Stress-enhanced diffusion in Yukawa crystals

Abstract

Self-diffusion in crystallized Coulomb (Yukawa) plasmas proceeds by the thermally activated formation of vacancy-interstitial pairs and the migration of these defects through the lattice, commonly known as Frenkel pairs in the materials literature. Molecular dynamics has recently resolved an Eyring law for diffusion in unstrained crystals, which we generalize to deformed crystals in this work. We simulate sheared Yukawa crystals and show that a static elastic strain exponentially enhances diffusion due to the additional elastic energy stored in the region that participates in Frenkel pair formation relative to the unstrained crystal: $D(\varepsilon)=D_0(Γ^{*})\exp[V^{*}σ/k_{\rm B}T]$, with $σ=\tfrac12μ\varepsilon^{2}$ the elastic energy density stored by the shear strain $\varepsilon$ and $V^{*}$ the activation volume. We find a single activation volume $N_{\rm act} = n_iV^{*}\simeq31$ suffices for typical astrophysical screenings with a reduction at higher screening. This suggests Frenkel pair formation requires only a brief coordination of the nearest neighbors at a thermal maximum in oscillation. Stress-enhanced diffusion supplies a microphysical mechanism for creep in strained neutron star crusts and crystallizing white dwarf cores.