α-UB$_{2}$C Structure: A2BC_oP8_51_i_a_f-001
| Prototype | BCU$_{2}$ |
| AFLOW prototype label | A2BC_oP8_51_i_a_f-001 |
| ICSD | 69767 |
| Pearson symbol | oP8 |
| Space group number | 51 |
| Space group symbol | $Pmma$ |
| AFLOW prototype command |
aflow --proto=A2BC_oP8_51_i_a_f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}$ |
- This is the ground state of UB$_{2}$C, stable up to 1675$^\circ$C. Above that temperature it transforms to rhombohedral $\beta$–UB$_{2}$C with the ThB$_{2}$C structure. (Rogl, 1991)
- We use the data taken at 29K.
- The origin has been shifted to put the carbon atoms on the (2a) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2a) | C 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) | U 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) | U 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) | B I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4i) | B I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (4i) | B I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (4i) | B I |
References
- P. Rogl and P. Fischer, Powder neutron diffraction of αUB$_{2}$C (αUB$_{2}$C-type), J. Solid State Chem. 90, 285–290 (1991), doi:10.1016/0022-4596(91)90144-7.
Prototype Generator
aflow --proto=A2BC_oP8_51_i_a_f --params=$a,b/a,c/a,z_{2},x_{3},z_{3}$