Method and system for indexing electron diffraction patterns

Abstract

A method is provided of indexing an electron diffraction pattern obtained from a crystalline sample. Indexing data comprising phase and crystallographic orientation information is obtained for first set of locations on the sample. A second set of locations to be indexed is identified. For each nominal location in the second set an experimental electron diffraction pattern is obtained, together with a simulated template from a number of previously indexed locations in the first set, the previously indexed locations being in a proximal region of the sample to the nominal location. Further simulated templates are generated by modifying the crystallographic orientation for the previously indexed locations at angular sub-intervals. The templates are compared with the experimental pattern for the nominal location and, using a similarity measure, a resultant indexing of the location is produced. A corresponding system is also disclosed.

1 . A method of indexing an electron diffraction pattern obtained from a sample of material having one or more crystalline phases, the method comprising:
 a) obtaining indexing data associated with a first set of locations on the sample, the indexing data comprising phase and crystallographic orientation information for each location;   b) identifying a second set of locations on the sample to be indexed;   c) obtaining a master dataset for each phase of the sample material, each master dataset representing the three dimensional distribution of the electrons scattered from a crystal of the given phase;   d) for each nominal location in the second set:
 i) obtaining an experimental electron diffraction pattern from the nominal location; 
 ii) generating at least one first simulated template from at least one respective related location to the nominal location, the related location being in the first set and in a proximal region on the sample to the said nominal location in the second set, wherein the at least one first simulated template represents a simulated electron diffraction pattern generated using the master dataset and the indexing data for the respective related location. 
 iii) for each at least one first simulated template, generating one or more further simulated templates representing simulated electron diffraction patterns for crystallographic orientations corresponding to that of the respective first simulated template and which are modified at one or more crystallographic orientation sub-intervals with respect to the first simulated template; 
 iv) comparing the first and further simulated templates with the experimental electron diffraction pattern from the nominal location so as to generate a corresponding similarity measure; and, 
 v) analysing the similarity measures so as to select at least one resultant indexed phase and orientation for each nominal location. 
   
     
     
         2 . A method according to  claim 1 , wherein each of steps d(ii) and d(iii) are performed using geometric calibration data describing the relative positions of at least the location on the sample, the electron beam and the detector. 
     
     
         3 . A method according to  claim 1 , wherein the first and further simulated templates are generated in accordance with similar experimental conditions as the obtained experimental diffraction pattern. 
     
     
         4 . A method according to  claim 1 , wherein the first set of locations is indexed using a Hough indexing, pattern matching or template matching method. 
     
     
         5 . A method according to  claim 1 , wherein, prior to step a, the method further comprises obtaining a number of experimental electron diffraction patterns from a sample of the material, according to a set of experimental conditions in which an electron beam is incident at a number of locations upon the sample and the scattered electrons are monitored by a detector; and attempting to index the patterns for each location. 
     
     
         6 . A method according to  claim 1 , wherein a location is selected for inclusion within the first or second sets of locations according to a confidence measure based upon one or more of the following:
 a measure of the diffraction pattern quality;   the number of detected Kikuchi bands, or groups of such bands, used for the indexing process;   the difference between the positions of the Kikuchi bands as detected and the equivalent bands in the result from the analysis; and   the relationship between the highest ranking and lower ranking solutions.   
     
     
         7 . A method according to  claim 1 , wherein the at least one related location is in a proximal region on the sample if it is a near neighbour of the nominal location. 
     
     
         8 . A method according to  claim 7 , wherein the near neighbour related location is a primary neighbour being directly adjacent to the nominal location. 
     
     
         9 . A method according to  claim 1 , where the locations are defined as points upon the sample at which an electron beam impinges on the sample surface, and wherein such points are provided in a pattern of points which are spaced apart from each other. 
     
     
         10 . A method according to  claim 1 , wherein a plurality of locations are arranged on the sample surface in an array. 
     
     
         11 . A method according to  claim 1 , wherein the first and further templates are generated from a master diffraction pattern which includes predicted diffraction intensities for all crystal directions for the relevant phase. 
     
     
         12 . A method according to  claim 11 , wherein the first and further templates use one or each of: the same geometry calibration values for the relevant location, and, the same resolution as the experimental diffraction pattern. 
     
     
         13 . A method according to  claim 1 , further comprising selecting a subset of locations to form the nominal locations, wherein the subset of locations comprises one or more of:
 (i) locations with no successful indexing;   (ii) locations with a low data confidence; and,   (iii) locations or small clusters of locations that were indexed with a different phase and/or orientation to their neighbouring locations.   
     
     
         14 . A method according to  claim 1 , further comprising, for a third set of locations which are in the first set of locations:
 e) for each nominal location in the third set:   vi) obtaining an experimental electron diffraction pattern from the nominal location of the third set;   vii) obtaining at least one first simulated template representing an electron diffraction pattern generated from the nominal location of the third set using the indexing data comprising phase and crystallographic orientation information, wherein the simulated template is according to similar experimental conditions as the obtained experimental diffraction pattern;   viii) for each at least one first simulated template, generating one or more further simulated templates represent simulated electron diffraction patterns for crystallographic orientations corresponding to that of the respective first simulated template and which are modified at one or more crystallographic orientation sub-intervals with respect to the first simulated template;   ix) comparing the first and further simulated templates with the experimental electron diffraction pattern from the nominal location of the third set so as to generate a corresponding similarity measure; and,   x) analysing the similarity measures so as to select at least one resultant indexed phase and orientation for each nominal location of the third set of locations.   
     
     
         15 . A method according to  claim 14 , wherein:
 a specific nominal location is present in each of the first set, second set and third set, such that a resultant indexed phase and orientation is produced for each nominal location in accordance with each of step d(v) and step e(x); and wherein the method further comprises comparing the said resultant indexed phases and orientations so as to produce an updated resultant indexed phase and orientation for each said nominal location.   
     
     
         16 . A method according to  claim 14 , wherein the image correlation measure is a normalised cross correlation coefficient, NCCC. 
     
     
         17 . A method according to  claim 14 , wherein one or each of step d(iii) or step e(viii), is performed using the Nelder-Mead or Downhill Simplex methods. 
     
     
         18 . A method according to  claim 1 , wherein the similarity measure is an image correlation measure. 
     
     
         19 . A method according to  claim 1 , wherein a resultant indexed phase and crystallographic orientation is only selected if the correlation measure meets a given threshold. 
     
     
         20 . A method according to  claim 1 , further comprising displaying information relating to one or more of the phase identity and orientation of the crystal at the or each location. 
     
     
         21 . A method according to  claim 1 , further comprising, repeating the method one or more further times, wherein for each repetition, the first set is updated using the newly indexed locations from the second set of locations indexed previously. 
     
     
         22 . A system for indexing an electron diffraction pattern obtained from a material having one or more crystalline phases, the system comprising:
 a computer system including a central processing unit having a primary memory, wherein the system is configured when in use to perform the method according to  claim 1 .   
     
     
         23 . A system according to  claim 22 , further comprising:
 an electron detector configured to receive electrons scattered from a sample as a result of an electron beam interacting with the sample and to generate data representing the detected scattered electrons for analysis.   
     
     
         24 . A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of  claim 1 .