Rhadophane (CePO$_{4}$) Structure: AB4C_hP18_180_c_k_d-001
| Prototype | CeO$_{4}$P |
| AFLOW prototype label | AB4C_hP18_180_c_k_d-001 |
| Mineral name | rhadophane |
| ICSD | 31563 |
| Pearson symbol | hP18 |
| Space group number | 180 |
| Space group symbol | $P6_222$ |
| AFLOW prototype command |
aflow --proto=AB4C_hP18_180_c_k_d-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
LaPO$_{4}$, NdPO$_{4}$
- This structure can also be found in the enantiomorphic space group $P6_{4}22$ #181.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}$ | (3c) | Ce I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{2}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{2}{3}c \,\mathbf{\hat{z}}$ | (3c) | Ce I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3c) | Ce I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3d) | P I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | P I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{5}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{5}{6}c \,\mathbf{\hat{z}}$ | (3d) | P I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{8}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{3} + 2\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{11}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{3} + 2 y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{3} + 2\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{13}}$ | = | $y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{3} - 2\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{16}}$ | = | $- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{3} - 2\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{3} + 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (12k) | O I |
| $\mathbf{B_{18}}$ | = | $x_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12k) | O I |
References
- R. C. L. Mooney, X-ray diffraction study of cerous phosphate and related crystals. I. Hexagonal modification, Acta Cryst. 3, 337–340 (1950), doi:10.1107/S0365110X50000963.
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=AB4C_hP18_180_c_k_d --params=$a,c/a,x_{3},y_{3},z_{3}$