AlCCr$_{2}$ Structure: ABC2_hP8_194_c_a_f-007
| Prototype | AlCCr$_{2}$ |
| AFLOW prototype label | ABC2_hP8_194_c_a_f-007 |
| ICSD | 42918 |
| CCDC | 1612531 |
| Pearson symbol | hP8 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=ABC2_hP8_194_c_a_f-007
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
Other compounds with this structure
AlCCr$_{2}$, AlCCrV, AlCNb$_{2}$, AlCNbTi, AlCNbV, AlCTa$_{2}$, AlCTaTi, AlCTi$_{2}$, AlCTiV, AlCV$_{2}$, AlCuO$_{2}$, AlNTi$_{2}$, AsCV$_{2}$, CGeV$_{2}$, CSnTi$_{2}$, CdCTi$_{2}$, CrC$_{2}$Ga, CrC$_{2}$Ge, CuCNb$_{2}$, GaCCr$_{2}$, GaCMo$_{2}$, GaCNb$_{2}$, GaCTa$_{2}$, GaCTi$_{2}$, GaCV$_{2}$, GaCY$_{2}$, GaNCr$_{2}$, GaNTi$_{2}$, GeCCr$_{2}$, GeCTi$_{2}$, GeCV$_{2}$, HfC$_{2}$In, HfC$_{2}$Pb, HfC$_{2}$Sn, HfC$_{2}$Tl, InCHf$_{2}$, InCNb$_{2}$, InCTi$_{2}$, InCZr$_{2}$, InNTi$_{2}$, InNZr$_{2}$, PCNb$_{2}$, PCV$_{2}$, PbCHf$_{2}$, PbCTi$_{2}$, PbCZr$_{2}$, SCTi$_{2}$, SCZr$_{2}$, SnCHf$_{2}$, SnCNb$_{2}$, SnCSc$_{2}$, SnCTi$_{2}$, SnCZr$_{2}$, TlCHf$_{2}$, TlCTi$_{2}$, TlCZr$_{2}$, ZnCTi$_{2}$, ZnCV$_{2}$, ZnNTi$_{2}$
- This is a MAX phase (layered M$_{n+1}$AX$_{n}$ hexagonal structure).
- Note that all of the atoms sit on close-packed $<$$0001$$>$ planes. The stacking sequence may be written
Atom Cr C Cr Al Cr C Cr Al Position B A C B C A B C
- AFLOW shifts the origin by (0 0 c/2), moving the aluminum atoms from the published (2d) Wyckoff position to the (2c) position.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | C 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) | Al 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) | Al 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) | Cr 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) | Cr 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) | Cr 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) | Cr I |
References
- W. Jeitschko, H. Nowotny, and F. Benesovsky, Kohlenstoffhaltige ternäre Verbindungen (H-Phase), Monatsh. Chem. Verw. Tl. 94, 672–676 (1963), doi:10.1007/BF00913068.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=ABC2_hP8_194_c_a_f --params=$a,c/a,z_{3}$