BPS$_{4}$ Structure: ABC4_oI12_23_a_b_k-001
| Prototype | BPS$_{4}$ |
| AFLOW prototype label | ABC4_oI12_23_a_b_k-001 |
| ICSD | 24618 |
| Pearson symbol | oI12 |
| Space group number | 23 |
| Space group symbol | $I222$ |
| AFLOW prototype command |
aflow --proto=ABC4_oI12_23_a_b_k-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2b) | P I |
| $\mathbf{B_{3}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8k) | S I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8k) | S I |
| $\mathbf{B_{5}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8k) | S I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8k) | S I |
References
- A. Weiss and H. Schäfer, Zur Kenntnis von Bortetrathiophosphat BPS$_{4}$, Z. Naturforsch. B 18, 81–82 (1963), doi:10.1515/znb-1963-0117.
Prototype Generator
aflow --proto=ABC4_oI12_23_a_b_k --params=$a,b/a,c/a,x_{3},y_{3},z_{3}$