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Radial Distribution Function for Hard Spheres

packing fraction

0.3

function

g(r)

S(k)

c(r)

B(r)

B(r), r>1

In statistical mechanics, the distribution of interparticle separations determines the radial distribution function [1].

This Demonstration shows the radial distribution function

g(r)

of a three-dimensional liquid composed of identical hard spheres of diameter

, making use of the exact solution of the Percus–Yevick integral equation [2, 3]. You can vary the packing fraction of the liquid, that is, the fraction of the total volume occupied by the spheres themselves. For a packing fraction greater than about 0.49, the corresponding

g(r)

can be regarded as that of a metastable liquid since the true stable phase is a crystal.

The Demonstration also includes three functions directly related to the radial distribution function

g(r)

: the structure factor

S(k)[4,5]

, the direct correlation function

c(r)

[6], and the bridge function

B(r)

[7].

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