VS$_{4}$ Structure: A4B_mC40_15_4f_f-001
| Prototype | S$_{4}$V |
| AFLOW prototype label | A4B_mC40_15_4f_f-001 |
| ICSD | 16797 |
| Pearson symbol | mC40 |
| Space group number | 15 |
| Space group symbol | $C2/c$ |
| AFLOW prototype command |
aflow --proto=A4B_mC40_15_4f_f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
- We use the coordinates from (Allmann, 1964) as corrected by (Downs, 2003).
- (Allmann, 1964) give the structure of VS$_{4}$ in the $I2/c$ setting of space group #15. We used FINDSYM to translate this to the standard $C2/c$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c \left(z_{1} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c \left(z_{1} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S I |
| $\mathbf{B_{5}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c \left(z_{2} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S II |
| $\mathbf{B_{7}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S II |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c \left(z_{2} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S II |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S III |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c \left(z_{3} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S III |
| $\mathbf{B_{11}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S III |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c \left(z_{3} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S III |
| $\mathbf{B_{13}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S IV |
| $\mathbf{B_{14}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c \left(z_{4} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S IV |
| $\mathbf{B_{15}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S IV |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c \left(z_{4} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | S IV |
| $\mathbf{B_{17}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | V I |
| $\mathbf{B_{18}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c \left(z_{5} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | V I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | V I |
| $\mathbf{B_{20}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | V I |
References
- R. Allmann, I. Baumann, A. Kutoglu, H. Rösch, and E. Hellner, Die Kristallstruktur des Patronits V(S$_{2}$)$_{2}$, Naturwissenschaften 51, 263–264 (1964), doi:10.1007/BF00638454.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A4B_mC40_15_4f_f --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$