α-V$_{3}$S Structure: AB3_tI32_121_f_g2i-001
| Prototype | SV$_{3}$ |
| AFLOW prototype label | AB3_tI32_121_f_g2i-001 |
| ICSD | 26515 |
| Pearson symbol | tI32 |
| Space group number | 121 |
| Space group symbol | $I\overline{4}2m$ |
| AFLOW prototype command |
aflow --proto=AB3_tI32_121_f_g2i-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Mo$_{3}$P, Zr$_{3}$Ir
- $\alpha$–V$_{3}$S is stable above 950°C, but metastable at 25°C, where this data was taken.
- Below 825°C the system transforms to the $\beta$–V$_{3}$S structure.
- We have shifted the origin by 1/2 c $\hat{z}$ from that used by (Pedersen, 1959).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (8f) | S I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (8f) | S I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{y}}$ | (8f) | S I |
| $\mathbf{B_{4}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{y}}$ | (8f) | S I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8g) | V I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8g) | V I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8g) | V I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8g) | V I |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8i) | V II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8i) | V II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8i) | V II |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8i) | V II |
| $\mathbf{B_{13}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{14}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8i) | V III |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8i) | V III |
References
- B. Pedersen and F. Grønvold, The Crystal Structures of α-V$_{3}$S and β-V$_{3}$S, Acta Cryst. 12, 1022–1027 (1959), doi:10.1107/S0365110X59002869.
Prototype Generator
aflow --proto=AB3_tI32_121_f_g2i --params=$a,c/a,x_{1},x_{2},x_{3},z_{3},x_{4},z_{4}$