Negative thermal expansion (NTE)-the phenomenon where some materials shrink rather than expand when heated-is both intriguing and useful but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, ScF 3 , from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes-the vibrations in which the scandium coordination octahedra remain undistorted-but also on modes that distort these octahedra. Furthermore, in contrast with previous predictions, we show that the quasiharmonic approximation coupled with renormalization through anharmonic interactions describes this behavior well. Our results point the way towards a new understanding of how NTE is manifested in real materials.

We report the results of a neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide, with a focus on the system of orientational distortions of the framework of PbI6 octahedra. The results are analysed in terms of symmetry-adapted lattice strains and normal mode distortions. The higher-temperature cubic–tetragonal phase transition at 327 K is weakly discontinuous and nearly tricritical. The variations of rotation angles and spontaneous strains with temperature are consistent with a standard Landau theory treatment. The lower-temperature transition to the orthorhombic phase at 165 K is discontinuous, with two systems of octahedral rotations and internal distortions that together can be described by five order parameters of different symmetry. In this paper we quantify the various symmetry breaking distortions and their variation with temperature, together with their relationship to the spontaneous strains, within the formalism of Landau theory. A number of curious results in the low-temperature phase are identified, particularly regarding distortion amplitudes that decrease rather than increase with lowering temperature.

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We report a study of the atomic structure of the multiferroic material bismuth ferrite BiFeO 3 using neutron total scattering measurements coupled with analysis using the Reverse Monte Carlo method. We have examined average neighboring interatomic distances and local coordination environments, together with their fluctuations, for temperatures between 16 and 800 K (the sample decomposed at higher temperatures). There is little change in the average structure as a function of temperature, but the results show unusually large thermal motion at higher temperatures. No anomalous behavior is seen within this range, suggesting that the anomalies reported to occur below room temperature most likely arise due to effects associated with surfaces and interfaces.

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