INTERRELATIONSHIP OF OCTAHEDRAL GEOMETRY, POLYHEDRAL VOLUME RATIO AND FERROELECTRIC PROPERTIES IN RHOMBOHEDRAL PEROVSKITES

A unifying, quantitative analytical framework has been developed for rhombohedral perovskite structures, ABO(3). Three principal parameters are defined: polyhedral volume ratio, V-A/V-B, mean octahedral tilt angle, <omega>, and octahedral distortion, Delta s. The first two of these parameters are directly related through the equation V-A/V-B = 6K cos(2)<omega> - 1, with K practically invariant between all crystal structures. The four permutations of zero or non-zero <omega> with zero or non-zero Delta s are related to the four space groups in which rhombohedral perovskites crystallize, R3m, R3c, R(3) over barm$ and R(3) over barc$. The most general space group is R3c, which can accommodate non-zero values of both <omega> and Delta s. The structural driving force for non-zero Delta s values (i.e. octahedral distortion) is examined by the bond-valence method, with the rationalization that octahedral distortions provide a mechanism for B-ion displacements which are parallel to one another and to the hexagonal z axis. Calculations of electrostatic energy further reveal the extra stabilization to be obtained by the adoption of electric dipole moments and parallel A- and B-ion displacements. It is these displacements which give rise to the ferroelectric properties of rhombohedral perovskites. The analysis is applied to the PZT system (PbZrO3-PbTiO3) and to the PbZrO3-BaZrO3 and PbZrO3-SrZrO3 systems. The influence of chemical composition on the relative stabilities of competing rhombohedral, orthorhombic and tetragonal phases is discussed, as is the physical basis of the morphotropic phase boundary in PZT. A method is also defined of predicting the temperatures at which the rhombohedral low-temperature phase in PZT transforms to the rhombohedral high-temperature phase, for a range of compositions.