TlCr$_{5}$Se$_{8}$ Structure: A5B8C_mC28_12_a2i_4i_c-001
| Prototype | Cr$_{5}$Se$_{8}$Tl |
| AFLOW prototype label | A5B8C_mC28_12_a2i_4i_c-001 |
| ICSD | 78157 |
| Pearson symbol | mC28 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A5B8C_mC28_12_a2i_4i_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}$ |
Other compounds with this structure
Tl(V$_{1-x}$Cr$_{x}$)$_{5}$Se$_{8}$, CsCr$_{5}$S$_{8}$
- The chromium atoms may be replaced with arbitrary amounts of vanadium. We used the data for the stoichiometric compound.
- The data for CsCr$_{5}$S$_{8}$ was taken much earlier, and so it could be used as the prototype, but the data for TlCr$_{5}$Se$_{8}$ is more accessible.
- There is no ICSD or CCDC entry for (Maier, 2015), so we link to the earlier work of (Bensch, 1994).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2c) | Tl I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Cr II |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Cr II |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Cr III |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Cr III |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se I |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se I |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se II |
| $\mathbf{B_{10}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se II |
| $\mathbf{B_{11}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se III |
| $\mathbf{B_{12}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se III |
| $\mathbf{B_{13}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se IV |
| $\mathbf{B_{14}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Se IV |
References
- S. Maier, R. Lefèvre, X. Lin, R. Nunna, D. Berthebaud, S. Hèbert, A. Marb, and F. Gascoin, The solid solution series Tl(V$_{1-x}$Cr$_{x}$)$_{5}$Se$_{8}$: crystal structure, magnetic and thermoelectric properties, J. Mater. Chem. C 3, 10509–10517 (2015), doi:10.1039/c5tc01766a.
- W. Bensch, E. Wörner, M. Muhler, and U. Ruschewitz, Single Crystal Structure, Magnetic Properties, and Electronic Structure of Tl$_{x}$Cr$_{5}$S$_{8}$ (x = 1.0 and 0.7), J. Solid State Chem. 110, 234–242 (1994), doi:10.1006/jssc.1994.1164.
Prototype Generator
aflow --proto=A5B8C_mC28_12_a2i_4i_c --params=$a,b/a,c/a,\beta,x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8}$