Vibrational thermodynamics: coupling of chemical order and size effects

Abstract

Abstract. The effects of chemical order on the vibrational entropy have been studied using firstprinciples and semi-empirical potential methods. Pseudopotential calculations on the Pd 3 V system show that the vibrational entropy decreases by 0.07k B upon disordering in the high-temperature limit. The decrease in entropy contradicts what would be expected from simple bonding arguments, but can be explained by the influence of size effects on the vibrations. In addition, the embeddedatom method is used to study the effects of local environments on the entropic contributions of individual Ni and Al atoms in Ni 3 Al. It is found that increasing numbers of Al nearest neighbours decreases the vibrational entropy of an atom when relaxations are not included. When the system is relaxed, this effect disappears, and the local entropy is approximately uniform with increasing number of Al neighbours. These results are explained in terms of the large size mismatch between Ni and Al. In addition, a local cluster expansion is used to show how the relaxations increase the importance of long-range and multisite interactions.

A relationship to estimate the excess entropy of mixing: Application in silicate solid solutions and binary alloys

“…In the middle of the transition metals series, the bulk moduli tend to have a maximum and hence, it is to be expected, that the A—B bonds will be stiffer than the A—A or B—B bonds. This situation was in fact found for the Pd 3 V alloy [23].…”

“…A small dependence of the heat capacity on cation ordering was also reported for NaAlSi 3 O 8 and KAlSi 3 O 8 [22]. A detailed first principles study [23] investigated the effect of chemical order on the vibrational entropy in Ni 3 Al and Pd 3 V. No such effect was found in Ni 3 Al, when the system was relaxed. However, disordering of the ordered Pd 3 V phase decreased the vibrational entropy by 1–2% because in ordered Pd 3 V, the symmetry constraints prevented the relaxation.…”

The effect of lattice vibrations on substitutional alloy thermodynamics

“…All the known sources of vibrational entropy differences can be conveniently summarized by the bond stiffness vs bond length model (Morgan et al, 2000;. In this picture, each type of chemical bond is characterized by a length-dependent spring constant.…”

Entropy of point defects calculated within periodic boundary conditions

“…The most important quantity to influence the calculated entropies is the accuracy of relaxation of the atoms surrounding the defect, compare, e.g., Ref. 23.…”