Dislocation cartography: Representations and unsupervised classification of dislocation networks with unique fingerprints

TL;DR

This work introduces an unbiased, unsupervised framework to fingerprint dislocation networks by converting discrete dislocation dynamics data into fixed-density fields and mapping them to two-dimensional embeddings via Isomap. The dislocation structure maps capture intrinsic relationships and evolution across compression directions, boundary conditions, initial densities, and misorientations, enabling quantitative comparison of complex microstructures. The study demonstrates distinct embedding patterns for open versus periodic boundaries and highlights how resolution, representation choices, and hyperparameters influence interpretability, pointing to future enhancements with higher-order descriptors. Overall, the approach provides a transferable, data-driven coordinate system for dislocation structures with potential applications in machine-learning-driven materials modeling and experimental data integration.

Abstract

Detecting structure in data is the first step to arrive at meaningful representations for systems. This is particularly challenging for dislocation networks evolving as a consequence of plastic deformation of crystalline systems. Our study employs Isomap, a manifold learning technique, to unveil the intrinsic structure of high-dimensional density field data of dislocation structures from different compression axis. The resulting maps provide a systematic framework for quantitatively comparing dislocation structures, offering unique fingerprints based on density fields. Our novel, unbiased approach contributes to the quantitative classification of dislocation structures which can be systematically extended.

Figures (7)

• Figure 1: Snapshot of simulated dislocation structures in perspective view initialized with randomly distributed Frank-Read sources. (a) Aspect ratio of $2$ for the open surface boundary condition with a low starting density of dislocation network. (b) Aspect ratio of $1$ for the periodic boundary condition with a high starting density of dislocation network. Strain rate-controlled displacement is applied in negative y direction.
• Figure 2: Isomap embedding maps for perfect crystal orientations at a discretization of $8 \times 16 \times 8$, with $k$ nearest neighbors set to $30$. (a) Initial density of 2.5e13m. (b) Initial density of 1e14m.
• Figure 3: Isomap embedding results for perfect crystal orientations at a discretization of $16 \times 32 \times 16$, with $k$ nearest neighbors set to $50$. (a) Initial density of 2.5e13m. (b) Initial density of 1e14m.
• Figure 4: Isomap embedding results for perfect crystal orientations ($\pm0$) and their deviations at angles of $\pm 5$ and $\pm10$ degrees. (a) Discretization of $8 \times 16 \times 8$, with $k$ nearest neighbors set to $30$. (b) Discretization of $16 \times 32 \times 16$, with $k$ nearest neighbors set to $50$.
• Figure 5: Isomap embedding results for perfect crystal orientations under PBC. (a) Discretization of $10 \times 10 \times 10$, with $k$ nearest neighbors set to 30. (b) Discretization of $20 \times 20 \times 20$, with $k$ nearest neighbors set to 50.