$D0_{10}$ (WO$_{3}$) Structure (Obsolete): A3B_oP16_57_a2d_d-001
| Prototype | O$_{3}$W |
| AFLOW prototype label | A3B_oP16_57_a2d_d-001 |
| Strukturbericht designation | $D0_{10}$ |
| ICSD | none |
| Pearson symbol | oP16 |
| Space group number | 57 |
| Space group symbol | $Pbcm$ |
| AFLOW prototype command |
aflow --proto=A3B_oP16_57_a2d_d-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
- All stable phases of WO$_{3}$ are distortions of the cubic $\alpha$–ReO$_{3}$ ($D0_{9}$) phase. Based on (Woodward, 1997 and Vogt, 1999), the known stable phases and their approximate temperature ranges are:
- Woodward notes that
The transition temperatures display large hysteresis effects and universal agreement is not found in the literature.
- In addition, several other structures have been proposed and/or found:
- The original $D0_{10}$ structure (Bräkken, 1931), (Hermann, 1937) (this structure), superseded by $\delta$–WO$_{3}$
- The original $\beta$–WO$_{3}$ (Salje, 1977)
- Hexagonal WO$_{3}$, presumably metastable, found by (Gerand, 1979) while dehydrating WO$_{3}$·H$_{2}$O
- (Bräkken, 1931) found a triclinic unit cell for WO$_{3}$ (this structure). As it was nearly orthorhombic, (Hermann, 1937) approximated it with the structure shown here and gave it the Strukturbericht symbol $D0_{10}$. Later (Diehl, 1978) showed that the near-room-temperature phase of WO$_{3}$ was indeed a triclinic crystal, but the unit cell was double that of Bräkken and is in fact a pseudo-cubic distorted perovskite.
- We retain this original structure for its historical interest.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4a) | O I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{8}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{12}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | W I |
| $\mathbf{B_{14}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | W I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | W I |
| $\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | W I |
References
- P. M. Woodward, A. W. Sleight, and T. Vogt, Ferroelectric Tungsten Trioxide, J. Solid State Chem. 131, 9–17 (1997), doi:10.1006/jssc.1997.7268.
- T. Vogt, P. M. Woodward, and B. A. Hunter, The High-Temperature Phases of WO$_{3}$, J. Solid State Chem. 144, 209–215 (1999), doi:10.1006/jssc.1999.8173.
- R. Diehl, G. Brandt, and E. Salje, The Crystal Structure of Triclinic WO$_{3}$, Acta Crystallogr. Sect. B 34, 1105–1111 (1978), doi:10.1107/S0567740878005014.
- H. Bräkken, Die Kristallstrukturen der Trioxyde von Chrom, Molybdän und Wolfram, Z. Kristallogr. 78, 484–488 (1931), doi:10.1524/zkri.1931.78.1.484.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- E. Salje, The Orthorhombic Phase of WO$_{3}$, Acta Crystallogr. Sect. B 33, 574–577 (1977), doi:10.1107/S0567740877004130.
- B. Gerand, G. Nowogrocki, J. Guenot, and M. Figlarz, Structural study of a new hexagonal form of tungsten trioxide, J. Solid State Chem. 29, 429–434 (1979), doi:10.1016/0022-4596(79)90199-3.
Prototype Generator
aflow --proto=A3B_oP16_57_a2d_d --params=$a,b/a,c/a,x_{2},y_{2},x_{3},y_{3},x_{4},y_{4}$