LeaPP: Learning Pathways to Polymorphs through machine learning analysis of atomic trajectories

TL;DR

A novel methodology called LeaPP is proposed that categorizes nucleation trajectories based on the temporal information of their constituent particles and provides a more nuanced understanding of nucleation through an unsupervised approach with lesser dependence on traditional order parameters.

Abstract

Understanding the mechanisms underlying crystal formation is crucial. For most systems, crystallization typically goes through a nucleation process that involves dynamics that happen at short time and length scales. Due to this, molecular dynamics serves as a powerful tool to study this phenomenon. Existing approaches to study the mechanism often focus analysis on static snapshots of the global configuration, potentially overlooking subtle local fluctuations and history of the atoms involved in the formation of solid nuclei. To address this limitation, we propose a methodology that categorizes nucleation pathways into reactive pathways based on the time evolution of constituent atoms. Our approach effectively captures the diverse structural pathways explored by crystallizing Lennard-Jones-like particles and solidifying Ni$_3$Al, providing a more nuanced understanding of nucleating pathways. Moreover, our methodology enables the prediction of the resulting polymorph from each reactive trajectory. This deep learning-assisted comprehensive analysis offers an alternative view of crystal nucleation mechanisms and pathways.

Figures (7)

• Figure 1: Overview of LeaPP. The time trajectory of the local environment of each particle is embedded into a low-dimensional latent space for a set of nucleation trajectories. The pairwise distances between particle paths in the latent space are then calculated and clustered to give particle path clusters. Each nucleation trajectory is then characterized by its distribution of particle path clusters. These distributions are used to calculate the pairwise distances between nucleation trajectories and cluster them into distinct pathways.
• Figure 2: (A) Latent space projection of the 7--6 training data with phase labels. Each panel represents a 2D plane of the 3D latent space containing the training data colored by phase labels. Labels are acquired based on the values of $\overline{q}_{4}$ and $\overline{q}_{6}$. (B) Latent space projection of the 7--6 particles from simulations of bulk phases. (C) Particle path clusters for 7--6 particles. The clustering protocol is detailed in Materials and Methods section. Each colored region of the dendrogram represents a cluster of particle paths ($\alpha$, $\beta$, $\gamma$). The percentage at the top center is the fraction of particle paths that belong to each cluster. The percentage of liquid, BCC, FCC, and HCP is calculated from the label of the particle in the last frame. (D-E) Radial composition analysis of configurations from 181 7--6 nucleation trajectories. $r$ is the distance from the nucleus center of mass, and f$_\text{str}$ is the fraction of each type of particle calculated at each spherical shell. In panel D, the radial composition is calculated using the particle path cluster labels ($\alpha$, $\beta$, $\gamma$) from panel B. The same calculation is performed for panel E with labels from their $\overline{q}_4$ and $\overline{q}_6$ values. Any particles that do not belong to the solid nucleus are labeled liquid. The analysis is performed using one configuration from each nucleation trajectory with an estimated committor of 0.9 or greater.
• Figure 3: (A-D) Radial composition analysis of 7--6 configurations from each trajectory cluster in SI Appendix, Fig. S5. Panel A and C use the particle path cluster labels from Fig. \ref{['fig:lj-vae-pp3-rcaoverall']}B for the analysis, whereas panel B and D use $\overline{q}_4$ and $\overline{q}_6$ values. The radial compositions are computed for (A-B) L-1 cluster and (C-D) L-2 cluster of trajectories from SI Appendix, Fig. S5. Configurations with committor estimates greater than or equal to 0.9 are again selected for the calculation. (E-J) Average composition of 7--6 nucleation trajectories from each trajectory cluster in SI Appendix, Fig. S5. The x-axis represents the average nucleus size of the configurations in the trajectories of each respective cluster. c$_\text{avg}$ represents the average composition of the nucleus at a specific size according to the three phases: BCC, HCP, and FCC. Blue lines represent the BCC composition, cyan lines represent the HCP composition and purple lines represent the FCC composition. The composition is calculated for trajectories in L-1 cluster (E-G) and trajectories in L-2 cluster (H-J). The error bars reflect the standard deviation of the average composition across all trajectories launched within each trajectory cluster.
• Figure 4: (A-C) Configuration selection for composition-based clustering of 7--6 nucleation trajectories. The y-axis reflects the number of configurations with the BCC/HCP/FCC fraction indicated on the x-axis. Color code: Blue -- BCC, cyan -- HCP, and purple -- FCC. Panel A shows the composition distribution of all 7--6 nucleation trajectories' last configuration. Panel B and C, respectively, show a distribution of configurations that have a higher fraction of BCC than FCC, and a distribution of configurations that have a higher fraction of FCC than BCC. (D-I) Average composition of extended trajectories from "BCC$>$FCC" and "FCC$>$BCC" configurations. The x-axis represents the average nucleus size of the configurations in the trajectories of each respective cluster. c$_\text{avg}$ represents the average composition of the nucleus at a specific size according to the three phases: BCC (D,G), HCP (E,H) and FCC (F,I). Each line in the plot represents the average composition of five trajectories extended from each "BCC$>$FCC" configuration (D-F) or "FCC$>$BCC" configuration (G-I).
• Figure 5: Average composition of extended trajectories from two nucleation trajectory clusters found via LeaPP in SI Appendix, Fig. S5 of the 7--6 system. Each line represents the average composition of five trajectories extended from configurations of L-1 trajectory cluster (A-C) or L-2 trajectory cluster (D-F).