α-Li$_{3}$BN$_{2}$ Structure: AB3C2_tP12_136_a_bd_f-001
| Prototype | BLi$_{3}$N$_{2}$ |
| AFLOW prototype label | AB3C2_tP12_136_a_bd_f-001 |
| ICSD | 655673 |
| Pearson symbol | tP12 |
| Space group number | 136 |
| Space group symbol | $P4_2/mnm$ |
| AFLOW prototype command |
aflow --proto=AB3C2_tP12_136_a_bd_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{4}$ |
- (Yamane, 1987) find a phase transition from $\alpha$- to $\beta$–Li$_{3}$BN$_{2}$ at 1135K. The $\beta$–Li$_{3}$BN$_{2}$ phase has space group $P2_{1}/c$ #14 and four formula units in a monoclinic cell, compared to two units in the $\alpha$- phase, but they did not describe the atomic positions for $\beta$–Li$_{3}$BN$_{2}$.
- (Yamane, 1987) put this in space group $P4_{2}2_{1}2$ #94, but the positions of the lithium atoms are such that there is an inversion cite, placing the system in space group $P4_{2}/mnm$ #136. (Cenzual, 1991)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | B I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Li I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (2b) | Li I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Li II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | Li II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Li II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | Li II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (4f) | N I |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (4f) | N I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | N I |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | N I |
References
- H. Yamane, S. Kikkawa, and M. Koizumi, High- and low-temperature phases of lithium boron nitride, Li$_{3}$BN$_{2}$: Preparation, phase relation, crystal structure, and ionic conductivity, J. Solid State Chem. 71, 1–11 (1987), doi:10.1016/0022-4596(87)90135-6.
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=AB3C2_tP12_136_a_bd_f --params=$a,c/a,x_{4}$