RhMnBi$_{3}$ Structure: A3BC_oC20_65_gq_ac_i-001
| Prototype | Bi$_{3}$MnRh |
| AFLOW prototype label | A3BC_oC20_65_gq_ac_i-001 |
| ICSD | 130688 |
| CCDC | 1850893 |
| Pearson symbol | oC20 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=A3BC_oC20_65_gq_ac_i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}$ |
- AFLOW rotates the lattice by 90$^\circ$ about the z-axis compared to the reported structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | Mn II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Bi I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Bi I |
| $\mathbf{B_{5}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (4i) | Rh I |
| $\mathbf{B_{6}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}$ | = | $- b y_{4} \,\mathbf{\hat{y}}$ | (4i) | Rh I |
| $\mathbf{B_{7}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Bi II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Bi II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Bi II |
| $\mathbf{B_{10}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Bi II |
References
- P. Kainzbauer, K. W. Richter, H. S. Effenberger, M. C. J. Marker, and H. Ipser, Single-crystal structure determination of two new ternary bismuthides: Rh$_{6}$Mn$_{5}$Bi$_{18}$ and RhMnBi$_{3}$, Acta Crystallogr. Sect. C 74, 863–869 (2018), doi:10.1107/S2053229618009087.
Found in
- P. Kainzbauer, M. C. J. M., and K. W. Richter, Reassessment of the Binary Mn-Rh Phase Diagram and Experimental Investigations of the Ternary Bi-Mn-Rh System, J. Phase Equilib. Diffus. 41, 282–298 (2020), doi:10.1007/s11669-020-00820-6.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3BC_oC20_65_gq_ac_i --params=$a,b/a,c/a,x_{3},y_{4},x_{5},y_{5}$