  Perovskite solid solutions PbHfO3-PbSnO3 offer valuable opportunities for
studying the formation mechsnisms of incommensurate phases, owing to the
presence of an intermediate (between cubic and incommensurate) phase, which is
stabilized in PbHfO3 upon PbSnO3 admixture. Here, x-ray diffuse scattering
signal is used to quantify the evolution of susceptibilities related to
different modes of distortion (ferroelectric, incommensurate,
antiferrodistortive) as a function of temperature and the results are
critically compared to the predictions of a minimal symmetry-based Landau-like
model with two coupled order parameters (ferroelectric and antiferrodistortive)
and incommensurate order parameter being interpreted as inhomogeneous
polarization. Experimentally, we observe a Curie-Weiss-like linear dependence
of ferroelectric stiffness (inverse of susceptibility related to homogeneous
polarization fluctuations) in the cubic phase down to about 50 K above the
transition to the intermediate phase, where this dependence nearly saturates.
Upon cooling down to the intermediate phase, the maximum of susceptibility
shifts gradually to the non-zero wavevector, where another Curie-Weiss-like
linear stiffness trend is established, but with respect to the incommensurate
order parameter. Symmetry of diffuse scattering distributions indicates an
orthorhombic symmetry of the intermediate phase. A notable temperature
dependence of the constant that describes the energy of polarization
inhomogeneities is observed experimentally, which is in disagreement with the
model expectations. Specifics of this dependence suggest the presence of a
nearly temperature-independent characteristic length scale for inhomogeneities
across several phases. Other differences with the model suggest that the
incommensurate order parameter cannot be straightforwardly identified with
weakly-inhomogeneous ferroelectric polarization.
