Self-consistent phonon calculation of structures and thermodynamic properties of small argon crystallites

The self-consistent phonon approximation is applied to small crystallites of $N$ argon atoms, in the range $3\le N\le 15$. The temperature dependence of the lattice constant, frequencies, internal energy, free energy, specific heat, and entropy, for each cluster size, is reported. The variation of these quantities with $N$ is also given. The equilibrium structures are quantum mechanically determined at each temperature and are found to agree with classical results. Comparisons with normal-mode calculations and with bulk behavior are given.