Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB2C12D4_tP76_75_2a2b_2d_12d_4d-001

This structure originally had the label AB2C12D4_tP76_75_2a2b_2d_12d_4d. Calls to that address will be redirected here.

If you are using this page, please cite:
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)

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https://aflow.org/p/MXLF
or https://aflow.org/p/AB2C12D4_tP76_75_2a2b_2d_12d_4d-001
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Hexagonal Hollandite (BaRu$_{4}$Cr$_{2}$O$_{12}$) Structure: AB2C12D4_tP76_75_2a2b_2d_12d_4d-001

Picture of Structure; Click for Big Picture
Prototype BaCr$_{2}$O$_{12}$Ru$_{4}$
AFLOW prototype label AB2C12D4_tP76_75_2a2b_2d_12d_4d-001
Mineral name hollandite
ICSD 100578
Pearson symbol tP76
Space group number 75
Space group symbol $P4$
AFLOW prototype command aflow --proto=AB2C12D4_tP76_75_2a2b_2d_12d_4d-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}$

  • This is a superstructure of conventional hollandite.
  • (Cadé, 1979) and the ICSD entry omit the coordinates for the O-VI atom. We have used the values provided by (Villars, 2016).
  • Space group $P4$ #74 allows for an arbitrary origin of the $z$-axis. We follow (Villars, 2016) and set $z_{1} = 0$ for the Ba-I atom. This is a shift of $c/2$ from the origin used by (Cadé, 1979).

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $z_{1} \, \mathbf{a}_{3}$ = $c z_{1} \,\mathbf{\hat{z}}$ (1a) Ba I
$\mathbf{B_{2}}$ = $z_{2} \, \mathbf{a}_{3}$ = $c z_{2} \,\mathbf{\hat{z}}$ (1a) Ba II
$\mathbf{B_{3}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (1b) Ba III
$\mathbf{B_{4}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (1b) Ba IV
$\mathbf{B_{5}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Cr I
$\mathbf{B_{6}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Cr I
$\mathbf{B_{7}}$ = $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Cr I
$\mathbf{B_{8}}$ = $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Cr I
$\mathbf{B_{9}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Cr II
$\mathbf{B_{10}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Cr II
$\mathbf{B_{11}}$ = $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Cr II
$\mathbf{B_{12}}$ = $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Cr II
$\mathbf{B_{13}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{14}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{15}}$ = $- y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{16}}$ = $y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{17}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{18}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{19}}$ = $- y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{20}}$ = $y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{21}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{22}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{23}}$ = $- y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{24}}$ = $y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{25}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{26}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{27}}$ = $- y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{28}}$ = $y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{29}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{30}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{31}}$ = $- y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{32}}$ = $y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{33}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{34}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{35}}$ = $- y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{36}}$ = $y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{37}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{38}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{39}}$ = $- y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{40}}$ = $y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{41}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{42}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{43}}$ = $- y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{44}}$ = $y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{45}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{46}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{47}}$ = $- y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{48}}$ = $y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{49}}$ = $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{50}}$ = $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{51}}$ = $- y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{52}}$ = $y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{53}}$ = $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{54}}$ = $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{55}}$ = $- y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{56}}$ = $y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{57}}$ = $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O XII
$\mathbf{B_{58}}$ = $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O XII
$\mathbf{B_{59}}$ = $- y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $- a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O XII
$\mathbf{B_{60}}$ = $y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O XII
$\mathbf{B_{61}}$ = $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) Ru I
$\mathbf{B_{62}}$ = $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) Ru I
$\mathbf{B_{63}}$ = $- y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $- a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) Ru I
$\mathbf{B_{64}}$ = $y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) Ru I
$\mathbf{B_{65}}$ = $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) Ru II
$\mathbf{B_{66}}$ = $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) Ru II
$\mathbf{B_{67}}$ = $- y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $- a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) Ru II
$\mathbf{B_{68}}$ = $y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) Ru II
$\mathbf{B_{69}}$ = $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a x_{21} \,\mathbf{\hat{x}}+a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) Ru III
$\mathbf{B_{70}}$ = $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $- a x_{21} \,\mathbf{\hat{x}}- a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) Ru III
$\mathbf{B_{71}}$ = $- y_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $- a y_{21} \,\mathbf{\hat{x}}+a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) Ru III
$\mathbf{B_{72}}$ = $y_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a y_{21} \,\mathbf{\hat{x}}- a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) Ru III
$\mathbf{B_{73}}$ = $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a x_{22} \,\mathbf{\hat{x}}+a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) Ru IV
$\mathbf{B_{74}}$ = $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $- a x_{22} \,\mathbf{\hat{x}}- a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) Ru IV
$\mathbf{B_{75}}$ = $- y_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $- a y_{22} \,\mathbf{\hat{x}}+a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) Ru IV
$\mathbf{B_{76}}$ = $y_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a y_{22} \,\mathbf{\hat{x}}- a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) Ru IV

References

Found in

  • P. Villars, Ba0.65Ru2.7Cr1.3O8 (BaCr2Ru4O12) Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.

Prototype Generator

aflow --proto=AB2C12D4_tP76_75_2a2b_2d_12d_4d --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22}$

Species:

Running:

Output: