ErNi$_{3}$Al$_{9}$ Structure: A9BC3_hR26_155_3cdef_c_f-001
| Prototype | Al$_{9}$ErNi$_{3}$ |
| AFLOW prototype label | A9BC3_hR26_155_3cdef_c_f-001 |
| ICSD | 105031 |
| Pearson symbol | hR26 |
| Space group number | 155 |
| Space group symbol | $R32$ |
| AFLOW prototype command |
aflow --proto=A9BC3_hR26_155_3cdef_c_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}, \allowbreak y_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}$ |
Other compounds with this structure
DyNi$_{3}$Al$_{9}$, ErNi$_{3}$Al$_{9}$, GdNi$_{3}$Al$_{9}$, YNi$_{3}$Al$_{9}$, YbNi$_{3}$Al$_{9}$, YbNi$_{3}$Ga$_{9}$
- DyNi$_{3}$Al$_{9}$ and YNi$_{3}$Al$_{9}$ have additional rare earth atoms on the (1b) (1/2 1/2 1/2) site and aluminum on another (6f) site, with partial occupancy on the rare earth (1b) and (1c) sites as well as the (3d) and both (6f) aluminum sites (Gladyshevskii, 1993, Table 2).
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al III |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Er I |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Er I |
| $\mathbf{B_{9}}$ | = | $y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a y_{5} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}$ | (3d) | Al IV |
| $\mathbf{B_{10}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}$ | (3d) | Al IV |
| $\mathbf{B_{11}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a y_{5} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}$ | (3d) | Al IV |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{6} + 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \left(6 y_{6} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Al V |
| $\mathbf{B_{13}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Al V |
| $\mathbf{B_{14}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{6} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \left(6 y_{6} + 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Al V |
| $\mathbf{B_{15}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{16}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{17}}$ | = | $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{18}}$ | = | $- z_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{19}}$ | = | $- y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{20}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6f) | Al VI |
| $\mathbf{B_{21}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
| $\mathbf{B_{22}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
| $\mathbf{B_{23}}$ | = | $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
| $\mathbf{B_{24}}$ | = | $- z_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
| $\mathbf{B_{25}}$ | = | $- y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
| $\mathbf{B_{26}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6f) | Ni I |
References
- R. E. Gladyshevskii, K. Cenzual, H. D. Flack, and E. Parthé, Structure of RNi$_{3}$Al$_{9}$ (R = Y, Gd, Dy, Er) with either ordered or partly disordered arrangement of Al-atom triangles and rare-earth-metal atoms, Acta Crystallogr. Sect. B 39, 468–474 (1993), doi:10.1107/S010876819201173X.
Prototype Generator
aflow --proto=A9BC3_hR26_155_3cdef_c_f --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},y_{5},y_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8}$