Strongly non-Arrhenius self-interstitial diffusion in vanadium

We study diffusion of self-interstitial atoms (SIAs) in vanadium via molecular-dynamics simulations. The ⟨111⟩-split interstitials are observed to diffuse one-dimensionally at low temperature, but rotate into other ⟨111⟩ directions as the temperature is increased. The SIA diffusion is highly non-Arrhenius. At $T<600\mathrm{K}$, this behavior arises from temperature-dependent correlations. At $T>600\mathrm{K}$, the Arrhenius expression for thermally activated diffusion breaks down when the migration barriers become small compared to the thermal energy. This leads to Arrhenius diffusion kinetics at low $T$ and diffusivity proportional to temperature at high $T$.

Figure 1

Typical trajectories of migrating SIAs for temperatures of (a) $300\mathrm{K}$, (b) $700\mathrm{K}$, (c) $900\mathrm{K}$, and (d) $1400\mathrm{K}$.

Figure 2

Frequency of rotations as a function of temperature. The solid line is an Arrhenius fit to the data with slope $\Delta E_r=0.44\mathrm{eV}$, preexponential factor ${\nu }_0=1.3\times {10}^{13}{\mathrm{s}}^{-1}$.

Figure 3

A plot of the diffusivity of the ⟨111⟩-split interstitial in the form suggested by the Arrhenius relation. The filled symbols (∎) correspond to the measured diffusivity $D$ and open symbols (◇) to $D$ normalized by the correlation factor $f$ (see text). The straight line is a low temperature fit to the $D∕f$ data, corresponding to $\Delta E_d=0.018\mathrm{eV}$ and a preexponential factor of ${\nu }_0=1.5\times {10}^{12}{\mathrm{s}}^{-1}$ in the Arrhenius form. Statistical errors are of order the symbol size. The inset to the figure shows the variation of $f$ as a function of $1∕k_{B}T$.

Figure 4

The diffusivity $D$ (∎) from Fig. 3 as a linear function of $T$, normalized by $\Delta E_d$. The thick solid line represents the diffusivity of a particle in a sinusoidal potential at finite temperature as described by Eq. (1) for a value of $\gamma =0.1{\tau }^{-1}$ where $\tau =\sqrt{m{\sigma }^2∕ϵ}$. The dashed line is the free particle limit of the same model, $D=k_{B}T∕ϵm\gamma$. The inset shows an Arrhenius plot of the diffusivity of the particle in the sinusoidal potential as a function of $ϵ∕k_{B}T$ as a solid line and the straight dashed line has slope one.