Detailed Crystal Structure
The arrangement of the groups in the structure of cubic ZrW2O8 is analogous to the simple NaCl structure, with ZrO6 octahedra at the Na sites, and W2O8 groups at the Cl sites. The unit cell consists of 44 atoms aligned in a primitive cubic Bravais lattice, with unit cell length 9.15462 Angstroms.
The ZrO6 octahedra are only slightly distorted from a regular conformation, and all oxygen sites in a given octahedron are related by symmetry. The W2O8 unit is made up of two crystallographically distinct WO4 tetrahedra, which are not formally bonded to each other. These two types of tetrahedra differ with respect to the W-O bond lengths and angles. The WO4 tetrahedra are distorted from a regular shape since one oxygen is unconstrained (an atom that is bonded only to the central tungsten (W) atom), and the three other oxygens are each bonded to a zirconium atom (i.e. the corner-sharing of polyhedra).
The structure has P213 space group symmetry at low temperatures. At higher temperatures, a centre of inversion is introduced by the disordering of the orientation of tungstate groups, and the space group above the phase transition temperature (~180C) is Pa.
Octahedra and tetrahedra are linked together by sharing an oxygen atom. In the image, note the corner-touching between octahedra and tetrahedra; these are the location of the shared oxygen. The vertices of the tetrahedra and octahedra represent the oxygen, which are spread about the central zirconium and tungsten. Geometrically, the two shapes can "pivot" around these corner-sharing oxygens, without a distortion of the polyhedra themselves. This pivoting is what is thought to lead to the negative thermal expansion, as in certain low frequency normal modes this leads to the contracting 'RUMs' mentioned above.
Read more about this topic: Zirconium Tungstate, Cubic Phase
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