A comprehensive first-principles study of pure elements: Vacancy formation and migration energies and self-diffusion coefficients

Abstract

A vast number of materials properties and phenomena are regulated by diffusion. However, diffusion coefficients from experiments and calculations are far from complete. Here, we report a compilation of vacancy formation energies ( ), vacancy migration energies ( ), vacancy activation energies ( ), vacancy concentrations (C Va ), and vacancy-mediated self-diffusion coefficients (D Va ) as a function of temperature for 82 pure elements in bcc, fcc, and hcp structures by means of a comprehensive first-principles study. We assess the accuracy of four exchange-correlation (X-C) functionals for first-principles calculations, including the local density approximation (LDA), two generalized gradient approximations (PW91 and PBE), andPBEsol  the focus of the present work. To gain temperature-dependent diffusion properties, transition state structure searches are performed by the climbing image nudged elastic band

Breakdown of Arrhenius law of temperature-dependent vacancy concentration in fcc lanthanum

“…We obtained a lattice constant of 5.29Å for the ground state, in perfect agreement with the experimental fcc lattice constant extrapolated to zero temperature [28]. The cubic 32 − 1-atom supercell with relaxed internal positions but fixed cell dimensions gave a vacancy formation energy of 1.46 eV, thus perfectly reproducing the previously reported values of 1.44 eV and 1.46 eV [29,30]. To test for a variation of the formation energy with thermal lattice expansion, we performed additional calculations at a lattice constant of 5.32Å corresponding to the experimental value around 780 K representative of the temperatures of measurement, which however resulted in only a minute increase of the formation energy to 1.50 eV.…”

Exceptionally High Ionic Conductivity in Na3P0.62As0.38S4 with Improved Moisture Stability for Solid‐State Sodium‐Ion Batteries

“…DFT Calculations : All DFT‐based first‐principles calculations in the present work were carried out by the Vienna Ab initio Simulation Package (VASP 5.4.1) with the ion–electron interaction described by the projector augmented wave method . The selected exchange‐correlation (X‐C) functional is the improved generalized gradient approximation for densely packed solids and their surfaces, i.e., the PBEsol, since it describes well structural and phonon properties of sulfides as well as diffusion properties . In addition, a hybrid X‐C functional of Heyd–Scuseria–Ernzerhof (HSE06) was also used to get accurate bandgap energy.…”

“…In addition, a hybrid X‐C functional of Heyd–Scuseria–Ernzerhof (HSE06) was also used to get accurate bandgap energy. The migration energies of Na‐ion were predicted by the climbing image nudged elastic band method using five images according to the monovacancy (Va) mediated diffusion mechanism, and all the Na‐Va migration pathways were calculated when possible. The reported migration energies were based on an average energy from all initial state structures.…”

Diffusion in the Ti-Al-V System

“…This includes the impurity diffusion coefficient of Al and V in a-Ti and the Ti selfdiffusion coefficient. [8,41,42] In the case of diffusion in the Ti-rich b-phase of the Ti-Al-V system, several experimental datasets are available. Huang et al [43] reviewed experimental data for interdiffusion in the Al-Ti system published before the year 2011.…”