CrS Structure: AB_mC8_15_a_e-003
- (Wyckoff, 1963) lists two structures for CrS. The first is this structure, where the sulfur (4e) site has 3% vacancies. The second is the NiAs ($B8_{1}$) structure. (Venkatraman, 1990) list this structure as the ground state and $B8_{1}$ as the high-temperature phase, with the transition occuring at 297K.
- Tenorite (CuO) and CrS have the same AFLOW prototype label, AB_mC8_15_a_e. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Cr I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | S I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | S I |
References
- F. Jellinek, The Structures of the Chromium Sulphides, Acta Cryst. 10, 620–628 (1957), doi:10.1107/S0365110X57002200.
- R. W. G. Wyckoff, The Structure of Crystals}, vol. I (John Wiley & Sons, 1963), 2$^{\mathrm{nd}$ edn.
- M. Venkatraman and J. P. Neumann, Binary Alloy Phase Diagrams (ASM International, 1990), vol. 2, chap. Cr-S (Chromium-Sulfur), ii edn. T. B. Massalski, Ed.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=AB_mC8_15_a_e --params=$a,b/a,c/a,\beta,y_{2}$