Intermediate Temperature Bornite (Cu$_{5/6}$Fe$_{1/6}$)$_{3}$S$_{2}$ Structure: A7B_cF256_225_f2k_ce-001
| Prototype | Cu$_{5}$FeS$_{4}$ |
| AFLOW prototype label | A7B_cF256_225_f2k_ce-001 |
| Mineral name | bornite |
| ICSD | 200424 |
| Pearson symbol | cF256 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A7B_cF256_225_f2k_ce-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
- Bornite can take on several forms at different temperatures (Martinelli, 2018).
- At temperatures above 508K it is cubic with an
anti
-fluorite ($C1)$ structure. - From 443K to 508K it becomes a a supercell of an anti-fluorite structure (this structure).
- Below 443K it becomes orthorhombic, in the $Pbca$ #61 space group.
- As temperatures drop into the 50-70K range it transforms in to the non-centrosymmetric $Pca2_{1}$ #29 space group.
- At temperatures above 508K it is cubic with an
- In all of these cases the sulfur atoms form a face-centered or nearly face-centered cubic lattice.
- Data for this structure was taken at 458K. There is considerable disorder here. The site we labeled Cu-II is occupied 33% of the time with a mixture of copper and iron atoms. The Cu-I and Cu-III sites are occupied 31% and 7% of the time, respectively, and are purely copper. The sulfur atoms form a nearly cubic fcc lattice, with one of the tetrahedral sites is occupied by a copper or iron atom, and the other site is either filled by a copper atom or remains vacant. (Kanazawa, 1978)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | S I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | S I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (24e) | S II |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (24e) | S II |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{y}}$ | (24e) | S II |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{y}}$ | (24e) | S II |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{z}}$ | (24e) | S II |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{z}}$ | (24e) | S II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{12}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+3 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{14}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{1}+3 x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{16}}$ | = | $3 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{17}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{18}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{19}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{20}}$ | = | $- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{21}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{22}}$ | = | $- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{23}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{24}}$ | = | $z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{25}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{26}}$ | = | $z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{27}}$ | = | $- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{28}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{29}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{30}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{31}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{32}}$ | = | $\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{33}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{34}}$ | = | $\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{35}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{36}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{37}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{38}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{39}}$ | = | $\left(2 x_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{40}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96k) | Cu II |
| $\mathbf{B_{41}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{42}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{43}}$ | = | $\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{44}}$ | = | $- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{45}}$ | = | $\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{46}}$ | = | $- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{47}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{48}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{49}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{50}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{51}}$ | = | $- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{52}}$ | = | $\left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{53}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{54}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{55}}$ | = | $- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{56}}$ | = | $\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{57}}$ | = | $- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{58}}$ | = | $\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{59}}$ | = | $- z_{5} \, \mathbf{a}_{1}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{60}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{61}}$ | = | $- z_{5} \, \mathbf{a}_{1}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{62}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{63}}$ | = | $\left(2 x_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
| $\mathbf{B_{64}}$ | = | $- \left(2 x_{5} - z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96k) | Cu III |
References
- Y. Kanazawa, K. Koto, and N. Morimoto, Bornite (Cu$_{5}$FeS$_{4}$); stability and crystal structure of the intermediate form, Can. Mineral. 16, 397–404 (1978).
Found in
- A. Martinelli, G. O. Lepore, F. Bernardini, A. Giaccherini, and F. D. Benedetto, The puzzling structure of Cu$_{5}$FeS$_{4}$ (bornite) at low temperature, Acta Crystallogr. Sect. B 74, 405–415 (2018), doi:10.1107/S2052520618009812.
Prototype Generator
aflow --proto=A7B_cF256_225_f2k_ce --params=$a,x_{2},x_{3},x_{4},z_{4},x_{5},z_{5}$