Unsupervised learning for structure detection in plastically deformed crystals

TL;DR

The paper introduces an unsupervised learning pipeline that detects fine-grained local structures in plastically deformed crystals by applying an autoencoder to a nine-dimensional BAD parameter space, selecting a compact set of $\{ \chi_4, \chi_5, \chi_7 \}$ and a 3-dimensional bottleneck. It then uses a dual clustering strategy (K-means for main structures and DBSCAN for isolated substructures) plus a logistic classifier to label new data, yielding six distinct structural motifs including FCC, HCP stacking faults, dislocation segments, and their interactions in a Ni FCC crystal under uniaxial deformation. The method demonstrates superior resolution of dislocation lines and stacking faults compared with CNA and hand-crafted BAD approaches, and is computationally efficient and extensible to more deformed states, though it relies on pre-defined BAD ranges and would benefit from universal BAD parameterization for broader applicability. Overall, this work provides a practical, scalable framework for automatic, high-precision local structure detection in crystalline materials under load, with potential applicability to alloys and more complex microstructures.

Abstract

Detecting structures at the particle scale within plastically deformed crystalline materials allows a better understanding of the occurring phenomena. While previous approaches mostly relied on applying hand-chosen criteria on different local parameters, these approaches could only detect already known structures.We introduce an unsupervised learning algorithm to automatically detect structures within a crystal under plastic deformation. This approach is based on a study developed for structural detection on colloidal materials. This algorithm has the advantage of being computationally fast and easy to implement. We show that by using local parameters based on bond-angle distributions, we are able to detect more structures and with a higher degree of precision than traditional hand-made criteria.

Figures (15)

• Figure 1: (a) Snapshot made with Ovito stukowski_visualization_2009 of the system used in this study. It consists of a cubic nanoparticle of nickel with edge length equals to 20nm. The two arrows represent the uniaxial compression performed with a flat indenter along the $[100]$ direction. The stress-strain curve obtained from this compression is shown on (b). The vertical red line corresponds to occurence of the first plastic event.
• Figure 2: Schematic representation of autoencoder neural network architecture for dimensional reduction. The neural network is trained in order to reproduce the input at the output while passing through a bottleneck of lower dimensions. The encoder network aims at finding a low-dimension representation of the input. The decoder network is trained to reconstruct the original input from the lower-dimension bottleneck.
• Figure 3: Means square error $E$ between the input and the output for different bottleneck dimensions. The error reaches a plateau for a bottleneck dimension of $N=3$ which corresponds to the relevant number of BAD parameters sufficient to reconstruct the input data.
• Figure 4: Relative importance index of the BAD parameters obtained from the input perturbation method. The index is calculated by perturbating consecutively each input parameter and measure how much this perturbation affected the output. The parameters $\{ \chi_4,\chi_5,\chi_7\}$ are shown to be the most relevant ones to study the different structures in the system.
• Figure 5: The upper part of the figure (a) represents a Scatter plot of the BAD parameters projected on the most relevant parameters: $\{ \chi_4,\chi_5,\chi_7\}$. The colors correspond to the substructures detected with K-means clustering. The lower part shows histograms showing the distribution of $\chi_4$ (b), $\chi_5$ (c), $\chi_7$ (d). On the $\chi_4$ histogram, we observe that most of the atoms are concentrated on two values, while on the $\chi_5$ and $\chi_7$ histograms, most atoms are concentrated on a single value. Note that two combinations of $\{ \chi_4,\chi_5,\chi_7\}$, $\{ 24,12,24\}$ and $\{ 21,12,24\}$, marked with a star and a plus symbol, respectively, contain most of the atoms and correspond in practice to the FCC and the stacking fault (HCP) structures. The K-means clustering method aims here at separating these two points corresponding to two very close clusters.