Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A22B5_oF216_43_11b_a2b-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/15LF
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Al$_{22}$Mo$_{5}$ Structure: A22B5_oF216_43_11b_a2b-001

Picture of Structure; Click for Big Picture
Prototype Al$_{22}$Mo$_{5}$
AFLOW prototype label A22B5_oF216_43_11b_a2b-001
ICSD 400888
Pearson symbol oF216
Space group number 43
Space group symbol $Fdd2$
AFLOW prototype command aflow --proto=A22B5_oF216_43_11b_a2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$

  • Space group $Fdd2$ #43 allows an arbitrary choice of the origin of the $z$-axis. Here we follow (Grin, 1995) and set $z_{1} = 0$ for the Mo-I atom.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ = $c z_{1} \,\mathbf{\hat{z}}$ (8a) Mo I
$\mathbf{B_{2}}$ = $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (8a) Mo I
$\mathbf{B_{3}}$ = $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (16b) Al I
$\mathbf{B_{4}}$ = $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (16b) Al I
$\mathbf{B_{5}}$ = $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al I
$\mathbf{B_{6}}$ = $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al I
$\mathbf{B_{7}}$ = $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16b) Al II
$\mathbf{B_{8}}$ = $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16b) Al II
$\mathbf{B_{9}}$ = $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al II
$\mathbf{B_{10}}$ = $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al II
$\mathbf{B_{11}}$ = $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (16b) Al III
$\mathbf{B_{12}}$ = $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (16b) Al III
$\mathbf{B_{13}}$ = $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al III
$\mathbf{B_{14}}$ = $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al III
$\mathbf{B_{15}}$ = $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (16b) Al IV
$\mathbf{B_{16}}$ = $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (16b) Al IV
$\mathbf{B_{17}}$ = $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al IV
$\mathbf{B_{18}}$ = $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al IV
$\mathbf{B_{19}}$ = $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (16b) Al V
$\mathbf{B_{20}}$ = $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (16b) Al V
$\mathbf{B_{21}}$ = $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al V
$\mathbf{B_{22}}$ = $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al V
$\mathbf{B_{23}}$ = $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (16b) Al VI
$\mathbf{B_{24}}$ = $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (16b) Al VI
$\mathbf{B_{25}}$ = $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VI
$\mathbf{B_{26}}$ = $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VI
$\mathbf{B_{27}}$ = $\left(- x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (16b) Al VII
$\mathbf{B_{28}}$ = $\left(x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(- x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (16b) Al VII
$\mathbf{B_{29}}$ = $- \left(x_{8} + y_{8} - z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} - z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VII
$\mathbf{B_{30}}$ = $\left(x_{8} + y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8} - z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8} + z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VII
$\mathbf{B_{31}}$ = $\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (16b) Al VIII
$\mathbf{B_{32}}$ = $\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (16b) Al VIII
$\mathbf{B_{33}}$ = $- \left(x_{9} + y_{9} - z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} - z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VIII
$\mathbf{B_{34}}$ = $\left(x_{9} + y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9} - z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9} + z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al VIII
$\mathbf{B_{35}}$ = $\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (16b) Al IX
$\mathbf{B_{36}}$ = $\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (16b) Al IX
$\mathbf{B_{37}}$ = $- \left(x_{10} + y_{10} - z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} - z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al IX
$\mathbf{B_{38}}$ = $\left(x_{10} + y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10} - z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10} + z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al IX
$\mathbf{B_{39}}$ = $\left(- x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (16b) Al X
$\mathbf{B_{40}}$ = $\left(x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(- x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (16b) Al X
$\mathbf{B_{41}}$ = $- \left(x_{11} + y_{11} - z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} - z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al X
$\mathbf{B_{42}}$ = $\left(x_{11} + y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{11} + y_{11} - z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11} + z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al X
$\mathbf{B_{43}}$ = $\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (16b) Al XI
$\mathbf{B_{44}}$ = $\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (16b) Al XI
$\mathbf{B_{45}}$ = $- \left(x_{12} + y_{12} - z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} - z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{12} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al XI
$\mathbf{B_{46}}$ = $\left(x_{12} + y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12} - z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{12} - y_{12} + z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{12} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Al XI
$\mathbf{B_{47}}$ = $\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (16b) Mo II
$\mathbf{B_{48}}$ = $\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (16b) Mo II
$\mathbf{B_{49}}$ = $- \left(x_{13} + y_{13} - z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} - z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{13} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Mo II
$\mathbf{B_{50}}$ = $\left(x_{13} + y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13} - z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13} + z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{13} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Mo II
$\mathbf{B_{51}}$ = $\left(- x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - y_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14} - z_{14}\right) \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (16b) Mo III
$\mathbf{B_{52}}$ = $\left(x_{14} - y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(- x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14} + z_{14}\right) \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (16b) Mo III
$\mathbf{B_{53}}$ = $- \left(x_{14} + y_{14} - z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{14} + y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14} - z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{14} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Mo III
$\mathbf{B_{54}}$ = $\left(x_{14} + y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{14} + y_{14} - z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14} + z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{14} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16b) Mo III

References

  • Y. N. Grin, M. Ellner, K. Peters, and J. C. Schuster, The crystal structures of Mo$_{4}$Al$_{17}$ and Mo$_{5}$Al$_{22}$, Z. Kristallogr. 210, 96–99 (1995), doi:10.1524/zkri.1995.210.2.96.

Prototype Generator

aflow --proto=A22B5_oF216_43_11b_a2b --params=$a,b/a,c/a,z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$

Species:

Running:

Output: