# 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)

## Bararite (Trigonal (NH4)2SiF6, $J1_{6}$) Structure : A6B2C_hP9_164_i_d_a

 Prototype : F6(NH4)2Si AFLOW prototype label : A6B2C_hP9_164_i_d_a Strukturbericht designation : $J1_{6}$ Pearson symbol : hP9 Space group number : 164 Space group symbol : $P\bar{3}m1$ AFLOW prototype command : aflow --proto=A6B2C_hP9_164_i_d_a --params=$a$,$c/a$,$z_{2}$,$x_{3}$,$z_{3}$

• Bararite is a trigonal form of (NH4)2SiF6, metastable at room temperature. The room temperature stable form is cubic cryptohalite, which takes on the $J1_{1}$ structure. Except for the hydrogen atoms, this structure is very similar to $J1_{13}$, K2GeF6. (Schlemper, 1966) state that the hydrogen atoms are on ($2d$) and ($6i$) sites, but were not able to determine the coordinates because of large thermal fluctuations. They were to study the system at 77 K, but we have not found any evidence that this work was ever published.
• The positions of the hydrogen atoms in the NH4 ions were not determined, so we only provide the positions of the nitrogen atoms (labeled as NH4).

### Trigonal Hexagonal primitive vectors:

$\begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array}$

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{Si} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{NH_{4}} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{NH_{4}} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{6} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{8} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \end{array}$

### References

• E. O. Schlemper and W. C. Hamilton, On the Structure of Trigonal Ammonium Flourosilicate, J. Chem. Phys. 45, 408–409 (1966), doi:10.1063/1.2716548.

### Found in

• J. Fábry, J. Chval, and V. Petrícek, A new modification of diammonium hexafluorosilicate, (NH4)2SiF6, Acta Crystallogr. E 57, i90–i91 (2001), doi:10.1107/S160053680101501X.

### Prototype Generator

aflow --proto=A6B2C_hP9_164_i_d_a --params=