Li3N Structure: A3B_hP4_191_bc_a
| Prototype | : | Li3N |
| AFLOW prototype label | : | A3B_hP4_191_bc_a |
| Strukturbericht designation | : | None |
| Pearson symbol | : | hP4 |
| Space group number | : | 191 |
| Space group symbol | : | $\mbox{P6/mmm}$ |
| AFLOW prototype command | : | aflow --proto=A3B_hP4_191_bc_a --params=$a,c/a$ |
Hexagonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{N} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(1b\right) & \mbox{Li I} \\ \mathbf{B}_{3} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}& \left(2c\right) & \mbox{Li II} \\ \mathbf{B}_{4} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}& \left(2c\right) & \mbox{Li II} \\ \end{array} \]References
- D. H. Gregory, P. M. O'Meara, A. G. Gordon, J. P. Hodges, S. Short, and J. D. Jorgensen, Structure of Lithium Nitride and Transition–Metal–Doped Derivatives, Li3–x–yMxN (M = Ni, Cu): A Powder Neutron Diffraction Study, Chem. Mater. 14, 2063–2070 (2002), doi:10.1021/cm010718t.
Found in
- P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko–Koblyuk, O. Pavlyuk, I. Savesyuk, S. Stoiko, and L. Sysa, Landolt–Börnstein – Group III Condensed Matter (Springer–Verlag Berlin Heidelberg, 2006). Accessed through the Springer Materials site.