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

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 (HVaF), vacancy migration energies (HVaM), vacancy activation energies (HVaQ), 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), and PBEsol - 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 method; and the needed equilibrium properties of energy (E₀), volume (V₀), bulk modulus (B₀) and its pressure derivative (B′) for each structure of each element are estimated via an energy versus volume equation of state. Examination of the predicted quantities and available experimental data indicates that (i) PBEsol is a better selection in terms of getting accurate equilibrium and diffusion properties; (ii) the facility of vacancy migration can be understood from the redistribution of differential charge density, and anomalous energy pathways for vacancy migration are found for hcp Ce, La, Pr, Ti, and Zr within the basal plane; (iii) HVaQ can be predicted well from the melting point of a pure element and in particular a new relationship (HVaQ=_B0V0/6), suggesting diffusivity is governed by interatomic bonding strength; and (iv) the computed quantities such as C_Va, D_Va, HVaF, HVaM, and HVaQ are in favorable accord with available experiments for most elements, but fall short for entropy-related properties. The present study of pure elements provides not only diffusion-related properties and a new understanding of diffusivity, but also a benchmark of first-principles calculations and a foundational dataset for the Materials Genome Initiative.