- Josephsmith
Contents
1. Fourier transform Multislice For larger arrays and thus larger numbers of diffracted beams it is faster to compute the multislice by recasting A1 into a form where the convolution is replaced by two Fourier transforms and a multiply operation as was done by early users of mul tislice in the Melbourne group Then 50 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory a Q 0 2 n 1 k i DN 2 0 1 3 2 4 F k Q k k 2 M 4 1 3 0 2 1 0 2 1 vU 1 0 pU 0 1 0 1 1 2 Y 1 0 2 3 2 1 2 2 1 1 0 0 1 1 2 2 b HE ei sid 2 1 0 1 2 43 2 1 0 1 2 3 4 2 0 2 1 2 2 2 3 2 4 1 1 1 0 L1 1 2 1 3 0 2 0 1 0 0 0 1 0 2 F k Q k k 1 3 1 2 1 1 1 0 1 1 2 4 2 3 2 2 2 1 2 0 2 1 0 1 2 F k Q k k k do Fig Al Convolution description of multiple scattering In order to include all scattering contributions to the dynamic electron wavefield Y k the phase grating coefficients Q k must extend out twice as far in re ciprocal space as do the coefficients of the wavefield For the five depicted diffracted beams P k where Ikl 2 1 0 1 2 the convolution requires nine phase grating coefficients Q k where Ikl 4 to 4 a sketch of the contributions to the five diffracted beam directions note that e g the contribution of the incoming 2 beam to the outgoing W 2 beam requires the presence of the Q 4 phase grating coeffi cient b Delta function representation2. 16 Objective Lens Back Focal Objective Dffraction d Plane Aperture Amplitude Lens Transfer Function exp Hy Lens Aperture Function Ag Image Image Amplitude Plane Fig 2 The simplified TEM left and the calculations required for an image simulation right The three principal planes are marked 7 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 The specimen exit surface In order to know the exit surface wavefield we must know with which physical prop erty of the specimen the wave interacts and describe that physical property for our par ticular specimen Cowley and Moodie 1957 showed that the interaction of an electron beam with a spec imen could be described by the so called multislice approximation in which electrons propagate through the specimen and scatter from the crystal potential the electron scat tering is described by the so called phase grating function a complex function of the potential and the electron propagation is computed with a propagation function depen dent on the electron wavelength 1 4 Simulating TEM images The problem of simulating images thus becomes a problem of computing the electron wavefields at the three microscope planes Currently the best way to produce simulat ed images is to divide the overall calculation into three parts 1 Model the specimen structure to find its potential in the direction of the incident beam 2 Produce the exit surface
3. ADJ CNT Brings up the SET CONTRAST menu page 44 for selection of contrast parameters before display FFT Performs a fast Fourier transform on the selected function and squares the result before display Performed on the image FFT produces the image power spectrum or optical diffractogram HUN CLS Enables input of the number of unit cells desired in the displayed image ZOOM Asks for a factor to use in magnification the image DISPLAY Directs the output to the display device EXECUTE Takes the selected function applies the selected operations and outputs the picture CANCEL Cancels the selected options usually because one was selected by mistake 40 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The SET UP Menu NCEMISS SH SET NOERASE ERASETHE DISPLAY SET MONTAGE WEITE TEST ON THE DISPLAY SET POS STORE FARTS OF THE DISPLAY M ONTAGE SPACE DISFLAY STORED IMAGE IHT ABS SCALE PRINT 4 STORED IMAGE ABS SCALE PG REAL SP LIST STORED IMAGE FILES HO APERTURE SET CONTRAST FOR LASERVFRITER TITLES SET DIY ANGLE FOR DP 3D FPOT SLICE OVERLAY ATOMS SET MIN INTENSITY LENS FIXED SET MIN INT TO DISPLAY FEINT SET CAMERA LENGTH REL FHASE INDEX II BINARY FILE CHANGE CENTER OF DIFFE QUT FILE READ THE CURSOR POSITION CUST
4. ncemss return this action will produce the SINGLE LAYERED menu page 12 by opening two win dows on the workstation screen one being the menu control window the other the im age window 14 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The SINGLE LAYERED Menu 55 SINGLE STRUCTURE LAYERED STRUCTURE 15 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 2 The SINGLE LAYERED menu The first menu encountered by the user on starting to work withNCEMSS consists of three labeled boxes Any one of these boxes or buttons can be activated by using the mouse to move the screen cursor into the area of the screen within the box and then pressing the LEFT button on the mouse At the lower right of the window is the EXIT box or button Selecting this box will cause the program to exit and return to the system prompt The two major boxes allow the user to specify a choice of either a SINGLE STRUC TURE calculation or a calculation of the images arising from a LAYERED STRUC TURE A SINGLE STRUCTURE calculation is one where the specimen structure repeats regularly in thedirection of the electron beam and is the usual type of image simulation A LAYERED STRUCTURE calculation is a simulation in which the spec imen structure is built up of a number of different structural layers in the electron beam direction so that the computation requires the use of more than one crystal structure file Selectin
5. ture Normally of course the use of the B 4 option is to be preferred as it produces a superior result and is far easier to use Other methods Van Dyck has proposed other methods to include the effects of HOLZ layers including the second order multislice with potential eccentricity Van Dyck 1980 and the improved phase grating method Van Dyck 1983 Tests of these procedures show that the extra computation involved in using potential eccentricity may be worthwhile but that the improved phase grating method diverges too easily to be useful 60 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 61 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 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 resolution transmission electron microscopy Ultrami croscopy 21 47 62 Self PG O Keefe MA Buseck PR Spargo AEC 1983 Practical computation of am plitudes and phases in electron diffraction Ultramicroscopy 11 35 52 Van Dyck D 1980 Fast computational procedures for the simulation of structure im ages in complex or disordered crystals A new approach J Microscopy 119 141 152 Van Dyck D 1983 High speed computation techniques for the simulation of high res olution electron micrograp
6. Appendix BHOLZ interactions 57 B 1 Identical slices with only one sub slice per unit cell repeat distance 57 B 2 Identical sub slices with n sub slices per unit cell repeat distance 57 Sub slices based on atom positions 57 B 4 Sub slices based on the three dimensional potential 57 B 5 NCEMSS sub slicing 59 B 6 Other methods 59 NCEM MSD Lawrence Berkeley Laborator Figures The SINGLE LAYERED Menu The FILE LIST Menu The MAIN Menu The MAIN Menu The MAIN Menu The BASIS Menu The SYMMTRY OPERATOR Menu The Atom List Menu The ATOM DISPLAY Menu The AMPLIT Menu The IMAGE DISPLAY Menu The SET UP Menu The SET UP Menu The Set Contrast Menu lil NCEMSS User Manual 12 14 16 18 20 22 24 26 30 32 36 38 40 42 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual NCEMSS a program for simulation of HRTEM images 1 1 1 1 2 Introduction to the simulation process Why simulate images Image simulation grew out of an attempt to explain why electron microscope images of complex oxides sometimes showed black dots in patterns corresponding to the patterns of heavy metal sites in complex oxides and yet other images sometimes showed white dots in the same patterns This first application was therefore to characterize the exper imental 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 ou
7. OFERATOR 1 XN 2 xyrl2zrl 3 H L 4 xTlyrli z a X V 3 T 8 9 u V LIZ z 172 X l 2 y 12 x 12 w 12 3 XW 3 xgrli 3 L2 z l 7 irl x 1 2 r Li z X V 3 x y lt zrll2 H LIZ y 3 02 xrTr1 2 v 1 2 z ZG zl 24112 mr z Xr Lit are 1 2 NCEM MSD Lawrence Berkeley Laboratory The S YMMTRY OPERATOR Menu 55 SYMMETRY OFERATOR 21 22 23 24 25 26 ar 28 29 30 31 32 33 34 35 36 37 38 39 40 Z X V zrli x 1 zril x lov a H lit 1H 2 47 z 2 x 13 z LIL u Lo 3 x l2 a Z 8 7 a Lx yti 52412 x 172 Y 3 x LIL vrl Yu yati x 172 41 z K 2 v Z X y lid z LE X gali il 122 102 CHANGE SY MMOF ADDSYMMOF DELETE SY MMOF EETUEN 27 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 6 SYMM OP menu The SYMM OP menu shows a list of the symmetry operators generated by the chosen space group or input by the user when a space group number of zero is entered in the MAIN menu see page 20 The right hand control boxes are used to page through long lists of symmetry operators CHANGE Any operator may be replaced by activating the CHANGE box clicking the mouse over the appropriate line and entering the new operator ADD SYMMOP Activating this control box enables the user to add a new operator to the list DELETE SYMMOP Activating this box then placing the cursor o
8. can be saved and printed at any time later NORM MONT lt gt CUSTOM allows extra control on the layout of montaged images 44 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The Set Contrast Menu MEEMSS SH SET BLACK WHITE CONTRAST 4 BRIGHTHESS DECE INCE 45 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 14 The SET CONTRAST menu When the ADJ CNT box of the IMAGE DISPLAY menu page 38 is activated it brings up the SET CONTRAST menu This menu displays the current contrast and brightness settings graphically The straight line shows the mapping of the image in tensity values horizontal axis into the displayed output intensity values vertical axis For a one to one mapping the values of contrast vertical bar graph and brightness horizontal bar graph should be 1 0 and 0 5 respectively To increase or decrease the contrast used to display the image tap the mouse with the cursor positioned over the UP or DOWN boxes underneath the vertical bar graph The contrast transfer graph will pivot about its mid point as the contrast is changed providing a plot of how input grey levels are mapped into output greyscale levels Note that a contrast value of less than zero will produce a negative image To increase or decrease the image brightness use the INCR and DECR boxes to move the mid point of the contrast transfer graph to the left or right The contrast transfer curve may b
9. identical to the command above LIST STORED IMAGE FILES sends the command Is im to the operating sys tem The output list of stored image files is displayed in the terminal session window SET CONTRAST FOR LASERWRITER allows the user to change the values of brightness normally 0 5 and contrast normally 1 0 of the printed image SET DIV ANGLE FOR DP use this to change the size of the displayed diffraction spots in case the size is not optimal for viewing IMAGE ONLY lt gt OVERLAY ATOMS controls whether atom positions are over layed on the image or not AUTOSCALE FIXED use this to either let the computer choose black and white lev els automatically or to use fixed values input by the user DISPLAY lt gt PRINT in the display position anything DISPLAYED goes to the im age window In the PRINT position the actual numeric data is sent to a file in a format that depends on the setting of the switch ascii binary below REL PHASE lt gt PHASE determines if the phases reported for diffracted beams in clude the phasechange due to the mean inner potential of the crystal ASCII FILE lt gt BINARY FILE determines if the numeric output data for an image projected potential or complex wavefunction is in ascii or binary OUT gt PRINTER lt gt OUT gt FILE normally when you reroute the output to the print er the program executes the command laserprinter ps Selecting OUT gt FILE will create a named postscript file that
10. of sub slices In this way the variation of the specimen structure in the electron beam direction is included in the simulation Of course it takes longer in 3 D SET MIN INTENSITY LENS sets the minimum diffracted beam intensity that will be considered to pass through the objective lens this minimum can be set to exclude very low intensity beams from large defect unit cells and so speed up the image calcu lation SET MIN INT TO DISPLA Y FFT determines down to what intensity diffracted beams will be drawn in a diffraction pattern display 42 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory he SET UP Menu 55 SET NOERASE ERASETHE DISPLAY T SET MONTAGE WRITE TEXT OM THE DISPLAY SET POS STORE FARTS OF THE DISPLAY MONTAGE SPACE DISPLAY STORED IMAGE IHT ABS SCALE PRINT A STORED IM AGE ABS SCALE PRINT THE SCREEN PG REAL SF LIST STORED IMLAGE FILES NG AFERTURE SET CONTRAST FOR LASERVFRITER TITLES SET DIV ANGLE FOR DF 3D POT SLICE OVERLAY ATOMS SET INTENSITY LENS FIXED SET MIN INT TO DISPLA Y FFT JISPL PRINT SET CAMERA LENGTH FEL PHASE INDEX ASK BINARY FILE CHANGE CENTER OF DIFTE FT OUT gt FILE READ THECURSOR POSITION CUSTOM RETURN 43 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual SET CAMERA LENGTH is used to adjust the magnifi
11. the current menu The rightmost box is the RETURN box and is used to go back to the previous menu Note that many menus have this facility with the RETURN box situated in the bottom right corner of the menu The bottom left box is used to notify NCEMSS that the user wishes to use one of the displayed structure files Moving the cursor to this USE DIS PLAYED FILE box and selecting it by clicking the mouse button removes all the other boxes and allows the user to select one of the displayed files by moving the cursor to the correct filename and clicking the mouse button Selecting a structure filename causes NCEMSS to read the file and display its parameters in the PARAMETER menu often referred to as the MAIN or CONTROL menu because it is the one from which the NCEMSS computation is controlled by the user The CONTROL menu is shown on page 16 The CREATE NEW FILE box is selected when the user desires to input a new struc tural file Selecting this box with the cursor causes NCEMSS to ask for a unique name for the structure Entry of the name then produces a PARAMETER menu with no pa rameter values and a series of prompts from NCEMSS explaining each parameter needed for input HELP If this is your first use of NCEMSS it may be helpful to try moving the cursor to each box in turn asking for the HELP facility by clicking the CENTER button on the mouse as each box is reached The HELP facility is available for every command box on every menu a
12. 61 3 61 Grax 2 00 of Sytometey Operators 197 No of atoms in the basis 1 Microscope Cs 2 30 Del 100 00 Th 0 60 Volt 1000 00 Cent of Laue circle h 0 00 k Defocus 3004 3009 1500 Aperture Radius 0 70 Cent of Obj Apit b 0 00 k NCEM MSD Lawrence Berkeley Laboratory The MAIN Menu NEEMSS SPACE GROUP 225 ALFHA 90 00 BETA 90 00 GAMMA 90 00 Zone Axis 001 No slices per umitcell 1 Ma of different ators 1 Foil Thickness 401401120 Amplit output for plotting ves The indicesae h k 1 Cent of Optic Axis h 0 00 k 0 00 CHANGE SHOW BASIS PHSGET IMAGE DISPLA Y CTF RUN SHOW ATOMS MSLICE AMPLIT WIEW FILE RETURN 23 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 4 2 Control boxes CHANGE When the CHANGE box is activated by clicking the mouse with the cursor within the CHANGE box boundaries any parameter value may be changed simply by moving the cursor to the parameter position clicking the mouse and entering the new value from the keyboard in response to the NCEMSS prompt To leave CHANGE mode deactivate the CHANGE box by clicking the mouse with the cursor once again positioned over the CHANGE box RUN Activating the RUN box will cause NCEMSS to run an image simulation for the current values of the parameters shown in the PARAMETER menu NCEMSS will au tomatically run the least required computation starting wit
13. AY Menu N ENSS LASERPRINTER CHANGE DEFAULTS AND RUM MISC FUNCTIONS F TENTIAL HISTOGE FUN CLS EXECUTE HIST EQ DIFFE PAT ADJ CHT UNUSED DISPLAY CANCEL RETURN 39 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 12 The IMAGE DISPLAY menu When DISPLAY is selected in the MAIN or CONTROL menu page 16 NCEMSS brings up the IMAGE DISPLAY menu This menu consists of 21 control buttons The top three are used to select various options that remain until reset The left hand column is used to select the function to be displayed Other control boxes select the actions to be taken WORKSTATION LASERPRINTER These two boxes are mutually exclusive and are used to select the output device for the image display CHANGE DEFAULTS AND RUN MISC FUNCTIONS This control is used to bring up the SET UP menu page 40 where various imaging options and defaults may be set POTENTIAL Selecting this input produces a display of the unit cell potential project ed in the incident electron beam direction EXIT WF The electron wavefield at the crystal exit surface may be displayed by se lecting this input function DIFFR PAT Selects the diffraction pattern for display IMAGE Selects the current image for display HISTOGR Produces a histogram of the intensity values in the function selected from column one HIST EO Stretches the image contrast by performing a histogram equalization oper ation before display
14. F SYMMETRY OPERATORS If a space group has been selected the correct value for this parameter will have been entered by NCEMSS If a value of zero has been entered for the SPACE GROUP then the correct number of operators must be entered here NO OF SLICES PER UNIT CELL For unit cells with large repeat distances in the beam direction moderate values of GMAX may allow the Ewald sphere to approach the so called pseudo upper layer line that the multislice allows at the reciprocal of the chosen slice thickness In this case NCEMSS will sub divide the slice into two or more subslices How this is done depends upon the potential setting chosen in the SET UP menu page 40 20 NCEMSS User Manual INPUT FOR copper A 3 61 B 341 C Sal Grax 7 00 Ho of Sytumetey Operators 102 No of atoms in the basis 1 Microscope Cs 780 Del 100 00 Th 0 00 Wolt 1000 00 Cent of Lave circle h 0 00 k Defocus 300 300 1500 Aperture Radius 0 70 Cent of Obj amp prt h 0 00 k NCEM MSD Lawrence Berkeley Laboratory The MAIN Menu NEEMSS SPACE GROUP 225 ALFHA 90 00 BETA 90 00 90 00 Zone Axis 001 Mo ofslicespeyunitcell 1 Mo of different atoms 1 Foil Thickness 401401120 Araplit output for plotting ves The indicesave bh 1 Cent of Optic Axis h 0 00 k 0 00 CHANGE SHOW BASIS FHSGET IMAGE DISFLAY CTF RUN SHOW ATOMS MSLICE AMPLIT WIEW FILE
15. Laborator NCEMSS User Manual 3 9 The ATOM DISPLAY menu When DISPLAY is selected in the ATOM LIST menu page 26 most of the control buttons are replaced to produce the ATOM DISPLAY menu The ATOM DISPLAY menu has only four control boxes UNIT CELL Activating this box splits it in two Selecting either option causes NCEMSS to ask for the viewing direction indices to be input from the keyboard NCEMSS then draws the unit cell either with or without perspective page 32 NEW UNIT CELL As for UNIT CELL but for drawing any new unit cell produced with the BUILD menu page 28 3 D ATOM DISPLAY This control box initiates a three dimensional atom drawing routine based on a routine written by W O Saxton It can be used to produce publica tion quality atom model drawings with a wide range of different lighting conditions This procedure is not implemented on most versions of NCEMSS specifically all unix version RETURN Return to previous ATOM LIST menu 34 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The AMPLIT Menu 55 This is the output file for copper This file contains amplitudes and phases for the bears 800 4 Plot Amplitude 200 E Plot Intensity 220 r Supericnpose Plots Individual Plots r r r 3 4 F Plot Phases OR AY CANCEL 35 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 10 The AMPLIT menu On activating the AMPLIT contro
16. OM RETURN 41 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 13 The SET UP menu Opting to change the various defaults by selecting the CHANGE box in the IMAGE DISPLAY menu page 38 brings up the SET UP menu This menu is used to change the default settings of some hard parameters and to manipulate the image display The nine two way switches on the left of the menu are normally set to default to the left hand setting SET ERASE lt gt NOERASE When ERASE is set the display screen will be erased be fore each new image is displayed except see MONTAGE SET NOMONTAGE lt gt MONTAGE When NOMONTAGE is set only one image will be displayed for each activation of the EXECUTE command from the IMAGE DISPLAY menu page 38 When MONTAGE is set then a full through thickness and or through focus series of images will be displayed at one EXECUTE command as suming the calculation was carried out for such a series by setting the appropriate pa rameter values in the PARAMETER menu page 16 Note that aMONTAGE will erase the screen before display regardless of the ERASE setting SET NOREO POS lt gt REO POS When NOREQ_POS is set individual images will be written to the center of the display screen assuming that NOMONTAGE is set When REQ_POS is set the user will be prompted for the coordinates at which the im age is to be displayed NOMONT SPACE lt gt MONTAGE SPACE is used to set the desired spacing be
17. RETURN 21 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual NO OF ATOMS IN THE BASIS This value is the number of independent atom po sitions 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 NO OF DIFFERENT ATOMS This value is the number of different types of atoms in the specimen structure difference is due to a different Debye Waller factor or differ ent atomic number MICROSCOPE The type of electron microscope used to generate the imaging param eters If a type known to NCEMSS is entered then NCEMSS provide values for CS the spherical aberration coefficient of the objective lens in mm DEL the halfwidth of a Gaussian spread of focus due to chromatic aberration in Angstrom units TH the semi angle of incident beam convergence in milliradian If the type of microscope is unknown to NCEMSS the above values must be entered seperately or the data file MI CROSCOPES DAT may be edited to include an appropriate microscope type FOIL THICKNESS The thickness of the specimen foil may be entered as one single number representing the thickness in Angstrom units or as a series of thicknesses rep resented by the upper and lower bounds and a thickness step e g 100 50 250 will cause NCEMSS to store the exit wavefield at specimen thicknesses of 100 to 250 in steps of 50 a total of four thicknesses AMPLIT OU
18. Return to previous FILE LIST menu 24 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory he BASIS Menu NCEMSS p NAME A z Lh acc 1 1 Cu 0 0000 0 0000 0 0000 0 5000 1 00 PAGE PAGE PAGES CHANGE ADD DELETE SHOW SY RIB OF RETURN 25 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 5 The BASIS menu The BASIS menu shows a list of the atom positions making up the basis when operated upon by the symmetry operators the basisyields the full set of unit cell atom positions The BASIS menu displays the atom positions showing the chemical symbol NAME for each atom its fractional coordinates X Y Z the Debye Waller factor and the site occupancy Subsequent pages of long lists can be viewed with the three right hand con trol boxes CHANGE The value of any parameter can be changed by activating the CHANGE box then moving the cursor to the parameter position clicking the mouse and entering the replacement value ADD Additional atom positions may be added by activating the ADD box and enter ing parameter values in response to prompts DELETE Activating the DELETE box then moving the cursor to the appropriate line will delete the line SHOW SYMM OP A list of the symmetry operators may be obtained by activating this control box in order to bring up the SYMM OP menu page 24 RETURN Return to previous MAIN menu 26 NCEMSS User Manual SYMMETRY
19. TPUT FOR PLOTTING A number of diffracted beams may be select ed for plotting of their intensity and phase variation as a function of specimen thickness If YES is answered to the NCEMSS prompt the number of beams and their indices may be entered VOLT The electron microscope accelerating voltage in kilovolts CENT OF LAUE CIRCLE Specimen tilt is specified by entering the center of the Laue circle in units of the h and k indices of the projected two dimensional reciprocal space unit cell DEFOCUS The defocus of the objective lens is entered in ngstrom units with a neg ative value representing underfocus weakening of the lens current As for the FOIL THICKNESS parameter a single value of defocus may be entered or a range specified by the upper and lower bounds and the interval 300 200 1100 means defocus values of 300 500 700 900 and 1100 APERTURE RADIUS The radius of the objective aperture is specified in reciprocal Angstrom units CENT OF OBJ APRT The center of the objective aperture is defined in units of the h and k indices of the two dimensional reciprocal space unit cell as for the Laue circle center CENT OF OPTIC AXIS The center of the optic axis of the electron microscope is specified 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 22 NCEMSS User Manual INPUT FOR copper A 361 3
20. Users Guide to NCEMSS The NCEM program for the simulation of HRTEM images Program written by Roar Kilaas Users Guide Written by Michael A O Keefe amp Roar Kilaas National Center for Electron Microscopy Materials Science Division Lawrence Berkeley Laboratory University of California Berkeley CA 94720 This work was supported by the U S Dept of Energy under Contract No DE AC03 76SF00098 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual Section Page 1 Introduction to the simulation process 1 1 1 Why simulate images 1 1 2 Describing the transmission electron microscope 1 1 3 Simplifying the description of the TEM 3 1 4 Simulating TEM images 5 2 Introduction to NCEMSS 7 2 1 The three simulation steps 7 22 NCEMSS files 7 3 Running NCEMSS 11 3 1 Getting started 11 3 2 The SINGLE LAYERED menu 13 3 3 The FILE LIST menu 15 3 4 The PARAMETER or MAIN or CONTROL menu 17 3 4 1 Parameters of the PARAMETER menu 17 3 4 2 Control boxes 21 3 5 The BASIS menu 23 3 6 The SYMM OP menu 25 3 7 The ATOM LIST menu 27 3 8 The BUILD menu 29 3 9 The ATOM DISPLAY menu 31 3 10 The AMPLIT menu 33 3 11 The CTF plot 35 3 12 The IMAGE DISPLAY menu 37 3 13 The SET UP menu 39 3 14 The SET CONTRAST menu 43 3 15 The SET LAYERS menu 45 Appendix AMultislice Size PhaseGrating Size and Maximum G 47 Reciprocal space multislice 47 2 Fourier transform Multislice 47 Real space multislice 49 A4 Storage requirements 51
21. a two dimensional calculation is selected NCEMSS will use one slice per cell if the cell repeat distance in the beam direction is small B 1 If the repeat dis tance is too large for one slice per unit cell NCEMSS will avoid pseudo upper layer lines by producing n identical sub slices B 2 When a three dimensional calculation is selected 3D POT SLICE activated NCEMSS uses a sub divided three dimensional potential B 4 when the repeat dis tance 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 MAIN menu p 16 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 itis modeling will interact only very weakly with the HOLZ reflections Use of the LAYERED STRUCTURE option p 12 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 slicing based on atom positions B 3 Thus the user could create a number of sub slices by assigning selected atoms to different struc ture files then forming a phasegrating for each sub slice and using the SET LAYERS menu p 46 to specify how the sub slices are to be used to describe the specimen struc
22. al space method for dynamical electron diffrac tion calculations in high resolution electron microscopy II Critical analysis of the de pendency of the input parameters Ultramicroscopy 15 41 50 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 Gronsky R 1983 Real space image simulation in high resolution electron microscopy Ultramicroscopy 11 289 298 Kilaas R 1987 Interactive software for simulation of high resolution TEM images Proc 22nd MAS R H Geiss ed Kona Hawaii 293 300 and Kilaas R 1987 In teractive simulation of high resolution electron micrographs In 45th Ann Proc EMSA G W Bailey ed Baltimore Maryland 66 69 Ishizuka K Uyeda N 1977 A new theoretical and practical approach to the multislice method Acta Cryst A33 740 749 O Keefe MA 1972 Lattice images of large unit cell oxide crystals by n beam theory M Sc thesis University of Melbourne O Keefe MA Buseck PR Iijima S 1978 Computed crystal structure images for high resolution electron microscopy Nature 274 322 324 O Keefe MA Kilaas R 1988 Advances in high resolution image simulation Scan ning Microscopy Supplement 2 225 244 Self PG O Keefe MA Buseck PR Spargo AEC 1983 Practical computation of am plitudes and phases in electron diffraction Ultramicroscopy 11 35 52 Van Dyck D 1983 High speed comp
23. al space wavefield array or set of diffracted beams Y k of 2n 1x2m 1 terms and a reciprocal space propaga tor array P k of 2n 1x2m 1 terms An equivalent parameter n m FFT multislice equation A2 requires a real space phase grating array q x of 2 x2 terms an electron wavefield array W k of 2 x2 terms and a reciprocal space propagator array of 2 x2 terms For a real space parameter n m multislice equation A3 both the y x and q x arrays need to hold 2 x2 terms whereas p x may be as small as thirteen Kilaas amp Gronsky 1983 giving a total requirement of slightly over 2x2 terms In imple menting the real space multislice it is important that the 2 x2 q x array should be formed from a full 2 x2 Q K terms whereas the 2 2 array should be formed from only 2 x2 W k terms in order to include correctly all the physical scattering contributions to each diffracted beam and to avoid aliasing problems fig A1 Any correctly implemented multislice of size 2 x2 parameter n m thus in cludes the effects of only 2 x2 diffracted beams This is true for all three formula tions of the multislice the reciprocal space method equation Al the FFT method equation A2 and the real space multislice equation A3 54 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 55 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual Coene W Van Dyck D 1984 The re
24. at only the same number of diffracted beams was used in Y k with the outer 5 9 of the diffracted beam array reset to zero after every slice A better method was to ensure that q x was formed from a Q k that extended out to twice the scattering angle as Y k and to reset the outer 3 4 diffracted beams to zero after each slice This latter method conforms to the physics of the scattering pro cess fig A1 and proved to yield the same results as the reciprocal space multislice A multislice program using this method was incorporated into the SHRLI81 suite and this method is used in the NCEMSS multislice program O Keefe and Kilaas 1988 Real space multislice A third method of computing the multislice is to carry out the calculation com pletely in real space this is an alternative to computing in reciprocal space as in equa tion Al or in both real and reciprocal space as in equation A2 Fourier transformation of Al gives 52 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 53 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual A 4 Vid 0 00 0 A3 In this formulation the real space wave function yn x is convolved by a real space propagator p X and the result multiplied by the real space phase grating Van Dyck 1983 has developed this method and shown that the convolution step need not be carried out with the full 2 x2 p x array but only with a such smaller array since p x is
25. be operated on directly to remove single slices one at a time by activating this button and clicking on the offending phase grat ing in the sequence 48 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 49 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual Appendix AMultislice Size PhaseGrating Size and Maximum G A 1 A 2 The size of a multislice calculation is defined conveniently by the size of the largest array the Q k or q x array For an array size of 2nx2m the multislice is said to be a parameter n m multislice thus a parameter 16 multislice will have a Q k ar ray size of 256x256 or 512x128 or 1024x64 or 2048x32 or 4096x16 depending upon the shape of the unit cell used in the computation This size parameter must apply to all multislice programs regardless of which of the three current algorithms recipro cal space Fourier transform or real space is employed by the program Reciprocal space multislice As introduced by Goodman and Moodie 1974 the basic recursive form of the multi slice description of dynamical diffraction can be written as Paa DEG POI 0 09 Al That is V k the wave function given in reciprocal space at the exit surface of the n 1 th slice is obtained by multiplying the wave function at the exit surface of the nth slice by P k the propagator for the n 1 th slice followed by the convolution of this result by Q k the
26. cation of the diffraction pat tern display The value is input in mm and has a default setting of 520mm INDEX DIFFR PT is used to index a diffraction pattern On moving the cursor to the selected diffraction spot and clicking the mouse the indices are written next to the spot CHANGE CENTER OF DIFFR PT The center of the displayed diffraction pattern can be changed by selecting this command and using the mouse to click on the desired position in the image display window READ THE CURSOR POSITION reads the cursor position within an image ERASE THE DISPLAY does just that WRITE TEXT ON THE DISPLAY is used to write text at the cursor position STORE PARTS OF THE DISPLAY after selecting this command mark the corners of an area of the display window image to be stored and the image will be saved in a file The user is prompted for a name and the program will automatically add the exten sion at DISPLAY STORED IMAGE use this command to displayed a stored image of the type lt name gt at created by the previous command PRINT STORED IMAGE FILE sends the content of the file lt name gt at to a connect ed laserprinter The program creates a file laserprinter ps and uses the command Ipr laserprinter ps to send the file to the printer It is up to the user to set up the appropriate redirection of the output to a valid printer PRINT THE SCREEN sends the content of the image window to a connected laser printer It otherwise works
27. e focused by a condenser 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 mag nified image of it called the second intermediate image I2 in turn this second inter mediate 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 viewing screen of the TEM by weakening the intermediate lens to place the microscope in dif fraction mode b Simplifying the description of the TEM Consideration of the description of the electron microscope in figure 1 shows that the projector lens and the intermediate lens or lenses merely magnify the original image Il 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 throu
28. e position and size of the objective aperture Thus PHSGRT considers only the specimen structure MSLICE treats the interaction of the specimen with the electron wave and IMAGE simulates how the wave leaving the specimen interacts with the lens system of the electron microscope Once a simulation has been made any additional simulation will usually not require a full re simulation any change in microscope parameters will not affect the results of the PHSGRT and MSLICE programs and only IMAGE will need to be re run any change in microscope voltage or in specimen thickness or tilt will not affect the results of PHSGRT but MSLICE and IMAGE will need to be re run Of course any change in the specimen structure will require the re running of all three subprograms NCEMSS files Supplied files NCEMSS uses four data files to store supplied information not normal ly altered by the user 1 spcgrp dat stores information on all 230 space groups for generation of crystal symmetry operators as required by the input specimen structures 2 scatt dat stores information on atomic scattering factors for the first 98 ele ments 10 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 11 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 microscopes dat stores information on the imaging parameters of various high resolution electron microscopes Note that the user has the option of adding ad ditional microscopes to the
29. e set directly by activating the SET BLACK WHITE box then clicking the mouse after positioning the cursor at one end point of the desired line then clicking at the other endpoint These end points need not be exactly on the lines forming the box enclosing the contrast transfer graph 46 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory NEEMSS mEXXEX eee Construct Phase grating sequence LAYER NAME DZ A LAYERS NAME DEA i 4 00 DEF LAV 2 lay 4 00 DELLAY TOF 0 00 A DEPOSIT INSERT 12 00 16 00 20 00 REMOVE REPEAT 24 00 PHASE GRATING SEQUENCE 1212121212 25 00 32 00 36 00 40 00 40 00 4 47 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 15 The SET LAYERS menu If the LAYERED STRUCTURE option is selected from the SINGLE LA YERED menu page 12 then the SET LAYERS menu appears This menu can be used to con struct a specimen consisting of multiple layers of different single structures DEF LAY To include a structure in the phase grating sequence thatwill comprise the final layered structure use the DEF LAY box and enter the name of the structure as it appears in the FILE LIST menu p 14 Up to six different structures may be used to make up the layered structure Note that aPHSGRT calculation p 21 must be carried out for any structure before it can be included in a layered calculation Also note that as well as existi
30. ecuting on a Digital Equipment Corporation micro Vax II computer un der the VMS operating systems The code has since been ported to other platforms and will run on DEC VMS and Ultrix workstations and on various flavors of Unix running X windows However because of the origin of the program it still an old style layout dictated by the tektronix terminal The program uses two windows One looking like a graphics window displaying push button style menus and one window for displaying graphics output such as images diffraction patterns and views of unit cells The pro gram does not have a modern style interface with a menubar and pull down menus NCEMSS is run interactively at a graphics screen using a mouse or other pointing de vice The graphics screen may be a a workstation console an X window terminal or any computer running as an x window server Commands are issued to NCEMSS by moving a cursor to select an appropriate item from a menu Sometimes selecting an item from a menu will produce another menu with additional options Because of constant changes the menus mentioned in this manual may not always cor respond to the current version of the program for a particular platform The text will be appropriate for the UNIX version of the program Getting started If started from an X terminal first type setenv DISPLAY lt IP address gt to set the out put to the X window terminal Start NCEMSS by typing ncemss followed by a carriage return
31. g the LAYERED STRUCTURE box produces the SET LAYERS menu page 46 Selecting SINGLE STRUCTURE produces the FILE LIST menu page 14 16 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The FILE LIST Menu PERSON AT COMMON FEEY FAGE NEXT PAGE SH inp ltest new test la 530203 500203 qian s n 530 USE DISPLAYED FILE CREATE NEW FILE RETURN 17 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 3 The FILE LIST menu The FILE LIST menu lists the user s structure files on the screen In addition there are four boxes across the top of the menu and three boxes across the bottom The four top boxes control the listing of the structure names the right hand pair allow the user to page through the list displaying subsequent pages of structure file names The top left boxes can be used to select lists of files from either the user s PERSONAL collection of structure files or from a COMMON collection available to all users on the system The files in the COMMON collection can often serve as useful templates for modification to the user s needs On entry to the FILE LIST menu the PERSONAL box is selected automatically To obtain the COMMON list move the cursor to the COMMON box and press the LEFT button on the mouse To return to your PERSON AL file collection move the cursor to the PERSONAL box and press the button The three boxes at the bottom of the menu are used to proceed from
32. gh 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 op tics In this description of the microscope we examine the amplitude of the electron wavefield on various planes within the TEM and attempt to determine how the wave field at the viewing screen comes to contain an image of our specimen By treating the electrons as waves and considering our simplified electron microscope fig 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 with our desired information the electron wavefield at the image plane this wavefield is derived from the wavefield at the focal plane of the ob jective lens by applying the effects of the objective aperture and the phase changes in troduced by the objective lens 2 The focal plane of the objective lens In turn the electron wavefield at the focal plane of the lens is derived from the wave field at the exit surface of the specimen by a simple Fourier transformation NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The Reduced Eletron Microscope Electron Microscope Image Calculation Scaled Structure We Factors Incident Beam Projected Potertial V 2 Specimen Object Transmission
33. h the PHSGRT program only if a structure parameter has been changed since the last run of this data and starting with the IMAGE program if the only change has been in the electron microscope imaging parameters SHOW BASIS This box will cause NCEMSS to display the BASIS menu a list of the atom positions making up the basis page 22 SHOW ATOMS this box will cause NCEMSS to display the ATOM LIST menu a list of all the atom positions in the unit cell page 26 PHSGRT Activating the PHSGRT control box will run the PHSGRT sub program for the current parameter values MSLICE Activating the MSLICE control box will run the MSLICE sub program for the current parameter values IMAGE Activating the IMAGE control box will run the IMAGE sub program for the current parameter values AMPLIT Activating the AMPLIT control box will open up a plotting window page 34 and ask the user which of the stored diffracted beam amplitudes to plot assuming that some diffracted beams were stored by specifying their indices before the MSLICE was run DISPLAY This control box is used to activate the IMAGE DISPLA Y menu page 38 for writing images to the display screen VIEW FILE Activating this control box causes NCEMSS to ask which print file to display then to display it CTF Activating this control box produces a linear image Contrast Transfer Function under the imaging conditions specified by the current parameter values page 36 RETURN
34. hin 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 slic 58 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 59 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual B 5 B 6 es a 128x128x128 potential would require over two million samples to be stored it is possible to derive an analytical expression for the potential within the sub slice z0 Dz projected onto the plane at zO Self et al 1983 It is possible to apply this method rou tinely 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 individ ual non repeating phase gratings Kilaas et al 1987 NCEMSS sub slicing While ensuring that the calculation remains sufficiently accurate NCEMSS will normally choose the simplest and quickest method of specifying how slices are de fined 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 unimportant If HOLZ interactions are important then the user should se lect the 3D POT SLICE box in the SET UP menu p 41 rather than the 2D POT SLICE box When
35. hs J Microscopy 132 31 42 62
36. ing coefficients under their condition the ef fects of aliasing will produce incorrect scattering results if array sizes are not made large enough to produce essentially zero electron amplitude over the outer five nineths of the phase grating and wave amplitude arrays This confusion appears to have arisen when the concept of FFT multislice was introduced to the Kyoto group by a visiting research er familiar with its use in the Physics Department of Melbourne University At Mel bourne it had been found that aliasing occurred when the convolution step of the reciprocal space multislice equation A1 was replaced by a forward inverse Fourier transform sequence This aliasing boosted the amplitudes of the outer beams in the cal culation until knock off parameters were introduced to set the outer beam amplitudes to zero after each slice However even after this procedure eliminated the aliasing ef fect results from the FFT multislice did not exactly match ones from the standard re ciprocal space formulation O Keefe 1972 For this reason the SHRLI80 programs O Keefe et al 1978 continued to use the slower reciprocal space form of the multi slice Experiments with various scattering algorithms Self et al 1983 led to the testing of different ways of avoiding aliasing in FFT multislice It was realized that one such method was by choosing a q x formed from Q k terms that extended only 2 3 of the way to the array edges provided th
37. is used to increment the unit cell in the x direction The INCR Y button does the same in the y direction When the INCR X button is activated NCEMSS will ask for the additional number of repeats to be input from the keyboard Note that the total length of the new cell in the x direction will be the original length plus the number of increments specified DISPLAY This control box is used to display the current defect cell and should be used on entering the menu and after each change made to the defect cell INSERT To insert an atom activate this box and move the cursor to the required po sition Note the changes in the fractional coordinates displayed in the bottom line of the menu as the cursor is moved NCEMSS will prompt for parameter values REMOVE To remove an atom activate this box and move the cursor to the appropri ate atom then click the mouse MOVE To move an atom activate this box move the cursor to an atom position click the mouse move the mouse to the new position note the fractional coordinates and click again CHANGE To change the atomic number of an atom activate this box and click the mouse at the atom position RETURN Return to previous ATOM LIST menu 32 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The ATOM DISPLAY Menu NCEMSS NAME x 0 0000 0 0000 0 5000 0 5000 UNIT CELL NEW UNIT CELL UNIMFLEMENTED RETURN 33 NCEM MSD Lawrence Berkeley
38. itional in formation about a computation is required by the user These files are 6 name p prnt contains information about the way in which the PHSGRT sub program processed the name at data to produce the specimen potential 7 name m prnt contains information about the way in which the MSLICE sub program processed the name pout data with name at data to produce the exit surface wave that is it contains information on the multislice computation Since NCEMSS images are stored in a file for interactive display the user has the op tion of writing any image to the display screen with any selected number of unit cells with any selected value of contrast and brightness and at any selected magnification In addition the user may elect to display i e write to the screen real space functions like the projected crystal potential the exit surface electron wavefunction or a drawing of the atom positions in addition reciprocal space functions such as the diffraction in tensities and the image power spectrum optical diffractogram may be displayed and indexed 12 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 13 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 3 1 Running NCEMSS Note on Platform dependency NCEMSS was originally written for a terminal emulating tektronix 4014 commands The menus were written to the terminal and the images were displayed on a framestore The code was ex
39. l box on the MAIN menu the user will be presented with a list of the diffracted beams for which the complex amplitudes are currently stored as a function of specimen thickness NCEMSS will ask the user to select which beams to plot whether to superimpose the plots and whether to include phase plots The plots will be drawn with thickness horizontal and marked in Angstrom units The various curves can be marked with the appropriate beam indices by using the TEXT option of the SET UP menu page 38 36 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory C 37 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 11 The CTF plot The result of activating the CTF control button on the MAIN menu is a plot of the lin ear image Contrast Transfer Function This function is first plotted as the undamped sine part of the complex phase change due to the objective lens spherical aberration and defocus The damping curves due to the effects of spatial and temporal coherence in cident beam convergence and spread of defocus are plotted next then finally the result of imposing the damping on the sine curve Remember that this curve is only useful for estimating the linear contribution to the image of the diffracted beams exiting a thin crystal one in which they have suffered only essentially kinematic scattering 38 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The IMAGE DISPL
40. nd should provide enough information that you will need to consult this Guide only infrequently 18 NCEMSS User Manual INPUT FOR copper A 3 61 B 341 C Sal Grax 7 00 Ho of Sytoumetey Operators 102 No of atoms in the basis 1 Microscope Cs 780 Del 100 00 Th 0 00 Wolt 1000 00 Cent of Lave circle hz 0 00 k Defocus 3007 3003 1500 Aperture Radius 0 70 Cent of Ob amp prt h 0 00 k NCEM MSD Lawrence Berkeley Laboratory The MAIN Menu MLEMSS SPACE GROUP 225 ALFHA 90 00 BETA 90 00 90 00 Zone Axis 001 Mo of slices per umitcell 1 Wo of different atoms 1 Foil Thickness 4023051120 Araplit output for plotting ves The indicesave bh k 1 Cent of Optic Axis h 0 00 k 0 00 CHANGE SHOW BASIS FHSGET IMAGE DISFLAY CTF RUN SHOW ATOMS MSLICE AMPLIT VIEW FILE RETURN 19 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 4 3 4 1 The PARAMETER or MAIN or CONTROL menu The main CONTROL menu lists a summary of the control parameters for the current simulation as well as twelve boxes for control of the computation When the CREATE NEW FILE option of the FILE LIST menu page 14 is selected an empty PARAMETER menu with no control boxes is presented and NCEMSS prompts for parameters These parameters have the same form as those presented in the PARAMETER menu when a structure filename is selected from
41. ng all the phase gratings used to build a layered structure must be the same shape and size i e each phase grating must have the same values for the projected two dimensional cell axes and cell angle and also be computed out to the same scat tering parameter GMAX DEL LAY This box is used to remove a previously defined layer name from consid eration DEPOSIT The layered structure can be built up by depositing layers of any member structure that was defined earlier using DEF LAY Each deposition is made by clicking on the DEPOSIT box then on the appropriate LAYER symbol then entering the layer thickness desired The final structure is built from the top down i e each subsequent layer is deposited onto the bottom of any existing sequence A graphical repesentation of the structure appears on the left of the menu and the phase grating sequence is also listed INSERT In addition to depositing a specified thickness of a chosen layer it is possible to insert a specified thickness at any chosen thickness of the final structure Clicking on this button followed by the appropriate LAYER symbol causes NCEMSS to ask for a layer thickness to be inserted and the structure thickness at which to insert it REPEAT This button is used to repeat a defined sequence a chosen number of times in order to build up a periodic layer structure RESET This button zeros everything in preparation for another try REMOVE The phase grating sequence can
42. of the scattering process showing each F k Q k k term contributing to the outgoing W k Ikl 2 to 2 Here the incoming function F k is equal to the product W k P k in equa tion Al Note the presence of the Q 3 and Q 4 coefficients in the table of interactions except for W 0 every outgoing P k contains a contribution from these outer coefficients and would be in error without them 51 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual A 3 Pi FIF Wn k Pe OI q X A2 Here the F represents the Fourier transform operation and q x is the real space form of i e the inverse Fourier transform of Q k Experience with the SHRLI pro grams has produced the not surprising result that in order to obtain the same results with A2 as with A1 q x must be formed from a Q k that extends twice as far in reciprocal space as do W k and Note that as well as correctly describing the physics of the scattering process by ensuring that all contributions from all the diffracted beams leaving the previous slice to each diffracted beam from the current slice are included the doubled phase grating also neatly eliminates the possibility of any aliasing arising from the neces sary sampling of the real space functions Unfortunately in their description of the FFT multislice Ishizuka and Uyeda 1977 stated that the number of diffracted beams must be no less than the number of phase grat
43. phase grating function given in reciprocal space for the n 1 th slice In multislice computer programs that use the above reciprocal space formula tion the three functions W k P k and are represented by two dimensional ar rays containing terms with indices that can be regarded as those of the diffracted beams within the diffracting specimen In order to impose no extra symmetry on the compu tation a circular aperture is usually placed on the terms in the arrays so that terms beyond a certain distance in reciprocal space are set to zero Note that the Q k array must extend out to twice as far in reciprocal space as the W k and P k arrays in order to correctly include all physical scatterings to each diffracted beam Figure Al shows how this doubled phase grating requirement arises because Q k is a probability map of terms that determine how much of each diffracted beam is to be scattered through the angle corresponding to the term Thus in order to compute the scattering of diffracted beams out to k h k the W k and P k must be 2h 1 x 2k 1 in size and Q k must be 4h 1 x 4k 1 For example the SHRLI80 programs used a 128x128 array for Q k making SHRLI80 a parameter 14 multislice and giving a maximum h k value of 31 31 this limits the number of diffracted beams to less than 4096 adequate for most perfect crystal computations but too small for simulation of many defect struc tures O Keefe et al 1978
44. res with short repeat distances in the beam direction such a computation is adequate since the Ewald sphere will not approach the relatively distant high order zones Identical sub slices with n sub slices per unit cell repeat distance For structures with large repeats in the beam direction a method of sub dividing the slice is required in order to compute the electron scattering with sufficient accuracy The simplest but most approximate method is to compute the projected 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 interac tion 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 direction From these sub sliced groups different projected potentials are produced to form n dif ferent phase gratings which are applied successively to produce the scattering from the full slice Sub slices based on the three dimensional potential A further improvement on sub dividing the atom positions is to sub divide the three dimensional potential of the full slice since an atom with a position wit
45. s or even find that the performance 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 speci men Describing the transmission electron microscope 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 pro duces the image As a first step we can consider the usual geometrical optics depiction of the transmission electron microscope TEM NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The Electron Microscope Electron Source Objective Lens Ocal Plane af lens l stintermediate Image S Selector gt Aperture Intermediate lens endltemediate Image Projecter Lens Imaging Mode Diffraction Mode b Fig 1 Geometrical optics representation of the TEM in imaging mode a and diffraction mode ib NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 1 3 Figure 1 shows such a diagram of a TEM operated in two distinct modes set up for mi croscopy a and for diffraction b In microscopy mode we see that the TEM consists of an electron source producing a beam of electrons that ar
46. sharply peaked in the forward direction for high energy scattering Since the modified p x array is so much smaller the computation time should take less time than either of the reciprocal space multislice A1 or the FFT multislice A2 however tests e g Kilaas and Gronsky 1983 have shown that the original formulation of the method required more beams and smaller slices to achieve the same precision as either the re ciprocal space multislice or the FFT multislice resulting in a longer time to produce the wavefield at the same total specimen thickness Van Dyck and Coene 1984 have since proposed a modified implementation of the real space multislice into a workable algorithm with results that approach those produced by the multislice formulations of equations Al and A2 Coene and Van Dyck 1984 Since the p x array is much small er procedure A3 does produce some saving in memory over the other multislice for mulations Storage requirements All three formulations of the multislice procedure require the computer or array processor to store three different complex arrays corresponding to the phasegrating function in real or reciprocal space q x or Q k the electron wavefield in real or re ciprocal space y x or Y k and the propagator function in real or reciprocal space p x or P k With a reciprocal space phasegrating Q k of 2nx2m terms a parameter n m reciprocal space multislice equation Al requires a reciproc
47. t for similar reasons or even as a means of struc ture determination Given a number of possible models for the structure under investi gation images are simulated from these models and compared with experimental 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 erystal thickness and microscope defocus Itis also a good idea to match simulations and experimental images for more than one orientation Some simulations are done in order to throughly explore one particular image by freeze framing the imaging process in the computer In this way we can obtain in formation that is not observable experimentally such as the electron wave amplitude at the exit surface of the specimen the magnitude and phase of each component of the im age intensity spectrum or even the amplitude contributed to the intensity spectrum by each pair of diffracted beam interferences The simulation programs can also be used to study the imaging process itself By sim ulating images for imaginary electron microscopes we can look for ways in which to improve the performance of present day instrument
48. table stored in MICROSCOPES DAT 4 Iprint ps stores a set of Postscript definitions that are used in order to print im ages to a Postscript Laserprinter Generated files NCEMSS generates and stores various data files in the course of a simulation The five data files are 1 name at stores all the structure and microscope information needed to run the simulation This information is derived from user input and the supplied data files In particular the string name is a unique name for the structure input by the user when creating the structure file 2 name pout is the result of running the PHSGRT subprogam from the informa tion stored in name at it contains the specimen potential in the direction of the electron beam 3 name mout is the result of running the MSLICE subprogram using the data in name pout with those in name at it contains the exit surface wave at one or more selected specimen thicknesses 4 is the result of running the IMAGE subprogram to apply the effects of the microscope parameters in the name at file to the exit surface wave it con tains one or more images ready to be displayed 5 name aout contains the complex amplitudes of several diffracted beams at one slice increments in specimen thickness The beams are specified by the user in the main menu and can be plotted as a function of specimenthickness In addition two print files are produced but rarely printed just in case add
49. the FILE LIST menu When every parameter has been entered NCEMSS re presents the PARAMETER menu with the control boxes drawn in and available for use Parameters of the PARAMETER menu INPUT FOR The parameter displayed next to this prompt is a short title for the struc ture SPACE GROUP NCEMSS generates symmetry operators for any one of the 230 space groups when given the number of the space group required listed in the Interna tional Tables for Crystallography If the space group required is not one listed in the Tables a value of zero can be entered A B C ALPHA BETA GAMMA These are the unit cell dimensions in Angstrom units and the unit cell angles in degrees GMAX The maximum value in reciprocal Angstrom units of g to be considered in the multislice diffraction calculation This value imposes an aperture on the diffract ed beams included in the dynamic scattering process It should be large enough to en sure that all significant beam interactions are included For light atoms and thin crystals values as low as 2 0 are adequate For structures with heavy atoms and large crystal thicknesses values of 3 0 to 4 0 are to be preferred Note that NCEMSS will compute phase grating coefficients out to twice GMAX in order to include dynamical interactions correctly Appendix A ZONE AXIS Specimen orientation is selected by specifying the zone axis desired Three indices are entered with one space between each NO O
50. tween the montaged images INT AUTO SCALE lt gt INT ABS SCALE To see the most detail in any image set INT AUTO SCALE to display the image with its minimum set to black and its maxi mum to white To intercompare images it is better to use INT ABS SCALE to choose the same absolute scale for all the images CTF AUTOSCALE lt gt CTF ABS SCALE Can be used to scale a CTF plot page 36 by fixing the maximum g value considered In AUTOSCALE mode the CTF is drawn to where it approaches zero PG REC SP lt gt PG REAL SP determines whether or not the calculation is done in re ciprocal space or in real space This switch should be set to reciprocal space since the real space calculation is not debugged yet APERTURE lt gt NO APERTURE determines whether or not the current objective ap erture radius is drawn on a displayed diffraction pattern TITLES lt gt NO TITLES determines whether titles are written under each displayed image Notice that MONTAGE will supress titles but a title for the montaged series may be added using WRITE TEXT 2D POT SLICE lt gt 3D POT SLICE When the number of slices per unit cell exceeds one in the MAIN menu page 16 NCEMSS will sub slice the unit cell in one of two ways When 2D POT is set the total potential within the cell will be projected and a portion assigned to each sub slice A more accurate method is to approximate the up per layer zones by sub slicing a three dimensional potential into the required number
51. utation techniques for the simulation of high res olution electron micrographs J Microscopy 132 31 42 Van Dyck D Coene W 1984 The real space method for dynamical electron diffrac tion calculations in high resolution electron microscopy I Principles of the method Ul tramicroscopy 15 29 40 56 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 57 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual Appendix BHOLZ interactions B 1 B 2 B 3 B 4 With suitable algorithms it is possible to include in the diffraction calculation the effects of out of zone scatterings or non zero or higher order Laue zone HOLZ interactions Basically there are four ways to produce the set of phasegratings or pro jected potentials that describe the multisliced crystal For structures with short re peat 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 NCEMSS Identical slices with only one sub slice per unit cell repeat distance A multislice computation in which every slice is identical contains no informa tion 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 tu
52. ver any operator and clicking the mouse will delete that operator RETURN Return to previous BASIS menu 28 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory The Atom List Menu NEEMSS NAME 0 0000 0 0000 0 5000 0 5000 DISFLAY KETUEN 29 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 7 The ATOM LIST menu The ATOM LIST menu shows a list of the atom positions making up the unit cell The list displays the atom positions one per line showing the chemical symbol NAME for each atom its fractional coordinates X Y Z the Debye Waller factor DW and the site occupancy OCC Subsequent pages of long lists of atom position parameters can be viewed with the three right hand control boxes BUILD CELL not implemented on Unix Versions Activating the BUILD control box brings up the BUILD menu page 28 with the facility of generating defect cells DISPLAY Activating this control box brings up the ATOM DISPLAY menu page 30 for the purpose of drawing an atom model of the current structure page 32 RETURN Return to previous MAIN menu 30 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory 31 NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 3 8 The BUILD menu The BUILD menu is used to create defect cells visually with the aid of the cursor The menu has a right hand column of control buttons activated in the usual way INCR X This button
53. wavefield by considering the interaction of the incident electron wave on the specimen potential 3 Compute the image plane wavefield by imposing the effects of the objective lens on the specimen exit surface wave Cowley J M amp Moodie A F 1957 The scattering of electrons by atoms and crystals I A new theoretical approach Acta Cryst 10 609 NCEMSS User Manual NCEM MSD Lawrence Berkeley Laboratory NCEM MSD Lawrence Berkeley Laborator NCEMSS User Manual 2 2 1 2 2 Introduction to NCEMSS The three simulation steps Since the simulation problem divides neatly into three parts NCEMSS treats these three parts with three sub programs 1 PHSGRT a program to generate the part of the crystal potential that produces electron scattering input is from a file containing structural data about the spec imen including unit cell dimensions symmetries and atom positions occupan cies and temperature factors 2 MSLICE a program to generate the electron wavefield at the specimen exit surface it uses PHSGRT data combined with information about the accelerating voltage of the electron microscope and the specimen thickness and tilt 3 IMAGE a program to generate the image intensity at the microscope image plane the effects of objective lens phase changes and resolution limiting aber rations are included via parameters like defocus spherical aberration incident beam convergence spread of focus and th
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