Crystal structure and thermal expansion of the low- and high-temperature forms of BaMIV(PO4)2 compounds (M=Ti, Zr, Hf and Sn)

The crystal structure of β -BaZr(PO4)2, archetype of the high-temperature forms of BaM (PO4)2 phosphates (with M =Ti, Zr, Hf and Sn), has been solved ab initio by Rietveld analysis from synchrotron X-ray powder diffraction data. The phase transition appears as a topotactic modification of the monoclinic (S.G. C2/mC2/m) lamellar α -structure into a trigonal one (S.G. View the MathML sourceP3¯m1) through a simple mechanism involving the unfolding of the View the MathML source[Zr(PO4)2]n2- layers. The thermal expansion is very anisotropic (e.g., −4.1<αi<34.0×10−6 K−1 in the case of α-BaZr(PO4)2) and quite different in the two forms, as a consequence of symmetry. It stems from a complex combination of several mechanisms, involving bridging oxygen rocking in M–O–P linkages, and “bond thermal expansion”.