Trigonal Au$_{7}$P$_{10}$I Structure: A7BC10_hP18_162_ceg_a_hk-001
| Prototype | Au$_{7}$IP$_{10}$ |
| AFLOW prototype label | A7BC10_hP18_162_ceg_a_hk-001 |
| ICSD | 8059 |
| Pearson symbol | hP18 |
| Space group number | 162 |
| Space group symbol | $P\overline{3}1m$ |
| AFLOW prototype command |
aflow --proto=A7BC10_hP18_162_ceg_a_hk-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
- There is some controversy about the structure of Au$_{7}$P$_{10}$I. (Binnewies, 1978) put it in the hexagonal $P\overline{6}2m$ #189 space group, but (Jeitschko, 1979) place it in the trigonal $P\overline{3}1m$ #162 space group. The structures are distinct, and to our knowledge the dispute has not been resolved, so we present both structures.
- We have shifted the origin, moving the iodine atoms from the (1b) to (1a) Wyckoff positions.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | I I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Au I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Au I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Au II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Au II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Au III |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Au III |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Au III |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4h) | P I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4h) | P I |
| $\mathbf{B_{11}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4h) | P I |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4h) | P I |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
| $\mathbf{B_{15}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
| $\mathbf{B_{16}}$ | = | $- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
| $\mathbf{B_{17}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
| $\mathbf{B_{18}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (6k) | P II |
References
- W. Jeitschko and M. H. Möller, The crystal structures of Au$_{2}$P$_{3}$ and Au$_{7}$P$_{10}$I, polyphosphides with weak Au-Au interactions, Acta Crystallogr. Sect. B 35, 573–579 (1979), doi:10.1107/S0567740879004180.
- M. Binnewies, Darstellung, Kristallstruktur und Eigenschaften von Au$_{7}$P$_{10}$I, Z. Naturforsch. B 33, 570–571 (1978), doi:10.1515/znb-1978-0521.
Prototype Generator
aflow --proto=A7BC10_hP18_162_ceg_a_hk --params=$a,c/a,z_{3},z_{5},x_{6},z_{6}$