α'-V$_{8}$O Structure: AB8_tP18_136_a_2fi-001
| Prototype | OV$_{8}$ |
| AFLOW prototype label | AB8_tP18_136_a_2fi-001 |
| ICSD | 166600 |
| Pearson symbol | tP18 |
| Space group number | 136 |
| Space group symbol | $P4_2/mnm$ |
| AFLOW prototype command |
aflow --proto=AB8_tP18_136_a_2fi-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
- (Villars, 2018) calls this $\beta$–V$_{8}$O, and refers to it as the room-temperature tetragonal structure. They also refer to a room-temperature triclinic structure.
- This is a supercell of the body-centered cubic ($A2$) lattice, with periodic interstitial oxygen atoms at the octahedral sites. In the real structure it is likely that there is considerable relaxation around the oxygen atoms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (4f) | V I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (4f) | V I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | V I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | V I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (4f) | V II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (4f) | V II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | V II |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | V II |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}$ | (8i) | V III |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}$ | (8i) | V III |
| $\mathbf{B_{13}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{14}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{17}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8i) | V III |
| $\mathbf{B_{18}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8i) | V III |
References
- L. N. Galkin, V. V. Vavilova, I. I. Kornilov, and L. E. Fykin, Investigation of the structure of ordered $\alpha'$-suboxide (V$_{8}$O) by the method of neutron diffraction, Dokl. Akad. Nauk SSSR 228, 1105–1108 (1976).
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Oxygen-Vanadium Binary Phase Diagram (1990 Wriedt H.A.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=AB8_tP18_136_a_2fi --params=$a,c/a,x_{2},x_{3},x_{4},y_{4}$