In the hard sphere model, the particles are described as impenetrable spheres with radius ; thus, their center-to-center distance  and they experience no interaction beyond this distance. Their interaction potential can be written as:
This model has an analytical solution in the Percus–Yevick approximation. Although highly simplified, it provides a good description for systems ranging from liquid metals to colloidal suspensions. In an illustration, the structure factor for a hard-sphere fluid is shown in the Figure, for volume fractions  from 1% to 40%.