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High‐resolution neutron powder diffraction has been used to investigate the structures and phase transitions in the double perovskites Ba2Bi3+Bi5+O6 (dibarium dibismuth hexaoxide) and Ba2BiSbO6 (dibarium bismuth antimony hexaoxide) in the temperature ranges 4.2–973 and 4.2–625 K, respectively. The charge‐ordered bismuthate adopts four structures in the temperature range – monoclinic in P21/n, monoclinic in I2/m, rhombohedral in , and finally cubic in . The low‐temperature monoclinic structure has been determined for the first time. The transitions from P21/n to I2/m, at 132 K, and to , at 820 K, are tricritical in nature; the transition from I2/m to at ca 430 K is discontinuous. The behaviour of Ba2BiSbO6 is very similar, except that the transition temperatures are lower – 250 K for I2/m to and 515 K for to – and the low‐temperature structure is not formed at all. The to transition in this compound is closer to second order in nature, although there is evidence for some contribution from higher‐order terms.