Pb()O3-type Perovskites: Part I. Pair-correlation Theory of Order-disorder Phase Transition

The limitation of the long-range order parameter and the necessity of the short-range order parameter for the thermodynamic description of Pb()O3-type perovskites are discussed. Based on the discussion, a statistical thermodynamic model that takes into account the configuration of the neighboring B-site ions (B′ and B″ cations) was developed. A pair-correlation approximation was used in the calculation of the configurational entropy and the long-range coulombic interaction energy between the nearest B-site ions. The theoretical calculations using Pb(Sc1/2Ta1/2)O3 (PST) and Pb(Sc1/2Nb1/2)O3 (PSN) systems indicate that the short-range order parameter persists over a wide range of temperatures examined (0–1800 K) and that there possibly occur consecutive long-range order-disorder transitions in the configuration of B-site cations. The possibility of the existence of short-range ordering above the long-range order-disorder transition temperature was also examined using the annealed PSN specimen as a typical example of Pb()O3-type perovskites.

Pb()O3-type Perovskites: Part II. Short-range Order Parameter as a Criterion of the Distinction Between Relaxor and Normal Ferroelectrics

A classification scheme of Pb()O3-type perovskites with respect to the B-site order parameters was proposed based on the theoretical calculation of the short-range order parameter (σ) using the pair-correlation model. The calculated order parameters predict that a Pb()O3-type perovskite without any charge difference between B′ and B″ cations [e.g., Pb(Zr1/2Ti1/2)O3 (PZT)] is represented by a completely disordered state with the absence of a finite coherence length. On the other hand, a Pb()O3-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()O3-type complex perovskites was then correlated either with a completely disordered state (σ = 0) or with a perfectly ordered state (σ = 0), whereas the relaxor behavior was attributed to the nanoscale short-range ordering (0 < σ < 1) in the configuration of the B-site cations.

Surface Ordering of MBE Grown 001 Ga1−xAlxAs- A Theoretical Study

ABSTRACTThe kinetics of MBE growth of Ga1-x.,Alx,As is studied theoretically using the stochastic model of MBE growth based on the master equation approach and the random distribution approximation. The surface ordering phenomenon during the 001 growth of Ga0.5Al0.5 As is investigated as a function of the growth conditions. The atom pair interaction energy parameters for various surface configurations were obtained from the first principle calculations. The other model parameters needed in the description of the kinetic processes are obtained from the available experimental data. The ordering kinetics is studied as a function of fluxes, flux ratio and growth temperature. The degree of ordering is estimated in terms of the short range order parameter. The short range order parameter increases with temperature till 650°K and 750°K for cation to anion flux ratios 2 : 1 and 1 : 5, respectively. Beyond this critical temperature, the short range order parameter decreases. This critical temperature is identified as the kinetic order-disorder temperature. The order-disorder phenomenon observed in this theoretical study is explained in terms of the dependence of the surface migration rate of the cations on the growth temperature. The dependence on the order-disorder temperature on the flux ratio is attributed to decreased surface migration for larger flux ratios.