Au$_{2}$V Structure: A2B_oC12_38_de_ab-001
| Prototype | Au$_{2}$V |
| AFLOW prototype label | A2B_oC12_38_de_ab-001 |
| ICSD | 58614 |
| Pearson symbol | oC12 |
| Space group number | 38 |
| Space group symbol | $Amm2$ |
| AFLOW prototype command |
aflow --proto=A2B_oC12_38_de_ab-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Cu$_{2}$Ti, Pt$_{2}$Ta
- The published atomic positions put the system in the $Cmcm$ #65 space group, despite the authors' statement that the system is in the $Amm2$ #38. We forced this system into $Amm2$ by slightly shifting the $y_{4}$ cordinate. If $y_{3} = y_{4}$ then the space group becomes $Cmcm$.
- Space group $Amm2$ #38 allows an arbitrary choice of the origin of the $z$-axis. Here we follow (Stolz, 1962) and set $z_{2} = 0$ for the Au-II position.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | V I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | V II |
| $\mathbf{B_{3}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4d) | Au I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4d) | Au I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Au II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Au II |
References
- E. Stolz and K. Schubert, Strukturuntersuchungen in einigen zu T$^4$-B$^1$ homologen und quasihomologen Systemen, Z. Metallkd. 53, 433–444 (1962), doi:10.1515/ijmr-1962-530701.
Found in
- P. Villars, Au2V Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Prototype Generator
aflow --proto=A2B_oC12_38_de_ab --params=$a,b/a,c/a,z_{1},z_{2},y_{3},z_{3},y_{4},z_{4}$