Quantitative correlation between structural (dis-)order and diffuseness of phase transition in lead scandium tantalate

Ferroelectrics show a phase transition to a paraelectric phase at a well-defined transition temperature. Introducing disorder makes this transition diffuse, and the system becomes a relaxor. Since the degree of (dis-)order is usually manipulated by varying the chemical composition, it is difficult to establish a direct relationship between disorder and the degree of diffuseness. Perovskite structured lead scandium tantalate (Pb[Sc$_{1/2}$Ta$_{1/2}$]O$_3$, PST) offers the opportunity to tune the character of the transition by thermal annealing without changing the stoichiometry. Here it is demonstrated that there is a linear correlation between the structural ordering, quantified by the intensity ratio $S$ of the pseudocubic (111)/(200) x-ray diffraction peaks, and the diffuseness parameter $\gamma$ deduced from temperature-dependent dielectric spectroscopy. The relation is universal, independent of whether the sample is a thin film, multilayer capacitor or bulk ceramic, and also independent of the absolute value of the dielectric permittivity.