• No current method is available for classifying crystal structures that do not have all of their atoms in the correct positions (defects). 
• A machine learning-based approach has now been developed to determine the symmetry and as a result classify crystal structures. 
• Crystal structures can be identified using this approach even at defect concentrations up to 40%.

One unmistakable trend is the continuing improvement in the efficiency of materials used in manufacturing. End-users are demanding that machinery operates at optimum performance levels for longer periods of time under more severe conditions, which may involve extreme temperatures and the presence of salt water when thinking about a wind turbine placed in the ocean. 

While continuing consideration for improving lubricant performance is focusing on the growing use of synthetic lubricants, which also are better able to handle severe operating conditions, development of new materials continues in an effort to further improve machinery performance.

One new class of materials that is under development are high-entropy alloys. These materials contain five or more metals in roughly equal concentrations. A recent article (1) described work done by researchers to convert a high-entropy alloy based on five metals (chromium, manganese, iron, cobalt and nickel) from a face-centered cubic arrangement to a hexagonal close-packed structure under high pressure. Once the pressure is relieved, the resulting alloy contains both crystal structures. The process can be tailored to produce alloys with specific hardness and ductility properties.

Devinder Kumar, senior doctorate candidate at the Vision and Image Processing Lab in the systems design engineering department at the University of Waterloo in Waterloo, Ontario, Canada, says, “Properties of metal alloys can be determined from their crystal structures. As an example, carbon solubility in iron (which is important in steel production) increases nearly 40 times in progressing from a body-centered cubic, alpha ferrite to a face-centered cubic, gamma austenite structure.”

The important element of a crystal structure is how the atoms are arranged. Kumar says, “Crystal structures are classified in specific space groups that describe the symmetric operations that are allowed.”

Ideally, this process works well for crystal structures that contain all of their atoms slotted in the correct positions. Kumar says, “Most metal crystal structures are not made perfectly and contain what are known as defects where atoms are missing from their expected positions because of manufacturing deformities. Two other causes of defects are impurities and experimental noise.”

No current method is available for classifying crystal structures with defects that occur in practice (a.k.a real life) according to Kumar. He adds, “Researchers apply certain thresholds to classify materials with defects.”

The barrier to finding a universal technique for identifying crystal structures with defects is the large number of calculations that need to be done. An approach has now been developed that uses artificial intelligence to teach a computer to handle this challenging task.

Recognition of local and global order
Kumar and his colleagues devised a procedure for classifying crystal structures using a machine learning-based approach to determine their symmetry. He says, “We wanted to devise an approach that can be used by other researchers in their work and that was not a black box.”

The procedure used by the researchers is shown in Figure 3. The first step was to generate a two-dimensional fingerprint of every crystal structure using a novel physics method. In the next step, a small subset of these structures was used by the computer as a training tool to develop a neural network model and then optimized using a neural network visualization filter. 


Figure 3. An artificial intelligence procedure shown was used to identify the crystal structures for materials with defects. (Figure courtesy of Devinder Kumar, University of Waterloo, under the Creative Commons Attribution 4.0 International license found at http://creativecommons.org/licenses/by/4.0/. No changes were made to the figure.)

Kumar says, “Our objective was to train the computer to properly use data from more than 100,000 crystal structures including heavily defective ones. As the computer processed a series of complicated mathematical calculations to produce crystal structures, a feedback loop was employed if the incorrect crystal structure was initially proposed. For a correct crystal structure, the computer then went through a more thorough analysis that involved creating a model to explain the results.”

Crystal structure development took into consideration local and global order. Kumar says, “Computer modeling started with local layers but kept on building to produce multiple structures. The process took place layer by layer to move from local order to global order.”

Once the computer properly identified crystal structures, an insightful convolutional neural network model was implemented that accurately predicted crystals with similar structures. Kumar says, “We are able to identify crystal structures with excellent accuracy even at defect concentrations up to 40%.”

Kumar stressed that the neural network used the same analysis that a researcher would in identifying a crystal structure though the computer is not explicitly instructed to do so. 

This work represents a starting point for researchers in identifying new materials suitable for use in extreme operating conditions according to Kumar. He says, “We hope this technique can be used by other researchers who can use it to extrapolate an idea about a material with specific properties to an actual structure. This artificial intelligence approach to modeling is a building block to new materials. An added benefit is that the analysis of incomplete and possibly noisy crystalline structures can now be realized.”

The researchers are looking in the future to develop a more robust model that will generate actual three-dimensional projections. Additional information on the classification of crystalline structures with defects can be found in a recent article (2) or by contacting Kumar at devinder.kumar@uwaterloo.ca. 

REFERENCES
1. Canter, N. (2017), “Hexagonal close-packed high-entropy alloys,” TLT, 73 (8), pp. 14-15.
2. Ziletti, A., Kumar, D., Scheffler, M. and Ghiringhelli, L. (2018), “Insightful classification of crystal structures using deep learning,” Nature Communications, Article number: 2775.