  We study the dependence of macroscopic polarization on composition and strain
in wurtzite III-V nitride ternary alloys using ab initio density-functional
techniques. The spontaneous polarization is characterized by a large bowing,
strongly dependent on the alloy microscopic structure. The bowing is due to the
different response of the bulk binaries to hydrostatic pressure, and to
internal strain effects (bond alternation). Disorder effects are instead minor.
Deviations from parabolicity (simple bowing) are of order 10 % in the most
extreme case of AlInN alloy, much less at all other compositions. Piezoelectric
polarization is also strongly non-linear. At variance with the spontaneous
component, this behavior is independent of microscopic alloy structure or
disorder effects, and due entirely to the non-linear strain dependence of the
bulk piezoelectric response. It is thus possible to predict the piezoelectric
polarization for any alloy composition using the piezoelectricity of the parent
binaries.
