Dynamic structure factor of a monatomic cubic crystal

The spectral function of density fluctuations, also known as the dynamic structure factor, of a monatomic cubic crystal with vacancies is derived from the macroscopic equations describing transport in crystalline solids. The resonances of the spectral function are identified as a Brillouin doublet of sound propagation, a central Rayleigh peak of heat diffusion, as for perfect crystals, and another central sharp peak associated with vacancy diffusion. Analytical expressions for the heat and vacancy diffusivities, speeds of sound, and sound damping coefficients are obtained. The theoretical results are compared to molecular dynamics simulations of a face-centered cubic crystal of hard spheres.