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

Abstract

The self-consistent phonon approximation is applied to small crystallites of N argon atoms, in the range 3 & N & 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.

Structure and thermodynamic properties of small rare-gas clusters

“…The relevant Lennard-Jones potential parameters are given-in Table 1. As the results obtained for Ar are quite similar to those of [4] we present in Pig. 1 to 6 our results for Ar, Kr, Xe mainly for the clusters of 13 (icosahedron) and 5 atoms (bipyramid).…”

“…On the other hand, our phonon frequencies are sensibly lower. This leads in our treatment to larger values for the specific heat and the entropy, the difference being of the order of 300,; for a temperature of 30 K. However, a disagreement is observed between our values for ( u 2 ) and those of [4] which are two times larger. It should be noticed that our lower frequencies should lead to larger values of ( u 2 ) .…”

100 Years of the Lennard-Jones Potential

“…Clusters of LJ atoms have served this purpose well and remain a popular choice for such tests. Some of the earliest work was motivated by efforts to understand nucleation from small clusters to the solid state, − where noble gases modeled using the LJ potential presented more tractable targets than water. The finite-size analogue of the first-order solid–liquid phase transition is interesting in its own right − and proved to be a useful testing ground for enhanced thermodynamic sampling, as outlined in section .…”

Extension of microscopic theory of nucleation to macroscopic clusters

“…In our calculation, however, we strictly used Eq. (39) and found it to be of the order of 10 -I . With the aid of the above relation, the steady state nucleation rate takes the form…”