installer will install MacTempas into a directory in your applications folder The driver for the hardware key will also be installed MacTempas uses a hardware copy protection key which must be installed on your computer If you already have installed a key for use with CrystalKit you do not need a second key to run MacTempas and you can proceed to the next paragraph describ ing how to activate the key for running MacTempas Just plug the USB key into an open USB slot on your computer keyboard or display When MacTempas is run for the first time it will put up its installation screen Enter your name and affiliation as appropri ate together with the installation code for the hardware key T If you have just changed your computer or installed a new clean version of the MacOS you must ensure that the driver for the USB key is installed Run the installation program for MacTem pas once more to install the driver Without the driver in place the program will not recognize the hardware key and MacTem pas will run in demonstration mode Ch
6. a b D a b vi Symmetric Strain Matrix E exx exy eyy Rotation angle B R cos amp sin amp sin amp cosB f Principal strain components e1 e2 an KD Results Depending on the requested output the result will be one or more of the following a the Deformation Matrix b the Symmetric Strain Matrix c the Rotation Angle d the Principal Strain Components The images on the next page illustrate the output produced by choosing to calculate and display the principal strain compo nents e and e5 Four images are produced the x and y compo nents of e and the x and y components of e Ch 11 The Geometric Phase p 179 MacTempas User Manual eoe AT ede Alter Ch 11 The Geometric Phase p 180 MacTempas User Manual Procedure The program first calculates the deformation matrix which relates the positions of a point r x y to its unstrained location r x y through the relationship r 1 D r Sr The matrix S is then decomposed into a symmetric matrix S and a rotation matrix W ga lte e ue mee and W E E sind cos with cos6 1 if sind 6 zlewy e Thus we have the symmetric strain matrix yx yy which is calculated and the three components are shown as images The strain can also be represented as two principal strain com ponents along the principal strain directions The two compo nents are represented as the two vectors e and e These ar
7. ioa VF e sg H ioAdE H vd me H 6 H 20A H V H sin x H 31 The last result is very useful and it leads to the frequently used concept of the Contrast Transfer Function CTF The CTF is defined as A H siny H The equation above states that each reflection H contributes to the image intensity spectrum with a weight that is proportional to the CTF Figure 3 shows a plot of a CTF including siny and the damping curves When siny H for a large range of frequencies H which is the condition referred to as Scherzer defocus 11 the image can be thought of as I x y 1 20U x y 32 where U x y is a potential related to the original crystal poten tial but keeping only the Fourier coefficients related to frequen cies transferred by the microscope The equation above shows the often used rule of thumb For thin specimens under Scherzer imaging conditions atoms are black Ch 2 Theory of Image Simulation p 23 MacTempas User Manual CONTRAST TRANSFER FUNCTION V 200 0kV Cs 1 0 mmDef 560 00 A Del 50 00A Div 0 60 mrad 1 00 0 70 0 40 0 10 0 20 0 50 0 80 0 06 0 14 0 22 0 30 0 38 0 46 0 54 1 Scattering Vector A Figure 3 Plot of the Contrast Transfer Function for a 200kV microscope with the parameters indicated References References Allpress J G et al 1972 n beam Lattice Images I Experimen tal and Computed Images from W4Nb 7 077 Acta Cryst A 28 528
8. 14 NBasis NAmp ApertureRad 15 NBasis NAmp Ah Ak 16 NBasis Namp Oh Ok Meaning The specimen thickness or T1 T2 DT First thickness last thickness increm The commas are required Amplitudes to be stored as for possible plotting YES NO The indices of the reflection to be stored or if Plot NO then Objective lens defocus or First defocus last defocus incre ment The commas are required Radius of the objective lens Aperture in units of A 1 The center of the objective lens aperture in units of h k of the transformed reciprocal unit cell The center of the optic axes in the same units as Ah Ak Ch 7 Input File Format p 141 MacTempas User Manual Ch 7 Input File Format p 142 Line Parameter s 17 NBasis Namp sl s2 s3 17 NBasis Namp NSymop istat 18 NBasis Namp NSymop Vibration Meaning Symmetry operator number 1 An example is x 1 3 y 5 6 z 1 3 The commas are required The calculation status of this structure For a new structure this should be 1 Halfwidth of mechanical Vibra tion in A Note If different wordprocessing software is used Microsoft Word Write Now etc make sure that the text file is saved at the end as type TEXT Chapter O MacTempas User Manual The Structure Sample Calculation As an example of a calculation using MacTempas we consider a BCSCO super conductor structure Using the structure deter
9. 4 b En od perd 250 ii 3 i od D ps5 DD ne pr Man E ht CHI mi pee Cana E O Projected Piei D br Aes Dirag H j irel Fan EET I usag Number of Atoms in the Basis This value is the number of independent atom positions in the basis or asymmetric unit of the cell When operated on by the symmetry operators the basis generates all the atom positions within the cell This value is never modified by the user since the program always recalculates this number depending on the data entered Ch 4 Running MacTempas p 33 MacTempas User Manual Show Symmetry Operators The symmetry operators are automatically created by specify ing the spacegroup By clicking on this button a window dis playing the symmetry operators are shown i Sumulstion Parameters Cria Farmer pscrrari Parurastars Se dae p s heel 1 Irdax ajil aani Aipha jeg 3n fn A in in mdi An M 13140 Beia deg anm Symmetry Operators CHI dono Garena Meg aD x cir ts Don 1 xyz TEEGEE lobe PEE d thaw PO G4LEYCIlERISl E 17 xW E Fal k D pees e m m mee a rt sante thew i X k 2 1E HAE RE RTE Val atomis in iced 1E f han crx ee Xa ST ul ET ETlfzcsrlizzc dlla 15 acd V al diarani sho z TIUIxE eerie pri j k BLE zn Hit Lie l Mbps cope andi Lene Dora Fan 4 eet r e E eee E 2t Yota keresre Hone tyres 223 wrliz xtli2 241 2 Volto 30D Omm sb 8 Y l Z xTlJzzrel T 23 Ghat Drag n
10. 5 133 151 14 H tch M J and Stobbs W M 1994 Quantitative compari son of high resolution TEM images with image simulations Ultramicroscopy 53 191 203 15 Thust A Lentzen M and Urban K 1994 Non linear reconstruction of the exit plane wave function from periodic high resolution electron microscopy images Ultramicroscopy 53 101 120 16 M bus G 1996 Retrieval of crystal defect structures from HREM images by simulated evolution I Basic technique Ultra Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 222 MacTempas User Manual microscopy 65 205 216 17 Press W H et al 1986 Numerical Recipes The art of sci entific computing Cambridge University Press 1986 ISBN 0 521 308119 p 521 Ch 14 Structure Refinement Through Matching of Ex
11. Ch 6 Menus p 92 image will show up in its own window after it has been loaded Note If the windows are covered by other windows it may be necessary to move these to bring the experimental image and the standard deviation image to the foreground since there is no command to bring these automatically to the front Compare Experiment With Simulation This brings up a dialog window which shows the loaded experi mental image and the standard deviation image if loaded The name of the experimental image together with the dimensions are shown to the left of the image Pte i un Experimental image Standard Deviation Mare Tetruc bete 144 Wih Eb Heise 14d ES 3 ipis Compare I Comparison Method i ehestical Cross Cmrrelatian Enesfszieni Real paret _ 5zarixtical Cross Coelan Coie Rr Faure Spee ry Ch Square L Age Mean Suae Ciffeneca Difference base Ci Fracxi penal Mean Abioia Difference iaf MacTempas User Manual When comparing images the experimental image will be resa mpled such that the sampling corresponds to the sampling of the calculated image The example used here will be that of a set of simulated images of Silicon in the 110 zone axis orientation The simulated images for a range of thickness and defocus are shown below e ce uem Se Tools Pointer Tool Used essentially to ensure that no other tool is active Selection Tool Use this to mark an area in t
12. II Katz CETTE ira F ath Compare XW Amplitue Phase with simulation works as with images but the experimental data is compared with the exit wave function either amplitude or phase Refine Parameters Refine Parameters will attempt to find the image simulation parameters that produce a simulated image that gives the best fit between the experiment and the theory The search routine is based on the concept of Simulated Thermal Annealing and requires a starting configuration of parameters a starting tem perature and an ending temperature a maximum change in parameters and a goodness of fit criteria that measures the Energy of the system For further explanation of Simulated Thermal Annealing see the last chapter in this manual Invoking the command brings up the following dialog which is Ch 6 Menus p 103 MacTempas User Manual used to give the input parameters to the algorithm Parameier Refinement Cone Temperature Active Parameters Starting ad 1000 ina Value max change Ending CETATE Li Thickness E 5 Fractional Change 0 9000 A Defocus A 1 25 0 100 For dagree of fraadam C Spherical Abb men babe a Artemios per Termi 25 Spread of Dafpcus A E 1 Successful ttemps 5 Li Convergence mead O20 l He Value regia E Cross Correlation OCF Ci crystal Tit mrad d 2 CCF Fourier Amplitudes Car Astigmatism A 0 00 0 00 in Chi Square CIAF Astigmatism JA 0
13. Sommet certo Transformations Criginal Opermioes xy aar was DEN pe 142 ey awe ee A me RT y ee aee pe 142 MEE PETER PART eee ANT Te re UE Original Basis Ds Gt mer Zr ESC SM 1 B LORD LEE 302 B n oo n On 90 268 u CCS CE DO Aa Orge Unir Cell Aram La d 000 1 D oS Ca d HOSES 5r d DID DD DUO E T3 rq Sn negas Br sn 0 c ia 2e 053p 0 Soma raa LIEU IL IE EL na Bi D SOL S000 Bor 060 000 BRE LED EE LUE Lists k New U peratees Xy sal 5a 1E pe PE aval e ee E82 re Baz yan CIRE CUITE TE YTE spa oe 34d pee CRI ee Are TNT Haw Bas is i DOO DEO I OR Zr DS 0 20 0 1 10 Bi LOO CLONE 302 B 0 DOO DODU 263 Cu D DORT D DOR Oba Maw nir Cell Ca 8D IL DD Sud Ca 6 SH SORS SOS Zu d ODD DOE 13 Za san Se 12 ULL ister 5s Zr Senn Santos B Duo OO UE Ei D 5 DOLO S DL LOS Ei DUOC URL LER Boe Trai eemal har takes the old ames inta the pre nues TransToe mation maris X TE rpm on Oo 0 000 1000 OD 0 000 napa Loo Trardlanan of origin 1 00 OOM oop Mae phar an oe betray ranslion of the origin canit gena ally be reprend by the sant ES LES ah Sa a ro iat Tetraganal Export Mar Set This list shows the symmetry operators of the current space group Initially these are those of the crystal in use but the spacegroup can be changed by the command Switch Space group Ch 6 Menus p 115 MacTempas User Manual Original Basis Th
14. and the calculations required for the image simulation right The three principal planes are marked Ch 1 Introduction to Image Simulation p 8 MacTempas User Manual Simulating TEM Images Cowley and Moodie 1957 showed that the interaction of an electron beam with a specimen could be described by the so called multislice approximation in which electrons propagate through the specimen and scatter from the crystal potential the electron scattering is described by the so called phase grating function a complex function of the potential and the electron propagation is computed with a propagation function dependent on the electron wavelength Since then there have been numer ous formulations of the multislice approximation derived from the Schr dinger equation The problem of simulating images thus becomes a problem of computing the electron wavefields wavefunction at three microscope planes Currently the best way to produce simulated images is to divide the overall calculation into three parts 1 Model the specimen structure to find its potential in the direction of the electron beam 2 Produce the exit surface wavefield by considering the interaction of the incident electron wave on the speci men potential 3 Compute the image plane wavefield by imposing the effects of the objective lens on the specimen exit surface wave Each of these steps will be covered in the next sections How ever because of space
15. only peaks within the selection rectangle are used to refine the lattice Ch 6 Menus p 131 MacTempas User Manual Analyze Displacements Allows for the analysis of displacements The displacements are relative to a reference lattice which normally come from a refined lattice Disclacement Analysis Cakulate Cie parame Huser an Labtine Pararnainen u v Origen dx llosS arg X 173930 Max Fraction of Lartice Parameter Deviation from Lattice Paint to be dy Oo 16 45 Y 220 28 included in the Caloalation aza B Creare image Showing Displacements Mot bl ricos Hack Oavicaian From Larics Paints Magnification EO C average Deuistion From Lattice Planes Min Dg oo average Derhathe Chr tien ef Plas Max 100 104 B Seve Displacements invert coordinate for export to Spneg lass Transform Include Derivatives of Axaraged Dizplacemanrs Average Along Planes L Hovizortal Displacement f Mang ain i macansi hariz oc al BI Vertical Displacement SJ Alang Bom ins conitr vertici Cancel e Geometric Phase Analysis allows for displacement analysis from variations around spatial Ch 6 Menus p 132 MacTempas User Manual ee frequencies Genmetrc Phase Anais Cras ge roe Luerens Displayed image Apre pex LITE al Ei ma mE Arve cain G wector ci ea se Ge 45 5 Gp 15E Ga n Min EF Sh G85 di n5haiz Cakidore Fie rie The geometric phase calculation is described in more
16. perhaps with defects that are aperiodic in the beam direction and require a large number of individual non repeat ing phase gratings Kilaas et al 1987 Ch 13 HOLZ Interactions amp Sub slicing p 202 MacTempas User Manual MacTempas sub slicing While ensuring that the calculation remains sufficiently accu rate MacTempas will normally choose the simplest and quick est method of specifying how slices are defined for any particular combination of specimen zone axis accelerating voltage and maximum g To this end the user can choose to neglect HOLZ interactions if these are judged to be unimpor tant If HOLZ interactions are important then the user should select the 3D Potential Calculation radiobutton in the Options menu rather than 2D Potential Calculation SD calculation is limited and depends on FI available RAM Sub slicing amp using a lLvered siructure is generaly easier and aon pions m 2D Petencial galoularign L3 3D Petential Calculation Cancel ok 3 When a two dimensional calculation is selected MacTempas will use one slice per cell if the cell repeat distance in the beam direction is small If the repeat distance is too large for one slice per unit cell MacTempas will avoid pseudo upper layer lines by producing n identical sub slices When a three dimensional calculation is selected 3D Potential Calculation activated MacTempas uses a sub divided three dimensional potential when the
17. the specimen in mradians It is used in determining the contrast transfer function for the microscope Peak Finding Criteria When search for ring maxima in the power spectrum the pro gram uses adjustable parameters in order to exclude spurious peaks and to determine the exact position of a ring Minimum distance between peaks If two peaks are closer than the specified distance in A the smaller of the two are discarded Use center of mass Intensity within given distance If the option is to use center of mass the peak position will be refined by using the intensities within the given distance in A to obtain a new position for the peak Report all peaks found If this option is set the program outputs data on all the peaks that it finds Focus Determination Criteria In assigning the ring indices the first maxima will be assigned the index 1 provided that the first ring gives a focus that lies within the range of acceptable focus values If it doesn t the program will move to the next maximum in the power spec trum Following rings are given indices 3 5 7 etc Generally the first ring has a large uncertainty associated with the location of its maximum and the program will not use the focus value obtained from the first ring if that option is set default Exclude the first ring This makes the program not include the focus calculated from the first ring when it finds the average focus value Ch 12 Finding Focus f
18. we go to Atomic Basis in the parameters menu to check that all atom parameters have been entered correctly At this stage it is also worthwhile getting MacTempas to display a model of the struc ture by going to the Commands menu and clicking on Draw the Unit Cell When we are satisfied that all data are correct we run the simu lation by clicking on Full Calculation in the calculate menu Note that MacTempas displays the current status of the calcula tion in the Status Window First MacTempas computes the Ch 8 Sample Calculation p 149 MacTempas User Manual Displaying the Results Ch 8 Sample Calculation p 150 phase grating for the structure the status window shows the number of coefficients generated so far then the dynamical diffraction for each slice of the specimen current slice number is shown in the Status Window then four images are computed at each of the three specimen thicknesses that we specified the image number is shown in the window Once MacTempas has finished the computation the results dif fraction patterns images and diffractograms can be displayed Also beam amplitude and phase plots if any of these has been stored To display the images we go to the Display Window and select IMAGE then DISPLAY MacTempas will ask which of the 12 images is to be displayed then display the requested image in the center of the screen The image can be moved around with the pointer tool
19. 1 Binary Files The data can be Real 4 or Integer 1 2 4 byte 2 TIFF Real 4 Integer 1 2 4 byte If the routine recognizes the file as a TIFF file it will just open the file and display the image For Binary files you will need to specify the data type the width and the height of the image Byte swapping is also sup ported If the program does not recognize the file as type TIFF it MacTempas User Manual will bring up the following dialog e t Ras iage port fms 12 Fil Foarhal Liig CAT Je Data Type meger Bes Sige ell LITT nay as Nu Parag li re de Hg ii qon 32 Tm choco ere Sine on Sampling Wikh 250 Height Jz Ange Bo Although the dialog box indicates that the program supports input of text files this is currently unsupported The dimensions of the simulated image are shown at the bottom of the dialog box for binary files Once the routine has read in the file it will display the image in a separate window Load Standard Deviation Image This command allows you to read in a standard deviation image to be used together with the average experimental image for comparison with simulated images The standard deviation image will be used in conjunction with the average image for computing c square deviations between the experimental data and the computed data Otherwise the input works exactly as for the loading of the average experimental image Again the Ch 6 Menus p 91 MacTempas User Manual
20. 1 of survivors which will be he parents of the next generation iii Create a new generation by applying the random generator after selecting and mixing a part of the parent s parameter vec tors iv Loop back to i until one of the following criteria are met a a maximum number of generations have been reached or b a critical goodness of fit has been reached Other Techniques There are other ways to do the refinement which is based upon changing the input parameters so that the system moves in a path where the gradient with respect to the fit is the largest 17 Each method has its advantages Simulated thermal annealing and simulated evolution are good techniques for getting close to the optimum fit Once close to the minimum gradient methods may be used for further refinement until the match is within the uncertainty of the measurement References 1 V lkl E et al 1994 Density correction of photographic material for further image processing in electron microscopy Ultramicroscopy 55 75 89 2 Ruijter W J de and Weiss J K 1992 Methods to measure properties of slow scan CCD cameras for electron detection Rev Sci Insts 63 4314 3 Mooney P E et al 1993 MTF restoration with slow scan CCD cameras Proc Annual Meeting of the Microsc Soc of America 51 262 263 4 Ruijter W J de and Weiss J K 1993 Detection limits in quantitative off axis electron holography Ultramicroscopy 50 269 283 Ch 14 Structure Refinem
21. Approximation p 154 MacTempas User Manual s ee X mmc AINSI US Ch 9 The Weak Phase Object Approximation p 155 MacTempas User Manual Ch 9 The Weak Phase Object Approximation p 156 Chapter 10 MacTempas User Manual Creating a Layered Structure A layered Structure is a special type of structure where the composition varies in the direction of the electron beam An example of this would be a crystalline material having surface layers of amorphous material Another example would be a crystalline structure where the repeat distance in the electron beam direction is too large for the repeat to be used as the slice thickness and the unit cell must be sub divided into several Lav La B M Points Lay A H Points Ch 10 Creating a Layered Structure p 157 MacTempas User Manual slices with different atomic content As an example we will work with three layers which we will call LayA LayB and LayC Each of these layers are what we would call a single structure That means they are defined as a unit cell with lattice parameters and atomic content The one thing they have in common is that the lattice parameters A and B with respect to the electron beam are the same and that we will use identical sampling in each case see figure above The idea of the layered structure is that the 3 layers can be arranged in any chosen sequence to make up the total structur
22. CTF Draw various representations of the 2D contrast transfer func Ch 6 Menus p 69 MacTempas User Manual Ch 6 Menus p 70 tion for both linear and non linear imaging AA 20 Centri Transfer Furctipa n AD Profis br adip CTE wwaQeiaey iar brel Spear CTI Baal nae Siina mal ieee MN D Hle ice Spe Certe ee ge ee te Un tag Mois Fa Don Met lan Fagit ta Lipire C wenosrope bage brel 100 D Phas Phir n iar Dijetar lara Deien LA Tir OD agbe Ena Abaran Ca mw Da CD keim Penguin Di free aaae Caviar roc waa Ml IDa C ges ju AI Tar Other Alvemachorst Lat ligi Ares Ub Dean ol ame C Tar ns r ia Otherto fa Ci Corea h ku Non linear image contributions can be examined in detail through the non linear analysis button on near appui 0 MacTempas User Manual Draw Pendellgssung Plots In case the user has selected to store a set of diffracted beams for plotting of amplitudes and phases as a function of specimen thickness this brings up a dialog box allowing the user to set the plotting conditions One can choose to have the amplitudes or the intensities plotted as well as the phases of the diffracted beams Each reflection can be plotted by itself or several reflections can be superimposed on the same plot Instead of plotting the values the values can also be written to a file for further manipulation or inspection eo Amplitude Intensity as a f
23. Gaussian distribution will lead to a modified criteria but still based upon 7 Structure determination In order to determine the unknown structure it is necessary to perform a comparison between calculated images exit wave functions or diffraction patterns and experimentally obtained data As described above the comparison can be done using dif ferent matching mismatching criteria Ideally the determination of the structure is done by modifying the structure until the mis match between the experimental and calculated data is within the error in the experimental data In principle the imaging parameters themselves can be allowed to vary together with the atomic coordinates However in practice the imaging parame ters are optimized separately if possible This reduces the com plexity of the problem and reduces the number of steps involved in the search for a solution which optimizes the matching crite ria In cases involving unknown defects in the presence of a known structure the imaging parameters and specimen thick ness are first determined from the known structure Determination of an unknown set of input parameters requires the following 1 An image in real or reciprocal space obtained from the experimental data Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 218 MacTempas User Manual 2 A computational method yielding an image to be compared to the 1 3 A method for
24. Haa Cee ee el Tie Maia Fisl aaan aa bel jae ED ein am meg n mn d En Dram bei ere Mi TM n T peu r D dwmri uad ee OM issus a di purus wm del mcdio iri es a K ma FRERE rt EET UII L i TEX ses wih a ad CORTE i a secs ROB us tn emi nd des iem Jas EG EG RON HN iur rin emira bam rm rens Miei Kd d S Dl 2 Paper Format T iaa uns ten Imam MPs ie ERR T Free at ORA RE 7 acl Were O0 agi MacTempas User Manual the structure that you want to create New Layered Structure Create a new layered simulation file A name is prompted for before input is made Enter a unique structure name the pro gram will append the extension lay A layered structure is char acterized by being made up of a sequence of pre calculated projected potantials Thus a layered simulation file does not contain atomic positions The structure information in the input dialog is replaced by Crestal Parameters Ap io Akaba deg 30 00 BTA AIT Bera deg moo CJA fm Appi Gares dea S00 Peig of paming E phase paliti Sachi ie Hg ice Difrea Pon eus Cale Tra cb bea Only A and B and Gamma have meaning for a layered struc ture The buttons Define PGratings and Define Stacking are used to choose the different projected potentials and to define their sequence to make up the entire specimen Open Structure File Open an existing structure or a leyered file The standard Mac intosh file open dialog is presented and only
25. Intensity to be considered in the Objective Lens 10 f Cancel ok Slice Method Allows the user to select the option to perform a three dimen sional calculation of the projected potential by summing over MacTempas User Manual the third dimension 1 in reciprocal space 3D calculation ix ler tad and dapends on availa RAM Sub sHicieeg amp using a lagerad sucres is ganerally easier Calulation Cethons 20 Potential calculation C ap Potentia Calrulatien C Cancel Show Microscopes Displays a dialog showing the user which microscopes are known to MacTempas The default parameters associated with a known microscope can be changed by the user and a new microscope may be made known to MacTempas MacTempas currently only allows a maximum of 10 microscopes to be made known Known Micrascopas Defined Microseapes Name HQE ABT mr 2000X 20 OF X CM200 VoR kv Cmm Diwimrad DellA 400 200 Eon aon 201 200 La 6 20 2 06 1 20 1 00 ano melee 2 55 20 CRT 50 B5 1t Miri scape Parameters mee an Microscope Parameters ols 2n me Mixrescpoe Name Unticl 1 Edit Accelerating Voltage ouf UD Spherical Abberation Constant men 1 2 Cancel Spread of Detocus tar 5g Dnerngence Angle half witthi mrad 5 i a D Use Fit For Electron Scattering Factors Use Fit For X Ray Scattering Factors MacTempas can use either the 8 parame
26. MacTempas Display Window This is where most of the results of a calculation are displayed All objects such as images diffraction patterns unit cell drawi ings etc in this window are all objects which can be manipu lated Objects are moved with the pointer tool If the Option key is held down a copy of the object will be created The magnify ing tool operates on each object separately Several objects can be selected and copied onto the clipboard and can be pasted into other applications Images in this window if double clicked will open up in their own separate window The selection tool will select any object which intersects the selection rectangle Each object have different properties An image can be scaled directly by dragging its corner A kinematical SAD pattern can be MacTempas User Manual rotated by using the rotation tool when the object is selected and the mouse down event takes place in one of the diffraction spots A drawing of the atomic structure can be magnified and OOO Copper rotated into different viewing directions Ch 5 Windows p 51 MacTempas User Manual Ch 5 Windows p 52 Chapter MacTempas User Manual File Menu Menus Many of the functions in MacTempas are run from one of the MacTempas menus including the multislice calculation In addition most options are set from one of the menus This is a list of the currently available menus and a des
27. Manual microscope Crystal Pamer Simulation Parameters Speximien Faraemeen Toca axm breat inde aj Seli alpha fdeg S00 m 1 m D d 1 g miM zoua seules mnn Horn skces ger cel z Laudis CW 5z00 Camena deg 9000 Res YIN Spapegrosp 4 der Tables Thick eur ire orai 4D D a Hal Ananias in Batis 3 E 3 Store Ampi Phe a m Hal Syn gs i toe Cant of Loue Circia h pm y uan aetema ries JE P aaae oem a3 M rzsrcpe ans lami Parametar i Aatigreatiion Coma aimes MAS Cite Pene 4ODOEX Angie 7 Woda ge kM 30 ABT an Han NIE Cense asgie mrad ARM Le Pie Two f ld D nn 200C T y 2 Spread of defocus LA 2000FX Du on Taree fold p pp Dehaces Gen der Er A RER coma oo Obj apen ead wr 1280 Mic honical Wibi LU irom ites hy to be arii faa ugma of fab joo aag Sane central Bear i u Angl S se ag Cant of Oj Larmi Apri D 00 020 E Ca o 0 MN MTM E Cem of re Optic Kx OM 000 n 0 0 Urges rite Cahn on maus Mark forde cabou Let Pregected Painriial L1 Ext restencion CT image Fark ax rakuna _ Projected Poteenal 1 an ar eer ii Wet Cancel a Voltage The electron microscope accelerating voltage in kilovolts Objective Lens Defocus The defocus of the objective lens is entered in ngstr m units with a negative value representing underfocus weakening of the lens current As for the speciment thickness param
28. RE LN x Hd d F OR e dede dee eI deo o ut o moo o fe thtt ete catt mettent n ge rt rereremtise Lots rhh tm st mitthtethitneet fret et ERS ORS RE Re the Gen che ne de dd de de me cc PRS SEAT th LAS ee me dodo de oo A oon om oom le ee th tt btp a h ee skis me mm 4 t tt ho OEE eh EES de te ENTE Rd ee L Z TZ T LLDALLb d LL PEELED OEE a didis de dx LL TDI TED lll a DIDI IP IT 66ST EERE SHEET OH ROH OE er ye ee ee ee A AU Am the tete de 6e tr dd me mt 0 i ii eee JC XX Dante G mme a md o8 de Ae RR OE fe F L le de de M de te STOTHERM OBOE rte bn mt mit ee de 0 0 am de de de de DESEO SEES EHTS EEE HEED HOH OS gt 1 L 4 gt Ka LI Lj L 4 s L1 LI gt 7 LA L B oe Re eee SEES ab te the OHHH tetes nets HOR POM ee ee eee ee eee ee ee in Ch 11 The Geometric Phase p 163 MacTempas User Manual BAM Geometric Phase Aealsis Create Mew Pin e Current Disglaged tn agi psu rper Ec JA em E nove calc G Werke e uu EN La D Ly c I LE Dn a Note 1 The image must be square and the dimensions must be pow ers of 2 Alternatively a selection satisfying the criteria above must exist for the image to be analyzed 2 By default the program automatically computes th
29. Spacer aa Statistical Dress Correlati ma CoeiTirsent hd adi m Fert T ip lib F rbummass case sh a tis Square C2 Bapt Frs Square Diffe ressce D Defererce Image C2 Feactngeas Mean Ai peime Diener T Co This is a straight calculation of the normalized cross correlation coefficient between the experiment and the calculated image s Ch 6 Menus p 95 MacTempas User Manual For it to give meaningful results the origin of the experimental image neeeds to coincide with the calculated image kai dit Ets re Ja Te TE ais Me qu iai aka IER DORIA ET idt xw Lo pi Walii imi Ln E hime mat IE end i IHE ich heb s jog lit LER EEH mac ia iem jnamm amet SETTI LIFI METI re Reciprocal Space There are two options for calculating the cross correlation in reciprocal space The first is an exact calculation which is equivalent to the real space CCC The entire Fourier transform of the experimental image is compared with the Fourier transform of the simulated image and the CCC is just the reciprocal space equivalent of the calculation in real space Thus the reciprocal space CCC is equal to the real space CCC Exact Ch 6 Menus p 96 MacTempas User Manual Exporiaenectal bbp i Ga vod aedi De ote hamer eo Gin citer Wh Hepat 37 a epee Yme ze Leospare Eine Himno H8 La Im prar bir Teri Coe pa Lie til OF Habire Crocs Correiatips pef riens Em al Spare
30. User Manual Ch 8 Sample Calculation p 152 MacTempas User Manual Chapter Wavefunction Approximations Ideal Scherzer Lens The Weak Phase Object Approxima tion The Weak Phase Object WPO approximation is a useful tool to find out what kind of information about a specific structure may be revealed at different levels of resolution The WPO approximation has already been described earlier and some of that information is repeated here There are two important assumptions that are made in the WPO approxima tion The wavefunction of the electron can be written as P x y 1 iot x y where x y is the electron wavefunction at a point x y and G x y is the projected electrostatic potential at the same point Sigma is the interaction parameter between the electron and the potential of the atoms and t is the specimen thickness This first approximation is good for very thin specimens containing light atoms An ideal Scherzer lens is a lens that transfers all diffracted beams with a g vector that is less or equal to 1 resolution and blocks all diffracted beams with a larger g vector In addition it adds a phaseshift of 90 degrees relative to the central beam to all beams passing through the lens This in addition to the 90 degree phaseshift introduced by the scattering event itself the 7 in the equation for V x y above causes all scattered beams that pass through the lens to be 180 deg
31. a file MAL input ve Sup An es ur Poma BG rary RI El Greg stake TFF Flesninrg Pisin TFF MAL bipi Fi L ASCII Wiss Li Exarapla Seriu UE Bass Fiber l ando a files are binary files used by the mal or TrueImage program for exit wave reconstruction from a through focal series Save Image As Similar to Save Image Import PICT File Import a PICT file and display it in the MacTempas image win dow Save Window Saves the content of the image window as a PICT file Page Setup Set the options for the page to be printed Print Print the front window Ch 6 Menus p 57 MacTempas User Manual Edit Menu Ch 6 Menus p 58 Redo Cut 36 X Copy C Paste 36V Clear Select All A dit Object _ di Arrange Object E Undo Undo Redo the last operation These operations do not cur rently work in MacTempas Cut Cut the selected Object or the Selection made by the selection tool Copy Copy the selection or the selected object Paste Paste the content of the paste buffer into the display window The source for the paste can be an image cut out from another application or through the cut copy commands of MacTempas If the object is an image the image will be pasted into the dis play window if it is currently selected or into a separate image window if not Clear Clears the selected objects made by the selection tool Select All Select all objects in the display windo
32. a relatively new technique for finding the global minimum of a multivariate function 15 The algorithm is based upon assigning an energy to the system which is a function of the parameters being varied with the optimum configuration of the system being the minimum energy state the ground state A temperature is also assigned to the system and the temperature is slowly being reduced as the configuration is changed From the initial configuration Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual EQ X X X5 the parameters are varied in a random fashion and for each variation the new energy Ej x x xy is calcu lated The new configuration is always accepted if AE Ej X1 X9 Xp Bj 1 X 1 X2 x5 lt 0 Otherwise the new config uration has a probability P of being accepted where E poe 7 E and T being dimensionless quantities For each temperature the system undergoes a given number of variations accepting or rejecting the new configuration based upon the above criteria When a specified number of successful transitions have taken place the temperature is lowered by a certain amount and the parameters are changed again As a function of iterations the energy of the system decreases towards what is hoped to be the minimum energy configuration and the process is terminated when either no more successful variations are made for a given number of attempts or the tem perature
33. an overall weight Band ree LE Perens Bond Serengah Calculator Criteria move From Ta Man Dite DA Valence Bond Core ne Welgha a x ET L LELS Lo LJ LJ i5 L LELS L a LIL FE 1 ias fie a lt r l LELE 1o Y LJLJ an L LELS Lo Cheral Weight an Ter FER i mr form Running the Refinement Once the parameters are set and OK has been clicked a progress window appears The current atomic configuration is shown together with the corresponding simulated energy The energy as a function of time temperature is shown in its own window and can be monitored to ensure that the system moves in a desirable fashion It is important to understand that no spe cific recipe can be given to ensure that the system finds a mean ingful minimum in the configuration energy The success of the optimization depends on how far the starting configuration is from the solution and the choice of annealing parameters It is not a straight forward just run and you get the correct answer black box approach An understanding of the system a good feel for choosing a reasonable starting structure and some expe rience in choosing annealing parameters is definitely a requirement in order to have confidence in the resulting ending configuration Experimenting with different input parameters is advised As with refining simulation parameters it is possible to save a log file or to produce a movie of the annealing process Saving a movie can be ve
34. automatically set the angles depending on the spacegroup if possible The pro gram will also automatically set lattice parameters depending Ch 4 Running MacTempas p 31 MacTempas User Manual Cry hearse on the spacegroup Thus if the user chooses a cubic system b and c are set equal to a Space group MacTempas generates symmetry operators for the any one of the 230 space groups when selecting the number or the symbol of the space group as listed in the International Tables for Crys tallography By clicking on the pop up menu Space Group one can choose one of the 230 spacegroups by first selecting the type of crystal structure i e hexagonal or cubic The user can choose one of the spacegroups by clicking on the symbol for the spacegroup or by entering the number for the spacegroup Sud ation Peeanieress IPH ree Pree ere Zeap aun peel LIN act it EL ug z m I 1 ys 7 1 EI M ees Miror mi il L bul CIN ii Tuta fiig nina Space sn Pil Tabled lenguas Trigagai B cb eoe om Faria 1 Hauge m KE ci Sem ac Le ovv 4 sci mara motel 4 m t TA iva amp Sof afer T i mere Teu dbepi s D H lekriBLeuga otal Lea Pac PTE Mead rope Himi EE ACER i a kutag hu Ai Lg ary Lm Convergence orgie Iran Ine Pars Fm Tea fall pa iru Dd Spread si disce A BO pP y Then to Cakes ibsisq inc ami Ji Sa EVI DIEN Hr Tu TEX HT edad Li pd bei 0x Dax Er Bacharel Vrai L rs i zh i mr ia A Bisaa beer ie ba
35. constraints it is impossible to cover everything in great depth For detailed derivation the reader is encouraged to read the many excellent texts on the subject Ch 1 Introduction to Image Simulation p 9 MacTempas User Manual Ch 1 Introduction to Image Simulation p 10 Chapter MacTempas User Manual Modeling the Specimen Theory of Image Simulation The specimen is a three dimensional objects consisting of a huge number of atoms From a modeling point of view it is nec essary to reduce the number of parameters to a more manage able number For crystalline materials described by a repeat of perfect unit cells this is easily accomplished The unit cell in this case is defined by the lattice parameters A B and C where A and B are in the plane the specimen perpendicular to the elec tron beam and C is in the main direction of the incoming elec trons A B and C are related to the normal lattice vectors a b and c depending on the orientation of the specimen The speci men is thus reduced to M number of unit cells where M C is equal to the thickness of the sample giving in the end a 2D image which covers the area given by A and B In the case of a defect structure which no longer can be modeled as a small repeating structure it is necessary to limit the extent of the calculation by defining a supercell which contains the defect The resulting image obtained from the calculation will contain artifacts whic
36. do not repre sent a periodic continuation of the image Streaking can be reduced by multiplying the image with a circular mask The mask is represented by a circle of pixels with value 1 up toa specified radius and then falling off gradually to 0 within 5 to 10 pixels close to the borders of the image A side effect of mask ing is the increase in noise in the Fourier transform which is dis cussed below If only the image of a single unit cell of the crystalline material need to be determined and compared with the image obtained through an image simulation calculation the image of the unit cell can be resampled onto the coordinate system and sampling interval used in the computation This is equivalent to determin ing the matrix M defined through the equations a Ma 1 Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual b Mb Two steps are necessary the rotation scaling required to make the lattice base vectors identical and secondly the determina tion of a common origin Finding the common origin between experimental and calcu lated image is determined by cross correlation between the sim ulated and the experimental image 5 Fourier transforms and masking The Fourier transform of HRTEM images of crystalline materi als provides useful information about lattice spacings and can also be used to compare experimental Fourier amplitudes with theoretical calculations Because the image being transfo
37. files of the type TEXT with the extension at or lay are displayed as selectable The name of the display window will change to reflect the name of the current structure Close Close the file image or window currently selected Save Structure Save the current data for the structure file in use The current data will be written to the file overwriting any old data Save Structure As Save the current structural information Do not use a name with Ch 6 Menus p 55 MacTempas User Manual an extension if the file being saved is a structure file for later use by MacTempas Open Image Open an image Supported images are currently tiff files and binary files RGB tiff files and compressed tiff files are not sup ported Binary files can be of integer or float types with differ ent length and byte order impot Faw imag report era 12 File P i rial Las grh 3 07lk1 Dura Type z DEL H Sine iy pH Wii T34 angke mz T rs Cate Evian ighe IH J Sissin a Gima bong Mi d ignc d Me MN New Image Create a new image of specified size and content Create Image New image Prepartias Bax Width 12 amp Pixels f Constant Real L imag g Height 128 Pixels MA esum p _ Gauss lan Height 1 Sigma 10 Tw ES O Discrost Grid Deltax 10 Della Y 10 pew D Compl D Randem p a i TE Ch 6 Menus p 56 MacTempas User Manual Save Image Saves the content of the image window into
38. four ways to produce the set of phasegratings or projected potentials that describe the multisliced crystal For structures with short repeat distances in the beam direction the simplest method is to use one slice per unit cell For structures with large repeats in the beam direction several methods may be used three of which rely on sub dividing the slice into sub slices Any of the four methods can be used in MacTempas Identical slices with only one sub slice per unit cell repeat distance A multislice computation in which every slice is identical con tains no information about the variation in structure along the incident beam direction and includes scattering interactions with only the zero order Laue zone ZOLZ layers For struc tures with short repeat distances in the beam direction such a computation is adequate since the Ewald sphere will not approach the relatively distant high order zones Identical sub slices with n sub slices per unit cell repeat dis tance For structures with large repeats in the beam direction a method of sub dividing the slice is required in order to compute the electron scattering with sufficient accuracy The simplest Ch 13 HOLZ Interactions amp Sub slicing p 201 MacTempas User Manual but most approximate method is to compute the projected potential for the full repeat period then use 1 n of the projected potential to form a phase grating function that can be applied n tim
39. in the presence of noise the cross correlation coef ficient CCF for the two images I and I n where n represent random noise superimposed on image Ip can be written as 13 2 ccra Reno cera tof 14 2 cera py f 82 2 15 oh with 2 _ 9 we A 16 The effect on the hyper angle 9 cos CCF is in the small angle approximation 8 9 Y 0 5 82 ED If two images are identical except for a small error in one of the image formation parameters defocus thickness etc the error in the angle 9 is proportional to the parameter error The error in the angle due to independent parameter errors is 0 JY 0 18 Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 216 MacTempas User Manual Typical mismatches in CCF pattern matching due to parame ter errors are Table 2 Parametet Error theta mrad Noise 0 06 Composition 0 03 0 02 Thickness 2nm 0 2 Defocus 15nm 0 4 Beam Tilt 5mrad 0 8 Astigmatism lt 15nm 0 2 Crystal Tilt lt 2mrad 0 6 Beam Diverg lt 0 3mrad 0 1 Focal Spread lt 5nm 0 15 Vibration lt 0 04nm 0 2 Chi Square or Chi based criteria Although all the methods above measure either the match or mismatch between two images the important questions is not to what degree do they match but how well do they match given systematic and non systematic errors Thus the fitting parameter must take into account t
40. inched in the Larr 10 af gra ei ra i1 o gt TIO Firre cama bur i k lc Ag ee a Angle with si auia to Cam of Obi Lani kor no ng mn a3 Cari of ha Opt Aa QOO S doo Bd Dii ribi caca lacia mani kick for dci arem Pmkexd Prions t L Due tee ELI KU Le sde FH LL Propos Priori ial EE II iz LI mam ti Ch 4 Running MacTempas p 32 The input also allows for choosing the second setting for a spe cific spacegroup if one exists If no space group is required one should use the space group P1 1 in which case the only sym metry operator is x y z Additional symmetry operators can be MacTempas User Manual EOE Garrak fez Tamie E Hal Tale Mea der d d Late ae tee Career Aeg e fre cat Dae hpm Ad entered by opening the dialog displaying the symmetry opera tors Show Basis atoms Use this button to bring up the dialog window that enables the input of the atoms in the basis Lire mures m be dr dei eke aa 1 nm non Cam of CL Lini Aar Cam ofthe ote fan BER o 0D Ies idi C vci aes Flash Kc re acu lee Aboma in the Motif Basis Waume s inceH y roerd z caurd dw fact rc za 1 8 jose ao om semo amo a ie dr LC pod o t c panno Lex pd zaii Ligai 3 B omowe acmon a302 260009 LEY O0 4 B oomo oowoo Aze semo oian 5 u D on nd 1 ooo Jaisa 3 6 RI imnogo E osamo CORD aama same LORD 5 m aooo oosa samon 7 100000D a 6 mmo aoo 020500 saion Troie
41. mined by Tarascon et al 1988 we show the steps necessary to input the model structure examine it compute the diffraction pattern and simulated images and display and print them As published by Tarascon et al in Phys Rev B 37 1988 p 9382 9389 the tetragonal structure has the following parame ters Space group 14 mmm Cell parameters a b 3 814 c 30 52 a b g 90 with nine atom positions in the basis Atom Wyckoff notation X y Z Occupancy Ca 2a 0 0 0 1 Sr 4e 0 0 0 1097 1 Bi 4e 0 0 0 3022 0 87 Bi 4e 0 0 0 2681 0 13 Cu 4e 0 0 0 4456 1 O 1 8g 0 5 0 0 446 1 O 2 4e 0 0 0 375 1 O 3 4e 0 0 0 205 1 O 4 4d 0 5 0 0 25 0 065 Isotropic thermal parameters for all atoms are fixed at 3 6 Ch 8 Sample Calculation p 143 MacTempas User Manual Entering the Structure Ch 8 Sample Calculation p 144 To enter a new structure into MacTempas we first go to the FILE menu Section 3 3 and select New Structure File After entering a filename in the New File dialog MacTempas will put up a dialog into which the relevant information must be entered Note that the program shows a default cubic structure We need to change the data to reflect that of our structure Filename BCSCO Specify a filename under which to file the input data It should be descriptive enough to be easily remembered when you need to open it later Make sure you use no extension Sar al azcam Parone CE Crysis Parreira See lPararmm
42. p 167 MacTempas User Manual Amplitude Image LL be Ceanienic Feke Ares sil ULL ae i Curr Ding lapidi magi Mure leer 1 hi esee Artem colt Ge Verbi ec lus Ge C13 amp 134 x ma Ci cy i rr minit gi mrap Payee 9 1 Mamai Pa 3 iC Note 1 After the phase image is calculated the next operation is to refine the local g vector This is performed by selecting an area in the phase image over which the lattice spacing are considered constant and invoking the menu command Find local average g vector This implies that the spacings found this way becomes a reference to which subsequent calculations are related 2 Before calculating displacements and strain two non colin ear frequencies g gt must be defined 3 After refining gi the next step would be to set g gt using the G2 tool in the same fashion as the previous step refining the local vector for the same area as when refining g Ch 11 The Geometric Phase p 168 MacTempas User Manual Refine local g vector Background In order to calculate displacements or strain one needs a refer ence lattice The vector g that is found when creating the phase image in the previous command is the one with the highest amplitude and is not necessarily the one that one would like to choose for the reference lattice In order to further refine the vector g one chooses an area with the selection tool that is the area that is to become the ref
43. phase shift relative to the path of the unscattered electron a 0 which is written as Scherzer 1949 2n A M4 C a 2x CH 24 If there were no other effects to consider the image would be obtained as follows Calculate the wavefield emerging from the specimen according to one of the approximations Fourier transform the wavefield which gives the ampli tude and phase of scattered electrons Add the phase shift introduced by the lens defocus and the spherical aberration to the Fourier coefficients Inverse Fourier transform to find the modified wave function Calculate the image as the modulus square of the wave field However there are two more effects that are usually consid ered Variations in electron energy and direction Chromatic Aberration Temporal Incoherence Electrons do not all have exactly the same energy for various Ch 2 Theory of Image Simulation p 20 MacTempas User Manual reasons They emerge from the filament with a spread in energy and the electron microscope accelerating voltage varies over the time of exposure The chromatic aberration in the objective lens will cause electrons of different energies to focus at different planes Effectively this can be thought if as rather than having a given defocus fp one has a spread in defocus values centered around f The value fp is what is normally referred to as Af as indicating defocus The images associated with different defo cus
44. repeat distance is large and defaults to one slice per cell if the distance is small enough Note that the number of sub slices per unit cell can be forced to be greater than one by setting it explicitly in the Parameter menu this will ensure that any HOLZ interactions are included even for small repeat distances Of course if the repeat distance is very small leading to a distant HOLZ in reciprocal space Ch 13 HOLZ Interactions amp Sub slicing p 203 MacTempas User Manual both the calculation and the experiment it is modeling will interact only very weakly with the HOLZ reflections Use of the Layered Structure option to produce the scattering from a structure that is layered or aperiodic in the incident beam direction is effectively an application of the method of sub slic ing based on atom positions Thus the user could create a num ber of sub slices by assigning selected atoms to different structure files then forming a phasegrating for each sub slice and using the Stack Phasegratings command to specify how the sub slices are to be used to describe the specimen structure This is the suggested method to try first if upper Laue layers are to be included or 3 dimensional effects are important as it is much faster than using a complete 3D calculation Other methods Van Dyck has proposed other methods to include the effects of HOLZ layers including the second order multislice with poten tial eccentricity Van Dyck 1980
45. starting at byte 80 and the file can contain more than one image Data is Real 4 lt structurename gt hout is the result of calculating the image plane electron wavefunction s instead of calcu lating the simulated images The data is complex pairs of numbers real and imaginary The data starts at byte 80 and the file can contain more than one image plane exit wavefunction lt structurename gt aout contains the complex ampli tudes of several diffracted beams at one slice increments Ch 3 Introduction to MacTempas p 29 MacTempas User Manual in specimen thickness The beams are specified by the user and can be plotted as a function of specimen thick ness In addition two print files are produced but rarely printed just in case additional information about a computation is required by the user These files are 7 lt structurename gt p_prnt contains information about the way in which the Projected Potential subprogram processed the lt structurename gt at data to produce the specimen potential 8 lt structurename gt m_prnt contains information about the way in which the Exit Wavefunctions s subpro gram processed the lt structurename gt pout data with the lt structurename gt at to produce the exit surface wave that is it contains information from the multislice computation Ch 3 Introduction to MacTempas p 30 MacTempas User Manual Chapter Generating an Inpu
46. then the remaining model is the correct one for the structure For this process to produce a correct result the investigator must ensure that all possible models have been examined and compared with experimental images over a wide range of crys tal thickness and microscope defocus It is also a good idea to match simulations and experimental images for more than one orientation The simulation programs can also be used to study the imaging process itself By simulating images for imaginary electron microscopes we can look for ways in which to improve the per formance of present day instruments or even find that the per formance of an existing electron microscope can be improved significantly by minor changes in some instrumental parameter Alternatively based on imaging requirements revealed by test simulations we can adjust the electron microscope to produce suitable images of some particular specimen or even of some particular feature in a particular specimen Ch 1 Introduction to Image Simulation p 4 MacTempas User Manual Describing the Transmission Electron Micro scope In order to simulate an electron microscope image we need firstly to be able to describe the electron microscope in such a way that we can model the manner in which it produces the image As a first step we can consider the usual geometrical optics depiction of the transmission electron microscope TEM Figure 1 shows such a diagram of a TEM operat
47. to the same mean value The second term measures the difference in con trast between the two images while the third term where is the same as the normalized cross correlation coefficient measures the difference similarity in the pattern of the two images Thus it is important to note that the normalized cross correlation coefficient CCF only measures similarity in patterns and ignores variation in contrast and differences in mean levels It is generally found that most of the mismatch between experimen tal and computer simulated images is due to the difference in contrast 14 The difference in contrast can be an order of mag nitude and the cause is generally attributed to the following fac tors misalignment specimen vibration inelastic scattering Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual specimen damage There is however an ongoing debate as to the nature of the dis crepancy in contrast as calculations indicate that the factors above are not sufficient to resolve the disparity A possible explanation is that there is a general background in experimen tal images that is not accounted for Effect of noise on matching criteria In order for two images to be considered equal we need to con sider the effect of the uncertainty or error in the matching crite ria due to noise and the parameters determining the image A study of the effect of noise on the cross correlation factor reveals that
48. 00 Deg Real lattice a 26 35 Px ga b 26 41 Px 120 00 M Show Lattice Delete Lattice Info Amplitude 11 14 9 13 16 9 7 6 Phase 76 117 75 83 76 100 29 159 81 Find Motif Ch 6 Menus p 135 MacTempas User Manual Ch 6 Menus p 136 After the lattice has been refined click on Find Motif This will extract all the phases and amplitudes from the Fourier transform at the lattice points and one can test for possible sym metries of the motif Pare Gren Sarmesereiaed image Ferias Wap gez EM pa gm pnm Ema FA CITITi pa pam p g pa 3117 Fm mcs pain aac pa 2 18 pam EZB Bl ckescliritiCali arira E hii Curran asa Cir ign O ire ap a LL IN Each symmetry can be tested and imposed on the reflections to form a new unit cell motif The origin of the unit cell motif is dhown on the right and can be changed eB Symesere zad Monit Sy mesr zed image zm Zy 73 3 Chick Defines Hase Cri pari E Saiar bigs Origine L ad Pure LT i pere TL ETES 1 Shoah Ra 5 f Cram rang ME tinea Ceporbnenta reagi Once a solution has been chosen a new image can be created with the imposed symmetry and can be used as an image to compare with simulation MacTempas User Manual Focus Determination Contains the following operations Find Focus From Image Find Focus Preferences Finding focus from a HRTEM image is outline
49. 00 loco 10 n For thickness ihis is an integer giving ihe number of a a m unir cell 3tice rhickriesses d EL Hmane Comparison Beginn Cuig Options ET Create log file with anergy versus tiene _ Create a movie of the progress wird Tame between frames seconds 1 Cancel _ Setting Image Comparison region The area to be used for the comparison is set using the button Set Image Comparison Region Soh The B Urin Dre Sn WHA Ch 6 Menus p 104 MacTempas User Manual Selecting the image region is done in the same fashion as under comparing images in the previous section Running the parameter refinement After selecting the area not needed if the entire image is com pared which is the default and selecting the parameters to be refined and clicking OK a progress window for the parameter Farana Rainer Corel Temperature ACOME Parameiert ining Korg inia wala max Change Bead isa nonolp Thickness T 5 Fractional Chege FE kau DA 319 110 Per riagres ni lnscn spherical Abi mes Reo s E Abba peu per Temp 25 Spread of Descrus pi Hs FSurcra1 d Alten 5 cereurqureza read 5250 a Fit let hired TFET TES Crows Correlation CF 4 Crate Tub read D 2 1 LS CCF Feng Ame ieedias Ci ar Ant meer D TH DG mi Jh Syre _ LE Aatgrnacum X BOS Gw jane For chicken chin bi qu brie gree that form bar o j i unti oe 3lce bh here ses Pom log
50. 0000 Display Window Display Potential Exit Wave Diffr Patt FFT Cells E IF Magnification 1 Display work on the region within or outside of the mask The mask parameters can be edited by double clicking on the mask or selecting the mask and choosing Edit Mask from the Pro cess menu The number of lattice spacings for the vector s for the lattice mask and line mask can also be changed by clicking in the end point of the vector with the Option key down Each click increments the number of lattice spacings to the endpoint by one Holding down the Shift key and the Option key decreases the number of lattice spacings by one This window shows the current position of the cursor within the image window and the intensity of the underlying pixel When dragging a rectangle the dimensions of the rectangle are shown Line lengths and angles are also displayed Image statistics is displayed in this window when invoked through the Statistics in the Process menu Use this window to define which part of the calculation to dis play The choices are Projected Potential Essentially the output of the projected potential routine There is a one to one correspondence between the points in the projected potential and those in the image if displayed under equivalent conditions Exit Wavefunction This is the output of the multislice compo nent of the programand shows the distribut
51. 189 MacTempas User Manual imately proportional to sin x lul C X fo where x SON 4_ On Fu This shows that there will be maxima in the power spectrum whenever n x a CN U 2Afu ns for n odd integer Thus if the spherical aberration is known the focus can be determined by finding the locations of the maxima in the power spectrum assigning indices n to the various maxima rings and solving for focus fo With several rings in the power spectrum the value for focus obtained from each ring will vary and the focus is expressed as the average value together with a standard deviation Before you do anything with these routines you will need to specify the microscope parameters that are used in the calcula tion of the focus from the HRTEM image The parameters that you will need to set are Microscope Voltage and Objective Lens Spherical Aberration Constant In addition there are a number of parameters used by the pro gram in its search for rings in the image power spectrum and the assignment of ring indices It is recommended that you first accept the default parameters until a better understanding of the Ch 12 Finding Focus from a HRTEM Image p 190 MacTempas User Manual influence of the parameters is gained by use of the program Find Focus Search Parameters Microscope Parameters Accelerating Voltage kw 300 0 Spherical Aberration Coefficient mm D 65 Spread of Defocu
52. 536 Cowley J M and Iijima S 1972 Electron microscope image contrast for thin crystals Z Naturforschung 27a 445 451 Doyle P A and Turner P S 1968 Relativistic Hartree Fock X ray and Electron Scattering Factors Acta Cryst A 24 390 397 Frank J 1973 The envelope of electron microscope transfer functions for partially coherent illumination Optik 38 519 536 Gibson J M 1994 Breakdown of the weak phase object Ch 2 Theory of Image Simulation p 24 MacTempas User Manual approximation in amorphous objects and measurement of high resolution electron optical parameters Ultramicroscopy 56 26 32 Goodman P Moodie A F 1974 Numerical evaluation of N beam wave functions in electron scattering by the multislice method Acta Cryst A30 322 324 Howie A 1963 Inelastic scattering of electrons by crystals Proc Roy Soc A271 268 275 Ishizuka K and Uyeda N 1977 A new theoretical and practi cal approach to the multislice method Acta Cryst A 33 740 Kilaas R et al 1987 On the inclusion of upper Laue layers in computational methods in High Resolution Transmission Elec tron Microscopy Ultramicroscopy 21 47 62 Kilaas R 1987 Interactive software for simulation of high resolution TEM images Proc 22nd MAS R H Geiss ed Kona Hawaii 293 300 Kilaas R 1987 Interactive simulation of high resolution elec tron micrographs In 45th Ann Proc EMSA G W Bailey ed Baltimore Maryland 66 69
53. Installation p 1 MacTempas User Manual Ch Installation p 2 Chapter MacTempas User Manual Introduction to Image Simulation The best High Resolution Transmission Electron Microscopes HRTEM have a resolution approaching 1 A which sometimes leads to the erroneous conclusion that using an electron micro scope all atoms in a structure can be resolved However it is not the inter atomic distances that matter but rather the pro jected distances between atoms seen from the direction of the incident electron In order to obtain interpretable results it is necessary to orient the specimen such that atomic columns are separated by distances that are of the order of the resolution of the microscope or larger This is a condition that very often is difficult to satisfy and often limits the use of the HRTEM to studies of crystals only in low order zone axis orientations The HRTEM image is a complex function of the interaction between the high energy electrons typically 200keV 1MeV with the electrostatic potential in the specimen and the magnetic fields of the image forming lenses in the microscope Although images obtained from simple mono atomic crystals often show white dots separated by spacings that correspond to spacings between atomic columns these white dots fall on or between atomic columns depending on the thickness of the specimen and the focus setting of the objective lens O Keefe et al 1989 Fortu
54. Joa a Tu ina inc jns LELEL l 7 addit TRE 11141 pao naTE1 au LE LEE LE ones on Jaara ums jore jume fanm jan CT LE We jom Ing os tome jama isr jn e jen les IDWE S mp n Tomi jn Lar td L Dees joe CET jane jan TT io n san jan CE Chi Square LANSEN e EY IE a 0 8425 user las pasze 1 m laure ore ILE ILI l zaar iiir LT Jar TTE ac T I ane osma igo jon This computes the chi square deviation between the calculated image s and the experimental images optionally using the standard deviation image for obtaining the uncertainty associ ated with the average pixel value MacTempas User Manual ee Ce OT mee ine Hame Sim Wide 5 Haigh 3i WesutWu Compare Eaire Imane IER Lise inane Dementia non Apt La Site al Crack Correlates Cogfficees Aaa beet me Uri s Died ies METRIS Lisa on Exact E 2 mpn Ch mare GSpot sean Square Ceres Terence image Qireactional Mean Assoluti Diffessser i Cem EJ If no standard deviation image is given the uncertainty in the pixel value is set to 10 of the intensity in the pixel The Chi square goodness of fit criteria is sensitive to the mean level of the images and the scales the calculated images so that they have the same mean as the experiment before computing chi square Lower values indicate better fit with a value of 1 mean in
55. LAALLILITIITITITITITITITITTIIIL HeRARALLLITIITIITYTTCTPH UN CE E Ccittttttt Gti ticle M LiL 4 A SP ee Se E HARAALLLLIILEFITTYTITTTTTTTTTTITYTIITITTY RARLLLLLLLIIZTTTIITTITTTITTTITTITIIIIILIT a a a a i IL LL ILES Se a A A a ee ee ee a a TELEL SSS TTT ee a a Eee ee ee D TLE ELELLLee S i RR LLILLLLILLILLILILILLLLALLLLALLALLLI i ee ee Bet Phas SS T E Cte ee ee eS ee LIRE ee EE A OM GE ci 9 un LE SSS ES Te LEREEERERLELEREEEELELLELELELLELELLECE LE LRRILELLLLLLLLLLLLLLLLLLLE L eh 84 TITTIUTTTTYTTIMXIITIT RGAIRLLILELLILILTIIITITTIYITITIIYTITTITINUT PEPE COED ee XLI TIIITTITYITY Litt i 2 eS eus n Ltt amp ee EE ae eS em TECER thane tS dO a a a eee ee yh and calibrate the line Ch 12 Finding Focus from a HRTEM Image p 195 MacTempas User Manual Calbrata Distance Transform Statistics m MM Lan Laregkh im pismis Pat r wel F r Weer se GTS EME De wal Extract From Can eair spaos ding ai nr ie length TA a el Tl Calkhrxiad length 7AE B nguirem brreerse length Sd T Angine _ ente CRT Cathratien bng amp rpexel 0 123258 l nanzmatar The calibration should be in or nm for the routine to work Once this is done select an area that is square with dimensions being powers of 2 hold down the Option key when you select the area that contains some amorphous region In this example the area is a 512 square region of a 1024 image If no selection is se
56. Length Les Length in pixels 179 01 6 Piel For inwarse unite enter the t Pixel corresponding nan imeerse length e uL FEE Calibraved length 173 01 A Angstrem Inverse length DOSSEE ioli satan L2 nanometer Calibration unit nixel 1 019000 C 1 nanaomerer Enel 89 is inactive The image can also be calibrated through the Edit Object menu command In that case no line needs to be drawn Extract From Complex If the front image is complex images can be created from vari ous component of the complex values Real Part Imaginary Part Modulus Modulus Squared Phase Correlation Convolution Ch 6 Menus p 125 MacTempas User Manual Contains the following operations Auto Correlation Cross Correlation Phase Correlation Convolute Deconvolute Align Auto Correlation operates on a single image and calculates the auto correlation function of the image Cross Correlation calculates the cross correlation image for two images r Image C nazs Corralrion Choose image 1 l bhcgen 1 2 fey 1 2 Choose image 2 A2 beseo 0 304152 H Carai E Phase Correlation calculates the correlation function based on the phases of the two images disregarding the amplitude of the Fourier compo Ch 6 Menus p 126 MacTempas User Manual nents imagu Phan Coiralation Chooses Image E LAT begin 3 308 be 52 He Chonsa Image a 3 AZ bso 3 HHS fragrep Cui zH DI 1
57. O Keefe MA Buseck PR Iijima S 1978 Computed crystal structure images for high resolution electron microscopy Na ture 274 322 324 O Keefe M A 1979 Resolution damping functions in non lin ear images Proc of EMSA 37 556 557 O Keefe M A et al 1989 Simulated Image Maps for use in Experimental High Resolution Electron Microscopy Mat Res Soc Symp Proc 159 453 458 Scherzer O 1949 The Theoretical Resolution Limit of the Electron Microscope Journal of Applied Physics 20 20 29 Self P G et al 1983 Practical computation of amplitudes and phases in electron diffraction Ultramicroscopy 11 35 Ch 2 Theory of Image Simulation p 25 MacTempas User Manual Ch 2 Theory of Image Simulation p 26 MacTempas User Manual Chapter The Three Simu lation Steps Full Calkculaman Projected Pote retin Imagelsi ncaherer summation iage ratan phanein Weak Phase Ohta images Ring Parr ineraatical SAC Pattern i israel Diffiactian Pamain Kinersatiral CRED Pattern CAPO Paltern STEM image Introduction to Maclempas Since the simulation of a HRTEM phase contrast image can be subdivided into independent calculations involving the struc ture the scattering process and the imaging process MacTem pas allows one to invoke these independent calculations separately through the Calculate menu Full Calculation This command will start the calculation from the required st
58. Sin 20 2320 Loma LU Obi apart cad A 1 tree d nb Ust 12h Mer rar cal Vobranan L s M CRM Wis imum imani ba eed pd in iba Lami 10 En Jona al fe hs am no g Al Er F k E rape L rang cme Ti i i b Ange dre ith canis Do Casi of OE Lens Apri ini tm O00 oto Tani of ihe Opin Bain Tol Gp of Dg TEE Er Cat ETAPE U Mart For ra ex calien Progacted Persi Est eeu re s _ imig Myt na akiri Propad Perai ai Ex Aiia _ imagi Came OK are determined by entering the hkl values for the reflection Only 10 reflections can be tracked this way Center of the Laue Circle Specimen tilt is specified by entering the center of the Laue cir cle in units of the h and k indices of the projected two dimen sional reciprocal space unit cell Equivalently the tilt angle and azimuthal angle can be specified instead The new indices and their relationship to the original reciprocal cell is found in the data file structurename p prnt Type of Absorption Absorption can be included in the program by introducing an Ch 4 Running MacTempas p 37 MacTempas User Manual imaginary projected potential Simulation Parameters Crpatal Parereeare Specimen Paramesars p Zoe wx irati 3 Irnx AA 38140 Aipha des mnn Mdr dun nii In vA terr FERAM mon Mur sbie per cell z T mub divecds CA 30500 Canina deg 1 eu max 1 210 z aP EE TERME EJ Thick bencerdd ED 0 5D 9 pi Aramu in Bain a xm Srove Amp
59. To get all 12 images onto the display screen simultaneously select the options menu and the Montage option Back in the source window set ZOOM to 0 5 to reduce the image mag nification in order to fit all 12 images on the screen then DIS PLAY Now go back to the montage option and deselect Montage To display the projected potential for comparison with images select PROJ POT in the source window then DISPLAY To display the diffraction patterns at the stored specimen thick nesses select DIFFR PATT in the source window then DIS PLAY To change the size of the patterns choose Diffr Patt from the Options Menu and choose a different camera length The size of the diffraction spots also depend on the divergence angle set in the main parameters It may be necessary to adjust both the camera length and the divergence angle to get a suit MacTempas User Manual able display of the diffraction pattern To display the power spectrum of one of the images we choose IMAGE from the source window Respond by answering which image and then choose FFT from the operand window Finally click on DISPLAY to view the power spectrum The options for the power spectrum are the same as those for display of diffraction patterns The circle drawn in diffraction patterns and power spectra corresponds to the objective aperture and can be turned off from the diffraction option Ch 8 Sample Calculation p 151 MacTempas
60. Trace Tool This tool is used to get a line trace for the line drawn with the Trace Tool being the current tool The integration width can be changed by double clicking on the trace line or choosing Edit Object when the line is selected Color Picker Tool This tool when selected allows the user to pick a color from the Color Window and color atoms selecting fore back ground colors and pseudo color atoms The selection of color is described under Color Window above Hand Tool Use this tool to move images around in the image window Ruler Tool Use this tool to measure distances in an image An image can be calibrated from the menu command under Process after a line is drawn using the ruler tool Rotate Tool This tool is used to rotate drawings of crystal structures In order for it to be active the structure must be selected and the mouse click must occur within an atom Masking Tools The last 5 tools are masking tool normally used in reciprocal space but they can be used in real space as well The masks are a Spot mask A reflection and its conjugate is selected b Lattice mask A mask defined by two lattice vectors c Band Pass mask This mask is defined by an inner and an outer circle d Wedge mask Defined by two lines e Line mask Defined by a line and a single lattice vector All these masks can be transparent or opaque meaning they MacTempas User Manual Info Window Info x 71 y 298 val 0
61. User Manual 2 2 4 1 3 3 0 0 4 Ene Ligtsod 0 2 2 0 0 2 1 1 1 Kinematical SAD Pattern calculates the diffraction pattern by adding up the intensities for each tilt angle within the cone of incident electron directions Ch 6 Menus p 80 MacTempas User Manual SAD Pattern Options Initial Settings Current Settings Zone Axis uvw 0 0 1 Zone Axis uvw 0 0 1 ds o EB 1 jo Resetto Initial Settings Initial Rotation Degrees about x 0 000 abouty 0 000 Bl Spot Color 8 Kikuchi Line Color Bl Text Color Options Settings Mi index Diffraction Spots Camera Length mm 150 C Show d spacings Microscope Voltage kV 800 in real units A Divergence Angle mrad 0 850 1 reciprocal units 1 Ie ect di y Mac Excitation Error 1 A 0 025 M Draw Kikuchi Lines v Include Higher Order Zones C1 Index Kikuchi Lines Minimum Structure Factor 0 100 Maximum G Vector 1 2 000 Cancel ok be SN Ch 6 Menus p 81 MacTempas User Manual Integrated Diffraction Pattern calculates the diffraction pattern by adding up the intensities for each tilt angle within the cone of incident electron directions Diffraction Fattann Thickness Al G mas fil 200 Disk Size ferd 020 knrags Ses dih miz Haight Taiz Kinematical CBED Pattern Will calculate the CBED pattern for the given input parameters using the Bloch Wave approximation Kinematical CBED P
62. alatian Coati ia st Era Speers pL Sot reca Dri CREL Deo IDEM oer SD Cet Wim ae Steen image in E Di Sauare o Lg Prat Miran Square Ohara nu l Wh pene pe iens Biene D Pres man ig Pues Ard ior DET he ete ceca ae There are two calculations performed in this case One gives a difference image s which are pseudo colored such that where the experiment and simulation agree within one standard devia tion the pixel is black less than 1 5 standard deviations the pixel is colored green and outside the pixels are shown in shades of red or blue depending on whether the values in the simulation are lower or higher than those in the experiment In addition to the difference image s the chi squared value is Ch 6 Menus p 101 MacTempas User Manual also computed for each image and shown in its own table Ch 6 Menus p 102 Fractional Mean Absolute Difference This calculates the fractional mean absolute difference between the experimental data and the simulated data Span images Srandmed Dewannn Mae Son n iwi 2 High X2 a ieiet ere za i aim Mo Esair ID lit at Abas poe So Berti rios Cy Statistical Orasi tere latima On er ment Heal tears C Ent Mhan bapa ri rere e De reer image WM fractional Mean Absolute ference MacTempas User Manual hss fa f essa ECO eas ER ECTS ETS Li a In is Lm nur Li ub
63. and the improved phase grat ing method Van Dyck 1983 Tests of these procedures show that the extra computation involved in using potential eccentric ity may be worthwhile but that the improved phase grating method diverges too easily to be useful Goodman P Moodie AF 1974 Numerical evaluation of N beam wave functions in electron scattering by the multislice method Acta Cryst A30 322 324 Kilaas R O Keefe MA Krishnan KM 1987 On the inclusion of upper Laue layers in computational methods in high resolu tion transmission electron microscopy Ultramicroscopy 21 47 62 Self PG O Keefe MA Buseck PR Spargo AEC 1983 Practi cal computation of amplitudes and phases in electron diffrac tion Ultramicroscopy 11 35 52 Ch 13 HOLZ Interactions amp Sub slicing p 204 MacTempas User Manual Van Dyck D 1980 Fast computational procedures for the sim ulation of structure images in complex or disordered crystals A new approach J Microscopy 119 141 152 Van Dyck D 1983 High speed computation techniques for the simulation of high resolution electron micrographs J Micros copy 132 31 42 Ch 13 HOLZ Interactions amp Sub slicing p 205 MacTempas User Manual Ch 13 HOLZ Interactions amp Sub slicing p 206 Chapter 14 MacTempas User Manual Structure Refine ment Through Matching of Experi mental and Simu lated HRTEM Images Introduction The goal of perfor
64. art ing point and proceed to calculate final images Projected Potential generates the crystal potential that produces electron scattering from the structural data unit cell dimensions symmetries and atom positions occupancies and temperature factors Exit Wavefunctions s generates the electron wavefield at the specimen exit surface it uses the projected potential combined with information about the accelerating voltage of the electron microscope the speci men thickness and tilt The computation algorithm is the multi slice approximation Image s normal calculation generates the image intensity at the microscope image plane the effects of the objective lens phase changes and resolution limiting aberrations are included via parameters like defocus spherical aberration incident beam convergence spread of defocus and the position and size of the objective aperture Image Plane Wavefunctions s generates the electron wave function at the imaging plane in the microscope This is equiva Ch 3 Introduction to MacTempas p 27 MacTempas User Manual lent to the application of the Contrast Transfer Function to the Fourier transform of the electron wavefunction at the exit sur face of the specimen followed by an inverse Fourier transform The calculation of the image plane wavefunction is used for comparing with the electron wavefunction found by the use of electron holography The remaining commands in the Calcu lat
65. atio From two equivalent regions the noise can be estimated from obtaining the cross correlation coefficient for two regions Given a cross correlation coefficient ccf the signal to noise ratio can be estimated as AR _CCF 2 1 CCF In order to reduce noise and to obtain a statistical average of the image of a single unit cell motif the positions of individual motifs can be determined by cross correlation Once these are found statistically equivalent regions can be averaged to find the average motif and to determine the signal to noise ratio associated with individual pixels as a function of position within the unit cell This determines a standard deviation for each pixel i and can be used to set confidence levels associated with matching of the experimentally averaged image with a cal culated image 7 M e ECO 3 M 1 3 where M is the number of equivalent regions being averaged Using a low pass filter to perform a smoothing of the image may be effective depending on the noise level present particu larly when averaging over statistically equivalent regions can not be performed Smoothing helps the eye see features more clearly but has the disadvantage that it causes correlation between image pixels which may distort the significance threshold of simulation mismatch criteria Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual Averaging can also be performed through symmetrization whic
66. attern Options Initial Settings Current Settings Zone Axis uvw fi 1 1 Zone Axis uvw FETE RIRE 2 0 2 Reset to Initial Settings Initial Rotation Degrees aboutx 0 000 abouty 0 000 Bl Spot Color B Kikuchi Line Color B CBED Line Color J Text Color Options Settings M Index Diffraction Spots Camera Length mm 363 C Show d spacings Microscope Voltage kV 150 In real units A Disk Radius 1 0 269 _ In reciprocal units 1 EE Mac Excitation Error 1 0 025 Index HOLZ Lines SRM Maximum G Vector 1 A 4 000 vi Draw Kikuchi Lines Index Kikuchi Lines Minimum Structure Factor 0 100 Cancel ok Ch 6 Menus p 82 MacTempas User Manual p 83 Ch 6 Menus E kc na K X Nes XR Will calculate the dynamical CBED pattern for the given input CBED Pattern MacTempas User Manual parameters using the Bloch Wave approximation CEBO Pater Pana Ash i 1 L ale Bore ad 3 n UL Th D erxtian n J g max icr calcula E R aam lneckren Thickness Ul Tor Macrrarags otip EV Loo Pt liue v Bio li ad Chi hire BB Sran se sent dicrances wage Hrer I Snap to soo center GE inchada parca aas Aj ous ardapug l 10i ol fn The x axis of the pattern can be set by dragging the green selec tion rectangle of the x axis arrow to a diffraction spot The pat tern will rotate so that the selected spot is along the x axis of the pattern The part
67. ault all elements are active Selecting an active element and clicking on the Make inactive button will move the selected element to the Inactive list Just because an element is listed under active elements does Ch 6 Menus p 107 MacTempas User Manual Ch 6 Menus p 108 not mean that one of its types will be used in the refinement pro Define Active Abom Active Four f Grid mL A been reactive Active Sr Cn E Cu cedure It is necessary to specify the area used for comparison and which atoms are to be optimized before the simulated ther mal annealing is carried out Set Are to Compare amp Active Atoms is used to set the image comparison region as previously explained and to select atoms for refinement The following window appears MacTempas User Manual irec Raffesecnr Centred Esp rmenta nace Statins Model mi Es EE Bei LE Le Es Le lc E Les deo b da rra ra pa bina roch ard irae Others mous accendang to symenetrigs f memwede rem 3 0 1 Shew ody nan syeamatry related atoms Reset Wew Use the tool to add individual atome tothe fet To remove stems use the teal Abami With same 72 wall m re rogerfer wales ridici removed with rhe tonl Area used for comparison Selection Comparison Area Seheoon In reimege Abnms to refine f TES E Addi Craup Selection 4 l1 E Arens Comp Ros 4 o Opie oy Sets the comparison regio
68. cal lattice vector in the multislice calcula tion The potential is evaluated out to twice this value units A l The direction of the electron beam in units of the real space crystal lattice vectors Number of symmetry operators number of slices per unit cell and a flag indicating 2d 0 or 3d 1 potential calculation only if Nslices is different from 1 Ch 7 Input File Format p 139 MacTempas User Manual Ch 7 Input File Format p 140 Line Parameter s 7 NBasis Ntypes 8 it symb x yz dw occf Meaning The number of atoms in the basis the number of different types of atoms A different type is associ ated with a different chemical symbol or a different Debye Waller factor The type of atoms a number from 1 NTypes Chemical sym bol x y z coordinates in relative units of the lattice vectors Debye Waller factor and occu pancy factor 9 The same as line 8 for atom number 2 10 The same as line 8 for atom number 3 8 NBasis MicName Cs Del Th The name of the microscope the 9 NBasis Voltage 10 NBasis Lh Lk spherical aberration mm the spread of defocus A and semi angle of divergence mrad Accelerating voltage kVolt The center of the Laue circle in units of the h and k of the trans formed reciprocal unit cell Real numbers MacTempas User Manual Line Parameter s 11 NBasis Thickness 12 NBasis Plot 13 NBasis ih ik il Defocus D1 D2 DD
69. calculation status Mark for re calculation 1 Exit Wavefunction Mark as calculated 1 Exit Wavefunction Eq Tilt mrad amp angle of Laue Circle h 0 00 k 0 00 0 00 0 0 __Astigmatism Coma Angle Mag wjhoriz Two fold 0 0 0 Three fold 0 0 0 Coma 0 0 0 Mechanical Vibration A Sigma of a b 0 00 0 00 Angle with x axis 0 0 Image 1 Image PES Care GD mation regarding the lattice parameters A and B etc There are no input for atoms because a layered structure has no atom information per se Even though you are asked to fill out a specimen thickness this value has no meaning at this time because the content of the structure has not been defined The values of A and B come from the structures LayA LayB and GATE TE AL El Drim Fae teen Ch 10 Creating a Layered Structure p 159 MacTempas User Manual LayC When you create the layered structure a default value of 2 A is supplied and you must change it in the main parameters if a different value was used in calculating the phase gratings for LayA LayB and LayC 4 Once the information in 3 has been filled out the file is created and you must define the structural or phasegrating content of the layered structure This is done by going to the Command Menu and executing the command Stack Phaseg ratings If this is a new file there will be no phasegratings listed and the command New must be used to define the la
70. comparing 1 and 2 4 A criteria based upon 3 for when 1 and 2 are statistically equivalent 5 An initial set of adjustable input parameters which are to be optimized so that the final configuration results in satisfying 4 6 A method for varying the adjustable parameters so that the final configuration is found within finite time There is an essential assumption being made above which states that the computational method used in 2 will produce the image in 1 given the correct choice of input parameters This is a separate issue which will not be addressed here The validity of this assumption can be debated and it is acknowledged that computational methods are in need of further refinement How ever in what follows the assumption is presumed to be valid Matching Images or Exit Wavefunctions In order to compare calculation with experiment one can com pare either images or diffraction patterns For perfect structures it may be beneficial to compare diffraction patterns since the number of data points to compare are given by the possible Bragg reflections of the structure 11 However for defect structures the information that describes the defect is located in the diffuse scattering between Bragg spots and it is more effi cient to compare images The entire discussion relates to both real space and reciprocal space although only real space images will be referred to Simulated Thermal Annealing Simulated thermal annealing is
71. continuing through 80A in steps of 20A That is at specimen thicknesses of 40A 60A and 80A Store Ampl Phases No As well as storing all the beam amplitudes at specified speci men thicknesses MacTempas can store a selected few beam amplitudes at each single slice increment in thickness then plot amplitude or intensity and phase as a function of thickness for any of the stored beams To store beams for plotting click on the command to enter the indices for the reflections that will be stored In this starting example we will not be entering any information here Voltage 400 The voltage would need to be entered if an unknown micro scope type were selected Since we have selected a 4000ex MacTempas will choose a value of 400keV Center of the Laue Circle 0 0 The pair of values specified as the Laue circle center are used by MacTempas to define the direction and amount by which the specimen is tilted from the exact zone axis orientation specified above and in fact specify the center of the Laue circle in units of the h and k coordinates in the diffraction plane Note that the values supplied need not be integers but should not define a tilt of more than a few degrees The default values of 0 0 specify exact zone axis orientation Objective Lens Defocus 200 200 800 So far we have supplied all the information MacTempas requires to carry out the dynamical diffraction part of the simu lation now we input the imaging condition
72. convert the film density into numbers which are stored in a computer i1 Recording the image on an image plate i1 Recording the image on a slow scan CCD camera with read out of deposited charge into a computer The first approach yields data that is not directly comparable to computer calculations because of the non linear response of the film It is however possible to calibrate the response of the film based upon a sequence of controlled exposures using varying exposure times and mapping the resulting scan values versus electron dosage 1 The image plate and the CCD camera both yield numbers that are linear with respect to the electron dosage and only require a scaling of the data in order to compare to computed values 2 There has been much discussion about the relative merits of the various recording media above and each has its own advantage The CCD camera is currently limited to 2K by 2K pixels although it may be possible to go to 6K by 6K by using multiple chips in the near future Since its Modulation Transfer Function MTF can be characterized it is straight for ward to use deconvolution to compensate for the drop in high frequency response due to spread of electrons and due to spill over of charge to neighboring cells 3 The image plate has many of the advantages of the CCD camera and covers a larger image area However the imaging plate is not gaining as much popularity as the CCD camera Many laboratories are now start in
73. cription of their New Normal Structure New Layered Structure Open Structure File Close STL Save Structure As Open Image New Image Import Pict File Save Window Page Setup Print N TEN 0 T2 V Na Fo VV r 385 TEO XEN S HP E P 36 P This menu contains the following commands Ch 6 Menus p 53 MacTempas User Manual Ch 6 Menus p 54 New Normal Structure Create a new structure file A name is prompted for before input is made Enter a unique structure name the program will append the extension at Make sure that you do not add an extension of the type at in which case MacTempas will not properly deal with the file later on Also make sure the filename does not have a period in it This opens a new structure with Sa An au Worl 3 Exmemple Secures in E K Eny H bcm B Eve canton t np LJ Example Structures T Mem Folder D Adda Favorites Con default values for all the parameters Change the input to reflect eet Peremir Epi Md iie iC ii Pini bt a rl Dhs AM tm ILI Eun a ii 1 r ERE x VEI DEMO nee na OTT L A EM amm ouai mum xia 1 II SO dir Mat L x amp miima 8 0 TA aheri HN ig dori Feat ai rr Rer c a n Prg ur Cmi a Lam Onie oc p EDE PW PUCES Dim By TETE mo in PTT i ee ee I mm Mere ge pg eral cg ww Drama HA a darama vn fil Da ma SH fan sr Es H va Bn E cipem Lor
74. culate din placemenis s sahe cf f Pocbure coordinates x vl O Lattice parameters ia bi Miller indices 1 fe ol he U g gz k o 7 RI Cancel we Ch 11 The Geometric Phase p 174 MacTempas User Manual producing the following output as the result of the operation Prerequisite Both g and g including the associated images Phase Image 1 amp Phase Image 2 must exist prior to executing this com mand Note MacTempas currently has no capability of displaying the dis Ch 11 The Geometric Phase p 175 MacTempas User Manual placements as a vector plot The following section demonstrates how the program Spyglass Transform may be used to display the data for the displacements The user is free to represent the displacements in any form he she chooses The first step is to export save the displacements as binary files Then open the files from within Spyglass Transform and fill in the required data so that the program knows how to interpret the file RS M pea Ej me Edit wiew Folsers Documents fender Sesert File inpet Fee Format Select the Tomas ofthe fie wedi tplncomonds Gh Text Matrix Bary Matrix Fest Coleen En Py Misni File yedispiacemests erect LJ Imari LJ swap bytes sep bytes 9 must FE Cnimminz Xp 5i2 cs Diaplnenrua ri Y Diapisceree Ei Y Diapicerms COO 0D S Expl ceni rii dd D
75. d SIatistical Crees Correlation Creer pps Fourier Sere Ex Gel plies Amam image Sissi TCR e Square Zr Ret Maen Square Difference XP Dffere ce page C Fracrsss i Moan Miosiete Di Tere eo ces C Only Amplitudes Exp eri genesi Bussegeir i Standard rei ote Name SipsOUsntell ener a Wilh CE Hag 37 Ens Vire a Loceape Eire nace 345 Lan rare eps Dri Cer pa Woe til TH Babica Crocs Correiatips pef riens Er al Spare Sabistical Crees Correlation Creer pps Fourier Sere Diet ie splits estimate image ses CQ Cu Square Zr Beet Mian Square Difference Dferemre mepe C Fracrrsss d Moan Micsiete Di Tere DEO ces COQ This calculates the CCC based only on the Fourier amplitudes and optionally the program will try to estimate the shift between the experimental and the calculated image This can be very useful for aligning images and to compare images when the origin of the experimental image is not known The numbers Ch 6 Menus p 97 MacTempas User Manual given are the shift of the origin that should be attempted to be made on the experimental image before the experimental data is compared to the simulation using the exact formulation mr ue ras ars ue on To TL La LL jan 3 7 jasara ja 4 129753 a CELLE In jars Im spa lao CELEI a77 jan ee FRE OD i Ch 6 Menus p 98 oe i fans foros j t Jon inum ni bano jan Ines it
76. d as to bring about a new simulation MacTempas User Manual Atomic Basis Brings up the list of all the atoms forming the set of basis atoms for the current structure The atomic coordinates etc can be edited and atoms can be added to or deleted from the list Aboma in the Motif lasts Mare x cuced vy rocerd z coord dw fact Ow io e amoo oaoa seme 1000000 3 F oomo aae L 260000 LD 3 N DMO acam 302200 SD rondo a 8 nooo oowoo Oem xe 0130000 5 Cu omo awo cade Sento 1000000 B oO D5DDID acm 0440 SAM LMM 2 nomom oomoo 037 000 Somo 100000 a Go moomo oomoo 20500 35000 Loa g a D5 DD D adamo 2560 ewi SD C Bees 7 coc So Symmetry Operators This brings up the list of symmetry operators either associated by the space group or entered manually by the user The sym metry operators can be edited and new ones may be added to Ch 6 Menus p 75 MacTempas User Manual the list or existing ones deleted ur m c4 mw e eu Foi ee See ee en v de ue DS E Symimazry Ciperators TE l 16 wELIAMlIAIAI 17 umo 18 charente 19 E Pall CALE LEE 21 mep 22 Wintel 23 Er 24 CHAN AUTANT UE 25 woz zh PESTE STE STE 2 FE EL LIN Lie THE 28 Fer 30 Te fee PT Be 16 Page 4 Atomic Coordinates This shows all the atoms within the unit cell This list of atoms are generated by applying the symmetry operators on to the set of basi
77. d in more detail in chapter 12 Always Create New Image Determins whether an operation on an image always should produce another image instead of modifying the original image Ch 6 Menus p 137 MacTempas User Manual This menu determines the appearance of text drawn in the Text Menu i MacTempas image window The following text attributes can be set Font Ld Size b Style b b Align Use this menu to bring a window to the top of the screen in case Windows Menu it has been completely covered by another window Wincow Minimize XM Arrange in Front AIM AD Experinent 43 Half tif v Image Calculator Al untitled Ch 6 Menus p 138 Chapter 7 MacTempas User Manual Input File Format The structure file created by New in the File Menu is a file of type TEXT and can be produced by a text editor At times it is desirable to edit the file directly rather than using MacTempas to create this file In fact the user may sometimes want to write a program to generate the data in the structure file For that pur pose in particular the format of the structure file lt structure name gt at is given below Line Parameter s 1 Title 2 SpaceGroupNumber 3 abcabg 4 Gmax 5 iu iv iw 6 NSymops Nslices 13d Meaning Arbitrary description of this structure Just as is says one of the 230 spacegroups 1 230 The lattice parameters and angles The maximum recipro
78. detail in Chapter 11 Cryst Image Processing Crystallographic Image Process ing Can be invoked on a real space image which is square or has a Ch 6 Menus p 133 MacTempas User Manual square selection In order to get started the Hanning Masked ee Crystallographic Image Processing 3 Set Reciprocal lattice h k si un o mo H B so 1 Px at 1 Px b 1 Px ga Deg Refine Lattice Real lattice a Px ga b Px __ Show Lattice Delete Lattice Info Amplitude Find Motif Fourier transform need to be calculated Once the Fourier trans form has been calculated the reciprocal space lattice needs to be set using the a and b tools and clicking on two consecutive Ch 6 Menus p 134 MacTempas User Manual reflections that defines the reciprocal space The number of oo Crystallographic Image Processing Set Reciprocal lattice I 207 1 Px at 1 Px b 1 Px ga Deg Refine Lattice Real lattice as Px ga b Px Info Amplitude 16 13 10 13 6 5 reflections used in the lattice refinement and information extrac tion can be limited by the circular aperture tool Once the lattice reflections have been marked the next action 1s to invoke the command Refine Lattice eo Crystallographic Image Processing Set Reciprocal lattice cim o gio i QI 207 ix a 22 44 1 Px b 22 39 1 Px ga 60
79. e The steps in creating and calculating the image for a layered structure are as follows 1 Define the 3 layers LayA LayB and LayC as single structures with the same unit cell dimensions perpendicular to the electron beam A and B 2 Calculate the phasegrating for each structure LayA LayB and LayC using the same value for Gmax 3 Now create a New Structure in MacTempas using the Ch 10 Creating a Layered Structure p 158 MacTempas User Manual option Layered Structure You will be asked to fill out infor Simulation Parameters Crystal Parameters _ A 4 0000 Alpha deg Specimen Parameters 90 00 Zone axis uvw CE aen BIA 4 0000 Beta deg 90 00 Total defined thickness 0 C Not Applic Gamma deg 90 00 Gmax 1 2 00 Stacking of phasegratings Thick beg inc end 100 100 Store Ampl Phases se No of phase gratings Stacking sequence 4 0 Cent Define PGratings f Define Stacking Type of Absorption Microscope and Lens Parameters 4000EX 400 Microscope Name Voltage kV 1 00 Cs mm Convergence angle mrad foss Phase Plate Spread of defocus A 80 0 00 m Defocus beg inc end A 600 0 600 Obj apert rad 1 Inner 0 00 Outer 0 70 Minimum Intensity to be included in the Lens 10 6 0 C Strong central beam h k Mag Angle Cent of Obj Lens Aprt 0 00 0 00 000 00 Cent of the Optic Axis Over ride
80. e also calculated and the images e1 e1 and e and e are dis played These are the x y components of the two principal strain vectors respectively Ch 11 The Geometric Phase p 181 MacTempas User Manual Contour map of the magnitude of one of the principal strain row components Ch 11 The Geometric Phase p 182 MacTempas User Manual Pseudo colored image of the magnitude of a principal strain row component Calculate Local Lattice This command is used to calculate the local lattice parameters a and b at different points in the image It uses the local values for g and g at each point together with the Miller indices of the two reflections to refer to a lattice given by the vectors a and b Not that the y coordinate can either refer to picture coordinates 0 0 top left or a normal coordinate system x y depending on Ch 11 The Geometric Phase p 183 MacTempas User Manual what is set under Preferences Calculate local lattice parameters This calculates the lattice parameters a and b xy coordinates at every position in the image The vectors a and b are given by the miller indices of gl and g Miller indices of the reciprocal vectors 1 hi 5 h 4 gl i ko aaa C E Prerequisite Both vectors g and g together with the respective phase images Phase Image 1 and Phase Image 2 must have been set Example The ima
81. e planes in the TEM at which we need to be able to compute the complex amplitude of the electron wavefield 1 The image plane Working backwards we start at our desired information the electron wavefield at the image plane this wavefield is derived from the wavefield at the focal plane of the objective lens by applying the effects of the objective aperture and the phase changes introduced by the objective lens 2 The focal plane of the objective lens In turn the electron wavefield at the focal plane of the lens is derived from the wavefield at the exit surface of the specimen by a simple Fourier transformation 3 The specimen exit surface In order to know the exit surface wavefield we must know with which physical property of the specimen the wave interacts and describe that physical property of our particular specimen Ch 1 Introduction to Image Simulation p 7 MacTempas User Manual The Reduced Electron Microscope Electron Microscope Image Calculation Incident Beam Structure Factors S eclitieh Specimen Projected Potential Vp y Plane m Object Transmission q x y i LIA Function y ITIN I bm Objective Lens VV E l Objective MOV M Objective Lens Aperture ONILN N Diffraction Amplitude g Lens Transfer Function exp ix g i 4 V Lens Aperture Function A I i N a E i Image Amplitude W x y Fig 2 The simplified TEM left
82. e Comeanion Rago Guiput Options C Craalr a bog file with nergy versum irre sente monte Gl the nagta wena Tima Eerwscen barre amara L Ces CE refinement appears If the refinement is not progressing in a sat isfactory way the computation can be canceled by hitting the Ch 6 Menus p 105 MacTempas User Manual zi erbe ss EX i e L Currest Parameter ealugs Apple Command Key together with the Period Optionally a Derrent Computed beage Exppsem pnta Image T 20 ipid b Crystal TEE eer ad nar Cenber id Lame Cirie BOCK 01701 0 L3 s ssam RES DE 288 O s O Come angie srad 05 O Spread of Deracus AJ 58080 Magnibudae A 1507 COM AE Ae Feld Axlsgmalises Agi wit Has Z 103 20 O a Fass Ksr matis Angle weth Horiz a 31 Energy GS bey Tie HOME Mien File HOME UA states stcuatien stet Ch 6 Menus p 106 log file can be written so that the energy as a function of time temperature can be plotted and also a Movie can be produced and played back The number of frames second for output can be set At the end of the run the dialog box can be just dismissed and the final configuration of parameters will be discarded or the parameters can be saved in the form of a new structure simula tion file Refine Structure The structure refinement works in the same way as the parame ter refinement However in this case it 1s t
83. e Fourier transform of the image and sets it as the Current Displayed Image The original image can be shown by selecting it from Ch 11 The Geometric Phase p 164 MacTempas User Manual Create Phase Image the pull down menu Current Displayed Image This routine calculates the geometric phase and other images associated with the chosen reflection The calculation performed is the inverse Fourier transform of the masked Fourier transform of the original image The mask in question is a mask of the type defined below and centered on the reciprocal spatial frequency g F Masked F Image A x exp 2rig r 0g r r A r exp 2m g r g ou r giving rise to an amplitude image A r and a phase image P r 27g du r The term 27g r has been subtracted from the phase which is equivalent to moving the origin to the position of the reflection g du r is the displacement field with respect to the lattice planes defined by the frequency g For calculating the local value of everywhere this is done as g r d or P r g Usage 1 A G vector must have been chosen using either the G1 or G2 tool for the Calculate Phase Image button to be activate By clicking on a reflection a circle will be drawn around the chosen reflection The size of the mask will be determined by the radius of the drawn circle which can be changed by its handles or by Ch 11 The Geometric Phase p 165 MacTempas User Manual typing in t
84. e a 2D image from the azimuthal average Template Matching will calculate an image containing the cross correlation coeffi cient for the template as a function of its position in the image The cross correlation coefficient is calculated for each pixel position in the original image r a Find Occurrences of Template in Image if a selection exists on the front image it is used as the template if the front image is chosen as the source of the template Choose template AO stair rod 512 Hd Normalize each instance by subtracting mean of image Cancel ok Peak Lattice Analysis Ch 6 Menus p 129 MacTempas User Manual Contains the following operations Find Peaks Edit Lattice Fit Lattice Analyse Displacements Find Peaks Finds all the peaks in the image which satisfy the criteria speci fied in the following dialog Find Peaks in Current Front Image Peak Finding Criteria i9 Find Maxima save Peaks to File C Find Minima Binary peak image Lower Threshold 0 855 Est Min O00 Upper Threshold 1 090 Est Max z 1 000 Eliminate Peaks within 0 pixels from edges m Radius far Center of Mass Refinement n Serves as an initial exclusion radius Pixels Min Distance between Refined Peaks ra Pixels Use Extreme Peak Within Exclusion Radius Cancel K The peaks will be marked on the image Changing the criteria and refinding peaks will mark a
85. e basis atoms are the atoms of the current crystal Original Unit Cell Atoms This list gives the atoms that are produce by the operation of the symmetry operators of the spacegroup in use on the original basis atoms New Operators These operators are the result of applying the transformation operations that are given by the change in coordinate system together with a translation of the origin to the generators of the original spacegroup New Basis This is the transformed basis Original Unit Cell Atoms This list gives the atoms that are produced by the operation of the new symmetry operators of the spacegroup used on the new set of basis atoms Convert Clicking on this button initiates the computation of the trans formed set of symmetry operators the transformed basis and the new atomic positions Ch 6 Menus p 116 MacTempas User Manual e Original Operators Ly ele ie lE ony el aye 24 142 px ye rdc rare 1 2 Yor yet os eee 114 ERE et ae ee Le Orginal Basis Ca 0000000000 Cr Sr E CO Oo Bi 00000 0000 30 Bi C O004 000 0 268 Cu 0 000 0 000 0 446 Original Unit Cell Atoms Ca 0 000 000m 0 000 Ca 0 500 0 500 0 500 Sr C0000 000 0 110 Sr 0 500 0 500 0 610 Sr COOL 000 0 H EO Sr O S0000 50000 390 Bi CHE CD 402 Bi CL SCO SG Bi Dno 0 000 0 ERR Bi D 500 0 800 0 198 5ymmetry Operator Transformations New Operators xy ee eel ee eee ayy we ys De PE PR PURE Ae yii Nya
86. e experimental data The peaks in the one dimensional data set are found and assigned ring indices The focus is calculated from each ring and the mean value for focus defocus is used to calculate the hypothetical Contrast Transfer Function CTF which is plotted as sin x u Cs f Af o based on the values that are listed The maxima for the CTF are shown by their vertical markers which can be dragged by the mouse Click on a marker hold down the mouse and the location of the maximum can be changed All the maxima changes and the corresponding value Ch 12 Finding Focus from a HRTEM Image p 198 MacTempas User Manual for focus is shown As an inset the experimental power spec trum is shown with a region showing the average data that the program uses for finding the rings Superimposed on the experi mental data are the rings corresponding to the current value for the focus By moving the markers the rings change position and the user can manually try to obtain the best fit for the value of focus Ch 12 Finding Focus from a HRTEM Image p 199 MacTempas User Manual Ch 12 Finding Focus from a HRTEM Image p 200 Chapter 13 MacTempas User Manual HOLZ Interactions amp Sub slicing With suitable algorithms it is possible to include in the diffrac tion calculation the effects of out of zone scatterings or non zero or higher order Laue zone HOLZ interactions Basi cally there are
87. e general for mulation which include non linear imaging terms O Keefe 1979 Each Fourier component is damped by the spread in energy and direction and the image is formed by adding this to the recipe in section 4 2 The Contrast Transfer Function CTF When reading about HRTEM it is impossible not to encounter the expression Contrast Transfer Function Loosely speaking the CTF of the microscope refers to the degree with which Fou rier components of the electron wavefunction spatial frequen cies are transferred by the microscope and contribute to the Fourier transform of the image Although the CTF only holds for thin specimen and linear imaging it is often generalized and wrongly applied to all conditions However the CTF does pro vide insight into the nature of HRTEM images In order to derive the expression for the CTF we start by calculating the image intensity as given by the Weak Phase Object approxima tion In the WPOA W x y z T 1 ioV x y T 28 and YCH 6 H ioV HT 29 Applying the phase shift due to the spherical aberration and the Ch 2 Theory of Image Simulation p 22 MacTempas User Manual objective lens defocus which we will call X H we get that the FT of the wavefunction is for simplicity V Vj H H ioV H eX P AH 30 where A H is the damping terms arising from partial coher ence The FT of the intensity is now given as I H FTQp 3p Z Y War H H H Y 8a
88. e menu will be covered under the Menus chapter Thus Projected Potential calculation considers only the spec imen structure Exit Wavefunctions s calculation treats the interaction of the specimen with the electron wave and the Image s calculation simulates how the wave leaving the specimen interacts with the lens system of the electron micro scope Once a simulation has been made any additional simula tion will usually not require a full re calculation any change in microscope parameters will not affect the results of the Pro jected Potential and Exit Wavefunctions s calculations and only Image s will need to be re run any change in microscope voltage or in specimen thickness and tilt will not affect the out put of Projected Potential but Exit Wavefunctions s and Image s will need to be re run Of course any change in the specimen structure will require the re running of all three sub programs Generated Files MacTempas generates and stores various files in the course of a simulation The 6 possible data files are 1 lt structurename gt at stores all the structure and micro scope information needed to run the simulation This information is derived from user input and the supplied data files In particular the string structurename is a unique name for the structure input by the user when creating the structure file This is an editable file of type TEXT 2 lt structurena
89. ed in two dis tinct modes set up for microscopy a and for diffraction b In microscopy mode we see that the TEM consists of an electron source producing a beam of electrons that are focused by a con denser lens onto the specimen electrons passing through the specimen are focused by the objective lens to form an image called the first intermediate image I1 this first intermediate image forms the object for the next lens the intermediate lens which produces a magnified image of it called the second intermediate image 12 in turn this second intermediate image becomes the object for the projector lens the projector lens forms the greatly magnified final image on the viewing screen of the microscope In microscopy mode electrons that emerge from the same point on the specimen exit surface are brought together at the same point in the final image At the focal plane of the objective lens we see that electrons are brought together that have left the specimen at different points but at the same angle The diffraction pattern that is formed at the focal plane of the objective lens can be viewed on the view ing screen of the TEM by weakening the intermediate lens to place the microscope in diffraction mode b Ch 1 Introduction to Image Simulation p 5 MacTempas User Manual ae Electron Source XN 7 N TON dy NN I NM BUE Condenser Lens M 7 N I I 7 Mx 7 4 Y4 Object CE l on Objective Lens Die
90. een calculated from relativistic electron wave functions and parameterized They can be found in various tables Doyle and Turner 1968 and are in use by most image simulation programs such as SHRLI O Keefe at al 1978 NCEMSS Kilaas 1987 and EMS Stadelman Taking into account any deviation from full occupancy at a par ticular site and the thermal vibration of the atom the Fourier Ch 2 Theory of Image Simulation p 12 MacTempas User Manual Simulating the Interaction Between the Elec trons and the Specimen coefficients of the crystal potential from one unit cell is calcu lated as PH Off d occ r expL B H p P 6 unit cell atoms i B Debye Waller factor Occ r The occupancy at position r The interaction between an electron of energy E and the crystal potential o r is given by the Schr dinger equation 2 8x m V eb r 1 EY r 7 where m is the relativistic electron mass and h is Planck s con stant Before entering the specimen the electron is treated as a plane wave with incident wavevector ko ky 27 A so that the inci dent electron wave is written Wo r exp i wmt 22k r 8 It is useful to define the quantity V r which will loosely be referred to as the potential as TT me 8 Vir E mr 9 Ch 2 Theory of Image Simulation p 13 MacTempas User Manual The Schr dinger equation above cannot be solved directly with out making vario
91. efficients V H are real true for all centro symmetric zone axis the WPOA illustrates clearly that 1 Upon scattering the electron undergoes a 90 phase shift ii The amplitude of a scattered electron is proportional to the Fourier coefficient of the crystal potential The Bloch Wave Approximation In the BWA the electron wavefunction of an electron with wavevector k is written as a linear combination of Bloch waves b k r with coefficients Howie 1963 Each Bloch wave is itself expanded into a linear combinations of plane waves which reflect the periodicity of the crystal potential pr eb sr Y e Y et expI 2ni K g r 14 J j g The formulation above gives rise to a set of linear equations expressed as ko K m If Y var xi 0 15 H which needs to be solved Detailed derivation of the Bloch wave approximation can be found elsewhere Characteristics of the Bloch wave formulation are Requires explicit specification of which reflections g are included in the calculation Easy to include reflections outside the zero order Laue zone Very good for perfect crystals not suited for calculating images from defects The solution is valid for a particular thickness of the speci men Ch 2 Theory of Image Simulation p 15 MacTempas User Manual Allows rapid calculation of convergent beam electron dif fraction patterns Includes dynamical scattering The Multislice Approximation The
92. ent Through Matching of Ex MacTempas User Manual 5 Frank J 1972 Two dimensional correlation functions in electron microscope image analysis Electron Microscopy The Institute of Physics 622 6 Saxton W O 1996 Pre processing of data registration dis tortions resampling noise removal and noise estimation NCEM workshop on quantitative HRTEM April 18 20 NCEM LBNL Berkeley CA USA 7 Zhang H et al 1995 Structure of planar defects in Sr0 9Ca0 3 1 1CuO2 infinite layer superconductors by quanti tative high resolution electron microscopy Ultramicroscopy 57 103 111 8 Smith A R and Eyring L 1982 Calculation display and comparison of electron microscope images modeled and observed Ultramicroscopy 8 65 78 9 Press W H et al 1986 Numerical Recipes The art of scien tific computing Cambridge University Press 1986 ISBN 0 521 30811 9 p 502 10 King W E and Campbell G H 1994 Quantitative HREM using non linear least squares methods Ultramicroscopy 56 46 53 11 Thust A and Urban K 1992 Quantitative high speed matching of high resolution electron microscopy images Ultra microscopy 45 23 12 M bus G and R hle M 1994 Structure determination of metal ceramic interfaces by numerical contrast evaluation of HRTEM micrographs Ultramicroscopy 56 54 70 13 H tch M J and Stobbs W M 1994 Quantitative criteria for the matching of simulations with experimental images Microsc Microanal Microstruct
93. ent and the simulation This plug in uses an algorithm based on simu lated thermal annealing which is described further in the chap ter at the end of this manual No claims are made as to the effectiveness of this method and there is no guarantee that the final solution represents the global maximum minimum in the goodness of fit parameter The effectiveness of optimization routines depend on the starting parameters There is no recipe for setting the initial starting condition and it is necessary to develop some experience using the optimizing routine in this program Some trial and error is a definitive part of the parame ter structure refinement Suffice it to say good hunting Ch 6 Menus p 89 MacTempas User Manual Ch 6 Menus p 90 Load Experimental Image Load Experimental Image is the starting point for loading in the image to be used in the comparison The command will bring up a standard File Open dialog with a look that depend on the version of the MacOS you are using and what else of Finder utilities you have loaded Chima a F Frem SO Phaum S 45 bLb2eeyLb26 2 aS Fea bS BSE AAC ASESI are d AMCULMgIIT ai adc AACE p ANE T AC LP a peni i Wirt lacurrer 3 Acea Sara Spe 1MB Com Add LOT cine ochee The dialog will show you all files and it is up to you to select an appropriate file to read in Currently two distinct types of files are supported These are
94. erence area from which to calcu late an average lattice spacing In order to define a reference lat tice one needs two vectors g and g which both will need to be refined with respect to the same area Usage Mark an area with the selection tool where you want to find the average g vector Run the command Find local average g vector The command will determine if there is a residual ramp 270g r within the selected area that should be subtracted out The correction dg is added to the vector g that was found during Calculate phase image The routine can be used iteratively to refine the vector g by using successively larger selections if the first selection needs to be small because of phase jumps Ch 11 The Geometric Phase p 169 MacTempas User Manual The images below show the original phase image with a selec Ag Phase Image 1 L d E amp tion marking the area which will be used to find the average local g vector To the right is displayed the result of the opera tion Note Ch 11 The Geometric Phase p 170 MacTempas User Manual Create Moir As mentioned above two vectors g and g are used for defin ing a reference lattice Thus normally this command is used for each vector g from which a phase image is calculated before the phase image is referred to as phase image 1 2 Add Phase Add Phase This routine adds a constant phase to the image Phase Image Under normal opera
95. es nzsam 237903 oere z amp zzp nama ziaan nisa4 lose nzess znzsan loege lens nas fissio oida nives Toss Tineia 7202 EL ess uded4 lose Jesus inposa 1 2az6 l2esoq7 nauma lasia 0283 033 bonds 036704 bors ET iras nasa social uz dpa 723320 24250 TTD D4578 31798 Ozga oao 1577748 TETTE FETTE uses MEE Eu ap j36 sun 21862 i 4861 nsss aime jante ek fas i gL aro eee fee mr dyanen EST Jee Oa legs 25769 _ 70 606 gisgit jae jagas 1 wem nese lite TANE a Epean AL leyms2 sas ligeras 11 7925 l aatat 23424 li4 ns 1 7588 j tail 2 litir d 1243 38520 iaai HT RIED RL UE EE NOTE xe urn fee Ls e Lane EERRR dec al BN ESL MEC 2 RR IL Luo BS JT JET zae 19200 22739 lsumzse zona uses Lans rises 35907 z sps inaese 15981 acts jassa zszw lasar us es 15620 ransazi 3eese issus fesse soin Ch 6 Menus p 67 MacTempas User Manual Commands Erase Display XME Draw Atomic Modei LU Draw CTF SiniChih Draw 20 CTF Slice Unit Cell Commands Menu FREE Erase Display Erases the MacTempas display window Draw Atomic Model Displays a dialog box from which the user can select to display the original or transformed unit cell from any direction includ ing perspective view The transformed cell corresponds to the unit cell that MacTempas uses in the multislice calculation To view the cell as seen by the electrons the transformed new un
96. es the position of the series of Ch 6 Menus p 61 MacTempas User Manual images and the number of pixels to leave between images Montage Options Automatically montage images Starting Location of the CRE Horizontal Separation of Images 0 Vertical Separation of Images 0 M Auto scale when images do not fit l Layout options fe Defocus Horizontal Thickness Vertical Thickness Horizontal Defocus Vertical User Defined Layout Click to Display and Set f Cancel ok gt Intensity Scaling Brings up a dialog box allowing the user to manually set the intensity values to be mapped to black and white The values shown correspond to the last image displayed with automatic scaling E aeai Sealen of aoe iantnalTics uale a idp Do k Wh sabii Valais Gb oie ai Ge for ias irap ds pd aped vale oad Ad wahectwhi 23 cancel Magnification Allows the user to set the magnification to a set value The magnification depends on a screen with a resolution of 72 dots Ch 6 Menus p 62 MacTempas User Manual inch If Auto scaling is set images will scale to fit the window Magnification options Fixed Magnification Magnification 30 0 Million M Auto scale when images do nat fit are a El Cancel CTF Scaling Brings up a dialog box allowing the user to set the maximum scale of the reciprocal axis during plotting o
97. es to complete the slice This method avoids interaction with any pseudo upper layer line Goodman and Moodie 1974 but ignores real HOLZ layers Sub slices based on atom positions An improvement on sub dividing the projected potential is to sub divide the unit cell atom positions In this procedure the list of atom positions within the unit cell is divided into n groups depending upon the atom position in the incident beam direc tion From these sub sliced groups different projected poten tials are produced to form n different phase gratings which are applied successively to produce the scattering from the full slice Sub slices based on the three dimensional potential A further improvement on sub dividing the atom positions is to sub divide the three dimensional potential of the full slice since an atom with a position within one sub slice can have a potential field that extends into the next sub slice Rather than compute a full three dimensional potential and then integrate over appropriate sub slices a 128x128x128 potential would require over two million samples to be stored it is possible to derive an analytical expression for the potential within the sub slice zo dz projected onto the plane at zp Self et al 1983 It is possible to apply this method routinely to structures with large repeats in the beam direction thus generating several dif ferent phase gratings for successive application and even to structures
98. eter the input is a range specified by the upper and lower bounds and an increment Min Intensity in the lens This specifies a cutoff in intensity for which a beam is included in the calculation Normally the default is adequate and saves Ch 4 Running MacTempas p 39 MacTempas User Manual Ch 4 Running MacTempas p 40 computation time However for large structures containing defects diffuse scattered beams are very weak and a lower cut off may be needed in order to compute the correct contrast Strong Central Beam If this box is checked only linear terms to the image intensity contribute Normally both linear and non linear terms are included in the calculation Cs Spherical Aberration The spherical aberration of the objective lens in mm Convergence Angle This is the spread in angle for the cone of incoming electrons depending on the condenser lens aperture The angle is given in mrad Spread of Defocus This is the effective spread in defocus which results from the distribution of energies of the imaging electrons and the chro matic aberration of the objective lens The unit is A Aperture Radius The radius of the objective aperture is specified in A Both an inner aperture and an outer aperture can be specified Normally the inner aperture would be zero Center of objective Aperture The center of the objective lens aperture is defined in units of h and k of the two dimensional reciprocal space uni
99. eters Main Parameters Atom Basis Symmetry Operators Atom Coordinates This brings up a dialog box showing the current conditions for the simulation The values are taken from the input given to the Semularion Parameters appe Dee NE Esne axe vei Finden i Pinna pina Eum In i de fo Wo di n Bera Mg att Hum slices per cell z L1 mit diirir Cama deg pcd Cmax fi zd Tables T dk iuwpeesed oi i bt 3 sow Store Sepi Phases 3 m M o smaw Cust nf Laud Circa soon uon ik saw Eq Tir mrad coreg lie nn fo E Tine of Absorption Mbcniunige and Lord Paramenerst Microscope Mame Ange 1 Wokage fd 00 G mm oan Mag al Coneergesce eagle mrad hid Phase Piare Tua rata 1 a n Spread ed detacus Al an non m Thmeefeid A a d Dafacus dg isa andi 2500 zn z370 Cora o 0 Uti apert rad h 1 inner Gn Outer 1 250 Mackanieal Vibration LA Missimum Issenniry 10 br included inthe Lens 10 4 0 tima af abi hog q Dn 7 Li Mireng central beam h k Mag Ange E LEM ee er ite Angle with amis n n Cast of Dix Lens Apri O00 ogg ng nu Cast of the Ook AKH add O00 d arcs cabelas viaua OOOO ME m Mark for me calculari r C1 Prajeczed Pr ential Lj Exit Waeefunrtiun _ Image Mork 42 calculated Proto d Potential J Exit Waseefuncri n Image a CR Ch 6 Menus p 74 New command in the FILE menu The parameters can be change
100. f the Contrast Transfer Function f Horizontally Scale the CTF automatically C3 Use Value below as Maximum Value for g Eum EE Maximum g valwe 1 D 4 i Cancel ok Diffraction Pattern Displays a dialog box allowing the user to select the position of the diffraction pattern the camera length and the minimum dif fracted intensity that can be displayed The user can also choose whether the objective lens aperture should be superimposed on the diffraction pattern The indices of the diffracted beams can be superimposed on the diffraction pattern as well as the corre sponding real space distances Selecting Circular Diffraction spots instead of Gaussian Diffraction Spots results in solid cir cles One can also set a cut off such that diffracted beams with Ch 6 Menus p 63 MacTempas User Manual Ch 6 Menus p 64 g vectors larger than the cut off will not be displayed Entfracrew Palbair 5Sertissis Ophons iahege Bg Display Ghjace lens Apamure Camara Length emi pea RES re Ears ia Dibergence Angle tire 2 2x4 s remped Min mmpeediry disp 10 4 5 Lo SD edexing dk i Lt Eh ic inden dr Bispiaycal ges 20 a wm d spacire A le raal urira A in reciprocal wita 4 1 Ci Gaussian Diffraction Spon CR Min Lens Intensity Displays a dialog box allowing the user to manually set the minimum intensity required of a diffracted beam for inclusion in the formation of the image Minimum Beam
101. feal dence gj statistical Gross Cerre amp ntinn Coedicie wt Fomrier Space i Exact OG nbynenpbtbwdes Estinnte unega min E f I x ia I ihi Suara 2 Enet Mean Square Diferesce C erene Image C Frarbiunad hran Ae valute Dsifere nce ECT Ch 6 Menus p 94 MacTempas User Manual Note The selection does not work for the Difference Image which automatically compares the entire image Selecting a method of comparison The method of comparison or goodness of fit criteria is chosen by a set of radio buttons and the choices and the corresponding description and output is given below The goodness of fit crite ria is computed for each image that is compared and displayed in a table This table can be saved in a text file for further use Statistical cross correlation coefficient CCC A note about the cross correlation coefficient The cross correlation coefficient measures similarity in the pat tern between the experimental image and the computed image Since the images to be compared are set to a mean level of 0 and normalized any scaling of the type I exp a I calc b would give a cross correlation coefficient of 1 Exact fit is given as CCC 1 and a reverse contrast gives CCC 1 Real Space Print i Destian Mame r e veio Widi Weight 37 Hat et p formers Enters Image Seb Cemgare Seberon Cormeartsqn Wie opel ik States ad Cross Comets CapiicignE Geel
102. g that the experiment and simulation agree within the uncer tainty of the experimental values mt ILLE I nite maa me ua UE mar 1220 os ons iiia ETIN TT ET NH Xm jm wii Ha Ka nin TRE amp Aa a iaa ippa IH Nid IE A Root Mean Square Difference This calculates the root mean square difference between the Ch 6 Menus p 99 MacTempas User Manual experiment and the simulation Lower values indicate better fit with 0 being exact fit between experiment and simulation Since the values depend on the mean level of the images that are com pared the simulation is scaled to have the same mean as the experiment Experimestal mege Stesdard Devsatenn Marre 5kb35ln ar Width 45 Haat 32 The eT k m IE mpare taime Insane unen hpiertssn Cha parican Liatin PR RR PRO PR RS ER SERIE ES ET as D sostistical Coss reao netten Heal spare e statistical Gross Correlatios Cnef rsent Fourier Space EA Esti mate Image his L3 Chi Square Rooc Mean Square Difference D Herme Image 3 Fractional Mean Alese amp ibe Difference o RMSD E Ch 6 Menus p 100 MacTempas User Manual Difference Image Esparmmnrtal lea 5 5ragnard Hersi aher hissar TT Warden 5 might 12 a Ba iH TE jm Cnt Bale ge iS Set Corn are 32a ie cli gri ls ee m ae nim oe Congo kinibas Sica Ones Cerr
103. g to do much of the recording on CCD cameras while still retaining the use of film Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 208 MacTempas User Manual Pre processing of data Once the image data has been converted to numbers any neces sary processing or transformation of the data can take place The required pre processing of the data depends on the nature of the information that is sought and thus there is no one opti mal method but rather a number of possible options Sampling and resampling of data If the image is distorted over the image field of view either by the action of the imaging system or the recording system the data can be re transformed by a warping transformation of the image This can be done if the transformation can be deter mined by imaging a perfectly crystalline material and noting deviations from where the atoms are known to be and where they are imaged 4 On some systems i e the Gatan Imaging Filter the distortions are measured by recording the image of a square grid of circular holes An image of a crystalline material can be resampled onto lattice relative coordinates such that the unit cell dimensions are rep resented by an integer number of pixels and commensurate with the dimensions of the final image This will eliminate streaking in the Fourier transform of the image which is due to the trunca tion of the image by the edges on boundaries that
104. ges shown on the next page illustrate the use of the rou tine on a HRTEM image of a quantum well in In Ga N Left image is the HRTEM image and the right image shows the power spectrum and one of the reflections used for calculating the lattice The third image at the bottom is a surface plot of the a lattice parameter as a function of position in the image Ch 11 The Geometric Phase p 184 MacTempas User Manual Ch 11 The Geometric Phase p 185 MacTempas User Manual Al Quantum Well Cac Pass Anyi Cote aoe ae DuaJape brag Fram Moon ar m RI M be cba Lek TT Tn Gy id EE Ln rire E asinis Flores image 375 250 Ch 11 The Geometric Phase p 186 MacTempas User Manual Unwrap Phase x y Unwrap Phase y x The command Unwrap Phase x y will try to unwrap the phase in the image Phase Image The user is prompted for a starting position which is assigned the phase at that point The routine then moves first along each row trying to preserve continuity in the phase value Instead of making a jump from 7 0 to 1 0 the phase will take on the value 7 0 and continue to increase or decrease when crossing phase jumps This command first does the rows and then the columns of the image The command Unwrap Phase y x will try to unwrap the phase in the image Phase Image The user is prompted for a starting position which is assigned the phase at that po
105. h arise from limiting the structure at arbi trary boundaries and care must be taken to ensure that the image gives a faithful representation of the area of interest The entire electrostatic potential of the specimen is now defined by one unit cell with axes a b and c angles alpha beta and gamma and N atoms with coordinates x y z For simplicity we use the nomenclature of the crystallographic unit cell even though we are referring to the transformed unit cell A B C as described above The electrostatic potential in the crystal can be written pr Ir r o r dr Ch 2 Theory of Image Simulation p 11 MacTempas User Manual where p r the charge density is pr p r 2 all atoms i with the sum extending over all atoms i at positions r each giv ing rise to a charge density pir Zeb r eyf 3 where Z atomic number e electronic charge y r the quantum mechanical many electron wavefunction for the atom The potential O r is described by its Fourier transform db u through the relationship g r 006 au yo Hye Ht i H since because of the periodicity of the unit cell u is non zero only when u H ha kb lc H being a reciprocal lat tice vector The potential P H is given as a sum over all atoms in the unit cell el miur Zi qui 2 2niur ds n P Ans at H atoms i atoms i 5 where the electron scattering factors pe and the x ray scattering factors f have b
106. h is to average the motif with copies of itself to which sym metry operations known to be present are performed This will reduce noise levels by a further factor of 1 M when M sym metry related copies are averaged but may also just disguise defects in imaging conditions Matching experimental and simulated images There are a number of various ways to measure similarity or mismatch between two images Below are a few of these 8 The mean square difference 2 _ 1 2 D h 5 Xn 6 4 The Root Mean Square Difference Dring 4D 5 The mean modulus difference 1 Dima fh n y nl 6 The Cross correlation Coefficient Ld 8 1 Q4 D CCF 7 LaO Y ux 5 The brackets lt gt all indicate the mean of the enclosed quantity In each of these equations the sum is over all the pixels i in the image and N is the total number of pixels The cross correlation coefficient above is a normalized coefficient where the images are normalized to zero mean The CCF which measures similarity rather than difference can also be interpreted as the cross product between two n dimen sional vectors n being the number of pixels in the image In that case one can associate an angle with the CCF CCF cos in the general interpretation of an inner product between two vectors as J J cos with the angle Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 212 MacTempa
107. have been entered MacTempas will need the parameters of the electron microscope for which to compute the simulation tons im the Moby Baste t Name soced poed ccoo eiee ke 1 fee nomo omom noman s LOTO 2 sr Gogo MOD Glera 34DJDJD LAN 1 hi r OO n Ce Menton Dent 1600000 0 3700080 4 LI f DO OO DO O onn o t 263106 3 5 o0 Di 0 1206000 5 E f OO Or f on rwn Ca assa 3 50000 n 1 0 Ce orn amp a LIIE PMO Aam 3 400000 LIMEN 7 c Joe owm DIMM 3eme LOM E n CT erty DzDSDJD Jamar Lomo E CE CCC TC CE CCE COTE EO mei f Cancel E o3 Microscope 4000EX If the input microscope name is listed in MacTempas s micro scope file various operating parameters will be set automati cally If the entered name is unknown to MacTempas values will need to be given for each of the operating parameters In this example we use 4000EX and find that MacTempas sets the spherical aberration coefficient to 1 0mm the Gaussian half width of depth of focus to 80 and the semi angle of beam convergence to 0 5milliradian Specimen Thickness 40 20 80 The foil thickness response may be in one of two forms either a single value in Angstrom units or a construction combining a starting and ending thickness with an incremental value The Ch 8 Sample Calculation p 147 MacTempas User Manual Ch 8 Sample Calculation p 148 construct that we have entered requests MacTempas to store dif fraction results for thicknesses starting at 40A and
108. he desired radius and clicking the set button Cecrrssrr Phase Ara b ia 2 Invoke the menu command Calculate Phase Image 3 A dialog will give you the options available or creating the phase image Type mi ssh Options Mask Ch 11 The Geometric Phase p 166 CL ES Moo Circe srular Bark Crase Ph imaga Baii Spree EI Mark or Wink GAIS irr M c oe Gd mi V goram jx wd onm zm V ee haw rige npr H bead ga AT made brag Bragg nieren image MacTempas User Manual The following choices to the type of mask can be made A sharp circular mask M 1 r lt R M 0 r gt R A soft circular mask using a Gaussian edge with a halfwidth of 1 5 of the radius M 1 r lt 0 8R M exp r 0 8R sigma for r gt 0 8R sigma 0 2R A Gaussian mask exp r7 sigma Output Keep the geometric phase image default Normally this is what you want Calculate and display the local g vector This calculates two images containing the x and y components of g r at each point in the image Keep and display the amplitude image Keep and display the masked FT from which the amplitude and phase images are calculated The resulting phase image is calculated by subtracting out the term where go is given by the value returned from finding the posi tion for the peak intensity in the power spectrum The resulting images are by default named Phase Image amp Ch 11 The Geometric Phase
109. he image must be square Power Spectrum Computes the Power spectrum of a rreal square image Edit Mask Allows the specific settings associated with a mask of a given type Example of the properties of a lattice mask is shown below Mask Paramatars Use soft erige of width Pimels Opaque maik E Sumber of Lattice vectors 1 BE Sumber of Lotte Vectors l Cancel E 3 Apply Mask s Applies the defined maks s on the image Fourier Filters Contains the following filters Wiener Filter Ww Gaussian Low Pass Filter Gaussian High Pass Filter Annular Low Pass Filter Annular High Pass Filter MacTempas User Manual The Wiener filter is an automatic filter that tries to determine the power spectrum of the noise and the creates an optimal filter based on the estimate of noise and signal Spatial Filters Contains the following filters Convolution Sharpen Smooth Laplacian Sobel Remove CCD Defects Convolution brings up the following dialog for defining the kernel Pre La Convolution kamols Feedafined Karger L De e Low Pasa Light 1x3 SE 2 a pu bat coef chenis as needed ES Creabe pour Can betel defined kernels are defined for your convenience but you can Ch 6 Menus p 121 MacTempas User Manual ii 2 1 EHE mcm Los Pass Medsum JsJ F z Lew Pasi Heaney 3x1 n UD Hn Low Fass Light 5x5 Low Fass Medsum 5x5 Lew Pass Heavy Ex
110. he image which will be used for comparison It is okay to go outside the image since the selec tion will be cropped to the actual image Hand Tool Use this tool to move the image within the display area Magnification Tool Use this tool to magnify the image Holding down the Option key when clicking within the image will reduce the magnifica Ch 6 Menus p 93 MacTempas User Manual IET TIT T Height 37 Compare Entire Henni tion Holding down the shift key when clicking will increase decrease the magnification by a factor of 2 Reset View Click here to reset the view pan zoom of the image Selecting an area for comparison The user choose to compare the entire image region or only a selection of the image Two radio buttons are provided Compare Entire Image By clicking on this radio button the selection area will automat ically be set to be that of the entire image The comparison area is shown as a red rectangle Set Compare Selection The user must first use the selection tool to mark a region of the image Upon clicking on the radio button the selection will be marked in red and this area will be used for comparing images For changing an already defined regions mark a new one and click again in the radio button Experimental Image Standard Deveatinm Maga Width 52 Reset View a Sel Oommen ane 5esectenn Cemparispa Miethnd Sraristecad Cass Cornelatisn Coe free nr
111. he statistical nature of the data and the accuracy to which we know the data points Thus the fitting parameter should depend on a maximum likelihood probabil ity model and be a measure of the probability that A is equal to B given knowledge of the probability distribution of the data points In the presence of Gaussian distribution of uncorrelated noise each data point has a Gaussian probability distribution with the noise in one pixel uncorrelated to the noise in adjacent pixels which leads to a X criteria The criteria takes into Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual account the number of adjustable parameters and the error in each data point As mentioned above any data point lying one sigma away from the expected value will add 1 to the sum in X Similarly any data point which has only 1 probability of being measured given A B adds a value of 6 63 to the sum in x Thus values of X greater than about 6 states that there is less than 196 probability that A is equal to B The fitting parameter depends on the model of the distribution of data points due to statistical noise with a Gaussian distribu tion of uncorrelated noise leading to the criteria However it is important to determine the statistical nature of the noise in the image This can be done by examining the noise distribution determined from a large number of image regions considered to be equivalent except for noise A non
112. he structure that is being varied notably the coordinates of selected atoms and pos sibly debye waller factors and occupancy After invoking the MacTempas User Manual command the following dialog box appears Simulated Thermal Asnealing Pasamaturs Tarmcer natures Acre An Faramasmsrs Janina mono Maximum shift Giro Ending C f SET Aktive EATER i 4 Fractional Change 0 2000 VS MEE f Comparison Area Active AONE Atternpes par Temp 2 4 Ser Chemical COALTAR 4 8 5uccesstul arenes j Set Bond valence n Finn g Ben Face Imaga Aqewarseri Mi use image agraament _ glide Bord Distante Constraints crass Corralaion C elado Bord Valence Sum Optimization Chi sauare Cheat Doro _ Create a log File with emerge versus me cs _ Create a rose of the progress window Time beraten frames 1 Cancel Re nes There are several options associated with the structure refine ment such as which elements are active which coordinates to be varied etc The standard parameters for the simulated ther mal annealing need to be specified together with the goodness of fit parameter Output options such as a log file and movie are identical to that under parameter refinement In addition it is possible to include in the calculation of the Configuration Energy terms that depend on selected bond distances and selected bond valence sum Set Active Elements brings up the following dialog By def
113. hickness of the specimen foil is entered as a beginning thickness an ending thickness and an incremental thickness AII numbers are in Angstrom units A series of thicknesses repre sented by the upper and lower bounds and a thickness step e g 100 50 250 will cause MacTempas to store the exit wavefield at specimen thicknesses of 100 to 250 in steps of 50 a total of four thicknesses Store Ampl Phases Set Clicking this button allows a number of diffracted beams to be selected for plotting of their intensity and phase variation as a MacTempas User Manual function of specimen thickness The reflections to be tracked Simulation Parama tors Creel Farapienes Species Parameters Teru anii hrm iain a x LL i Sj piu cha PT a L D a o 1 B EFT Amm na nnd rru Hues sboer per cul 2 C1 was rezin cA 3 52D8 Garma iag 15 mas fil I mi l Spacegreun 3 ile Tablet Thick begirncend um 10 Share amplitudes and phases Tar 3 ol anand in Daas mes 7 Sere Amph Phases I h k i Torann Opa M tow Ci Carr si Lous Cieta h EE p Ip p 30 qmi e dni Ue aM mz Ca Tit fread k arada ioe 2 D za 3 of diferenr ni TA 00 etree SSSR ne E ERIS TPE ee za FL d EI ENS Tees al Abeorpe or Ho 1 o Lil Micros cape and Leni Poramerers 4 i Cama osse ane T LT ET Cok ddd an ur Char Cones ance are mad ai Muse Pure Two fed P m F i x Cancel E Jpraad cf dakaran ij 3 nm i Dime sn pi 7 Galice keni endi A
114. ical within the uncertainty given by the noise The expected value for statistically equivalent images consist ing of N points is 1 and random deviations from this value by more than 2 N are considered unlikely X Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual Writing x 3 1 5 o o 1 2 zou 10 leads to the definition of a Residual Image fi 10 which is used to visualize and to quantify the mis match between two images It has the advantage that instead of pre senting a single number for how well two images match it is a two dimensional mapping of the local fit Thus a difference image will more clearly reveal areas of greater mismatch The optimum match is still defined by minimizing X It is important to note that the fitting parameters can also be applied to the Fourier transforms of the images which some times will lead to a reduction in the number of the data points to be compared 11 In the case of images of crystalline material containing no defects the Fourier components will be non zero only for frequencies corresponding to Bragg reflections of the lattice although this is strictly only true if the motif has been averaged over many repeating regions and resampled onto lat tice coordinates such that streaking due to discontinuities at the boundaries is eliminated The complex values for the Fourier coefficients take the place of the image intensities It is interesting to no
115. icts the calculation in reciprocal space as well The maximum reciprocal lattice vector for orthogonal axes is given as H2 Vmax k vt 2 5 21 max max max 2a 2 b Because most implementations of the multislice formulation makes use of Fourier transforms the calculation grid N and M is adjusted so that both are powers of 2 This is because Fourier transform algorithms can be performed much faster for powers of 2 rather than arbitrary dimensions This results in uneven sampling intervals dx dy when a z b In order to not impose an arbitrary symmetry on the calculation a circular aperture is imposed on the propagator In practice this aperture is set to 1 2 of the minimum of himax Kmax as defined above in order to avoid possible aliasing effects associated with digital Fourier transforms The sampling must be chosen such that the calcula tion includes all or sufficiently enough scattering that takes place in the specimen After the electron wavefield emerge from the specimen it is subjected to the varies magnetic field of the lenses that form the imaging and magnification part of the microscope Of these lenses only the first lens the objective lens is considered in the image formation calculation Since the angle with which the electron forms with the optic axis of the lens varies inversely with the magnification only the aberrations of the objective lens are important The remaining lenses serve to just magnify the image for
116. int The routine then moves first along each column trying to preserve continuity in the phase value Instead of making a jump from 7 0 to 1 0 the phase will take on the value 1 0 and continue to increase or decrease when crossing phase jumps This command first does the columns and then the rows of the image Ch 11 The Geometric Phase p 187 MacTempas User Manual Ch 11 The Geometric Phase p 188 Chapter 12 MacTempas User Manual Background where Finding Focus froma HRTEM Image The amount of defocus in a HRTEM image can be determined from its power spectrum if sufficient amount of amorphous material is present Under these conditions it assumed that the weak phase object approximation can be applied to describe the features in the power spectrum that derives from the effect of the objective lens on the scattered electrons passing through a thin amorphous material Under the weak phase object approxi mation the power spectrum for a HRTEM image is propor tional to sin x u Cs fy Af e i reciprocal lattice vector Cs spherical aberration coefficient electron wavelength fo objective lens defocus Af spread of focus a convergence angle In the absence of any astigmatism and ignoring the effect of the spread of focus temporal incoherence and convergence spa tial incoherence the intensity in the power spectrum is approx Ch 12 Finding Focus from a HRTEM Image p
117. ion of electrons as they emerge from the bottom of the specimen or at a predefined depth in the specimen By holding down the Option key when selecting the button one can select to display either the magni Ch 5 Windows p 47 MacTempas User Manual tude squared default the complex amplitude or the complex Cheas wimi tn opto Fi Comply Modulus Squared cetenzityi D Ar inde Phase 1 Resolution limited laso phase of the electron wavefunction at the exit surface of the specimen Diffraction Pattern Select this option to display the diffrac tion pattern for one of the selected specimen thicknesses This is a dynamical diffraction pattern including multiple scattering in the specimen Image When selected one of the calculated images becomes the source of the operations defined by clicking in the Operand Window By holding down the Option key when selecting the button one can select to display either the image intensity Choc ifi 10 urgiut I8 Complex E Modulus Squared intensity Amplitude a Phase l Resolution limited 9 590 A magnitude squared default or if the image plane wavefunc tion s has been calculated the complex amplitude or the com Ch 5 Windows p 48 MacTempas User Manual plex phase of the electron wavefunction at the image FFT Use this to perform a Fourier Transform on the selected source Operating on the Projected Potential will yield the structure fac t
118. ion represents a convolution in real space and is solved more efficiently in Fourier space Ishizuka and Uyeda 1977 where the equation transforms to YCH z dz exp inddzH YH z pH dz Y Hz 19 where V H z are the Fourier coefficients of w x y z p H dz is called the propagator The multislice formulation is a repeated use of the last two equations and will give the wavefield at any arbitrary thickness T of the specimen If the slice thickness is chosen as the repeat distance of the crystal in the direction of the electron beam only the zero order Laue reflections are included in the calculation as the unit cell content is projected along the direction of the elec tron beam Three dimensional information which involves including higher order Laue reflections can be included by reducing the slice thickness Kilaas et al 1987 Sampling Criteria Any numeric calculation must be performed for a limited set of data points x y or reciprocal spatial frequencies u Working with periodically repeated structures if the lateral dimensions of the unit cell is a and b which we for simplicity make orthog onal so that the axes are associated with an orthogonal x y coor dinate system then for a given sampling interval dx dy we have 20 ele Ch 2 Theory of Image Simulation p 17 MacTempas User Manual The Image For mation defining the calculation to a grid of N M points The sampling interval automatically restr
119. irra Tata br fore api p rit i r ap go aahi P l d LE 1D RAD 221433 Beta Eg Hosts o hice pes Cell imo Cok 365203 Camden xi trun h 1 m Spacagreup s Jri Tath Los Thick bime m 2X D E Bo Amin Es L oue Gore Jmol Phat z Ea ua Fu Spem Dm n f dien fam nf Less Cie 07 a 3l ECL uer ae Cr mee Ea Tn piera A aedis 001 04 fof diesen xci 5 Tapa of Anearpucn iL Mivescope and Less lFarameriarr P higmaien EE Coa Borie Bagva 7 a er shea 2000 Open 069 Fi pese Convergence angie rrrad 0 15 Phase Pang Tet Pod a EL Spread of deire A 200 np m Teele S HAD Before eg fret eran DA HO au al Cama 1508 bn CM bmi aperi cad ft LES inc haere ui rir arca on Hn bt MTS rire epe dp Dro 2E fr ey cai state baka ee Cent ofthe Doc Ax OD DDD CD DD gue ai ET Crezr ricia cokulation uistun kixi ui eo le Peg per Pa Een Waaa lissage Bek x calcula Fabre Ferenial _ Tak Wasser ron image Space group 139 From the structure information we know that the cell is tetrago MacTempas User Manual nal with a space group I4 mmm From Table 6 2 1 of the Inter national Tables for Crystallography we find that the space group number for I4 mmm is 139 Choose the correct space group from the popup menu a 3 814 Enter the correct value for the lattice parameter a In this exam ple MacTempas knows that b is equal to a for the tetragonal space group 139 and so enters b automatically once a has bee
120. istent with random dis placements of atoms according to their debye waller factors Frozen Phonons Options for Frozen Phonon Calculamon Number of specimen confiqurations i L3 Show average potential for configuration _ Show potential far each slice Cancel Weak Phase Object Images is a Separate module that allows the calculation of images that would be produced in the case of an ideal Scherzer lens and MacTempas User Manual validity of the weak phase object approximation The wpo calculation is discussed more in detail elsewhere Weak Phase Object Caloulation Ruesolutiam Cypaboes Enchng Resolution Ad 1 06 8 Auro D cremari Resalicior C Feed Deecraments im stapes af z Starting Resolution C Viewing Options Humber af Unit Cells re dismay x S Y 1 L 200m Factor fo be Used in Displaying images ra On Ring Pattern Ga Zz calculates the diffraction pattern by adding up the intensities for each tilt angle within the cone of incident electron directions Ring Pattern Options Basic Setting Indexing amp Ring Type Camera Length mm Maximum G Vector 1 A 1 500 vi Draw Center spot B Line Color Mi text Color No Text Background O White Text Background f Draw Partial Circles Arcs _ Semi Circles Right side Left side Index Diffraction Rings Show d spacings In real units A In reciprocal units A 1 Ch 6 Menus p 79 MacTempas
121. it cell should be viewed in the 001 orientation It should be noted that the viewing direction is in units of the real space unit cell axes One can also view a cross section of the material in a given direction A dialog box allows the user to specify the field of view in A for the two directions Draw Momist Model Type af View H rigeeat Unit Call B Transtemed Weer Call O01 is Electron Beam Director Dxtemded View Width 25 Haight 20 View Cptiones Viewing Direction WI n m L initial Scaling Factor to be used for Displaying The Unit Cells 3 cf Wimdmad sn Ch 6 Menus p 68 MacTempas User Manual Draw CTF Sin chi Draws the Contrast Transfer Function for the current micro scope values The original microscope values are taken from the structure data but the user is free to change the values associ ated with the CTF independent of the values used in calculating the image Clicking in the CTF will show a bar with the values Contras Transfer Furctice CON TRAST TRANSFER FUMCTIOH Y REE ee Tes NODE Ae 2 OON Tira el Daw Erredhoge Fuscran EI Cv cnid ET Draw Zare Ain G Uarors Ersen Werte A Label Haiman 3ais in Be ici zr dE ir 10 30 05 js gg eu LAL an E 2400 a Cr mon v L M Ll 0 600 Oo Dhv rreadi NT B 30 Dei p Vaki Th 300 10 of the CTF and the resolution The bar moves with the mouse Draw 2D
122. l Ch 4 Running MacTempas p 42 MacTempas User Manual Chapter Status Window Atom Window Windows This chapter explains the windows of Mactempas the informa tion presented in each and how one interacts with the contents of the windows Status IDLE This window shows the current status of the program indicating the number of phasegrating coefficients calculated the current slice number being calculated the current image being calcu lated etc Atoms ca sr e leu o e This window shows which atoms are present in the structure the color the atom will be drawn in if colored atoms are set and the relative sizes of the atoms to be drawn To change the color of an atom choose the Color Picker tool from the Tools Window click on a color in the Color Bar in the Image Control Window and deposit that color on an atom by clicking on the colored circle representing the atom The color of the atom will be set to the new color Ch 5 Windows p 43 MacTempas User Manual Image Control Window Image Control Whole Image Cross Hair Min 0 Max 255 Black 9 White 255 Apply B W Values Ch 5 Windows p 44 To change the atomic radius double click on the chemical sym aha For tha Amen Rdii Liz lA es bol A dialog window will pop up and a new value for the atomic radius can be entered units in This window is used primarily to control the appea
123. l Prades r Ta is CRIRE foshom Cant sf Laum Circe h 000 p uad W nl mema in Call ELT F i Ca Ez Tik mad X angle hon laa fot dite i 5 n reni atm Ty al Abami Hane Micrescape and Lers Faeanreners Wicepscpge Hame Aeg Absorption Parameters valage EV TM cule n FB M absorption Cameergence ange jarai CET Prove Plate Tea Cin hielt Sonering Facio Spread of delacus A an doo n hm Destes Des anc endi Hi ain m 2330 Car mm ee Dh pers mad QU ins it Maker 250 Tess CENE L1 M Mindray larensity ra be included in rhe Lens 1D ED is nia K ne fan Re E Ceri the Gertie Axm ff dii o00 d Exur rizu calrelation stain Mark far perature _ Pred Pomni Beet Wawelerchon _ Image Via ric aa cod ca Lod CT Projected Poisniial C1 Exsi Waas lerton Cl image Microscope The type of electron microscope used to generate the imaging parameters Predefined microscopes are shown in the popup menu together with one undefined microscope If a predefined microscope is used MacTempas provides values for Cs the spherical aberration coefficient of the objective lens in mm Delta the halfwidth of a Gaussian spread of focus due to chro matic aberration in Angstrom units Theta the semi angle of incident beam convergence in milliradian If the type of microscope is unknown to MacTempas the above values must be entered separately We will see later how to define a new Ch 4 Running MacTempas p 38 MacTempas User
124. lculation p 146 Number of slices per unit cell default 1 This value will be computed by MacTempas from the repeat distance of the structure in the beam direction and the current value of Gmax This number can be changed if desired as of course can all the parameters entered in response to the prompts listed in this chapter Show Basis 9 Click on the command to bring up the dialog box for entering the information regarding the number of atoms in the basis We enter the nine different atom positions listed for the basis atoms For each of the atoms in the basis MacTempas requires the chemical symbol x y z coordinates DW factor and occupancy factor From the information given above we use the following information for the nine atoms that are given in the structural basis Chemical Symbol Ca Xy 0 0 0 Debye Waller Factor 3 6 Occupancy 1 The data for the first atom include the chemical symbol for cal cium used by MacTempas to select the correct scattering factor table the atom coordinates the temperature factor or Debye Waller factor and the occupancy factor The second atom position is entered in the same way with responses of Chemical Symbol Sr X Y Z 0 0 0 1097 Debye Waller Factor 3 6 Occupancy 1 The third atom position is similar except that the occupancy is set at 0 87 Chemical Symbol Bi X y Z 0 0 0 3022 MacTempas User Manual B Factor 3 6 Occupancy 0 87 After all nine atom positions
125. me gt pout is the result of running the pro jected potential routine from the information stored in Ch 3 Introduction to MacTempas p 28 MacTempas User Manual 3 4 5 6 lt structurename gt at it contains the specimen potential in the direction of the electron beam This is a BINARY file of type Real 4 The first 80 bytes consists of record information and the data starts at byte 80 The first line of data contains the data for the bottom line of the image since the coordinate system for MacTempas is at the lower left corner of the image unit cell Thus if the data is imported into a program for viewing the image will appear flipped lt structurename gt mout is the result of running the multislice routine using the data in lt structure name gt pout with those in lt structurename gt at it con tains the exit surface wavefunction at one or more selected specimen thicknesses This is also a BINARY file with the same structure as lt structurename gt pout except for the fact that the data is complex pairs of numbers real and imaginary The data starts at byte 80 and the file can contain more than one exit wavefunc tion lt structurename gt iout is the result of running the image formation routine to apply the effects of the microscope parameters in the lt structurename gt at file to the exit surface wave it contains one or more images ready to be displayed This again is a BINARY file with data
126. med by the objective lens The effects of the lens which normally are included in the calculation are spherical aberration chromatic aberration and lens defocus Two fold and three fold astigmatism including axial coma are considered correctable by the operator although they can be included in the equations Without any aberrations no instabilities and with the specimen Ch 2 Theory of Image Simulation p 18 MacTempas User Manual in the focal plane of the objective lens the image observed in the electron microscope would be am magnified version of I x y hp x y z exitplane of specimen 4 elx Ye Gs y 22 Objective Lens Defocus Consider an electron traveling from the plane defined by the exit surface of the specimen to the plane given as the plane of focus for the objective lens This distance is referred to as the objective lens defocus Af Exit plane Object plane Af cosa Af The electron traveling along the optic axis will have a path length of Af while an electron that has been scattered an angle o HA will travel a distance Af cosa This can be expressed as a phase difference 2n AY ce B ay MH 23 Spherical Aberration Electrons crossing the optic axis with an angle a at the focal Ch 2 Theory of Image Simulation p 19 MacTempas User Manual plane of the objective lens should form parallel paths emerging from the lens Sa However the spherical aberration of the lens causes a
127. ming simulation of HRTEM images is to compare these with the experimental data in order to determine the structure In practice this means that various models are pro posed and that images are calculated until a match is found At that point the structure is presumed to be known atomic posi tions and atomic numbers with some given uncertainty Alter natively one starts with a given model and varies the model in a systematic fashion searching for a global maximum in the fit between experiment and simulation This entails that one needs an efficient method to compare the experimental and the calcu lated image It also requires knowledge of the uncertainty in the measurement image intensities in the experimental image and a way to relate this uncertainty to the uncertainty in chemical composition and atomic positions This area of quantitative electron microscopy is fairly new and most images are still compared visually However it is an active area of research and many techniques from statistics are just now beginning to be used in HRTEM Ch 14 Structure Refinement Through Matching of Ex MacTempas User Manual Acquiring quantitative data In order to extract quantitative information from electron micro graphs the data must be represented by a set of numbers Usu ally images from TEMs are brought into a digital representation by one of the following methods 1 Recording the image on a photographic plate and using a scanner to
128. mu mx irsquapc 0 i 3 E Let Pops Seam Gur ES Convolute will calcululate the convolution image from two images a Convalubian Deconuelutien Choose image A1 besco 3 304by152 Is Chape image 2 Point Spread Funcien A3 besto 9 3Odby 152 wy Shift center of Image 2 to engin Cl TEENS SSS L Carel i T Deconvolute will produce a third image which is the first image deconvoluted Ch 6 Menus p 127 MacTempas User Manual with the second image r Conwalunan Desonwelutian Choose image CESE Chege image 2 iPoint Spread Fancii ni A35 besee 9 10H 152 Shift center of Image 2 to engin 0 0 Ui GE Ca Align will try to align two images by either the cross correlation image or the phase correlation image Choose image amp 1 ALS bemo 3 304byl52 HM Choose Image amp 2 A2 hesep 9 3ddby12 E 8 Align by cross correlation 2 Align by phase correlation Frequency Ce o 0 2 mas image Frequency nurum Sot Celtas el A 300 hr Cancel Azimuthal Average Ch 6 Menus p 128 MacTempas User Manual Contains the following operations 1D Image 2D Image Split Plane 2D Image 1D Image calculates the azimuthal average and siplays it as a one dimen sion trace 2D Image Split Plane will display the original left half of the image and replace the right half with the 2D azimuthal average 2D Image will creat
129. mulated from a structure model A Automatic refinement of parameters such as the thickness of the specimen the defocus of the objective lens crystal tilt aberra tions etc MacTempas User Manual eA Automatic refinement of structural parameters such as atomic positions debye waller factors and occupancy factors for selected atoms in the structure The experimental image can be compared with the computed images using a number of goodness of fit criteria A sub area of the experimental image can also be compared to a sub area of the simulated image For more information on quantitative com parison methods and structure refinement see the chapter on Introduction to Quantitative Comparison of simulated HRTEM images with experiment Note All the procedures expect that the experimental image covers the exact area of that of the unit cell used in the calcula tion Thus it is up to the user to make sure that the unit cell motif is extracted from the experimental data prior to usage The term Unit Cell is loosely used since it only refers to the size of the model used in the simulation The experimental image does not need to be sampled equal to the simulation since the routines will resample the experimental data to fit that of the simulation For parameter refinement and structure refinement there are a number of algorithms that attempt to look for the one solution of parameters that maximize the fit between the experim
130. multislice formulation Goodman and Moodie 1974 amp Self et al 1983 i s by far the most commonly used method of cal culating the electron wavefield emerging from the specimen Although it does not as easily include scattering outside the zero order Laue zone as the BWA the multislice formulation is more versatile for use with structures containing any kind of defects either they be point defects stacking faults interfacial structures etc The multislice solution gives the approximate solution to the electron wavefunction at a depth z dz in the crystal from the wavefunction at z In the multislice approxima tion one has gt dz Y Qs y z dz expl iodzV y exp io VC y z ide hp Gy 2 16 Thus starting with the wavefunction at z 0 one can iteratively calculate the wavefunction at a thickness n dz by applying the multislice solution slice by slice taking the output of one calcu lation as the input for the next Equation 16 is solved in a two step process The potential due to the atoms in a slice dz is projected onto the plane t z giving rise to a scattered wavefield p x yz dz expl io Vy dz hp G5 y z q x yp x y z 17 The function q x y is referred to as the phasegrating Ch 2 Theory of Image Simulation p 16 MacTempas User Manual Subsequently the wavefield is propagated in vacuum to the plane t z dz according to Yp x y z dz exp iodzV y p x y z 18 The last equat
131. n set Similarly MacTempas puts in the correct unit cell angles since they are defined by the space group in this partic ular example Note that cell parameters are input in not in nm c 30 52 The value of the C cell parameter is input in A Gmax default 2 Gmax is the size of the multislice aperture and defines how far out in reciprocal space the diffraction calculation will extend The value of G max is automatically set to 2 0 reciprocal Angstrgm units so that MacTempas will compute all of the dynamically diffracted scattered beams out to this value by considering all their interactions with phase grating coeffi cients out to twice Gmax a default of 4 0 reciprocal Angstrgm units Note that these default values 2 for the multislice and 4 for the phase grating are normally large enough to ensure that all significant contributions to the dynamic scattering are included however Gmax is displayed in the MacTempas menu so that it can be set to a larger value if greater precision is required with a structure that includes heavy atoms Zone Axis 0 1 0 The correct response is the set of three integers that defines the direction of the electron beam with respect to the specimen or the specimen orientation with respect to the incident electron beam direction In this example we choose to enter 0 1 0 in order to image the specimen down the b axis Ch 8 Sample Calculation p 145 MacTempas User Manual Ch 8 Sample Ca
132. n to the selection rectangle Entire Image Sets the comparison region to the entire image Atoms to optimize Add Selection Includes in the list of atoms the ones th tion rectangle set in the model window Add Group Selection at fall within the selec Adds the atoms to the refinement list but constrains all the atoms in this list to move as a unit Ch 6 Menus p 109 MacTempas User Manual Ch 6 Menus p 110 Atoms Within the Comparison rectangle Sets the refinement list to include the atoms that lie within the rectangle set for comparing images Optimize Specifies which properties of the selected atoms those in the refinement list that are varied The following window appears Atom Rafiacenenr Parem tars prireeze checked proces for arms in the selected Bt Name X Of On 7 Of DW Of OCC On 0 npa D aai 04454 Dadin 02661 2 000 Oooo 9 000 0 0000 D nn 3 000 gwign n3nzz 01087 04540 0 5000 07319 1 0000 a Dar put Dao 0 SUD Click isg Ge The tex On rogghes refinement col for all atari Tost each variable zeparareby cancel Ge XX 4 X x ox od or Xo Normally varying the z coordinate will not have any effect since the image simulation procedure uses a 2d projection of the atoms in the unit cell However in the case where symmetry operators are used changing he z position may result in changes in x and y for symmetry related atoms Each time an atom or grou
133. nately in many cases it is only necessary to see the general pattern of image intensities to gain the desired knowledge However in general the image can be best thought of as a com plex interference pattern which has the symmetry of the pro jected atomic configuration but otherwise has no one to one correspondence to atomic positions in the specimen It is because of this lack of directly interpretable images that the need for image simulation arose Image simulation grew out of an attempt to explain why electron microscope images of com plex oxides sometimes showed black dots in patterns corre Ch 1 Introduction to Image Simulation p 3 MacTempas User Manual sponding to the patterns of heavy metal sites in complex oxides and yet other images sometimes showed white dots in the same patterns Allpress et al 1972 This first application was there fore to characterize the experimental images that is to relate the image character the patterns of light and dark dots to known features in the structure Most simulations today are carried out for similar reasons or even as a means of structure determination Given a number of possible models for the structure under investigation images are simulated from these models and compared with experimen tal images obtained on a high resolution electron microscope In this way some of the postulated models can be ruled out until only one remains If all possible models have been examined
134. new set of peaks replacing the old The peaks can be selectedm as a whole and deleted as for an object The peaks can also be copied and pasted into another image preferably of the same size A list of peaks can be used in a displacement analysis in conjunction with an associated lat tice that can be refined through a set of peak positions Edit Lattice Ch 6 Menus p 130 MacTempas User Manual will allow the editing of the parameters for the lattice Lattice Parameters Chen Lnice Paare uU y Lattice Drigin qs 85732 221 82 k as dy u02 2 4E Y 122343 Bl umberorlanke vero Wl Sumber of lartice vectors E antel EE Fit Lattice will provide the refinement of a lattice based on a least square refinement procedure using the list of peaks associated with the image in which the lattice is defined Refine Lattice Pararnaters Initial Estima fer Lattice u v de 1104 3 81 M 173 85 dY 0 00 10 41 Y 223 43 Tolerance in distance away from lattice point fraction of Lattice constant tar peak to be used 0 10 and CR The lattice needs to be created with the Lattice Tool The origin of the lattice should be placed on near a peaks in the center of the peaks The lattice is movable and the lattice vectors are adjustable Don t move a lattice after it has been refined A lat tice is an object and thus can be copied and pasted into another image If a selection rectangle exists in the image
135. nual The Geometric Phase Background The Geometric phase routines attempt to determine displace ment and strain relative to a reference lattice by analyzing the the variations around specific reciprocal lattice frequencies Many of the routines will be illustrated using an example of a HRTEM image of a stair rod calculation Invoke the Geometric Phase Analysis from the menu with the image to be analyzed as the front window ied re ree o9 A ono FT RARO Moe Ah d mnn R4 Rad d on ELLER ERS ODES e de o Ad dee ARCA OR ARA um AAA A OOD idet dt om m e C QUIA 9 9 949 9o dA o n4 44 999 o AR R9 omo uU IHR dM d edm RAO oem qo uU Im UR rer he LHS THORS LA UR AR AAA mo o eA oo d Io o A0 9o ohh ot m LLL EA EEE AEE GOO eH OES ED EEO bb gt A9 eoe Ro m A mm de ne ee ee PEER dh b dr EOE QUOS 99 9 9 42m 9 boh 9 Haandi aas P IPPTP LI ete de Et nn d Ld Art LXX XL RE ESO 2220 TRE EEE Ce rte ed de ne le de the bear dite t am pee HOH He OO LIL LOS het lle nt den Ati he de de d de de Ge AE Lt EE REPRE RHE ee Se OOS 6 SO F666 Ee Oe ren ne de OH EROS t de RS AS dor de edo OHS EF gt OF OEE ORE EE ED OR RH RARE EAE EEE A Ro OH ee QUO TERRES EHH Oh Rm do ORE DOSE BA OE Rh da dh af gh mh oom OS BOE ln CPS Oe e SOE om 6 al uA mo ORES OOS CRP SERRA HE RHEE OOH HERERO SE gt Aee e E eee ee TUTTI a atarata Ga a a Maa Mr ded eR qom d eo emo d mmo A Va a a dh do dede RR ORA eo Roo od VA UH moo oo o
136. of the pattern that will be shown in the cal culated image is that which is within the red Image rectangle which can be sized and dragged around The spot size conver gence angle is modified by changing the size of the central disk Ch 6 Menus p 84 MacTempas User Manual STEM Image Will calculate the STEM image for the given input parameters using the by doing a multislice simulation for each position of the electron probe The image intensity for that position is the integrated intensity that falls within the annular detector JE Parameters Promise Probie 5pecamen Scan ares P met Ma au Ama pue LE ah BI aren Sean J Une Sean T w Pararessterz Left labor amp ermw ber ad jeetsh Artiqraytem A J Cara EDEMEN r sgke I e k Bi Microvcogm Focus jA Mag ahii tan ncnesne nm Ip 1 Fu T Jn image Simpi BL Amk Probe Sasipling Aipa 0 100 Twofold D i Fi Fr zen Phono Mode Jf Sampling Points pe 255 i Three fold ud umt Lo J5emi Angle mrad 15 0 i Coma n Lio Getector ETEN bape E 3 amp Celle Wide l High 3 Inner Aperture mrad 50 0 635 A Outer Apertere mad 000 606 z Image Size 36 bv d Creme Probe Image Cancel Calculate Ch 6 Menus p 85 MacTempas User Manual Tables Menu Tables The current operations in this menu are Reciprocal Space Info Displays information about reciprocal space data for the current structure The data can be sorted on the reci
137. ors operating on the Exit Wavefield will yield the diffraction pattern and operating on the image will give the Power spec trum of the image Unit cells Use this to specify the number of unit cells that should be dis played The input determines the number of cells in the a direc tion and b direction Zoom Use this selection to Zoom the object to either magnify the object or to reduce the object A zoom factor greater than 1 magnifies and a zoom factor less than 1 reduces the object Display Before the result of operating on a selected source is displayed in the image window Display must have been clicked Choos ing the source and operations only selects the functions to be performed When Display gets activated the functions get exe cuted gt File This will allow for output of the numeric values of images amplitudes and phases to a file Options allow for writing the data in ascii format or binary format Images can also be written Ch 5 Windows p 49 MacTempas User Manual Main Display Win dow Ch 5 Windows p 50 as TIFF files in this fashion Sat taxe di United Farm Grayscale TH where Foaling Point TIFF 3 MAL input File ASCII O Ewample Strucbores EE New Folder Addto Favoritas Conc e Cancel Use this button in case the wrong sequence of commands was chosen or anything else was entered wrong This cancels the set functions Main
138. p is varied a new set of parameters for this atom group is created and tested If Test each variable separately is checked each try will only vary one parameter Thus if x and y are checked above both x and y for an atom are changed at the same time unless Test each is checked in which case one time x is varied and another time y is varied Deselect All Atoms clears the refinement list and allows the user to start all over defining the set of atoms to optimize MacTempas User Manual Show only symmetry related atoms Use Symmetry elements If the structure is a perfect crystal defined by a set of basis atoms and a set of symmetry operators it is possible to refine positions of the atoms in the basis and to move symmetry related atoms accordingly such as to preserve the crystalline spacegroup Checking this options will result in only atoms in the basis to be visible in the model Thus the atoms to be refined is selected from the basis and any change in the basis is reflected in the entire structure amatam Befineenenz Comal Expesienental Image Sraning Model Comparison Area f D E Sekcuen 3 Entire rame Avams bo refine Add Selection f aid Group Sdecrion 7 Atpras in Comp Ran al x ni E lee keie ia mard pd eee inde i me mie o B how only ran symmetry related atome Gebers mowe according to sommes f cenlctalatonm ResetWew View Mootle From li se the
139. penice andre rica am Phasa Piru a XQ I z4 apt 2 x4142 24142 Tarmad cl deux A ib T 11 xTl zg c1 2 241 2 35 m Desacgs tbe Hac edi DAI Est 20 10 xz 26 HI LI 112 Dj apart radi 4 11 hrar 08 Dever 1 ctii y 24172 77 xyi ririn bareas my 16 baeid in the Leas Lt T i3 ve 2H o XtljzATijA2Tl 2 empties NR kW qu Treas er Cemi of Db Lans dpri up id 00 om aub r LIS iz Cim oe ike Optic Anin foo oo0 am op lF 3t in eed te Ule elg Dr ride coralie niminn u M E I kik for ital lain Frapcisd Forantial d Oetebe E f Cancel ok 3 birt at rozar Praiecian Pr ontial Show Atoms in Unit Cell The atoms in the unit cell are automatically created by the oper ation of the symmetry operators on the atoms in the basis The number of atoms is given and by clicking on the button Show Ch 4 Running MacTempas p 34 MacTempas User Manual a window displaying the atoms in the unit cell appears Sraglation Parameters Crypta Paramaears 5pecarem Fararetnrs ee pat Tore aski jawetil J inzux ADM SEIADO Alpha see anin In fa m Un ix tu BA zeian Bara jing 3D ED trece rennes 1 i i CN Ge V Cuma ping PAT Ahora in the Unit Cell pacsaragr amp jini Taten 190 d a kee eek F ES Type Mare X coard Y need Z co rd EMMST Dect Egi Syn pt Er Shon i I zu QD CoE JI SADO 100 Sl 1 I Cu 13D CO gawo Jawo A V nfaterm ini Hia 4 Es E 2 s
140. procal vector or the structure factor extinction distance Reciprocal Space infa Spacing amp Angle Calculator Search Tor Are Seaech for Angle One cacn search for reflections which satisfy a search criteria based on the ratio of the length of the vectors and or the angle between the measured reflections This can be used when trying Ch 6 Menus p 86 MacTempas User Manual se Lattice Axas A A SEN a Jaano c 3n 5200 Angles Alpha 30 05 feta 30 00 Gamma 90 00 to index diffraction patterns One can give aan accepted toler Angle Search Search for specified angle Angle betw rafactions 45 00 Talant 5 00 Bel Exclude Kinematically Forbedden Reflections Search Maibhad Search Only Based on Desired Angle Ouse Angle amp Ratia Measwrad d spacing Ratia 1 50 orane 500 7 D Use Angle amp Measured Values Measured d xpacing 2 00 A Towrance 200 J Mravared d spacipg 2 200 Tolerance 200 A C anse for the ratio the measured spacings and the measured angle Spacing and Angle Calculator Shows the lengths and d spacing for a type family of reflec tions Two reflections can be displayed and the zone in which a set of reflection exist and the angle between them is shown in the right part of the window The reflections can be typed in and Angle y Plano Calculatar iude Box bor som qan Tl ee mm mus leet Placer Spacing 22140 Da g hi Reflection
141. r Qn rr 0 10930 5500 igw dehet ert 7 4 2 ar OID OSM CAWO 35DD A E 2 sr Qon Gin 0 3606 0 5600 i000 Micros pene and boe Pariser i dr 05000 DEMO 030 3600 iom bicipiti Kame T 5 B OMG oo spz2n 5400 DATI okie Tid z 5 r E 3 B Qi f Bie gaitzi 3600 04 pei Le ie J 5 5 B 1000 Fe OST 3A ato Careergesce angle nra im Paani In 3 Bi OIG HN Teo Zaw aaa Spread of clocan 4 i 3 Bi Qon roO 2681 D 3800 012 ae Iz 3 Bi OD GCN d2 EID JAW QI Delais dae nc endi A zm ja i 5 Bi diDID Di d2 i9D L o dixi Di spar rad A uj toner 0000 uh 44 3 g asiwi DEMO 0232390 3600 dim Bien m rendre ro be ipckagded ie the ess 10 13 4 Ca DAG Ce DE E gama BIET LI ueram Er 1 dmm Mom ee da dm 1 LA ud o MIB m 3 15 RSR Dea iens nm am EP IB 4 cu DSW CON OO 3AM 100 E ars me gom pa d ola asmo aww odat 3600 iaw m 3 a DID Amam G30 SE Ja Cser ri s cacelation saia Ew les Or EoLA LIEU Mocis Fresnriar LI CEN eee MEL TTL kia di caabnes C Projected Friantal CT Catt Boarertusriiar _ mags Cancel Gk Number of different atoms This value is the number of different types of atoms in the spec imen structure difference is due to a different atomic number or a different Debye Waller factor The correct value is calculated by MacTempas and displayed Zone Axis Specimen orientation in relative real space axes units Number of slices per unit cell For unit cells with large repeat distances in the beam direction mode
142. rZ E rr dodi yt P yl New Basis Cs 0 000 0000000 O00 5r 01 T 0 0 DOR OL OK Bi D SO 2 0 00 0 OL CR Bi CL 26B D OD DO pig Cu d 4465 0 0 03 00000 Hew Unit Cell Ca DCI 0 000 DLODO 0 ca 0 590 0 50 DC S DO 5r 0 1 10 000 000 5r 0 61 0 0 500 0 500 Sr BaN 0 0 HO A Sr 3900 50000200 Bi0 302 0008 0 040 Bi 02 D SOR el Bi 0 538 0 060 0 006 Bi 0 198 0 500 0 800 alee Note A RU lacri sje Transformation that takes the old axes into the new axes Transformation matrix W TX o l 1 m D a Translation of origin 0 000 0 000 0 000 Note that zz arbitrary translabon of the origini Cannet generally be represented by the same pacegrnu Switch Spacegroup Tetragonal E Export Mew Ser It is important to realize that arbitrary input does not result in a symmetry which still can be presented by the same spacegroup with a change in symmetry operators Export New Set Allows the user to export the new basis and the symmetry oper ators as a new structure file Ch 6 Menus p 117 MacTempas User Manual The Process menu is the largest menu and is the source of all image processing functions There are menu sub menus as well Process Process Menu Image Calculator TEC FFT d6F Hanning Masked FFT EF Soft Circular Masked FFT XEF Inverse FFT a6 Power Spectrum Edit Mask X ir 3 M Apply Mask s NX 268M Fourier Filters Ld Spatial Filters b Inver
143. rance of images The active image can be the image in a image window or the selected image in the MacTempas main window The black and white values of the current selected image is shown and can be changed by typing in new values The contrast and brightness can be changed by using the appropriate sliders An image can be shown on a logarithmic scale which is the default for images in frquency space reciprocal space The line in the graph represents how input image values are mapped to output display values Thus an image can be pseudo colored by choos ing a color from the color bar with the color picker tool selected and depositing this color in the vertical gray scale bar show ing the display vlaues The histogram of the current image is shown and black and white values can be chosen by clicking and dragging to select a region of the histogram To invert the display click in the Invert button Similarily the image is reset to the original values through the Reset button This window is also used to set the color of a particular atom species and the color of lines and text To choose a color the Color Picker Tool must have been chosen MacTempas User Manual Tools Window The following tools are currently defined Pointer Used for general moving around objects in the display window If an object is selected and the Option key is held down while dragging an object a copy is made of the object In an image
144. rate values of Gmax may allow the Ewald sphere to approach the so called pseudo upper layer line that the multi Ch 4 Running MacTempas p 35 MacTempas User Manual Ch 4 Running MacTempas p 36 slice allows at the reciprocal of the chosen slice thickness In this case MacTempas will sub divide the slice into two or more subslices How this is done depends upon the potential setting chosen in the Option menu If 2 D calculation is set and the checkbox sub divide unit cell is NOT checked the projected potential is calculated for the entire unit cell in the zone axis orientation and is used n times to cover the unit cell If 2 D cal culation is set and the checkbox sub divide unit cell is checked n potentials are calculated from the atoms within each sub layer and used to cover the unit cell If 3 D calculation is set n potentials are calculated by appropriate integration of the potential from all atoms in the unit cell Gmax The maximum value in reciprocal ngstr m units of any scat tering vector to be included in the multislice diffraction calcula tion This value imposes an aperture on the diffracted beams included in the dynamic scattering process It should be large enough to ensure that all significant beam interactions are included The default value is 2 0 MacTempas will compute phase grating coefficients out to twice Gmax in order to avoid aliasing in the multislice calculations Specimen Thickness The t
145. reaches a lower limit When comparing calculated and experimental images the energy of the system can be chosen to be X or any of the other quantities that measures image mismatch When basing the comparison on the cross correlation coefficient the energy can be taken as 1 CCF Simulated thermal annealing is a straight forward technique that has proven to be very powerful for finding global minimum without getting trapped in local minima It is sensitive to the starting conditions and the choice of starting temperature and some experimentation may be required Near the minimum it tends to be less optimal than search techniques based upon gra dient methods and switching to a different search algorithm may be an alternative once the simulated annealing algorithm has terminated Simulated Evolution Simulated evolution is another technique for obtaining the glo bal minima which is modeled after Darwin s principle of sur vival of the fittest 16 It starts with an initial configuration of Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 220 MacTempas User Manual all the variables to be fitted and produces a number of sets from the initial set using a random generator mutation genera tor This set l represents the first generation of children The algorithm proceeds in the following way 1 Evaluate a quality function Q goodness of fit for all 1 chil dren ii Select a subset u lt
146. rees out of phase Ch 9 The Weak Phase Object Approximation p 153 MacTempas User Manual with the central beam Under the two assumptions above the image intensity in the WPO approximation can be written as V x y 1 iot x y such that the image intensity is low in areas of high electrostatic potential the location of atoms Atoms of higher atomic num ber show up as larger and darker regions in the image This type of image will often be similar in appearance to images cal culated by a full multislice calculation for equivalent resolution for a thin specimen for Scherzer defocus The WPO approximation is invoked from the menu bar in the same fashion as the multislice calculation The input to the WPO calculation is a starting resolution in A and an ending resolution The steps in resolution can be fixed user deter mined or automatic When automatic steps are chosen the program will calculate the first image corresponding to the reflections that lie within 1 BeginningResolution and each new image will be calculated for the next set of reflections corre sponding to a higher resolution until the end resolution is reached Weak Phas bject Calculation Bresoluan Opern Starting Resolutio rA 3o Erag Resolution I LD f8 Aute Decrement Besplution Cl Fixed Decrements in steps of a2 Vici ra Dori pes Sumer of Lin Calls to divers X3 X Y 5 2 som Factor to De Used in Dip sying Images Z Ch 9 The Weak Phase Object
147. rmed is rarely a periodic function in W width and H height the Fourier transform of the image of a pure crystalline material is the convolution of the Fourier transform of a perfectly periodic signal the crystal with the transform of a window the size of the image dimensions making a Bragg peak take on the shape of the transform of the window Table 1 rel name window function transform peak profile falloff noise level 1 siw i none E sod E d N conf kL 1 2 3 E ox AP JIN F2 cosine P3 sin xk N 1 1 23 t costtr SIN ETES JIN Von PAIN TONNERRE Hann The use of a mask changes the transform of the window and can be used to make the peak profiles decay faster but at the expense of increasing the noise level This is illustrated above Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 210 MacTempas User Manual showing the effects of employing masks on a 1 dimensional signal 6 This also has an effect on locating peak positions in order to determine lattice spacings and on the estimate of the amplitude of the Fourier component The standard error in both estimates increases as a function of applying a mask with the cosine window being a good compromise Noise reduction In addition to reducing noise it is also important to have an esti mate for amount of noise present and to quote a signal to noise r
148. rom a HRTEM Image p 192 MacTempas User Manual Find Focus from Image UEUITIELTIC rrdse Ard Cryst Image Processing Exit Wave Reconstruction gt Shiske Filter Restoration Focus Determination gt Find Focus From Image v Always Create New Image _ o Use maximum rings The program might find many maxima which increasing uncer tainty with respect to whether they should be included in the focus determination The program will not use any more than the number specified Focus Range The program will use this range to help the algorithm determine if certain peaks are spurious and should not be used in assigning ring indices Find Focus Preferences This will attempt to find the focus value from a single HRTEM image The accuracy to which the focus can be determined depends on many factors the resolution of the image the size of the Fourier transformed region the resolution in reciprocal space the number of rings in the power spectrum the value of the focus and the amount of amorphous material present in the image Ch 12 Finding Focus from a HRTEM Image p 193 MacTempas User Manual Procedure You will first need to calibrate the image you are working on Tools Use the line Ruler tool to create a line of known dimension in the HRTEM image Ch 12 Finding Focus from a HRTEM Image p 194 MacTempas User Manual IIIITETTTTTETTTTTTTS MARRLLILLLALIIITTTITTITTTTT HPAAAR
149. ry useful when the refinement takes hours days and it is necessary to see how the system varied over time It is important to realize that a movie file grows quickly in size and that the number of frames second should be chosen appropri Ch 6 Menus p 113 MacTempas User Manual Current biih Dairo Energy LISA Hates scalceation CanceBen Ch 6 Menus p 114 ately if the movie is to cover a period of many hours Cerrent Cassgesterd imant Experimental biki Log Fite MME Save Ringel A Hym ss Dismiss j At the end of the run the final structure can be dismissed or saved as a structure file for later use The run can also be aborted by the normal Apple Period key combination Symmetry Transform Calculator Choosing the Symmetry Transform Calculator brings up a modal dialog window that can help the user find another set of symmetry operators and basis atom positions in the case of a change in axis and origin of the unit cell Input is the original symmetry operators which come from the spacegroup that is in use together with the original basis atoms The new unit cell axes a b and c are given by the transformation matrix T such MacTempas User Manual Original Operators that a Tij To Tis a b T4 Ty Tb E T31 T32 T33 LE together with a translation of the origin specified in the old unit cell system fractional coordinates Invoking the command brings up the following window
150. s The first imaging condition prompt is for the objective lens defocus We choose to enter four values of defocus by specifying defocus values from 200A to 800A in steps of 200A Note that a negative value denotes an objective lens weakened from the Gaussian condi MacTempas User Manual Verifying the Input Running the Cal culation tion that is underfocus is negative Aperture Radius 0 67 The value for the radius of the objective aperture should corre spond to the radius in reciprocal Angstrom units as measured from a diffraction pattern exposed with the aperture superim posed We will enter 0 67 to represent a typical value Center of the Objective Aperture 0 0 In order to simulate dark field images MacTempas provides for an objective aperture displaced from the center of the diffrac tion pattern As for the Laue circle center the aperture center is defined in units of h and k We leave the default values of 0 0 Center of the Optic Axis 0 0 To provide for microscope misalignment or for conditions of tilted beam imaging the coordinates of the diffraction pattern at which the optic axis lies can be specified in the same manner as the center of the aperture Again we use default values of 0 0 To display the input information click on the Main Parameters in the Parameters menu At this stage any desired changes can be made by just modifying the input field When all the data in the top field are satisfactory
151. s User Manual being cos CCF This angle is zero for identical images If the images are normalized to zero mean and unit length as in the definition of the normalized cross correlation coefficient above the angle is 180 deg for a reversal in contrast between the two images I and I Significance and Noise Each of the above criteria must be tested for the significance of the measured value D canbe compared to the mean square intensity or inten sity deviation due to noise in either image D can be compared with standard deviation of the inten sity in either image A good way to test for the mismatch between two images is to use a statistical measure for the probability of two images being equal given knowledge of the noise in the images If one assumes Gaussian uncorrelated noise for each pixel in the experimental image the optimum statistical measure is given by 2_ dy 50 7 1G X y Ix m 8 where N is the number of pixels in the image 9 The value co i is the standard deviation associated with the pixel i and can be found as described above from a number of equivalent regions If an experimental image I is compared to a calculated image I and there are M adjustable parameters in the calcula tion the equivalent expression becomes 7 2 x 1 y 607 10 9 N M o A mismatch by one standard deviation adds one to the sum in the expressions above and a value of X of 1 implies that the two images are ident
152. s atoms above This list can not be changed the changes must take place in the atomic basis or the symmetry operators Anns in the deir Celi Perry ETT EC RETETYT AAT CE r SY DETENTE TT us Yat p3l1i2 x 162 rT431 42 ELE MelfjdrEliz T41 f F xci Ixtlie urlinztli2 Xp atly tiini 7 2 L rA TELI Cond e Ch 6 Menus p 76 Maa Mame Seaton Teie feconnd i Le Do QN i Li Dee NI O5 z LL DODGOG DONEE RO INR z 5r DX CUXYMO DEMN ri ar Case CUEKEX AFIN 1 r Diiw G GELLEL 1 5 DOG I Lae 1 amp Lee EE amp Case FERE abia 1 Es DES UD PARLE 1 amp Ch KNO e 1 e Deomm im CETLE 1 m DOG URI Q5 3 1 B DS OREN SIN 4 Ea Tumawa EXE 44 amp hli d En prre TPI dD 4 Ca Co A 55448 4 ca Cie RD DEd Li r DENEN MEI aam 3 L i UEN CL LIL DA f Geet sam dO Tid iXX SAM 10 ten 10m Tin iE d dixi a ns Xm nz l uod Tam DA sn DIM iam Dr ED nm zem GUN Te dun mam Lo Crags zam OO Ed 1000 MH Lem Dm I nsa ua MacTempas User Manual Calculate Menu The active commands in this menu depends on the current sta Calculate Full Calculation Projected Potential nage Plan Waiver Imagers ncoherenr summmatonj Image s Frozen phonons Weak Phase Object images Ring Pattern kinematical SAD Pattern Integrated Diffraction Pattern Kinematical CBED Pattern CBED Pattern STEM image
153. s tchromatic aberr k A 30 Peak Finding Criteria Minirurm distance between peaks A 1 0 040 Fl Use center of mass refinement Center of mass radius A 1 0 020 Electron beam convergence angle mrad 0 15 Report data on all peaks found and excluded Image Scale if uncalibrated jA pixel nan Defocus Determination Criteria Tes For assisting in the assignment of ring indicies E Always RARE AIRE FRANC PER indicate the range of axpacted defocus A When possible use maximum 2 peaks rings Smallest defocus EDD Largest defoous 2000 Camel ax Microscope Parameters Voltage This is the accelerating voltage of the microscope in kV It is used in determining the contrast transfer function for the micro scope Spherical Aberration This is the spherical aberration coefficient of the objective lens in mm It is used in determining the contrast transfer function for the microscope Spread of Defocus This is the effective spread of defocus which is a due to of the chromatic aberration of the objective lens in conjunction with fluctuations in accelerating voltage lens current and the energy of the electrons emerging from the filament It is given in A and is used in determining the contrast transfer function for the Ch 12 Finding Focus from a HRTEM Image p 191 MacTempas User Manual microscope Convergence Angle This is the half angle for the cone of incoming electrons onto
154. t Repeat Transform 2 Statistics 2 Calibrate X C Extract From Complex b Correlation Convolution b Azimuthal Average b Template Matching Peak Lattice Analysis b Average Extract Motif Change Image Origin Geometric Phase Analysis Cryst Image Processing Focus Determination v Always Create New Image Ch 6 Menus p 118 MacTempas User Manual eo 3 Stack Image Calculator Perform polish notation HP style calculator mathematics on images and numbers Image Calculator EINE Leer Max stav Phase imag P ceiting floor Conj Create Window DRE De a EE EE ets es Coles GAGs A Perform a Fourier transform on a 2 dimensional image Unlike many implementations the image is not required fo have dimensions that are powers of two However the image must be square Hanning Masked FFT Perform a Fourier transform on a 2 dimensional image The image is first maksed with a circular 2 dimensional Hanning mask Soft Circular Masked FFT Perform a Fourier transform on a 2 dimensional image The Ch 6 Menus p 119 MacTempas User Manual Ch 6 Menus p 120 image is first maksed with a circular 2 dimensional mask Inverse FFT Perform an Inverse Fourier transform on a 2 dimensional image Unlike many implementations the image is not required fo have dimensions that are powers of two However t
155. t the routine will use the entire image In this particular example choosing a 256 square region would give insufficient sampling in reciprocal space to give good results Ch 12 Finding Focus from a HRTEM Image p 196 MacTempas User Manual kok i Me iy ie ns AEALLLLLLLLAL tek ee a eT CTTTITIIIL Ect eee ee ee ee ee ee Eee ett ce LELLA PERLE REREREARER ERED ES SRG AEA ESTAS SSS SOS 4 EL RER LE EL LE LALRLLLILILLLALLLLLA i i ee IL 85 5 amp ee 1h he ee a ZXIIZETTIITITTTIEITTTTYITYITYTIIXIT ARILIITDTIITITITITTITIIILLIIIIIT a A ETLLLLLLLALLEE 225 864545 29 amp WIRES LIL EL ee Before you execute the command Find Focus from Image make sure that there is only one selection set in the image Executing the command brings up the following result window Ch 12 Finding Focus from a HRTEM Image p 197 MacTempas User Manual ann Focus Control far J 2 E 102 Ea Cs men 001 foes BM Div mrad 001 Eos EH Del A 50 20 0 EM Voltage kW io Bw g nua 0 7 Qe Oe oF D A na Scedbering vector 145 v Make CTF follow ring markers i Print Update The program attempts to calculate the power spectrum associ ated with the amorphous content as a function of the radius reciprocal distance This is calculated by producing the median value for the magnitude of the power spectrum for each radius The median is plotted in blue green and corresponds to th
156. t Structure Running Maclempas The first step in running a simulation is generating the structure input file This is done through New Structure File in the FILE menu This generates the input dialog window with val ues for a default cubic structure Use this template to modify the date to fit your structure Situ ation Porrenes Copa heir rare Parm mers R TEsg qum keel il iiitr LIN Mise Aigha bg BE oo 1 ie Dm CERERI LIE unm die dir deli L cid CETTE Cas hiig TA Gr PEE 3 0E Haegrnas 8 de Tisiani P25 Thick ibn inr andi JM E Lad 8 cb Aon m Fatis 1 F e Y era epi ener p Be For Gyran Dac ue e Cuarta Las Cree DET PET vecta iride z Ds La Tt iria acce rn T a rd eer were i Ae od i Coran Mucha apn Miri AWF Bagir EBL amd Sel LBAL a RII Ewing ie AD Co pari Len adj rv Cema gece orgy auri ns Paca Poca Tasks 00 pn Zerpsri oi detec 1 IE y Thai bo Cabas deg inc endi JA TTT ET TEN 7 m TEX axe ead Lite rd kei OO Uwe Bechara irain lA limus mai ie ba inckaclad ie ihe Lure 107 d gra ef La i IDC gm _ fren ca ber i k iig Aaye n celere fie ar nag om mnm PAR Td Lu Carn of the Opm ad Od E dO i Ow ide a lc hache mann Werk for cuites Pre pursed Priori iat L Duk Werin _ no Luke den FRE LI Pmj Part ial _ bk Waren L me Lan ma a b c alpha beta gamma These are the unit cell dimensions in Angstrgm units and the unit cell angles in degrees MacTempas will
157. t cell as for the Laue circle center Again tilt angle and azimuthal angle can be specified instead Center of the Optic Axis The center of the optic axis of the electron microscope is speci fied in terms of the h and k indices of the two dimensional reciprocal space unit cell just as for the Laue circle center and the aperture center MacTempas User Manual Two fold astigmatism The two fold astigmatism of the objective lens and the angle with the x axis The magnitude is given in A Three fold astigmatism The two fold astigmatism of the objective lens and the angle with the x axis The magnitude is given in A Coma The coma of the objective lens and the angle with the x axis The magnitude is given in A Mechanical Vibration This simulates the effect of a slight vibration of the microscope One finds that often the simulated images show details that are not present in the experimental data regardless of other imaging conditions This may be due to image degradation caused by microscope vibration or other effects not included and thus one can introduce a slight mechanical vibration in an attempt to cre ate more realistic simulated images It is possible to specify an anisotropic vibration by introducing the amplitude in two per pendicular directions with the diagonal of the ellipse at an angle with the a axis as in the unit cell viewed in the zone axis orien tation Ch 4 Running MacTempas p 41 MacTempas User Manua
158. te that the use of different matching criteria can lead to slightly different values for optimized parame ters 12 Adjusting for different means and contrast levels Since absolute values for image intensities are not known and an experimental image may be linearly related to a calculated image a useful way of normalizing the image intensities is to subtract the mean and divide by the standard deviation This ensures that D 0 for linearly related images and a value of around 2 for unrelated data Similarly the Cross correlation coefficient will lie in the range from 1 to 1 taking the extreme values when the two images are linearly related and being near 0 for unrelated data Another approach is to scale the images to the same mean This is done as follows Ch 14 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 214 MacTempas User Manual 2 Late II vMew 11 V calc Tale where the calculated image is scaled to the mean of the experi mental image In order to understand how the mean value contrast and image pattern affect the image matching criteria it is useful to con sider how the Root Mean Squared Difference D can be separated into three terms 13 Dm JU bY 837 02 ei cos a ee 12 where 2 015 yu n5 13 and Mib Vh Ab 14 19 The first term measures the difference in the mean of the two images and vanishes if both images are normalized
159. ter fit for the Electron Scattering Factors or the 9 parameter fit for the X Ray Scatter Ch 6 Menus p 65 MacTempas User Manual Ch 6 Menus p 66 ing factors The menu item text will reflect the current setting Edit Scattering Factor Parameters Brings up a table of the fitting parameters Double clicking in the value field brings up a dialog box prompting for a new value See next page Unit Cell is Entire Specimen When this option is set the calculation treats the unit cell as a non repeating structure such that the entire specimen is repre sented by a single unit cell with the thickness of the specimen as the thickness of the unit cell Modify Specimen Bounds When the unit cell is the entire specimen this will allow the user to trim the bouning volume for the cell in the specified zone axis orientation Change Bog rdg Windus o m m s EFP Pasar i m a 1 5 zYE ES B tarmo E L Alaa phy one baw ug ital Ports di 256 6 s 5s pe epe 1 Selena Geo Q GO i 0 bree A is koa Cosi jo i iag i CLEO larg A1 dii ace ft Balls i t aval o a MacTempas User Manual ap Fit for Ebectenm Strectere Factors 2 02022 305479 j 2422 85444 D 825 12726 omda n nosaa imjasi nie azine ninos jisoms ousar nitas Er Um M E Ee Es nnems nav pam amena pe nime jns nori aan uem dousa 10577 0 7307 36 999 ereere Ea 01247 nsee Ing fameace inas langaz nasar zans imis Jon
160. tion this command is not used It can be used to remove discontinuities associated with wrap around effects as the phase crosses 27 Usage Use this routine to create a Moir image calculated from the image Phase Image It is equivalent to moving the origin for the reciprocal space inverse FFT to the point lgl M along the line from the origin to the spatial frequency g Mathematically the Moir image becomes P r 2ng r M 2rg du r where M is the magnification chosen Ch 11 The Geometric Phase p 171 MacTempas User Manual in the dialog box Enter Moire Magnification Ar Gaomeric Fharr Aruhpri Cou Bratnia Cent Dieu ped maus Aum Mince eT bb AA CCE eu Ce Rb a ao LE x Eu Li Ay AET LE Aii Fon Lote Pe E Lens Fie TH M gt gives the geometric phase image calculated in the Cal culate phase image s command Calculate Displacements Executing this command produces two images ux and uy which are the local x y displacements with respect to the lattice defined by g amp g2 The command requires that the two images Phase Image 1 and Phase Image 2 exist together with the associated values Ch 11 The Geometric Phase p 172 MacTempas User Manual for g and gp AS Phase Image 1 44 Phase Image Ch 11 The Geometric Phase p 173 MacTempas User Manual Invoking the command brings up the following dialog box Cal
161. toc to add individual atoms ta the list To remove atoms use the tool TET Arems wir same 77 wall eye gether unes axplicizely removed war rhe rel f Cancel E x 3 Ch 6 Menus p 111 MacTempas User Manual Ch 6 Menus p 112 Set Chemical Constraints brings up the following window B Dit Energy Ch inical Lanspbraint Bani Eater Opin CE RATE e Ca Ca A xen a a RE 34 constralm ies Foc amp ih Cu Cu Erargy cori been Ww nam BE Wd in z ur etae Sia HI Ca Ca EOD OR Se Hi 200 Od rer ET TUE Pind by Cancel SO which can be used to specify a configuration energy that includes terms that depend on bond distances It is possible to specify the optimum bond distance between two atoms whether it is a 2d or 3d constraint and to specify the weight of the term in the energy calculation Even though bond distances have been defined the inclusion of a bond distance energy term can be turned off on from the main Refine Structure window Include Bond Valence Sum Optimization This allows the bond valence sum to be used to measure the energy of the configuration It brings up the following window in which the active bonds are specified the maximum distance between atoms for calculating the bond valence sum the valence of the first atom in the atom pair and the bond constant Each bond has its own weight and the entire bond valence MacTempas User Manual energy terms has
162. u 11 Dr Ch 11 The Geometric Phase p 176 MacTempas User Manual row Below is shown a vector plot using the x displacements as the D 2c vd N n 125 250 3757 500 gt gt 7 om 4 ii t t t f t f gt gt a a YN NN YN YN NNNM NON NN WW ON XN s X NN OU ON ON NON ON x NN NNN NNN 4 5 LU SR Re ne NOR c9 NON OO as Nw O89 e S NON NOM MP XN LUN Toe NN NOUN x x WN NON ON NON ON ON ON hi oW NOM ON ON ON MN w pepa u u eu o length of the x component of the vector and the y displacement as the y component of the vector The data can also be shown as a surface plot depicting the mag Ch 11 The Geometric Phase p 177 MacTempas User Manual nitude of the displacement Alternatively the magnitude of the displacement can be shown as a contour map as illustrated below 125 375 500 Ch 11 The Geometric Phase p 178 MacTempas User Manual Calculate Strain This command calculates the strain with respect to the reference lattice defined by g amp g Prerequisite The two phase images Phase Image 1 and Phase Image 2 must have been calculated Calculate and show the following images f Deformation Matrix D
163. unction of thickness 2 o E No ooo on Oooooommm Options 9 Amplitude O Intensity Cl Plot Phases Thickness Save As File Define Projected Potentials This allows the user to specify which potentials to be used in a layered structure Ch 6 Menus p 71 MacTempas User Manual Ch 6 Menus p 72 Stack Potentials This allows the user to specify the sequence of potentials that should be used in the multislice calculation This applies only to layered structures See Chapter 9 for a more detailed instruc tion on how to create a layered structure Dafinzd Phasegratings Mama az Nama Az Mani Az b i Hama Az j c 0 3 00 2 c k 1 3 00 Bi chic 2 3 00 Mi bos 3 Specimen rae 1 3 3 4 1 2 4 4 L Deposit E men Repeat f Reset 24 0 Slice Unit Cell Use this option to subdivide a structure into separate layers for use in a layered structure calculation The direction perpendicu lar to the slices and the number of slices must be specified MacTempas User Manual Slicing options a Ci Y Zone axis for slicing B 1 Number af separare layers 1 alculate Each Projected Potential Ch 6 Menus p 73 MacTempas User Manual Parameters Menu Cry Parameters AJA Sargi ETA 236140 CIA 325200 Speregrpsg Int E of tams in Basis of Symm Opi sed aama in LiCall 8 of darent akama Main Parameters Param
164. us approximations Depending on how the problem is formulated one can derive the most common solu tions to the electron wavefield at a position T within the speci men The Weak Phase Object Approximation In the Phase Object Approximation POA Cowley and Iijima 1972 the phase of the electron wavefunction after traversing a specimen of thickness T is given as PCxy z T P x y z 0 exp ioV x MT 10 with E o 2e 1 E fn 11 mc where V x y is the average potential per unit length The speci men is considered thin enough so that electrons only scatter once and are subject only to an average projected potential In the weak phase object approximation the exponent is consid ered much less than one so that the electron wavefunction emerging from the specimen is y yz T p x y z 0 7 oV x y T 12 The WPOA only applies to very thin specimens of the order of a few tenths of A depending on the atomic number of the atoms in the structure Gibson 1994 The FT of the wavefunction gives the amplitude and phase of scattered electrons and in the WPOA one has Wu u i0V u T 13 Ch 2 Theory of Image Simulation p 14 MacTempas User Manual where u is a spatial frequency Again for periodic crystals V u are non zero only for fre quencies u H where H is a reciprocal lattice vector in the crys tal We will now use V to mean Vp Thus for single electron scatter ing and when the Fourier co
165. values add to make the final image Assuming a Gaussian spread in defocus of the form te 2 DEP epic E 25 gives T MCF fol DU fodf PCH gt WGDexpEI 26 4By 26 This states that each Fourier term diffracted beam is damped according to the equation above Beam Divergence Spatial Incoherence The electron beam is not an entirely parallel beam of electrons but form rather a cone of an angle a This implies that electrons instead of forming a point in the diffraction pattern form a disk with a radius related to the spread in directions As for a varia tion in energy the images formed for different incoming angles are summed up by integrating over the probability function for the incoming direction It turns out that this also leads to another damping of the diffracted beam Frank 1973 so that 1G h o Dada YH gt Y Hexpho C H N Af f 27 Ch 2 Theory of Image Simulation p 21 MacTempas User Manual The Final Image Equation 26 and equation 27 are only valid when the intensities of the scattered beams are much smaller than the intensity of the central beam Thus the image results from scattered beams interfering with the central beam but not with each other This is referred to as linear imaging Although the formulation is slightly more complicated in the general case the expressions above give sufficient insight into the image formation Image simulation programs do however include the mor
166. w or an entire image MacTempas User Manual Edit Object Shows the information associated with a selected object if the object is editable The displayed dialog box will depend on the object being edited Arrange Object Will arrange objects in the main MacTempas window in terms of their stacking order Ch 6 Menus p 59 MacTempas User Manual Options Menu Live microscope Control v Automatic Erase a6E Atom Overlay L Montage fr 38M Intensity Scaling Magnification CTF Scaling Diffraction patterns D Slice Method Show Microscopes v Use Electron Parameter Fit Edit Scatt Fact Parameters Unit Cell is Entire Specimen Modify Specimen Bounds Live Microscope Control When a calculated image is selected this command can be invoked to bring up an interactive window for changing the cal culation parameters for this image Changes in the parameters Ch 6 Menus p 60 MacTempas User Manual are reflected live as long as the calculation time is reasonable Automatic Erase Toggles whether previous content in the MacTempas display window is erased when a new object is displayed Atom Overlay If set the atom positions will be drawn in as circles on top of images The circles are scaled to the atomic radius and the color is the color set for that atom species Montage Brings up a dialog box allowing the user to select automatic montage of a series of imag
167. window the pointer tool will also act as a hand tool if nothing is selected Text Tool Clicking on this tool turns the cursor into an i beam cursor which can be used to select an insertion point for text To set the insertion point for text to be typed in the image window click the mouse at the desired point The Font Size and style of the text is determined from the menu bar The text will be drawn in the current foreground color and can be left canter or right jus tified Magnifying Glass When selected the cursor turns into a magnifying glass which can be used to zoom in on a selected part of the display Each time the mouse is clicked in the image window the image is zoomed by a factor of two By holding down the Option key while clicking the image will be zoomed out by a factor of 1 2 for every click Double clicking the magnifying glass returns the image to normal Line Tool This tool is used to draw lines on the display If the Shift key is down only vertical or horizontal lines will be drawn Selection Tool This tool is used to select a portion of the screen for several pos sible operations such as copying cutting histogram computa tion etc To select an area click at a point in the display and drag the cursor while the mouse button is pressed In the main Ch 5 Windows p 45 MacTempas User Manual Ch 5 Windows p 46 MacTempas window all objects intersecting the selection rect angle will be selected
168. y ers By invoking New you get a list of the available phaseg fare for rating files pout Double Click on LayA pout and fill in the value for the slice thickness that was used in the calculation of LayA pout Continue and do the same for LayB and LayC Pacey rating Infa Mame of this layer Thickness inp z 3 0000 Cancel ES Now the program has information as to which phase gratings it can use and the final part is to define the sequence of these pha segratings up to the desired thickness Use Stack and the sequence can be defined in different ways One way is to type Ch 10 Creating a Layered Structure p 160 MacTempas User Manual mum URSS in the sequence as 1 1 1 1 1 1 2 2 2 2 2 23 3 3 3 3 1 1 1 where 1 stands for LayA 2 for LayB and 3 for LayC One can also use the commands to define the sequence At all times the specimen is drawn as a colored bar at the left Once this is done you have defined the structure Defined Phasegratings Name Az amp Mame Az B Hame Az Hame az inn ti Cooper 3 00 Au 3 00 bpecmen TOP 111222333 Deposit inga Repeat 1 Reset 27 0 5 Now check the Main Parameters to see that everything is cor rect and finally run the calculation The calculation will begin with multislice Ch 10 Creating a Layered Structure p 161 MacTempas User Manual Ch 10 Creating a Layered Structure p 162 Chapter 1 MacTempas User Ma

Installation - Total Resolution

Contents

Download Pdf Manuals

Related Search

Related Contents