Frustrated Soft Modes and Negative Thermal Expansion in ZrW sub 2 O sub 8

Negative Thermal Expansion in cubic Zr W sub 2 O sub 8 has generated much interest due to its large and istropic behavior. Previous work showed that NTE in ZrW sub 2 O sub 8 is constant over a large temperature range and driven by a set of modes of anomalously low energy. Here we use X-ray Absorption Fine Structure (XFAS) to elucidate the underlying wavefunction of these modes. The data analysis for various atom pairs provides evidence that the low-energy modes causing NTE correspond to the correlated vibrations of a WO sub 4 tetrahedron and its three nearest ZrO sub 6 octahedra - this involves translations of the WO sub 4 as a rigid unit along each of the four equivalent 111> axes. It is shown that the interconnectivity of these motions prevents an anisotropic soft mode from developing, a new geometrical phenomenon that we call the "frustrated soft mode."