Low Temperature TmNi$_{2}$ Structure: A2B_cF192_216_2e2h_ab2eg-001
| Prototype | Ni$_{2}$Tm |
| AFLOW prototype label | A2B_cF192_216_2e2h_ab2eg-001 |
| ICSD | 105432 |
| Pearson symbol | cF192 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A2B_cF192_216_2e2h_ab2eg-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}$ |
- TmNi$_{2}$ is found in three forms (Deutz, 1989):
- A low temperature face-centered cubic structure (this structure) at room temperature and below,
- a simple cubic structure near 700$^\circ$, and
- the $C15$ cubic Laves structure for higher temperatures.
- The data for this structure was taken at 4.2K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Tm I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Tm II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Ni I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Ni I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Ni I |
| $\mathbf{B_{6}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Ni I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Ni II |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Ni II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Ni II |
| $\mathbf{B_{10}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Ni II |
| $\mathbf{B_{11}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Tm III |
| $\mathbf{B_{12}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Tm III |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Tm III |
| $\mathbf{B_{14}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Tm III |
| $\mathbf{B_{15}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Tm IV |
| $\mathbf{B_{16}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- 3 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Tm IV |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{1}- 3 x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Tm IV |
| $\mathbf{B_{18}}$ | = | $- 3 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Tm IV |
| $\mathbf{B_{19}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{20}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{21}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{22}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{23}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{24}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Tm V |
| $\mathbf{B_{25}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{26}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{27}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{28}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{29}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{30}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{31}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{32}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{33}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{34}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{35}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{36}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | Ni III |
| $\mathbf{B_{37}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{38}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{39}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{40}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{41}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{42}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{43}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{44}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{45}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{46}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{47}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
| $\mathbf{B_{48}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | Ni IV |
References
- A. F. Deutz, R. B. Helmholdt, A. C. Moleman, D. B. D. Mooij, and K. H. J. Buschow, Superstructure in the intermetallic compound TmNi$_{2}$, J. Less-Common Met. 153, 259–266 (1989), doi:10.1016/0022-5088(89)90120-3.
Found in
- A. Jain, S. Ping, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1, 011002 (2013), doi:10.1063/1.4812323.
Prototype Generator
aflow --proto=A2B_cF192_216_2e2h_ab2eg --params=$a,x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},z_{8},x_{9},z_{9}$