Chapter 6 User manual of EDiff: A unit
Contents
1. Tolerance QBs No of pai DS 20 ck 1 2hkI 8 AtcBackground retaion Matic QT Dietnecrent Oro MosaicT ype Threshold Drowmosaic ca B Figure 5 A Pattern fitting of the main facet and the peaks of the autocorrelation image to unit cell parameters Crosses mark the peaks of the spots of the 132 User manual of EDiff autocorrelation image blue circles mark the best fitting diffraction simulation of a given unit cell B Control Panel of the Pattern Fitting and Indexing Refinement window in EDiff V1 0 all options highlighted and described below 1 Slide bar to select an image its sequence number will be shown on the right When the bar is active the left and right arrow key can also be used for controlling the bar 2 Search box locate a file using its name and pressing enter if more files match the name press enter to switch between them 16 Fitted_facets spinbox select a specific facet if more than one facet was generated by FitFacets 17 FitFacets find all the potential facets that fit V1 amp V2 3 ShowIndex show turn off the fitted pattern and its index 15 GenMosaic generate a diffraction pattern using the mosaic parameters described below 4 amp 5 Resolution range from which select No of pairs facets 11 for refining the orientation using RefineOrient 10 fitting and indexing the high resolution reflections in order to find a more accura2. in order to select a main facet on which the indexing refinement will be based When the window opens a rough fitting is showing It s the same as in the Pattern Fitting window the program finds the best fitting facet in a simulated 3D unit cell model for the main facet V1 amp V2 then cuts through the 3D model lattice along the plane defined by the selected facet in order to generate a simulated 2D diffraction pattern show as small blue circles If the diffraction image is taken right from the main zone this provides an accurate indexing However in more usual cases the experimental diffraction pattern is tilted away from the main zone In order to find the exact orientation of an individual diffraction image so as to index the reflections correctly we need to select Refine Orient which opens a new window fig 6 The RefineOrient is based on the index of the main facet V1 amp V2 Hence the MainVectorMatching or BrightestSpots algorithms are strongly suggested for indexing refinement 135 Chapter 6 m Indexing Refinement Images No i QQ Unit Cell Edges 32 0137 53 2363 63 9863 Angles 90 90 90 CloseZone 0 0 1 RMSE 1 25 AngleEn 0 21 OverallRMSE 13 32 FitFacets Fitted_facets 0 4 ShowlIndex GeniMosaic RefineDrient Resolution 6 2 68 Tolerance 08 No otpairs f3 3 K I okV1V2hkl I AtcBackground Rotation Matrix 0 El RefineOrient RF2 RF3 ShowRF Mosai
3. typical 0 5 50 0 66 MaxFitError For one spot max distance error in pixels the distance between fitted and real spots should be smaller typical value 7 pixels ScaleTolerance max value of scale tolerance 0 01 is 1 typical 0 01 0 03 0 05 VectLengthTolerance Vector Length Tolerance 0 1 is 10 for fitFacet of FullVector amp MainVector matching method fitFacet is a function to calculate the fitting residue of two facets which is used to judge the similarity of two facets 120 User manual of EDiff VectAngleTolerance Vector Angle Tolerance in degrees for fitFacet of FullVector amp MainVector Matching Method AngleLowerBoundary Angular Lower Boundary in degrees for UniqFacet in lattice Lattice2MainFacet BEval AngleUpperBoundary Angular Upper Boundary in degrees for UniqFacet in lattice Lattice2MainFacet_BEval AngleLowerBoundary Angular Lower Boundary for MainVectorPair in lattice Lattice2FacetTri_BEval AngleUpperBoundary Angular Upper Boundary for MainVectorPair in lattice Lattice2FacetTri_BEval 6 5 Checking the Data After having run AMP to prepare the data for EDiff the data can be checked by entering the data directory in EDiff SetDataDir button 27 and clicking the CheckData button 28 This opens the window shown in Figure 4 The purpose of checking the data is to allow the user to verify that the peak positions of the auto correlation images an
4. 127 Chapter 6 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to FullVectorMatching 2 Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images It is important to set the resolution range as narrow as possible as this solution is very time consuming since it uses all the vectors in the resolution range in its calculations Close the window of CheckData Save V1V2 is NOT necessary 3 Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress 4 The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable When the user clicks the DoSearch button the program will use all the possible vectors pairs not only the main facet in each autocorrelation image for its calculations For matching an observed vector pair a facet in List1 to a simulated facet in List2 a 2D lattice is generated from the simulated facet and compared with the observed diffraction pattern to get a
5. is that the main facets V1 amp V2 have to be examined and possibly reset by the user using the CheckData tool The main facets in Listl are checked by hand and a quality remark Bad Normal Good or Important can be given to each individual image Congruent facets extracted from different diffraction pattern are not removed from Listl When the experimental data are very noisy and lots of mis tilted diffractions were collected this solution is more reliable in the hands of an experienced user The user is encouraged to run CheckData and try this method for more accurate results Main steps 126 User manual of EDiff Set the basic microscope and diffraction parameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to Main VectorMatching Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images In the window of CheckData verify that the V1 and V2 spots auto selected by the program are the closest two spots near the center If there are any other spots closer to the center reset the V1 or V2 to these spots Normally a correct choice for V1 amp V2 result in a hig
6. reflection 2 Absolute distance the reciprocal distance between a reflection and the Ewald sphere 3 side elongation simulate the spot elongation along the main direction of the unit cell that lies most closely to the direction of the electron beam and calculate the reciprocal distance to the Ewald sphere useful for very thin plate like crystals that have characteristics of 2D crystals 6 8 Indexing an Electron Diffraction Image with Known Unit cell Parameters Once unit cell parameters have been inferred clicking the Indexing 53 in figure 2 button opens the Indexing Refinement window figure 6 This window is used for indexing centered background corrected diffraction images The main difference between Indexing Refinement figure 6 and Pattern Fitting figure 5 is that in the 134 User manual of EDiff former a diffraction pattern is indexed and in the latter an autocorrelation image is indexed The default background of Indexing Refinement window is the diffraction image while the default background for Pattern Fitting is the autocorrelation image After having found unit cell parameters the global Resolution Range set in the EDiff main window can be increased for Indexing Refinement The Search Algorithm should be changed to MainVectorMatching no matter what algorithm was used for getting the unit cell parameters It is necessary to run Check Data
7. time by roughly one 113 Chapter 6 minute Removing the background can still go wrong so a user should only enable the option Removed beamstop to see the results of one single image If one is satisfied the user can proceed by enabling the autocorrelation map and show plt output When this output is reasonable as well the user can disable all figure outputs and process all images of the data set in a single run 6 3 3 Output Data of the Pre processing Program AMP This program calculates autocorrelation images and extracts peak positions from diffraction patterns and their corresponding autocorrelation images Four output files of each EM image are generated e lt image name gt atc plt the peaks positions of autocorrelation map e lt image name gt atc jpg the autocorrelation map e lt image name gt ctr pks the peak positions of centered background removed diffraction image e lt image name gt ctr png the centered background removed diffraction image It is good practice to save these output files in another directory to avoid mixing with the original diffraction data 6 4 EDiff Finding Units Cells EDiff exe is the main program of the electron diffraction EDiff software package It finds and optimizes unit cell parameters and fits and indexes diffraction patterns The input data for EDiff are not the original electron diffraction images but the pre processed output data from AMP see above P
8. to select an image for checking the sequence number will show on the right 123 Chapter 6 When the bar is active the left and right arrow keys can also be used to slide the bar 2 Search box used for locating a file by typing in the filename and pressing enter If more files match the name pressing enter switches between them 3 Slide bar to set the fitting threshold show on the right which is used in the Find Next function 4 Find Next gt gt click this button to find the next pattern that has a fitting value larger or smaller than the Fitting Threshold Fitting value is a measure of how well the simulated lattice fits with the experimental autocorrelation pattern 5 7 Mark the quality of the image as Bad Normal Good or Important This is used to weigh the images as sometimes certain orientations are rare but give vital information on one of the cell parameters Only in such cases and provided the image is nice it should be marked as Important 16 ResolutionRange allows entering the resolution range manually Don t forget to press lt Enter gt to validate it If the values of resolution range are changed here they will also be changed in the main window of EDiff 17 ShowRange shows the resolution range as two black circles in the pattern 25 AtcBackground shows the autocorrelation image or background removed diffraction pattern as background By default the autocorrelation patter
9. 20 22 LowerBoundary smallest unit cell edge in Angstrom for a unit cell parameter search 23 25 SearchStepSize step size in Angstrom for unit cell parameter search Usual values are about 0 5 or 1 Angstrom 60 62 UpperBoundary upper boundary in degrees for unit cell parameters search 57 59 LowerBoundary Lower Boundary in degrees for unit cell parameters search 54 56 SearchStepSize Step Size in degrees for unit cell angle search Initially set this to about 1 degree 63 SearchList the user can define a list of angles to be checked instead of performing exhaustive angle searching The angle list should be saved as a text file with each line a tri angle group alpha beta and gamma in degrees and separated by blank space 64 The file of the angle search list 65 Remove the angle search list 26 SearchAlgorithm there are three unit cell parameters search algorithms that can be selected e Unique Facet Matching the friendliest algorithm you don t even need to run CheckData except perhaps for setting the proper ResolutionRange and it gives quick results e Main Vector Matching requires running CheckData to select verify and save the facets of each diffraction image that are to be used in the calculation This option is User manual of EDiff 29 30 31 33 36 39 53 52 useful for very noisy and or marginal data e Full Vector Matching does not require r
10. Chapter 6 User manual of EDiff A unit cell determination and indexing software EDiff is a scientific software package to determine the unit cell of nano crystals from the randomly oriented electron diffraction data EDiff is used to index the reflections in the electron diffraction images and is the first step in reconstructing the 3D atomic structure of organic and inorganic molecules and proteins EDiff includes the data pre processing program AMP which cleans up diffraction patterns and calculates their autocorrelation patterns which serve as input for EDiff EDiff Copyright 2007 2008 BFSC Leiden Univ the Netherlands A paper about the pre processing program AMP was accepted and will be published in the proceeding of the 2009 IEEE International Conference on Image and Signal Processing CISP 09 Jiang L Georgieva D IJspeert K Abrahams J P 2009 An Intelligent Peak Search Program for Digital Electron Diffraction Images of 3D Nano crystals Chapter 6 6 1 The Electron Diffraction Software EDiff Package for Windows Users The package includes the following executable files e EDiff exe e Patternson_dir_gui exe e FirstInstall bat e MCRInstaller msi and other supporting archives 6 2 Configuring and running EDiff on Windows Platforms 1 Open Unpack the package in a new directory 2 Run FirstInstall bat once on the machine where you want to use the software MATLAB Component Runtime MCR Libra
11. al User Interface of pre processing program AMP V1 2 with all options highlighted 1 Run button to start the program with the desired settings Selection of images types that will be processed Image window Slider to select current image in directory Change to original pattern Autocorrelation pattern png output pattern Progress tracker Information box containing error messages and help files CO ION 6 eo S Parameter input allowing the user to change area of the center beam that needs to be removed 112 User manual of EDiff 9 Allows the user to make the program more or less flexible in finding the center of the diffraction pattern automatically The number indicates the allowed error that is based on the difference in length between two different independent calculations of the beam center Setting it to a higher value allows the program to accept more elliptic or irregular shapes of the central beam whereas setting it to 0 automatically redirects the user to a window for interactively setting the center 10 Instead of setting the value to 0 one can also chose to use the beam stop removal tool for any given shape of beam stop This comes in handy when the user suspects that the center is found far from its actual position 11 Allows the user to smooth the image This option is only advised when salt and pepper noise is present because this type of noise is not removed well with the standard background removal tools The u
12. arameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to UniqFacetMatching 2 Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images Close the window of CheckData Save V1V2 is NOT necessary 3 Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress 4 The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not This algorithm is the most automated one After the user has clicked the DoSearch button the program first generates a main facet for each autocorrelation pattern and accumulates all the facets in Listl then analyses Listl to remove any congruent facets shrinking Listl to contain only unique facets The matching procedure is described in fig 5 6 6 2 Algorithm 2 Main Vector Matching This algorithm requires more user interaction compared to the Unique Facet Matching algorithm The most important difference
13. ation by turning off the radio button 25 AtcBackground This solution proved also valid and reliable in various test cases in which the experimental data were very noisy and lots of miss tilted diffractions were collected We encourage all experienced users to try this method at least once Main steps 1 Set the basic microscope and diffraction parameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test 129 Chapter 6 out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to BrightestSpotsMatching Click CheckData and set a large resolution range to cover most of the brightest spots in different images In the window of CheckData visually check the main facet V1 amp V2 Button 20 Refine in figure 4 can be used to refine the position of V1 amp V2 Button 27 V1V2 gt Aff in figure 4 is used to add V1 amp V2 to an affiliate spots list Button 23 BrightV1V2 will find the brightest two spots in the diffraction image and reset V1 amp V2 to them The user can switch the background from the autocorrelation pattern to centered diffraction pattern for a better visualisation by turning off the radio button 25 AtcBackground Be careful of Button 22 and 29 as their operation will affect all the i
14. cType 1 Threshold 0 03 ShowMosaicl Rotation Matrix 0 5 Fitted Main Facet 0 0 E electrondiff lyso tit serials bakup 040708_1 2 ctr pks W1 13 30 1 A V2 8 15 1 A Ratio 1 63 Angle 89 79 degree Figure 6 Indexing of a background corrected diffraction pattern using unit cell parameters that were inferred in earlier steps Crosses mark the peak positions of the reflections of the diffraction image Small blue circles are the best fitted diffraction simulation of the selected unit cell Here the unit cell was determined using the Bright Spots Matching algorithm V1 amp V2 are the two brightest spots of the diffraction pattern AO and l are the affiliate spots of the autocorrelation image The control panel of this window shares its interface with the Pattern Fitting window fig 5B Steps of orientation refinement and indexing 1 Visually check whether the main facet V1 amp V2 fits well and is reasonable indexed If not click FitFacets 17 in figure 5B to generate all possible solutions and pick a better fitting facet The RefineOrient procedure is based on this fitted facet If this fitting is not correct the orientation refinement and indexing will be meaningless 2a Select RefineOrient Select the Resolution range from which No of pairs facets are used for the refinement 4 5 7 11 in figure 5B need to be set The RefineOrient procedure will select pairs of high re
15. cell but cannot be used for further steps in the structure determination 6 3 1 Preparing the Input Data for the Pre processing Program AMP AMP expects electron diffraction images of about 1024 by 1024 pixels though they needn t to be exactly this size Furthermore diffracted intensity should be positive white on most display programs if the spots are black on a white background you have to invert the image The beam center of the diffraction pattern should be more or less in the centered Make sure that all the images that you want to process are in the same directory It is good practice to store all the data of one EM session in a single directory ensuring that all diffraction patterns were collected with the same voltage camera length and digitization parameters If these microscopy parameters are changed during a session then separate the data set into different directories for proper processing 111 Chapter 6 6 3 2 Working with the Pre processing Program AMP Image Data Type m 77 Quit u ra u 2 f ui i Options Y TOS S N pm t SE Smooth image atlab figure output C Original Image C Removed beamstop C Autocorrelation map C plt output Save directory of autocorrelation map Save directory of plt file a 4 Original_Image A J 3 alae 5 Information Box Directory containing images 7 J ANew Guide Matlab JPG G ee File currently processed Figure 1 Graphic
16. d peaks positions of the background removed diffraction patterns coincide It also automatically finds the main facet also called main vectors V1V2 for each autocorrelation image Here the peaks of the spots within the resolution range are visualized as crosses the points of simulated lattice generated from this main facet are indicated by small circles Normally if the crosses Lattice2MainFacet BEval is a function to generate main facets from electron diffraction images for the Unique Facet Matching algorithm calculation The angle of the facet is limited in between AngleLowerBoundary and AngleUpperBoundary of Find UniqFacet in Pattern Lattice2FacetTri_ BEval is a function to generate main facets from electron diffraction images for the Main Vector Matching algorithm calculation The angle of the facet is limited in between AngleLowerBoundary and AngleUpperBoundary of Find MainVectorPair in Pattern 121 Chapter 6 overlap the circles very well then that means the diffraction image is a well oriented pattern and the main facet was correctly found by the program Sometimes the program can t find the correct main facet in which case the user has to set it manually by first choosing ResetV1 or ResetV2 and then double clicking the correct peak cross in the image The selected V1 or V2 will be automatically switched if the length of V1 is larger than V2 There are lots of tricks for ma
17. dered In RF3 The difference between RF2 and RF3 is spike function of a reflection is considered in RF3 an elongation in reciprocal space of a reflection is simulated The most meaningful MosaicType is 3 for RF3 although you could try selecting mosaic type 1 or 2 there is no error message MosaicType 3 indicates a lengthwise elongation of the diffraction spot in a principal direction of the lattice its default threshold value is 0 05 See section 6 7 for an explanation of the various mosaic types For inorganic materials that have crisp diffraction patterns RefineOrient and RF2 will be fine for reasonable indexing For the crystals with a large unit cell e g the protein nano crystals the reflection spots can be elongated along the unit cell edge direction normal to the plane of the crystal In this case RF3 is a wise choice 3 Potential orientations found by RefineOrient RF2 or RF3 are stored in a list of rotation matrices sorted according to their quality of fit You can inspect all these orientations and check how well they match the diffraction pattern by selecting their sequence number in the Rotation Matrix spin box 6 in figure 5B Most of the time the orientation at the top of the list fits best One way of picking the best indexing solution is e Clicking ShowMosaic to show the indexed mosaic pattern all the model reciprocal lattice spots that a
18. e sorted by quality the top matrices fit best 10 RefineOrient finds a more accurate orientation of a diffraction image using known and or found unit cell parameters by selecting pairs of high resolution reflections and fitting and indexing these pairs 19 RF2 provides a different method for orientation refinement sampling all different tilt orientations based on the orientation of V1 amp V2 and their indices to find the best fitting 18 RF3 provides yet another method for orientation refinement sampling all different tilt orientations based on the orientation of V1 amp V2 to find the best fitting The spike function of the reflection is considered that is the elongation of the reflection is simulated The MosaicType must be 3 side elongation threshold default value 0 05 9 ShowRF show turn off the simulated refined pattern and its indices for indexing an autocorrelation image ShowMosaic may be a better choice 12 ShowMosaic show turn off the simulated pattern with increased mosaicity together with its indices 13 Threshold for the simulation an increased mosaicity For mosaic type 1 the default is 0 03 for mosaic type 2 it is 0 004 for mosaic type 3 the default is 0 05 14 MosaicType encodes different models for simulating the mosaic spread of the diffraction pattern It defines whether an off Ewald sphere reflection should be shown on the simulated diffraction or not 1 Angular mosaic the angular error of a
19. ed a large number of spots is used in the calculation and this may cost too much computing time If the resolution range is too narrow the absence of essential of information may prevent finding the right answer In practice a resolution range that is a 117 Chapter 6 118 bit wider than that defined by the main facet is fine As a rule of thumb a reasonable resolution range is from half of the estimated smallest unit cell dimension to double of the largest unit cell dimension For example if the smallest unit cell dimension is expected to be around 30 Angstrom and the largest dimension is around 80 Angstrom it is reasonable to set the resolution range between 15 and 160 Angstrom 15 CrystalSystem all seven different crystal systems are supported in the unit cell parameters determination If we know the crystal system beforehand we can apply its constraints in the exhaustive search of edges and angles sometimes dramatically speeding up the calculations and improving their precision If we don t know the crystal system we have to use the most time consuming option Triclinic 66 Parameter Suggestion gives the user a suggestion for filling in the UnitCellSearchRange based on an analysis of the main vectors generated in CheckData step This option requires first running CheckData and saving the main vectors V1 V2 17 19 UpperBoundary largest unit cell edge in Angstrom for a unit cell parameter search
20. ern with the Refined UnitCell model or if this does not exist with the BestFit UnitCell instead The Pattern Fitting window will index the auto correlation image Therefore the control panel see fig 5 has the same interface as the Indexing Refinement window This Pattern Fitting algorithm works as follows 1 find the facet in a simulated 3D lattice that best fits the main facet of an autocorrelation pattern 2 then cut through the 3D model lattice using the plane defined by the best fitting facet to generate a 2D diffraction simulation In figure 5 crosses mark the peaks of the spots of the autocorrelation image and blue circles mark the model lattice If the unit cell is correct the crosses and the blue circles should overlap well When almost of the images gt 90 fit well the unit cell most probably is correct The outliers might be caused by the inclusion of some deviant crystals in the data set by poor crystals with streaked rocking curves by unfortunate orientations or unexpected failures to index the pattern properly Only an experienced eye can tell However don t be fooled into certainty when the information of one unit cell dimension is missing in the original data some crystals have a preferred orientation and if you haven t tilted the diffraction grid you may not have sampled the reciprocal lattice well enough If you don t believe a certain indexing click FitFacets 17 in
21. eter defines the scale of the diffraction pattern in A per pixel 8 Alternatively the Digitization parameter can be entered defining the step size in millimeter per pixel when scanning films or the resolution of the CCD digital camera In this case the user also needs to set the ED Constant parameter 9 or the CameraLength and WaveLength parameters 11 and 4 from which the ED Constant is calculated The ScaleBarParam 5 is calculated from the ED Constant 9 and the 116 User manual of EDiff Digitization parameter 42 amp 43 Image center of the autocorrelation image in pixels this is also the center of centered background corrected electron diffraction pattern For files generated by the pre processing program AMP these two values are always 513 corresponding to the center of a 1024 by 1024 size image 44 MissingSpots indicates how many spots are allowed to be absent between the spots of main vector and the center This parameter is used in MainVectorMatching and FullVectorMatching methods which allow the user to include extra information on the symmetry of the crystal If this parameter is not selected MaxMissingNo is zero only prime index reflections will be considered in the unit cell searching Prime means no common factor for the h k 1 index e g index 5 4 3 is prime but 6 4 2 isn t because the h k and 1 have 2 as a common divisor If you don t ha
22. figure 5B to go through all potential fittings in a spin box 16 in figure 5B The fitted facets are sorted and a smaller number should give a better fitting The buttons and options in RefineOrient group box are not originally designed for this Pattern Fitting window but for refining the orientation of diffraction image in the Indexing Refinement window However if you really want to you can use this RefineOrient operation to index the autocorrelation pattern for testing and comparing even though some buttons to do with refining diffraction patterns may be not fully functional for refining autocorrelation images 131 Chapter 6 m Pattern Fitting with Auto Correlation Image Images No Unit Cell Edges 32 0137 53 2363 63 9863 Angles 90 90 90 CloseZone 0 0 1 RMSE 0 86 AngleErr 0 42 OveralRMSE 5 21 FitFacets Fitted_facets 0 4 ShowlIndex Genmosaid RefineDrient Resolution 4 2 4 6 Tolerance 0 8 No of paits 10 iv I ckVIV2hkI AtcBackground Rotation Matric 1 RefineOrient RF2 RF3 ShowRF MosaicType 2 Threshold 0 004 ShowMosaic Rotation Matrix 1 7 0 Fitted Main Facet 0 0 E electrondif lyso it serials bakup 040708_12 atc pt V1 53 31 1 A V2 32 56 1 A Ratio 1 64 Angle 89 58 degree A Images No 6 e Unit Cell Edges Angles CloseZone RMSE AngErr OverallRMSE Diitracets Fitted_facets O ovne Benosa RefineDrient Resoliton D gt
23. fitting value The fitting value is used as the accumulated residual which is different from the residual of two fitted facets in the other solutions By using all the vector pairs and simulating 2D diffraction patterns this algorithm requires heavy computing and is therefore slow 6 6 4 Algorithm 4 Brightest Spots Matching especially suited for large unit cells The Brightest Spots Matching algorithm is a variation of the Main Vector Matching algorithm It s the most accurate algorithm and is especially useful for thin nano crystals with large unit cell However it does require some expertise and you need to know what you re doing Try it out if you have plate like nano crystals that lie in preferred orientations on the grid If this is the case the information of the unit cell dimension in the direction of the beam is not well determined If this is the case 128 User manual of EDiff make sure to tilt the samples away from the main zones before diffracting them by as high an angle as the microscope allows Moreover if the unit cell is large the reflection spots will often be elongated in the direction normal to the plane of the crystal due to the wide spike function or rocking curve in X ray terms in this particular direction This can be caused by the limited number of unit cells in this direction As a result of this elongation the positions of the reflections present on the diffraction patterns may no
24. h fitting value between the image peaks and a lattice using V1 amp V2 as a basis Please read the section 6 5 on Checking the Data for more details Save V1V2 or Save As a V1 amp V2 file before closing the window of CheckData Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not When the user clicks the DoSearch button the program will use the main facets saved in the CheckData step in List For the Main Vector Matching algorithm this List is filled interactively using the CheckData tool In testing out potential unit cells unit cells are skipped if none of its facets can be matched to the measured patterns marked as Important 6 6 3 Algorithm 3 Full Vector Matching To the user the Full Vector Matching algorithm appears very similar to the Unique Facet Matching algorithm but its inner workings are different Normally it s rather slow and we advise you to only use it for comparison and verification On the other hand as it uses more data it can be more accurate Main steps Set the basic microscope and diffraction parameters in the graphic interface figure 2
25. king your life easier lt double click left mouse button gt will capture a cross near the place you clicked lt double click middle mouse button gt will locate the exact place that you clicked by pressing lt Ctrl gt at the same time it will try to find a intensity peak near the place you clicked There are more complicated options for advanced users if you press the key lt Shift gt lt Alt gt or lt Ctrl gt when you do lt double click left mouse button gt or lt double click middle mouse button gt on the peaks of the image the 1 2 1 3 or 1 4 position is located relative to the cross that you selected or the point that you clicked You even can combine use the lt Shift gt and lt Alt gt key which will locate 1 6 position When the peaks are not correctly generated by the pre processing program AMP these operations are very useful to help you to manually reset the correct V1 and V2 provided you know what you re doing which requires understanding reciprocal space The user can run CheckData to find the proper ResolutionRange for the unit cell parameter search A very large resolution range is fine from a theoretical perspective but may include too many spots in the calculation and therefore cost too much computing time A resolution range that is too narrow may lose essential information When adjusting the resolution range don t forget to press enter after having filled in the numbers Let the resolution range sho
26. lease read the part of manual on the pre processing program AMP for more details All the input data should be in one directory typically 4 files for each electron diffraction image lt image name gt atc plt lt image name gt atc jpg lt image name gt ctr pks lt image name gt ctr png All the data in one directory are assumed to be generated from one EM session that is with the same voltage camera length of microscopy and digitization parameter If not the data have to be separated into different directories 114 User manual of EDiff For unit cell determination only lt image name gt atc plt and lt image name gt atc jpg files are required For indexing lt image name gt ctr pks and lt image name gt ctr png files are required please see the part of Indexing an Electron Diffraction Image with Known Unit cell Parameters Click the SetDataDir button to set the directory with the data that need to be processed The selected directory will be shown in a line above the button Some definitions of electron diffraction images that are used in this document e A reflection is a spot corresponding to a vector from beam or image center to this spot e Two reflection spots together with the beam or image center point form a triangle we call this a facet e The facet defined by the two shortest vectors corresponding to two reflection spots closest to the center is called a main facet In short every reflectio
27. mages not just current one Find the proper ResolutionRange In the window of CheckData adjust the resolution range to cover all the brightest spots and affiliate spots in all images that must be used in the calculation Save V1V2 or Save As a V1 amp V2 file and then close the window of CheckData Click the DoSearch button to perform unit cell search The console window running in the background will indicate progress The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not When the user clicks the DoSearch button the program will use both the V1 amp V2 and main facets as affiliate spots saved in CheckData step In the searching every diffraction simulation of a potential unit cell has to match the V1 amp V2 spots and all the affiliate spots at the same time Because this method needs to check the additional affiliate spots it s a bit slower than the normal Main Vector Matching method 6 7 Pattern Fitting of the Autocorrelation pattern Verifying the Unit cell Parameters After unit cell parameters have been found Show Fitting 39 in figure 2 can open a pattern fitting window for verification The Pattern Fitting window will fit each 130 User manual of EDiff auto correlation patt
28. n is shown 26 ImageSpots show the peaks of the background removed diffraction pattern as dark blue crosses or show the peaks of autocorrelation pattern as black crosses or show both 27 V1V2 gt Aff add V1 and V2 to An affiliate spots list 28 ClearAff delete all the spots in the affiliate spots list 29 SetAff if this button is checked V1V2 gt Aff and ClearAff operations will only apply to the current image When clicking in the image with this button selected a new affiliate spot will be added to the affiliate spots list 23 BrightV1V2 find the brightest two spots in the diffraction pattern and select these as the main facet 22 All do the BrightV1V2 search for all the images not only for the current one 7 An affiliate spots list is a list of reflections that is used for checking a simulated 2D lattice Every diffraction simulation of a potential unit cell must contain the main facet V1 amp V2 spots and all the affiliate spots in the same time otherwise it s not a correct simulation 124 User manual of EDiff 8 ShowSimu show the simulated lattice as small blue circles by tiling the main facet 9 ShowV1V2 show in red labels V1 and V2 in the image 10 ResetV1 reset the main vector V1 spot in the image V1 or V2 will be automatically switched if the length of V1 is larger than V2 11 ResetV2 reset the main vector V2 spot in the image 20 Refine use all the
29. n pair defines a facet The main facet defines the smallest repeating unit of the 2D lattice defined by the low resolution spacings but not any higher order Laue zone HOLZ that may be visible at high resolution EDiff exe also has a Graphical User Interface GUI a snapshot is shown in figure 2 115 Chapter 6 File Tool Help aa wm Microscopy Search Params Voltage Ke V 8 ResolutionR ange Ang 13 O C WaveLengthlAng h CrystalSystem Fino Cubic Crystal Monoclinic 2 ImageD ata 3 a Tetragonal 5 i e Orthorhombic Triclinic ScaleB arParam 1 4 pixel k Rhombo C Digitization mm pixel o UnitCellE dgesS earchR ange Angstrom n A 2 J 1 i LowerBoundary F lt Q 2 UpperBoundary ey SearchStepSize a gt a AutoCorrelation ImageCenter Pixel OS g om 44 MissingSpots W 61 7 63 rs 27 EEST 20 E Oa TA TTA i Search lgorithm Qarun atching z CO eee BestFit UnitCelk 2899 sgg Refined UnitCelt 36 J 37g 38 DG Dow Fitting roro owmosaic Figure 2 Main graphical user interface of the program EDiff V1 0 with all options highlighted 1 Voltage in KeV of the electron microscope The wave length 4 will be automatically calculated from the voltage 2 Alternatively the user can enter the wave length and ignore the voltage In the final calculation the wave length is used rather than the voltage 5 ScaleBarParam the Scale Bar Param
30. nal options 138
31. ol Config menu a window opens that allows detailed configuration of some global parameters see Figure 3 The default parameters are empirical settings they work well with most of the data used for testing Don t change them unless you do really know the meaning of each parameter and know what you re doing 119 Chapter 6 W Global Params Configuration Files 1 0 MaxFilesReadin Facet VectorPair Fitting ScaleT olerance Full ector Matching VectLengthT olerance VectAngleT olerance Find UnigFacet in Pattern AngleLowerB oundary Diffraction Patterns Fitting MinPattsFitR atio MinSpotsFitR atio MaxFitE rror Pixels Main ector Matching VectLengthT olerance 0 15 VectAngleT olerance 5 Find MainYectorPair in Pattern AngleLowerB oundary AngleU pperB oundary 30 Cancel Figure 3 More detail global technique parameters configuration of EDiff V1 0 AngleUpperB oundary If you re really interested a brief description of each variable is MaxFilesReadIn Maximum number of plt data files that are read in memory MinPattFitRatio for all patterns Minimal fraction of properly fitting diffraction patterns If this is high many patterns must be explained well by the proposed unit cell Unit cells that fail to reach this threshold are discarded Normal values are 0 5 50 0 66 0 8 MinSpotsFitRatio For one pattern minimum spots fit ratio to detect correct fitting if larger mean fit
32. re close to the Ewald sphere e then go through all the possible orientations in the Rotation Matrix spin box starting from the most likely fitting sequence number zero to find the best fit For certain unit cells in certain orientations it may be that more than one orientations 137 Chapter 6 indexing solution fits well This depends on the unit cell parameters and unfortunate combinations can exist in which it is not possible to distinguish on the basis of the positions of the diffraction spots alone In this case you would also need to include intensity information and 3D merging of the diffraction data This is beyond the current scope of EDiff In these rare cases you have to judge for yourself which is the most reasonable indexing 6 9 Conclusion The program EDiff will allow you to determine the unit cell of a crystal type even if you can only collect single shots from randomly oriented crystals It will index the diffraction images and allows considerable user interaction in determining verifying and assessing the results This is required as every crystal may have its own peculiarities and only by understanding the way in which the program its results can you truly appreciate the relevance of the suggested solution Next steps include integration of the data determining the intensities of the diffraction spots and phasing These are currently beyond the capacities of EDiff and I am working towards these additio
33. ries will install automatically 300M space on the C disk is needed Note if installation fails double click the file MCRiInstaller msi to install it 3 Run Patternson_dir_gui exe to start working with electron diffraction EM images The fist time this program is started it will unpack the supporting archives taking several minutes This software will generate four output files for each EM image lt image name gt atc plt lt image name gt atc jpg lt image name gt ctr pks and lt image name gt ctr png Put these outputs in a separate directory for the next step 4 Run EDiff exe to determine the Unit Cell parameters and index individual EM image 6 3 AMP Pre processing diffraction data The pre processing program AMP Autocorrelation Mapping Program with the executable file name Patternson_dir_gui exe has a Graphical User Interface GUD 110 User manual of EDiff This program is used to remove the background and for picking reflection spots from diffraction images A snapshot of the user interface is shown in figure 1 This program creates an autocorrelation pattern of the electron diffraction pattern which fills up gaps or absences in the data enhances the signal to noise ratio and centers the diffraction pattern The autocorrelation map and peak coordinates serve as input files for EDiff the main program that determines the unit cell of a crystal The autocorrelation patterns are essential for finding the unit
34. ser is notified that using this option might result in a minor loss of data 12 Allows the user to decide which intermediate output images are shown while running the program This output consumes large amounts of memory so when you process more than ten images you would better not choose this option 13 Selects the directory that contains the original images jpeg tiff 14 amp 15 Selects the directory that will be used to store the plt files and autocorrelation images 16 Quits the program The program processes all images in one directory One can chose to work with jpeg tiff or both file types simultaneously The program takes about 2 minutes to process a single image In the current version we strongly advise against dragging or changing any windows that are related to the GUI during image processing or you might crash the program Currently AMP is a single thread program which means that it can t handle more than one job at a time Furthermore there is a limited amount of virtual memory available which allows a maximum of 50 figure windows to be open simultaneously Jf you have a lot of images in one directory make sure you have disabled the option of figure output To work efficiently it is advised to work with electron diffraction data sets that all have been recorded in the same session For a quick test do not save any autocorrelation maps or plt files just yet because this option extends the running
35. solution reflections fitting and indexing these high resolution facets to find a more accurate orientation of the diffraction pattern using the known or inferred unit cell parameters If 136 User manual of EDiff ckV1V2hk 20 in figure 5B is checked the procedure will ensure that V1 amp V2 together with their indices are present in the simulated pattern when indexing the high resolution reflections If youw re uncertain of the correctness of the indices of V1 amp V2 click the radio button checkV1V2 21 in figure 5B to ensure the existence of two reflections shown on the positions of V1 amp V2 but without fixing their indices so in this case other orientations that change the indices of V1 amp V2 are also allowed 2b Alternatively to RefineOrient the algorithms RF2 and RF3 can be selected Some parameters for RefineOrient 4 5 7 11 20 21 options in figure 5B are not used by RF2 and RF3 Other parameters MosaicType and the mosaic Threshold are required Selecting the correct parameters for MosaicType and mosaic Threshold can be critical for the program to find the correct orientation The program samples all different tilt orientations based on the orientation and indices of V1 amp V2 and selects the best fit between the simulated and the observed diffraction pattern In RF2 the rocking curve or spike function of the reflections is not consi
36. spots on a single line or a multi regression method if option regression 24 is selected to recalculate the V1 and V2 the operation makes V1 and V2 fit the image better and their coordinates can now be non integer pixel multiples 21 All Refine all the images not only current one 24 Use the multi regression method to for Refine and refine AIP 12 amp 13 Save V1V2 In order to validate the main facets vectors selected here the user has to save the main vectors by clicking the Save V1V2 button or Save As a V1V2 file 14 Close this window 20 21 amp 24 are optional tools while 22 23 27 29 are only used in the Brightest Spots Matching method 6 6 Unit cell Determination One of the main functions of EDiff is to determine the unit cell of nano crystals from the randomly oriented electron diffraction data Our algorithm is based on matching the observed crystal facets to model facets extracted from a simulated 3D lattice or a detailed description of the algorithm see chapter 5 EDiff has several variations of the general algorithm for identifying unit cell parameters which are discussed below 6 6 1 Algorithm 1 Unique Facet Matching This algorithm is the most straightforward one It is a good idea to try this method first especially for first time users Below we walk you through the procedure 125 Chapter 6 Main steps 1 Set the basic microscope and diffraction p
37. t represent the centroid of the reflection As this is an implicit assumption of the algoritms discussed previously they may not be reliable any more for thin plate like nano crystals with a large unit cell This may be compounded by missing information on the unit cell dimension normal to the plane a few ultra high tilted diffraction images may still have some useful information but may have a very poor quality due to the high tilt This algorithm abandons the idea of using the main facets and instead uses the two brightest spots in the diffraction image not the autocorrelation image The brightest spots are most likely to have their centroids closest to the Ewald sphere and can be further from the center thus containing higher index information also in the direction normal to the plane of the crystal The main practical difference from the users perspective is that the two brightest spots are set as the new main facet V1 amp V2 in CheckData tool It is strongly advised to set the original main facet old V1 amp V2 as affiliate spots Buttons 22 23 27 29 of the CheckData window see figure 4 allow these actions Button 27 V1 V2 gt Aff must be used to add V1 and V2 to the affiliate spots list Button 23 BrightV1V2 will find the brightest two spots in the diffraction image and reset V1 amp V2 to them The user can switch the background from the autocorrelation pattern to centered diffraction pattern for verific
38. te orientation of the diffraction image Don t forget to press lt enter gt after having inserted a value The resolution range will show up as blue circles Be sure this resolution is within the global ResolutionRange show as black circles set on EDiff main interface figure 2 7 Tolerance maximum index error tolerance used for indexing high resolution reflections in RefineOrient 11 Maximum No of pairs facets for refining the orientation using RefineOrient 20 ckV1V2hkl check the existence of V1 amp V2 with their indices when indexing the high resolution reflections in RefineOrient Only useful when the MainVectorMatching algorithm was selected V1 amp V2 must exist for this option to be meaningful 21 checkV1V2 check the existence of the two reflections V1 amp V2 and show their positions when indexing the high resolution reflections in RefineOrient Only useful when the MainVectorMatching algorithm was selected V1 amp V2 must exist for this option to be meaningful 8 AtcBackground show the autocorrelation image or background removed diffraction image as background The default for Pattern Fitting is to show the autocorrelation image for Indexing Refinement the default is to show the background removed diffraction image 6 Rotation matrix defining the potential orientations found by RefineOrient RF2 or 133 Chapter 6 RF3 The matrices ar
39. unning CheckData as it uses all vectors within the resolution range It can be rather slow but it is useful for refinement and comparison e Brightest Spots Matching a variation of Main Vector Matching especially useful for thin nano crystals with a large unit cells For more details please see the chapter on Unit cell Parameters Determination SaveParms save all the parameters in a file so that the parameters can be loaded next time by select File Open menu DoSearch to start unit cell parameter determination The result will show on the console window and the BestFit UnitCell column DoRefine refine the unit cell parameters refinement edge parameters steepest descend refinement with decreasing step size starting from the BestFit UnitCell and reporting the result in Refined UnitCell BestFit UnitCell reports the best fitting unit cell parameters found by DoSearch procedure Refined UnitCell reports the refined unit cell parameters generated by DoRefine procedure Show Fitting fit each auto correlation image with the Refined UnitCell model if there is no refined unit cell it uses the BestFit UnitCell instead Used for indexing an auto correlation pattern and verifying the search result of the unit cell parameters Indexing index the centered background removed diffraction image EDMosaic simulating a diffraction pattern for testing By selecting the To
40. ve information about known missing reflections just leave it unchecked 27 SetDataDir set the input data directory which is the output directory of the pre processing program AMP see 6 3 28 CheckData allows some types of verification It allows checking whether the peak positions of the auto correlation images and peak positions of the background removed diffraction pattern coincide This helps the user to select the proper ResolutionRange for the unit cell parameter search Setting CheckData allows checking the main vectors for the MainVectorMatching and Brightest Spots Matching methods The option saves the main vectors to a V1V2 file 40 ReadV1V2 reads the main vectors V1V2 the main facet from a file 41 ClearV1V2 clears the main vectors and unique facets from memory If the user wants to re select the main vectors or redo the unit cell parameters search it s better to erase the old settings or to restart the EDiff program altogether 32 Information Panel some status information and results of the EDiff program will show up here 13 amp 14 ResolutionRange A The resolution range in Angstrom is used for finding the unit cell parameters and for indexing Only peak positions within the specified resolution range will be used for the calculation When the user starts CheckData only reflections spots within the resolution range will show up If a very large resolution range is select
41. wn as two black circles in the image window just cover all the main vectors or make it just a little larger A reasonable resolution range extends from half of the estimated smallest unit cell dimension to double the largest unit cell dimension e g if the smallest unit cell dimension is around 30 A and the largest dimension is around 80 A a reasonable resolution range extends from 15 to 160 A The main vectors generated in CheckData will be used in the MainVectorMatching algorithm and in the Brightest Spots Matching method In order to validate the main facets vectors selected here the user has to save the main vectors by clicking the Save 122 User manual of EDiff V1V2 button or Save As a V1V2 file For the UniqFacetMatching method the program will generate the main facets automatically when the unit cell parameter search is started Running CheckData is not required for the UniqFacetMatching and Full VectorMatching algorithms Fitting Values 1 040708_12 atc plt Images No 9J ad ritting Threshold lt refine Sam pas R Find Next gt gt Wark Bad Sark Normal hark Gooch nportant get ResolutionR ange Angstrom A ShowRange rave V1V2 AtcBackground f nageSpots Fiv2 gt Aff Clearaft pave AS Bright V1v2 Sell ShowSimu ShowV 1 2 Reset 1 Reset 2 SetAff Close J Figure 4 Check data window in EDiff V1 0 all options highlighted 1 Slide bar
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