Pt$_{8}$Ti Structure: A8B_tI18_139_hi_a-001
| Prototype | Pt$_{8}$Ti |
| AFLOW prototype label | A8B_tI18_139_hi_a-001 |
| ICSD | 105818 |
| Pearson symbol | tI18 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A8B_tI18_139_hi_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
Ni$_{8}$Mo, Ni$_{8}$Nb, Ni$_{8}$Ta, Ni$_{8}$V, Pd$_{8}$Mo, Pd$_{8}$V, Pd$_{8}$W, Pt$_{8}$Ce, Pt$_{8}$Ti, Pt$_{8}$V, Pt$_{8}$Zr
- When $a=3/(\sqrt{2})a_{fcc}$, $c=a_{fcc}$, $x_{2}=1/3$, and $x_{3}=1/3$ the atoms are on the sites of the fcc lattice. Compare this structure to the very similar V$_{4}$Zn$_{5}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ti I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Pt I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Pt I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Pt I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (8h) | Pt I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8i) | Pt II |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8i) | Pt II |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (8i) | Pt II |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (8i) | Pt II |
References
- P. Pietrokowsky, Novel Ordered Phase, Pt$_8$Ti, Nature 206, 291 (1965), doi:10.1038/206291a0.
- R. H. Taylor, S. Curtarolo, and G. L. W. Hart, Predictions of the Pt$_{8}$Ti Phase in Unexpected Systems, Journal of the American Chemical Society 132, 6851–6854 (2010), doi:10.1021/ja101890k.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=A8B_tI18_139_hi_a --params=$a,c/a,x_{2},x_{3}$