Howard Christopher J, Stokes Harold T
Australian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia, and School of Physics, University of Sydney, NSW 2006, Australia.
Acta Crystallogr B. 2004 Dec;60(Pt 6):674-84. doi: 10.1107/S0108768104019901. Epub 2004 Nov 11.
Group-theoretical methods are used to enumerate the structures of ordered perovskites, in which 1:2 and 1:3 ordering of B and B' cations is considered in combination with the ubiquitous BX6 (or B'X6) octahedral tilting. The cation ordering on the B-cation site is described by irreducible representations of the Pm3 m space group of the cubic aristotype: Lambda1 (k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A3BB2'X9 and M1+ (k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A4BB3'X12. The octahedral tilting is mediated by the irreducible representations M3+ and R4+. Ten distinct structures have been identified in the 1:2 case and 11 structures for 1:3.
群论方法用于枚举有序钙钛矿的结构，其中考虑了B和B'阳离子的1:2和1:3有序排列，并结合了普遍存在的BX6（或B'X6）八面体倾斜。B阳离子位点上的阳离子有序排列由立方原型Pm3 m空间群的不可约表示来描述：对于1:2化合物A3BB2'X9中的阳离子有序模式为Lambda1（k = 1/3,1/3,1/3），对于1:3化合物A4BB3'X12中的阳离子有序排列为M1+（k = 1/2,1/2,0）。八面体倾斜由不可约表示M3+和R4+介导。在1:2的情况下已确定了10种不同的结构，1:3的情况下有11种结构。
