β-UH$_{3}$ Structure: A3B_cP32_223_k_ac-001
| Prototype | H$_{3}$U |
| AFLOW prototype label | A3B_cP32_223_k_ac-001 |
| ICSD | none |
| Pearson symbol | cP32 |
| Space group number | 223 |
| Space group symbol | $Pm\overline{3}n$ |
| AFLOW prototype command |
aflow --proto=A3B_cP32_223_k_ac-001
--params=$a, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Zn$_{3}$Au
- UH$_{3}$ exists in two different structures, both with space group $Pm\overline{3}n$ #223 (Halevy, 2004).
- $\alpha$–UH$_{3}$ forms in the Cr$_{3}$Si ($A15$) structure, but rapidly transforms into the ground state $\beta$–UH$_{3}$ structure shown here.
- In this case, all of the uranium atoms sit on the sites of the $A15$ structure, with the hydrogens in the interstitials.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | U I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | U I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | U II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | U II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6c) | U II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6c) | U II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | U II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | U II |
| $\mathbf{B_{9}}$ | = | $y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{10}}$ | = | $- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{11}}$ | = | $y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{12}}$ | = | $- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{13}}$ | = | $z_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{14}}$ | = | $z_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{15}}$ | = | $- z_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{16}}$ | = | $- z_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{17}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (24k) | H I |
| $\mathbf{B_{18}}$ | = | $- y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (24k) | H I |
| $\mathbf{B_{19}}$ | = | $y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (24k) | H I |
| $\mathbf{B_{20}}$ | = | $- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (24k) | H I |
| $\mathbf{B_{21}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{25}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{27}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{29}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{30}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{31}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | H I |
| $\mathbf{B_{32}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | H I |
References
- I. Halevy, S. Salhov, S. Zalkind, M. Brill, and I. Yaar, High pressure study of β-UH$_{3}$ crystallographic and electronic structure, J. Alloys Compd. 370, 59–64 (2004), doi:10.1016/j.jallcom.2003.09.124.
Prototype Generator
aflow --proto=A3B_cP32_223_k_ac --params=$a,y_{3},z_{3}$