$D0_{7}$ (CrO$_{3}$) Structure (Obsolete): AB3_oC16_20_a_bc-001
| Prototype | CrO$_{3}$ |
| AFLOW prototype label | AB3_oC16_20_a_bc-001 |
| Strukturbericht designation | $D0_{7}$ |
| ICSD | none |
| Pearson symbol | oC16 |
| Space group number | 20 |
| Space group symbol | $C222_1$ |
| AFLOW prototype command |
aflow --proto=AB3_oC16_20_a_bc-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This is the determination of the orthorhombic structure of CrO$_{3}$ given the $D0_{7}$ structure by (Hermann, 1937). This structure is superceded by the one found by (Byström, 1950), which we call the
orthorhombic CrO$_{3}$ phase.
The current structure has the Cr atom at the center of a distorted oxygen octahedron, while the newer structure as the Cr atom at center of a distorted tetrahedron.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (4a) | Cr I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | Cr I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
References
- H. Bräkken, Die Kristallstrukturen der Trioxyde von Chrom, Molybdän und Wolfram, Z. Kristallgr. 78, 484–488 (1931), doi:10.1524/zkri.1931.78.1.484.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturebericht Band II, 1928-1932 (Akademsiche Verlagsgesellschaft M. B. H, Leipzig, 1937).
Found in
- A. Byström and K.-A. Wilhelmi, The Crystal Structure of Chromium Trioxide, Acta Chem. Scand. 4, 1131–1141 (1950), doi:10.3891/acta.chem.scand.04-1131.
Prototype Generator
aflow --proto=AB3_oC16_20_a_bc --params=$a,b/a,c/a,x_{1},y_{2},x_{3},y_{3},z_{3}$