Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A13BC18D20E5_cF228_216_dh_b_fh_2eh_ce

  • 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)

Zunyite [Al13(OH,F)18Si5O20Cl, $S0_{8}$] Structure : A13BC18D20E5_cF228_216_dh_b_fh_2eh_ce

Picture of Structure; Click for Big Picture
Prototype : Al13ClF18O20Si5
AFLOW prototype label : A13BC18D20E5_cF228_216_dh_b_fh_2eh_ce
Strukturbericht designation : $S0_{8}$
Pearson symbol : cF228
Space group number : 216
Space group symbol : $F\bar{4}3m$
AFLOW prototype command : aflow --proto=A13BC18D20E5_cF228_216_dh_b_fh_2eh_ce
--params=$a$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$
View the structure from several different perspectives
View the primitive and conventional cell
  • We use the structure proposed by (Kamb, 1960), a refinement of the original (Pauling, 1933) $S0_{8}$ structure. The only major difference is the $y$ coordinate of the OH/F–I site, which is now at a more reasonable distance from the chlorine atom.
  • For easy of visualization, we have used fluorine atoms to represent all of the (OH,F)18 positions, but in reality the system is dominated by OH, not F. Kamb argues that the physics of hydrogen bonding makes it likely that the actual structure has composition (OH)16F2, with the fluorine atoms substituting for OH on the second ($48h$) site.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]
Picture of Structure; Click for Big Picture

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \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(4b\right) & \text{Cl} \\ \mathbf{B}_{2} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(4c\right) & \text{Si I} \\ \mathbf{B}_{3} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(4d\right) & \text{Al I} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O I} \\ \mathbf{B}_{5} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-3x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O I} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{1}-3x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O I} \\ \mathbf{B}_{7} & = & -3x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O I} \\ \mathbf{B}_{8} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O II} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-3x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O II} \\ \mathbf{B}_{10} & = & x_{5} \, \mathbf{a}_{1}-3x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O II} \\ \mathbf{B}_{11} & = & -3x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{O II} \\ \mathbf{B}_{12} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{Si II} \\ \mathbf{B}_{13} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2}-3x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{Si II} \\ \mathbf{B}_{14} & = & x_{6} \, \mathbf{a}_{1}-3x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{Si II} \\ \mathbf{B}_{15} & = & -3x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(16e\right) & \text{Si II} \\ \mathbf{B}_{16} & = & -x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{17} & = & x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{18} & = & x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{y}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{19} & = & -x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{y}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{20} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{z}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{21} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{z}} & \left(24f\right) & \text{F I} \\ \mathbf{B}_{22} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{23} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{24} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{25} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{26} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{27} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{28} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{29} & = & z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{30} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{31} & = & z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{32} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{33} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{Al II} \\ \mathbf{B}_{34} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{35} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{36} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{37} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{38} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{39} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{40} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{41} & = & z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{42} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{43} & = & z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{44} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{45} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{F II} \\ \mathbf{B}_{46} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{47} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{48} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{49} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{50} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{51} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{52} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{53} & = & z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{54} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{55} & = & z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{56} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \mathbf{B}_{57} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O III} \\ \end{array} \]

References

  • L. Pauling, The Crystal Structure of Zunyite, Al13Si5O20(OH,F)18Cl, Zeitschrift für Kristallographie – Crystalline Materials 84, 442–452 (1933), doi:10.1524/zkri.1933.84.1.442.

Geometry files

Prototype Generator

aflow --proto=A13BC18D20E5_cF228_216_dh_b_fh_2eh_ce --params=

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