A new general procedure for constructing Helmholtz thermodynamic poten
tials (free energies) of solids within the quasi-harmonic approximatio
n is devised. A Helmholtz free energy is expressed as an explicit anal
ytical function of volume and temperature. Using cesium iodide as an e
xample, it is shown that the proposed expression for the free energy a
llows us to. calculate thermodynamic parameters of materials (compress
ibility, heat capacity, coefficient of thermal expansion, etc.) under
static conditions and in shock waves over the pressure range from zero
to hundreds of gigapascals at temperatures from room temperature to s
everal thousands degrees.