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MacTempas-Manual - Total Resolution

1. Treat as monolayer Automatic Erase Toggles whether the screen is automatically erased before the image window is being drawn into Request Position Toggles whether you are prompted for the position of the upper left corner of the image to be displayed Automatic Titling Toggles whether each image will be shown with a descriptive title below the image Ch 6 Menus p 54 MacTempas User Manual 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 images and the number of pixels to leave between images aes O Automatic montage of images M Starting Location of the Montage o D i Horizontal Separation of Images pixels Vertical Separation of Images pixels Mi Auto scale when images do not fit Defocus Horizontal Thickness Yertical Q Thickness Horizontal Defocus Vertical User Defined Layout Click to Display and Set 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 Ch 6 Menus
2. Wottage k Come rgesce angle mrad Spriied if detiris LA Dehra hag ae orl jA Cent of Ob Less Aprt Cent of ther Optic Anis AIA ama Alpha aieg anan Zone anis uty BA aman Beta deg anan st or al Slices pe cell cia user samme pdeng sum Geax Aa S croscege and Lens Paramegers CO ene Mame ARA a window displaying the atoms in the unit cell appears Specimen Parameters Lim Thatk eq ine eni Show Share Al PARLES j thew Cent of Laws Oircie DTA A i i LE LE o b h ob ES Li el a Le EI C0 Les OU PO RS He DOSSCSTESSENSEE EEES Se Pp Pa TU H i HHS 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 G max may allow the Ewald sphere to approach the so called pseudo upper layer line that the multi 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 Ch 4 Running MacTempas p 35 MacTempas User Manual Ch 4 Runnin
3. Amplitudes to be stored as for possible plotting YES NO The indices of the reflection to be stored or if Plot NO then Objective lens defocus or First defocus last defocus incre ment The commas are required Radius of the objective lens Aperture in units of A 1 The center of the objective lens aperture in units of h k of the transformed reciprocal unit cell The center of the optic axes in the same units as Ah Ak Ch 7 Input File Format p 75 MacTempas User Manual Ch 7 Input File Format p 76 Line Parameter s 17 NBasis Namp s1 52 53 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 T
4. 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 h2 ee V e r P r 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 kg ko 27 A so that the inci dent electron wave is written P r exp i t 27k r 8 It is useful to define the quantity V r which will loosely be referred to as the potential as 87 me he V r or 9 The Schr dinger equation above cannot be solved directly with out making various approximations Depending on how the problem is formulated one can derive the most common solu Ch 2 Theory of Image Simulation p 13 MacTempas User Manual tions to the electron wavefield at a position T within the speci men The Weak Phase Object Approximation In the Phase Object Approximation POA 4 the phase of the electron wavefunction after traversing a specimen of thickness T is given as P x y 2 T P x y z O exp ioV x y T 10 with o 2amed ma E ji 11 mc where V x y is the average potential per unit length The speci men is considered thin enough so that electrons only scatter once and are subject only to an average projected potential In the weak phase object approximation th
5. The pro gram will also automatically set lattice parameters depending on the spacegroup Thus if the user chooses a cubic system b Ch 4 Running MacTempas p 31 MacTempas User Manual and c are set equal to a Space group MacTempas generates symmetry operators for the any one of the 230 space groups when selecting the number or the symbol of the space group as listed in the International Tables for Crys tallography By clicking on the pop up menu Space Group one can choose one of the 230 spacegroups by first selecting the type of crystal structure i e hexagonal or cubic The user can choose one of the spacegroups by clicking on the symbol for the spacegroup or by entering the number for the spacegroup Specimen Parameters Crystal Parameters Aj Alpha deg 0 anal i ml nal 48080 Beta ieg emer of Slices percel cA 8000 Gammafdeg 30 emia a 5 Monoclinic i Spacegresss jint Tables of Abe Batis D oT imm Ops i ihien ben e D Orthorhombic Tetragonal Trigonal Hexagonal Set Basis kiprescept and Lens Parameters Wicrocouge hame amk Voltage kv wn amp imm 10 Convergesce angle mrad 25 rie eia Spread ei defocus A Three foli Mie chan Defocus leq inc cr A fs frnfrn ne Fromm res room rue no P c2 P62m P62c P tmmm P imec P6 mem P mme Shj lans apert
6. an attempt to explain why electron microscope images of complex oxides sometimes showed black dots in patterns corresponding to the patterns of Ch 1 Introduction to Image Simulation p 3 MacTempas User Manual heavy metal sites in complex oxides and yet other images sometimes showed white dots in the same patterns 2 This first application was therefore 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 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 micros
7. and say to contact Total Resolution or to run the instal lation program If you have just changed your computer or installed a new clean Changing Hard version of the MacOS you must ensure that the extension ware or Versions TRSecurity is placed on the new machine new extension folder of the MacOS Without the extension in place the program will not recognize the hardware key and MacTempas will run in demonstration mode MathLib is a shared library that is used on PowerMacs When MacTempas runs on a PowerMac it uses the math routines that are contained in the file Mathlib Unfortunately the first Math Lib provided by Apple was very poorly optimized and thus the Mathlib provided with MacTempas is intended for your use in case the version you have on your computer is older than the one provided with MacTempas If you are running MacOS 7 5 3 the Mathlib is automatically built into the operating system and you don t need the supplied MathLib The file Mathlib if present is found in the Extension Folder inside the System Folder 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 p
8. 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 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 a L cl a a 3 G T a qa Ca Ch 8 Sample Calculation p 81 MacTempas User Manual Ch 8 Sample Calculation p 82 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 80A and the semi angle of beam convergence to 0 5milliradian Specimen Thickness 40 80 20 The foil thickness response may be in one of two forms either a single value in Angstrgm units or a construction combining a starting and ending thickness with an
9. 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 By selecting to print with this window being the B 0 05 0 15 M Draw Grid Ch 6 Menus p 62 CONTRAST TRANSFER FUNCTION V 8000kY Cs 2 0 mm Def 500 00 Del 150 00 Div 0 85 mrad Scattering Vector A O Draw Envelope Function Step Defocus A 3 0000 Cs mm m Ae Div mrad CE Del A m Afsa Voltage kV ro ICE 0 25 0 35 10 45 0 55 0 65 0 75 Label Horizontal axis in A 1 Label Horizontal axis inA front window the CTF is printed Draw Pendellgssung Plots In case the user has selected to store a set of diffracted beams for plotting of amplitudes and phases as a function of specimen thickness this brings up a dialog box allowing the user to set the plotting conditions One can choose to have the amplitudes 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 Ampitude output file for Indium Phosphide This file contains amplitudes and phases for the reflections below Reflection s Oooo M 1 1 1 Options GAMERS A DD A EP
10. higher order Laue reflections can be included by reducing the slice thickness 10 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 a M b 0 N m dx dy defining the calculation to a grid of N M points The sampling interval automatically restricts the calculation in reciprocal space as well The maximum reciprocal lattice vector for orthogonal axes is given as 2 2 M 2 Hax Rinax kinax D z F 21 2a 2b Ch 2 Theory of Image Simulation p 17 MacTempas User Manual The Image For mation 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 h yax gt Kmax as defined above in order to avoid possi
11. of different atoms Type of Absorption Microscope and Lens Parameters Microscope Name Angle Voltage kV Cs mm Mag Convergence angle mrad on no Spread of defocus A 80 00 Defocus begincena A 500 Jo 500 Obj lens apert rad A 1 0 70 Sigma of a b 0 00 0 00 i Cent of Obj Lens Aprt Angle with x axis oo Cent of the Optic Axis Ch 8 Sample Calculation p 78 w horiz Comment BCSCO by Tarascon et al MacTempas has a field for an optional comment or title The MacTempas User Manual user should enter a comment such as the above short enough to fit yet detailed enough to jog the memory when referred to six months hence Space group 139 From the structure information we know that the cell is tetrago nal with a space group I4 mmm From Table 6 2 1 of the Inter national Tables for Crystallography we find that the space group number for I4 mmm is 139 Choose the correct space group from the popup menu a 3 814 Enter the correct value for the lattice parameter a In this exam ple MacTempas knows that b is equal to a for the tetragonal space group 139 and so enters b automatically once a has 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 defau
12. p 55 MacTempas User Manual Ch 6 Menus p 56 scaling Automatic Scaling of Image Intensities Herne Q Scale the Image to Black White values err Values below are values used for last image displayed Value of Black Value of White Magnification Allows the user to set the magnification to a set value The magnification depends on a screen with a resolution of 72 dots inch If Auto scaling is set images will scale to fit the window f Magnification options O Fixed Magnification i Magnification Factor RUAUURE Million Auto scale when images do not fit 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 Horizontally Scale the CTF automatically Use Yalue below as Maximum Yalue forg Maximum g value ee MacTempas User Manual 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 cle
13. produce the exit surface wave that is it contains information from the multislice computation 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 in the FILE menu This generates the input dialog window below which requests the following information All fields have default values and in order to create a valid input file only valid data for the atoms must be entered Crerial Parameters 4pecimen Parameters ALAL Aipha deg al Annes inaa npay 40000 Beta deg Mamer of Slices per cell cid eco Gammagoegg 0 ee Pet Pb ke LA eg ier ern Spacegrems int Tables CI sees Ampi Phacas of AD sre in Basis O SetBasis pe eee ee Sof Sym Ops i ___ mew oline ii Type St Absorpiees Wicres cept and Lens Parameters MC Po CO Maint Vottage jk ane timmy fia k s KE E a a AVErgESte angle mrad 55 fered ei defocus ao Three fold ke Jle Detocus greinen A venant ration A Obj lend apert rad jAi ur digma aiga IL Center of dbj Lens prt h e k amp Angle tisane jo Center ofthe ocic axis h a em Asbigesa i sem Al 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
14. standard Macintosh menu items for formatting the text produced by the Text Tool Help Image Window Status Window v Atom Window Source Window Operand Window Color Window Tools Window MLUT Window v Cursor Window Pseudo Window Use this menu to bring a window to the top of the screen in case it has been completely covered by another window The use of the Option Key can make the windows invisible visible Ch 6 Menus p 71 MacTempas User Manual Ch 6 Menus p 72 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 the editor EDIT At times it is desirable to edit the file directly rather than using MacTem pas 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 purpose in particular the format of the structure file lt struc turename gt at is given below Line Parameter s Meaning 1 Title Arbitrary description of this structure 2 SpaceGroupNumber Just as is says one of the 230 spacegroups 1 230 including 0 3 abcabg The lattice parameters and angles 4 Gmax The maximum reciprocal lattice vector in the multislice calcula tion The potential is evaluated out to twice this value units 1 5 iu iv iw The direction of the electron beam in units of the real space crystal lattice vectors 6 NSymops Ns
15. tals Proc Roy Soc A271 268 275 Goodman P Moodie A F 1974 Numerical evaluation of N beam wave functions in electron scattering by the multi slice method Acta Cryst A30 322 324 Self P G et al 1983 Practical computation of amplitudes and phases in electron diffraction Ultramicroscopy 11 35 Ishizuka K and Uyeda N 1977 A new theoretical and practical approach to the multislice method Acta Cryst A 33 740 Kilaas R et al 1987 On the inclusion of upper Laue lay ers in computational methods in High Resolution Trans mission Electron Microscopy Ultramicroscopy 21 47 62 Scherzer O 1949 The Theoretical Resolution Limit of the Electron Microscope Journal of Applied Physics 20 20 29 Frank J 1973 The envelope of electron microscope trans fer functions for partially coherent illumination Optik 38 519 536 O Keefe M A 1979 Resolution damping functions in non linear images Proc of EMSA 37 556 557 Ch 2 Theory of Image Simulation p 25 MacTempas User Manual Ch 2 Theory of Image Simulation p 26 MacTempas User Manual Chapter r 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 Proj Potential generates the crystal potential that pro The
16. 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 98 MacTempas User Manual MacTempas sub slicing While ensuring that the calculation remains sufficiently accu rate MacTempas will normally choose the simplest and quick est method of specifying how slices are defined for any particular combination of specimen zone axis accelerating voltage and maximum g To this end the user can choose to neglect HOLZ interactions if these are judged to be unimpor tant If HOLZ interactions are important then the user should select the 3D Potential Calculation radiobutton in the Options menu rather than 2D Potential Calculation available RAM Sub slicing amp using a layered structure is generally easier A 3D calculation is limited and depends on Fable Calulation Opti ONS mme 2D Potential calculation 3D Potential Calculation When a two dimensional c
17. 0 0 870 0 3 Bi 0 50000 0 50000 0 19780 3 600 0 870 1 3 Bi 0 00000 0 00000 0 26810 3 600 0 130 12 3 Bi 0 50000 0 50000 0 76810 3 600 0 130 Bo a 0 00000 0 00000 0 73190 3 600 0 130 4 3 Bi 0 50000 0 50000 023190 3 600 0 130 15 4 Cu 000000 000000 044560 3600 1000 gt 16 4 Cu 0 50000 0 50000 0 94560 3 600 1 000 7 4 0 00000 0 00000 0 55440 3 600 1 000 C J 18 4 Cu 0 50000 0 50000 0 05440 3 600 1 000 19 5 o 0 50000 0 00000 0 44600 3 600 1 000 20 5 o0 0 00000 0 50000 0 94600 3 600 1 000 Ch 6 Menus p 68 MacTempas User Manual Calculate Menu The active commands in this menu depends on the current sta Statistics Text Win Full Calculation Projected Potential Exit WaveFunction s Image s wpo Image Plane Wavefunction s 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
18. A RE 4 Q Amplitude Intensity Q Plot each reflection seperately Superimpose plots M Plot Phases Plot the Data Q Write Data to File instead of Plotting V 400 kV Gme 1 9 4Z 42 50 70 Thickness A Ch 6 Menus p 63 MacTempas User Manual White Ch 6 Menus p 64 Set Contrast Curve Instead of changing the hardware lookup tables to effectively change brightness and contrast values the brightness and con trast can be set before the images are displayed on to the screen This is performed from this menu command Set Black White Contrast Set Black White allows the user to specify the curve by selecting two points on the input output curve Stack Phasegratings This allows the user to specify a sequence of phasegratings that should be used in the multislice calculation This applies only to layered structures See Chapter 9 for a more detailed instruc tion on how to create a layered structure MacTempas User Manual Defined Phasegratings Name Az Name Az E i copper 3 61 2 inp 4 50 Specimen 1 1 1 1 1 2 2 2 2 2 1 1 1 1 Deposit Insert Repeat Slice Unit Cell Use this option to subdivide a structure into separate layers for use in a layered structure calculation The direction perpendicu lar to the slices and the number of slices must be specified Slicing options u v w Zone axis for slicin
19. Define PGratings Define Stacking Define Stacking Microscope and Lens Parameters Microscope Name Voltage KV Cs mm Convergence angle mrad Spread of defocus 100 00 i Defocus beg inc end A Mechanical Vibration A Obj lens apert rad A 1 CE pom Mag a i SAN 0 00 0 00 Cent fb Lens Apr or us au Cent of the Optic Axis Cent of Laue Circle Eq Tilt mrad amp angle Type of Absorption wao o e threefold o Joo mation regarding the lattice parameters A and B etc There are no input for atoms because a layered structure has no atom information per se Even though you are asked to fill out a specimen thickness this value has no meaning at this time because the content of the structure has not been defined The values of A and B come from the structures LayA LayB and Defined Phase gratings 1 copper dz 3 61A 2 inp dz 4 50A Ch 10 Creating a Layered Structure p 93 MacTempas User Manual LayC When you create the layered structure a default value of 2 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 execu
20. Mac lempas HRTEM Image Simulation Software Package User Manual MacTempas User Manual CONTENT Page Installation 1 Installing the Hardware Protection Key 1 Activating the Hardware Key and Personalizing the Program 1 Changing Hardware or MacOS version 2 Introduction to Image Simulation 3 Simplifying the Description of the Microscopee 7 Simulating TEM Images 9 Theory of Image Simulation 11 Modeling the specimen 11 Simulating the Interaction Between the Electrons and the Specimen 13 The Image Formation 18 References 24 Introduction to MacTempas 27 The Three Simulation Steps 27 Generated Files 28 Running MacTempas 31 Generating an Input Structure 31 a b c 31 alpha beta gamma 31 Space group 32 Set Basis 33 Number of Atoms in the Basis 33 Show Symmetry Operators 33 Show Atoms in Unit Cell 34 Number of different atoms 35 Zone Axis 35 Number of slices per unit cell 35 Gmax 36 SpecimenThickness 36 Store Ampl Phases Set 36 Center of the Laue Circle 37 Type of Absorption 37 MacTempas User Manual CONTENT Windows Microscope Voltage Objective Lens Defocus Cs Spherical Abberation Convergence Angle Spread of Defocus Aperture Radius Center of objective Aperture Center of the Optic Axis Two fold astigmatism Three fold astigmatism Mechanical Vibration Status Window Atom Window Color Window Tools Window Eraser Text Tool Magnifying Glass Line Tool Selection Tool Histo
21. Stare AmpliPhases af Symin bgi Sew Cento Laue Circle 2 al atiii in UHI m EETA Lg Tt piradi amp angle aai Aerem snes S Type of Absorption Sbcroscape and Lens Faremeters Microscege Mame i W Astigmatism 4 Votege ky mnn Csimmi am Cu lt w hon Convergence angle mre ET Tes Tole i Spread ai dedecus E Teema p ue Defacus Geqineend lh Si b s00 ie chanical Vibration Al Obj lend ap r r d 4 1 Li BOF bugar SHOOT OOH am Centofeb less Apri oo an oon oe ENT JL I am am n00 ns Cent of ther Optic Awis Ce 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 Crystal Para cent Ala EEL Alpha D s een fone ans uv BJA aman Betaldeu men est Gr of Sica per call ThA Gamma deg anan Caix Aaa ip teyr up ink lables CE Deck Greg ane en al Aomen in Basis 5 Sh
22. Three Simu pieces Porental g PaE P duces electron scattering from the structural data unit cell dimensions symmetries and atom positions occupancies and temperature factors lation Steps ExitWavefunctions s generatestheelectron wavefieldatthe specimen exit surface it uses projected potential combined with information about the accelerating voltage of the electron microscope and the specimen thickness and tilt The computa tion algorithm is the multislice approximation LUE Statistics Quantitati Full Calculation Projected Potential Image s generates the image intensity at the microscope eae DEEE image plane the effects of the objective lens phase changes and WDO resolution limiting aberrations are included via parameters like image Plane Wavetunctionts defocus spherical aberration incident beam convergence spread of defocus and the position and size of the objective aperture wpo 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 ImagePlaneWavefunctions s generatestheelectronwave 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 wavef
23. 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 97 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 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
24. 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 A new file can either describe a sin gle structure or a layered structure see Chapter 8 on how to cre ate a layered structure depending on the radiobutton selected Many of the parameters will have default values MacTempasPPC Save K File Edit View Folders Documents Finder Cp Example Structures a Modum besco n lt lt rhea prnt 8K Sun Ja Eject Lb co iout 40 un Ja FA inp pout 16k Wed M 20 items Sr New structure name newstructure Single Structure Q Layered Structure Open Open an existing structure file The standard Macintosh file open dialog is presented and only files of the type TEXT with the extension at are displayed as selectable The name of the imaging window will change to reflect the name of the current structure Close Close the file currently in use Save Save the current data for the structure file in use The current data will be written to the file overwriting any old data MacTempas User Manual Save As Save the current structural information Do not use a name with an extension if the file being saved is a structure file for later use by MacTempas Save Selection Saves th
25. acts with the contents of the windows Status B 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 AtomTypes H cof fsr lefefel fe This window shows which atoms are present in the structure the color the atom will be drawn in if colored atoms are set and the relative sizes of the atoms to be drawn To change the color of an atom choose the Color Picker tool from the Tools Window click on a color in the Color 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 41 MacTempas User Manual To change the atomic radius double click on the chemical sym Value for the Atomic Radius A bol A dialog window will pop up and a new value for the atomic radius can be entered units in A Color Window This window is used to set the color of a particular atom spe cies the color of the foreground the color of lines and text and the background color Colors for use in pseudocoloring is also picked from the color window To choose a color the Color Picker Tool must have been chosen To select the foreground color click on the color with the Option Key held down Hold ing down the Option key and the Shift key selects the back ground color Tools Wi
26. alculation 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 with the HOLZ reflections Ch 11 HOLZ Interactions amp Sub slicing p 99 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
27. ametersinthe lt structurename gt _ at filetothe 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 isthe result of calculating the image plane electron wavefunction s instead of calcu lating the simulated images The data is complex pairs of numbers real and imaginary The data starts at byte 80 and the file can contain more than one image plane exit wavefunction lt structurename gt aout contains the complex ampli tudes of several diffracted beams at one slice increments 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 8 Ch 3 Introduction to MacTempas p 30 lt structurename gt p_prnt containsinformationabout thewayinwhichthe ProjectedPotential subprogram processedthe lt structurename gt at data to produce the specimen potential lt structurename gt m_prnt containsinformationabout the way in which the Exit Wavefunctions s subpro gram processed the lt structurename gt pout data with the lt structurename gt at to
28. arascon et al in Phys Rev B 37 1988 p 9382 9389 the tetragonal structure has the following parame ters Space group 14 mmm Cell parameters a b 3 814A c 30 52A 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 77 MacTempas User Manual Entering the Structure To enter a new structure into MacTempas we first go to the FILE menu Section 3 3 and select New After entering a filename in the New File dialog MacTempas will put up a dia log into which the relevant information must be entered Note that many of the input parameters have default values The only data that must be entered in ordered to create a valid file is the atoms in the basis 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 Spacegroup Int Tables Alpha deg Beta deg Number of Slices per cell Gmax A 1 Thick beg inc end of Atoms in Basis 9 Store Ampl Phases of Symm Ops 32 Cent of Laue Circle of atoms in UCell 38 Eq Tilt mrad amp angle
29. ation 3D Potential Calculation 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 Ch 6 Menus p 58 MacTempas User Manual known Defined Microscopes Name Yolt k Cs mm Div mrad Del A p Parameters for the microscope Microscope Name Accelerating Voltage KV Spherical Abberation Constant mm Spread of Defocus A Divergence Angle half width mrad Us ifolectrorScattering actorSUs if orX 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 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 Ch 6 Menus p 59 MacTempas User Manual Parameter Fit for Ele
30. ble 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 formed 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 in the focal plane of the objective lens the image observed in the electron microscope would be am magnified version of I x y W x y z exitplane of specimen y x y W x y 22 Ch 2 Theory of Image Simulation p 18 MacTempas User Manual Objective Lens Defocus Consider an electron traveling from the plane defined by the exit surface of the specim
31. can be written g r dr POD I r r Ch 2 Theory of Image Simulation p 11 MacTempas User Manual where p r the charge density is pr p r 2 all atoms i with the sum extending over all atoms i at positions r each giv ing rise to a charge density pil Z e5 r er 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 P u through the relationship g r Pe du Dene j since because of the periodicity of the unit cell u is non zero only when u H ha kb le H being a reciprocal lat tice vector The potential H is given as a sum over all atoms in the unit cell _ el Qniur _ Z f Al 2 zrur y Pa me ATE ai H atoms i atoms i where the electron scattering factors fel and the x ray scattering factors f have been calculated from relativistic electron wave functions and parameterized They can be found in various tables which are used by image simulation programs 3 Taking into account any deviation from full occupancy at a par ticular site and the thermal vibration of the atom the Fourier coefficients of the crystal potential from one unit cell is calcu Ch 2 Theory of Image Simulation p 12 MacTempas User Manual Simulating the Interaction Between the Elec trons and the Specimen lated as H Y f Occ exp B H Je
32. 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 W po This will calculate the weak phase object images for a range of Ch 6 Menus p 69 MacTempas User Manual Statistics Menu Ch 6 Menus p 70 resolutions specified by the user See the introduction and the later chapter for information on the WPO Approximation and its use Image Plane Wavefunction s This will calculate the complex wavefunction at the image plane based on only linear terms in the contrast transfer func tion i e only interference between the central beam and scat tered beams SUITE Text W Histogram Column Average The current operations in this menu are Histogram Displays the histogram distribution of an area selected by the selection tool or of the entire image screen if selected through the Select All command Column Average Shows an average intensity along the horizontal line defined by the rectangle chosen by the selection tool The trace being cal culated by the program corresponds to the average of the pixels defined by the width of the rectangle This menu determines the appearance of text drawn in the MacTempas image window The following text attributes can be set MacTempas User Manual Text Menu Windows Menu LEON Windox Left Justified Center Justified Right Justified These are the
33. copes 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 operated in two dis tinct modes set up for microscopy a and for diffraction b In microscopy mode we see that the TEM consists of an electron source producing a beam of electrons that are focused by a con denser lens onto the specimen electrons passing through the specimen are focused by the objective lens to form an image called the first intermediate image I1 this first intermediate image forms the object for the next lens the intermediate lens which produces a magnified image of it called the secon
34. ction Chromatic berrationTemporalncoherence Electrons do not all have exactly the same energy for various reasons They emerge from the filament with a spread in energy and the electron microscope accelerating voltage varies over the Ch 2 Theory of Image Simulation p 20 MacTempas User Manual 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 f one has a spread in defocus values centered around f The value f is what is normally referred to as Af as indicating defocus The images associated with different defo cus values add to make the final image Assuming a Gaussian spread in defocus of the form a 2 D f fs expl So 25 gives 1 MCF fol DU odf gt YA gt YD exp 1 2 aAH 26 This states that each Fourier term diffracted beam is damped according to the equation above 11 Beam Divergence Spatial Incoherence The electron beam is not an entirely parallel beam of electrons but form rather a cone of an angle 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 t
35. ctron Structure Factors Ch 6 Menus p 60 MacTempas User Manual Commands Menu Parameters Ca Erase Draw the Unit Cell 3U Draw the CTF Draw Pendellsssung Plots Set Contrast Curve Define Phasegratings Stack Phasegratings Slice Unit Cell Erase Erases the selection made by the selection tool Draw the unit Cell 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 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 gum Type OFVIEW ne Original Unit Cell Q Transformed Unit Cell 001 is Electron Beam Direction Q Extended View l rs Direction UYW Co The Amount of Perspective view o Scaling Factor to be used for Displaying The Unit Cells of Window Co Ch 6 Menus p 61 MacTempas User Manual Draw the CTF Draws the Contrast Transfer Function for the current micro scope values The original microscope values are taken
36. d 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 X Electron Source ae 7 TON 17 17 op Condenser Lens Af 7 x 77 A T A 4 Object _ __ Woody PINE M td Objective Lens Focal Plane of Objective lens X N 1 1 st Intermediate me af N vA wars Intermediate Lens N s r i VA 2 nd Intermediate W AN Image VA EN Projecter pey N 7 Lens y 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
37. e exponent is consid ered much less than one so that the electron wavefunction emerging from the specimen is W x y 2 T W 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 5 The FT of the wavefunction gives the ampli tude and phase of scattered electrons and in the WPOA one has Yu d u ioV WT 13 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 V Thus for single electron scatter Ch 2 Theory of Image Simulation p 14 MacTempas User Manual ing and when the Fourier 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 11 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 6 Each Bloch wave is itself expanded into a linear combinations of plane waves which reflect the periodicity of the crystal potential wir eb kr Pe Y ch expl 2ai ky g r 14 j j g The formulation above gives rise to a set o
38. e operations such as copying cutting histogram computa tion etc To select an area click at a point in the display and drag the cursor while the mouse button is pressed Histogram Tool When this tool is selected a histogram will be produced for a rectangular region defined by dragging a rectangle while the mouse button is held down Double clicking on the histogram tool produces a histogram distribution of the entire image screen Ch 5 Windows p 43 MacTempas User Manual Cursor Window Curs H 4 Y 016 209 INT 000 MLUT Window Ch 5 Windows p 44 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 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 Mono Lookup Table window show the linear relationship between input values and output grey levels Under normal con ditions each input value maps to the same output value To change the mapping the line can be modified by use of the cur sor To change the contrast of the image the endpoints can be moved by the mouse if the mouse is c
39. e selected portion of the screen into a file The filetype PICT grayscale Tiff or Palette Tiff can be selected from the file Save Dialog Save Window Saves the content of the image window into a file The filetype PICT grayscale Tiff or Palette Tiff can be selected from the file Save Dialog Open PICT File Open a PICT file and display it in the MacTempas image win dow Only pictures that will fit within the MacTempas image window can be opened this way Page Setup Set the options for the page to be printed Print Print the MacTempas image window If a Selection is made the selection will be printed out If a histogram window or Trace Window is the foremost window that window will be printed Quit Quit MacTempas Ch 6 Menus p 51 MacTempas User Manual Edit Menu Ch 6 Menus p 52 ilies Options Undo Cut Copy Paste Clear Select All Cor Show Clipboard Preferences Undo Undo the last operation This operation does not work in MacTempas Cut Cut out the selection made by the selection tool The cut selec tion can be moved by holding the mousebutton down when the cursor is within the selected area Copy Copy the selection made by the selection tool The copied selec tion can be moved around as described in Cut above Paste Paste a selection onto the image window The source for the paste can be an image cut out from another application or throug
40. e what to output se Complex Magnitude Squared Q Complex Amplitude Complex Phase squared default the complex amplitude or the complex phase of the electron wavefunction at the exit surface of the specimen Ch 5 Windows p 45 MacTempas User Manual Operand Window 1 I EE 7 7 4 DISPLAY FILE CANCEL Ch 5 Windows p 46 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 gaat Choose what to output RAA A CNRS i Complex Magnitude Squared Complex Amplitude Complex Phase 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 Selecting functions in this window defines the actions to be per formed on the source defined by clicking in the Source Window Prior to selecting an operation a source must have been selected The operation currently available are FFT Use this to perform a Fourier Transform on the source selected in the So
41. ea Stare AmiplPhaces 2 al ymin Ope 2 tirs Cent of Lew Artie 2 af al in LE I Sal erci ais 5 Mirroscape and Lens Parameters Microscope Mame 3H FA ETC HEATERS B or Cf ed n folni lagina Poem al Pere emage eat PEER ae Portentiage CHE Spread if d t ui LA Defer Court Magie anih LA Cent of Obj less Apri au Cent of tee Giptic Anis bao aae aoa ao kpr tone Para dir se inelastic Scatherte y Sectors does dore be mere di Ce Le 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 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 MacTempas User Manual may be made known to MacTempas a Be Ses conso Param beri Alpha deg Foreest jot le oa he feta dept Au bier of eres pardi CA ee nn max jAi ne tinh Thick begint em of Afama in Basiu Shore Ampl Pia ses af Symin tet Li ET Cent oi Lave Gircle sf aliom
42. een stored To display the images we go to the source 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 To increase the area of image keeping the magnification the same select CELLS in the source window and double the size in the x direction by choos ing 2 unit cells in this direction and one in the y direction then MacTempas User Manual select DISPLAY To get all 12 images onto the display screen simultaneously select the options menu and the Montage option Back in the source window set ZOOM to 0 5 to reduce the image mag nification in order to fit all 12 images on the screen then DIS PLAY Now go back to the montage option and deselect Montage To display the projected potential for comparison with images select PROJ POT in the source window then DISPLAY Notice that the current values of ZOOM and CELLS remain set from the last update To display the diffraction patterns at the stored specimen thick nesses select DIFFR PATT in the source window then DIS PLAY To change the size of the patterns choose Diffr Patt from the Options Menu and choose a different camera length The size of the diffraction spots also depend on the divergence angle set in the main parameters It may be necessary to adjust both the camera length and the divergence angle to get a suit able d
43. en 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 a HA will travel a distance Af cosa This can be expressed as a phase difference an a ne ay TAMPA 23 Spherical Aberration Electrons crossing the optic axis with an angle a at the focal plane of the objective lens should form parallel paths emerging from the lens Ch 2 Theory of Image Simulation p 19 MacTempas User Manual Sla However the spherical aberration of the lens causes a phase shift relative to the path of the unscattered electron a 0 which is written as 11 2n A 1 4C 04 1 2200 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 dire
44. f linear equations expressed as ky k m VH cH yy 0 15 a 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 Allows rapid calculation of convergent beam electron dif fraction patterns Includes dynamical scattering Ch 2 Theory of Image Simulation p 15 MacTempas User Manual The Multislice Approximation The multislice formulation 7 8 is by far the most commonly used method of calculating the electron wavefield emerging from the specimen Although it does not as easily include scat tering outside the zero order Laue zone as the BWA the multi slice 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 solu tion gives the approximate solution to the electron wavefunction at a depth z dz in the crystal from the wavefunction at z In the multislice approximation one has de W x y z dz exp iodzV lt exp io VC y 2 dz I x y 2 16 Thus starting with the wa
45. g OI 1 Number of separate layers O O Calculate Each Projected Potential CxJ Ch 6 Menus p 65 MacTempas User Manual Main Parameters Parameters Menu Lili Calculate Main Parameters Atomic Basis Symmetry Operators Atomic Coordinates This brings up a dialog box showing the current conditions for the simulation The values are taken from the input given to the Crystal Parameters mens coon SR ACIMEN Parameters Alpha deg i Zone axis uvw t Beta deg ii Number of Slices per cell Gmax A 1 Spacegroup Int Tables Thick beg inc end of Atoms in Basis 9 Store Ampl Phases of Symm Ops 32 Cent of Laue Circle of atoms in UCell 38 Eq Tilt mrad amp angle of different atoms 5 Type of Absorption 2 Microscope and Lens Parameters Microscope Name m Voltage KY Cs mm g w horiz Convergence angle mrad Two fold a oo Spread of defocus A Three fold CE eS _ Defocus beg inc end A soo Jo 50 PE E TO I Obj lens apert rad A 1 mi i Si f a b Cent of Obj Lens Aprt Ro Angle with x axis 00 Cent of the Optic Axis New command in the FILE menu The parameters can be changed as to bring about a new simulation Ch 6 Menus p 66 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 ed
46. g MacTempas p 36 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 imposes an aperture on the diffracted beams included in the dynamic scattering process It should be large enough to ensure that all significant beam interactions are included The default value is 2 0 MacTempas will compute phase grating coefficients out to twice G max 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 Angstrgm units A series of thicknesses repre sented by the upper and lower bounds and a thickness step e g 100 250 50 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 Crestal Parameters igecimen Foram leri AAD amas Alpha tg Zomeu o 1e Bag 28148 Betalien an Ma bier of Ses par co CHA Gammaldeg am marihi Spetegreup Cink Tables Thick begint red of Afroman in Basit abra
47. ge s Wpo Image Plane Wavefunction s Statistic Menu Histogram Column Average Font Font Menu Size Style Left Justified Center Justified Right Justified Page 58 58 58 59 59 59 61 61 61 62 62 64 64 66 66 67 67 68 69 69 69 69 69 69 70 70 70 70 71 71 71 71 71 71 71 MacTempas User Manual CONTENT Windows Menu Input File Format Sample Calculation The Structure Entering The Structure Verifying The Input Running The Calculation Displaying the Results The Weak Phase Object Approximation Wavefunction Approximation Ideal Scherzer Lens Creating a Layered Structure HOLZ Interactions amp Sub slicing Page 71 73 77 T11 78 83 84 84 87 87 87 89 95 MacTempas User Manual MacTempas User Manual Chapter I Installing the Hardware Protec tion Key Activating the Hardware Key and Personalizing the Program Installation The application MacTempas and its associated files are all com pacted in the file MacTempas sea which is a self extracting archive After double clicking on the application on the disk select a location on your hard disk for placement of the folder MacTempas Folder which will be created automatically as part of the extraction procedure There are two versions of MacTempas supplied on your disk MacTempasPPC and MacTempas68K for the PowerPC and 680XX Macintoshes respectively You should run the appropriate ver
48. gram Tool Trace Tool Color Picker Tool Cursor Window MLUT Window Pseudo Window Source Window Operand Window FFT Unit cells Zoom Histeq Histog Page 38 39 39 39 39 39 40 40 40 40 40 40 41 41 41 42 42 42 43 43 43 43 43 44 44 44 44 45 45 46 46 46 47 47 47 MacTempas User Manual CONTENT Page Display 48 gt File 48 Cancel 48 Menus 49 File Menu 49 New 50 Open 50 Close 50 Save 50 Save As 51 Save Selection 51 Save Window 51 Open PICT File 51 Page Setup 51 Print 51 Undo 52 Edit Menu 52 Cut 52 Copy 52 Paste 52 Clear 52 Select All 52 Show Clipboard 53 Preferences 53 Automatic Erase 54 Options Menu 54 Request Position 54 Automatic Titling 54 Atom Overlay 55 Montage 55 Intensity Scaling 55 Magnification 56 CTF Scaling 56 Diffraction Pattern 57 Min Lens Intensity 57 MacTempas User Manual CONTENT Atom Shading Slice Method Show Microscopes Use Fit For Electron Scattering Factors Use Fit For X Ray Scattering Factors Edit Scattering Factor Parameters Treat as Monolayer Erase Commands Menu Draw the unit Cell Draw the CTF Draw Pendellgssung Plots Set Contrast Curve Stack Phasegratings Main Parameters Parameters Menu Atomic Basis Symmetry Operators Atomic Coordinates Calculate Menu Full Calculation Projected Potential Exit Wavefunctions s Ima
49. 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 as TIFF files in this fashion MacTempasPPC Save File Edit View Folders Documents Finder Gp Example Structures Eject copper pout a 4 copper p_prnt 24 B besco pout 40 k 3 x bcsco p prnt 24 k besco mout 20 it 2 tems ai D Save Data in File untitled ASCII Binary Options Grayscale TIFF Floating Point TIFF 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 ite Edit Options NeW Open Close Save ds Save As gt Save Selection Save Window Open PICT File Page Setup ST Print F Quit a0 This menu contains the following commands Ch 6 Menus p 49 MacTempas User Manual Ch 6 Menus p 50 New Create a new structure file A name is prompted for before input is made Enter
50. 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 x axis The magnitude is given in A Mechanical Vibration This simulates the effect of a slight vibration of the microscope One finds that often the simulated images show details that are not present in the experimental data regardless of other imaging conditions This may be due to image degradation caused by microscope vibration or other effects not included and thus one can introduce a slight mechanical vibration in an attempt to cre ate more realistic simulated images It is possible to specify an anisotropic vibration by introducing the amplitude in two per pendicular directions with the diagonal of the ellipse at an angle with the a axis as in the unit cell viewed in the zone axis orien tation 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 inter
51. h the cut copy commands of MacTempas Clear Clears the selection made by the selection tool Select All Select the entire MacTempas image screen for the next opera tion MacTempas User Manual Show Clipboard Shows the clipboard and the content of the clipboard Preferences The maximum size of a calculation and the maximum number of atoms in MacTempas is by default set to 256 256 and 2500 These numbers can be changed if the size of the program is modified accordingly and sufficient memory is present in the computer Since running MacTempas with virtual memory turned on is very slow all memory requirement should be satis fied by physical Random Access Memory effect It will probably be necessary to adjust the size of the program under Get Info in Finder A You must restart the program for these changes to take Maximum Product of the Number of Sampling Points in X and Y Direction Q 128 128 128 256 256 256 Q 256 512 Q 512 512 Q 512 1024 Q 1024 1024 Maximum Number of Atoms in Unit Cell Suggested Size of Program K 4096 Ch 6 Menus p 53 MacTempas User Manual Witten Commands Parameter Automatic Erase Request Position Automatic Titling Atom Overlay Options Menu Montage Intensity Scaling Magnification CTF Scaling Diffr Patterns hin Lens Intensity Atom Shading Slice Method Show Microscopes Use Fit For Electron Scatt Fact Edit Scatt Fact Parameters
52. hat this also leads to another damping of the diffracted beam 12 so that I r wir o Dada gt W H gt Y H exp raA C H 4 A 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 for mulation which include non linear imaging terms 13 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 in
53. ill 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 electron beam A and B 2 Calculate the phasegrating for each structure LayA LayB and LayC using the same value for Gmax 3 Now create a New Structure in MacTempas using the Ch 10 Creating a Layered Structure p 92 MacTempas User Manual option LayeredStructure You will be asked to fill out infor Crystal Parameters Specimen Parameters ATA 4 0000 Alpha deg 90 00 BIA 4 0000 Beta deg 90 00 Zone axis uvw t 0 Total defined thickness A i Gmax A 1 CIA N A Gamma deg 90 00 i A deg Thick beg inc end Stacking of phasegratings Store Ampl Phases x of phase gratings Stacking sequence Not Set Define PGratings ine
54. in Uel WW ate Dy THe jira Bangle Saf diferent snes Type ofAbsorption Seti ni artisan CTI Aah Meg whorir Comergeace angie m Tan Tole fo Jus Spread ef diedecis LA T Taree fold p_e Data cu egine emip LA ae i sm ia Ch nical Vibration A Cent of ther Cie Awis Ohj bena apr rad A 1 oa maa oe Sipeaetiam in ion Cent of Ob bens Aprt r 5 oe Angle wath x axis 00 Voltage The electron microscope accelerating voltage in kilovolts Objective Lens Defocus The defocus of the objective lens is entered in Angstrom units with a negative value representing underfocus weakening of the lens current As for the SPECIMEN THICKNESS parame ter 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 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 Ch 4 Running MacTempas p 39 MacTempas User Manual Ch 4 Running MacTempas p 40 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
55. incremental value The 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 80 Store Ampl Phases No As well as storing all the beam amplitudes at specified speci men thicknesses MacTempas can store a selected few beam amplitudes at each single slice increment in thickness then plot amplitude or intensity and phase as a function of thickness for any of the stored beams To store beams for plotting click on the command to enter the indices for the reflections that will be stored In this starting example we will not be entering any information here Voltage 400 The voltage would need to be entered if an unknown micro scope type were selected Since we have selected a 4000ex MacTempas will choose a value of 400keV Center of the Laue Circle 0 0 The pair of values specified as the Laue circle center are used by MacTempas to define the direction and amount by which the specimen is tilted from the exact zone axis orientation specified MacTempas User Manual Verifying the Input 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 Objecti
56. ion techniques for the simulation of high resolution electron micrographs J Micros copy 132 31 42 Ch 11 HOLZ Interactions amp Sub slicing p 101
57. isplay 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 85 MacTempas User Manual Ch 8 Sample Calculation p 86 MacTempas User Manual Chapter Wavefunction Approximations Ideal Scherzer Lens The Weak Phase Object Approxima tion The Weak Phase Object WPO approximation is a useful tool to find out what kind of information about a specific structure may be revealed at different levels of resolution The WPO approximation has already been described earlier and some of that information is repeated here There are two important assumptions that are made in the WPO approxima tion The wavefunction of the electron can be written as P x y 1 iot x y where x y is the electron wavefunction at a point x y and P 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 go
58. ited and atoms can be added to or deleted from the list Name x coord y coord z coord dw fact Occ Bi onoono 0 000000 0302200 2600000 0 870000 Bi Jonconoo 0 000000 0268100 2600000 0 130000 0 o o00000 0 000000 0205000 2600000 1 000000 0 os00000 0 000000 0250000 2600000 065000 1 2 3 4 5 6 7 8 9 O9 Coe 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 67 MacTempas User Manual the list or existing ones deleted Symmetry Operators 2 3 4 5 6 7 8 9 10 11 12 x 1 2 y41 2 2 1 2 13 14 15 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 Type Name X coord Y coord Z coord DW f Occf pees le 0 00000 0 00000 0 00000 3 600 1 000 2 OUT CE 0 50000 0 50000 0 50000 3 600 1 000 3 2 sS 0 00000 0 00000 0 10970 3 600 1 000 4 2 Sr 0 50000 0 50000 0 60970 3 600 1 000 5 2 Sr 0 00000 0 00000 0 89030 3 600 1 000 6 2 sr 0 50000 0 50000 0 39030 3 600 1 000 ke eee 0 00000 0 00000 0 30220 3 600 0 870 8 3 Bi 0 50000 0 50000 0 80220 3 600 0 870 9 3 Bi 0 00000 0 00000 0 69780 3 60
59. lices Number of symmetry operators 13d number of slices per unit cell and a flag indicating 2d 0 or 3d 1 potential calculation only if Nslices is different from 1 Ch 7 Input File Format p 73 MacTempas User Manual Ch 7 Input File Format p 74 Line Parameter s 7 NBasis Ntypes 8 it symb x y z 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
60. licked near the endpoint and the mouse button is held down while the mouse moves The brightness is changed by clicking near the center of the line and dragging it to the desired location To reset the lookup tables just double click in the MLUT window Note The above only currently works when the monitor is set to 256 colors MacTempas User Manual Pseudo Window Source Window PROJ POT DIFFER FATT EXIT W AVEF AGE Use this window to pseudo color images to enhance certain fea tures in the image To pseudo color an image with grey levels color is substituted for certain grey levels To do this select the Color Picker Tool select a color from the Color Window and deposit the color anywhere in the grey scale by dragging in the pseudo color window Double clicking in this window resets the grey levels Use this window to define which part of the calculation to dis play The choices are Projected Potential Essentially the output of the PHSGRT subprogram There is a one to one correspondence between the points in the projected potential and those in the image if dis played under equivalent conditions ExitWavefunction Thisis the output of the MSLICE subpro gram and 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 magnitude pur Choos
61. ll 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 88 MacTempas User Manual reached _ Starting Resolution A Ending Resolution A 200 Auto Decrement Resolution Fixed Decrements in steps of Number of Unit Cells to display X amp Y ces Zoom Factor to be Used in Displaying Images i Lj Print Data to File instead of Displaying Ch 9 The Weak Phase Object Approximation p 89 MacTempas User Manual Ch 9 The Weak Phase Object Approximation p 90 Chapter 10 MacTempas User Manual Creating a Layered Structure A layered Structure is a special type of structure where the composition varies in the direction of the electron beam An example of this would be a crystalline material having surface layers of amorphous material Another example would be a crystalline structure where the repeat distance in the electron beam direction is too large for the repeat to be used as the slice thickness and the unit cell must be sub divided into several LayA LayB LayC A A N Points Ch 10 Creating a Layered Structure p 91 MacTempas User Manual slices with different atomic content As an example we will work with three layers which we w
62. lt 2 Gmax is the size of the multislice aperture and defines how far out in reciprocal space the diffraction calculation will extend The value of G mnax 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 G max 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 G max 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 Note that MacTempas may be forced to choose a lower value of G max if a Ch 8 Sample Calculation p 79 MacTempas User Manual Ch 8 Sample Calculation p 80 large unit cell is used This occurs because MacTempas has a limit on the array dimensions used in the multislice calcula tions Although this limit can be changed under Preferences the current limit is in effect until the program is restarted The array dimensions are required to be powers of two An upper limit of 256 by 256 is limited by array dimensions to a parame ter 16 multislice calculation like 256 by 256 or 512 by 128 or 1024 by 64 so that G max for the diffracted beam
63. mber of parameters to a more manage able number For crystalline materials described by a repeat of perfect unit cells this is easily accomplished The unit cell in this case is defined by the lattice parameters A B and C where A and B are in the plane the specimen perpendicular to the elec tron beam and C is in the main direction of the incoming elec trons A B and C are related to the normal lattice vectors a b and c depending on the orientation of the specimen The speci men is thus reduced to M number of unit cells where M C is equal to the thickness of the sample giving in the end a 2D image which covers the area given by A and B In the case of a defect structure which no longer can be modeled as a small repeating structure it is necessary to limit the extent of the calculation by defining a supercell which contains the defect The resulting image obtained from the calculation will contain artifacts 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
64. n of the potential and the electron propagation is computed with a propagation function dependent on the electron wavelength Since then there have been numer ous formulations of the multislice approximation derived from the Schr dinger equation The problem of simulating images thus becomes a problem of computing the electron wavefields wavefunction at three microscope planes Currently the best way to produce simulated images is to divide the overall calculation into three parts 1 Model the specimen structure to find its potential in the direction of the electron beam 2 Produce the exit surface wavefield by considering the interaction of the incident electron wave on the speci men potential 3 Compute the image plane wavefield by imposing the effects of the objective lens on the specimen exit surface wave Each of these steps will be covered in the next sections How ever because of space 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 nu
65. ndow The following tools are currently defined Eraser By selecting the eraser tool the cursor turns into an eraser which can be used to erase any part of the image screen Dou ble clicking the eraser erases the entire screen The eraser Ch 5 Windows p 42 MacTempas User Manual EP A Q Sr LA FA A erases the screen with the current background color Text Tool Clicking on this tool turns the cursor into an i beam cursor which can be used to select an insertion point for text To set the insertion point for text to be typed in the image window click the mouse at the desired point The Font Size and style of the text is determined from the menu bar The text will be drawn in the current foreground color and can be left canter or right jus tified Magnifying Glass When selected the cursor turns into a magnifying glass which can be used to zoom in on a selected part of the display Each time the mouse is clicked in the image window the image is zoomed by a factor of two By holding down the Option key while clicking the image will be zoomed out by a factor of 1 2 for every click Double clicking the magnifying glass returns the image to normal 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 sibl
66. od 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 W 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 87 MacTempas User Manual with the central beam Under the two assumptions above the image intensity in the WPO approximation can be written as B x y 1 iot x y such that the image intensity is low in areas of high electrostatic potential the location of atoms Atoms of higher atomic num ber show up as larger and darker regions in the image This type of image will often be similar in appearance to images cal culated by a full multislice calculation for equivalent resolution for a thin specimen for Scherzer defocus The WPO approximation is invoked from the menu bar in the same fashion as the multislice calculation The input to the WPO calculation is a starting resolution in A and an ending resolution The steps in resolution can be fixed user deter mined or automatic When automatic steps are chosen the program wi
67. of the description of the electron microscope in figure 1 shows that the projector lens and the intermediate lens or lenses merely magnify the original image I1 formed by the objective lens For the purposes of image simulation we can reduce the TEM to three essential components 1 an electron beam that passes through 2 a specimen and then through 3 an objective lens fig 2 Our next step in describing the electron microscope for image simulation is to move from the geometrical optics description of the TEM to a description based on wave optics In this descrip tion of the microscope we examine the amplitude of the elec tron wavefield on various planes within the TEM and attempt to determine how the wavefield at the viewing screen comes to contain an image of our specimen By treating the electrons as waves and considering our simpli fied electron microscope Figure 2 we see that there are 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 f
68. rad Asi or Stigma SpaceGroup Number Tables Cancer af dj Lans Apr h eju Angew Center afthe Optic amis n amp em Cox J The input also allows for choosing the second setting for a spe cific spacegroup if one exists If no space group is required one should use the space group P1 1 in which case the only sym metry operator is x y z Additional symmetry operators can be entered by opening the dialog displaying the symmetry opera tors Ch 4 Running MacTempas p 32 MacTempas User Manual Set Basis Use this button to bring up the dialog window that enables the input of the atoms in the basis Crystal Parameters tpetimen Parameters Ald Ema Aphapaeg anan Zone anis own BA 2140 Getaldeu anan Seber af Slices pes cuil ci Gamme deg mao Omas 1A 11 ip tbgr ap int Tables ae best pagine mn of Aomen in Baie q Shire Ampl Practices an Symi Gps pe of afore in Lie 2 GT Seren abet 5 Sbcroscege and Lens Parameters Aa Crone Mame a Woitepe kv mm Coreergeace angle mrad Sp rie of deteta DA Cent of Ob Less Aprt Cont of ther Optic Anis Number of Atoms in the Basis This value is the number of independent atom positions in the basis or asymmetric unit of the cell When operated on by the symmetry operators the basis generates all the atom positions within the cell This value is never modified by the
69. ro 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 1 Fortunately 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 complex interfer ence pattern which has the symmetry of the projected 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
70. rom 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 Projected Potential Vp y Object Transmission X so Specimen Specimen Plane ee IA DTA A FIV yo Objective Lens W 7 NI Fa Objective _ Objective Diffraction Lens M Aperture Amplitude 8 Lens Transfer Function exp ix g MN i A 117 Lens Aperture Function i MASI j Imse fy A image anne Wa dna Image Amplitude W x y Fig 2 The simplified 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 functio
71. rred 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 mm Def 560 00 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 o 1l Scattering Vector A Figure 3 Plot of the Contrast Transfer Function for a 200kV microscope with the parameters indicated References 1 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 2 Allpress J G et al 1972 n beam Lattice Images I Exper imental and Computed Images from W4Nb26077 Acta Cryst A 28 528 536 3 Doyle P A and Turner P S 1968 Relativistic Hartree Fock X ray and Electron Scattering Factors Acta Cryst A 24 390 397 4 Cowley J M and Iijima S 1972 Electron microscope References Ch 2 Theory of Image Simulation p 24 MacTempas User Manual 10 11 12 13 image contrast for thin crystals Z Naturforschung 27a 445 451 Gibson J M 1994 Breakdown of the weak phase object approximation in amorphous objects and measurement of high resolution electron optical parameters Ultramicros copy 56 26 32 Howie A 1963 Inelastic scattering of electrons by crys
72. s One can also set a cut off such that diffracted beams with g vectors larger than the cut off will not be displayed O Display Objective lens Aperture O Display Laue Circle Center of the Diff Patt X 470 _ Center of the Diff Patt Y 357 Camera Length mm Divergence Angle mrad 0 850 Min Intensity to display 10 O Display only g lt M Show hkl OQ 2D indexing h k 0 3D indexing h k FA Display d spacings Gaussian Diffraction Spots 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 Ch 6 Menus p 57 MacTempas User Manual Atom Shading Allows the user to select whether atoms drawn should be dis played in color circles or as shaded balls grey Shading Options Halftone Shading Colored Spheres Slice Method Allows the user to select the option to perform a three dimen sional calculation of the projected potential by summing over the third dimension 1 in reciprocal space available RAM Sub slicing amp using a layered structure is generally easier 3D calculation is limited and depends on oa Calulation Options uouousvevebceot srensnncenttsossteetanuveittnisvosusvesistonsiovbue 2D Potential calcul
73. s is limited to 2n 2a along one reciprocal lattice coordinate and to 2m 2b along the other where n m 16 hence parameter 16 Note that MacTempas will choose values of n and m to maximize G max Up to the default value of 2 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 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 G mnax This number can be changed if desired as of course can all the parameters entered in response to the prompts listed in this chapter Set Basis 9 Click on the command to bring up the dialog box for entering the information regarding the number of atoms in the basis We enter the nine different atom positions listed for the basis atoms For each of the atoms in the basis MacTempas requires the chemical symbol x y z coordinates DW factor and occupancy factor From the information given above we use the following information for the nine atoms that are given in the structural basis Chemical Symbol Ca X Y Z 0 0 0 MacTempas User Manual Debye Waller Factor 3 6 Occupancy 1 The data for the first atom include the
74. sion for your machine 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 Before installing the hardware key drag the file TRSecurity found inside the folder MacTempas Folder Put In System Folder Put in Extension Folder to a closed System Folder If you are run ning System 7 or later the file will be automatically placed in the extension folder within the System Folder Make sure you install the init TRSecurity before installing the hardware protec tion key Shut down the computer With the computer turned off unplug the keyboard from the back of the computer and plug the hardware key into the freed up port in the back of the computer Connect the keyboard cable to the other end of the hardware protection key making sure that all connections are good Restart the computer Before MacTempas can be run on a new system you must run the program MacTempasKey Enter your name and affiliation as appropriate This program is not required again unless the program is moved to another machine At times when the oper ating system is changed it may also be necessary to run the Ch Installation p 1 MacTempas User Manual installation program once more If this happens a message will come up
75. t information Ch 8 Sample Calculation p 83 MacTempas User Manual Running the Cal culation Displaying the Results Ch 8 Sample Calculation p 84 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 inthe parameters menu to check that all atom parameters have been entered correctly At this stage it is also worthwhile getting MacTempas to display a model of the struc ture by going to the Commands menu and clicking on Draw the Unit Cell When we are satisfied that all data are correct we run the simu lation by clicking on Full Calculation in the calculate menu Note that MacTempas displays the current status of the calcula tion in the Status Window First MacTempas computes the 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 b
76. 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 computational methods in high resolu tion transmission electron microscopy Ultramicroscopy 21 47 62 Self PG O Keefe MA Buseck PR Spargo AEC 1983 Practi cal computation of amplitudes and phases in electron diffrac tion Ultramicroscopy 11 35 52 Van Dyck D 1980 Fast computational procedures for the sim Ch 11 HOLZ Interactions amp Sub slicing p 100 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 computat
77. the string structurename isa 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 PHSGRT subprogram from the information stored in lt structurename gt _ at itcontainsthespecimenpotential Ch 3 Introduction to MacTempas p 28 MacTempas User Manual 3 4 5 6 in the direction of the electron beam This is a BINARY file of type Real 4 The first 80 bytes consists of record information and the data starts at byte 80 The first line of data contains the data for the bottom line of the image since the coordinate system for MacTempas is at the lower left corner of the image unit cell Thus if the data is imported into a program for viewing the image will appear flipped lt structurename gt mout is the result of running the MSLICE subprogram using the data in lt structure name gt pout withthosein lt structurename gt at itcon tains the exit surface wavefunction at one or more selected specimen thicknesses This is also a BINARY filewiththesamestructureas 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 subprogram to apply the effects of the micro scope par
78. ting 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 W File Edit View Folders Documents far ER Example Structures aw capar pari AE agir E kmi pou JIE San Jun 2a 177 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 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 94 MacTempas 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 Defined Phasegratings Name Az Name Az Name Az M1 copper 3 61 2 inp 4 50 Specimen 11 1 1 1 2 2 2 2 2 1 1 1 1 Deposit Insert Repeat 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 La
79. to 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 YH 6 H ioV H T 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 H we get that the FT of the wavefunction is for simplicity V Vp H 6H ioV 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 IH FT w y YY H H hn Z SCH icACH VE Je 5H H ic ACH HVH H jet 1 6 H 20A H V H sin yH 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 transfe
80. unction 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 ProjectedPotential calculationconsidersonlythespec imenstructure ExitWavefunctions s calculation treats the interaction of the specimen with the electron wave and the Image s calculation simulates how the wave leaving the specimen interacts with the lens system of the electron micro scope Once a simulation has been made any additional simula tion will usually not require a full re calculation any change in microscope parameters will not affect the results of the Pro jecte otential and ExiWavefunctions s calculationsand 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 putof ProjectedPotential but ExiWavefunctions 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 storesallthestructureandmicro scope information needed to run the simulation This information is derived from user input and the supplied data files In particular
81. urce Window Operating on the Projected Potential will yield the structure factors operating on the Exit Wavefield will yield the diffraction pattern and operating on the image will give the Power spectrum of the image Unit cells Use this to specify the number of unit cells that should be dis played The input requires the number of cells in the a direction and b direction The number of unit cells stay in effect until MacTempas User Manual explicitly changed Enter the of cells inthe x andy 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 As Enter the zoom factor 0 240 51 5 22 8 etc with the number of unit cells to be displayed the zoom factor stays in effect until explicitly changed Histeq This operation performs a histogram equalization on the source Only a final object of the type image is suitable for histogram equalization Histog Ch 5 Windows p 47 MacTempas User Manual Ch 5 Windows p 48 Selecting this operation will produce the histogram of the source Display Before the result of operating on a selected source is displayed in the image window DISPLAY must have been selected Choosing the source and operations only selects the functions to be performed When DISPLAY gets activated the functions get executed
82. 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 Snel Parameters Specimen Parameters ADA Pamo senaqegy 00 anna pevettil DPA 280 Beta ien ETE Sumber al Slices per rell C Sed Gammap eg 9000 Gmax 4 1 Sparegrnup pla Tables a Thicke egi end pikoms is Basis 9 Shire of ithe Opa Er hrs of atama ia Utell 3 Sofdifierentstoms S yd L NTI k rror opr and Less Parcamelers rr Merescope Name Ama ET ottage EV cx pmm i Convergence angle mrad oe hat LS Spread of defocus AJ pelea hrel A elem Rae La Defecustbegincend Ay 5 0 TEA Rar ot APO NE Mag Cant af Obj Lens aart ruon nen ane me Cent af le Optic Awis LEO iai ae we eyed here 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 Crystal Paramebers Apt eyresp fink tables of Aom in Baus a 2 ar yin ge pr of aon in Lie J E afere Mbit 5
83. ve Lens Defocus 200 800 200 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 tion that is underfocus is negative Aperture Radius 0 67 The value for the radius of the objective aperture should corre spond to the radius in reciprocal Angstrgm 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 inpu
84. vefunction 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 y x yz dr expl io Vix 3 2 dz W x y z q x YW y Z 17 The function q x y is referred to as the phasegrating Subsequently the wavefield is propagated in vacuum to the plane t z dz according to W x y z dz expl iodzV W x y 2 18 The last equation represents a convolution in real space and is Ch 2 Theory of Image Simulation p 16 MacTempas User Manual solved more efficiently in Fourier space 9 where the equation transforms to W H z dz exp irAdzH Y EH z pH dz H z 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
85. yered Structure p 95 MacTempas User Manual Ch 10 Creating a Layered Structure p 96 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 distance A multislice computation in which every slice is identical con tains no information about the variation in structure along the incident beam direction and includes scattering interactions with only the zero order Laue zone ZOLZ layers For struc tures with short repeat distances in the beam direction such a computation is adequate since the Ewald sphere will not approach the relatively distant high order zones Identical sub slices with n sub slices per unit cell repeat distance For structures with large repeats in the beam direction

MacTempas-Manual - Total Resolution

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