<i>Ab Initio</i> Local-Energy and Local-Stress Calculations for Materials Science and Engineering

Abstract

Revealing atomic-scale distributions of energy and stress in defective or complex systems, based on the behavior of electrons, should contribute much to materials science and engineering, while only few practical ab initio methods were developed for this purpose. Thus, we developed computational techniques of local-energy and local-stress calculations within the plane-wave PAW (projector augmented wave)-GGA (generalized gradient approximation) framework. This is natural extension of ab initio energy-density and stress-density schemes, while the inherent gauge dependency is removed by integrating these densities in each local region where the contained gauge-dependent terms are integrated to be zero. In this overview, we explain our scheme with some details and discuss the concepts or physical meanings of local energy and local stress via the comparison with related schemes using similar densities, LCAO (linear combination of atomic orbitals) methods, Green's function formulation implemented by multiple scattering or TB (tight-binding) methods, or EAM (embedded-atom method) potentials. We present recent applications to metallic surfaces, grain boundaries (GBs) with and without solute segregation, tensile tests of metallic GBs, local elastic constants of microstructures in alloys, and machine-learning based GB-energy prediction, where the local-energy and local-stress analyses provide novel aspects of phenomena, deep insights into the mechanism, and effective data for novel machine-learning based modelling. We discuss unsettled issues and future applications, especially for large-scale metallic systems.

Insight into segregation sites for oxygen impurities at grain boundaries in silicon

“…We first discuss the impact of local stresses on oxygen segregation in terms of the atomic hydrostatic stresses at bond-centered sites around Σ9{114} GBs, as determined by ab initio local stress calculations. 35) A cuboid cell with two Σ9{114} GBs consisting of 248 atoms (4.09 × 1.64 × 0.77 nm 3 ) is constructed with HAADF-STEM data, and it is relaxed by ab initio calculations using the projector augmented wave method based on the generalized gradient approximation implemented by the Quantum Materials Simulator (QMAS) package. 36) A stable structural model with no dangling bonds is obtained, and the á ñ 110 projection of the model matches the corresponding HAADF-STEM images [Fig.…”

Segregation mechanism of arsenic dopants at grain boundaries in silicon

“…Comparing the 1D profile with the atomic arrangement in the GB revealed by HAADF-STEM (shown in Fig. 3), as well as with the distribution of atomic strains at the GB estimated by ab initio local stress calculations [57], it is hypothesized that a number of As atoms would segregate nearby the single atomic columns composed of the longest 〈11 0〉 reconstructed bonds, like oxygen segregation.…”

“…According to an ab initio local stress calculation [57], before As segregation, the site 6 with the lowest γ seg of -0.15 eV is under the highest compressive hydrostatic stress (about -3.5 GPa), due to short Si-Si bonds (see the site 6 in Fig. 2(b)), while the site 8 with the highest γ seg of +0.06 eV is under the highest tensile one (about +2.0 GPa) in Σ9{221} GBs, due to long Si-Si bonds (see the site 8 in Fig.…”

First-principles atomic level stresses: application to a metallic glass under shear

“…It may unveil the details of electronic structure and its connection with atomic stress state in MGs. However, in contrast to classical atomic stresses, the nature of the first-principles atomic stresses [25] is far from being fully understood, especially in glassy systems. Most previous studies have focused on the methodology for computing the first-principles atomic stress itself [26][27][28][29].…”