Au$_{5}$Mn$_{2}$ Structure: A5B2_mC14_12_a2i_i-001
| Prototype | Au$_{5}$Mn$_{2}$ |
| AFLOW prototype label | A5B2_mC14_12_a2i_i-001 |
| ICSD | 144447 |
| Pearson symbol | mC14 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A5B2_mC14_12_a2i_i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- As noted by (Pearson, 1972), this structure is very nearly cubic close-packed. As such, it is frequently used for cluster expansion models.
- (Humble, 1964) puts this structure in space group $Cc$ #5, but the coordinates given are consistent with space group $C2/m$ #12.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Au I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Au II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Au II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Au III |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Au III |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Mn I |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Mn I |
References
- S. G. Humble, Establishment of an ordered phase of composition Au$_{5}$Mn$_{2}$ in the gold-manganese system, Acta Cryst. 17, 1485–1486 (1964), doi:10.1107/S0365110X64003723.
- W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972).
Found in
- G. van Tendeloo, R. Wolf, and S. Amelinckx, The Microstructure of the Alloy Au$_{5}$Mn$_{2}$: A Domain Structure with 84 Variants, Phys. Stat. Solidi A 40, 531–550 (1977), doi:10.1002/pssa.2210400220.
- W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972).
Prototype Generator
aflow --proto=A5B2_mC14_12_a2i_i --params=$a,b/a,c/a,\beta,x_{2},z_{2},x_{3},z_{3},x_{4},z_{4}$