α-SiU$_{3}$ ($D0_{c}$) Structure: AB3_tI16_140_b_ah-001
| Prototype | SiU$_{3}$ |
| AFLOW prototype label | AB3_tI16_140_b_ah-001 |
| Strukturbericht designation | $D0_{c}$ |
| ICSD | 31627 |
| Pearson symbol | tI16 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=AB3_tI16_140_b_ah-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
Other compounds with this structure
AlPt$_{3}$, GaPt$_{3}$, GePt$_{3}$, SiIr$_{3}$, SiPt$_{3}$ (HT)
- This is the ground state of SiU$_{3}$. Above 770$^\circ$C it transforms into $\beta$–SiU$_{3}$ in the Cu$_{3}$Au ($L1_{2}$) structure. (Okamoto, 2013).
- When $c=2 a$ and $x_{3}=1/4$ the atoms are at the positions of the Cu$_{3}$Au ($L1_{2}$) structure.
- Many references define both a $D0_{c}$ and a $D0'_{c}$ (Ir$_{3}$Si) structure. The primary difference seems to be positioning the Si atoms on the (2a) or (2b) sites. Since this is merely an origin shift we will ignore the $D0'_{c}$ label.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | U I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | U I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Si I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Si I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | U II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | U II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (8h) | U II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (8h) | U II |
References
- W. H. Zachariasen, Crystal chemical studies of the 5f-series of elements. VIII. Crystal structure studies of uranium silicides and of CeSi$_2$, NpSi$_2$, and PuSi$_2$, Acta Cryst. 2, 94–99 (1949), doi:10.1107/S0365110X49000217.
- H. Okamoto, Si-U (Silicon-Uranium), J. Phase Equilibria Diffus. 34, 167–168 (2013).
Prototype Generator
aflow --proto=AB3_tI16_140_b_ah --params=$a,c/a,x_{3}$