δ-GaSe Structure: AB_hP16_186_2a2b_2a2b-001
| Prototype | GaSe |
| AFLOW prototype label | AB_hP16_186_2a2b_2a2b-001 |
| ICSD | 2002 |
| Pearson symbol | hP16 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=AB_hP16_186_2a2b_2a2b-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}$ |
- GaSe takes on a variety of structures depending on the stacking of the Ga$_{2}$Se$_{2}$ layers:
- $\beta$–GaSe is in space group $P6_3/mmc$ #194.
- $\gamma$–GaSe is in space group $R3m$ #160.
- $\delta$–GaSe (this structure) is in space group $P6_{3}mc$ #186.
- $\epsilon$–GaSe is in space group $P\overline{6}m2$ #187.
- The origin of the $z$ coordinates is arbitrary in space group $P6_{3}mc$ #186.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
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) | Ga 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) | Ga I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Ga II |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Ga II |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2a) | Se I |
| $\mathbf{B_{6}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Se I |
| $\mathbf{B_{7}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (2a) | Se II |
| $\mathbf{B_{8}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Se II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2b) | Ga III |
| $\mathbf{B_{10}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Ga III |
| $\mathbf{B_{11}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2b) | Ga IV |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Ga IV |
| $\mathbf{B_{13}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (2b) | Se III |
| $\mathbf{B_{14}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Se III |
| $\mathbf{B_{15}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (2b) | Se IV |
| $\mathbf{B_{16}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Se IV |
References
- A. Kuhn, A. Chevy, and R. Chevalier, Crystal Structure and Interatomic Distances in GaSe, phys. stat. sol. (a) 31, 469–475 (1975), doi:10.1002/pssa.2210310216.
- K. Schubert, E. Dörre, and M. Kluge, Zur Kristallchemie der B-Metalle. III. Kristallstruktur von GaSe und InTe, Z. Metallkd. 46, 216–224 (1955), doi:10.1515/ijmr-1955-460312.
Prototype Generator
aflow --proto=AB_hP16_186_2a2b_2a2b --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8}$