Cu$_{2}$Sb ($C38$) Structure: A2B_tP6_129_ac_c-001
| Prototype | Cu$_{2}$Sb |
| AFLOW prototype label | A2B_tP6_129_ac_c-001 |
| Strukturbericht designation | $C38$ |
| ICSD | 42323 |
| CCDC | 1612021 |
| Pearson symbol | tP6 |
| Space group number | 129 |
| Space group symbol | $P4/nmm$ |
| AFLOW prototype command |
aflow --proto=A2B_tP6_129_ac_c-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
Cr$_{2}$As, Cu$_{2}$As, Cu$_{2}$Sb, Cu$_{2}$Te, Fe$_{2}$As, Fe$_{2}$Se, Fe$_{2}$Te, Mn$_{2}$As, Mn$_{2}$Sb, Nd$_{2}$S, Ni$_{2}$Se, Ni$_{2}$Te, O$_{2}$Eu, O$_{2}$Gd, Si$_{2}$Al, As$_{2}$Th, As$_{2}$U, Bi$_{2}$Th, Bi$_{2}$U, Pu$_{2}$U, S$_{2}$Ce, S$_{2}$Yb, Sb$_{2}$Hf, Sb$_{2}$Th, Sb$_{2}$U, Se$_{2}$Ce, Se$_{2}$Ho, Te$_{2}$Ce, Te$_{2}$La, Te$_{2}$U
- Cu$_{2}$Sb ($C38$), UP$_{2}$, and LaSe$_{1.85}$ have similar AFLOW prototype labels, A2B_tP6_129_ac_c for the first two and AB2_tP6_129_c_ac for the third. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. - We consider all of these to be binary forms of Matlockite ($E0_{1}$)/PrOI.
- We somewhat arbitrarily assign
- Structures with c/a $<$ 2 to the Cu$_{2}$Sb prototype,
- Structures with 2 $<$ c/a $<$ 3 to the UP$_{2}$ prototype, and
- Structures with c/a ≈ 4 to the LaSe$_{1.85}$ prototype.
- The ICSD distinction between Cu$_{2}$Sb and UP$_{2}$ is not the same as ours, and they often assign binary compounds to the ternary prototypes.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (2a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (2a) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Cu II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Cu II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2c) | Sb I |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2c) | Sb I |
References
- W. B. Pearson, The Cu$_2$Sb and related structures, Zeitschrift für Kristallographie 171, 23–39 (1985), doi:10.1524/zkri.1985.171.14.23.
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=A2B_tP6_129_ac_c --params=$a,c/a,z_{2},z_{3}$