Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B_hR8_167_e_b

  • 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)

FeF3 ($D0_{12}$) Structure : A3B_hR8_167_e_b

Picture of Structure; Click for Big Picture
Prototype : F3Fe
AFLOW prototype label : A3B_hR8_167_e_b
Strukturbericht designation : $D0_{12}$
Pearson symbol : hR8
Space group number : 167
Space group symbol : $R\bar{3}c$
AFLOW prototype command : aflow --proto=A3B_hR8_167_e_b
--params=
$a$,$c/a$,$x_{2}$


Other compounds with this structure

  • CoF3, RuF3, RhF3, PdF3, IrF3, $\alpha$–AlF3, and AlH3

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

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(2b\right) & \text{Fe} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Fe} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(- \frac{1}{8} +\frac{1}{2}x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{\sqrt{3}}{8}-\frac{\sqrt{3}}{2}x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & \left(- \frac{1}{8} +\frac{1}{2}x_{2}\right)a \, \mathbf{\hat{x}} + \left(- \frac{\sqrt{3}}{8} +\frac{\sqrt{3}}{2}x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\left(\frac{1}{2}x_{2}+\frac{3}{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{8\sqrt{3}} +\frac{\sqrt{3}}{2}x_{2}\right)a \, \mathbf{\hat{y}} + \frac{5}{12}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{8}-\frac{1}{2}x_{2}\right)a \, \mathbf{\hat{x}}-\left(\frac{\sqrt{3}}{2}x_{2}+\frac{5}{8\sqrt{3}}\right)a \, \mathbf{\hat{y}} + \frac{5}{12}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{5}{12}c \, \mathbf{\hat{z}} & \left(6e\right) & \text{F} \\ \end{array} \]

References

  • M. A. Hepworth, K. H. Jack, R. D. Peacock, and G. J. Westland, The crystal structures of the trifluorides of iron, cobalt, ruthenium, rhodium, palladium and iridium, Acta Cryst. 10, 63–69 (1957), doi:10.1107/S0365110X57000158.

Geometry files


Prototype Generator

aflow --proto=A3B_hR8_167_e_b --params=

Species:

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