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MacTempasX Manual - Total Resolution

1. Ch 5 Windows p 50 as TIFF files in this fashion Cen sme ar Uintitied Forme Gravscale TIFF Where Flaating Point TIFF MAL input File E CORAN don E Evet Carbon L2 Enample Sir inp at EE E Wew Folder Amd to Favorires 4 for es Cancel Use this button in case the wrong sequence of commands was chosen or anything else was entered wrong This cancels the set functions 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 description of their function New Normal Structure N New Layered Structure 36N Open Structure File 0 Close zew Save Structure As O S Open Image 230 Save image NS save Image A NX OSS Import Pict File Save Window Page Setup HP Print 36P This menu contains the following commands Ch 6 Menus p 51 MacTempas User Manual Ch 6 Menus p 52 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 Thi
2. 7 DE 1436 e259 mate i eae RENE i 226 ___SI413 4 ites 9766 r pee 11430 00 Eee KE 122 11 2206 DFE Lu USE 136107 35 IS iD BIT ja Angles Between Reflections Shows the angles between a set of the reflections in the struc ture co Esem elect sans dss AA LME ET Hs ou pea Paws Ee irasa om oa CEBE a EALE ins EEFE EES 454 ET Hing i E E E la i aa 13202 daea e Ch 6 Menus p 77 MacTempas User Manual Ch 6 Menus p 78 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 to index diffraction patterns One can give aan accepted toler Angle Search Search for specified angle Angle berw reflections 45 00 Tolerance 15 0 M Exclude Kinematically Forbedden Reflections Search Naihi Search Only Based on Desired Angle Us Angi amp Ratio Moaserad d spacing Ratio l 50 Tolorance 5 00 a Use Angie amp Measured Wales Measured d spacing 2 08 A Toerance 2 Messred d spacing Z200 Tolerance ZOD 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
3. Focal Plane of Objective lens A M st Intermediate ee mel Uy 4 a i i y n 7 Intermediate Lens w N 4 vu 4 lt lt V 2 nd Intermediate W YA Image S l Projecter 4 NN Wi Lens 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 ar
4. ABS Let Miri scope Parameters mee ot Microscope Parameters 51S 20 a brroscope Mame Untiti i Edit Accelerating Voltage ouf Mo Spherical Abberation Constant men 12 Cancel Spread of Detocus tar Ea Dergence Angle half witthi mrad 3 i a D Use Fit For Electron Scattering Factors Use Fit For X Ray Scattering Factors MacTempas can use either the 8 parameter fit for the Electron Scattering Factors or the 9 parameter fit for the X Ray Scatter Ch 6 Menus p 63 MacTempas User Manual Ch 6 Menus p 64 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 Treat as Monolayer 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 MacTempas User Manual ap Fit for Ebectrom Strectere Factors 2 o2092 308679 j0S427 Edid JOUA 12926 omda pong inyasa iaimta azine ninos jisoms ousar jo reaa AAEE SIs jO peas 0 4051 pam mme SS4 _ 0 108 A potas anan zean dousa 10577 0 7307 36 999 ereere Ea A Joga fameace inas langaz nasar zans loysi Jones ogag 257005 jostrs zezz0 nama ziaan nieaa 0259 ozsa6 anzsao loege l
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. 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 poten tial 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 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 11 HOLZ Interactions amp Sub slicing p 140 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 accelerat
7. THLIE a Pal reas Fea RES oar Page 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 basis atoms above This list can not be changed the changes must take place in the atomic basis or the symmetry operators 16 17 18 14 Pals al 24 a3 24 25 z 2F ch z9 ai Set LZ wt Lien irl ie Pen Pol SEELIZ APPZ Ate liz GE ee ma mm Oe eee OUEST MES ASE lktili yrili zril ie Az atlas tir cle a 16 2 ali HE LH coc CERN Argens iri ue Lit Cell Tot Mane Sider Tec 1 Tf Li DPN i Li Lens SN z LL DO z Er LS 0T H Sr Cute CNE 3 r Caen CARRE 1 5 D FENI 1 Lee CRE a a Cue E a Ee DL 1 i 86d 1 a Dit 1 La CL 1 LS OS 4 Es Eee UNI 4 Es La DPI 4 Ca Co URENNI 4 Ea Ce Car L r im NN 1 i i EN cord LUN LI LL SEE CNE LED LCI LEE GETTEN GETEEL ELTEL CET eat Le a dessin ery TY Lane azm COR LETT I DELELE osia EITEN GETETI ELETI Di ha See bem Mia Late Lai hon he Lede he Se Lii biaia bian Tate he ETL ae hem Lei Lo id Lo Lo Er i dE arm aad oa am witi arm BL Lo Lo Lo ni ii Ch 6 Menus p 73 MacTempas User Manual The active commands in this menu depends on the current sta Calculate Full Calculation Projected Potential Calculate Menu Weak Phase Object Images
8. mal method but rather a number of possible options 12 3 1Sampling 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 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
9. 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 Ch 9 The Weak Phase Object Approximation p 130 MacTempas User Manual reached Weak Phase Object Calculation Resolution Options Starting Resolution tA Ending Resolution GM Log Auto Decrement Resolution CFised Decrement in steps of C2 Viewing Options Number of Unit Cells to display X amp Y 1 1 Zoom Factor to be Used in Displaying Images 2 00 Cancel E Ch 9 The Weak Phase Object Approximation p 131 MacTempas User Manual Ch 9 The Weak Phase Object Approximation p 132 Chapter
10. 0 00 D A q 2 00 Cent ofthe Optic Axes 0 000 900 0 90 0 9 arme nie ae Over r de caloulat on status Mark for recalculation _ Projected Potential Exit Wave function _ Image Mark as calculated Projected Potential leet Wavefunction image Cane E New command in the FILE menu The parameters can be changed as to bring about a new simulation Ch 6 Menus p 71 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 Modif Basis T Hame x tood w coord z coord os dw fact Ow L at booms aoo aaow Seo 100000 DMO amw 3 m omw awm om sec LEPOM 4 F now owo azes Ramo HOMO Eu Como 000 oa emo Lomo 6 i SOND am 044800 Loom 1 nwm oomoo Gaam 360000 1000000 a 5 moomo ooon oaeo emio Loam 4 Dodo Ao 02 Samim SO Ce cance sen 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 72 MacTempas User Manual the list or existing ones deleted OM deo ee ee te See ee we i eS oS e Sptimanry Operari i title t RTE TEE EST Hye YALE KHIL mim HUE ihl etli Zyta a Pets eat pH
11. 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 Point Ch 10 Creating a Layered Structure p 133 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 structure 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 electro
12. 16 Ca Cotte ba HO Se 0000001 10 Ba LU CLONE Se B OLEH eo Cu EL ET be 0 445 eww Unie Call Cu 0 00 0 0 000 0 005 Ca 6 SO SOLE S de Tanmaya Sr 000 S00 12 Be G00 SG ag Sr 1 000 na aTe E Bo LOS Gi D500 DL LEO A 00 Go BS oe af Tree ler lien tar takes the old ames into the pu ares T anilo naii Matrix Ya imo on amo 1 00 Lw om 0 000 O9 Loo Trarelanor af gnyn 1 00 osm oop Rone than an ar birar anslion of the origin Co OE gear er ally be reprend bp the sane preamp Switch Sa ao ro bi Tetrapanal Export Mew Set Eome 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 MacTempas User Manual Original Basis The 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
13. 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 Ful Calculation Frojected Potential Weak Phase Object images nlegrabed Diffraction Patherr CRED Pattern Introduction to Maclempas Since the simulation process can be subdivided into indepen dent calculations involving the structure the scattering process and the imaging process MacTempas allows one to invoke these independent calculations separately through the Calcu late menu Full Calculation This command will start the calculation from the required start ing point and proceed to calculate finale images Projected Potential generates the crystal potential that produces electron scattering from the structural data unit
14. H ioA H HR VH H e H 6 H 20A H V A 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 1 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 28 528 536 Cowley J
15. 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 O Keefe MA
16. 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 117 MacTempas User Manual Ch 7 Input File Format p 118 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 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 gro
17. OP hie heb Pied by Cancel 0 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 Ch 6 Menus p 103 MacTempas User Manual Ch 6 Menus p 104 energy terms has an overall weight Bond Si fare LE Paredes Bond Sorengah Calculation Chers Move fam To Max Distence Al Valence Bond Comum Wega fa 39 L LELS Lo CI CJ 30 L LSLS L 5 OO MT us i 5 DO ir EE 30 L LELS L Tverai Weight an ta mre fore E 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 tem
18. a dialog box allowing the user to set the plotting conditions One can choose to have the amplitudes Ch 6 Menus p 67 MacTempas User Manual 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 80 Amplitude Intensity as a function of thickness 0 0 Ch 6 Menus p 68 Plot 0 0 0 M 2 0 2 M 4 0 0 Options Amplitude O Intensity Cl Plot Phases 100 C Thickness Save As File Define Projected Potentials This allows the user to specify which potentials to be used in the layered structure 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 MacTempas User Manual tion on how to create a layered structure Dofinad Phasegratings 5 Mama az Nama z Mme iz Mame r j lt bskc_ 0 3 00 2 cGfsie 1 3 00 Ms c t 4 00 Ma ciska 4 00 Specimen Tor 1 2 4 4 1 2 3 4 SS a mie f inser FO Ropar _ E Reset 24 0 Slice Unit Cell Use this option to subdivide a structure into separate layers for use in a layered structure calculation T
19. a phase shift relative to the path of the unscattered electron a 0 which is written as Scherzer 1949 Qn A Y4C a 2nC 7H 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
20. 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 ing to do much of the recording on CCD cameras while still retaining the use of film Ch 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 146 MacTempas User Manual 12 3 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
21. 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 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 x y above causes all scattered beams that pass through the lens to be 180 degrees out of phase Ch 9 The Weak Phase Object Approximation p 129 MacTempas User Manual with the central beam Under the two assumptions above the image intensity in the WPO approximation can be written as P x
22. cell dimensions symmetries and atom positions occupancies and temperature factors Exit Wavefunctions s generates the electron wavefield at the specimen exit surface it uses projected potential combined with information about the accelerating voltage of the electron microscope and the speci men thickness and tilt The computation algorithm is the multi slice approximation Image s 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 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
23. 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 12 5 1Matching 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 12 5 2Simulated Thermal Annealing Simulated thermal annealing is 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
24. in UCell 58 The Eg TI Bead angie 000 E Th a a ol citer ni sain 5 eaters werent i lo il ET Microscope aed Lens Parameters Sa Aignan JA Com E voltage v 23 s imm aso Mag wih E Car 7 Convergence angle mrad az Eva fold Eu jat Eancel CE paread of daferus 5 Three fold 0 LE j Defocus begincendi JA 2400 i o 2700 Coma on ae Dei loans apart rad 4 1 is Mechanical vitro Ul Cant of Obj Lens Apr TE TA TS Er Sonor eut 400 0 00 Cent ofthe Optic Axis G00 0 00 0 00 6 0 eh EE Override calculaton status Mark for re caloulation Projected Potential Li tsit Wavefenctios _ image Mark as catculated Srrojected Potential C Exit Wavefunection C Image cancel on 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 The new indices and their relationship to the original reciprocal cell is found in the data file lt structurename gt 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 Mmulation Parameters Crpstal Parameters Specimen Parameters A AI aei Alpha deg 90 00 a oO pore o a LA 3 2140 Bo
25. 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 distribution 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 Choose what bo castpui Complex Magnitude Squared fomolew Smpleude _ Complis Ahaz A Resolution limined 1 0 LA 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 Choose what bo maipu f Complex Vagnirud
26. 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 12 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 12 3 2Fourier 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 transformed 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 no
27. 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 107 MacTempas User Manual 8 Original Operators yt de TE El fe ee ed me eee ie 24 z FAT ye fecal fee ie Yoel Entrer ile LT Rte TEE re Lie Oniginal Basis Ca 000000 000 0 000 Sr 1 OO TTE Bi GO 0 0000 4z Bi CO0G 00 0 268 Cu 0 000 0 000 0 446 Original Unit Cell Atoms 0 Ca 0 0810 0 0K CCG Ca 0 000 Conn oon Ca 0 500 0 500 0 500 Sr C 000 0 000 0 110 Sr 0 500 0 500 0 610 Sr OOO 0 00 Si Sr 6 50000 S000 390 BOO BO SCO S00 E DITADO 638 Bi OS O00 20000 1 6 Process Menu Ch 6 Menus p 108 ajel Symmetry Operator Transformations New Operators Cho ee eel ee eee ay ae HEME De Fr PR wee eal ee Niay APERTAR CANT yt at Pare ee New Basis Cs 0 000 0 500000 000 Sr 00 1020 00 a a BOS 0F O00 Bi OL268 0 000 0 000 Cu 446 0 000 00000 Hew Unit Cell Ca 0900 0 500 0 500 Sr O1 1 O00 CHI ON Sr 0 61 0 0 500 0 510 Sr ES 0 COO Sr 0 9900 5000 20 Bi 0 3992 0090 OS Bi TBE Sd ha Bi 098 C0 006 Big ta 0500 Oh Note aie Transformation that takes the old axes into the new axes Transformation matrix E Tx D o l 1 uo D CC Translation ef origin 0 000 0 000 0 000 Note that an arbitrary translation of the erin Cannet generally be represen
28. structures LayA LayB and hefined Phase gratings 1 copper dz 260A 2 ing idz 4504 Ch 10 Creating a Layered Structure p 135 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 lay ers By invoking New you get a list of the available phaseg biir Tii PPE Op ei G Fit Edit Vira Fours Diim Flirt CE ampie reee 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 Name ofthis layer Thickness A C 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 136 MacTempas
29. 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 12 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 12 4 3 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 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 cera Reno cerata 14 2 coran ho 2 15 oh with 2 _ 9 5 7 16 The effect on the hyper angle 9 cos CCF is in the small angle approximation OU Lay YO hh 02 1 If two images are identical except for a small error in one of the image formation parameters def
30. the upper left corner of the image to be 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 If the Option key is held down while the image is drawn only the circles are drawn no image Montage Brings up a dialog box allowing the user to select automatic montage of a series of images the position of the series of Ch 6 Menus p 59 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 Layout options Defocus Horizontal Thickness Vertical Thickness Horizontal Defocus Vertical User Defined Layout Click to Display and Set Cancel ox 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 lererstiigs Haki a idp D k Wh sabii Valais Gb oie ai Ge for 145 dge ds dl ape vale oad Aa walt White 13 cancel Magnification Allows the user to set the magnification to a set value The magnification depend
31. 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
32. 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 After the response to the last data entry prompt MacTempas draws the windows it uses To re display the input information click on the Main Parameters in the Parameters menu At this stage any desired changes can be made by using the mouse to move the cursor to the desired parameter and making the change When all the data in the top field are satisfactory 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 Comman
33. 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 12 6 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 12 Structure Refinement 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 Structur
34. values add to make the final image Assuming a Gaussian spread in defocus of the form te 2 DEP ee In 25 gives T GR DU fodf PCH FHDexpt 1 20 AH 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 lar 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 more general fo
35. 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 MacTempas User Manual 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 Manual 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 le leu slo This window shows which atoms are pr
36. 00 100 id 3B asim maw ozmay sam dim Obj tens apem rad A I LES 15 4 Cu QD oo 044840 zaw 100 h b Msz de 16 4 Ci DSi 8 feo RAT 300 eri ol bi Lens Apt DO ooo og Gi aww O00 OSEO 3600 100 pe cfitctictiies HO DOOUDOU RE D 13D DIE OOHO SAD 100 on 1 5 J Oo O E E Ci 3600 igm Over ride calculation staqus an 3 a omwat DS F0 Saw 1000 fon Wark farre cakcefation I Projected Pocanti Mark as oolculabed 1 Projected Potential txt Warefurction C image 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 moderate 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 Gmax The maximum value in reciprocal Angstrgm units of any scat tering vector to be included in the multislice diffraction calcula tion This value i
37. 2 _ 1 2 D h by y Lh 2 4 The Root Mean Square Difference D ms VD The mean modulus difference 1 Dima lh 1 wy li D 6 The Cross correlation Coefficient Ya 1 G 1 CCF 7 LaO ERO 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 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 150 MacTempas 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 12 4 1Significance 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
38. After invoking the Ch 6 Menus p 97 MacTempas User Manual command the following dialog box appears Sheulated Thonmal Asnealing Paranecturs Temperatiire Aivo Atom Faram ters staring 0 146 Maximum shift Al 0 100 Endang GLS 4 fot clive Elements Fractionad Change 0 9000 Coepmion Area f Acte Aboms Far Dagraa Alerts per Temi 15 4 Set Chemical Citan i Soccasstul Attemps 5 r Get Bond aan Feng Method image Agreamani Muka emage aged mean Eons Correlation include Bord Destance Comstrainas 5 Chi Square lanc e Bord Valence Sum Organisation Cutpei Options CT Greate a log file wath energy versus time secs Create a movie of the progress mondes Time bebween frames l 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 default all elements are active Selecting an active element and clicking on the Make inactive button will move the selected element to the Inactive li
39. Ch 12 Structure Refinement Through Matching of Ex MacTempas User Manual Eo X X9 X the parameters are varied in a random fashion and for each variation the new energy E X1 X9 X is calcu lated The new configuration is always accepted if AE Ej X1 X9 Xp Ej_1 1 X9 Xn lt 0 Otherwise the new config uration has a probability P of being accepted where p e 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 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 sensitiv
40. DMO Ca QUE CET TT 3 Ce Co Ci L a Ce Can a LIIE PMO Aam 3 400000 LIMEN 7 c Joe owm DIMM 3eme LOM E a CT erty G20S00 Jamar Lomo 3 CE CCC TC CE CCE COTE EO mei f Cancel fo 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 123 MacTempas User Manual Ch 8 Sample Calculation p 124 construct that we have entered requests MacTempas to store dif fraction results for thicknesses starting at 40A and 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 fo
41. Ferier Aan aoa F CI Astig recites LA ami Er fp Onl ha ane C1 F Antigrmetsuns jy em em een tf mage Cecparioen Eegine For thickoessithis iy am imteger qh the e anit ee slice Cine Ce E F Super Optics itresbe abp Se wiih energ versus me CT EE b oie of Olsen ero mre 52 wii Tine bate cis kraner reed he i Setting Image Comparison region The area to be used for the comparison is set using the button Ch 6 Menus p 95 MacTempas User Manual Set Image Comparison Region ipei Area to Cope he SMA WHA Ean C 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 Parent Rehine nr Control Tenpersture ACHE Parmeter Sung ea inis vaka fa diege Baig noolt THK ksass A Ed E Fraction Change PET C tacu 4 Le ae Fer degre ol lean E SpA ru Abi ra Dea Alben po per Tang 35 Sead of eoru BA g la F Success Art le _ Ceswergerces lmrad tia LIJA Fit et hired Crows Cove lation oP Crynai Tet mrad D CEF Fournir Aires BEL nu NET Che Sere _ IF Agma fA DOA For thicken chin b oe erisqur gaie tha rors bar oe r i Woe ce phe thie se f Set loge Comeanion Rego Guiput Optics Cena
42. 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
43. Integrated Diffraction Pattern CBED Pattern 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 Execute this command if you only want to run the PHSGRT program at this time After the phasegrating is run the multi slice option is highlighted Exit Wavefunctions s Execute this command if you only want to run the MSLICE program at this time Image s Execute this command if you only want to run the IMAGE pro gram at this time Ch 6 Menus p 74 MacTempas User Manual 66 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 validity of the weak phase object approximation The wpo calculation is discussed more in detail elsewhere Weak Phase Object Caloulation Re souni ar Opaka ere Starting Resoli ion CA Ending Aosolusiom J 1 00 dt Auto Decremant Resolutio Feed Decranrants i stapes of 2 Viewing Options Number of Unit Cells co display K amp Y 1 L 200m F
44. M show Lattice Delete Lattice Info Amplitude 7 tt 14 9 13 16 9 7 6 Phase 76 117 75 83 76 100 29 159 81 Find Motif Ch 6 Menus p 112 MacTempas User Manual 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 Flare Caen Sarrewenrized imag Feria Map pe pm Fa cm pnm z eng FA Cm pa Eti pag z pa 3117 gm1 5 26 pdin LG p 2 18 l pam BoB B Shem tire cal tira E Be Curie Pis Corie Tar oer mmap fede bore image O 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 6 amp iymeieniced Monit Face Grou ammeg ina pe Bencal Map pl Loi PE 3330 EM L Pu 213 A AAt 3 mi bypue oe iE er RARES iy Lu yin Sve23 E Emra iw CHIC at E Cure Defines Heer Origa E San Carma Dikin ae Origin tar F1 l mit A Pura Gree perk priina f Skowl ka 5 f Cram lrg AEO UesaaGeputrentd image 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 Ch 6 Menus p 113 MacTempas User Manual This menu determines the appearance of text drawn in the Text Menu f f MacTempas image w
45. Over nide calculation status p Mark for re cakudation Mark af calculated l Penjected Potential C Pajectiod Potential a 1 Pages EO Deew area Fook 4 Corel E 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 Simulation Parameters Crystal Parameters Species Paramaners SS Dares dust ure Feeds ATA AR Alpha kieg aaa b it of D 5 1 6 ELA 3814 Bota deg 3300 Aboras in ihe Unit Cel CfA 30 530 Gimma pi g 90 01 Spaceqreve Int Tabien 1 Type Mare cocon Yetta Zco rd OW f Gecf fof Atomsin Basis 9 ene i oo 1000 DOM o SA tae fof aye Ops aE show 1 I Es 10M DM aawo Zaw 10w fof aens bn Aall SE a a J ar Oto Ci 0 1090 Selo igw aoe E 4 z Sr O30 OS QAO JAD 100 5 ns B foa LH Ho gawo 1a im 2 ar DSi GEI 3606 0 3600 100 Micros and Lenk Puramevers T 5 Bi amw CoM a zawo aam Micrescoess Mama CHOC 3 E Qi f Bie gaitzi jal jar a f m 1200 DEME ASTD SAD gaT Vohage kY 300 Colmml AE in og B O10 DIE OITA Jaw aawa Con egenos angle fritid G2 i 3 Bi Do titi 2681 D 3800 012 Spread of defocus A E 1 3 2 O30 DS Q760 JAW Ga F es is Hi JD Didi 0290 H dl Detocus Ibepincend py Z4
46. Q not bean Square Deiterem e G erene mage Q Fractional Mean Absolute Hide Ch 6 Menus p 90 MacTempas User Manual 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 ing that the experiment and simulation agree within the uncer tainty of the experimental values Root Mean Square Difference This calculates the root mean square difference between the 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 Ch 6 Menus p 91 MacTempas User Manual EXperimestsd mege Hasard Deviation Mink Nebo by ae Width 45 Heiget 42 A Ds E si Com p are Est pe mage G Chi Square Rooc Mean Square Diferenta D Herme Image 9 Fractional Mean Absatute Difference The table below shows the result from the RMSD comparison E Z Difference Image Ch 6 Menus p 92 MacTempas User Manual E
47. Use this template to modify the date to fit your structure Sidon Parent Greil Paramena foetinen Faremererns Fosse ami heme d s ATA Ae Aipha pieg LES Fi i 4 EMI di sel deg af wi Mumber pf benr par cull i coy 4 Carepa eg 314 Gras W E 3 Sacegeeg dar Takie bb beprei 100 O L Puf acn is Buca 1 EME Score Armpl Pha of yam ne WO is fir of lice ob l Eu of mnam ir Cal 4 sl by Tel rerai amp aroia Dir C1 F of fermet shore 1 Tape Amen Wiromo end Less Fourier a dipem Cee Sbcrercopa hiama ss a ji Wakapa NT dE Cap L Ma Their arepane ma a 1 Tec hid U dpreaa al defocus A IC Three fol Eu De bou hg inca A cot D sl Ces Dai wer acari rad A E 3 09 CRE Mg ir Conf Obl Lans Apn oii nib di a0 Las a De UHE Akii Dl DEG hao i Sqm of da fai ETS OL deh Ang with aiii iLO Cr hier alaha pes Blada For re rabpi aan ngeon Popa Exe Basri ear liege Mok ay erwart Projected Patonia Sia Hasrita rage a b c alpha beta gamma These are the unit cell dimensions in ngstr m units and the unit cell angles in degrees MacTempas will automatically set the angles depending on the spacegroup if possible The pro gram will also automatically set lattice parameters depending on the spacegroup Thus if the user chooses a cubic system b and are set equal to a Ch 4 Running MacTempas p 31 MacTempas User Manual Space group MacTempas generates symmetry operators for the an
48. User Manual 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 Deane Paaseqretangs Kame Ar hame Ar copper 181 inp 454 CRRARESSEITERE 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 137 MacTempas User Manual Ch 10 Creating a Layered Structure p 138 Chapter 11 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 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 dis
49. a bog fie with energ varsia tors see morie H the Ses Kendo Time bebanen turer ammar L coc Sri 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 96 MacTempas User Manual Apple Command Key together with the Period Optionally a Currest Parameter values fa Ther kness A FET ES Dec ee A a GA Orvstal Tet p ra Li Center ed Lame Dirce BE DIFDD hki 100 80 0 CC ening s D ior angle jrd 015 Cerent Computed beage Expommmicinbal mage O Spreaa of Detocus A en CA 2 Feld Axton metives Wsgntoude fia Aigh wiii Harli 107 1934230 O 4 Fa At gmaticnn Ala gant inthe Ae Angle wath Horiz a Pam abus of calcelatiqnc Fans have Parameters amp Oran 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 is the structure that is being varied notably the coordinates of selected atoms and pos sibly debye waller factors and occupancy
50. actor fo be Used in Displaying images 2 on J Ga SR Integrated Diffraction Pattern calculates the diffraction pat tern by adding up the intensities for each tilt angle within the cone of incident electron directions Diffraction Fattam Thickness al no amaa fie 00 Dick Size farad 020 kuga Ses dih DE p Haight CTI Cance CBED Pattern Will calculate the CBED pattern for the given input parameters Ch 6 Menus p 75 MacTempas User Manual using the Bloch Wave approximation CRED Parameters Use Bloch Wave calculation Use Multistice calculation Zone Axle 1 fl Surface Normal 14 i i Tit Direction a o lo g max for calculation LAJ 5 50 Specimen Thickness A 1500 Microscope Voltage kV 100 Radius of desk In pixels 64 Disk Size Snap to spot distances Image Size Shap to spat centers include partial beams Lo Ce gman Mr display FES 1 0 The current operations in this menu are Tables P Reciprocal Space Info Displays information about reciprocal space data for the current structure The data can be sorted on the reciprocal vector or the Tables Reciprocal Snace info Angles Between Reflets Search for Amgle Spacing amp Angle Calculater Ch 6 Menus p 76 MacTempas User Manual structure factor extinction distance 6 Pi Reciprocal Space Data 153531 mer DUR NE L SE pee ae See eer ae ei cl ied ma pA a as nf mn ep 2e eo dg el
51. ages 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 note that the use of different matching criteria can lead to slightly different values for optimized parame ters 12 12 4 2 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 v
52. all over defining the set of atoms to optimize Ch 6 Menus p 101 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 Strecture ahinanant Canino Experimental heaga Starting Model Ei Show only no symemetre related atoms Others move according to symmetries pese f Ve Medelfrom iyo 2 Lae the 4 tool to add isa atone bo tie fest Te remove atoms use thee toed Aloe WHE same 2 mill ayva together unless explic Hely rende with he nel Set Chemical Constraints Ch 6 Menus p 102 Store in Comp Am Comparison Area Selection Entire aapa X Atama bo roiie FO sidro Selection g k MES L DO Cesekcralrom Y face GS MacTempas User Manual brings up the following window foe Die Energy Ch nical Consiraint Boi atari Olin stare ae Ca Ca on 60 a a FE 34 constrain ies Fc eu i Erargy comnibateon ta u W ein JE Mid ference 10 Ca Ca 200 one A Hi Gee Bi 2 00
53. alue 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 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 152 MacTempas User Manual o9 Late II Vex 1D calc Teale 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 NU bY K 16 o1 of a vo 12 where 2 O12 Wie ia 13 and 2 Wibd UiXb 14 Do The first term measures the difference in the mean of the two images and vanishes if both images are normalized 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
54. arious 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 2men 1 E r 11 mc where V x y is the average potential per unit length The speci men 1s 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 1s y yz T p x y z 0 1 ioV 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 6 u io V 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 Fouri
55. ating 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 eQ Quantitative comparison of experimental images with those simulated 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 A 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 samp
56. 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 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 Ch 6 Menus p 83 MacTempas User Manual CORNE m Cuperimental image Sandar Deviation Marne Ter bte 148 oh Be High 144 7 NOIRE Compare Comparison Method LE Seah tical Cross Crrelsttan Coefcieni Res Sur ei L Satta Cross Correliinin Coheni Pout Spel d Chu kruaa 7 Rost Mean Sgar Diane Difference irae Cl Fracri cent Mean Abiada Detarance int gt Fiame 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
57. bergence Argle tire 12o0 aR Min iitesdicy e displ 15 4 5 Ea HD die ne gi dn be CN EL E LD ning dr Fogi ges 200 a Tea dipiin A le raal urira GA Diin raciprocal wita 4 1 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 Intensity to be considered in the Objective Lens 10 Cancel ox gt 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 40 calculation amp lereted and dapends on availa RAM Sub tlcheey amp using a lagerad sucres is qarerally easier Calulation Cethons 20 Potential calculation 9 40 Potentia Caiculation 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 Micrdscopas Belined Micnsegpes Kane HQE ABT ARH 2000X 200 OF x CM200 Voie Cmm Drvimrad Del 400 200 Boo 220 200 200 La 6 20 2 06 Lig 1 00 CG GG Delete 2 55 20 CRT 50
58. ce 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 121 MacTempas User Manual Ch 8 Sample Calculation p 122 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 t
59. d TEM left 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 becau
60. d 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 Pia rlincanal Aem hame E Widi pal eae Heart et oi J Compare Ent rs Image Seb Cemgare Sehecbon Comearnses Whe tome Statice Cross Correia Cooficiont Geel Spacey aa States ter al Cress Corretiad ma CerMicsent Ferier eh m Peer Le split oer Fosse image the D the Square T En Fe Square CATE rere D Difference mepe G Aaina Mean Airam CHIEN EME This is a straight calculation of the normalized cross correlation coefficient between the experiment and the calculated image s For it to give meaningful results the origin of the experimental image neeeds to coincide with the calculated image Ch 6 Menus p 87 MacTempas User Manual fees He ian Regie ne Jr a k 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 a A Cher artist Aa eiai With Harpia F Temet Vi
61. d evolution I Basic technique Ultra Ch 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 160 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 12 Structure Refinement Through Matching of Ex
62. ds menu and clicking on Draw the Unit Cell When we are satisfied that all data are correct we run the simu Ch 8 Sample Calculation p 125 MacTempas User Manual Displaying the Results Ch 8 Sample Calculation p 126 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 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 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 t
63. e Squared Mi Compier Ample de Complis Phasa MiResolition limited 1 0 A magnitude squared default or if the image plane wavefunc tion s has been calculated the complex amplitude or the com 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 Ch 5 Windows p 48 MacTempas User Manual tors 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
64. e 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 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 numb
65. e model window Add Group Selection Adds the atoms to the refinement list but constrains all the atoms in this list to move as a unit Ch 6 Menus p 100 MacTempas User Manual 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 Arom Ratinan Parem tars Diniz checked peoeeeties foe atoms if Be selected Esr Mas x Ca Y On Z on D Ce OCC On Click ite on The jesi On Dogohes refinement Ceol for all aor Tost gach variable s pararely cancel Soe 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 group 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
66. e 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 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 simulate
67. e three 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 Sectes Specimen Projected Potential Vp y Plane osi Object Transmission q x y i l LIA Function y AVER I or y Objective Lens VV me An l Objective KUOA Objective Lens Aperture DIAYyA N Diffraction Amplitude g Lens Transfer Function exp ix g 3 7 VA Lens Aperture Function A I i a E i Image Amplitude W x y Fig 2 The simplifie
68. e 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 12 5 3Simulated 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 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 158 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 1 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 1i Select a subset u lt 1 of survivors which will be he parents of the next generation 1ii 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 12 5 40ther Techniques There are other ways to do the refinement which is based
69. 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 11 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 AY 7 N TON dy 7 KT Condenser Lens KR I I 7 x l 7 4 lt Object Hd Objective Lens LL
70. eens nas fissio oida 0 2735 tozas Tineia 7202 leg na D495 ess ogia lose Jesus inposa 1 2az6 l2esoq7 nauma lasia 0283 033 bonds 136704 bors E ives nasa social desar oes 723220 20 TTD D8STE 30790 Ozga oao 1577748 mazaa lama a ELU NN eee LE PSE 36500 2 286 11 4861 nsss aime jante ek fas i gL aro eee fee TT JAI EST Jee Oa legs 25769 _ 70 606 gisgit jae jagas 1 emag nese lite TANE a Epean AL lerrase sas ligeras 11 7925 l aatat 23d34 li4 ns 1 7588 j tail 2 litir ji 1243 S530 iaai HT RL RL UE EE NOTE SAGE ARS fee Ls er RARES Ls LE RL ARLE ec BS JT JET zae 19200 22739 Jinecse zona uses Lans 2148 aasan jouer Jigdoss 15981 acts jassa zozvi lasar us es 15620 rapaz 3 eses issus fesse sain Ch 6 Menus p 65 MacTempas User Manual Commands Erase Display NE Draw Atomic Model 3U Draw CTF Slice Unit Cell Commands Menu Erase Erases the selection made by the selection tool 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 unit cell should be viewed in the 001 orientation It should be noted that the viewing direction is in units of
71. er ent length and byte order impot Faw imag repeat oma 11 File P i rial Las grh JJ07LEH Curs Type PEL E ane E bury Oat wiae P Angie s rs Cate Evian ighe IH Sissin a Gima bong Mi J hegit d Me MN Save Image Saves the content of the image window into a file MAL input Save Sy An ET Pome TS E Gr pecuke TIFF Where Flawiirg Pint TFF fa fed GL bipil Fir L SCI u eee os T miia Fil s l anjima Con 7 files are binary files used by the mal or Truelmage program for exit wave reconstruction from a through focal series MacTempas User Manual Edit Menu Cut x Copy C Paste V Clear Select All 3A bier t Into Arrange Object gt 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 Undo Ch 6 Menus p 55 MacTempas User Manual Ch 6 Menus p 56 Undo Redo the last operation These operations do not cur Cut ox Loapy HL Paste EW Clear Select All BA UBGIeCcE H E Arrange Object b 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
72. er coefficients 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 e Howie 1963 Each Bloch wave is itself expanded into a linear combinations of plane waves which reflect the periodicity of the crystal potential pr e bkr ec expl 2mi ky g r 14 J J g The formulation above gives rise to a set of linear equations expressed as ko K m If Y VE ett 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 m
73. eriment 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 12 Structure Refinement Through Matching of Ex MacTempas User Manual 12 2 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 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
74. ers 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 in specimen thickness The beams are specified by the Ch 3 Introduction to MacTempas p 29 MacTempas User Manual 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 Input 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
75. esent 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 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 Invert Reset E log scale e rn Black 0 White 255 Apply B W Values Ch 5 Windows p 44 To change the atomic radius double click on the chemical sym Waina Pow tha denk Aadi LiF A cs bol A dialog window will pop up and a new value for the atomic radius can be entered units in A This window 1s used primarily to control the appearance of images 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 appro priate 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 choosing a color from the color bar with the color picker tool selected and depositing this color in the ver tical gray scale bar showi
76. ew Ji Casa ro Flit re linda ia pare pal Cemmerisem Metiond CE Babica ross Correia ion Cee ies Era Spare a Strtestiral Gress Correlation Cresciem Fourier eee QG Exec Eu amipiliteses Biestimatr Imaue LE Ch ON Square Cr Fat kitaa Square ference lt HONeremre ope Gh Fractions Moan A s bete Hieronta Ch 6 Menus p 88 MacTempas User Manual Only Amplitudes Exporiiensdtal itsoegen i Standard Dewi othe pene er Aiken Yih E Hiig 7 yet lee P Osma Fiii linia he Mn pare bhh haa Comer open Lie tip OF Babica iror Coreietion Conf cie Peal Spare Satistical Cress Correlation Ceet iciee Fourier Smee Ghee fel aeplineses Amam Image Sean oh Cea Square heat Maes Square Difference TP Herem less Frac Moat Acer Hieronta 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 given are the shift of the origin that should be attempted to be made on the experimental image before the experimental data is Ch 6 Menus p 89 MacTempas User Manual compared to the simulation using the exact formulation Leo Ja sun 3 oi 5 s AFTER OA UAS ar jpn a 3 Le CORRE ma 9 5 ea L nor amma
77. eyperireeestal imane Standard Deri ah pan Harmar ETT ar El M might 12 a Bec blew E ine ihe nan 4 pE Seb ports are beeen f Cogariven hriba iea Orows Cerralation Coati cast imal Space po GE SOA One Cab FORM LEE CRETE GP mr gee Cie ER aie Dao lege ine Gib Square LJ Beat Mian Sqeore iare ncu UE ree Wage LA Pre GT PRE A ina Deis re bet Ce Ce 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 also computed for each image and shown in its own table Ch 6 Menus p 93 MacTempas User Manual Fractional Mean Absolute Difference This calculates the fractional mean absolute difference between the experimental data and the simulated data pained iimis Standerd heaton i Mame tra watte High a pera Eira jini lipa el ST a TES r Con paren Fohet bone Shatestical irar Dern La peus Cr erent Real pu CCE on ined Care tie CR Centre Sancta ni
78. f dien won 5 Tapa of angrpuon iL Bicescope ond Less Faroese igen EE Coa Borie Are 7 a er shea 2000 Open 069 Fi pese Convergence angie ra 0 15 Pruit Pang Tet Pod a EL Spread of deire A 2101 0 00 mj Teele HAD De lotte eg rate rad CA HO 9 al Cama iii b CL bmi apari red jA LES inc haere miraia J on Hn bt H argk aisat 6 angie dar poo 2E fr ey cai state baka ee Cent ofthe Doir Aa 000 DDD OJD DD Roger TT Greer rice cokulation uistun kixi dp eo le Peg ped Pa Een Waaa lissage Bek s calcula Fabre Foereial _ Tak Wrasse 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 4 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 been 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 A 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 spa
79. he 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 X Y Z 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 have been entered MacTempas will need the parameters of the electron microscope for which to compute the simulation tons bn the Moby Baste t Name soced poed ccoo eiee ke 1 fee nomo omom noman s LOTO 3 or Gogo MOD Glera 360IDND LAN 4 hi 0 0000 Ce Menton Dent 1600000 pama 4 hi a Ca Ce Ceci O Co ec Ca G saiio 3 Ce Co Di Le Re a 5 E foo
80. he direction perpendicu lar to the slices and the number of slices must be specified Ch 6 Menus p 69 MacTempas User Manual Slicing options Le L we Zane avis for sicing 0 a l Number of separate layers j A Calculate Each Projected Potential CR Ch 6 Menus p 70 MacTempas User Manual Main Parameters Parameters Main Parameters Atom Basis Symmetry Operators Atom Coordinates Parameters Menu This brings up a dialog box showing the current conditions for the simulation The values are taken from the input given to the Srnularton Parameters Crystal Parameters Specimen Parameters akm freed Indes A A 38140 Alpha deg 130 09 et fl z Ci BA 36140 Beta deg 139 69 Humber of ces per cell L PEE M GE TIRE Mick thegincend 30 P 30 of Moms in Basis g Show Store Ampt Phases Sen Mo H Symm Ops 4 a of atoms in UColl a8 a of different aoma 5 Cent of Laue Circle 8 00 Fons Eq Tilt mrad amp angle 0 00 E typeof Abrorptan Microscope and Lens Parameters Aatigeialicm A Cora Microscope Name CeO ange 1 Waltage kW 300 Csimm 960 nes Convergence angle mrad 20 Tao Fold L a Spread of defocus Al Go eue Id Defocus beginc endi A 2400 ion l 2 Coma 1000 ap Obj lens apert rad A 1 L25 Mechanical ibration Al h b Mop Angke r a ai Sigma c ia 0 00 0 00 Cent of Obj Lens Apr 19 00 9 90
81. he 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 MacTempas User Manual 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 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 127 MacTempas User Manual Ch 8 Sample Calculation p 128 MacTempas User Manual Chapter Wavefunction Approximations Ideal Scherzer Lens The Weak Phase Object Approxima tion The Weak Phase Object WPO
82. 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 Ch 6 Menus p 84 MacTempas User Manual Ce es Ho _ seers le Tools Pointer Tool Used essentially to ensure that no other tool is active Selection Tool Use this to mark an area in the 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 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 Ch 6 Menus p 85 MacTempas User Manual Ramp SoC ei DC Coreen F ef Height 37 LS Compare Entire lea 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 cl
83. hould use the space group P1 1 in which case the only sym metry operator is x y z Additional symmetry operators can be entered by opening the dialog displaying the symmetry opera tors Show Basis atoms Ch 4 Running MacTempas p 32 MacTempas User Manual Use this button to bring up the dialog window that enables the input of the atoms in the basis Oneill Paala ac Jano Abed tag um BMY 39140 fe Mag 501 CN Cok 36550 Gare ldm Lin Spacegrane ikri Taies So homes am thew of Semen One LE mn dj siora n UE j eet fof iter mame 5 Birescoge ard Len Pamamaraan Abrric eit Haras Ze kakaga i 20 Di pren 05 Canvergence angie ruse 0 Si Spread af detonus Celem they or eer LM 2400 i CL bni apri rad i i is b Mg M de Do oan E Dob DM go Diak ai Gii bens Ape Gea ofthe Omii Len Cvar ride caloulaiion terime Bizik br s cmiachn l Pei Roba Blab mi cica loved ined Foenn E aera mw Li he malien Parate Atama in the Modif Gass Name x coced y oa z ooord dw fact Ore sn em ao oaa sewo Liat E coomo aooo diea Zaw Ln B Peo ammen aazma 3em rl oT E Owo aon Oes zaw IEC T cu TOMO OOO oats 36000 Lo a Tomo ammon ose Sama OO CT CORNE MTL g uamo aoimo ozo semia 1000000 a csomo aooo w aawa EMD EE Cancer es fo a oo Number of Atoms in the Basis This value is the number of independent atom positions in the basis or asym
84. 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 structurename gt pout is the result of running the pro jected potential routine from the information stored in lt structurename gt at it contains the specimen potential Ch 3 Introduction to MacTempas p 28 MacTempas User Manual 3 4 5 6 in th
85. icking 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 Exmerigversiod Image Standard Deviatoe Width SF Re sud View 2 et Oomeare Setecin r Camparisos Metal ow W Statistica Crass Conse ation Coe ferent eal ieace Statistical Gross Carreistion Coeaficicet Fomrier Space jm Exact on vamp Jeles Eii nata i aos if i J SORE mg asd mdr eme eee da ak sere tes 2 de mes de e Ee pee e m mu ment Chi Suara Enst Mean Square Miere ere erene Imee Q achoa hran Ab polite Dference Ch 6 Menus p 86 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 MacTempas User Manual 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 compare
86. icts the calculation in reciprocal space as well The maximum reciprocal lattice vector for orthogonal axes is given as H Zax Vmax k vf 2 S 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 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 fo
87. ifacts which 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 pa mr o r fa r Ch 2 Theory of Image Simulation p 11 MacTempas User Manual where p r the charge density is po 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 p r Ze 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 u through the relationship g r fe au yo We Ht j 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 Qniur E Zi HI 2 2niu r ee wet G AT Eo at H atoms i atoms i 5 where the electron scattering factors fe and the x ray scattering factors f ha
88. in MacTempas User Manual 86 Latiie amp Axes A A 3 8 14 a 3 8 144 Gamma 90 00 Quantitative Menu the right part of the window The reflections can be typed in and Angle Plaso Caleulatar Reflection FO ps jee Je at mer n Length iA D2522 Bp Lb chap ral Place Spacing 3 2140 oa y im Reflection Lengti AA 262 i L Plane pacing 3 2140 Caiculate Updste Angles 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 Standard Deviation image Compare image with Simulation Compare XW Amplitude with Simulation Compare SW Phase with Slemuiation Ren Parameters Refine Mructure Symenebry Transform Calculator Make Front Image the Experimental image invoked from this menu Ch 6 Menus p 79 MacTempas User Manual Ch 6 Menus p 80 Oper
89. indow The following text attributes can be set Font b 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 Window Minimise HM Anrange in Front AIN AQ Experiment 44 Half tif Image Calculator Al untitled Ch 6 Menus p 114 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 reciprocal 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 calc
90. ing 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 available RAMA Sub slicing amp using a layered Structure is generally casber Celulation Options 20 Potential Calcalation ob dD Potential Cal cel atho ni 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 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 both the calculation and the experiment it is modeling will interact only very weakly
91. ional 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 Van Dyck D 1980 Fast computational procedures for the sim Ch 11 HOLZ Interactions amp Sub slicing p 142 MacTempas User Manual 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 11 HOLZ Interactions amp Sub slicing p 143 MacTempas User Manual Ch 11 HOLZ Interactions amp Sub slicing p 144 Chapter 12 MacTempas User Manual Structure Refine ment Through Matching of Experi mental and Simu lated HRTEM Images 12 1 Introduction The goal of performing 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 exp
92. ise level rt siw 1 none E sod E A N cokk kL 1 2 12 L dS AP JIN F2 cosine ne sin xk AN 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 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 148 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 12 3 3Noise 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 ratio 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 A 3 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
93. ked on a real space image which is square or has a Ch 6 Menus p 110 MacTempas User Manual square selection In order to get started the Hanning Masked l 09 Crystallographic Image Processing y LC Hanning Masked FFT J Set Reciprocal lattice h k ao Wo Hi 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 111 MacTempas User Manual reflections that defines the reciprocal space The number of eo Crystallographic Image Processing Set Reciprocal lattice QI 207 17Px at 1 Px b 1 Px ga Deg CM Refine Lattice Real lattice a Px ga b x 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 is to invoke the command Refine Lattice Crystallographic Image Processing A Set Reciprocal lattice hk aj 7 0 Fi 7 EE I 207 1 Px a 22 44 1 Px b 22 39 1 Px ga 60 00 Deg Real lattice a 26 35 Px ga b 26 41 Px 120 00
94. led 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 experiment and MacTempas User Manual 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 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 Chocia a Fix From JC Phooe E Si A1 Y bib es4LRL a ET AMAR bed die SE AU CLP MT gree SE AM Cu MST ai au up si ee AAC UE HE
95. ma megu Dhs Aen eS ELA ve EXT MTS hi Square G Root hitan ages re CHER tere DI M rere mape Fractional Mean ste Deene ME IEE oran ua pu A Dmr EERE D IREE ji ji 7 caer ET 3 H h CIE L CS EENI i 1 L SEIKH ERIM DIr i css ETHIE E 3 CI LELE DURE ik anm Mike asan omi ESNI Es jouer en CEE Etat CCR LELLE H F ETAN REIN Ch 6 Menus p 94 MacTempas User Manual 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 used to give the input parameters to the algorithm Tiap cr aterc det thse Parameters Staring Erny Eracbianas Chazo s GA Teferus AI Por di FR of Er Co E Serk o ie Cire Aen ps per Tera E Ee cael cette E Pie te Anis O temeraryqemoe fra ui Wita Valet man Cars Sf Mictonsu ss A Fit Fin ksd alee M Cross Comelation OOF Cl drata Tilt iad a oh h GOOF
96. metric 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 Show Symmetry Operators The symmetry operators are automatically created by specify ing the spacegroup By clicking on this button a window dis Ch 4 Running MacTempas p 33 MacTempas User Manual playing the symmetry operators are shown mulation Parameters Crystal Paramepers Seecimen Paraimere A ERTE Alpha deg 2200 PURE n ee n EU 3 6140 ea deg S00 Symmery Operatore CA 305200 Gemma kieg SUN Seacrorun im Taies 1 asa 5 HARRIS a or cies RS pn O RHL Ea L E2412 17 ky 8 so Symm Ops ae Fos i Fe Br tk Perit ice of moms in Well 38 Show 1 4 Crtir vrileatlie 1 19 ua odifferentatoms a rt aA E eT 5 EEE 20 RADE tL 24112 Microscope and Lens Parameters a eed rti a Merascoae Mar 1 nn 22 tle ete ere vonage ky 000s en gen E FL Roeder lye 23 t Convurgence angle bre 020 3 EE 24 wv td fax412 24i ia Spssad of defocus A 30 Lp PA ee ES Dafecus iagincend Ay 2400 100 10 wna 25 eta yt ize 1i2 Ob lens aner rad 1l L25 WZ ethle y i 2 412 2 eye bo b Mug May 14 yat Be werd sewed seri lz Cam of by iam awt DOODO O00 G0 14 HUB 29 ce OOOO O Cen of me pir Axe 800 O00 Goo 0 15 lt lt e 30 ALFER
97. microscope is unknown to MacTempas the above values must be entered separately We will see later how a new microscope Ch 4 Running MacTempas p 38 Lo image EI hrs ges MacTempas User Manual may be made known to MacTempas Siret dE Hin Patani hes Orpial Parameiere teerimen Farareaisre Atay ERIN sate Goo a Pin SAT 30140 Leu deg 3090 humber of ces per cell l CA S0 5200 Ganmaldeg 9000 peter es aa Seaceqreug 4 sine Taller Teck bag eah 30 6 30 fof Mons in Baig 4 f Show Crowe AmplrPhasas of e Mo of Sem Ope m cama sec a Cher of Lai Cire ON OO a OD ERARE A ABT a Fq Tit parad angle ne a of dAerent wine ARM Type of Absoration 1 Z0OCK q Microscope awd Lento 2ndoex D SORTENT A fa tigerativm A Cora ata voltage kai aop Ur news Ten bas Le Cnivergenee ange Email 0 20 Two tok N ag Sera of defocus JA 30 Three Feld 0 me Demus ibegincendl jay 220 100 arp Obha Loon oo tien lens vert rad 4 1 125 ahpa Abration Ai fi k bisi Argia Samaai O0 0 0 Cent of Dbi Lere Apit 660 0 09 000 00 at Cent ofthe Optic Axis O0 00 QUO 0 Ro PET ES Qver ride calculations etais Mark for recalculation 2 Projected Pororsial CEt Wawafunctias C image Mark as coloutwted Projected Potential Est Wavelunction image Cancel Voltage The electron microscope accelerating voltage in kilovolts Objective Lens Defocus The defocus of the objective lens is entered in Angstrom
98. mposes 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 thickness of the specimen foil is entered as a beginning thickness an ending thickness and an incremental thickness All 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 100A to 250A 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 Paramete Crysta Parameters Specimen Parameters m Tone aiie v 3m AA 38140 Alka deg 9000 1 Il 1 19 Bia Z 140 Bara dg 40 00 Humber of Shee por cel l Al T5200 Gamma deg 90 00 Gmax 4 2 200 wey ital age a Thick Cheganceerd 32 0 Stare amplitudes and phases far fof Atoms in Basis 9 late Sore Ampl Phases RE SERIES of Syren Ops d Cosh Cant of Law Circle h 0 00 o Ip oD 7 of abonis
99. n adjacent pixels which leads to a x criteria The criteria takes into Ch 12 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 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 Thus values of x greater than about 6 states that there is less than 1 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 Gaussian distribution will lead to a modified criteria but still based upon 7 12 5 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 s
100. n 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 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 MacTempas User Manual Info Window Info x 71 y 298 val 0 0000 Display Window Display Exit Wave Potential Cells E IE Magnification 1 Display Cancel 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
101. n 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 134 MacTempas User Manual option Layered Structure You will be asked to fill out infor Crystal Paranbebors forces Parameters Dene ads uw oo aul 4 0008 PEREN 1 Total defend thk kens A BEA 4000 Beta fee SERRE CAE H Gama deu THIS long Jier aml Hacking H shasenratings Sate Aman FtsnS es Sefphese gratings Stacking sequence ie Mot Sat _ 1 Cent Laise Cercle Penne sacia yy ct tiered E ample i i 7 Type of amp hbhsonptinm Maui scope Eh FES FRET iMiersscape Mae ATMEX_ Ange Vaitape JEW cs ma Misg wwihoriz CORE Once angio mran Teo told fe ao i Spread ef detocus AJ Three tral je jan 1 I Before eg inc en LA a p haere mir al Vibration ay Astigesatism JA Ob less apert ru A il momar Geo jou Centot d j Lens Apert ooo Cem ot the Gotic Ais 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
102. n ru AH CLP MES nar AMC gga FETE AMEL gS pra E Kin lcurmear AACH arial it 1ME i Dom nad Favorites cance gt e 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 1 Binary Files Ch 6 Menus p 81 MacTempas User Manual Ch 6 Menus p 82 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 will bring up the following dialog Gt Ras imag mport frm 12 Fil Fiama unk Sah ot Daia Tepe mepri Byes Sioned ell iira fran PAL Heu PTT Pr Le Has it et a3 mts eet ee Sins on Saging Hikki 256 Hegh Jg Ange SD eo oad y 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 MacTempas User Manual This command allows you to read in a standard deviation image to be used together with the
103. 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
104. ng 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 histo gram To invert the display click in the Invert button Similar ily 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 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 zo
105. ocus 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 6 o 18 Ch 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 154 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 lt 1 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 12 4 4Chi 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 the 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 i
106. omed out by a factor of 1 2 for every click Double clicking the magnifying glass returns the image to normal Currently no other tools work in zoomed mode 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 Ch 5 Windows p 45 MacTempas User Manual Ch 5 Windows p 46 drag the cursor while the mouse button is pressed Trace Tool This tool is used to get a line trace for the line drawn with the Trace Tool being the current tool 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 a structure must have been selected first Masking Tools The last 5 tools are masking tool normally used in reciprocal space but they ca
107. ow 1 ous bees ime jana jism an ane loi D E jaa j nn ia ja ma j lo jae a n CRU ae OMT FA z LE jose ra o har mare oT P iari LE L ec RE sap ns A lue jaa os T ti Las joo ii jamm jaam oes AA JA 7 Lt Fs JO Pd 0 6 9 jou A jan Perr assez los A LI T Parr A EAST ja ares rue lgay jonen a aa N D j S D ard Jon james ENA Ci i Lait Jamii ja a jon no cut Cc oo ia nad amnas inai aig news Tm names IeM D Laret to sa ans nas prar LU aa jon E L io i J n LF E lD a LE i i merma ja 2813 bano PETITE D PE 7 D 752 bales ci LIET joe 1 oers 5E jae jon uo joa ra aa z aa joe ICE EE LL LEE RELLO Vecchi eee id i Ok sisi i iiki j tia po Jajka Oaa ous A a a mur nn i a i EUR 0 li i i IDA Jat CEA fausse lome nazis isa Jouve aE E lots lasse ICO hao lu us G ILF us ma Jo jia u joa J nessa arts joss oem oe CoM TEIE OM 7 jama urrin omma osm iom jao jon o os o oa o a joo jra SC Jaa Chi Square 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 ee COUR OT i Mama BRAVE Widts 25 eight ar IE CN en Compare Estime Image f E Sub Conant St Den Comparison hirtigi D Stma Cross Correlates Co ci citant ial ipaa p A Oa 6 Dii ch rr TE eari
108. perature 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 very 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 MacTempas User Manual Current hein Cast raion Enemy LOS Hates sicalceation CanceBen ately if the movie is to cover a period of many hours rini Csiga image Esp rimoitai iiki Log Flic MONE Save Ringel amp sees At the end of the run the final
109. r 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 5 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 y H we get that the FT of the wavefunction is for simplicity V V H H i0V H e AH 30 where A H is the damping terms arising from partial coher ence The FT of the intensity is now given as 1H FTQp y YA Y H H H L 8a ioA VF e 5H
110. r 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 conditions 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
111. 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 EEK 3 M 15 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 12 Structure Refinement Through Matching of Ex MacTempas User Manual Averaging can also be performed through symmetrization which 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 12 4 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
112. rmed 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 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 2x AY ce z 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
113. s on a screen with a resolution of 72 dots Ch 6 Menus p 60 MacTempas User Manual inch If Auto scaling is set images will scale to fit the window Magnification options Fixed Magnification Magnification 30 0 siltion M Auto scale when images do mot fit r 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 of the Contrast Transfer Function E Horizontally Scale the CTF automatically 7 Use Value below as Maximum Value for g ee et ee Maximum g valwe 11 0 i k Cancel i 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 61 MacTempas User Manual Ch 6 Menus p 62 g vectors larger than the cut off will not be displayed Difitactiad Pallein eblis Ophons iahege Display Ghjace kni Aperture Camara Length rim pea RES re are ia Di
114. s opens a new structure with Sa An au mere J exempt Secures in E K Eny H tow Ea Eve Carbon 1 p LE pampe Srudues gt T Wiw Folder add to Fawries Con default values for all the parameters Change the input to reflect Ld es Pii ee Crus Parme HHD es Pua eeee PREEN Lemm ava jarani ae AD OEE tatin ect roe iF E bai EH tie h wid niahi il tidied ces ah i LC 087 La i mii Cais Pa Li CO CR ica od Abe E bed L Ti Fon img Fiun C n Ho Po im RO te Din of ieee Cie b Di J polusan 4 Cas En TH ewe he Po Diman xe l To a A le Bere sra rrr Ferg a Barman L ome Menia RUE ima T Vei dd he Lis bris ee genie ge al OO Phare Fait Tec fed T am Send mi dias Ll ii T oe een ee 19 Decancrimg ras jh 000 2 Cee I a Dhi ores amri red Pe GE CESSE TT Pong eee sg ms Bad bis ue im Cea af Oe bee URI TO Ti T Ce Cit Cora a ul hes mirat nih Oye rhh lt a Fara Bai i nm okika Ped ara n i Meh ay eed Begue Pre mor ni Are hy mare img 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
115. se of space 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 art
116. 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_ LG LE X N y a 8 where N is the number of pixels in the image 9 The value o i is the standard deviation associated with the pixel 7 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 1 y lOLO 9 N M o A mismatch by one standard deviation adds one to the sum in the expressions above and a value of 7 of 1 implies that the two images are identical 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 12 Structure Refinement Through Matching of Ex MacTempas User Manual Writing x oY 1 5 D oi 1 avi 2 10 leads to the definition of a Residual Image fi 10 which is used to visualize and to quantify the mis match between two im
117. 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 selection made by the selection tool Select All Select all objects in the display window or an entire image Object Info Shows the clipboard and the content of the clipboard MacTempas User Manual Arrange Object Shows the clipboard and the content of the clipboard Linda Hed Cut Copy Paste Clear Select All Bring To Front Ering Forward tong To Back Send Bithia Ch 6 Menus p 57 MacTempas User Manual pnas SANE Live microscope Control v Automatic Erase SE Atom Overlay 3L Montage 238 M Intensity Scaling Magnification CTF Scaling Diffr patterns 3D Min Lens Intensity Slice Method Show Microscopes v Use Electron Parameter Fit Edit Scatt Fact Parameters Treat as monolayer 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 58 MacTempas User Manual are reflected live aslong as the calculation time is reasonable Automatic Erase Toggles whether you are prompted for the position of
118. st Just because an element is listed under active elements does Ch 6 Menus p 98 MacTempas User Manual not mean that one of its types will be used in the refinement pro Define Active Abom Bu D Fo Pan Gare dr LL D ni 3 lractive Active Sr Ca E Cu 4 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 Ch 6 Menus p 99 MacTempas User Manual imec Rofieaaoet Centred Experimental mace tatin Model Comparison Area El section Entre trage 7 al Aboms to refine E f Add Section y E Addi Croup Salectan E Hi i Ammi h Corm Age 4 Show ody non svmmatrs related atoms Othars move according to symenebias E arit Al itam D nettes D DOO en 3 0 0 Use the tool to add indewidual atome tothe Bus To remove stems use the 7 teal eS Atore Wilh Same 2 wall Mowe together ules explicirely remewed with the tool canca oo Area used for comparison Selection Sets the comparison region 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 that fall within the selec tion rectangle set in th
119. 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 Ch 6 Menus p 105 MacTempas User Manual that a i Tii Ti T3 a b Ta Ty T3l b g g 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 igina Dpem oey Iys male Eee aye awe Re mE we eel fae LT ne YEE FLE PART bee ET re UE Original Bases ER Sr LAHT Bi H E BE 02 Cu CCR 0 Ce 1 4 d Origa Unit Cell Atom Ca 0000 0 000500 Ca 0 So EH 1 000 AAt Sr 00 120061 Es 0660 ee Sr 0500 00000 H CON 6 HO D Pee di CSC 00 0 BE a CON 000 E B i iha Se Lists Original Operators Ch 6 Menus p 106 timmere Gcermor Transformations LA Hew Operators ENT wa Ay DEN TS LS av pe Li ee LE ye oe ere ie SRE eth PAR PRE AT Te TE re r Hew Bae
120. structure information in the input dialog is replaced by Crestal Parameters ADA io Akaba deg 00 BTA AII Bena leg moo CJA fm Appi Gares dea S00 Peig of paming o phaisg paliti Sachi ie Hg ice Difrea Pon erage Cale riches 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 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 53 MacTempas User Manual Ch 6 Menus p 54 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 diff
121. ta deg 40 08 Humber of Sires pir cell 1 CEA 300200 Camma deg 50 05 Gmax A 200 Spaceqroup dint Tables Thick fbagiwcandn 20 0 30 fof Asoc in Basis thee 4 Store Ampl Pases fe ha ih i baat ee Chem Cent of Lawe Cire fF 0 06 k 0 00 Pe ee ee O Sheer g Tilt mrad amp angle pop op F of dierri arms 5 Typa of Absorpcion None Microscope and Lent Parametors Microscope Mame cus Antic Absorption Parameters Voltage kv 3000s men 060 Mo absorption Convergence angle mrad 4 20 Twa Cire Inelastic Seatbering Factory Spree rt ind 30 a ae J magnar Potential Percentage fet Raal Poreririali Dafocus beg iac end J 2d00 10 170 Coma Farid rT 3 Obs dens apart rad A 1 1 25 ect LE k Maz sghe Sig a ee CO 5 cm Ga Cent of the Optic Axis DOI 6 00 200 0 0 Over nde calculation status Mark for re cabculaton _ Projected Pntenthal Mark at cabtulaped J Frejected Perilia Ext Wave Function Eeit Wanton 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 DEL the halfwidth of a Gaussian spread of focus due to chro matic aberration in Angstrom units TH the semi angle of incident beam convergence in milliradian If the type of
122. tance 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 distance 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 but most approximate method is to compute the projected Ch 11 HOLZ Interactions amp Sub slicing p 139 MacTempas User Manual 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 times 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
123. ted by the same CPaCegroup Saitch Spacegroup Tetragonal Hey Export New Set 4 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 The Process menu is the largest menu and is the source of all MacTempas User Manual image processing functions There are menu sub menus as well image Calculator ORC FFT HF Hanning Masked FFT WF Pawer Spectrum Withee Fibber CHW Spatial Filters k Invert Transform a Statistics F Ex ET Extract From Complex E Auto Correlateomn Creda Corretation Azimuthal 4venage E Template Matching Find Peaks Were T PA Change image Origin Cryst image Processing Find Focus From Image Find Focus Preferences Always Create New Image Image Calculator This is a general image and number calculator using reverse Ch 6 Menus p 109 MacTempas User Manual polish notation HP style calculator e 9 Image Calculator Stack Image Selector Al untitled x iy Yy 1 x ke gg EH ne M e ceiling 3 an all Create Window El el Eh Ux sin Fee el Hate EE H EN EE Ses ell SE lal Halll HE es a x Crystallographic Image Processing Can be invo
124. 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 Ainmistic Model Type of View C Origceal Unir Cail M Transtormed Wee Cell 001 is Electron Beam Director Ci riendod View Width 30 Haight 20 View Options Viewing Direction WWI 0 T t iniia Scaling Factor to be used fos Displaying The Unit Cell 66 of Wordomd toh Ch 6 Menus p 66 MacTempas User Manual Draw the CTF 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 aa Contrast Transfer Function CONTRAST TRANSFER FUNCTION Step RESM Fe MORT Gelino Da a 400 00 AT oS A Diya ED el ER 20 ed 2400 Ce fmm Eu oh a pag Div irad 5 a 200 Dei jay 10 30 00 M Voltage ikw 10 S00 L Drew Envelope function A shel Horizontal axis in A 1 ful Dra Grid ne er LI Draw saone Axis G Vechors Label Ge a of the CTF and the resolution The bar moves with the mouse Draw Pendell ssung 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
125. tion 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 Y 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 SI 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
126. tructure 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 12 Structure Refinement Through Matching of Experimental and Simulated HRTEM Images p 156 MacTempas User Manual 2 A computational method yielding an image to be compared to the 1 3 A method for 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
127. ulation only if Nslices is different from 1 Ch 7 Input File Format p 115 MacTempas User Manual Ch 7 Input File Format p 116 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 IPlot 13 NBasis ih ik il Defocus D1 D2 DD 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
128. ultislice 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 WC y z dz expl iodzV y 1 expl io VC y z ide hp x y 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 y z dz expl io Vy Jaz hp x 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 expl iodV y Wy x y 2 18 The last equa
129. units with a negative value representing underfocus weakening of the lens current As for the speciment thickness parameter the input is a range specified by the upper and lower bounds and an increment Cs Spherical Aberration The spherical aberration of the objective lens in mm Convergence Angle Ch 4 Running MacTempas p 39 MacTempas User Manual Ch 4 Running MacTempas p 40 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 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 unit cell as for the Laue circle center 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 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
130. up 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 05 0 0 446 1 O 2 4e 0 0 0 375 1 O 3 4e 0 0 0 205 1 O 4 4d 05 0 0 25 0 065 Isotropic thermal parameters for all atoms are fixed at 3 6 Ch 8 Sample Calculation p 119 MacTempas User Manual Entering the Structure Ch 8 Sample Calculation p 120 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 Sin glace Parone CE Crysis Parreira See Pare Tata br fore arip lowered i r ap go aahi t l a o 116 RAI 13140 Sea ied Hosts of Vices ges cel m Cok AGEN Camden LR trun Ae m Spacegroup Jri Tath Los Thick bime m Seb Fai Sc fon in lace L T oa Gore Amp hn z te en Fu Sen Dm R thes Cam of Less Cie O00 p o soi dng fer Ba Tiffen dade 001 99 fo
131. ve been 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 fW Occ r exp B H 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 2xk r 8 It is useful to define the quantity V r which will loosely be referred to as the potential as TT 2me 8 Vir he or 9 Ch 2 Theory of Image Simulation p 13 MacTempas User Manual The Schr dinger equation above cannot be solved directly with out making v
132. with the HOLZ reflections Ch 11 HOLZ Interactions amp Sub slicing p 141 MacTempas User Manual 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 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 computat
133. y 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 Sirum Euro er Oneal Parser fascia Firemeners oe Poe auis bemi i l ba ADA dE pra fie LE b 4 i R 5 BA LRA eu lei LE Sumber of Soran parcel i CE db Garea lu 304 min mi 20 i 3 dar Tablet J Meare aii 3 T J Sa eee LE fir keg taie att 100 gt Leet df MES i fea God 1 Tegea au E rin of yam Dee Iag Ce Trquesi Gra ln k T onem mi 4 B Hegna P of durent niera dHere 1 EN MHW Sera ond Lons Fearin ee kiam brrercpn heme TE zi Vege 0 Gp L Cerergeec mgh ima oS Tac tah ipaa al dcan JA ID Thre i Dba hag Incl A EG C l Lives Dai wer acari rad A E 9 79 ea H CE b b Mg my me 3 heya Bd Go Cam af Obl Lans Aden ie i ib ao Agee er enh a be Caan al de Ok Sais 0 CD EC DD Angee wih sarip 0 rer ihe coca les Mak forre nmbniates Precio Fons _ Eee Basten ones Meek a cacuair Predeo Roierial _ Eek Suche _ frags Paie fic 4 jaa The input also allows for choosing the second setting for a spe cific spacegroup if one exists If no space group is required one s

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