# Encyclopedia of Crystallographic Prototypes

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)

## Predicted Li2MgH16 High–Temperature Superconductor (250 GPa) Structure : A16B2C_cF152_227_eg_d_a

 Prototype : H16Li2Mg AFLOW prototype label : A16B2C_cF152_227_eg_d_a Strukturbericht designation : None Pearson symbol : cF152 Space group number : 227 Space group symbol : $Fd\bar{3}m$ AFLOW prototype command : aflow --proto=A16B2C_cF152_227_eg_d_a --params=$a$,$x_{3}$,$x_{4}$,$z_{4}$

• This structure was predicted by (Sun, 2019) as a metastable state of Li2MgH16 at 250 GPa and $T=0$ K. If it is possible to construct this compound, or if it becomes stable due to thermodynamic considerations, it is predicted to have a superconducting transition $T_{\mathrm{c}}$ between 430 and 473 K.
• The predicted $T=0$ K ground state at 300 GPa is a $P\overline{3}m1$ #164 structure with molecular hydrogen.
• (Sun, 2019) give the Wyckoff positions in setting 1 of space group $Fd\overline{3}m$ #227. (They list the Wyckoff positions of the magnesium and lithium atoms as ($8b$) and ($16c$), respectively. They are actually at ($8a$) and ($16d$), as in their 300 GPa data.) We used FINDSYM to shift this to our standard setting 2.

### Face-centered Cubic primitive vectors:

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

Basis vectors:

$\begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{Mg} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{Mg} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Li} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Li} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Li} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Li} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{12} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{13} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H I} \\ \mathbf{B}_{15} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{16} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{17} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{19} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{21} & = & z_{4} \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{22} & = & z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{23} & = & z_{4} \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{24} & = & z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{26} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{27} & = & -z_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{28} & = & -z_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{29} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{31} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{33} & = & -z_{4} \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{34} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{35} & = & -z_{4} \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{36} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{37} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \mathbf{B}_{38} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H II} \\ \end{array}$

### References

• Y. Sun, J. Lv, Y. Xie, H. Liu, and Y. Ma, Route to a Superconducting Phase above Room Temperature in Electron–Doped Hydride Compounds under High Pressure, Phys. Rev. Lett. 123, 097001 (2019), doi:10.1103/PhysRevLett.123.097001.

### Prototype Generator

aflow --proto=A16B2C_cF152_227_eg_d_a --params=