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Perovskite solid solutions PbHfO3-PbSnO3 offer valuable opportunities forstudying the formation mechsnisms of incommensurate phases, owing to thepresence of an intermediate (between cubic and incommensurate) phase, which isstabilized in PbHfO3 upon PbSnO3 admixture. Here, x-ray diffuse scatteringsignal is used to quantify the evolution of susceptibilities related todifferent modes of distortion (ferroelectric, incommensurate,antiferrodistortive) as a function of temperature and the results arecritically compared to the predictions of a minimal symmetry-based Landau-likemodel with two coupled order parameters (ferroelectric and antiferrodistortive)and incommensurate order parameter being interpreted as inhomogeneouspolarization. Experimentally, we observe a Curie-Weiss-like linear dependenceof ferroelectric stiffness (inverse of susceptibility related to homogeneouspolarization fluctuations) in the cubic phase down to about 50 K above thetransition to the intermediate phase, where this dependence nearly saturates.Upon cooling down to the intermediate phase, the maximum of susceptibilityshifts gradually to the non-zero wavevector, where another Curie-Weiss-likelinear stiffness trend is established, but with respect to the incommensurateorder parameter. Symmetry of diffuse scattering distributions indicates anorthorhombic symmetry of the intermediate phase. A notable temperaturedependence of the constant that describes the energy of polarizationinhomogeneities is observed experimentally, which is in disagreement with themodel expectations. Specifics of this dependence suggest the presence of anearly temperature-independent characteristic length scale for inhomogeneitiesacross several phases. Other differences with the model suggest that theincommensurate order parameter cannot be straightforwardly identified withweakly-inhomogeneous ferroelectric polarization.

Ferroelectric to incommensurate fluctuations crossover in PbHfO3-PbSnO3