Nonlinear Arrhenius behavior of self-diffusion in beta-Ti and Mo

While anomalous diffusion coefficients with non-Arrhenius-like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and beta-Ti by coupling quasiharmonic transition state theory and large-displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as beta-Ti. The effect of thermal expansion is found to be crucial for the nonlinear, non-Arrhenius "anomalous" self-diffusion in both bcc systems, with beta-Ti showing a 60% larger relative nonlinearity parameter than Mo. Our results point to temperature dependence in the diffusion prefactor from thermal expansion as the major origin of anomalous self-diffusion. The methodology proposed for beta-Ti is general and simple enough to be applicable to other mechanically unstable crystals.