Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B_hP8_158_d_a

  • 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)

$\beta$–RuCl3 Structure: A3B_hP8_158_d_a

Picture of Structure; Click for Big Picture
Prototype : RuCl3
AFLOW prototype label : A3B_hP8_158_d_a
Strukturbericht designation : None
Pearson symbol : hP8
Space group number : 158
Space group symbol : $P3c1$
AFLOW prototype command : aflow --proto=A3B_hP8_158_d_a
--params=
$a$,$c/a$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$


  • Pearson comments that space groups #185, #188, #193, could not be rejected, but this structure is consistent with space group #158. We also provide the structure with space group #185: β–RuCl3 (A3B_hP8_185_c_a) structure.

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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ru} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ru} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{2}+y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \mathbf{B}_{4} & = & -y_{2} \, \mathbf{a}_{1} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \mathbf{B}_{5} & = & \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}+\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \mathbf{B}_{6} & = & -y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{2}+y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \mathbf{B}_{7} & = & \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(x_{2}-\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(6d\right) & \text{Cl} \\ \end{array} \]

References

  • J. M. Fletcher, W. E. Gardner, A. C. Fox, and G. Topping, X–Ray, infrared, and magnetic studies of α– and β–ruthenium trichloride, J. Chem. Soc. A pp. 1038–1045 (1967), doi:10.1039/J19670001038.

Geometry files


Prototype Generator

aflow --proto=A3B_hP8_158_d_a --params=

Species:

Running:

Output: