The Einstein model and the heat capacity of solids under high pressures

We use the Einstein model to compute the heat capacity of a crystalline solid where the effect of high pressures is simulated through a confined harmonic oscillator potential. The partition function and the heat capacity are calculated in terms of the box size (pressure), finding a clear tendency of the latter quantity to diminish as the pressure increases. For a strong confinement regime (high pressures) the heat capacity increases monotonically with the temperature, whereas at moderate and low pressures, it attains a maximum and asymptotically becomes that corresponding to a set of free (non-interacting) particles in a box. At high temperatures we find that the specific heat value of a crystalline solid under high pressures departs from that predicted by the Dulong-Petit model.