[Paper Review] Universality of grain boundary phases in fcc metals: Case study on high-angle [111] symmetric tilt grain boundaries

T. Brink, Lena Langenohl+2 more|arXiv (Cornell University)|Nov 25, 2022

Microstructure and mechanical properties4 citations

TL;DR

This study uses classical atomistic simulations to investigate high-angle [111] symmetric tilt grain boundaries in seven fcc metals (Ni, Cu, Pd, Ag, Au, Al, Pb), revealing two universal families of grain boundary (GB) phases across all materials. The results show that these phases are primarily governed by sphere-packing geometry and medium-ranged interactions, with material-specific bonding physics influencing only the GB free energy, not the atomic structures, indicating a high degree of universality in GB phase formation for fcc metals.

ABSTRACT

Grain boundaries often exhibit ordered atomic structures. Increasing amounts of evidence have been provided by transmission electron microscopy and atomistic computer simulations that different stable and metastable grain boundary structures can occur. Meanwhile, theories to treat them thermodynamically as grain boundary phases have been developed. Whereas atomic structures were identified at particular grain boundaries for particular materials, it remains an open question if these structures and their thermodynamic excess properties are material specific or generalizable to, e.g., all fcc metals. In order to elucidate that question, we use atomistic simulations with classical interatomic potentials to investigate a range of high-angle [111] symmetric tilt grain boundaries in Ni, Cu, Pd, Ag, Au, Al, and Pb. We could indeed find two families of grain boundary phases in all of the investigated grain boundaries, which cover most of the standard fcc materials. Where possible, we compared the atomic structures to atomic-resolution electron microscopy images and found that the structures match. This poses the question if the grain boundary phases are simply the result of sphere-packing geometry or if material-specific bonding physics play a role. We tested this using simple model pair potentials and found that medium-ranged interactions are required to reproduce the atomic structures, while the more realistic material models mostly affect the grain boundary (free) energy. In addition to the structural investigation, we also report the thermodynamic excess properties of the grain boundaries, explore how they influence the thermodynamic stability of the grain boundary phases, and detail the commonalities and differences between the materials.

Motivation & Objective

• To determine whether grain boundary (GB) phases in fcc metals are universal or material-specific.
• To investigate the role of atomic structure, bonding physics, and interatomic potential accuracy in GB phase formation.
• To compare simulated GB structures with experimental atomic-resolution TEM/STEM images for validation.
• To quantify thermodynamic excess properties (e.g., free energy) of GB phases and assess their stability across different fcc metals.
• To evaluate whether GB phases arise from geometric constraints (sphere packing) or material-specific electronic effects.

Proposed method

• Classical molecular dynamics and static energy minimization simulations using empirical many-body interatomic potentials (EAM) for Ni, Cu, Pd, Ag, Au, Al, and Pb.
• Systematic investigation of high-angle [111] symmetric tilt grain boundaries with varying misorientation angles.
• Application of the quasi-harmonic approximation (QHA) to compute free energies and assess thermodynamic stability of GB phases.
• Comparison of simulated GB atomic structures with experimental high-resolution transmission electron microscopy (HRTEM/STEM) images.
• Use of simplified model pair potentials to isolate the influence of medium-ranged interactions on GB phase stability.
• Careful numerical validation of interatomic potentials, including high-precision tabulation and spline interpolation to eliminate noise in second and third derivatives of potential energy.

Experimental results

Research questions

• RQ1 Are the observed grain boundary phases in fcc metals universal across different elements, or are they material-specific?
• RQ2 To what extent do sphere-packing geometry and medium-ranged interatomic interactions govern the formation of grain boundary phases?
• RQ3 Can the same GB phase structures be observed across multiple fcc metals despite differences in electronic structure and bonding?
• RQ4 How do thermodynamic excess properties (e.g., free energy) of GB phases vary across different fcc metals, and what determines their relative stability?
• RQ5 To what extent do material-specific interatomic potentials affect GB phase structure versus only influencing free energy?

Key findings

• Two distinct families of grain boundary phases were identified across all seven fcc metals studied, indicating a high degree of universality in GB phase formation.
• The atomic structures of these GB phases match experimental high-resolution TEM/STEM images, confirming the reliability of the simulations.
• Medium-ranged interactions are essential for reproducing the observed GB phase structures; simple pair potentials fail to capture them.
• Material-specific bonding physics primarily affect the grain boundary free energy, not the atomic structure of the phases, suggesting structural universality.
• Numerical noise in interatomic potentials—particularly in Al, Pd, and Au—was traced to insufficient precision in tabulated data or abrupt cutoff functions, resolved by high-precision re-tabulation.
• The revised EAM potential for Al, constructed with machine-precision interpolation, yielded smooth second and third derivatives, improving QHA-based free energy calculations.