  We present total energy and force calculations on the
(GaN)$_{1-x}$(ZnO)$_{x}$ alloy. Site-occupancy configurations are generated by
Monte Carlo (MC) simulations, based on a cluster expansion (CE) model proposed
in a previous study. Surprisingly large local atomic coordinate relaxations are
found by density-functional calculations using a 432-atom periodic supercell,
for three representative configurations at $x=0.5$. These are used to generate
bond length distributions. The configurationally averaged composition- and
temperature-dependent short-range order (SRO) parameters of the alloys are
discussed. Entropy is approximated in terms of pair distribution statistics and
thus related to SRO parameters. This approximate entropy is compared with
accurate numerical values from MC. An empirical model for the dependence of
bond length on local chemical environments is proposed.
