Anharmonicity Contributions to Dislocation Drag

Abstract

A unified theory of the effect of phonon‐phonon scattering on the drag force Bv acting upon a dislocation moving with velocity v, much less than the sound velocity, is presented. A formalism is developed in terms of a frequency‐ and wave‐vector‐dependent bulk viscosity. Thermoelastic damping, phonon viscosity, phonon scattering, and, in the case of oscillatory motion, reradiation damping are all included in this framework. It is shown that the dominant mechanism is that resulting from phonon scattering and gives rise to the form $B_S{\mathrm{=\beta \hspace{0.17em}[k}}^2{\text{R(0)/θΩ}}_a^2{\mathrm{]J}}_5\mathrm{(T/\theta )}$ for a straight dislocation. Here R(0)=W_DT²/Λ)_T→0, where W_D is the dislocation contribution to the phonon component of the thermal resistance, Λ the dislocation density, Ω_a the atomic volume, κ is the Boltzmann constant, and T and θ the ambient and Debye temperatures, respectively. The function $J_5{\mathrm{(x)}}^5{\mathrm{=(x)}}^5{\text{/5!)∫\hspace{0.17em}}}_0^{\text{1/x}}{x}^5{e}^x{\mathrm{(e}}^x{\text{−1)}}^{\text{−2}}\mathrm{dx}$ , and the numerical constant β is estimated to be 1.2×10⁴. The physical processes underlying all the above mechanisms are explored in detail and the theory is compared at length with the work of previous authors.