Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001

If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

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https://aflow.org/p/GGPS
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Y$_{3}$Cu$_{9}$(OH)$_{19}$Cl$_{8}$ Structure: A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001

Picture of Structure; Click for Big Picture
Prototype Cl$_{3}$Cu$_{9}$H$_{19}$O$_{19}$Y$_{3}$
AFLOW prototype label A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001
CCDC 1532410
Pearson symbol hR63
Space group number 148
Space group symbol $R\overline{3}$
AFLOW prototype command aflow --proto=A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$

  • Only 1/6 of the sites allocated for H-I (18f) are occupied. These H-I hydrogen sites are arranged in hexagons around the oxygen O-I atoms. As the separation between them is only 0.82Å it is likely that the atoms are all in one of the two possible isosceles triangles surrounding each oxygen.
  • Hexagonal settings of this structure can be obtained with the option --hex.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (1a) O I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (1b) Y I
$\mathbf{B_{3}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $c x_{3} \,\mathbf{\hat{z}}$ (2c) Cl I
$\mathbf{B_{4}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- c x_{3} \,\mathbf{\hat{z}}$ (2c) Cl I
$\mathbf{B_{5}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $c x_{4} \,\mathbf{\hat{z}}$ (2c) Y II
$\mathbf{B_{6}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $- c x_{4} \,\mathbf{\hat{z}}$ (2c) Y II
$\mathbf{B_{7}}$ = $\frac{1}{2} \, \mathbf{a}_{1}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Cu I
$\mathbf{B_{8}}$ = $\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Cu I
$\mathbf{B_{9}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Cu I
$\mathbf{B_{10}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{11}}$ = $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{12}}$ = $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{13}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{14}}$ = $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{15}}$ = $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (6f) Cl II
$\mathbf{B_{16}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{17}}$ = $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{18}}$ = $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{19}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - 2 y_{7} + z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{20}}$ = $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{7} - y_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{21}}$ = $- y_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} + y_{7} - 2 z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{7} + y_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (6f) Cu II
$\mathbf{B_{22}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{23}}$ = $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{24}}$ = $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{25}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - 2 y_{8} + z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{26}}$ = $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{8} - y_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{27}}$ = $- y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} + y_{8} - 2 z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{8} + y_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ (6f) H I
$\mathbf{B_{28}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - 2 y_{9} + z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{29}}$ = $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{9} - y_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{30}}$ = $y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} + y_{9} - 2 z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{31}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - 2 y_{9} + z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{32}}$ = $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{9} - y_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{33}}$ = $- y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} + y_{9} - 2 z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{9} + y_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ (6f) H II
$\mathbf{B_{34}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} - 2 y_{10} + z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{35}}$ = $z_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{10} - y_{10} - z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{36}}$ = $y_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} + y_{10} - 2 z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{37}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} - 2 y_{10} + z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{38}}$ = $- z_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{10} - y_{10} - z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{39}}$ = $- y_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} + y_{10} - 2 z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{10} + y_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ (6f) H III
$\mathbf{B_{40}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} - 2 y_{11} + z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{41}}$ = $z_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{11} - y_{11} - z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{42}}$ = $y_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} + y_{11} - 2 z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{43}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} - 2 y_{11} + z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{44}}$ = $- z_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{11} - y_{11} - z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{45}}$ = $- y_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} + y_{11} - 2 z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{11} + y_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ (6f) H IV
$\mathbf{B_{46}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{47}}$ = $z_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{48}}$ = $y_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{49}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{50}}$ = $- z_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{51}}$ = $- y_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ (6f) O II
$\mathbf{B_{52}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{53}}$ = $z_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{54}}$ = $y_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{55}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{56}}$ = $- z_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{57}}$ = $- y_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ (6f) O III
$\mathbf{B_{58}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV
$\mathbf{B_{59}}$ = $z_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV
$\mathbf{B_{60}}$ = $y_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV
$\mathbf{B_{61}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV
$\mathbf{B_{62}}$ = $- z_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV
$\mathbf{B_{63}}$ = $- y_{14} \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ (6f) O IV

References

  • P. Puphal, M. Bolte, D. Sheptyakov, A. Pustogow, K. Kliemt, M. Dressel, M. Baenitze, and C. Krellner, Strong magnetic frustration in Y$_{3}$Cu$_{9}$(OH)$_{19}$Cl$_{8}$: a distorted kagome antiferromagnet, J. Mater. Chem. C 5, 2629–2635 (2017), doi:10.1039/C6TC05110C.

Prototype Generator

aflow --proto=A8B9C24D19E3_hR63_148_cf_df_4f_a3f_bc --params=$a,c/a,x_{3},x_{4},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$

Species:

Running:

Output: