High temperature neutron diffraction studies of PrInO3 and the measures of perovskite structure distortion

The crystal structure of PrInO(3) was investigated in the temperature range 303-1123 K by high-resolution neutron-powder diffraction. The PrInO(3) adopts a highly distorted variant of the perovskite structure with the orthorhombic Pnma space group in the whole temperature range investigated. The bond length and bond-angle analysis revealed a very slow tendency to decrease structural distortion with increasing temperature. Comparison of different parameters quantifying perovskite structure distortion calculated for PrInO(3) and the similar PrAlO(3) and PrGaO(3) shows the advantage of using the tolerance factor t12 calculated for the 12-fold coordinated Pr by geometrical averaging of the individual interatomic distances. An additional advantage of the tolerance factor method results from the possibility of extending it to predict the average structural distortion and the geometrical stability of the perovskites at various temperatures once the accurate dependence of t(x,T,d) on the composition, temperature and oxygen content is found. By comparing PrInO(3) with several AMO(3) perovskites containing ions in the fixed oxidation state on the A and M crystal sites it was found that structural distortion and the tolerance factor t12 for PrInO(3) are consistent with the empirical thermal expansion coefficient based on the bond strength calculation [R. M. Hazen, and C. T. Prewitt, Am. Mineral., 1977, 62(3-4), 309]. In contrast to perovskites AMO(3-d) containing mixed-valent M ions, which allow for a wide range of changes of the tolerance factor t(12)(T,d) as a function of oxygen content, perovskites AMO(3) with M ions in the fixed oxidation state show much less flexibility. This flexibility is further reduced for the A(3+)M(3+)O(3) perovskites like PrInO(3) for which even a large change of the synthesis temperature has a minor effect on controlling the resulting t(12)(T) and the structural phase in comparison with A(2+)M(4+)O3 perovskites. The only parameter left for A(3+)M(3+)O(3) materials allowing formation of various perovskites and hexagonal phases is the total pressure, which may significantly change t(12)(T,P).