METHOD AND SYSTEM FOR INDEXING ELECTRON DIFFRACTION PATTERNS

Abstract

A method of indexing an electron diffraction pattern comprises obtaining a number of experimental electron diffraction patterns at a low resolution from a sample of material using a detector. A master simulation dataset is loaded into the primary memory of a computer system for each phase of the sample material. A simulated template is generated at the low resolution in the primary memory of the computer by using the master simulation dataset from the primary memory wherein the simulated template represents a simulated electron diffraction pattern for a nominal crystallographic orientation. The simulated template is compared with the experimental electron diffraction pattern so as to generate a corresponding similarity measure which is stored. The process is repeated for all crystallographic orientations using crystallographic orientation intervals, and for each phase and each location on the sample. The similarity measures stored in step f are then analysed so as to select at least one resultant indexed phase and orientation for each location. A system configured to perform the method is also provided.

Claims

1. A method of indexing an electron diffraction pattern obtained from a material having one or more crystalline phases, the method comprising: a) 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; b) 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, according to a set of simulation conditions; c) loading the master dataset into the primary memory of a computer; d) generating a simulated template at a first resolution in the primary memory of the computer by using the master dataset from the primary memory and geometric calibration data describing the relative positions of at least the location on the sample, the electron beam and the detector, wherein the simulated template represents a simulated electron diffraction pattern for a nominal crystallographic orientation; e) comparing the simulated template with the experimental electron diffraction pattern so as to generate a corresponding similarity measure; f) storing the crystallographic orientation and the corresponding similarity measure for the given simulated template; g) repeating steps d to f for all crystallographic orientations according to one or more crystallographic orientation intervals; h) repeating steps d to g for each location of the sample; i) repeating steps c to h for each phase; and, j) analysing the similarity measures stored in step f so as to select at least one resultant indexed phase and orientation for each location.

2. A method according to claim 1, wherein, during step d, the simulated templates are only generated whilst the master dataset is present within the primary memory of the computer.

3. A method according to claim 1, wherein the simulated templates are discarded from the primary memory before step g.

4. A method according to claim 1, wherein step h is repeated more than 100000 times.

5. A method according to claim 1, wherein the crystallographic orientation interval used is in the range 1 to 3 degrees.

6. A method according to claim 1, wherein, following the selection of a resultant indexed phase for a location, the method further comprises: i) obtaining the experimental electron diffraction pattern used in step a at a second resolution; ii) generating second simulated templates at the second resolution using the master dataset based upon the selected indexed phase, wherein the second simulated templates represent simulated electron diffraction patterns for crystallographic orientations corresponding to that of the indexed phase and which are modified at one or more crystallographic orientation sub-intervals which are smaller than the intervals in step f; iii) comparing the second simulated templates with the experimental electron diffraction pattern so as to generate a corresponding similarity measure; and, iv) analysing the similarity measures relating to the second simulated templates so as to select at least one resultant indexed phase and orientation for the location which has an improved similarity measure in comparison with that obtained using the simulated templates.

7. A method according to claim 6, wherein step (ii) is performed using the Nelder-Mead or Downhill Simplex methods.

8. A method according to claim 1, wherein the first resolution is lower than a native resolution at which the experimental electron diffraction pattern was originally produced by the detector.

9. A method according to claim 1, further comprising converting the experimental diffraction patterns to the first resolution prior to step d.

10. A method according to claim 1, wherein the simulated templates generated in step d have a resolution of fewer than 50 pixels for each dimension.

11. A method according to claim 1, wherein a plurality of locations are arranged on the sample surface in an array.

12. A method according to claim 1, wherein the similarity measure is an image correlation measure.

13. A method according to claim 12, wherein the image correlation measure is a normalised cross correlation coefficient, NCCC.

14. 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.

15. 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.

16. A system according to claim 15, 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.

17. 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.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0053] We now describe a system and method with reference to the accompanying drawings, in which:

[0054] FIG. 1 is a schematic illustration of part of the vacuum chamber of a scanning electron microscope which includes a computer system;

[0055] FIG. 2 is a flow diagram of a method according to an embodiment;

[0056] FIG. 3 shows examples of master simulation datasets for two different phases;

[0057] FIG. 4 shows an experimental EBSP (left) and simulated templates austenite (centre) and ferrite (right);

[0058] FIG. 5 shows a method of refining the indexing result;

[0059] FIG. 6 shows an experimental EBSD (left) with corresponding refined simulated template (right); and,

[0060] FIG. 7 shows the results of indexing a nanocrystalline sample using a Hough-transform method (left) and the method of the embodiment (right).

DETAILED DESCRIPTION

[0061] With reference to the accompanying drawings, FIG. 1 is a schematic representation showing some parts of a system that are employed in a scanning electron microscope (SEM) 1 for analysing a sample of material. The SEM electron beam 5 is produced inside an evacuated chamber and usually focussed with a combination of magnetic lenses forming the “SEM column”, the final part of which, the SEM final lens pole piece 10 is shown in FIG. 1. When the focussed beam 5 strikes a sample held in a sample holder 15, some electrons are scattered back from the specimen (backscattered electrons or BSE in this embodiment) or interact with the specimen to produce secondary electrons (SE) and a number of other emissions such as X-rays. Kikuchi band patterns are caused by diffraction of the emerging backscattered electrons. The backscattered electrons BSE 20 are detected by an EBSD detector 25. A separate x-ray detector 30 is used to detect the x-rays for analysis.

[0062] An alternative geometry configuration uses a thin sample that is supported so that the focussed electron beam is transmitted through the sample and the detector is placed below the sample so that electrons scattered from beneath the sample strike the detector which is used to form an image that contains a “transmitted electron Kikuchi pattern” or TKD pattern.

[0063] The SEM 1 includes a computer system 50 which is used to operate the microscope, including receiving data from the EBSD detector 25. The computer system 50 takes a conventional form having input devices 55 such as a keyboard and mouse, and output devices 60 such as a display and printer. The computer system 50 has a central processing unit CPU 55. The CPU 55 includes a control unit 65 which controls the operation of the system 50 including its component parts. The CPU 55 includes an arithmetic and logic unit 70 which performs the majority of the processing underlying the method to be described. The CPU 55 also includes primary memory 75 in the form of RAM. External to the CPU 55 there is provided secondary memory 80 arranged as a solid state hard disc which has a much larger memory capacity than the primary memory 75. The secondary memory 80 is provided as a non-volatile memory. The control unit 65 may cause data from the secondary memory 80 to be loaded into the arithmetic and logic unit 70, although in order for this to be achieved it must be firstly loaded into the primary memory 75.

[0064] In this embodiment electron backscatter diffraction patterns are analysed from a steel sample using the SEM 1. The steel sample is known to comprise two principal phases: austenite (which has a face centred cubic structure) and ferrite (which has a body centred cubic structure). The sample is prepared for analysis using standard metallurgical techniques and is then loaded into the chamber of the SEM 1.

[0065] Reference is now made to FIG. 2 which shows a summary of the steps of the method now described.

[0066] At step 100 the electron beam 5 is caused to be incident on the surface of the sample at each location of a 100 by 100 square grid array, with the distance between the locations being 1 micrometre. An electron backscatter diffraction (EBSD) pattern is generated at each location due to the interaction between the electron beam 5 and the sample material, and this is detected by the EBSD detector 25 forming part of the SEM 1. The EBSD pattern is stored by the computer system 50 in the primary memory 75 forming part of the microscope system, together with the position of the relevant location on the sample and the relative positions of the electron beam, sample and the EBSD detector.

[0067] The purpose of the use of an array of locations is to provide EBSD analysis information from an area of the sample, for example to provide information including one or more of the size, orientation, distribution and relative quantities of the phases within the steel sample.

[0068] At step 105, the parameters are defined which are needed for the calculation, in step 110, of simulated master diffraction patterns for the two known phases in the sample. Thus in this case there are two known “candidate phases” in the dataset which is to be generated, here these being the ferrite and austenite phases. The input parameters are the phase crystallography (space group and unit cell parameters), the atomic coordinates, the atom types and their occupancy at each atomic site, the electron beam energy, the minimum desired diffracted reflector intensity, the minimum lattice plane spacing, the Debye-Waller factor and the master simulation resolution. The phase atomic and crystallography data are usually included in a standard crystallography information file (*.cif format) and therefore can be readily obtained from such a file.

[0069] At step 110, a simulated master diffraction pattern in the form of a master simulation file is generated using the computer system 50 for each of the phases (ferrite and austenite), using the parameters defined in step 105. The computer system 50 used for this purpose is that used to control the microscope, although a separate computer system could be used instead. The master simulation file includes the predicted diffraction intensities for all crystal directions and is stored in the primary memory 75 of the computer system 50 for subsequent reference. The master simulation can be generated using full dynamical, 2-beam dynamical or kinematical models as desired. Alternatively, it could be derived from experimentally collected diffraction patterns. FIG. 3 shows examples of master simulation files, generated using dynamical simulations with a beam energy of 20 kV, for austenite (left) and ferrite (right).

[0070] The method then proceeds by analysing the experimental EBSD pattern at each location in the grid in turn, according to the following series of steps performed for each location.

[0071] At step 115 the “next” location in the grid of measurements (for example, starting at location x=1, y=1, referring to position in the grid) the experimentally collected EBSD pattern (from step 100) is loaded by the software running on the computer system to become the current location for processing by the software. This EBSD pattern may be at the native detector resolution, although for the sake of data storage and transfer, it can be that the images in the original detector resolution are downsized (“binned”) to a smaller resolution prior to the start of this pattern matching process.

[0072] At step 120 the experimental EBSD pattern from step 115 is downsized to a lower resolution, in this case about 40×30 pixels. In the following steps simulated “template” EBDS patterns of the same low resolution will be calculated and compared with this experimental pattern.

[0073] At step 125, the relative geometry of the measurement location on the sample surface with respect to the detector 25 is defined. This is typically expressed as the position of the EBSD pattern centre on the detector (the pattern centre being defined as the point on the detector that is closest to the electron beam—sample interaction point, i.e. the “current location” which is the origin of the diffraction pattern) and the detector distance (the distance from the detector to the electron beam—sample interaction point). These geometry calibration values are calculated from the detector calibration values taking into account the focal plane of the electron beam (“working distance”) and the detector insertion distance in the chamber of the SEM 1. It should be noted that the standard measurement of the pattern centre and detector distance is typically not very accurate, and so these values are usually refined prior to the pattern matching process.

[0074] At step 130, using the simulated master diffraction pattern of a first of the known phases (austenite or ferrite) held in the master simulation file within the primary memory 75, a simulated diffraction pattern template is derived for a nominal crystallographic orientation, using the geometry calibration values for the relevant location (from step 125 above) and at the same resolution as the downsized experimental diffraction pattern (e.g. approximately 40×30 pixels). Referring again to FIG. 3, the nominal crystallographic orientation used relates to a nominal small part of the pattern shown in FIG. 3.

[0075] At step 135 the simulated template is then correlated to the experimental pattern within the primary memory 75. The similarity between the two images is calculated, for example using the normalised cross correlation coefficient (NCCC) technique. This gives a value between 0 (images are completely different) and 1 (images are identical, or an inverse of each other).

[0076] At step 140, the NCCC value and corresponding crystallographic orientation (for which the template has been simulated) are stored in the primary memory 75. Notably the template is discarded from the primary memory 75 as this frees up space for the next template and ensures the method does not require large amounts of memory to be occupied by the large number of templates which are generated as the method progresses.

[0077] At step 145, the above steps 130 to 140 are repeated for all possible crystallographic orientations of the phase in question, at a predefined orientation spacing (typically 2°). Quaternions may be used as a method of representing the orientations so as to allow their systematic variation. This is performed for all candidate phases, for which in the present example there are two (austenite and ferrite). The resulting data therefore includes the NCCC values for all possible orientations (at the predefined orientation spacing) and for all phases. The present step could therefore be divided into two steps, for example firstly in which all possibly orientations are explored for a current phase, and then doing the same for the next phase until all phases had been investigated.

[0078] With reference to FIG. 4, there is shown an example experimental diffraction pattern from an austenite crystal (left), downsized to 39×32 pixels, with the best fitting simulated template for ferrite (centre—with NCCC=0.34) and for austenite (right—with NCCC=0.81).

[0079] At step 150 the phase and orientation corresponding to the template that matches the experimental pattern with the highest NCCC value is then stored in the primary memory 75.

[0080] Depending upon the application in question, including considerations such as the number of phases, crystal systems of those phases and the orientation spacing used, it may be beneficial to perform an optional series of steps to refine the best fitting template. Such optional refinement steps are now described in steps 155 to 170 below, and in association with FIG. 5.

[0081] At step 155 the template which provided the best match (from step 150) with the experimental pattern is now used as an initial template for refinement, such refinement including the generation of a number of further templates with slightly modified orientations. Using the orientation corresponding to the best matching template, a higher resolution template for that orientation is then calculated, again using the master simulation pattern held in the computer primary memory 75. The resolution chosen for this simulated higher resolution “image” of the template, and other templates involved in the refinement process, may use the same native resolution of the original experimental diffraction pattern (which is dependent upon the EBSD detector 25), although an intermediate resolution between this and the low resolution used in step 130 is also possible. It will be understood that higher resolutions allow greater precision of the data. The NCCC value is calculated using the new higher resolution image for the template, in this case the comparison being with the experimental diffraction pattern at its native resolution, rather than at the lower resolution generated by step 120. Again, the template is discarded from the primary memory 75.

[0082] At step 160, a new template is generated for a slightly modified crystallographic orientation and is matched to the experimental pattern at the new resolution and the corresponding NCCC value is calculated. The modification of the crystallographic orientation is less than the predefined orientation spacing (2°) of step 145. A typical orientation step change would be in the range of 1 mrad, which is about 0.005°. A number of different approaches can be used to decide upon how the orientation is modified as are discussed further below. The NCCC value is compared to that measured in the previous step to determine whether the match has improved or worsened. The template is then discarded from the primary memory 75.

[0083] At step 165 a new template is generated for a further slightly modified crystallographic orientation, where the direction of crystallographic rotation is determined by the change in NCCC value in step 160 and according to the overall approach being used to improve the NCCC value. The new template is matched to the experimental pattern and a new NCCC value calculated. The template is again discarded from the primary memory 75.

[0084] At step 170 steps 160 and 165 are repeated, using the chosen optimisation approach (e.g. Nelder-Mead or Downhill Simplex) to find the crystallographic orientation that gives the highest NCCC value. In the Nelder-Mead method for example, the orientation parameter angles are each modified individually to generate each template, in a first stage, and then combinations of these are considered in a later stage. The orientation changes are made progressively smaller between each new template until the change in NCCC between successive solutions is below a predetermined threshold, e.g. 0.0005. FIG. 6 shows an example experimental diffraction pattern from an austenite crystal (left) at the native 156×128 pixel resolution, with the corresponding simulated template (right) following the orientation refinement process. The increase in resolution is notable in comparison with that shown in FIG. 4.

[0085] At step 175, returning to the method of FIG. 2, the NCCC of the final solution (best matching phase and orientation) is compared with a predefined threshold (e.g. NCCC=0.15). If the NCCC value equals or exceeds this threshold, then the phase and orientation values are assigned to the measurement location of the grid and then stored to the primary memory 75. If the NCCC is below the threshold, then the results are discarded and the measurement is designated as “not indexed”.

[0086] At step 180, having achieved an indexed or non-indexed solution for the first location in the grid array, steps 115 to 174 are then repeated for each measurement location in the 100×100 grid of measurements on the sample surface.

[0087] Once an indexed or non-indexed solution has been produced for each of the locations, this data may then be used in later analysis or display steps depending upon the particular application. For example the analysis software running on the computer system 50 may process the information further so as to assign a colour scheme to the phases for the purposes of displaying to a user. Another approach might be to provide further analysis in order to provide the user with information concerning the crystallographic texture of the sample. The orientation and phase data determined for each of the locations may also be used to calculate grain sizes, to quantify the extent of plastic deformation in the sample or to calculate the crystallographic properties of boundaries, all of which will influence the bulk physical properties of the material.

[0088] The principal benefit of this new approach of dynamic template matching is one of speed. As an example, the reanalysis of an experimentally obtained dataset with a single, cubic phase using dictionary indexing has been reported to take approximately 1 second to initially index and refine the data for each location on the sample, on top of the time taken to generate the library of simulated templates at different orientations, initially. With the dynamic template matching method, using a comparable computing system, approximately 45 locations per second can be indexed and no time is required for an initial orientation dependent library of patterns to be created.

[0089] In order to further illustrate the practical use of this dynamic template matching method, an analysis was performed of experimental EBSPs from nanocrystalline hydroxyapatite crystals in human tooth enamel. The small size of the grains in this material, coupled with significant amounts of crystal defects, results in very poor diffraction pattern quality and thus poor results using conventional Hough-transform based indexing. Referring now to FIG. 7, the left-hand image in the figure shows an orientation map collected using Hough-transform indexing, with only 29% of patterns indexed (black areas indicate non-indexed locations). The patterns were then reanalysed using dynamic template matching, with 72% indexing as shown on the right-hand image. The full reanalysis took 70 minutes (including master simulation pattern creation and orientation refinement), whereas the dictionary indexing method using the same hardware would likely take in excess of 24 hours (plus the time to create the library of templates).