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The structure of LaAlO 3  has been investigated around the phase transition at T c  ≈ 800 K by neutron powder diffraction in vacuum and by X-ray powder diffraction under nitrogen atmosphere as well as by a very high resolution synchrotron experiment in air. The results were analysed in frame of the Landau theory using the fluctuation-dissipation theorem to relate the susceptibility to the atomic displacement parameters. The room temperature structure is a rhombohedrally distorted perovskite structure, space group R-3c , which undergoes a transition to the ideal perovskite structure, space group Pm-3m , at high temperatures. The order parameter is a rotation of the O 6 -octahedron described by one x(O)-parameter. This parameter and the spontaneous strain (c/a-√6), as well as the relevant atomic displacement parameter U op  11 (O) in the order parameter system, show a critical behaviour in agreement with a second order phase transition. Although the critical exponents of the order parameter and strain show the expected coupling behaviour, there is a striking difference of the transition temperature: the metric becomes cubic roughly 30 K below the proper T c . This is related to spontaneous formation of domains imposing the average cubic symmetry via internal stresses.

A powder diffraction study of the phase transition in LaAlO 3