Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB3C2_cI96_206_c_e_ad

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

AlLi3N2 ($E9_{d}$) Structure: AB3C2_cI96_206_c_e_ad

Picture of Structure; Click for Big Picture
Prototype : AlLiN
AFLOW prototype label : AB3C2_cI96_206_c_e_ad
Strukturbericht designation : $E9_{d}$
Pearson symbol : cI96
Space group number : 206
Space group symbol : $Ia\bar{3}$
AFLOW prototype command : aflow --proto=AB3C2_cI96_206_c_e_ad
--params=
$a$,$x_{2}$,$x_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • GaLi3N2, ScLi3N2, TiLi3N2, ZnLi3N2, SiLi3N2, GeLi3N2

Body-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, a \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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(8a\right) & \text{N I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(8a\right) & \text{N I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(8a\right) & \text{N I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{N I} \\ \mathbf{B}_{5} & = & 2x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} + 2x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{9} & = & -2x_{2} \, \mathbf{a}_{1}-2x_{2} \, \mathbf{a}_{2}-2x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Al} \\ \mathbf{B}_{13} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{14} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{15} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{17} & = & \left(\frac{1}{4} +x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{4} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{19} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} - x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{20} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{21} & = & -x_{3} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{23} & = & \left(\frac{3}{4} - x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{24} & = & \left(\frac{3}{4} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \text{N II} \\ \mathbf{B}_{25} & = & \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} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{27} & = & \left(y_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{29} & = & \left(x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} - x_{4} - y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{y}} + y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{32} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{33} & = & \left(x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{34} & = & \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4} - y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} - x_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} +x_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{37} & = & \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} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{39} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +y_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{41} & = & \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +x_{4} + y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}}-y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{44} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + y_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{45} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{46} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4} + y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} +x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{2} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} - x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(48e\right) & \text{Li} \\ \end{array} \]

References

  • R. Juza and F. Hund, Die ternären Nitride Li3AlN2 und Li3GaN2. 17. Mitteilung über Metallamide und Metallnitride, Z. Anorg. Allg. Chem. 257, 13–25 (1948), doi:10.1002/zaac.19482570102.

Found in

  • J. F. Herbst and L. G. {Hector, Jr.}, Exploration of the formation of XLi3N2 compounds (X=Sc–Zn) by means of density functional theory, Phys. Rev. B 85, 195137 (2012), doi:10.1103/PhysRevB.85.195137.

Geometry files


Prototype Generator

aflow --proto=AB3C2_cI96_206_c_e_ad --params=

Species:

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