TaRh Structure: AB_oP12_51_ei_fj-001
| Prototype | RhTa |
| AFLOW prototype label | AB_oP12_51_ei_fj-001 |
| ICSD | 105938 |
| Pearson symbol | oP12 |
| Space group number | 51 |
| Space group symbol | $Pmma$ |
| AFLOW prototype command |
aflow --proto=AB_oP12_51_ei_fj-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
NbIr, TaIr, NbRh
- (Giessen, 1964) give the actual composition as (Ta$_{0.79}$Rh$_{0.21}$)Rh, with similar compositions for the related compounds.
- (Pearson, 1967) and others refer to this as $\alpha_{1}$-TaRh.
- (Giessen, 1964) give the structure in the $Pmcm$ setting of space group #51. We used FINDSYM to transform this to the standard $Pmma$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{1} \,\mathbf{\hat{z}}$ | (2e) | Rh I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{1} \,\mathbf{\hat{z}}$ | (2e) | Rh I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2f) | Ta I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2f) | Ta I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4i) | Rh II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4i) | Rh II |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (4i) | Rh II |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (4i) | Rh II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4j) | Ta II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4j) | Ta II |
| $\mathbf{B_{11}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4j) | Ta II |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4j) | Ta II |
References
- B. C. Giessen and N. J. Grant, New intermediate phases in system of Nb or Ta with Rh, Ir, Pd, or Pt, Acta Cryst. 17, 615–616 (1964), doi:10.1107/S0365110X64001438.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=AB_oP12_51_ei_fj --params=$a,b/a,c/a,z_{1},z_{2},x_{3},z_{3},x_{4},z_{4}$