High-pressure cI16 Li Structure: A_cI16_220_c-001
| Prototype | Li |
| AFLOW prototype label | A_cI16_220_c-001 |
| ICSD | 109012 |
| Pearson symbol | cI16 |
| Space group number | 220 |
| Space group symbol | $I\overline{4}3d$ |
| AFLOW prototype command |
aflow --proto=A_cI16_220_c-001
--params=$a, \allowbreak x_{1}$ |
Other compounds with this structure
Na (under pressure)
- This is a high-pressure phase of lithium. We use the data from (Hanfland, 2000) at 38.9 GPa. When $x_{1} = 0$ this becomes a body-centered cubic ($A2$) system.
- We have used the fact that all vectors of the form $(\pm a/2 \hat{x} \pm a/2 \hat{y} \pm a/2 \hat{z})$ are primitive vectors of the body-centered cubic lattice to simplify the positions of some atoms in both lattice and Cartesian coordinates.
- The ICSD entry was recorded at 45 GPa.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $2 x_{1} \, \mathbf{a}_{1}+2 x_{1} \, \mathbf{a}_{2}+2 x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{3}}$ | = | $- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{4}}$ | = | $- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{5}}$ | = | $\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{7}}$ | = | $- 2 x_{1} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Li I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{1} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Li I |
References
- M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, New high-pressure phases of lithium, Nature 408, 174–178 (2000), doi:10.1038/35041515.
Prototype Generator
aflow --proto=A_cI16_220_c --params=$a,x_{1}$