Source-linked AI summary
Predicting phase behavior of grain boundaries with evolutionary search and machine learning
Qiang Zhu, Amit Samanta, Bingxi Li, Robert E. Rudd, Timofey Frolov
TL;DR
Grain-boundary phase behavior required a computational approach that could predict complex interface structures beyond fixed-atom constructions. The paper combines grand-canonical evolutionary search with clustering, finding new ground and metastable states across Cu symmetric tilt boundaries. Multiple phases and structural transitions occur throughout the misorientation range, supporting grain-boundary phase behavior as a general phenomenon.
Problem
Atomistic modeling lacked a robust tool to predict complex grain-boundary structures and explore phase behavior with variable atomic density.
Method
The authors combine evolutionary algorithms for grand-canonical grain-boundary searches with clustering that automatically identifies phases from generated configurations.
Results
Multiple grain-boundary phases and new ground and metastable states are found across the entire misorientation range of Cu symmetric tilt boundaries.
Takeaways & Limitations
Grain boundaries exhibit rich polymorphism and structural transitions, including phases associated with different atomic densities and finite-temperature behavior.
Abstract
from arXiv · showhide
The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that can predict interface structure. Here we develop a new computational tool based on evolutionary algorithms that performs efficient grand-canonical grain boundary structure search and we design a clustering analysis that automatically identifies different grain boundary phases. Its application to a model system of symmetric tilt boundaries in Cu uncovers an unexpected rich polymorphism in the grain boundary structures. We find new ground and metastable states by exploring structures with different atomic densities. Our results demonstrate that the grain boundaries within the entire misorientation range have multiple phases and exhibit structural transitions, suggesting that phase behavior of interfaces is likely a general phenomenon.
2 Lawrence Livermore National Laboratory, Livermore, California 94550, USA
The paper develops evolutionary grand-canonical sampling and clustering to predict grain-boundary structures and phases across misorientation and atomic density. Applied to symmetric tilt boundaries in Cu, the approach reveals diverse structural families, new states, and transitions.
- Introduction: Grain boundaries influence the properties of advanced structural and functional materials used in high-temperature and aggressive environments.Their structures are inherited from synthesis and processing, making interface control relevant to materials optimization.
- Introduction: Atomistic modeling lacked a robust tool for predicting complex grain-boundary structures and phase behavior.Existing questions concerned phase structures, transition kinetics, and effects on mobility, diffusivity, and mechanical strength.
- Method: The study extends evolutionary structure prediction to variable atom numbers and cell sizes, enabling grand-canonical exploration of grain-boundary configurations.The method searches a higher-dimensional space while balancing structural quality and population diversity.
- Method: Clustering groups individual configurations into grain-boundary phases using similarities in thermodynamic and symmetry-related properties.The analysis distinguishes macrostates from individual microstates and can identify metastable phases within a finite energy interval.
- Method: The conventional γ-surface method fixes the number of atoms, whereas the new search reconstructs grain-boundary energy as a function of misorientation angle and atomic density.This variable-density treatment samples structures that conventional construction can miss.
- Results: Across the full misorientation range, the search finds new ground states and multiple phase-like minima, including dense Split-Kite and Extended-Kite families.Strong minima occur near half of the atomic plane fraction in 0°<θ<53.13° and 73.74°<θ<90.0°, while a narrow region near 65° disfavors unconventional densities at 0 K.
- Results: High-temperature simulations show that several boundaries have different low- and high-temperature structures and undergo first-order transitions.Clustering is especially useful when high-temperature phases are not among the lowest-energy 0 K configurations.
Discussion
The evolutionary search and clustering methodology reveals diverse grain-boundary phases across Cu symmetric tilt boundaries, including ground and metastable states with distinct structures and densities. Finite-temperature simulations confirm transitions between these phases, supporting their relevance to interface phase behavior and materials design.
- Method: The evolutionary algorithm explores grain-boundary structures by adding and removing atoms while varying grain-boundary dimensions.This expands sampling across compositional, dimensional, and structural space using simplified structure representations.
- Results: The search reconstructs the grain-boundary energy surface across misorientation and atomic density, predicting new ground states throughout the full misorientation range.For most misorientations, it identifies multiple grain-boundary phases.
- Method: Clustering identifies multiple metastable phases within a finite energy interval, including higher-energy macro-states that are not minima of any single property.This complements searches focused only on the lowest-energy configuration.
- Finite-temperature validation: High-temperature molecular-dynamics simulations with open surfaces demonstrate first-order transitions between phases predicted independently by 0 K calculations.The agreement supports the relevance of the computed ground and metastable states at finite temperature.
- Structural families: Kite, Split-Kite, and Extended-Kite structures form distinct families across the entire misorientation range, with Split-Kites generally having higher atomic density and serving as high-temperature phases.Their differing properties may help explain discontinuous mobility transitions and guide control of interface structures through alloying or temperature.
- Broader relevance: The same evolutionary sampling strategy predicts new ground states for low-angle boundaries composed of rows of edge dislocations.These searches require varying atomic arrangements and adding or removing atoms from dislocation cores.
2 Lawrence Livermore National Laboratory, Livermore, California 94550, USA
The method searches grain-boundary structures in a grand-canonical setting by varying atomic configurations, density, and cell dimensions, then characterizes candidates using thermodynamic and structural excess properties.
- Evolutionary search: The evolutionary algorithm optimizes grain-boundary atoms and the relative translation between grains for the lowest grain-boundary energy.The model separates upper-grain, lower-grain, and grain-boundary regions, with the grain regions typically 40–60 Å thick.
- Evolutionary search: Heredity and mutation operations rearrange atoms, add or remove atoms, and sample structures with different atomic densities.Atoms with low local order can be removed, while vacant sites on a 1 Å3 grid can be filled during insertion.
- Evolutionary search: The search varies grain-boundary dimensions and explores models containing roughly 500–5000 atoms, including 30–300 atoms in the grain-boundary region.Variable cell sizes allow large-scale reconstructions to be sampled automatically.
- Sampling strategy: To improve sampling in large systems, the method balances individual quality with population diversity and initializes structures using prescribed symmetries rather than fully random configurations.The representations also include vibrational modes and local order.
- Structure characterization: Each structure is characterized by eight excess properties, including free energy, excess volume, grain-boundary stresses, atomic density, and excess Steinhardt order parameters.The order parameters include Q4, Q6, Q8, and Q12, and are introduced per unit grain-boundary area analogously to thermodynamic excess properties.
- Structure characterization: The analysis compares grain-boundary atomic density separately from excess volume and treats density periodically because adding a complete atomic plane returns the same structure.Atomic density distance between structures is defined using the minimum periodic difference.