La$_{3}$Al$_{11}$ Structure: A11B3_oI28_71_bf2m_ai-001
| Prototype | Al$_{11}$La$_{3}$ |
| AFLOW prototype label | A11B3_oI28_71_bf2m_ai-001 |
| ICSD | 57937 |
| Pearson symbol | oI28 |
| Space group number | 71 |
| Space group symbol | $Immm$ |
| AFLOW prototype command |
aflow --proto=A11B3_oI28_71_bf2m_ai-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
Ce$_{3}$Al$_{11}$, (La$_{\frac12}$Nd$_{\frac12}$)$_{3}$Al$_{11}$, Sr$_{3}$In$_{11}$, Yb$_{3}$Zn$_{11}$, Yb$_{3}$(Al$_{x}$Zn$_{11-x}$, Ce$_{3}$(Al$_{9.13}$Ga$_{1.78}$Ni$_{0.08}$)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | La I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2b) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4f) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4f) | Al II |
| $\mathbf{B_{5}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4i) | La II |
| $\mathbf{B_{6}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4i) | La II |
| $\mathbf{B_{7}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (8m) | Al III |
| $\mathbf{B_{8}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (8m) | Al III |
| $\mathbf{B_{9}}$ | = | $- z_{5} \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (8m) | Al III |
| $\mathbf{B_{10}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (8m) | Al III |
| $\mathbf{B_{11}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (8m) | Al IV |
| $\mathbf{B_{12}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (8m) | Al IV |
| $\mathbf{B_{13}}$ | = | $- z_{6} \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (8m) | Al IV |
| $\mathbf{B_{14}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (8m) | Al IV |
References
- A. H. G. de Mesquita and K. H. J. Buschow, The crystal structure of so-called α-LaAl$_{4}$ (La$_{3}$Al$_{11}$), Acta Cryst. 22, 497–501 (1967), doi:10.1107/S0365110X67001045.
Found in
- O. Janka, T. Shang, R. E. Baumbach, E. D. Bauer, J. D. Thompson, and S. M. Kauzlarich, Structure and Magnetic Properties of Ce$_{3}$(Ni/Al/Ga)$_{11}$-A New Phase with the La$_{3}$Al$_{11}$ Structure Type, Crystals 5, 1–8 (2015), doi:10.3390/cryst5010001.
Prototype Generator
aflow --proto=A11B3_oI28_71_bf2m_ai --params=$a,b/a,c/a,x_{3},z_{4},x_{5},z_{5},x_{6},z_{6}$