Editing Zirconium tungstate (section)

==Cubic phase==
[[Cubic (crystal system)|Cubic]] zirconium tungstate (alpha-ZrW<sub>2</sub>O<sub>8</sub>), one of the several known [[phase (matter)|phases]] of zirconium tungstate (ZrW<sub>2</sub>O<sub>8</sub>) is perhaps one of the most studied materials to exhibit [[negative thermal expansion]]. It has been shown to contract continuously over a previously unprecedented [[temperature]] range of 0.3 to 1050 K (at higher temperatures the material decomposes). Since the structure is cubic, as described below, the thermal contraction is isotropic - equal in all directions. There is much ongoing research attempting to elucidate why the material exhibits such dramatic negative thermal expansion.{{cn|date=September 2023}}

This phase is [[thermodynamics|thermodynamically]] [[unstable]] at [[room temperature]] with respect to the binary [[oxides]] [[zirconia|ZrO<sub>2</sub>]] and [[tungsten oxide|WO<sub>3</sub>]], but may be [[Chemical synthesis|synthesised]] by heating [[stoichiometric]] quantities of these oxides together and then quenching the material by rapidly cooling it from approximately 900&nbsp;°C to room temperature.

The structure of cubic zirconium tungstate consists of corner-sharing ZrO<sub>6</sub> [[octahedral]] and WO<sub>4</sub> [[tetrahedral]] structural units. Its unusual expansion properties are thought to be due to vibrational modes known as [[Rigid Unit Modes]] (RUMs), which involve the coupled rotation of the polyhedral units that make up the structure, and lead to contraction.

===Detailed crystal structure===
[[Image:ZrW2O8 W2O8 diagonal.JPG|thumb|left|304x304px|An image of the crystal structure of cubic ZrW<sub>2</sub>O<sub>8</sub>, showing the corner-sharing octahedral (ZrO<sub>6</sub>, in green) and tetrahedral (WO<sub>4</sub>, in red) structural units. An incomplete unit cell is shown so that the positioning of the W<sub>2</sub>O<sub>8</sub> unit along the body diagonal of the unit cell may be seen.]]

The arrangement of the groups in the structure of cubic ZrW<sub>2</sub>O<sub>8</sub> is analogous to the simple [[NaCl structure]], with ZrO<sub>6</sub> octahedra at the Na sites, and W<sub>2</sub>O<sub>8</sub> 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 [[Angstrom]]s.

The ZrO<sub>6</sub> [[octahedra]] are only slightly distorted from a regular conformation, and all oxygen sites in a given octahedron are related by symmetry. The W<sub>2</sub>O<sub>8</sub> unit is made up of two crystallographically distinct WO<sub>4</sub> tetrahedra, which are not formally [[chemical bond|bonded]] to each other. These two types of tetrahedra differ with respect to the W-O bond lengths and angles. The WO<sub>4</sub> 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 ''P2<sub>1</sub>3'' [[Space group|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<math>\bar3</math>''.

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.