Khatyrkite (Al$_{2}$Cu, $C16$) Structure: A2B_tI12_140_h_a-001
| Prototype | Al$_{2}$Cu |
| AFLOW prototype label | A2B_tI12_140_h_a-001 |
| Strukturbericht designation | $C16$ |
| Mineral name | khatyrkite |
| ICSD | 198177 |
| Pearson symbol | tI12 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A2B_tI12_140_h_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}$ |
Other compounds with this structure
Co$_{2}$B, Cr$_{2}$B, Fe$_{2}$B, Fe$_{2}$Bi, Ge$_{2}$Fe, Hf$_{2}$Al, Hf$_{2}$Ga, Hf$_{2}$Ge, Hf$_{2}$Ni, Hf$_{2}$Si, Hf$_{2}$Th, Hf$_{2}$Zr, In$_{2}$Ag, Mn$_{2}$B, Mo$_{2}$B, Na$_{2}$Au, Ni$_{2}$B, Pb$_{2}$Au, Pb$_{2}$Pd, Pb$_{2}$Rh, Sb$_{2}$Ti, Sb$_{2}$V, Sc$_{2}$Co, Sn$_{2}$Co, Sn$_{2}$Fe, Sn$_{2}$Rh (HT), Ta$_{2}$B, Ta$_{2}$Ni, Ta$_{2}$Si, Ta$_{2}$Zr, Th$_{2}$Ag, Th$_{2}$Al, Th$_{2}$Au, Th$_{2}$Cu, Th$_{2}$Ga, Th$_{2}$Ge, Th$_{2}$Pd, Th$_{2}$Zn, Tl$_{2}$Au, Tl$_{2}$Pd, Tl$_{2}$Pt, W$_{2}$B, Zr$_{2}$Co, Zr$_{2}$Ga, Zr$_{2}$Ni, Zr$_{2}$Rh
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Cu I |
| $\mathbf{B_{3}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Al I |
References
- J. B. Friauf, The Crystal Structures of Two Intermetallic Compounds, J. Am. Chem. Soc. 49, 3107–3114 (1927), doi:10.1021/ja01411a017.
Prototype Generator
aflow --proto=A2B_tI12_140_h_a --params=$a,c/a,x_{2}$