Non-Linear Arrhenius Behavior of Self-Diffusion in $\beta$-Ti and Mo

Abstract

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. Thermal expansion is found to weakly affect the activation enthalpy but has a strong effect on the prefactor of the diffusion coefficient, reproducing the non-linear, non-Arrhenius "anomalous" self-diffusion in both bcc systems with good agreement between calculation and experiment. The proposed methodology is general and simple enough to be applicable to other mechanically unstable crystals.

arXiv comment11 pages, 6 figures

References in corpus (9)

• Phonons and related properties of extended systems from density-functional perturbation theory
• Lattice dynamics of anharmonic solids from first principles
• Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles
• Classical potential describes martensitic phase transformations between the $\alpha$, $\beta$ and $\omega$ titanium phases
• High-Throughput ab-initio Dilute Solute Diffusion Database
• Superionic-like diffusion in an elemental crystal: bcc Titanium
• Fast Free Energy Calculations for Unstable High-Temperature Phases
• Defects from phonons: Atomic transport by concerted motion in simple crystalline metals
• Phonon-assisted diffusion in bcc phase of titanium and zirconium from first-principles