Hexagonal Delafossite (CuFeO$_{2}$) Structure: ABC2_hP8_194_a_c_f-005
| Prototype | CuFeO$_{2}$ |
| AFLOW prototype label | ABC2_hP8_194_a_c_f-005 |
| Mineral name | delafossite |
| ICSD | 60845 |
| Pearson symbol | hP8 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=ABC2_hP8_194_a_c_f-005
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
Other compounds with this structure
AlCCr$_{2}$, AlCNb$_{2}$, AlCTa$_{2}$, AlCTi$_{2}$, AlCV$_{2}$, AsCNb$_{2}$, AsCV$_{2}$, AlCuO$_{2}$, BBiHf$_{2}$, BPbHf$_{2}$, CdCTi$_{2}$, CuAlO$_{2}$, CuGaO$_{2}$, CuScO$_{2}$, CuYO$_{2}$, GaCCr$_{2}$, GaCMo$_{2}$, GaCNb$_{2}$, GaCTa$_{2}$, GaCTi$_{2}$, GaCV$_{2}$, GaNTi$_{2}$, GeCCr$_{2}$, GeCTi$_{2}$, GeCV$_{2}$, InCHf$_{2}$, InCNb$_{2}$, InCTi$_{2}$, InCZr$_{2}$, InNTi$_{2}$, InNZr$_{2}$, PbCHf$_{2}$, PbCTi$_{2}$, PbCZr$_{2}$, SCNb$_{2}$, SCTi$_{2}$, SCZr$_{2}$, SCZr$_{2}$, SeCZr$_{2}$, SnCHf$_{2}$, SnCNb$_{2}$, SnCZr$_{2}$, TlCHf$_{2}$, TlCTi$_{2}$, TlCZr$_{2}$
- Delafossite appears in two forms which differ in the stacking of the layers: rhombohedral, prototype CuFeO$_{2}$, and hexagonal, shown here. Most of the structures found in the hexagonal phase can also be found in the rhombohedral structure (Marquardt, 2006).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Cu I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Cu I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O I |
References
- B. U. Köhler and M. Jansen, Darstellung und Strukturdaten von ,,Delafossiten︁ CuMO$_{2}$ (M = Al, Ga, Sc, Y), Z. Anorganische und Allgemeine Chemie 543, 73–80 (1986), doi:10.1002/zaac.19865431209.
Found in
- M. A. Marquardt, N. A. Ashmore, and D. P. Cann, Crystal chemistry and electrical properties of the delafossite structure, Thin Solid Films 496, 146–156 (2006), doi:10.1016/j.tsf.2005.08.316.
Prototype Generator
aflow --proto=ABC2_hP8_194_a_c_f --params=$a,c/a,z_{3}$