LiGaGe Crystal Structure: ABC_hP6_186_b_b_a-003
| Prototype | GaGeLi |
| AFLOW prototype label | ABC_hP6_186_b_b_a-003 |
| ICSD | 25310 |
| CCDC | 1601055 |
| 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
CaAgBi, CaAuBi, CaAuSb, CaHgSn, CaSnZn, CeAgGe, CeAgPb, CeAgSn, CeAuGe, CeAuSn, CeCuSn, DyAgPb, DyAgSn, DyAuGe, DyAuSn, DyCuGe, DyCuPb, DyCuSn, DyPbSb, ErAgSn, ErAuGe, ErCuGe, ErCuPb, ErGaZn, EuAuGe, EuCdPb, EuCdSn, EuHgPb, EuHgSn, GdAgPb, GdAgSn, GdAuGe, GdAuSn, GdCuGe, GdCuPb, GdCuSn, GdPbSb, HfCuSn, HoAgPb, HoAgSn, HoAuGe, HoAuSn, HoCuGe, HoCuPb, LaAgGe, LaAgPb, LaAgSn, LaAuGe, LaAuSn, LaCuSn, LiBiSb, LiBiZn, LiSbZn, LuAgSn, LuAuGe, LuCuPb, LuCuSn, NdAgPb, NdAgSn, NdAsPd, NdAuGe, NdAuSn, NdCuSn, NdPbSb, NdPtSb, PmAuGe, PrAgPb, PrAgSn, PrAuGe, PrAuSn, PrCuSn, PrPdSb, PrPtSb, ScAuGe, ScCuPb, ScCuSn, SmAgPb, SmAsPd, SmAuGe, SmAuSn, SmCuPb, SmCuSn, SrHgPb, SrHgSn, TbAgPb, TbAgSn, TbAuGe, TbAuSn, TbCuGe, TbCuPb, TiCuSn, TmAuGe, TmCuPb, UAuSn, UPdSn, YAgSn, YAuGe, YAuSi, YAuSn, YCuPb, YCuSb, YCuSn, YbAgBi, YbAuBi, YbAuGe, YbAuSb, YbBiCu, YbCuGe, YbHgSn, YbPbZn, YbSnZn
- 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).
- We have attempted to list the
other compounds
so that the (2a) atom is first, but do not guarantee that we are always correct.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
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) | Li 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) | Li 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.
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=ABC_hP6_186_b_b_a --params=$a,c/a,z_{1},z_{2},z_{3}$