The dynamical structure factor of a Coulomb crystal of ions is calculated a
t arbitrary temperature below the melting point, taking into account multip
honon processes in the harmonic approximation. In a strongly coupled Coulom
b ion liquid, the static structure factor is split into two parts, a Bragg
diffraction-like one, describing incipient long-range order structures, and
an inelastic part corresponding to thermal ion-density fluctuations. It is
assumed that the diffractionlike scattering does not lead to the electron
relaxation in the liquid phase. This assumption, together with the inclusio
n of multiphonon processes in the crystalline phase, eliminates large disco
ntinuities of the transport coefficients (jumps of the thermal and electric
conductivities, as well as shear viscosity, reported previously) at a melt
ing point.