Low Temperature KBD$_{4}$ Structure: AB4C_tP12_137_a_g_b-001
| Prototype | BD$_{4}$K |
| AFLOW prototype label | AB4C_tP12_137_a_g_b-001 |
| ICSD | 99264 |
| Pearson symbol | tP12 |
| Space group number | 137 |
| Space group symbol | $P4_2/nmc$ |
| AFLOW prototype command |
aflow --proto=AB4C_tP12_137_a_g_b-001
--params=$a, \allowbreak c/a, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This is the low temperature structure of KBD$_{4}$, stable below 70K, with data taken at 1.5K. Above that it transforms into the cubic room temperature KBD$_{4}$ structure, also known as the NaBH$_{4}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2a) | B I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2b) | K I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2b) | K I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{7}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{8}}$ | = | $y_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{9}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{11}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8g) | D I |
| $\mathbf{B_{12}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8g) | D I |
References
- G. Renaudin, S. Gomes, H. Hagemann, L. Keller, and K. Yvon, Structural and spectroscopic studies on the alkali borohydrides MBH$_{4}$ (M = Na, K, Rb, Cs), J. Alloys Compd. 375, 98–106 (2004), doi:10.1016/j.jallcom.2003.11.018.
Found in
- S. D. Cataldo, C. Heil, W. von der Linden, and L. Boeri, LaBH$_{8}$: the first high-T$_{c}$ low-pressure superhydride, Phys. Rev. B 104, L020511 (2021), doi:10.1103/PhysRevB.104.L020511.
Prototype Generator
aflow --proto=AB4C_tP12_137_a_g_b --params=$a,c/a,y_{3},z_{3}$