Natrolite (Na2Al2Si3O10·2H2O, $S6_{10}$) Structure : A2B4C2D12E3_oF184_43_b_2b_b_6b_ab

Picture of Structure; Click for Big Picture
Prototype : Al2H4Na2O12Si3
AFLOW prototype label : A2B4C2D12E3_oF184_43_b_2b_b_6b_ab
Strukturbericht designation : $S6_{10}$
Pearson symbol : oF184
Space group number : 43
Space group symbol : $Fdd2$
AFLOW prototype command : aflow --proto=A2B4C2D12E3_oF184_43_b_2b_b_6b_ab
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$


  • We use the data from the sample that (Kirfel, 1984) call Crystal II. The origin has been arbitrarily set so that $z_{1} = 0$.

Face-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{Si I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{Si 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} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Al} \\ \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} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Al} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Al} \\ \mathbf{B}_{6} & = & \left(\frac{1}{4} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Al} \\ \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} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H I} \\ \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} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H I} \\ \mathbf{B}_{9} & = & \left(\frac{1}{4} - x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H I} \\ \mathbf{B}_{10} & = & \left(\frac{1}{4} +x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H I} \\ \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} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H II} \\ \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} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H II} \\ \mathbf{B}_{13} & = & \left(\frac{1}{4} - x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{4} +x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{H II} \\ \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} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Na} \\ \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} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Na} \\ \mathbf{B}_{17} & = & \left(\frac{1}{4} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{5}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Na} \\ \mathbf{B}_{18} & = & \left(\frac{1}{4} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Na} \\ \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} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O I} \\ \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} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O I} \\ \mathbf{B}_{21} & = & \left(\frac{1}{4} - x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{6}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O I} \\ \mathbf{B}_{22} & = & \left(\frac{1}{4} +x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{6}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O I} \\ \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} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O II} \\ \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} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & \left(\frac{1}{4} - x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{7} - y_{7} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{7}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O II} \\ \mathbf{B}_{26} & = & \left(\frac{1}{4} +x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{7}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O II} \\ \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} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O III} \\ \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} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & \left(\frac{1}{4} - x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{8} - y_{8} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{8}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O III} \\ \mathbf{B}_{30} & = & \left(\frac{1}{4} +x_{8} + y_{8} + z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{8} - y_{8} + z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{8} + y_{8} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{8}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O III} \\ \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} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O IV} \\ \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} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O IV} \\ \mathbf{B}_{33} & = & \left(\frac{1}{4} - x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{9} - y_{9} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{9}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O IV} \\ \mathbf{B}_{34} & = & \left(\frac{1}{4} +x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{9}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O IV} \\ \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} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O V} \\ \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} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O V} \\ \mathbf{B}_{37} & = & \left(\frac{1}{4} - x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{10} - y_{10} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{10}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O V} \\ \mathbf{B}_{38} & = & \left(\frac{1}{4} +x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{10}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O V} \\ \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} & = & x_{11}a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O VI} \\ \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} & = & -x_{11}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O VI} \\ \mathbf{B}_{41} & = & \left(\frac{1}{4} - x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{11} - y_{11} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{11}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O VI} \\ \mathbf{B}_{42} & = & \left(\frac{1}{4} +x_{11} + y_{11} + z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{11} - y_{11} + z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{11} + y_{11} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{11}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{O VI} \\ \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} & = & x_{12}a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Si II} \\ \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} & = & -x_{12}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Si II} \\ \mathbf{B}_{45} & = & \left(\frac{1}{4} - x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{12} - y_{12} - z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{12}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{12}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Si II} \\ \mathbf{B}_{46} & = & \left(\frac{1}{4} +x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{12}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{12}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(16b\right) & \mbox{Si II} \\ \end{array} \]

References

  • A. Kirfel, M. Orthen, and G. Will, Natrolite: refinement of the crystal structure of two samples from Marienberg (Usti nad Labem, CSSR), Zeolites 4, 140–146 (1984), doi:10.1016/0144-2449(84)90052-6.

Geometry files


Prototype Generator

aflow --proto=A2B4C2D12E3_oF184_43_b_2b_b_6b_ab --params=

Species:

Running:

Output: