TiSi$_{2}$ ($C54$) Nowotony Chimney-Ladder Structure: A2B_oF24_70_e_a-001
| Prototype | Si$_{2}$Ti |
| AFLOW prototype label | A2B_oF24_70_e_a-001 |
| Strukturbericht designation | $C54$ |
| ICSD | 1089 |
| Pearson symbol | oF24 |
| Space group number | 70 |
| Space group symbol | $Fddd$ |
| AFLOW prototype command |
aflow --proto=A2B_oF24_70_e_a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}$ |
Other compounds with this structure
RuAl$_{2}$, RuGa$_{2}$, TiGe$_{2}$, ZrSn$_{2}$
- This is the simplest example of a
Nowotny chimney-ladder structure
(Pearson, 1970), T$_{n}$X$_{m}$, whereT
is a transition metal,X
is a row III or IV metal (or semiconductor), and $1.25 \le m/n {<} 2$. The transition metal atoms are arranged similarly to the atoms in the $\beta$–Sn ($A5$).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ti I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}b \,\mathbf{\hat{y}}+\frac{7}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ti I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{5}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Si I |
References
- W. Jeitschko, Refinement of the crystal structure of TiSi$_2$ and some comments on bonding in TiSi$_2$ and related compounds, Acta Crystallogr. Sect. B 33, 2347–2348 (1977), doi:10.1107/S0567740877008462.
- W. B. Pearson, Phases with Nowotny chimney-ladder structures considered as `electron' phases, Acta Crystallogr. Sect. B 26, 1044–1046 (1970), doi:10.1107/S0567740870003564.
Prototype Generator
aflow --proto=A2B_oF24_70_e_a --params=$a,b/a,c/a,x_{2}$