Chabazite (Ca1.4Sr0.3Al3.8Si8.3O24·13H2O, $S3_4$ (I)) Structure : A5B21C24D12_hR62_166_a2c_ehi_fg2h_i

Picture of Structure; Click for Big Picture
Prototype : (Ca1.4,Sr0.3)(H2O)13O24(Si8.3,Al3.8)
AFLOW prototype label : A5B21C24D12_hR62_166_a2c_ehi_fg2h_i
Strukturbericht designation : $S3_{4}$ (I)
Pearson symbol : hR62
Space group number : 166
Space group symbol : $R\bar{3}m$
AFLOW prototype command : aflow --proto=A5B21C24D12_hR62_166_a2c_ehi_fg2h_i
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$x_{5}$,$x_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$


  • The structure given here, from (Calligaris, 1982), has substantially the same Wyckoff positions as the structure designated $S3_{4}$ by (Gottfried, 1937). The largest change is the splitting of the calcium site from one stoichiometric ($2c$) site to three partially filled sites, one ($1a$) and two ($2c$).
  • (Calligaris, 1982) did not give the exact positions of the water molecules, so we use the positions given by (Downs, 2003). However, this leaves us with only 7.7 water molecules per formula unit, rather than the 13 claimed by (Calligaris, 1982).
  • Only the oxygen sites are fully occupied. For the remaining sites, according to (Downs, 2003),
    • The ($1a$) site is 9.06% Ca and 1.94% Sr, with the remaining sites vacant.
    • The first ($2c$) site is 43.65% Ca and 9.35% Sr.
    • The second ($2c$) site is 19.76% Ca and 4.24% Sr.
    • The ($3e$) is only occupied by a water molecule 50% of the time.
    • The ($6h$) H2O site is only occupied 57% of the time.
    • The ($12i$) H2O site is only occupied 23% of the time.
    • The remaining ($12i$) is 69% Si and 31% Al.
  • (Gottfried, 1937) gave chabazite the Strukturbericht designation $S3_{4}$. However, (Gottfried, 1940) ignored this and designated catapleiite, Na2ZrSi3O9·2H2O as Strukturbericht $S3_{4}$. We resolve this by using $S3_{4}$ (I) to designate chabazite and $S3_{4}$ (II) to designate catapleiite.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

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(1a\right) & \mbox{Ca I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ca II} \\ \mathbf{B}_{3} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ca II} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ca III} \\ \mathbf{B}_{5} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ca III} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & - \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{3}c \, \mathbf{\hat{z}} & \left(3e\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & - \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{3}c \, \mathbf{\hat{z}} & \left(3e\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{3}c \, \mathbf{\hat{z}} & \left(3e\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} & = & -\frac{1}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & -x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(- \frac{1}{4} +\frac{1}{2}x_{6}\right)a \, \mathbf{\hat{x}}-a\left(\frac{\sqrt{3}}{2}x_{6}+\frac{1}{4\sqrt{3}}\right) \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +\frac{1}{2}x_{6}\right)a \, \mathbf{\hat{x}} + \left(- \frac{1}{4\sqrt{3}} +\frac{\sqrt{3}}{2}x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & -x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{18} & = & -x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -a\left(\frac{1}{2}x_{6}+\frac{1}{4}\right) \, \mathbf{\hat{x}} + \left(- \frac{1}{4\sqrt{3}} +\frac{\sqrt{3}}{2}x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{19} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-\frac{1}{2}x_{6}\right)a \, \mathbf{\hat{x}}-a\left(\frac{\sqrt{3}}{2}x_{6}+\frac{1}{4\sqrt{3}}\right) \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{22} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{23} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{24} & = & -z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{25} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{26} & = & -x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{27} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{8}-z_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{8}-z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{8}+z_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{8}-z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{8}+z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{30} & = & -z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{8}-z_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{8}+z_{8}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{31} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{8}+z_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{8}+z_{8}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{32} & = & -x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(x_{8}-z_{8}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{8}+\frac{1}{3}z_{8}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{33} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{9}-z_{9}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{9}-z_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{34} & = & z_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + x_{9} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{9}+z_{9}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{9}-z_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{35} & = & x_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + x_{9} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{9}+z_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{36} & = & -z_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2}-x_{9} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{9}-z_{9}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{9}+z_{9}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{37} & = & -x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{9}+z_{9}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{9}+z_{9}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{38} & = & -x_{9} \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2}-x_{9} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(x_{9}-z_{9}\right)a \, \mathbf{\hat{y}}-c\left(\frac{2}{3}x_{9}+\frac{1}{3}z_{9}\right) \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O IV} \\ \mathbf{B}_{39} & = & x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{10}-z_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{10}+\frac{1}{\sqrt{3}}y_{10}-\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{40} & = & z_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + y_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{10}+z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{10}-\frac{1}{2\sqrt{3}}y_{10}-\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{41} & = & y_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + x_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{10}+y_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{10}-\frac{1}{2\sqrt{3}}y_{10}+\frac{1}{\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{42} & = & -z_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2}-x_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{10}-z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{10}-\frac{1}{\sqrt{3}}y_{10}+\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{43} & = & -y_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{10}+z_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{10}+\frac{1}{2\sqrt{3}}y_{10}+\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{44} & = & -x_{10} \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2}-y_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{10}+y_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{10}+\frac{1}{2\sqrt{3}}y_{10}-\frac{1}{\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{45} & = & -x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{10}+z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{10}-\frac{1}{\sqrt{3}}y_{10}+\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{46} & = & -z_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2}-y_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{10}-z_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{10}+\frac{1}{2\sqrt{3}}y_{10}+\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{47} & = & -y_{10} \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2}-x_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{10}-y_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{10}+\frac{1}{2\sqrt{3}}y_{10}-\frac{1}{\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{48} & = & z_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + x_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{10}+z_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{10}+\frac{1}{\sqrt{3}}y_{10}-\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{49} & = & y_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{10}-z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{10}-\frac{1}{2\sqrt{3}}y_{10}-\frac{1}{2\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{50} & = & x_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + y_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{10}-y_{10}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{10}-\frac{1}{2\sqrt{3}}y_{10}+\frac{1}{\sqrt{3}}z_{10}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{10}+y_{10}+z_{10}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{51} & = & x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{11}-z_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{11}+\frac{1}{\sqrt{3}}y_{11}-\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{52} & = & z_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + y_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{11}+z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{11}-\frac{1}{2\sqrt{3}}y_{11}-\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{53} & = & y_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + x_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{11}+y_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{11}-\frac{1}{2\sqrt{3}}y_{11}+\frac{1}{\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{54} & = & -z_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2}-x_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{11}-z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{11}-\frac{1}{\sqrt{3}}y_{11}+\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{55} & = & -y_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{11}+z_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{11}+\frac{1}{2\sqrt{3}}y_{11}+\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{56} & = & -x_{11} \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2}-y_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{11}+y_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{11}+\frac{1}{2\sqrt{3}}y_{11}-\frac{1}{\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{57} & = & -x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{11}+z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{11}-\frac{1}{\sqrt{3}}y_{11}+\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{58} & = & -z_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2}-y_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{11}-z_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{11}+\frac{1}{2\sqrt{3}}y_{11}+\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{59} & = & -y_{11} \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2}-x_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{11}-y_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{11}+\frac{1}{2\sqrt{3}}y_{11}-\frac{1}{\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{60} & = & z_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + x_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{11}+z_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{11}+\frac{1}{\sqrt{3}}y_{11}-\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{61} & = & y_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{11}-z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{11}-\frac{1}{2\sqrt{3}}y_{11}-\frac{1}{2\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \mathbf{B}_{62} & = & x_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + y_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{11}-y_{11}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{11}-\frac{1}{2\sqrt{3}}y_{11}+\frac{1}{\sqrt{3}}z_{11}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{11}+y_{11}+z_{11}\right)c \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Si} \\ \end{array} \]

References

  • M. Calligaris, G. Nardin, L. Randaccio, and P. C. Chiaramonti, Cation–site location in a natural chabazite, Acta Crystallogr. Sect. B Struct. Sci. 38, 602–605 (1982), doi:10.1107/S0567740882003483.
  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933–1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • C. Gottfried, ed., Strukturbericht Band V 1937 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1940).

Geometry files


Prototype Generator

aflow --proto=A5B21C24D12_hR62_166_a2c_ehi_fg2h_i --params=

Species:

Running:

Output: