Correlated atomic motions in the negative thermal expansion materialZrW2O8:A local structure study

Recent studies of zirconium tungstate, ${\mathrm{ZrW}}_{2}{\mathrm{O}}_{8},$ show an isotropic negative thermal expansion (NTE) over a wide temperature range. It has been proposed that the low-energy phonon vibrational modes, observed in both specific heat and phonon density-of-states measurements, are responsible for this unusual NTE. We have carried out x-ray-absorption fine-structure (XAFS) experiments at both the W ${L}_{\mathrm{III}}$ edge and Zr K edge to study the detailed local structure in ${\mathrm{ZrW}}_{2}{\mathrm{O}}_{8}.$ Our XAFS results show a very small temperature dependence of the broadening parameter, $\ensuremath{\sigma},$ for the W-Zr atom pair and the W-O-Zr linkage; consequently, the displacements of the W, O, and Zr atoms must be correlated. The data show a much larger temperature dependence of $\ensuremath{\sigma}$ for the nearest ${\mathrm{W}}_{1}\ensuremath{-}{\mathrm{W}}_{2}$ pair as well as for the nearest Zr-Zr pair. These combined results indicate that it is the correlated motion of a ${\mathrm{WO}}_{4}$ tetrahedron and its three nearest ${\mathrm{ZrO}}_{6}$ octahedra that leads to the NTE effect in this material instead of primarily transverse vibrations of the middle O atom in the W-O-Zr linkage. The data for both W-W and Zr-Zr atom pairs also indicate a hardening of the effective spring constant near 100 K, which is consistent with the shift of the lowest mode with T in the phonon density of states. A simple model is developed to explain the NTE in terms of the local structure results; it also provides a natural explanation for the lack of a soft-mode phase transition.