Quantifying the anomalous self-diffusion in molybdenum with first-principles simulations

First-principles molecular-dynamics simulations based on a recently developed exchange-correlation functional show that self-diffusion in the refractory metal molybdenum is associated with strongly temperature-dependent activation energies for vacancy formation and migration. While static calculations of self-diffusion rates based on transition-state theory deviate systematically from experiments, with up to two orders of magnitude, the current results are accurate to within a mean deviation of 4 over the experimental range in temperature.

Figure 1

(Color online) The formation energy of a vacancy in Mo, as a function of temperature. The error bars are based on the fluctuations in the DFT-MD calculations and correspond to two standard deviations. The statistical inefficiency was determined using block averages. The major part of the temperature dependence in $H_{\text{v}}^{\text{f}}$ comes from anharmonic lattice vibrations. The shaded area illustrates the enthalpy contribution due to thermal effects in the occupation of electronic states, see text.

Figure 2

(Color online) Calculated vacancy jump rates. Squares show direct jump rates obtained in first-principles MD simulations, while the dashed line represents the harmonic TST result. The solid line was drawn under the assumption that the activation energy for vacancy migration varies quadratically with temperature, see text.

Figure 3

(Color online) Self-diffusion rates in Mo calculated with DFT-MD compared to experiments (Ref. 34). The main calculation uses the AM05 functional, results for PBE are included for comparison. The error bars correspond to two standard deviations in the estimation of the mean jump rate, which is the dominating source of error.

Figure 4

(Color online) Positron trapping rate $\sigma c_{\text{v}}$. The full line is fitted to experimental data (Ref. 36) assuming a temperature variation in $H_{\text{v}}^{\text{f}}$ as in Fig. 1. The dashed line is the corresponding linear term.