Ab initiolocal-energy and local-stress analysis of tensile behaviours of tilt grain boundaries in Al and Cu

Abstract

Tensile deformation and failure of Σ9 tilt grain boundaries (GBs) in Al and Cu have been examined by first-principles tensile tests (FPTTs). Local-energy and local-stress schemes were applied to clarify the variations of local energies and local hydrostatic stresses for all atoms during the deformation process. The GBs in Al and Cu exhibited quite different tensile behaviours in the FPTTs, despite their similar initial configurations. For the Al GB, there are two stages of deformation before failure. In the first stage, the back bonds of the interfacial bonds are mainly stretched, due to special high strength of the interfacial reconstructed bonds. In the second stage, the interfacial bonds begin to be significantly stretched due to high concentrated stresses, while stretching of the back bonds is suppressed. The atoms at the interfacial, back and bulk bonds have very different variations of local energies and local stresses during each stage, because the behaviour of each atom is significantly dependent on each local structural change due to the high sensitivity of sp electrons to the local environment in Al. The Cu GB has much higher tensile strength, and a natural introduction of stacking faults (SFs) occurs via the {111} shear slip in the bulk regions between the interfaces before the maximum stress is reached. This is caused by the smaller SF energy and lower ideal shear strength of Cu than Al, and is triggered by highly accumulated local energies and stress at the interface atoms. The local-energy distribution around the SF is consistent with the previous theoretical estimation. After the introduction of the SF, the local energies and stresses of all the atoms in the Cu GB supercell tend to become similar to each other during the tensile process, in contrast to the inhomogeneity in the Al GB. The origins of the different tensile behaviours observed for Al and Cu GBs are discussed with respect to the different bonding natures of Al and Cu, which are dominated by three sp valence electrons per atom for Al and by fully occupied d bands and s electrons for Cu.

Influences of Multicenter Bonding and Interstitial Elements on Twinned γ-TiAl Crystal

“…N segregation at I4 site Figure 3d is the atomic energy of each Al atom. When an interstitial atom is added, the atomic energy of the two Al atoms on each layer is different due to its long-ranged sp orbitals [27,44]. By comparing the Al atomic energy in each layer in the pure twin, it can be found that when the C is added, the Al13 atomic energy is more greatly reduced than Al14 on TB.…”

Correlation analysis of strongly fluctuating atomic volumes, charges, and stresses in body-centered cubic refractory high-entropy alloys

“…These values are even higher than those reported previously for fcc FeCoNi and CrFeCoNi [22], indicating larger local stresses in refractory bcc HEAs than in 3d-transition-element fcc HEAs. The computed atomic stresses are also substantially higher than those at dislocation cores in bcc Fe [68,69], fcc Al [70], and B2 TiNi [71] as well as higher than the atomic stresses at grain boundaries of bcc Fe [30][31][32] and fcc Al and Cu [25,[33][34][35].…”

“…To compute atomic stresses we utilized the concept of stress densities. Electronic-structure-based stress densities have been widely used to analyze local properties, e.g., at grain boundaries [25,[30][31][32][33][34][35][36], at surfaces [37][38][39], in superlattices [40], to analyze chemical bonding in molecules [41][42][43], in metal clusters [44][45][46], in metal complexes [47], in lithiumionic conductors [48], and in Si-Fe [49], as well as to analyze electronic shell structures of atoms [50]. In the present study, the method by Filippetti and Fiorentini [51], later modified to fit the plane-wave basis projector augmented-wave (PAW) method [37], was employed to compute the stress density.…”

Active-learning-based efficient prediction of ab-initio atomic energy: a case study on a Fe random grain boundary model with millions of atoms

“…This local-energy analysis scheme, incorporated in the computational code QMAS [14], has already been applied to defect systems such as fcc-Al (111) surfaces [7], fcc-Al and fcc-Cu [110] GBs [15,16,17], and bcc-Fe [110] GBs [18,19]. We use the generalized gradient approximation [20] for the exchangecorrelation functional and a cut-off energy of 544 eV for the valence wave function.…”