Understanding the role of anharmonic phonons in diffusion of bcc metals

Abstract

Diffusion in the high-temperature bcc phase of IIIB-IVB metals such as Zr, Ti, and their alloys is observed to be orders of magnitude higher than bcc metals of group VB-VIB, including Cr, Mo, and W. The underlying reason for this higher diffusion is still poorly understood. To explain this observation, we compare the first-principles-calculated parameters of monovacancy-mediated diffusion between bcc Ti, Zr, and dilute Zr- Sn alloys and bcc Cr, Mo, and W. Our results indicate that strongly anharmonic vibrations promote both the vacancy concentration and the diffusive jump rate in bcc IVB metals and can explain their markedly faster diffusion compared to bcc VIB metals. Additionally, we provide an efficient approach to calculate diffusive jump rates according to the transition state theory (TST). The use of standard harmonic TST is impractical in bcc IIIB/IVB metals due to the existence of ill-defined harmonic phonons, and most studies use classical or ab initio molecular dynamics for direct simulation of diffusive jumps. Here, instead, we use a stochastically sampled temperature-dependent phonon analysis within the transition state theory to study diffusive jumps without the need of direct molecular dynamics simulations. We validate our first-principles diffusion coefficient predictions with available experimental measurements and explain the underlying reasons for the promotion of diffusion in bcc IVB metals/alloys compared to bcc VIB metals.