Au$_{31}$Mn$_{9}$ Structure: A31B9_tP40_83_ae3j4k_cjk-001
| Prototype | Au$_{31}$Mn$_{9}$ |
| AFLOW prototype label | A31B9_tP40_83_ae3j4k_cjk-001 |
| ICSD | 58552 |
| Pearson symbol | tP40 |
| Space group number | 83 |
| Space group symbol | $P4/m$ |
| AFLOW prototype command |
aflow --proto=A31B9_tP40_83_ae3j4k_cjk-001
--params=$a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak x_{12}, \allowbreak y_{12}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Au I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (1c) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (2e) | Au II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2e) | Au II |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}$ | (4j) | Au III |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}$ | (4j) | Au III |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (4j) | Au III |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (4j) | Au III |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (4j) | Au IV |
| $\mathbf{B_{10}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (4j) | Au IV |
| $\mathbf{B_{11}}$ | = | $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (4j) | Au IV |
| $\mathbf{B_{12}}$ | = | $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}$ | (4j) | Au IV |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}$ | (4j) | Au V |
| $\mathbf{B_{14}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}$ | (4j) | Au V |
| $\mathbf{B_{15}}$ | = | $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}$ | (4j) | Au V |
| $\mathbf{B_{16}}$ | = | $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}$ | (4j) | Au V |
| $\mathbf{B_{17}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}$ | (4j) | Mn II |
| $\mathbf{B_{18}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}$ | (4j) | Mn II |
| $\mathbf{B_{19}}$ | = | $- y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}$ | (4j) | Mn II |
| $\mathbf{B_{20}}$ | = | $y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}$ | (4j) | Mn II |
| $\mathbf{B_{21}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VI |
| $\mathbf{B_{22}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VI |
| $\mathbf{B_{23}}$ | = | $- y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VI |
| $\mathbf{B_{24}}$ | = | $y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VI |
| $\mathbf{B_{25}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VII |
| $\mathbf{B_{26}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VII |
| $\mathbf{B_{27}}$ | = | $- y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VII |
| $\mathbf{B_{28}}$ | = | $y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VII |
| $\mathbf{B_{29}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VIII |
| $\mathbf{B_{30}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VIII |
| $\mathbf{B_{31}}$ | = | $- y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VIII |
| $\mathbf{B_{32}}$ | = | $y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au VIII |
| $\mathbf{B_{33}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au IX |
| $\mathbf{B_{34}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au IX |
| $\mathbf{B_{35}}$ | = | $- y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au IX |
| $\mathbf{B_{36}}$ | = | $y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Au IX |
| $\mathbf{B_{37}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Mn III |
| $\mathbf{B_{38}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Mn III |
| $\mathbf{B_{39}}$ | = | $- y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Mn III |
| $\mathbf{B_{40}}$ | = | $y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Mn III |
References
- K. Hiraga, D. Shindo, M. Hirabayashi, O. Terasaki, and D. Watanabe, A study of the ordered structures of the Au-Mn system by high-voltage-high-resolution electron microscopy. I. Two-dimensional antiphase structure of Au$_{31}$Mn$_{9}$ based on the Au$_{4}$Mn structure, Acta Crystallogr. Sect. B 36, 2550–2554 (1980), doi:10.1107/S0567740880009417.
Found in
- URL: http://icsd.fiz-karlsruhe.de/. ICSD Entry 150552.
Prototype Generator
aflow --proto=A31B9_tP40_83_ae3j4k_cjk --params=$a,c/a,x_{4},y_{4},x_{5},y_{5},x_{6},y_{6},x_{7},y_{7},x_{8},y_{8},x_{9},y_{9},x_{10},y_{10},x_{11},y_{11},x_{12},y_{12}$