CrB ($B33$) Structure: AB_oC8_63_c_c-001
| Prototype | BCr |
| AFLOW prototype label | AB_oC8_63_c_c-001 |
| Strukturbericht designation | $B33$ |
| ICSD | 44250 |
| CCDC | 1613667 |
| Pearson symbol | oC8 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=AB_oC8_63_c_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak y_{2}$ |
Other compounds with this structure
AgCa, AlHf, AlTh, AlY, AlZr, AuGd, BNb, BNi, BTa, BV, BaPb, CaGe, CaSi, CaSn, CeNi, CePt, CeRh, CoTh, DyGa, DyGe, ErNi, GaGd, GaPr, GdGe, GeHo, GeNi, GePr, HfNi, HfPt, HoNi, ITl, IrTh, LaNi, LaPt, LaRh, LuNi, NdNi, NdRh, NiPr, NiPu, NiSm, NiTb, NiTm, NiZr, PrRh, PtTh, PtZr, RhTh, RuTh, SiSr, SnSr, SiY, (Ge, Si)Ho
- (Gottfried, 1938) originally gave the $B33$ Strukturbericht designation to thallium iodide, TiI. Later, (Smithells, 1955) gave CrB structure the new designation $B_{f}$. These structures are identical, and we follow (Parthé, 1993) in using $B33$ to designate both structures.
- Removing either the Cr or B atoms transforms this into the $\alpha$–U (A20) structure.
- $\beta$–SnS and CrB ($B33$) have the same AFLOW label, AB_oC8_63_c_c. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Cr I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Cr I |
References
- S. Okada, T. Atoda, and I. Higashi, Structural investigation of Cr$_{2}$B$_{3}$, Cr$_{3}$B$_{4}$, and CrB by single-crystal diffractometry, J. Solid State Chem. 68, 61–67 (1987), doi:10.1016/0022-4596(87)90285-4.
- C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
- C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.
- E. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzula, and R. Gladyshevskii, Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Gmelin Handbook of Inorganic and Organometallic Chemistry, vol. 2 (Springer-Verlag, Berlin, Heidelberg, 1993), 8 edn., doi:10.1007/978-3-662-02909-1_3.
Found in
- P. Villars, CrB Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
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=AB_oC8_63_c_c --params=$a,b/a,c/a,y_{1},y_{2}$