Inelastic neutron scattering in solids allows to measure the frequency vs wave vector dispersion relations of the vibrational modes, w = w (qj). These frequencies, multiplied by the Planck's constant, constitute the phonon energies defined as eigenvalues of the Hamiltonian describing the dynamics of the atoms in the crystals. In a anharmonic crystal they depend on volume V. These energy eigenvalues constitute the basic ingredients needed to construct the partition function Z (T,V) and, via Z, the Helmholtz thermodynamic potential F.
The knowledge of F (T,V) enables one to derive a number of macroscopic properties of the material, such as the specific heat at constant volume, the isothermal bulk modulus and the Grueneisen parameter, of interest in many thermal and mechanical problems and applications.