CeRu$_{2}$B$_{2}$ Structure: A2BC2_oF40_22_ej_ac_fi-001
| Prototype | B$_{2}$CeRu$_{2}$ |
| AFLOW prototype label | A2BC2_oF40_22_ej_ac_fi-001 |
| ICSD | 40800 |
| Pearson symbol | oF40 |
| Space group number | 22 |
| Space group symbol | $F222$ |
| AFLOW prototype command |
aflow --proto=A2BC2_oF40_22_ej_ac_fi-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak x_{6}$ |
Other compounds with this structure
CeOs$_{2}$B$_{2}$, GdOs$_{2}$B$_{2}$, GdRu$_{2}$B$_{2}$, LaOs$_{2}$B$_{2}$, LaRu$_{2}$B$_{2}$, NdOs$_{2}$B$_{2}$, NdRu$_{2}$B$_{2}$, PrOs$_{2}$B$_{2}$, PrRu$_{2}$B$_{2}$, SmOs$_{2}$B$_{2}$, SmRu$_{2}$B$_{2}$, ThOs$_{2}$B$_{2}$, ThRu$_{2}$B$_{2}$
- As noted by (Horvath, 1987) a small amount of uncertainty in the positions of the atoms would allow this system to be placed in the centrosymmetric space group $Fddd$ #70.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Ce I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Ce II |
| $\mathbf{B_{3}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8e) | B I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8e) | B I |
| $\mathbf{B_{5}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (8f) | Ru I |
| $\mathbf{B_{6}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}$ | (8f) | Ru I |
| $\mathbf{B_{7}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8i) | Ru II |
| $\mathbf{B_{8}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8i) | Ru II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8j) | B II |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8j) | B II |
References
- C. Horvath, P. Rogle, and K. Hiebl, The crystal structure of CeRu$_{2}$B$_{2}$ and isotypic compounds M(Ru, Os)$_{2}$B$_{2}$, M $=$ La, Pr, Nd, Sm, Gd, and Th, J. Solid State Chem. 67, 70–77 (1987), doi:10.1016/0022-4596(87)90340-9.
Prototype Generator
aflow --proto=A2BC2_oF40_22_ej_ac_fi --params=$a,b/a,c/a,x_{3},y_{4},y_{5},x_{6}$