Chalcopyrite (CuFeS$_{2}$, $E1_{1}$) Structure: ABC2_tI16_122_a_b_d-001
| Prototype | CuFeS$_{2}$ |
| AFLOW prototype label | ABC2_tI16_122_a_b_d-001 |
| Strukturbericht designation | $E1_{1}$ |
| Mineral name | chalcopyrite |
| ICSD | 2518 |
| Pearson symbol | tI16 |
| Space group number | 122 |
| Space group symbol | $I\overline{4}2d$ |
| AFLOW prototype command |
aflow --proto=ABC2_tI16_122_a_b_d-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
Other compounds with this structure
AgAlS$_{2}$, AgAlSe$_{2}$, AgAlTe$_{2}$, AgFeS$_{2}$, AgGaS$_{2}$, AgGaSe$_{2}$, AgGaTe$_{2}$, AgInS$_{2}$, AgInSe$_{2}$, AgInTe$_{2}$, AgTlS$_{2}$, AgTlSe$_{2}$, AgTlTe$_{2}$, BeNSi$_{2}$, CdGaSe$_{2}$, CdGaTe$_{2}$, CdGeAs$_{2}$, CdGeP$_{2}$, CdGeSb$_{2}$, CdSiAs$_{2}$, CdSiP$_{2}$, CdSiSb$_{2}$, CdSnAs$_{2}$, CdSnP$_{2}$, CdSnSb$_{2}$, CuAlS$_{2}$, CuAlSe$_{2}$, CuAlTe$_{2}$, CuGaS$_{2}$, CuGaSe$_{2}$, CuGaTe$_{2}$, CuInS$_{2}$, CuInSe$_{2}$, CuInTe$_{2}$, CuLaS$_{2}$, CuTlS$_{2}$, CuTlSe$_{2}$, CuTlTe$_{2}$, GaHgTe$_{2}$, GaZnTe$_{2}$, GeZnAs$_{2}$, GeZnP$_{2}$, GeZnSb$_{2}$, SiZnAs$_{2}$, SiZnP$_{2}$, SiZnSb$_{2}$, SnZnAs$_{2}$, SnZnP$_{2}$, SnZnSb$_{2}$, SrZnBi$_{2}$, SrZnSb$_{2}$
- When $c = 2 a$ and $x_{3} = 1/8$ the atoms are on the sites of the diamond ($A4$) structure. In that case if we replace the Fe atoms by Cu we get the zincblende ($B3$) structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4b) | Fe I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Fe I |
| $\mathbf{B_{5}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | S I |
| $\mathbf{B_{6}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | S I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | S I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | S I |
References
- S. R. Hall and J. M. Stewart, The Crystal Structure Refinement of Chalcopyrite, CuFeS$_2$, Acta Crystallogr. Sect. B 29, 579–585 (1973), doi:10.1107/S0567740873002943.
Prototype Generator
aflow --proto=ABC2_tI16_122_a_b_d --params=$a,c/a,x_{3}$