LaB$_{2}$C$_{2}$ Structure: A2B2C_tP10_131_j_l_f-001
| Prototype | B$_{2}$C$_{2}$La |
| AFLOW prototype label | A2B2C_tP10_131_j_l_f-001 |
| ICSD | 23300 |
| Pearson symbol | tP10 |
| Space group number | 131 |
| Space group symbol | $P4_2/mmc$ |
| AFLOW prototype command |
aflow --proto=A2B2C_tP10_131_j_l_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
CaB$_{2}$C$_{2}$, CeB$_{2}$C$_{2}$, DyB$_{2}$C$_{2}$, EuB$_{2}$C$_{2}$, GdB$_{2}$C$_{2}$, HoB$_{2}$C$_{2}$, LuB$_{2}$C$_{2}$, NdB$_{2}$C$_{2}$, PrB$_{2}$C$_{2}$, SmB$_{2}$C$_{2}$, TbB$_{2}$C$_{2}$, TmB$_{2}$C$_{2}$, YB$_{2}$C$_{2}$, YbB$_{2}$C$_{2}$
- (Bauer, 1980) placed this structure in space group $P\overline{4}2c$ #112, with lanthanum atoms at the (2a) Wyckoff site, boron at (4h), and carbon at (4i). (Cenzual, 1991) showed that these Wyckoff positions imply an inversion site not present in $P\overline{4}2c$, and so the true space group is $P4_{2}/mmc$ #131.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2f) | La I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2f) | La I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (4j) | B I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (4j) | B I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4j) | B I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4j) | B I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4l) | C I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4l) | C I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (4l) | C I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (4l) | C I |
References
- J. Bauer and O. Bars, The ordering of boron and carbon atoms in the LaB$_{2}$C$_{2}$ structure, Acta Crystallogr. Sect. B 36, 1540–1544 (1980), doi:10.1107/S0567740880006541.
Found in
- K. Cenzual, L. M. Gelato, M. Penzo, and E. Parthé, Inorganic structure types with revised space groups. I, Acta Crystallogr. Sect. B 47, 433–439 (1991), doi:10.1107/S0108768191000903.
Prototype Generator
aflow --proto=A2B2C_tP10_131_j_l_f --params=$a,c/a,x_{2},x_{3}$