LaRhC$_{2}$ Structure: A2BC_tP16_76_2a_a_a-001
| Prototype | C$_{2}$LaRh |
| AFLOW prototype label | A2BC_tP16_76_2a_a_a-001 |
| ICSD | 100986 |
| Pearson symbol | tP16 |
| Space group number | 76 |
| Space group symbol | $P4_1$ |
| AFLOW prototype command |
aflow --proto=A2BC_tP16_76_2a_a_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
CeRhC$_{2}$
- This structure may also be found in the enantiomorphic space group $P4_{3}$ #78.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{3}}$ | = | $- y_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{4}}$ | = | $y_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{7}}$ | = | $- y_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{8}}$ | = | $y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4a) | La I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | La I |
| $\mathbf{B_{11}}$ | = | $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | La I |
| $\mathbf{B_{12}}$ | = | $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | La I |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4a) | Rh I |
| $\mathbf{B_{14}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Rh I |
| $\mathbf{B_{15}}$ | = | $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | Rh I |
| $\mathbf{B_{16}}$ | = | $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (4a) | Rh I |
References
- A. O. Tsokol\', O. I. Bodak, E. P. Marusin, and V. E. Zavodnik, X-ray diffraction studies of ternary $R$RhC$_{2}$ ($R$ = La, Ce, Pr, Nd, Sm) compounds, Sov. Phys. Crystallogr. 33, 202–203 (1988). Translated from Kristallografiya.
Found in
- P. Villars, LaRhC$_{2}$ Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Prototype Generator
aflow --proto=A2BC_tP16_76_2a_a_a --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$