Pb(B-1/2'B-1/2'')O-3-type perovskites .2. Short-range order parameter as a criterion of the distinction between relaxor and normal ferroelectrics

A classification scheme of Pb(B-1/2'B-1/2'')O-3-type perovskites with respect to the B-site order parameters was proposed based on the theoretical calculation of the short-range order parameter (sigma) using the pair-correlation model. The calculated order parameters predict that a Pb(B-1/2'B-1/2'')O-3-type perovskite without any charge difference between B' and B '' cations [e.g., Pb(Zr1/2Ti1/2)O-3 (PZT)] is represented by a completely disordered state with the absence of a finite coherence length. On the other hand, a Pb(B-1/2'B-1/2'')O-3-type perovskite system having different ionic charges is characterized either by the short-range ordering with a nanoscale coherence length or by the macroscopic long-range ordering, depending on the magnitude of ionic charge difference between B' and B '' ions. The normal ferroelectricity in Pb(B-1/2'B-1/2'')O-3-type complex perovskites was then correlated either with a completely disordered state (sigma = 0) or with a perfectly ordered state (sigma = 1), whereas the relaxer behavior was attributed to the nanoscale short-range ordering (0 < sigma < 1) in the configuration of the B-site cations.