  Particle models with finitely many types of particles are considered, both on
$\mathbb{Z}^d$ and on discrete point sets of finite local complexity. Such sets
include many standard examples of aperiodic order such as model sets or certain
substitution systems. The particle gas is defined by an interaction potential
and a corresponding Gibbs measure. Under some reasonable conditions on the
underlying point set and the potential, we show that the corresponding
diffraction measure almost surely exists and consists of a pure point part and
an absolutely continuous part with continuous density. In particular, no
singular continuous part is present.
