Catapleiite (Na2ZrSi3O9·2H2O) Structure : A2B3C9D3E_mC144_15_2f_bcdef_9f_3f_ae

Picture of Structure; Click for Big Picture
Prototype : (H2O)2Na2O9Si3Zr
AFLOW prototype label : A2B3C9D3E_mC144_15_2f_bcdef_9f_3f_ae
Strukturbericht designation : None
Pearson symbol : mC144
Space group number : 15
Space group symbol : $C2/c$
AFLOW prototype command : aflow --proto=A2B3C9D3E_mC144_15_2f_bcdef_9f_3f_ae
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{5}$,$y_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$,$x_{17}$,$y_{17}$,$z_{17}$,$x_{18}$,$y_{18}$,$z_{18}$,$x_{19}$,$y_{19}$,$z_{19}$,$x_{20}$,$y_{20}$,$z_{20}$,$x_{21}$,$y_{21}$,$z_{21}$


  • This is a refinement of the crystal structure of catapleiite. The original hexagonal structure was given the Strukturbericht designation $S3_{4}$ by (Gottfried, 1937).
  • The sodium atom sites are only 66.7% occupied in this structure. However, the stoichiometry in the AFLOW label treats the Na sites as fully occupied (i.e., a stoichiometric ratio of three as opposed to two).
  • (Ilyushin, 1981) gave the lattice parameters and Wyckoff positions in terms of the $B2/b$ setting of space group #15. We used FINDSYM to transform this to the standard $C2/c$ setting. This required the $y–$ and $z–$axes to be swapped.

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Zr I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c\cos\beta \, \mathbf{\hat{x}} + \frac{1}{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Zr I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4b\right) & \mbox{Na I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(a+c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Na I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} & \left(4c\right) & \mbox{Na II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}a+\frac{1}{2}c\cos\beta\right) \, \mathbf{\hat{x}}- \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{1}{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Na II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}a+\frac{1}{2}c\cos\beta\right) \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{1}{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Na III} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4}b \, \mathbf{\hat{y}} & \left(4d\right) & \mbox{Na III} \\ \mathbf{B}_{9} & = & -y_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c\cos\beta \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + \frac{1}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Na IV} \\ \mathbf{B}_{10} & = & y_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c\cos\beta \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \frac{3}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Na IV} \\ \mathbf{B}_{11} & = & -y_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c\cos\beta \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + \frac{1}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Zr II} \\ \mathbf{B}_{12} & = & y_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c\cos\beta \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \frac{3}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Zr II} \\ \mathbf{B}_{13} & = & \left(x_{7}-y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{14} & = & \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{7}a - z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{15} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}}-z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{16} & = & \left(x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{7}a + z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{17} & = & \left(x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{18} & = & \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{8}a - z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{19} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}}-z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{20} & = & \left(x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{8}a + z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{21} & = & \left(x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Na V} \\ \mathbf{B}_{22} & = & \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{9}a - z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Na V} \\ \mathbf{B}_{23} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Na V} \\ \mathbf{B}_{24} & = & \left(x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{9}a + z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Na V} \\ \mathbf{B}_{25} & = & \left(x_{10}-y_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}+y_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{26} & = & \left(-x_{10}-y_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{10}a - z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{27} & = & \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}-y_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}a-z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}}-z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{28} & = & \left(x_{10}+y_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}-y_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{10}a + z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{29} & = & \left(x_{11}-y_{11}\right) \, \mathbf{a}_{1} + \left(x_{11}+y_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{30} & = & \left(-x_{11}-y_{11}\right) \, \mathbf{a}_{1} + \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{11}a - z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{31} & = & \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{1} + \left(-x_{11}-y_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}a-z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}}-z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{32} & = & \left(x_{11}+y_{11}\right) \, \mathbf{a}_{1} + \left(x_{11}-y_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{11}a + z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{33} & = & \left(x_{12}-y_{12}\right) \, \mathbf{a}_{1} + \left(x_{12}+y_{12}\right) \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{34} & = & \left(-x_{12}-y_{12}\right) \, \mathbf{a}_{1} + \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{12}a - z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{12}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{35} & = & \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{1} + \left(-x_{12}-y_{12}\right) \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & \left(-x_{12}a-z_{12}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}}-z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{36} & = & \left(x_{12}+y_{12}\right) \, \mathbf{a}_{1} + \left(x_{12}-y_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{12}a + z_{12}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{37} & = & \left(x_{13}-y_{13}\right) \, \mathbf{a}_{1} + \left(x_{13}+y_{13}\right) \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IV} \\ \mathbf{B}_{38} & = & \left(-x_{13}-y_{13}\right) \, \mathbf{a}_{1} + \left(-x_{13}+y_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{13}a - z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{13}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IV} \\ \mathbf{B}_{39} & = & \left(-x_{13}+y_{13}\right) \, \mathbf{a}_{1} + \left(-x_{13}-y_{13}\right) \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & \left(-x_{13}a-z_{13}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}}-z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IV} \\ \mathbf{B}_{40} & = & \left(x_{13}+y_{13}\right) \, \mathbf{a}_{1} + \left(x_{13}-y_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{13}a + z_{13}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IV} \\ \mathbf{B}_{41} & = & \left(x_{14}-y_{14}\right) \, \mathbf{a}_{1} + \left(x_{14}+y_{14}\right) \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O V} \\ \mathbf{B}_{42} & = & \left(-x_{14}-y_{14}\right) \, \mathbf{a}_{1} + \left(-x_{14}+y_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{14}a - z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{14}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O V} \\ \mathbf{B}_{43} & = & \left(-x_{14}+y_{14}\right) \, \mathbf{a}_{1} + \left(-x_{14}-y_{14}\right) \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & \left(-x_{14}a-z_{14}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}}-z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O V} \\ \mathbf{B}_{44} & = & \left(x_{14}+y_{14}\right) \, \mathbf{a}_{1} + \left(x_{14}-y_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{14}a + z_{14}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O V} \\ \mathbf{B}_{45} & = & \left(x_{15}-y_{15}\right) \, \mathbf{a}_{1} + \left(x_{15}+y_{15}\right) \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VI} \\ \mathbf{B}_{46} & = & \left(-x_{15}-y_{15}\right) \, \mathbf{a}_{1} + \left(-x_{15}+y_{15}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{15}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{15}a - z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{15}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VI} \\ \mathbf{B}_{47} & = & \left(-x_{15}+y_{15}\right) \, \mathbf{a}_{1} + \left(-x_{15}-y_{15}\right) \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & \left(-x_{15}a-z_{15}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}}-z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VI} \\ \mathbf{B}_{48} & = & \left(x_{15}+y_{15}\right) \, \mathbf{a}_{1} + \left(x_{15}-y_{15}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{15}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{15}a + z_{15}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{15}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VI} \\ \mathbf{B}_{49} & = & \left(x_{16}-y_{16}\right) \, \mathbf{a}_{1} + \left(x_{16}+y_{16}\right) \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{16}b \, \mathbf{\hat{y}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VII} \\ \mathbf{B}_{50} & = & \left(-x_{16}-y_{16}\right) \, \mathbf{a}_{1} + \left(-x_{16}+y_{16}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{16}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{16}a - z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{16}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VII} \\ \mathbf{B}_{51} & = & \left(-x_{16}+y_{16}\right) \, \mathbf{a}_{1} + \left(-x_{16}-y_{16}\right) \, \mathbf{a}_{2}-z_{16} \, \mathbf{a}_{3} & = & \left(-x_{16}a-z_{16}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}}-z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VII} \\ \mathbf{B}_{52} & = & \left(x_{16}+y_{16}\right) \, \mathbf{a}_{1} + \left(x_{16}-y_{16}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{16}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{16}a + z_{16}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{16}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VII} \\ \mathbf{B}_{53} & = & \left(x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}+y_{17}\right) \, \mathbf{a}_{2} + z_{17} \, \mathbf{a}_{3} & = & \left(x_{17}a+z_{17}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}} + z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VIII} \\ \mathbf{B}_{54} & = & \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{17}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{17}a - z_{17}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{17}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VIII} \\ \mathbf{B}_{55} & = & \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{2}-z_{17} \, \mathbf{a}_{3} & = & \left(-x_{17}a-z_{17}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}}-z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VIII} \\ \mathbf{B}_{56} & = & \left(x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}-y_{17}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{17}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{17}a + z_{17}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{17}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O VIII} \\ \mathbf{B}_{57} & = & \left(x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}+y_{18}\right) \, \mathbf{a}_{2} + z_{18} \, \mathbf{a}_{3} & = & \left(x_{18}a+z_{18}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}} + z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IX} \\ \mathbf{B}_{58} & = & \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{18}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{18}a - z_{18}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{18}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IX} \\ \mathbf{B}_{59} & = & \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{2}-z_{18} \, \mathbf{a}_{3} & = & \left(-x_{18}a-z_{18}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}}-z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IX} \\ \mathbf{B}_{60} & = & \left(x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}-y_{18}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{18}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{18}a + z_{18}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{18}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O IX} \\ \mathbf{B}_{61} & = & \left(x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}+y_{19}\right) \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & \left(x_{19}a+z_{19}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si I} \\ \mathbf{B}_{62} & = & \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{19}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{19}a - z_{19}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{19}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si I} \\ \mathbf{B}_{63} & = & \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{2}-z_{19} \, \mathbf{a}_{3} & = & \left(-x_{19}a-z_{19}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}}-z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si I} \\ \mathbf{B}_{64} & = & \left(x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}-y_{19}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{19}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{19}a + z_{19}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{19}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si I} \\ \mathbf{B}_{65} & = & \left(x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}+y_{20}\right) \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & \left(x_{20}a+z_{20}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si II} \\ \mathbf{B}_{66} & = & \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{20}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{20}a - z_{20}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{20}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si II} \\ \mathbf{B}_{67} & = & \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{2}-z_{20} \, \mathbf{a}_{3} & = & \left(-x_{20}a-z_{20}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}}-z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si II} \\ \mathbf{B}_{68} & = & \left(x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}-y_{20}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{20}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{20}a + z_{20}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{20}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si II} \\ \mathbf{B}_{69} & = & \left(x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}+y_{21}\right) \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & \left(x_{21}a+z_{21}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + z_{21}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si III} \\ \mathbf{B}_{70} & = & \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{21}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{21}a - z_{21}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{21}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si III} \\ \mathbf{B}_{71} & = & \left(-x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(-x_{21}-y_{21}\right) \, \mathbf{a}_{2}-z_{21} \, \mathbf{a}_{3} & = & \left(-x_{21}a-z_{21}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}}-z_{21}c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si III} \\ \mathbf{B}_{72} & = & \left(x_{21}+y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21}-y_{21}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{21}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{21}a + z_{21}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{21}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si III} \\ \end{array} \]

References

  • G. D. Ilyushin, A. A. Voronkov, V. V. Ilyukhin, N. N. Nevskii, and N. V. Belov, Crystal structure of natural monoclinic catapleiite, Na2ZrSi3O9 · 2H2O, Doklady\ Akademii\ Nauk\ SSSR 260, 623–627 (1981).
  • C. Gottfried, ed., Strukturbericht Band V 1937 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1940).

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A2B3C9D3E_mC144_15_2f_bcdef_9f_3f_ae --params=

Species:

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