Ab initio study of symmetrical tilt grain boundaries in bcc Fe: structural units, magnetic moments, interfacial bonding, local energy and local stress

Survey of Grain Boundary Energies in Tungsten and Beta-Titanium at High Temperature

Heat treatment is a necessary means to obtain desired properties for most of the materials. Thus, the grain boundary (GB) phenomena observed in experiments actually reflect the GB behaviors at relatively high temperature to some extent. In this work, 405 different GBs were systematically constructed for body-centered cubic (BCC) metals and the grain boundary energies (GBEs) of these GBs were calculated with molecular dynamics for W at 2400 K and β-Ti at 1300 K and by means of molecular statics for Mo and W at 0 K. It was found that high temperature may result in the GB complexion transitions for some GBs, such as the Σ11{332}{332} of W. Moreover, the relationships between GBEs and sin(θ) can be described by the functions of the same type for different GB sets having the same misorientation axis, where θ is the angle between the misorientation axis and the GB plane. Generally, the GBs tend to have lower GBE when sin(θ) is equal to 0. However, the GB sets with the <110> misorientation axis have the lowest GBE when sin(θ) is close to 1. Another discovery is that the local hexagonal-close packed α phase is more likely to form at the GBs with the lattice misorientations of 38.9°/<110>, 50.5°/<110>, 59.0°/<110> and 60.0°/<111> for β-Ti at 1300 K.

How does the Li-distribution in the 16d sites determine the stability of A3(Li,Ti5)O12 (A = Li and Na)?

Li₃(Li,Ti₅)O₁₂ (LTO) is a stable and safe negative electrode material for Li-ion batteries, and its Na substitute Na₃(Li,Ti₅)O₁₂ (NTO) is a counterpart for the Na-ion battery. In LTO and NTO, a sixth of the Ti-sites (16d) in the spinel framework are replaced by Li: Li mixing in the 16d sites. For conducting theoretical studies on these materials, e.g., density functional theory (DFT) calculations, one has to confront the astronomical number of combinations of Li distribution in 16d sites to construct model structures, of which the size is sufficiently large to represent the bulk material properties. Only a limited number of models, whose structures are a priori specified by “researcher intuition,” have been examined thus far, and how Li-mixing determines the material stability has yet to be clarified. Herein, we statistically analyzed the DFT total energy of more than 2 × 10⁴ model structures of LTO and NTO that were extracted from the 4 × 10⁸ possible combinations of Li-mixing with computer-aided symmetry analysis and an automated model building system. The local energy analysis further revealed the local stability/instability of each structure. We found that LTO and NTO stability can be well explained by the apparent coulombic repulsion between Li⁺ in the 16d sites as if they were placed in a matrix of dielectric constants of 1.92 and 2.04 for LTO and NTO, respectively. That is, the sum of the inverse of the Li–Li distance (S) serves as a good descriptor in predicting the stability of these materials. The extent to which the O²⁻ anions are displaced from the Wyckoff position (32e) is considered to differentiate NTO from LTO. However, the electronic structure of NTO does not significantly differ from that of LTO unless S exceeds a certain limit. These results suggest that the spinel framework tolerates the structural instability and variety to some extent, which is important in constructing a spinel structure with the mixing of other cations, thereby replacing the rare element Li.

Li₃(Li,Ti₅)O₁₂ (LTO) is a stable and safe negative electrode material for Li-ion batteries, and its Na substitute Na₃(Li,Ti₅)O₁₂ (NTO) is a counterpart for the Na-ion battery.

Hydrogen Trapping in bcc Iron

Fundamental understanding of H localization in steel is an important step towards theoretical descriptions of hydrogen embrittlement mechanisms at the atomic level. In this paper, we investigate the interaction between atomic H and defects in ferromagnetic body-centered cubic (bcc) iron using density functional theory (DFT) calculations. Hydrogen trapping profiles in the bulk lattice, at vacancies, dislocations and grain boundaries (GBs) are calculated and used to evaluate the concentrations of H at these defects as a function of temperature. The results on H-trapping at GBs enable further investigating H-enhanced decohesion at GBs in Fe. A hierarchy map of trapping energies associated with the most common crystal lattice defects is presented and the most attractive H-trapping sites are identified.

The Nucleation and the Intrinsic Microstructure Evolution of Martensite from 332113β Twin Boundary in β Titanium: First-Principles Calculations

A clear understanding on the inter-evolution behaviors between 332113β twinning and stress-induced martensite (SIM) α″ in β-Ti alloys is vital for improving its strength and ductility concurrently. As the preliminary step to better understand these complex behaviors, the nucleation and the intrinsic microstructure evolution of martensite α″ from 332113β twin boundary (TB) were investigated in pure β-Ti at atomic scale using first-principles calculations in this work. We found the α″ precipitation prefers to nucleate and grow at 332113β TB, with the transformation of 332113β TB→130310α” TB. During this process, α″ precipitation firstly nucleates at 332113β TB and, subsequently, it grows inwards toward the grain interiors. This easy transition may stem from the strong crystallographic correspondence between 332113β and 130310α” TBs, and the region close to the 332113β TB presents the characteristics of intermediate structure between β and α″ phases. Kinetics calculations indicate the α″ phase barrierlessly nucleates at 332113β TB rather than in grain interior, where there is higher critical driving energy. Our calculations provide a unique perspective on the “intrinsic” microstructure evolution of martensite α″ from 332113β TB, which may deepen our understanding on the precipitation of martensite α″ and the inter-evolution behaviors between 332113β twinning and martensite α″ in β-Ti alloys at atomic scale.

Failure mode in first-principles computational tensile tests of grain boundaries: effects of a bulk-region size, dominant factors, and local-energy and local-stress analysis

A first-principles computational tensile test (FPCTT) is a powerful tool to investigate intrinsic strength and failure processes of grain boundaries (GBs), according to atomic and electronic behaviors based on density-functional theory, while careful interpretation is required in comparison with experiments, because of ideal conditions used in FPCTTs. We observed serious effects of a bulk-region size in FPCTTs of the {0 0 1} [Formula: see text]5 GB in Al. For a GB supercell with enough thick bulk regions, the energy-strain curve shows spontaneous failure with catastrophic energy release just after the maximum stress point, which we name Type-A failure. For a GB supercell with thin bulk regions, the energy increases gradually even after the maximum stress and continuously becomes that of relaxed fracture surfaces, which we name Type-B failure, although the stress-strain curves are almost common until the maximum stress point in both the supercells. The peculiar failure of Type B occurs by the lack of accumulated strain energies for creating fracture surfaces even after the maximum stress point, because the accumulated strain energy is nearly proportional to the bulk-region size. We clarified that the failure mode in a FPCTT depends on the relationship among the three factors; the accumulated strain energy depending on the bulk-region size, the work of separation (the formation energy of fractured surfaces into a GB), and the maximum stress of the GB (the GB strength). We showed that the failure mode of previous FPCTTs of Al tilt GBs with segregated impurities can be reinterpreted from this viewpoint, by considering the changes of the work of separation and the GB strength by impurities. We should be aware of the distinction of the failure mode in FPCTTs, because experimentally Type-B failure does not occur except for special cases. Finally, we applied ab initio local-energy and local-stress analysis to the FPCTT of the {0 0 1} [Formula: see text]5 GB in Al, and discussed how to extract local energy-strain or energy-separation relations independent of the bulk-region size to be combined with meso- or macroscopic simulations.

Si segregation at Fe grain boundaries analyzed by ab initio local energy and local stress

Using density-functional theory calculations combined with recent local-energy and local-stress schemes, we studied the effects of Si segregation on the structural, mechanical and magnetic properties of the Σ3(1 1 1) and Σ11(3 3 2) Fe GBs formed by rotation around the [1 1 0] axis. The segregation mechanism was analyzed by the local-energy decomposition of the segregation energy, where the segregation energy is expressed as a sum of the following four terms: the local-energy change of Si atoms from the isolated state in bulk Fe to the GB segregated state, the stabilization of replaced Fe atoms from the GB to the bulk, the local-energy change of neighboring Fe atoms from the pure GB to the segregated GB and the local-energy change of neighboring Fe atoms from the system of an isolated Si atom in the bulk Fe to the pure bulk Fe. The segregation energy and value of each term greatly depends on the segregation site and Si concentration. The segregation at interface Fe sites with higher local energies in the original GB configurations naturally leads to higher segregation-energy gains, while interface sites with lower local energies can lead to larger energy gains if stronger Si-Fe interactions occur locally in the final segregated configurations. The high Si concentration reduces the segregation-energy gain per Si atom due to the local-energy increases of Si atoms neighboring to each other or through the reduction in the number of stabilized Fe atoms per Si atom as observed in a Si dimer in bulk Fe. In the Si-segregated GBs, Si-Fe bonds enhance local Young's moduli and tend to suppress the interface weakening, while the GB adhesion is slightly reduced. And Fe atoms contacting Si atoms have reduced magnetic moments, due to Si-Fe sp-d hybridization interactions.