  Using a combination of density-functional perturbation theory and the
itinerant coherent potential approximation, we study the effects of atomic
relaxation on the inelastic incoherent neutron scattering cross sections of
disordered Ni$_{50}$Pt$_{50}$ alloys. We build on previous work, where
empirical force constants were adjusted {\it ad hoc} to agree with experiment.
After first relaxing all structural parameters within the local-density
approximation for ordered NiPt compounds, density-functional perturbation
theory is then used to compute phonon spectra, densities of states, and the
force constants. The resulting nearest-neighbor force constants are first
compared to those of other ordered structures of different stoichiometry, and
then used to generate the inelastic scattering cross sections within the
itinerant coherent potential approximation. We find that structural relaxation
substantially affects the computed force constants and resulting inelastic
cross sections, and that the effect is much more pronounced in random alloys
than in ordered alloys.
