LiGaGe Crystal Structure: ABC_hP6_186_b_b_a-003
| Prototype | GaGeLi |
| AFLOW prototype label | ABC_hP6_186_b_b_a-003 |
| ICSD | 25310 |
| Pearson symbol | hP6 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=ABC_hP6_186_b_b_a-003
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
BeLiSb, CaAgBi, CeAuGe, DyAuGe, DyCuGe, ErAuGe, ErCuGe, EuAuGe, GdAuGe, HoAuGe, HoCuGe, LaAgSn, LaAuGe, LaAuSn, LaCuSn, LuAuGe, NdAgSn, NdAuGe, NdAuSn, NdCuSn, PmAuGe, PrAgSn, PrAuGe, PrAuSn, PrCuSn, SmAuGe, TbAuGe, TbCuGe, TiCuSn, TmAuGe, YAuGe, YCuPb, YbAuGe
- This is the ternary form of the $C27$ (CdI$_{2}$) structure.
- The choice of the origin of the $z$-axis in space group $P6_{3}mc$ #186 is arbitrary, we use the values given by (Bockelmann, 2012).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | La I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | La I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | Ga I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Ga I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | Ge I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Ge I |
References
- W. Bockelmann and H.-U. Schuster, Ternäre Phasen im Dreistoffsystem Lithium‐Gallium‐Germanium, Z. Anorganische und Allgemeine Chemie 410, 233–240 (1974), doi:10.1002/zaac.19744100303.
Prototype Generator
aflow --proto=ABC_hP6_186_b_b_a --params=$a,c/a,z_{1},z_{2},z_{3}$