PdGa$_{5}$ Structure: A5B_tI24_140_cl_a-001
| Prototype | Ga$_{5}$Pd |
| AFLOW prototype label | A5B_tI24_140_cl_a-001 |
| ICSD | 103908 |
| Pearson symbol | tI24 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A5B_tI24_140_cl_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{3}$ |
- There is no ICSD entry for (Grin, 1997). It is a refinement of the work of (Schubert, 1959), and we list that ICSD entry.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Pd I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Pd I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (4c) | Ga I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4c) | Ga I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{6}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{7}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{11}}$ | = | $\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16l) | Ga II |
References
- Y. Grin, K. Peters, and H. G. von Schnering, Refinement of the crystal structure of palladium pentagallide, PdGa$_{5}$, Z. Kristallogr. 212, 6 (1997), doi:10.1524/zkri.1997.212.s1.6.
- K. Schubert, H. Lukas, H. Meißner, and S. Bhan, Zum Aufbau der Systeme Kobalt-Gallium, Palladium-Gallium, Palladium-Zinn und verwandter Legierungen, Z. Metallkd. 50, 534–540 (1959).
Prototype Generator
aflow --proto=A5B_tI24_140_cl_a --params=$a,c/a,x_{3},z_{3}$