β-LiNH$_{2}$ ($Iba2$) Structure: A2BC_oI32_45_2c_c_c-001
| Prototype | H$_{2}$LiN |
| AFLOW prototype label | A2BC_oI32_45_2c_c_c-001 |
| ICSD | 116487 |
| CCDC | 2273728 |
| Pearson symbol | oI32 |
| Space group number | 45 |
| Space group symbol | $Iba2$ |
| AFLOW prototype command |
aflow --proto=A2BC_oI32_45_2c_c_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
- Under pressure LiNH$_{2}$ has at least three phases (Yamawaki, 2014): tetragonal $\alpha$–LiNiH$_{2}$, or Phase I, the ground state, stable up to 10GPa.
- Monoclinic Phase II, stable between 10 and 13 GPa.
- $\beta$–LiNH$_{2}$, or Phase III, is stable above 13 GPa. The structure is very uncertain. (Yamawaki, 2014) discuss two possible structures: orthorhombic space group $Pccn$ #56 and body-centered orthorhombic space group $Iba2$ #45 (this structure).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8c) | H I |
| $\mathbf{B_{2}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8c) | H I |
| $\mathbf{B_{3}}$ | = | $\left(- y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | H I |
| $\mathbf{B_{4}}$ | = | $\left(y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | H I |
| $\mathbf{B_{5}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8c) | H II |
| $\mathbf{B_{6}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8c) | H II |
| $\mathbf{B_{7}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | H II |
| $\mathbf{B_{8}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | H II |
| $\mathbf{B_{9}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{11}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{12}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{13}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | N I |
| $\mathbf{B_{14}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | N I |
| $\mathbf{B_{15}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | N I |
| $\mathbf{B_{16}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | N I |
References
- H. Yamawaki, H. Fujihisa, Y. Gotoh, and S. Nakano, Structure of Intermediate Phase II of LiNH$_{2}$ under High Pressure, J. Phys. Chem. B 118, 9991–9996 (2014), doi:10.1021/jp505133q.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2BC_oI32_45_2c_c_c --params=$a,b/a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$