The software program SPuDS has been developed to predict the crystal structures of perovskites, including those distorted by tilting of the octahedra. The user inputs the composition and SPuDS calculates the optimal structure in ten different Glazer tilt systems. This is performed by distorting the structure to minimize the global instability index, while maintaining rigid octahedra. The location of the A-site cation is chosen so as to maximize the symmetry of its coordination environment. In its current form SPuDS can handle up to four different A-site cations in the same structure, but only one octahedral ion. Structures predicted by SPuDS are compared with a number of previously determined structures to illustrate the accuracy of this approach. SPuDS is also used to examine the prospects for synthesizing new compounds in tilt systems with multiple A-site coordination geometries (a + a + a +, a 0 b + b +, a 0 b − c +).

In transition metal oxides, preferential occupation of speci®c d orbitals on the transition metal ion can lead to the development of a long-range ordered pattern of occupied orbitals. This phenomenon, referred to as orbital ordering, is usually observed indirectly from the cooperative Jahn±Teller distortions (CJTDs) that result as a consequence of the orbital ordering. This paper examines the interplay between orbital ordering, octahedral tilting and cation ordering in perovskites. Both ternary AMX 3 perovskites containing an active Jahn± Teller (J±T) ion on the octahedral site and quaternary A 2 MM H X 6 perovskites containing a J±T ion on one-half of the octahedral sites have been examined. In AMX 3 perovskites, the tendency is for the occupied 3d 3x 2 Àr 2 and 3d 3z 2 Àr 2 orbitals to order in the ac plane, as exempli®ed by the crystal structures of LaMnO 3 and KCuF 3 . This arrangement maintains a favorable coordination environment for the anion sites. In AMX 3 perovskites, octahedral tilting tends to enhance the magnitude of the J±T distortions. In A 2 MM H X 6 perovskites, the tendency is for the occupied 3d 3z 2 Àr 2 orbitals to align parallel to the c axis. This pattern maintains a favorable coordination environment about the symmetric M H -cation site. The orbital ordering found in rock-salt ordered A 2 MM H X 6 perovskites is compatible with octahedral rotations about the c axis (Glazer tilt system a 0 a 0 c À ) but appears to be incompatible with GdFeO 3 -type octahedral tilting (tilt system

The preparation, modeled and refined crystal structures, and structure−dielectric property relationships of five Ba3MM‘2O9 (M = Mg, Ni, Zn; M‘ = Nb, Ta) perovskites are reported. Crystal structure modeling was used to generate initial structure models for Rietveld refinements of the neutron powder diffraction data. Bond valence sums calculated from the bond distances indicate Ba−O bonds are compressed and the M−O and M‘−O6 bonds are expanded from ideal lengths. A shift of Ta5+ and Nb5+ out of center of the [M‘O6] octahedra forms three short and three long M‘−O bonds. The octahedral distortion is driven by the asymmetry in the O bonding network and aided by the second-order Jahn−Teller distortion of the d0 Nb5+ and Ta5+ cations. Differences in the atomic coordination environments in the crystal structures were utilized to propose crystal structure−dielectric property relationships. The coordination of the divalent B-site cation (M2+) was correlated with the temperature coefficient of the resonant frequency (τf); a more under-bonded M2+ exhibited a more negative τf. Also, if the bond valences sums of the B-site cations were closer to the formal oxidations states, then a higher Q×f was observed.

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The software package SPuDS has previously been shown to accurately predict crystal structures of AMX(3) and A(1 - x)A'(x)MX(3) perovskites that have undergone octahedral tilting distortions. This paper describes the extension of this technique and its accuracy for A(2)MM'X(6) ordered double perovskites with the aristotype Fm\overline 3m cubic structure, as well as those that have undergone octahedral tilting distortions. A survey of the literature shows that roughly 70% of all ordered double perovskites undergo octahedral tilting distortions. Of the 11 distinct types of octahedral tilting that can occur in ordered perovskites, five tilt systems account for approximately 97% of the reported structures. SPuDS can calculate structures for the five dominant tilt systems, Fm\overline 3m (a(0)a(0)a(0)), I4/m (a(0)a(0)c(-)), R\overline 3 (a(-)a(-)a(-)), I2/m (a(0)b(-)b(-)) and P2(1)/n (a(-)a(-)b(+)), as well as two additional tilt systems, Pn\overline 3 (a(+)a(+)a(+)) and P4/mnc (a(0)a(0)c(+)). Comparison with reported crystal structures shows that SPuDS is quite accurate at predicting distortions driven by octahedral tilting. The favored modes of octahedral tilting in ordered double perovskites are compared and contrasted with those in AMX(3) perovskites. Unit-cell pseudosymmetry in Sr- and Ca-containing double perovskites is also examined. Experimentally, Sr(2)MM'O(6) compounds show a much stronger tendency toward pseudosymmetry than do Ca(2)MM'O(6) compounds with similar tolerance factors.