β-TiCu$_{3}$ ($D0_{a}$) Structure: A3B_oP8_59_ae_b-001
| Prototype | Cu$_{3}$Ti |
| AFLOW prototype label | A3B_oP8_59_ae_b-001 |
| Strukturbericht designation | $D0_{a}$ |
| ICSD | 197784 |
| Pearson symbol | oP8 |
| Space group number | 59 |
| Space group symbol | $Pmmn$ |
| AFLOW prototype command |
aflow --proto=A3B_oP8_59_ae_b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
HfAu$_{3}$, InAu$_{3}$, MoNi$_{3}$, NbNi$_{3}$, $\alpha$-NbPt$_{3}$, $\beta$-SbCu$_{3}$ (H.T.), SbNi$_{3}$ (L.T.), TaNi$_{3}$ (L.T.), TaPt$_{3}$, TiAu$_{3}$, $\beta$-TiCu$_{3}$ (L.T.), ZrAu$_{3}$
- We have been so far unable to obtain the original reference (Karlsson, 1951), and Pearson does not give the exact atomic coordinates. Wyckoff positions have been deduced from the structure of Cu$_{3}$Sb, which Villars (1991) lists as having the TiCu$_{3}$ structure.
- Atomic positions are set to give the approximate nearest-neighbor distances listed in Pearson.
- (Giessen, 1971) says that the (Karlsson, 1951) structure of $\beta$–TiCu$_{3}$ is mistaken. They do find a metastable $\beta$–TiCu$_{3}$ phase which has the same space group and Wyckoff positions, but substantially different lattice constants than the original determination for $\beta$–TiCu$_{3}$.
- The ICSD entry is from (Karlsson, 1951).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | Ti I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2b) | Ti I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
| $\mathbf{B_{7}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
References
- B. C. Giessen and D. Szymanski, A metastable phase TiCu$_3$(m), J. Appl. Crystallogr. 4, 257–259 (1971), doi:10.1107/S0021889871006824.
- N. Karlsson, An X-ray study of the phases in the copper-titanium system, J. Inst. Metals 79, 391 (1951).
Found in
- N. Karlsson, , Journal of the Institute of Metals 79, 391 (1951).
Prototype Generator
aflow --proto=A3B_oP8_59_ae_b --params=$a,b/a,c/a,z_{1},z_{2},y_{3},z_{3}$