Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B7C2_aP44_2_4i_14i_4i-001

This structure originally had the label A2B7C2_aP44_2_4i_14i_4i. Calls to that address will be redirected here.

If you are using this page, please cite:
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)

Links to this page

https://aflow.org/p/VN5Q
or https://aflow.org/p/A2B7C2_aP44_2_4i_14i_4i-001
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α-Ho$_{2}$Si$_{2}$O$_{7}$ Structure: A2B7C2_aP44_2_4i_14i_4i-001

Picture of Structure; Click for Big Picture
Prototype Ho$_{2}$O$_{7}$Si$_{2}$
AFLOW prototype label A2B7C2_aP44_2_4i_14i_4i-001
ICSD 23619
Pearson symbol aP44
Space group number 2
Space group symbol $P\overline{1}$
AFLOW prototype command aflow --proto=A2B7C2_aP44_2_4i_14i_4i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \alpha, \allowbreak \beta, \allowbreak \gamma, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}$

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \cos{\gamma} \,\mathbf{\hat{x}}+b \sin{\gamma} \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c_{x} \,\mathbf{\hat{x}}+c_{y} \,\mathbf{\hat{y}}+c_{z} \,\mathbf{\hat{z}}\\c_{x} & = & c \cos{\beta} \\ c_{y} & = & c (\cos{\alpha} - \cos{\beta}\cos{\gamma}) / {\sin{\gamma}} \\ c_{z} & = & \sqrt{c^2 - c_{x}^2- c_{y}^2} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $\left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}+\left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}+c_{z} z_{1} \,\mathbf{\hat{z}}$ (2i) Ho I
$\mathbf{B_{2}}$ = $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ = $- \left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}- \left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}- c_{z} z_{1} \,\mathbf{\hat{z}}$ (2i) Ho I
$\mathbf{B_{3}}$ = $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $\left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}+\left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}+c_{z} z_{2} \,\mathbf{\hat{z}}$ (2i) Ho II
$\mathbf{B_{4}}$ = $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ = $- \left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}- \left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}- c_{z} z_{2} \,\mathbf{\hat{z}}$ (2i) Ho II
$\mathbf{B_{5}}$ = $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}+\left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}+c_{z} z_{3} \,\mathbf{\hat{z}}$ (2i) Ho III
$\mathbf{B_{6}}$ = $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- \left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}- \left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}- c_{z} z_{3} \,\mathbf{\hat{z}}$ (2i) Ho III
$\mathbf{B_{7}}$ = $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\left(a x_{4} + b y_{4} \cos{\gamma} + c_{x} z_{4}\right) \,\mathbf{\hat{x}}+\left(b y_{4} \sin{\gamma} + c_{y} z_{4}\right) \,\mathbf{\hat{y}}+c_{z} z_{4} \,\mathbf{\hat{z}}$ (2i) Ho IV
$\mathbf{B_{8}}$ = $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- \left(a x_{4} + b y_{4} \cos{\gamma} + c_{x} z_{4}\right) \,\mathbf{\hat{x}}- \left(b y_{4} \sin{\gamma} + c_{y} z_{4}\right) \,\mathbf{\hat{y}}- c_{z} z_{4} \,\mathbf{\hat{z}}$ (2i) Ho IV
$\mathbf{B_{9}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\left(a x_{5} + b y_{5} \cos{\gamma} + c_{x} z_{5}\right) \,\mathbf{\hat{x}}+\left(b y_{5} \sin{\gamma} + c_{y} z_{5}\right) \,\mathbf{\hat{y}}+c_{z} z_{5} \,\mathbf{\hat{z}}$ (2i) O I
$\mathbf{B_{10}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \left(a x_{5} + b y_{5} \cos{\gamma} + c_{x} z_{5}\right) \,\mathbf{\hat{x}}- \left(b y_{5} \sin{\gamma} + c_{y} z_{5}\right) \,\mathbf{\hat{y}}- c_{z} z_{5} \,\mathbf{\hat{z}}$ (2i) O I
$\mathbf{B_{11}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\left(a x_{6} + b y_{6} \cos{\gamma} + c_{x} z_{6}\right) \,\mathbf{\hat{x}}+\left(b y_{6} \sin{\gamma} + c_{y} z_{6}\right) \,\mathbf{\hat{y}}+c_{z} z_{6} \,\mathbf{\hat{z}}$ (2i) O II
$\mathbf{B_{12}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \left(a x_{6} + b y_{6} \cos{\gamma} + c_{x} z_{6}\right) \,\mathbf{\hat{x}}- \left(b y_{6} \sin{\gamma} + c_{y} z_{6}\right) \,\mathbf{\hat{y}}- c_{z} z_{6} \,\mathbf{\hat{z}}$ (2i) O II
$\mathbf{B_{13}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\left(a x_{7} + b y_{7} \cos{\gamma} + c_{x} z_{7}\right) \,\mathbf{\hat{x}}+\left(b y_{7} \sin{\gamma} + c_{y} z_{7}\right) \,\mathbf{\hat{y}}+c_{z} z_{7} \,\mathbf{\hat{z}}$ (2i) O III
$\mathbf{B_{14}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- \left(a x_{7} + b y_{7} \cos{\gamma} + c_{x} z_{7}\right) \,\mathbf{\hat{x}}- \left(b y_{7} \sin{\gamma} + c_{y} z_{7}\right) \,\mathbf{\hat{y}}- c_{z} z_{7} \,\mathbf{\hat{z}}$ (2i) O III
$\mathbf{B_{15}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $\left(a x_{8} + b y_{8} \cos{\gamma} + c_{x} z_{8}\right) \,\mathbf{\hat{x}}+\left(b y_{8} \sin{\gamma} + c_{y} z_{8}\right) \,\mathbf{\hat{y}}+c_{z} z_{8} \,\mathbf{\hat{z}}$ (2i) O IV
$\mathbf{B_{16}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- \left(a x_{8} + b y_{8} \cos{\gamma} + c_{x} z_{8}\right) \,\mathbf{\hat{x}}- \left(b y_{8} \sin{\gamma} + c_{y} z_{8}\right) \,\mathbf{\hat{y}}- c_{z} z_{8} \,\mathbf{\hat{z}}$ (2i) O IV
$\mathbf{B_{17}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $\left(a x_{9} + b y_{9} \cos{\gamma} + c_{x} z_{9}\right) \,\mathbf{\hat{x}}+\left(b y_{9} \sin{\gamma} + c_{y} z_{9}\right) \,\mathbf{\hat{y}}+c_{z} z_{9} \,\mathbf{\hat{z}}$ (2i) O V
$\mathbf{B_{18}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- \left(a x_{9} + b y_{9} \cos{\gamma} + c_{x} z_{9}\right) \,\mathbf{\hat{x}}- \left(b y_{9} \sin{\gamma} + c_{y} z_{9}\right) \,\mathbf{\hat{y}}- c_{z} z_{9} \,\mathbf{\hat{z}}$ (2i) O V
$\mathbf{B_{19}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $\left(a x_{10} + b y_{10} \cos{\gamma} + c_{x} z_{10}\right) \,\mathbf{\hat{x}}+\left(b y_{10} \sin{\gamma} + c_{y} z_{10}\right) \,\mathbf{\hat{y}}+c_{z} z_{10} \,\mathbf{\hat{z}}$ (2i) O VI
$\mathbf{B_{20}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- \left(a x_{10} + b y_{10} \cos{\gamma} + c_{x} z_{10}\right) \,\mathbf{\hat{x}}- \left(b y_{10} \sin{\gamma} + c_{y} z_{10}\right) \,\mathbf{\hat{y}}- c_{z} z_{10} \,\mathbf{\hat{z}}$ (2i) O VI
$\mathbf{B_{21}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $\left(a x_{11} + b y_{11} \cos{\gamma} + c_{x} z_{11}\right) \,\mathbf{\hat{x}}+\left(b y_{11} \sin{\gamma} + c_{y} z_{11}\right) \,\mathbf{\hat{y}}+c_{z} z_{11} \,\mathbf{\hat{z}}$ (2i) O VII
$\mathbf{B_{22}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- \left(a x_{11} + b y_{11} \cos{\gamma} + c_{x} z_{11}\right) \,\mathbf{\hat{x}}- \left(b y_{11} \sin{\gamma} + c_{y} z_{11}\right) \,\mathbf{\hat{y}}- c_{z} z_{11} \,\mathbf{\hat{z}}$ (2i) O VII
$\mathbf{B_{23}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $\left(a x_{12} + b y_{12} \cos{\gamma} + c_{x} z_{12}\right) \,\mathbf{\hat{x}}+\left(b y_{12} \sin{\gamma} + c_{y} z_{12}\right) \,\mathbf{\hat{y}}+c_{z} z_{12} \,\mathbf{\hat{z}}$ (2i) O VIII
$\mathbf{B_{24}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- \left(a x_{12} + b y_{12} \cos{\gamma} + c_{x} z_{12}\right) \,\mathbf{\hat{x}}- \left(b y_{12} \sin{\gamma} + c_{y} z_{12}\right) \,\mathbf{\hat{y}}- c_{z} z_{12} \,\mathbf{\hat{z}}$ (2i) O VIII
$\mathbf{B_{25}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $\left(a x_{13} + b y_{13} \cos{\gamma} + c_{x} z_{13}\right) \,\mathbf{\hat{x}}+\left(b y_{13} \sin{\gamma} + c_{y} z_{13}\right) \,\mathbf{\hat{y}}+c_{z} z_{13} \,\mathbf{\hat{z}}$ (2i) O IX
$\mathbf{B_{26}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ = $- \left(a x_{13} + b y_{13} \cos{\gamma} + c_{x} z_{13}\right) \,\mathbf{\hat{x}}- \left(b y_{13} \sin{\gamma} + c_{y} z_{13}\right) \,\mathbf{\hat{y}}- c_{z} z_{13} \,\mathbf{\hat{z}}$ (2i) O IX
$\mathbf{B_{27}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $\left(a x_{14} + b y_{14} \cos{\gamma} + c_{x} z_{14}\right) \,\mathbf{\hat{x}}+\left(b y_{14} \sin{\gamma} + c_{y} z_{14}\right) \,\mathbf{\hat{y}}+c_{z} z_{14} \,\mathbf{\hat{z}}$ (2i) O X
$\mathbf{B_{28}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ = $- \left(a x_{14} + b y_{14} \cos{\gamma} + c_{x} z_{14}\right) \,\mathbf{\hat{x}}- \left(b y_{14} \sin{\gamma} + c_{y} z_{14}\right) \,\mathbf{\hat{y}}- c_{z} z_{14} \,\mathbf{\hat{z}}$ (2i) O X
$\mathbf{B_{29}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $\left(a x_{15} + b y_{15} \cos{\gamma} + c_{x} z_{15}\right) \,\mathbf{\hat{x}}+\left(b y_{15} \sin{\gamma} + c_{y} z_{15}\right) \,\mathbf{\hat{y}}+c_{z} z_{15} \,\mathbf{\hat{z}}$ (2i) O XI
$\mathbf{B_{30}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ = $- \left(a x_{15} + b y_{15} \cos{\gamma} + c_{x} z_{15}\right) \,\mathbf{\hat{x}}- \left(b y_{15} \sin{\gamma} + c_{y} z_{15}\right) \,\mathbf{\hat{y}}- c_{z} z_{15} \,\mathbf{\hat{z}}$ (2i) O XI
$\mathbf{B_{31}}$ = $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $\left(a x_{16} + b y_{16} \cos{\gamma} + c_{x} z_{16}\right) \,\mathbf{\hat{x}}+\left(b y_{16} \sin{\gamma} + c_{y} z_{16}\right) \,\mathbf{\hat{y}}+c_{z} z_{16} \,\mathbf{\hat{z}}$ (2i) O XII
$\mathbf{B_{32}}$ = $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ = $- \left(a x_{16} + b y_{16} \cos{\gamma} + c_{x} z_{16}\right) \,\mathbf{\hat{x}}- \left(b y_{16} \sin{\gamma} + c_{y} z_{16}\right) \,\mathbf{\hat{y}}- c_{z} z_{16} \,\mathbf{\hat{z}}$ (2i) O XII
$\mathbf{B_{33}}$ = $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $\left(a x_{17} + b y_{17} \cos{\gamma} + c_{x} z_{17}\right) \,\mathbf{\hat{x}}+\left(b y_{17} \sin{\gamma} + c_{y} z_{17}\right) \,\mathbf{\hat{y}}+c_{z} z_{17} \,\mathbf{\hat{z}}$ (2i) O XIII
$\mathbf{B_{34}}$ = $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ = $- \left(a x_{17} + b y_{17} \cos{\gamma} + c_{x} z_{17}\right) \,\mathbf{\hat{x}}- \left(b y_{17} \sin{\gamma} + c_{y} z_{17}\right) \,\mathbf{\hat{y}}- c_{z} z_{17} \,\mathbf{\hat{z}}$ (2i) O XIII
$\mathbf{B_{35}}$ = $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $\left(a x_{18} + b y_{18} \cos{\gamma} + c_{x} z_{18}\right) \,\mathbf{\hat{x}}+\left(b y_{18} \sin{\gamma} + c_{y} z_{18}\right) \,\mathbf{\hat{y}}+c_{z} z_{18} \,\mathbf{\hat{z}}$ (2i) O XIV
$\mathbf{B_{36}}$ = $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ = $- \left(a x_{18} + b y_{18} \cos{\gamma} + c_{x} z_{18}\right) \,\mathbf{\hat{x}}- \left(b y_{18} \sin{\gamma} + c_{y} z_{18}\right) \,\mathbf{\hat{y}}- c_{z} z_{18} \,\mathbf{\hat{z}}$ (2i) O XIV
$\mathbf{B_{37}}$ = $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $\left(a x_{19} + b y_{19} \cos{\gamma} + c_{x} z_{19}\right) \,\mathbf{\hat{x}}+\left(b y_{19} \sin{\gamma} + c_{y} z_{19}\right) \,\mathbf{\hat{y}}+c_{z} z_{19} \,\mathbf{\hat{z}}$ (2i) Si I
$\mathbf{B_{38}}$ = $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ = $- \left(a x_{19} + b y_{19} \cos{\gamma} + c_{x} z_{19}\right) \,\mathbf{\hat{x}}- \left(b y_{19} \sin{\gamma} + c_{y} z_{19}\right) \,\mathbf{\hat{y}}- c_{z} z_{19} \,\mathbf{\hat{z}}$ (2i) Si I
$\mathbf{B_{39}}$ = $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $\left(a x_{20} + b y_{20} \cos{\gamma} + c_{x} z_{20}\right) \,\mathbf{\hat{x}}+\left(b y_{20} \sin{\gamma} + c_{y} z_{20}\right) \,\mathbf{\hat{y}}+c_{z} z_{20} \,\mathbf{\hat{z}}$ (2i) Si II
$\mathbf{B_{40}}$ = $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ = $- \left(a x_{20} + b y_{20} \cos{\gamma} + c_{x} z_{20}\right) \,\mathbf{\hat{x}}- \left(b y_{20} \sin{\gamma} + c_{y} z_{20}\right) \,\mathbf{\hat{y}}- c_{z} z_{20} \,\mathbf{\hat{z}}$ (2i) Si II
$\mathbf{B_{41}}$ = $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $\left(a x_{21} + b y_{21} \cos{\gamma} + c_{x} z_{21}\right) \,\mathbf{\hat{x}}+\left(b y_{21} \sin{\gamma} + c_{y} z_{21}\right) \,\mathbf{\hat{y}}+c_{z} z_{21} \,\mathbf{\hat{z}}$ (2i) Si III
$\mathbf{B_{42}}$ = $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ = $- \left(a x_{21} + b y_{21} \cos{\gamma} + c_{x} z_{21}\right) \,\mathbf{\hat{x}}- \left(b y_{21} \sin{\gamma} + c_{y} z_{21}\right) \,\mathbf{\hat{y}}- c_{z} z_{21} \,\mathbf{\hat{z}}$ (2i) Si III
$\mathbf{B_{43}}$ = $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $\left(a x_{22} + b y_{22} \cos{\gamma} + c_{x} z_{22}\right) \,\mathbf{\hat{x}}+\left(b y_{22} \sin{\gamma} + c_{y} z_{22}\right) \,\mathbf{\hat{y}}+c_{z} z_{22} \,\mathbf{\hat{z}}$ (2i) Si IV
$\mathbf{B_{44}}$ = $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ = $- \left(a x_{22} + b y_{22} \cos{\gamma} + c_{x} z_{22}\right) \,\mathbf{\hat{x}}- \left(b y_{22} \sin{\gamma} + c_{y} z_{22}\right) \,\mathbf{\hat{y}}- c_{z} z_{22} \,\mathbf{\hat{z}}$ (2i) Si IV

References

  • J. Felsche, A new silicate structure containing linear [Si$_{3}$O$_{10}$] groups, Naturwissenschaften 59, 35–36 (1972), doi:10.1007/BF00594623.

Found in

  • A. I. Becerro and A. Escudero, Revision of the crystallographic data of polymorphic Y$_{2}$Si$_{2}$O$_{7}$ and Y$_{2}$SiO$_{5}$ compounds, Phase Transit. 77, 1093–1102 (2004), doi:10.1080/01411590412331282814.

Prototype Generator

aflow --proto=A2B7C2_aP44_2_4i_14i_4i --params=$a,b/a,c/a,\alpha,\beta,\gamma,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22}$

Species:

Running:

Output: