Diffraction Studies of Liquids

Abstract

Simple liquids are those for which the intermolecular potential-energy function Φ(r ₁? r ₂,..., r _N ) has the special form given by

$$\Phi \left( {{r_1},{r_2}, \ldots ,{r_N}} \right) = \sum\limits_{i < j} {\Phi \left( {{r_k},{r_j}} \right)} $$

(1.1.1)

where r _k is the position vector of the kth atom or ion in the liquid, N is the total number of atoms, and Φ is the so-called pair potential. We also assume that Φ is spherically symmetric, i.e., it is a function of $\left| r \right| = \left| {{r_k} - {r_j}} \right|$ . For a simple mixture composed of, say, a and b atoms, the interactions are characterized by three pair potentials, each spherically symmetric, given by Φ _aa (r), Φ _bb (r)? and Φ _ab (r)? There is a considerable body of evidence which suggests that Φ for the liquid form of the rare gases (Ar, Kr, Ne, and Xe) approximates very closely a sum of spherically symmetric pair potentials. An example of the potential Φ used for liquid rare gases is given in Figure 1.1. More surprisingly, a model based on pair potentials can also be justified for liquid nontransition metals like Na and Al. In these cases, the form of Φ is not so well defined, but the general features presented in Figure 1.1 do not probably involve a serious error. A review of the usefulness of pair potentials for metallic systems lies outside the scope of this treatment; the reader is referred to the book by Faber⁽¹⁾ and to the references cited therein. Pair potentials are also very useful in molten salts. This topic has been revewed by Sangster and Dixon.⁽²⁾