ThBC Structure: ABC_tP24_91_d_d_d-001
| Prototype | BCTh |
| AFLOW prototype label | ABC_tP24_91_d_d_d-001 |
| ICSD | 2368 |
| Pearson symbol | tP24 |
| Space group number | 91 |
| Space group symbol | $P4_122$ |
| AFLOW prototype command |
aflow --proto=ABC_tP24_91_d_d_d-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This structure can also be found in the enantiomorphic space group $P4_{3}22$ #95.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{3}}$ | = | $- y_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{4}}$ | = | $y_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{5}}$ | = | $- x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{6}}$ | = | $x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{7}}$ | = | $y_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{8}}$ | = | $- y_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | B I |
| $\mathbf{B_{9}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{11}}$ | = | $- y_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{12}}$ | = | $y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{13}}$ | = | $- x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{14}}$ | = | $x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{15}}$ | = | $y_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{16}}$ | = | $- y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | C I |
| $\mathbf{B_{17}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{18}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{19}}$ | = | $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{20}}$ | = | $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{21}}$ | = | $- x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{22}}$ | = | $x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{23}}$ | = | $y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
| $\mathbf{B_{24}}$ | = | $- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8d) | Th I |
References
- P. Rogl, The Crystal Structure of ThBC, J. Nucl. Mat. 73, 198–203 (1978), doi:10.1016/0022-3115(78)90560-3.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=ABC_tP24_91_d_d_d --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$