Automating SAED phase identification using machine learning

Abstract

A method is provided for automating a selective area electron diffraction (SAED) phase identification process. Experimental data and a list of candidate phases are received, with the experimental data including experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles. Simulated SAED patterns for the list of candidate phases are generated. A first neural network is trained using the simulated SAED patterns to predict a phase and zone axis of each simulated SAED pattern, and an output of the trained first neural network is combined simulated data arrays fed into a second neural network for training. The experimental SAED patterns are then fed through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern. An output of the trained first neural network is combined experimental data arrays fed through the trained second neural network to determine phase matches for the experimental SAED patterns. The predicted phase matches for the experimental SAED patterns are displayed.

Description

Attorney Ref. No. 10457-586PC0 AUTOMATING SAED PHASE IDENTIFICATION USING MACHINE LEARNING Cross-Reference To Related Applications

[0001] The present application claims the benefit of U.S. Provisional Patent Application Serial Numbers 63 / 549,328 filed February 2, 2024 and 63 / 566,694 filed March 18, 2024, all of which are fully incorporated by reference. Technical Field

[0002] The present disclosure relates to computing systems, and, more particularly, to a computing system using machine learning for automating phase identification of selective area electron diffraction (SAED) patterns, and associated methods. Background

[0003] Crystallographic information on a material of interest can be obtained experimentally through illumination of a sample by a radiation source (neutron, x-ray, or electron). The diffraction of the incoming radiation is dependent on the arrangement of atoms in the solid, such that each periodic arrangement of atoms (crystal structure) will produce unique diffraction patterns.

[0004] The two most often used approaches for crystallographic phase identification are X-ray diffraction (XRD) and selective area electron diffraction (SAED). XRD produces very precise signals that enable measurement of crystal parameters, but the size of the incoming X-ray beam limits the achievable resolution from this technique. In addition, XRD measures the phases present in the entire sample without ability to identify phases in a select location. SAED, on the other hand, is acquired using a transmission electron microscope (TEM) and enables characterization of nanoscale phases. Such phases would be unresolvable in XRD and thus SAED allows phase identification at a specific location, providing valuable insight into the structure of materials. This makes SAED a powerful technique for microstructure characterization, especially when combined with other electron microscopy tools.Attorney Ref. No. 10457-586PC0

[0005] The phase identification is done by comparing experimentally obtained SAED patterns to simulated patterns. Several commercially available software can simulate diffraction patterns. In all available software, SAED patterns are manually uploaded, and an operator must match an individual pattern to a possible phase by overlaying an experimentally captured SAED pattern over a simulated pattern. This must be repeated for all possible phases until a match in the diffraction spot pattern has been found. For a single experimentally obtained pattern, a researcher would potentially need to sift through hundreds of simulated patterns to obtain a match.

[0006] For illustration purposes, a manual classification workflow is provided in FIG. 1. Step 1 is labeled data collection, where data is collected experimentally by a user using a TEM. The experimental data typically includes SAED data or energy dispersive spectroscopy (EDS) data. At step 100, SAED patterns are obtained for the sample of interest at a specific region of interest, preferably at multiple tilt angles to increase confidence in the potential phase match. At step 102, EDS scans are analyzed using third-party software from a TEM instrument vendor. Energy peaks are matched to determine the approximate elemental composition in the region. The elemental composition allows a user to down-select possible phases for phase identification. At step 104, all experimental data is exported into an easily processible image file (e.g., .TIF, .PNG, etc.) for use in phase identification. The export of the data into commonly recognizable image file formats allows standardizing the data as each TEM instrument vendor has their own proprietary data files that cannot be opened on a different microscope. At step 106, based on the elemental scans and knowledge of the sample, the possible candidate phases are determined. Crystallographic Information Files (CIF) are obtained using an external crystal database.

[0007] During manual classification, at step 108, a phase and a zone axis are chosen. Software (e.g., SingleCrystal) may be used to simulate the diffraction pattern for that phase at that zone axis. At step 110, one of the experimentally acquired patterns is chosen. The experimental pattern is overlayed onto the simulated pattern. Attention must be paid to the scale bars to ensure both patterns are at the same scale. At step 112, the patterns are manually aligned as best as possible through user rotation and translation of one of the patterns. At step 114, the user checks if the patterns visually match after best alignment. At step 116, if patterns do not visually match in step 114, then the user checks if all other zone axes have been tested for the current phase against the experimental pattern. At step 116, if there are remaining zone axes to check for the current phase at step 114, then the user selects a new zone axis and restarts the process. At step 118, if all zoneAttorney Ref. No. 10457-586PC0 axes have been checked for the current phase, then the user selects a new phase and restarts the process. Step 118 may be repeated for clarity. At step 120, the user checks if the patterns visually match after best alignment. At step 122, if patterns match in step 120, then the user checks if all other phases and zone axes have been checked against this experimental pattern. At step 124, if all other phases and zone axes have not been checked for this pattern, the user continues checking the remaining phases and zone axes. At step 126, if all other phases and zone axes have been checked for this pattern in step 122, the user checks if all other experimental patterns for the sample have been matched. At step 124, if there are experimental patterns remaining to be matched at step 126, the user must restart the process for the remaining experimental patterns. At step 130, if all other experimental patterns have been matched at step 128, the user can make a final determination of the sample phase based on the matches.

[0008] In view of the above described manual classification approach, automating phase identification and eliminating manual processing for SAED patterns is highly desirable to accelerate materials characterization. To remedy this, researchers have created algorithms that attempt to automate the identification of SAED patterns.

[0009] Previous automation attempts can very broadly be categorized as either deterministic or stochastic. Deterministic methods are those that use completely defined parameters to determine the phase. These algorithms are not reliable as they will re-produce input as the result. Past deterministic approaches include those by Lábár et. al., Li et. al, and Honglong et. al. published in various journals. Each of these approaches is different but have in common that they pull features from an SAED pattern, process these features, and compare it to reference patterns (i.e., simulated patterns). For example, Lábár et. al. uses the distance and angle between diffraction spots as the feature, while Honglong et. al. uses rotational averaging to create one-dimensional diffraction peaks as the feature of interest, but both ultimately compare these features to a reference based on simulated patterns. The comparison is done by defining an error tolerance. If the features of interest are within the tolerance value, then the reference pattern is marked as a potential match.

[0010] Stochastic methods, on the other hand, are either partly or entirely based on methods that rely on probability for phase determination. An example would be a neural network, as the nature of the training process means that two neural networks trained on the exact same input may not produce the same output.Attorney Ref. No. 10457-586PC0

[0011] As outlined, specific methodology varies but is generally based on calculating point-to- point distance for the experimental and simulated patterns, and then determining which simulated patterns fall within some defined tolerance of the experimental pattern. The problem with these approaches is two-fold.

[0012] The first problem is that there is no universal acceptable tolerance value, and too strict of a tolerance may preclude the correct pattern without the user knowledge. Conversely, too loose of a tolerance may still result in many patterns that need to be manually sifted through. As a result, the heuristically defined tolerance value can either lead to a false negative or to a long list of matching patterns with no clear indication of which pattern is most likely.

[0013] The second problem with current methods is the difficulty in considering multiple diffraction patterns of the same sample, with the only difference being the electron beam direction. In a manual analysis, the confidence in each phase identification can be increased by tilting the sample while it is in the instrument to allow for multiple diffraction patterns to be obtained with different tilts. Each individual pattern will look different, but all should be able to be traced back to the same crystallographic phase. Some automated algorithms have attempted to consider multiple patterns to make a more confident determination, for example by using the sample tilt angles from the instrument to inform the expected beam direction of the patterns. However, this process is still ultimately susceptible to the issues in the previous paragraph. Furthermore, the sample tilt information may not be available during data processing, making this approach untenable. Summary

[0014] A method for automating a selective area electron diffraction (SAED) phase identification process includes receiving experimental data and a list of candidate phases, with the experimental data comprising experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles. Simulated SAED patterns for the list of candidate phases are generated. The method includes training a first neural network using one of the simulated SAED patterns to predict a phase and zone axis of the simulated SAED pattern used for the training, and feeding the simulated SAED patterns through the trained first neural network to predict a phase and zone axis of each simulated SAED pattern. The predictions are combined into combined simulated data arrays. The method includes training a second neural network using theAttorney Ref. No. 10457-586PC0 combined simulated data arrays, and feeding the experimental SAED patterns through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern. The predictions are combined into combined experimental data arrays. The combined experimental data arrays are fed through the trained second neural network to determine phase matches for the experimental SAED patterns. The predicted phase matches for the experimental SAED patterns are displayed.

[0015] The displayed predicted phase matches may include a final predicted phase match having a highest confidence for the experimental SAED patterns. The displayed predicted phase matches may include overlay of one of the simulated SAED patterns that best matches with one of the experimental SAED patterns.

[0016] The method may include calculating diffraction spot spacing on the experimental SAED patterns to be fed into the trained first neural network.

[0017] The predictions in the combined simulated data arrays share a common phase, and the predictions in the combined experimental data array share a common phase. The predictions for the combined simulated data arrays are combined based on concatenation of the predictions, and the predictions for the combined experimental data arrays are combined based on concatenation of the predictions.

[0018] The combined simulated data array are arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the simulated SAED patterns matching one of the predicted phase and zone axis, and wherein the combined experimental data arrays are an arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the experimental SAED patterns matching one of the predicted phase and zone axis.

[0019] The number of zone axis included in the combined experimental data arrays corresponds to a number of experimental SAED patterns that were received.

[0020] The experimental data may further include energy dispersive x-ray spectroscopy (EDS) data on the material of interest. The experimental SAED patterns are at a specific region of interest.

[0021] Another aspect is directed to a computing system for automating a selective area electron diffraction (SAED) phase identification process as described above. The computing system includes a memory to store experimental data and a list of candidate phases, with theAttorney Ref. No. 10457-586PC0 experimental data comprising experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles.

[0022] A processor is coupled to the memory and is configured to generate simulated SAED patterns for the list of candidate phases, train a first neural network using one of the simulated SAED patterns to predict a phase and zone axis of the simulated SAED pattern used for the training, and feed the simulated SAED patterns through the trained first neural network to predict a phase and zone axis of each simulated SAED pattern. The predictions are combined into combined simulated data arrays. A second neural network is trained using the combined simulated data arrays, and the experimental SAED patterns are fed through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern. The predictions are combined into combined experimental data arrays. The combined experimental data arrays are fed through the trained second neural network to determine phase matches for the experimental SAED patterns. The predicted phase matches for the experimental SAED patterns are displayed on a display coupled to the processor.

[0023] Yet another aspect is directed to a non-transitory computer readable medium having computer-executable instructions for causing a computing system to automate a selective area electron diffraction (SAED) phase identification process, with the computing system to perform steps as described above. Brief Description of the Drawings

[0024] FIG. 1 is a flow diagram for a selective area electron diffraction (SAED) phase identification process based on a manual phase identification according to the prior art.

[0025] FIG. 2 is a block diagram of a computing system with a layered neural network for automating the SAED phase identification process in which various aspects of the disclosure may be implemented.

[0026] FIG. 3 is a flow diagram for the SAED phase identification process to be performed by the computing system illustrated in FIG. 2.

[0027] FIG. 4a-4c are screenshots of a graphical user interface (GUI) for the SAED phase identification process illustrated in FIG. 3.

[0028] FIGS. 5a-5d are screenshots showing diffraction spot spacing for experimental and simulated SAED images based on the SAED phase identification process illustrated in FIG. 3.Attorney Ref. No. 10457-586PC0

[0029] FIG. 6 is a block diagram of a layered neural network workflow of the SAED phase identification process illustrated in FIG. 3.

[0030] FIG. 7 is a confusion matrix showing predicted phases versus true phases for the SAED phase identification process illustrated in FIG. 3.

[0031] FIG. 8 is a flowchart for automating the SAED phase identification process illustrated in FIG. 3. Detailed Description

[0032] The present description is made with reference to the accompanying drawings, in which exemplary embodiments are shown. However, many different embodiments may be used, and thus the description should not be construed as limited to the particular embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete. Like numbers refer to like elements throughout, and prime notations may be used to indicate similar elements in different embodiments.

[0033] Referring initially to FIG. 2, a computing system 20 for automating a selective area electron diffraction (SAED) phase identification process will be discussed. Learning algorithms are used for automating phase identification of individual SAED patterns. This approach is based on a two-layered neural network structure. In this case, the term “layers” refers to the two distinct neural networks that work in sequence, not to the number of traditional layers within a given neural network.

[0034] The computing system 20 includes a memory 22 to receive experimental data 24 and a list of candidate phases 28. The experimental data 24 includes experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles. The list of candidate phases 28 helps to identify possible candidate phases to reduce the time needed to identify the phase of a SAED pattern. As will be discussed in greater detail below, a processor 30 is coupled to the memory 22 and is configured execute a phase identification process algorithm 29.

[0035] In response to execution of the phase identification process algorithm 29, simulated SAED patterns 32 are generated which are then used to train first and second neural networks 34a, 36a. The first neural network 34a is trained using one of the simulated SAED patterns 32 to predict a phase and zone axis of the simulated SAED pattern used for the training. The simulated SAED patterns 32 are fed through the trained first neural network 34b to predict a phase andAttorney Ref. No. 10457-586PC0 zone axis of each simulated SAED pattern 32, with the predictions being combined into combined simulated data arrays. The second neural network 36a is trained using the combined simulated data arrays.

[0036] Next in the process, the experimental SAED patterns 24 are fed through the trained first neural network 34b to predict a phase and zone axis of each experimental SAED pattern 24, with the predictions being combined into combined experimental data arrays. The combined experimental data arrays are fed through the trained second neural network 36b to determine phase matches for the experimental SAED patterns 24. Based on the output of the trained second neural network 36b, the final phase predictions 52 for the experimental SAED patterns 24 are displayed on a display 50 coupled to the processor 30.

[0037] The first neural network 34a classifies the phase and electron beam direction (hereafter referred to as the “zone axis”) of a SAED pattern based on many potential simulated patterns 32. Each unique phase and zone axis is denoted as a “P+Z class”. The output of the first neural network 34a are arrays of numbers, where the value at each index corresponds to the probability of a given P+Z class being correct. Patterns from multiple tilts of the same sample are independently fed through this first layer, and the output probability arrays from each sample are then combined into combined simulated arrays. These arrays, which represent the independent predictions for each sample tilt, are then fed into the second neural network 36a that is trained to determine the overall phase based on P+Z predictions for the simulated SAED patterns 32.

[0038] This layered approach produces higher confidence and greater accuracy compared to a single model. It also produces a confidence value for each final phase prediction, providing the user with a ranked list of potential matches rather than an unordered list that is provided by current methods. The use of learning algorithms utilized herein allows incorporation of elemental scan data directly into the prediction, as elemental scans can be vectorized to be used as input into either layer of the neural network.

[0039] The computing system 20 is distinctively different from prior attempts to automate phase identification. First, the present disclosure does not rely on reference tables as the deterministic approaches do. Instead, simulated patterns are used to create training data for a neural network. The neural network learns to distinguish between patterns based on a feature of interest (e.g., the distance and angles between diffraction spots) without relying on heuristically set tolerance values. Not only does this eliminate the possibility of excluding the true phaseAttorney Ref. No. 10457-586PC0 because of too strict of a tolerance value, but the neural network produces a probability associated with each prediction, yielding a ranked list of possible matches. This is a distinct advantage over the deterministic methods, which do not have the ability to rank potential matches. The deterministic methods may still leave a significant amount of manual matching to be done if the number of matches that fall within tolerance is high. Neural networks also allow for easy featurization of data, meaning that other information about the sample (e.g., the chemical composition) can easily be incorporated into the prediction without defining another set of tolerance values or modifying the overall method.

[0040] Second, prior attempts for SAED processing used convolutional neural networks, which use the entire image as input. Convolutional neural networks then learn to process the image to extract useful information. The present disclosure does not use convolutional networks, instead opting to pull features out using deterministic image processing algorithms. The pulled features are then used as input to a neural network. This reduces the computational burden of processing the full image within the neural network and focuses the training on the most relevant features.

[0041] Another difference in the present disclosure is in what the algorithm is predicting. In past efforts, the researchers used machine learning to classify the symmetry of the crystal, predicting either the space group or crystal system. This makes it easier to accumulate training data, as many different crystals can be used to train a single class if they have the same underlying symmetry. The limitation with this, though, is that it cannot identify specific phases, which is a goal of the present disclosure. If the potential phase list contains phases that have the same symmetry, past approaches would be unable to distinguish them. The present disclosure trains to learn the specific phase that the SAED pattern portrays, allowing for a direct prediction of the target variable.

[0042] The final and most significant difference between the present disclosure and previous machine learning approaches is the use of two neural networks in the prediction, where the output from the first neural network 34a is used as input to the second neural network 36b. The trained first neural network 34b predicts the phase and zone axis of the experimental SAED pattern, and the trained second neural network 36b uses multiple independent predictions from the trained first neural network 34b with different sample tilts to predict the overall phase common to the first layer inputs. Essentially, the trained second neural network 36b learns toAttorney Ref. No. 10457-586PC0 generalize based on the specific predictions of the trained first neural network 34b. This paradigm provides a significantly improved prediction performance. Use of a neural network that feeds into another neural network to enhance the prediction capability is unique not only to SAED phase prediction, but to the neural network field in general.

[0043] Referring now to FIG. 3, an overall workflow for automating a selective area electron diffraction (SAED) phase identification process will be discussed in greater detail. Reference will also be made to the graphical user interfaces (GUI) in FIGS. 4a-4f supporting the workflow. Part 1 is labeled data collection, and part 2 is labeled software algorithm. The software algorithm in part 2 corresponds to the phase ID process algorithm 29 discussed above. Part 1 data is collected experimentally by a user using a transmission electron microscope (TEM), following the procedure previously described in FIG. 1. The experimental data typically includes experimental SAED data 24 at step 300 and optionally EDS scans 26 at step 302. At step 300, the experimental SAED patterns 24 are obtained for the sample of interest at a specific region of interest, preferably at multiple tilt angles to increase confidence in the potential phase match. At step 302, the EDS scans 26 are analyzed using third-party software based on TEM instrument vendor. Energy peaks are matched to determine the approximate elemental composition in the region. This step is optional and does not preclude phase identification that is conducted by the software algorithm. At step 304, all experimental data 24, 26 is exported into an easily processible image file (e.g., .TIF, .PNG, etc.) for use in phase identification. The export of the data into commonly recognizable image file formats allows standardizing the data as each TEM vendor has their own proprietary data files that cannot be opened on a different microscope.

[0044] At step 306, based on the elemental scans and knowledge of the sample, it is helpful to identify possible candidate phases 28 to reduce the time needed to identify the phase of the SAED sample. For instance, if after considering the material of interest, a researcher identifies 50 possible phases that are predicted as possible by existing phase diagrams, computational time can be greatly reduced by only considering these 50 possible phases instead of thousands of phases. Crystallographic Information Files (CIF), available through external crystal databases, can be uploaded into the computing system 20. These .CIF files provide crystallographic information for each phase, are standard source file format for phase identification, and are available through various open access crystallographic databases. This step may optionally be incorporated into the algorithm in part 2. If no information is available on the material of interest,Attorney Ref. No. 10457-586PC0 all possible phases may be run through the software algorithm to find a possible phase match. If this is the case, processing time will be longer as the algorithm will have to match experimental data to all possible phases.

[0045] At step 308, the user starts the program, and the graphical user interface (GUI) is displayed on the display 50. At step 310, the GUI is used to input the experimentally obtained SAED patterns 24 and other available elemental data. In screenshot 200 in FIG. 4a, the experimental SAED patterns 24 may be loaded via section 202. The other experimental element data includes energy dispersive spectroscopy (EDS) data 26, for example, as would be displayed in section 204.

[0046] At step 312, the experimental SAED images 24 are processed to improve quality. The position of diffraction spots in each image is found and displayed to the user for visual verification. Two of the experimental SAED images 24 are shown in screenshots 210, 212 in FIG. 4b. For each experimental SAED image 24, the white dots are diffraction spots and the + placed in each diffraction spot corresponds to matching simulated SAED images 32 being overlaid thereon. For each of the diffraction spots (i.e., white dots) on the SEAD pattern, the physical distance between individual diffraction spots can be measured by referencing a scale bar in each experimental SAED image 24 (i.e., TEM camera length used to acquire the experimental SAED data).

[0047] At step 314, the user inputs the .CIF files from step 306 to the GUI. This is shown by screenshots 220, 222 in FIG. 4c and 4d. Screenshot 220 displays that there are 22 phases and 974 phase and zone axes are being examined. Screenshot 222 displays detailed information on each of the phases. At step 316, each .CIF file is parsed to simulate the experimental SAED diffraction patterns for all possible zone axes for each possible phase (denoted as P). Here, zone axis (referred to as Z) refers to the diffraction pattern taken with an incident electron beam traveling along the lattice direction of the crystal. The small wavelength of the electron beam in TEM produces a very large Ewald sphere radius, and thus diffraction spots with g-vectors that are perpendicular to Miller indices of the crystal. Note that Miller indices are standard form of a noting lattice planes in a crystal. For example, in low-Miller index lattice planes, electron beam will have small spatial frequencies (g-values) and hence large lattice spacing (d-spacing). For accurate phase identification, it is a standard practice to acquire experimental SAED data 24 at several possible zone axes by tilting TEM holder to different tilt angles. Different tilt angles willAttorney Ref. No. 10457-586PC0 produce diffraction patterns with varying d-spacing, which is important to capture to discern phases that have similar lattice parameters. Therefore, the software algorithm, i.e., the phased ID process algorithm 29, will read the crystallographic file and simulate all possible crystallographic zone axes to use as a training dataset. This ensures that even minute differences in lattice positions have been captured to the highest degree of accuracy.

[0048] Steps 318-330 are unique, where the software algorithm 29 is used to automate the phase identification of the experimental SAED patterns 24. As noted above, an advantage of this approach lies in the two-layered neural network (NN) structure. In this case, the term “layers” refers to the two distinct neural networks that work in sequence, not to the number of traditional layers within a given neural network.

[0049] At step 318, a first neural network (NN1) 34a is initialized to receive an input based on parsed .CIF files simulated in step 316. The first neural network 34a uses one of the simulated SAED patterns 32 to predict a phase and zone axis of the simulated SAED pattern used in the training.

[0050] At step 320, after the first neural network 34a has been trained to produce “P+Z” predictions, all of the simulated SAED patterns 32 from multiple tilts are independently fed through the first neural network 34a again to ensure the accuracy of the prediction. The uniqueness of the output of first neural network 34a are arrays where each value corresponds to the probability of a given phase and zone axis. This ensures that the first neural network 34a performs as expected and is capable of producing reliable “P+Z” predictions before the software algorithm 29 is applied to the experimental SAED patterns 24. The output of each simulated pattern fed through the first neural network 34a is saved.

[0051] At step 322, the output probability arrays for each phase are then combined into combined simulated data arrays, which represents the independent predictions for each sample tilt. Here, the number of zone axes included in each combined array depends on the number of experimental patterns that were provided in step 310. For instance, if the experimental data 24, 26 consisted of three tilt angles and thus three individual SAED patterns with distinctive g-values and d-spacing, the first neural network 34a output will produce a number of SAED patterns that matches the experimental conditions. The output probability arrays generated in step 322 will ensure that the software algorithm 29 can predict the phase with a high degree of accuracy, regardless of which zone axis was used to simulate the SAED pattern.Attorney Ref. No. 10457-586PC0

[0052] At step 324, the combined simulated data arrays from step 322 are fed into a second neural network (NN2) 36a, which is trained to determine the overall phase based on P+Z predictions. The predictions in the combined simulated data arrays share a common phase. The predictions for the combined simulated data arrays are combined based on concatenation of the predictions. In other words, multiple concatenated data arrays are created from the first neural network 34a output. The number of outputs concatenated into an array is equal to the number of experimental SAED patterns (i.e., number of tilts) that the user provided. For example, if three experimental SAED patterns were input, then the first neural network 34a output from three simulated SAED patterns that share a phase would be concatenated into an array, which serves as one piece of training data for the second neural network 36a. This creation of concatenated arrays happens for all phases. So the input to the second neural network 36a is really multiple arrays that were created by concatenating different combinations of the first neural network 34a outputs.

[0053] This layered approach produces a higher confidence and greater accuracy compared to a single model. The use of two NNs allows generating a confidence value for each final phase prediction, thus providing the user with a ranked list of potential matches rather than an unordered list that is provided by current methods. Training of NNs on simulated SAED patterns 32 will ensure that the software algorithm 29 is fully equipped to differentiate between variations in experimental results (e.g., strains induced by sample preparation or the presence of another phase in the immediate vicinity that will create interference in g-values). Once NNs have been appropriately trained on a simulated data and the prediction accuracy has reached 100%, the software algorithm 29 is ready to analyze the experimental data 24, 26.

[0054] At step 326, the experimental SAED patterns 24 are fed through the trained first neural network 34b, resulting in a phase and zone axis prediction for each experimental SAED pattern 24. At step 328, the output probability arrays for each phase prediction are then combined into combined experimental data arrays, which represents the independent predictions for each sample tilt.

[0055] The predictions in the combined experimental data arrays share a common phase. The predictions for the combined experimental data arrays are combined based on concatenation of the predictions. In other words, multiple concatenated data arrays are created from the trained first neural network 34b output. The number of outputs concatenated into an array is equal to theAttorney Ref. No. 10457-586PC0 number of experimental SAED patterns (i.e., number of tilts) that the user provided. For example, if three experimental SAED patterns were input, then the trained first neural network 34b output from three simulated SAED patterns that share a phase would be concatenated into an array, which serves as one piece of training data for the trained second neural network 36b. This creation of concatenated arrays happens for all phases. So the input to the trained second neural network 36b is really multiple arrays that were created by concatenating different combinations of the trained first neural network 34b outputs.

[0056] At step 330, the combined experimental data arrays from the previous step are fed through the trained second neural network 34b, resulting in a single prediction for all phase present in the analyzed sample. The elemental scan data 26 can be directly incorporated into the prediction, as elemental scans can be vectorized to be used as input into either layer of the neural networks. The advantage of using 2 NNs in phase identification will ensure that all independent predictions are considered during analysis. For instance, if there is more than one possible match for an individual phase, the use of 2 independent NNs will allow determination of a confidence index in the prediction.

[0057] At step 332, the user is presented with the highest confidence phase matches through a user interface, as shown in screenshot 230 in FIG. 4e. The predicted phase in this example has a 99.11% confidence. The software algorithm 29 produces a confidence value for each final phase prediction, providing the user with a ranked list of potential matches. The use of a layered approach will increase the accuracy of the potential match to greatly exceed the accuracy of the prediction conducted through a manual approach. For example, the current degree of accuracy of this process exceeds 95%, even when lattice spacing differences between individual phases is <0.1 nm. These minute variations in diffraction spot spacing cannot be detected visually by the human eye. Thereby, the process algorithm 29 not only decreases the amount of time required to identify a phase, but also increases the overall accuracy of the prediction.

[0058] At step 334, the user has an option to view the phase and zone axes matches to ensure or verify the accuracy of the results. The user will be presented with all potential phase matches overlaid on the experimental SAED patterns 24, along with accuracy of the prediction for each phase match. Two of the experimental SAED images 24 are shown in screenshots 232, 234 in FIG. 4f. For each experimental SAED image 24, the white dots are diffraction spots and the + placed in each diffraction spot corresponds to matching simulated SAED images 32 beingAttorney Ref. No. 10457-586PC0 overlaid thereon. This will provide the user with the flexibility to evaluate the probability of the match and assess if the predicted phase match is consistent with the expected results. At step 336, based on predictions and visual verification, the user makes a determination about the crystal phases of the sample. This allows a manual validation of the phase prediction and allows the user to provide feedback to refine the process algorithm 29.

[0059] As an illustrative application in the area of materials science, phase identification can be conducted to understand constituent redistribution in metallic fuels. Metallic fuels are candidates for next generation nuclear reactor designs, and offer passive safety benefits as well as the capability to consume long-lived actinides produced in the current fleet of light water reactors.

[0060] During operation in a nuclear reactor, metallic fuels will undergo constituent redistribution and cause subsequent phase transformations throughout the material. This problem is further complicated by non-equilibrium conditions, the accumulation of fission product elements during operation, and the diffusion of cladding elements into the fuel. Characterizing this redistribution process requires the phase identification of many samples taken from the fuel matrix. In such a problem, it can be assumed that there is a large but finite set of possible phases that each sample may contain, if a phase diagram is available, and the history of the sample is known.

[0061] Example operations associated with training the phase ID process algorithm 29 as described above will be discussed. The example training operations are directed to phase identification in a plutonium-zirconium (Pu-Zr) system. At step 300, a total of 865 experimentally obtained SAED patterns 24 were acquired using a FEI Titan Scanning Transmission Electron Microscope (TEM). At step 304, the experimental SAED images 24 were converted to .JPG files for processing with Tensorflow and scikit-image. Each image was manually classified, with its phase and zone axis being recorded. At step 306, users evaluated the system of interest based on prior knowledge of the material and identified 9 possible phases, as summarized in Table 1.

[0062] The experimental SAED patterns 24 were processed to remove those with significant image artifacts and noise. Examples are those with imperfect patterns images, such as patterns that were acquired in thick areas and on precipitates, in which the precipitate was smaller than the beam size, resulting in a contribution from the underlying matrix phase. The images withAttorney Ref. No. 10457-586PC0 noise caused by a thick sample may be removed. The images with noise caused by high contribution from an undesired pattern may also be removed. Images with a small amount of noise can be easily cleaned based on a manual cleaning.

[0063] Some patterns with only a small number of artifacts were individually processed to remove these artifacts and improve data quality. This included contrast and brightness adjustments, as well as markup to remove bright regions that did not contribute to the primary diffraction pattern. This processing did not change the structure of the primary diffraction pattern and would not influence the phase identification in a manual process. After removing images with significant artifacts, the number of experimental SAED images 24 have been reduced to 639 images amongst nine different material phases, with six unique space groups.

[0064] At step 316, to increase the quantity of data, simulated diffraction patterns were created using the SingleCrystalTMv4.1.8 software. These diffraction patterns were generated for each phases’ unique zone axes represented by their associated experimental patterns. The complete breakdown of available images is shown in Table 1, along with the space group of the phase. Table 1 Phase Label Space group Experimental occurrences Simulated occurrences

[0065] Two methods of labeling the data were considered. The first method classified each image solely by its crystalline phase (e.g., αZr, PuO, δ-(Pu,Zr)), resulting in nine classes. While predicting a material’s phase is the goal of this work, using this class distinction neglects theAttorney Ref. No. 10457-586PC0 large differences in appearance from changes in the zone axis. Patterns taken with a

[0111] zone axis will appear different from those with a

[0100] zone axis even with an identical phase, causing a wide intra-class distribution and thus making it more difficult for a ML algorithm to determine the defining features of a given class. Given the relatively small data set, it may be difficult for an algorithm to learn and accommodate the differences within a given phase caused by the zone axis.

[0066] The second method labeled each image according to both its phase and zone axis (P+Z). For example, a class label might be α-Zr

[0111] , where α-Zr is the phase and

[0111] is the zone axis. The resulting number of classes is much larger than the first method because each phase was split into multiple classes based on the zone axis. This approach narrows the intra- class distribution, as each diffraction pattern of a given P+Z should be identical neglecting the presence of any lattice distortions, image artifacts, image translations, and image rotations. The drawback to this labeling scheme is that an increased number of classes must be learned: there are 99 P+Z classes compared to nine phase classes.

[0067] A train / test data split could not be performed through a simple random split because of the large data imbalance. The data was first processed and labeled according to its P+Z class. For each P+Z class, the greater of 1 sample or 20% of the P+Z class cardinality was randomly selected and pulled out into the testing data set. The zone axis label was then dropped if the classification was to be done on the phase alone. Splitting the data in this way ensures that each P+Z combination will appear at least once in both the training and testing data set. Ten test / train splits were created to ensure that the reported performance of each algorithm was not highly dependent on the split being used. The metrics for each ML algorithm are given as an average across the ten splits plus or minus one standard deviation.

[0068] At steps 318-330, different machine learning techniques are used in classifying SAED patterns given a finite number of possible phases. The viability of machine learning algorithms for SAED phase identification is determined. The machine learning techniques include a Convolutional Neural Network (CNN), a Feature Engineered Neural Network (i.e., a Radii feature and a Lattice feature), a Layered Neural Network, a K-Nearest Neighbors (K-NN), and a Line Graphic Neural Network (GNN).

[0069] The initial investigation explored how well a model without material science specific features could perform given exclusively a single image of an SAED pattern. ConvolutionalAttorney Ref. No. 10457-586PC0 neural networks (CNN) are well-known for their ability to learn and extract both high and low- level features. These discovered features are then passed along to a fully connected network that maps the input to a N-dimensional feature space, where N is the number of possible classes that the model can identify.

[0070] One difficulty in creating a model is finding an optimal architecture. This involves fine- tuning many model hyper-parameters, such as the number of layers and the learning rate. To achieve an optimal model structure, a neural architecture search (NAS) was conducted. NAS is a technique that defines a search space, a method to traverse the search space, and a way to evaluate the explored regions. In our case, the global search space was defined by a set of parameters, shown in Table 2, that could be changed between models; each combination of variables was created. A total of 41,472 models were trained and evaluated by their testing accuracies. The parameter values used by the model with the greatest testing accuracy, 299-AN, are both highlighted and bolded in Table 2. Table 2 Variables to be Adjusted Possible Values

[0071] The rotated dataset means that images were rotated before being fed into the model, the idea being that one can artificially increase their dataset size without physically acquiring more data. 299-AN was trained on a dataset split of 80% training and 20% testing, divided along eachAttorney Ref. No. 10457-586PC0 class. All images were center-cropped to a size of 800 pixels by 800 pixels and resized to 200 pixels by 200 pixels. During training, the images were passed through 24 times per epoch, each with a random rotation applied. The testing samples, kept separate throughout the entire training process, were not rotated, and were only fed through once. Ten models were trained and their testing accuracies as well as both weighted and macro F1 scores were noted. The macro F1 score does not consider the representational size of each class within the dataset while the weighted F1 score does. All ten results were averaged and reported. Feature Engineered NNs

[0072] The CNN approach uses an 800 pixel by 800 pixel image resized to 200 pixels by 200 pixels as its input, meaning that the input layer consists of 40,000 parameters. This is a high number of input parameters per image, which is difficult to train on given the limited availability of images (865 images is low compared to standard image classification data sets such as MNIST, which consists of 60,000 training and 10,000 testing images of 28×28 size). Feature engineering refers to a broad class of machine learning techniques that aim to simplify the inputs of a data set to improve training. It can include encoding categorical variables to quantitative variables (one-hot encoding) or trimming a data set to only the features that are most relevant for training. Trimming a data set to include only the most relevant features is a useful technique, as it can greatly reduce the dimensionality of the problem.

[0073] To extract features from a SAED image, the position of diffraction spots within the image were determined using a Python-based image processing algorithm. The algorithm reads each image as a grayscale 2D floating-point array with a maximum value of one. To reduce noise in the image, a median filter is applied. The filter moves a 3×3 window throughout the image pixel by pixel and replaces the value of each pixel in the middle of this window with the median value of its neighboring pixels within the window. Next, a mean filter is used to eliminate dim peaks within the image and thereby highlight the diffraction spots of interest. This filter calculates the average pixel intensity over the entire image and subtracts this value from each pixel. The image is then rescaled back to the original pixel range by setting each value less than 0 equal to 0 and dividing all pixel values by the greatest within the image. Another median filter is applied to ensure no singular bright pixels remain.Attorney Ref. No. 10457-586PC0

[0074] The difference of Gaussian (DoG) function in the scikit-image package is then used to find the pixel coordinates of diffraction spot centers. The DoG function finds bright clusters of pixels on a dark background. Each found cluster will correspond to a diffraction spot in the SAED pattern. No maximum or minimum cluster size was imposed. In the case of overlapping clusters, only the largest was kept. The algorithm returns a 2D floating-point array with the x and y coordinates of the detected diffraction spots. Due to the implicit limitations in image feature extraction, the extracted diffraction spot positions and therefore any resulting features are at best approximations. Different feature extraction algorithms will produce slightly different diffraction spot positions. However, given that the manual process classification process involves imperfect human judgement in diffraction spot position matching, it is unlikely that the small position discrepancies introduced using a feature extraction algorithm pose a significant challenge to an automated process.

[0075] The image processing algorithm performed well for most images, however there were some experimental images that gave poor diffraction spot identification. All simulated images were successfully processed. Some images were manually cleaned to improve quality, but some poor experimental images had to be removed from the data set for the feature engineered NNs (a loss of 21 images and three zone axes). While this dependence on the algorithm performance might seem to pose a significant challenge in the overall workflow, in a real use case this could be easily mitigated by having manual user corrections on any experimental images processed. For this work, however, this was not feasible due to the number of experimental images that needed to be repetitively processed. The results of the feature extraction algorithm applied to experimental patterns (top images) are shown in screenshots 240, 242 in FIGS. 5a-5b, and as applied to simulated patterns (bottom images) are shown in screenshots 244, 246 in FIGS. 5c-5d. The dots on the right-side images indicate diffraction spots located by the process algorithm 29. These figures illustrate the outputs that the user will see at step 334.

[0076] After determining the positions of the diffraction spots, features can be created for training. In the first method, the “radii feature” approach, a central diffraction spot was found based on the proximity to the centroid of all the diffraction spot positions. The distance from the central spot to all other spots was calculated using a basic two-dimensional distance calculation. These distances were used as the input features for training a dense NN (DNN). Plotting each of the found distances as a radius creates an image that physically represents a subset of the ringsAttorney Ref. No. 10457-586PC0 seen in a ring diffraction pattern, which served as the motivation for training based on this feature.

[0077] A challenge with the radii feature approach is the inconsistency in the number of diffraction spots that each image has, and therefore the inconsistency in the input shape that could be obtained from each image. Some diffraction patterns will have more diffraction spots than others, so to even out the input shape, radii could be duplicated or truncated to ensure a consistent input shape. Finding the optimal number of input features introduces another parameter requiring tuning and thus represents a drawback to the radii feature approach. For this work, the number of radii to consider was set to five.

[0078] For the next approach, the “lattice feature” approach, it is assumed that the diffraction spots form a 2D Bravais lattice. Thus, the lattice parameters can be found by selecting one reference point and then the two closest points that are not co-linear. The distance between the central point to the other two points, as well as the angle formed, characterizes the two- dimensional lattice using three parameters. These lattice parameters are calculated for each diffraction spot as the reference point, and the median of each parameter is calculated to be used as the overall feature. These distances were used as input features. Because there is ambiguity for which nearest point could be selected in a hexagonal lattice resulting in the same distances but varying angles, any degree measurements near 120°are divided by 2 to enforce a consistent unit cell (this is analogous to considering all hexagonal lattices to be monoclinic lattices with 60◦angles).

[0079] The use of exactly three parameters eliminates the issue associated with the radii approach where the number of input parameters must be manually set and optimized. While there are other parameters that could be introduced to characterize the lattice (e.g., the area of lattice or the b / a ratio), any additional parameters are ultimately derivative from the three fundamental parameters described, and therefore, can be expected to be learned in the training process without the need to explicitly supply them.

[0080] When the lattice parameters were used for training, data augmentation was applied. The mean and standard deviation for each parameter was calculated for each P+Z class. A normal distribution created from these values was then sampled to create synthetic training data. The testing data set was separated from the training data set prior to any augmentation steps to ensure that the mean values did not include information from the testing set. Augmentation was appliedAttorney Ref. No. 10457-586PC0 to bring the number of samples per P+Z class up to 1,000. This enforces an even cardinality for each P+Z class in the training data set. The features were then standardized between zero and one to improve training performance.

[0081] Both approaches rely on the distance between diffraction spots to characterize the image. The distances given by the image processing algorithm are in units of pixels. To compare images with different scales, the pixel distances were converted to distances in units of nm−1using the scale bar.

[0082] A neural architecture search was performed for each feature engineered NN using a hyperband search, with the validation accuracy set as the target parameter. The hyperparameter search values are shown in Table 3. The dropout rate refers to the rate of a dropout layer after each dense hidden layer. Table 3 Hyperparameter Search values 1Layered NN

[0083] Even for a non-automated workflow, phase classification based on a single SAED pattern is not reliable enough due to experimental limitations and the possibility of multiple 3D crystal lattices producing the same 2D slice. Therefore, in a typical workflow, multiple zone axes are taken from a single sample to make a reliable overall phase classification. This process of considering multiple zone axes in an overall determination can be mimicked by independently feeding three images into a NN that is trained to predict a P+Z, then concatenating and feeding those outputs into a second NN that is trained to predict an overall phase. Training in this way could also feature embedding (first NN) followed by prediction on the embedded featuresAttorney Ref. No. 10457-586PC0 (second NN), where the embedded features are P+Z predictions used to make a phase prediction. Doing this allows for multiple images to be considered in making an overall phase determination of a sample.

[0084] A similar effect might be achievable by instead training a single model to accept multiple images, however the method discussed above yields a distinct advantage in the explainability of the model. Because each image is first processed independently, it is easier to follow how the model arrives at a final determination based on the independent predictions that can be easily seen rather than obscured in a NN’s hidden layers. It is therefore much more straightforward to identify whether deficiencies in the model are caused by the independent P+Z predictions, or from synthesizing these predictions into an overall phase prediction. For the layered NN approach, the lattice feature NN was used as the first layer classifier, however any of the NN algorithms considered in this paper could have also been used as the first layer classifier (i.e. the initial features to be embedded can be changed). An example workflow for the layered NN 250 is shown in FIG. 6. The same hyperparameter search range was used for the layered NN as for the feature engineered NNs (Table 3), with the addition of zero to the number of possible hidden layers as it was noted in preliminary testing that a very shallow network performed well.

[0085] Still referring now to FIG. 6, the layered neural network workflow 250 of the SAED phase identification process will be discussed. As shown in FIG. 6, three experimental SAED images 24 are fed into a lattice feature NN. The SAED images are based on a single image but at different tilt angles. Each lattice feature NN makes a phase prediction based on the received SAED image. In other words, independent phase predictions are determined in the first layer 34b (i.e., first neural network). The second NN 36b (i.e., second neural network) combines the independent phase predictions from the first NN 34b into an overall phase prediction for the single SAED image. The workflow in FIG. 6 does not reflect training of the first and second neural networks 34a, 36a. Rather the workflow illustrates a general overview of the software algorithm steps 318-330 shown in FIG. 3.

[0086] Several neural networks were accessed as part of this disclosure to determine which NN is the most suitable for use in the formal analysis. Below is the detailed description of each accessed NN and evaluation of its performance based on the analysis of a model dataset.Attorney Ref. No. 10457-586PC0 K-nearest neighbors

[0087] K-Nearest Neighbors (K-nn) is a supervised learning algorithm that can be used for both classification and regression tasks. It is a non-parametric and lazy learning algorithm, meaning it does not make any assumptions about the underlying distribution of the data fed to it. In addition, K-nn does not perform any explicit training of a model; rather, it stores the entire training data set within the model and creates predictions based on the similarity between new data points and the training data. K-nn classification involves calculating the distance between new data and all existing training data and then classifying the new data based on the majority class of the K number of nearest neighbors. The parameter K denotes the number of data points closest to the new data to consider, and this value is set before classification.

[0088] The lattice parameter features were used as the input data to the algorithm, and the same train / test split method was applied. This duplicate methodology provides a useful comparison with the lattice feature NN, one can explore whether NNs are well-suited for learning features of interest when compared to a non-NN ML algorithm. K-nn classification was implemented using the ‘KNeighborsClassifier’ function from the scikit-learn package v1.2.2. Relevant hyperparameters include the number of nearest neighbors or K value to consider during classification, the weight parameter which determines whether distances of the K nearest neighbors will be weighted while classifying new data, and the metric for how distances between new data and training data are calculated. Two distance metrics were considered, namely Euclidean distance, which is the straight-line distance between two points, and Manhattan distance, which is the sum of the absolute differences between the corresponding coordinates of two points.

[0089] To increase the performance of the K-nn model, the hyperparameters of the model were tuned using a grid search. It was determined that having the weights of each neighbor be inversely proportional to their calculated distance during classification gave the best performance, regardless of which combination of the number of neighbors or distance metric is used. This process was repeated for all combinations of the K and distance metric parameters, with K ranging from 1 to 20 and the distance metric being either Manhattan or Euclidean distance, to find the combination of these hyperparameters that would result in the best overall performance of the K-nn model.Attorney Ref. No. 10457-586PC0 Line graph neural networks

[0090] Graph neural networks (GNNs) learn based on non-Euclidean graph data structures that consist of nodes connected by edges. Graphs allows for learning complex behavior based on the relationships between nodes and have been employed in the materials science field mostly for structure-property relationship predictions. Atomistic line graph neural networks (ALIGNNs) were originally developed to improve upon the existing GNN performance by explicitly incorporating bond angle information. ALIGNNs were shown to also be effective at classifying 2D Bravais lattices.

[0091] One of the benefits of using GNNs is the ability to capture the interconnectivity of diffraction spots irrespective of rotation or translation. No 2D Bravais lattice assumptions are necessary as was done in the feature engineered lattice DNN approach. Additionally, the inconsistency in the number of diffraction spots between images is not an issue as it was for the radii feature approach, as there is no requirement for a consistent number of graph nodes.

[0092] For a given image, a graph was constructed using each diffraction spot as a node. The edges of the graph were weighted according to the nm−1distance between nodes. Only the four nearest neighbors to a node were connected, as a fully connected graph performed poorly and was unable to effectively learn features. This graph was then used to create a line graph, where each node is an edge in the original graph. In the line graph, the edge weights corresponded to the angle between edges in the original graph. Because there is no useful node information in the original graph (including the node pixel coordinate position would make the graph dependent on any image translations and rotations), only the line graph was used for training. This line graph neural network (LGNN) retains the most important features of the image in a transformation independent manner.

[0093] Graph augmentation through subgraph sampling was conducted by duplicating the graphs in the training data set and then randomly performing node dropping throughout the graphs. For the node dropping, 10% of the nodes in the line graph were removed, and 100 augmented graphs were created for each P+Z class. The percent of nodes dropped was chosen to ensure that enough useful training information is preserved in the input layers. The Networkx package was used for graph creation and augmentation and the Tensorflow-gnn v0.5.0 library was used for GNN implementation. A vanilla message passing neural network was the modelAttorney Ref. No. 10457-586PC0 used for graph classification, with the hyperparameters manually tuned. After message passing, the node features were pooled using a mean read out function.

[0094] The performance for each ML model and class labeling is given in Table 4. Among the metrics, the macro averaged F1 score is the best indicator of overall performance because of the data imbalance, as each phase prediction performance should be considered equally important regardless of class size. Table 4 Model Labeling Accuracy Weighted F1 score Macro F1 score

[0095] Referring now to FIG. 7, a confusion matrix 260 for the layered neural network workflow 250 will be discussed. A confusion matrix relates an image’s true phase / class (vertical axis) to the phase / class predicted by the model (horizontal axis). The confusion matrix 260 is scaled between zero and one for each row to give a better visualization with the large data imbalance.

[0096] There is a comparable performance between the two-feature (radii & lattice) engineered NNs when performing a phase only prediction. The lattice DNN then slightly outperforms theAttorney Ref. No. 10457-586PC0 radii DNN for the P+Z predictions, in particular, for the latter half of the confusion matrix. It also appears that the lattice DNN leads to less overfitting in the P+Z predictions. This may be shown by the lesser number of vertically aligned predictions in the P+Z confusion matrices that indicate a particular class is being predicted frequently. The K-nn algorithm did not perform significantly different from the lattice DNN that shared the same input features.

[0097] The CNN had the worst performance of those approaches investigated using the P+Z class labeling system. In terms of phase label classification, it performed similarly to the feature engineered NNs, but seemed to suffer from more overfitting with the α-Zr class (class A in the figures) being predicted more frequently than all the other phases.

[0098] The GNN had the worst performance in the phase class predictions but outperformed the CNN and radii DNN in the P+Z predictions. It was unable, however, to match the performance of the K-nn or lattice DNN approaches. During testing, classification was improved when the angular information (edge weights in the line graph) was set to an empty feature and not used. These results suggest that the GNN was unable to learn and utilize the underlying lattices present in the diffraction patterns. The layered NN approach 260 had the best performance out of all the approaches tried, outperforming in all metrics. Each phase performed well except for Zr3O-R3C (class H), which also had poor performance across the other approaches.

[0099] Another aspect is directed to a method for automating a selective area electron diffraction (SAED) phase identification process as discussed above. Referring now to the flowchart 400 in FIG. 8, from the start (Block 402), the method includes receiving experimental data 24 and a list of candidate phases 28 at Block 404, with the experimental data including experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles. Simulated SAED patterns 32 are generated for the list of candidate phases 28 at Block 406. A first neural network 34a is trained at Block 408 using one of the simulated SAED patterns 32 to predict a phase and zone axis of the simulated SAED pattern used for the training. The simulated SAED patterns 32 are fed through the trained first neural network at Block 410 to predict a phase and zone axis of each simulated SAED pattern, with the predictions being combined into combined simulated data arrays. A second neural network 36a is trained at Block 412 using the combined simulated data arrays. The experimental SAED patterns 24 are fed through the trained first neural network 34b to predict a phase and zone axis of each experimental SAED pattern atAttorney Ref. No. 10457-586PC0 Block 416, with the predictions being combined into combined experimental data arrays. The combined experimental data arrays are fed through the trained second neural network 36b at Block 416 to determine phase matches for the experimental SAED patterns 24. The predicted phase matches for the experimental SAED patterns 24 are displayed at Block 418. The method ends at Block 420.

[0100] Many modifications and other embodiments will come to the mind of one skilled in the art having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is understood that the foregoing is not to be limited to the example embodiments, and that modifications and other embodiments are intended to be included within the scope of the appended claims.

Claims

Attorney Ref. No. 10457-586PC0 CLAIMS:

1. A method for automating a selective area electron diffraction (SAED) phase identification process comprising: receiving experimental data and a list of candidate phases, with the experimental data comprising experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles; generating simulated SAED patterns for the list of candidate phases; training a first neural network using one of the simulated SAED patterns to predict a phase and zone axis of the simulated SAED pattern used for the training; feeding the simulated SAED patterns through the trained first neural network to predict a phase and zone axis of each simulated SAED pattern, with the predictions being combined into combined simulated data arrays; training a second neural network using the combined simulated data arrays; feeding the experimental SAED patterns through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern, with the predictions being combined into combined experimental data arrays; feeding the combined experimental data arrays through the trained second neural network to determine phase matches for the experimental SAED patterns; and displaying the predicted phase matches for the experimental SAED patterns.

2. The method according to claim 1 wherein the displayed predicted phase matches include a final predicted phase match having a highest confidence for the experimental SAED patterns.

3. The method according to claim 1 wherein the displayed predicted phase matches include overlay of one of the simulated SAED patterns that best matches with one of the experimental SAED patterns.

4. The method according to claim 1 comprising calculating diffraction spot spacing on the experimental SAED patterns to be fed into the trained first neural network.Attorney Ref. No. 10457-586PC0 5. The method according to claim 1 wherein the predictions in the combined simulated data arrays share a common phase, and the predictions in the combined experimental data arrays share a common phase.

6. The method according to claim 1 wherein the predictions for the combined simulated data arrays are combined based on concatenation of the predictions, and the predictions for the combined experimental data arrays are combined based on concatenation of the predictions.

7. The method according to claim 1 wherein the combined simulated data arrays are arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the simulated SAED patterns matching one of the predicted phase and zone axis; and wherein the combined experimental data array are arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the experimental SAED patterns matching one of the predicted phase and zone axis.

8. The method according to claim 1 wherein a number of zone axis included in the combined experimental data arrays corresponds to a number of experimental SAED patterns that were received.

9. The method according to claim 1 wherein the experimental data further includes energy dispersive x-ray spectroscopy (EDS) data on the material of interest.

10. The method according to claim 1 wherein the experimental SAED patterns are at a specific region of interest.

11. A computing system for automating a selective area electron diffraction (SAED) phase identification process comprising: a memory configured to store experimental data and a list of candidate phases, with the experimental data comprising experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles; a processor coupled to the memory and configured to perform the following: generate simulated SAED patterns for the list of candidate phases,Attorney Ref. No. 10457-586PC0 train a first neural network using one of the simulated SAED patterns to predict a phase and zone axis of the simulated SAED pattern used for the training, feed the simulated SAED patterns through the trained first neural network to predict a phase and zone axis of each simulated SAED pattern, with the predictions being combined into combined simulated data arrays, train a second neural network using the combined simulated data arrays, feed the experimental SAED patterns through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern, with the predictions being combined into combined experimental data arrays, and feed the combined experimental data arrays through the trained second neural network to determine phase matches for the experimental SAED patterns; and a display coupled to the processor and configured to display the predicted phase matches for the experimental SAED patterns.

12. The computing system according to claim 11 wherein the displayed predicted phase matches include a final predicted phase match having a highest confidence for the experimental SAED patterns.

13. The computing system according to claim 11 wherein the displayed predicted phase matches include overlay of one of the simulated SAED patterns that best matches with one of the experimental SAED patterns.

14. The computing system according to claim 11 wherein the processor is configured to calculate diffraction spot spacing on the experimental SAED patterns to be fed into the trained first neural network.

15. The computing system according to claim 11 wherein the predictions in the combined simulated data arrays share a common phase, and the predictions in the combined experimental data arrays share a common phase.

16. The computing system according to claim 11 wherein the predictions for the combined simulated data arrays are combined based on concatenation of the predictions, and theAttorney Ref. No. 10457-586PC0 predictions for the combined experimental data arrays are combined based on concatenation of the predictions.

17. The computing system according to claim 11 wherein the combined simulated data array are arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the simulated SAED patterns matching one of the predicted phase and zone axis; and wherein the combined experimental data arrays are arrays of numbers, with a value of each index in the arrays corresponding to a probability of one of the experimental SAED patterns matching one of the predicted phase and zone axis.

18. The computing system according to claim 11 wherein a number of zone axis included in the combined experimental data arrays corresponds to a number of experimental SAED patterns that were received.

19. The method according to claim 1 wherein the experimental SAED patterns are at a specific region of interest.

20. A non-transitory computer readable medium having computer-executable instructions for causing a computing system to automate a selective area electron diffraction (SAED) phase identification process, with the computing system to perform steps comprising: receiving experimental data and a list of candidate phases, with the experimental data comprising experimental SAED patterns of a sample taken on a material of interest at multiple tilt angles; generating simulated SAED patterns for the list of candidate phases; training a first neural network using one of the simulated SAED patterns to predict a phase and zone axis of the simulated SAED pattern used for the training; feeding the simulated SAED patterns through the trained first neural network to predict a phase and zone axis of each simulated SAED pattern, with the predictions being combined into combined simulated data arrays; training a second neural network using the combined simulated data arrays;Attorney Ref. No. 10457-586PC0 feeding the experimental SAED patterns through the trained first neural network to predict a phase and zone axis of each experimental SAED pattern, with the predictions being combined into combined experimental data arrays; feeding the combined experimental data arrays through the trained second neural network to determine phase matches for the experimental SAED patterns; and displaying the predicted phase matches for the experimental SAED patterns.

Images