Monoclinic (Cc) Low Tridymite (SiO2) Structure: A2B_mC144_9_24a_12a

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_mC144_9_24a_12a
Strukturbericht designation : None
Pearson symbol : mC144
Space group number : 9
Space group symbol : $\mbox{Cc}$
AFLOW prototype command : aflow --proto=A2B_mC144_9_24a_12a
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$ 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}$,$x_{23}$,$y_{23}$,$z_{23}$,$x_{24}$,$y_{24}$,$z_{24}$,$x_{25}$,$y_{25}$,$z_{25}$,$x_{26}$,$y_{26}$,$z_{26}$,$x_{27}$,$y_{27}$,$ z_{27}$,$x_{28}$,$y_{28}$,$z_{28}$,$x_{29}$,$y_{29}$,$z_{29}$,$x_{30}$,$y_{30}$,$z_{30}$,$x_{31}$,$y_{31}$,$z_{31}$,$x_{32}$,$y_{32}$,$z_{32}$,$x_{33}$,$y_{33}$,$z_{33}$,$x_{34}$,$ y_{34}$,$z_{34}$,$x_{35}$,$y_{35}$,$z_{35}$,$x_{36}$,$y_{36}$,$z_{36}$


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} & =& \left(x_{1} - y_{1}\right) \, \mathbf{a}_{1} + \left(x_{1} + y_{1}\right) \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{1} \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{2} & =& \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1} + \left(x_{1} - y_{1}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \left(x_{1} \, a + \left(\frac12 + z_{1}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{1} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{3} & =& \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1} + \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O II} \\ \mathbf{B}_{4} & =& \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1} + \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =& \left(x_{2} \, a + \left(\frac12 + z_{2}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{2} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O II} \\ \mathbf{B}_{5} & =& \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O III} \\ \mathbf{B}_{6} & =& \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& =& \left(x_{3} \, a + \left(\frac12 + z_{3}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{3} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O III} \\ \mathbf{B}_{7} & =& \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O IV} \\ \mathbf{B}_{8} & =& \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =& \left(x_{4} \, a + \left(\frac12 + z_{4}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O IV} \\ \mathbf{B}_{9} & =& \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O V} \\ \mathbf{B}_{10} & =& \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =& \left(x_{5} \, a + \left(\frac12 + z_{5}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{5} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O V} \\ \mathbf{B}_{11} & =& \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O VI} \\ \mathbf{B}_{12} & =& \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& =& \left(x_{6} \, a + \left(\frac12 + z_{6}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{6} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O VI} \\ \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(4a\right) & \mbox{O VII} \\ \mathbf{B}_{14} & =& \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{7}\right) \, \mathbf{a}_{3}& =& \left(x_{7} \, a + \left(\frac12 + z_{7}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{7} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{7}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O VII} \\ \mathbf{B}_{15} & =& \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(4a\right) & \mbox{O VIII} \\ \mathbf{B}_{16} & =& \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{8}\right) \, \mathbf{a}_{3}& =& \left(x_{8} \, a + \left(\frac12 + z_{8}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{8} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{8}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O VIII} \\ \mathbf{B}_{17} & =& \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(4a\right) & \mbox{O IX} \\ \mathbf{B}_{18} & =& \left(x_{9} + y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{9}\right) \, \mathbf{a}_{3}& =& \left(x_{9} \, a + \left(\frac12 + z_{9}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{9} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{9}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O IX} \\ \mathbf{B}_{19} & =& \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(4a\right) & \mbox{O X} \\ \mathbf{B}_{20} & =& \left(x_{10} + y_{10}\right) \, \mathbf{a}_{1} + \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{10}\right) \, \mathbf{a}_{3}& =& \left(x_{10} \, a + \left(\frac12 + z_{10}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{10} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{10}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O X} \\ \mathbf{B}_{21} & =& \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(4a\right) & \mbox{O XI} \\ \mathbf{B}_{22} & =& \left(x_{11} + y_{11}\right) \, \mathbf{a}_{1} + \left(x_{11} - y_{11}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{11}\right) \, \mathbf{a}_{3}& =& \left(x_{11} \, a + \left(\frac12 + z_{11}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{11} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{11}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XI} \\ \mathbf{B}_{23} & =& \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(4a\right) & \mbox{O XII} \\ \mathbf{B}_{24} & =& \left(x_{12} + y_{12}\right) \, \mathbf{a}_{1} + \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{12}\right) \, \mathbf{a}_{3}& =& \left(x_{12} \, a + \left(\frac12 + z_{12}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{12} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{12}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XII} \\ \mathbf{B}_{25} & =& \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(4a\right) & \mbox{O XIII} \\ \mathbf{B}_{26} & =& \left(x_{13} + y_{13}\right) \, \mathbf{a}_{1} + \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{13}\right) \, \mathbf{a}_{3}& =& \left(x_{13} \, a + \left(\frac12 + z_{13}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{13} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{13}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XIII} \\ \mathbf{B}_{27} & =& \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(4a\right) & \mbox{O XIV} \\ \mathbf{B}_{28} & =& \left(x_{14} + y_{14}\right) \, \mathbf{a}_{1} + \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{14}\right) \, \mathbf{a}_{3}& =& \left(x_{14} \, a + \left(\frac12 + z_{14}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{14} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{14}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XIV} \\ \mathbf{B}_{29} & =& \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(4a\right) & \mbox{O XV} \\ \mathbf{B}_{30} & =& \left(x_{15} + y_{15}\right) \, \mathbf{a}_{1} + \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{15}\right) \, \mathbf{a}_{3}& =& \left(x_{15} \, a + \left(\frac12 + z_{15}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{15} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{15}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XV} \\ \mathbf{B}_{31} & =& \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(4a\right) & \mbox{O XVI} \\ \mathbf{B}_{32} & =& \left(x_{16} + y_{16}\right) \, \mathbf{a}_{1} + \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{16}\right) \, \mathbf{a}_{3}& =& \left(x_{16} \, a + \left(\frac12 + z_{16}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{16} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{16}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XVI} \\ \mathbf{B}_{33} & =& \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(4a\right) & \mbox{O XVII} \\ \mathbf{B}_{34} & =& \left(x_{17} + y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{17}\right) \, \mathbf{a}_{3}& =& \left(x_{17} \, a + \left(\frac12 + z_{17}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{17} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{17}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XVII} \\ \mathbf{B}_{35} & =& \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(4a\right) & \mbox{O XVIII} \\ \mathbf{B}_{36} & =& \left(x_{18} + y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{18}\right) \, \mathbf{a}_{3}& =& \left(x_{18} \, a + \left(\frac12 + z_{18}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{18} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{18}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XVIII} \\ \mathbf{B}_{37} & =& \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(4a\right) & \mbox{O XIX} \\ \mathbf{B}_{38} & =& \left(x_{19} + y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19} - y_{19}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{19}\right) \, \mathbf{a}_{3}& =& \left(x_{19} \, a + \left(\frac12 + z_{19}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{19} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{19}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XIX} \\ \mathbf{B}_{39} & =& \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(4a\right) & \mbox{O XX} \\ \mathbf{B}_{40} & =& \left(x_{20} + y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20} - y_{20}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{20}\right) \, \mathbf{a}_{3}& =& \left(x_{20} \, a + \left(\frac12 + z_{20}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{20} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{20}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XX} \\ \mathbf{B}_{41} & =& \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(4a\right) & \mbox{O XXI} \\ \mathbf{B}_{42} & =& \left(x_{21} + y_{21}\right) \, \mathbf{a}_{1} + \left(x_{21} - y_{21}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{21}\right) \, \mathbf{a}_{3}& =& \left(x_{21} \, a + \left(\frac12 + z_{21}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{21} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{21}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXI} \\ \mathbf{B}_{43} & =& \left(x_{22} - y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22} + y_{22}\right) \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3}& =& \left(x_{22} \, a + z_{22} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{22} \, b \, \mathbf{\hat{y}}+ z_{22} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXII} \\ \mathbf{B}_{44} & =& \left(x_{22} + y_{22}\right) \, \mathbf{a}_{1} + \left(x_{22} - y_{22}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{22}\right) \, \mathbf{a}_{3}& =& \left(x_{22} \, a + \left(\frac12 + z_{22}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{22} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{22}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXII} \\ \mathbf{B}_{45} & =& \left(x_{23} - y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23} + y_{23}\right) \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3}& =& \left(x_{23} \, a + z_{23} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{23} \, b \, \mathbf{\hat{y}}+ z_{23} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXIII} \\ \mathbf{B}_{46} & =& \left(x_{23} + y_{23}\right) \, \mathbf{a}_{1} + \left(x_{23} - y_{23}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{23}\right) \, \mathbf{a}_{3}& =& \left(x_{23} \, a + \left(\frac12 + z_{23}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{23} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{23}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXIII} \\ \mathbf{B}_{47} & =& \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24} + y_{24}\right) \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3}& =& \left(x_{24} \, a + z_{24} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{24} \, b \, \mathbf{\hat{y}}+ z_{24} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXIV} \\ \mathbf{B}_{48} & =& \left(x_{24} + y_{24}\right) \, \mathbf{a}_{1} + \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{24}\right) \, \mathbf{a}_{3}& =& \left(x_{24} \, a + \left(\frac12 + z_{24}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{24} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{24}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{O XXIV} \\ \mathbf{B}_{49} & =& \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25} + y_{25}\right) \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3}& =& \left(x_{25} \, a + z_{25} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{25} \, b \, \mathbf{\hat{y}}+ z_{25} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si I} \\ \mathbf{B}_{50} & =& \left(x_{25} + y_{25}\right) \, \mathbf{a}_{1} + \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{25}\right) \, \mathbf{a}_{3}& =& \left(x_{25} \, a + \left(\frac12 + z_{25}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{25} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{25}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si I} \\ \mathbf{B}_{51} & =& \left(x_{26} - y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26} + y_{26}\right) \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3}& =& \left(x_{26} \, a + z_{26} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{26} \, b \, \mathbf{\hat{y}}+ z_{26} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si II} \\ \mathbf{B}_{52} & =& \left(x_{26} + y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26} - y_{26}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{26}\right) \, \mathbf{a}_{3}& =& \left(x_{26} \, a + \left(\frac12 + z_{26}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{26} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{26}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si II} \\ \mathbf{B}_{53} & =& \left(x_{27} - y_{27}\right) \, \mathbf{a}_{1} + \left(x_{27} + y_{27}\right) \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3}& =& \left(x_{27} \, a + z_{27} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{27} \, b \, \mathbf{\hat{y}}+ z_{27} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si III} \\ \mathbf{B}_{54} & =& \left(x_{27} + y_{27}\right) \, \mathbf{a}_{1} + \left(x_{27} - y_{27}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{27}\right) \, \mathbf{a}_{3}& =& \left(x_{27} \, a + \left(\frac12 + z_{27}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{27} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{27}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si III} \\ \mathbf{B}_{55} & =& \left(x_{28} - y_{28}\right) \, \mathbf{a}_{1} + \left(x_{28} + y_{28}\right) \, \mathbf{a}_{2} + z_{28} \, \mathbf{a}_{3}& =& \left(x_{28} \, a + z_{28} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{28} \, b \, \mathbf{\hat{y}}+ z_{28} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si IV} \\ \mathbf{B}_{56} & =& \left(x_{28} + y_{28}\right) \, \mathbf{a}_{1} + \left(x_{28} - y_{28}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{28}\right) \, \mathbf{a}_{3}& =& \left(x_{28} \, a + \left(\frac12 + z_{28}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{28} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{28}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si IV} \\ \mathbf{B}_{57} & =& \left(x_{29} - y_{29}\right) \, \mathbf{a}_{1} + \left(x_{29} + y_{29}\right) \, \mathbf{a}_{2} + z_{29} \, \mathbf{a}_{3}& =& \left(x_{29} \, a + z_{29} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{29} \, b \, \mathbf{\hat{y}}+ z_{29} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si V} \\ \mathbf{B}_{58} & =& \left(x_{29} + y_{29}\right) \, \mathbf{a}_{1} + \left(x_{29} - y_{29}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{29}\right) \, \mathbf{a}_{3}& =& \left(x_{29} \, a + \left(\frac12 + z_{29}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{29} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{29}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si V} \\ \mathbf{B}_{59} & =& \left(x_{30} - y_{30}\right) \, \mathbf{a}_{1} + \left(x_{30} + y_{30}\right) \, \mathbf{a}_{2} + z_{30} \, \mathbf{a}_{3}& =& \left(x_{30} \, a + z_{30} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{30} \, b \, \mathbf{\hat{y}}+ z_{30} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VI} \\ \mathbf{B}_{60} & =& \left(x_{30} + y_{30}\right) \, \mathbf{a}_{1} + \left(x_{30} - y_{30}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{30}\right) \, \mathbf{a}_{3}& =& \left(x_{30} \, a + \left(\frac12 + z_{30}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{30} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{30}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VI} \\ \mathbf{B}_{61} & =& \left(x_{31} - y_{31}\right) \, \mathbf{a}_{1} + \left(x_{31} + y_{31}\right) \, \mathbf{a}_{2} + z_{31} \, \mathbf{a}_{3}& =& \left(x_{31} \, a + z_{31} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{31} \, b \, \mathbf{\hat{y}}+ z_{31} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VII} \\ \mathbf{B}_{62} & =& \left(x_{31} + y_{31}\right) \, \mathbf{a}_{1} + \left(x_{31} - y_{31}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{31}\right) \, \mathbf{a}_{3}& =& \left(x_{31} \, a + \left(\frac12 + z_{31}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{31} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{31}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VII} \\ \mathbf{B}_{63} & =& \left(x_{32} - y_{32}\right) \, \mathbf{a}_{1} + \left(x_{32} + y_{32}\right) \, \mathbf{a}_{2} + z_{32} \, \mathbf{a}_{3}& =& \left(x_{32} \, a + z_{32} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{32} \, b \, \mathbf{\hat{y}}+ z_{32} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VIII} \\ \mathbf{B}_{64} & =& \left(x_{32} + y_{32}\right) \, \mathbf{a}_{1} + \left(x_{32} - y_{32}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{32}\right) \, \mathbf{a}_{3}& =& \left(x_{32} \, a + \left(\frac12 + z_{32}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{32} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{32}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si VIII} \\ \mathbf{B}_{65} & =& \left(x_{33} - y_{33}\right) \, \mathbf{a}_{1} + \left(x_{33} + y_{33}\right) \, \mathbf{a}_{2} + z_{33} \, \mathbf{a}_{3}& =& \left(x_{33} \, a + z_{33} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{33} \, b \, \mathbf{\hat{y}}+ z_{33} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si IX} \\ \mathbf{B}_{66} & =& \left(x_{33} + y_{33}\right) \, \mathbf{a}_{1} + \left(x_{33} - y_{33}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{33}\right) \, \mathbf{a}_{3}& =& \left(x_{33} \, a + \left(\frac12 + z_{33}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{33} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{33}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si IX} \\ \mathbf{B}_{67} & =& \left(x_{34} - y_{34}\right) \, \mathbf{a}_{1} + \left(x_{34} + y_{34}\right) \, \mathbf{a}_{2} + z_{34} \, \mathbf{a}_{3}& =& \left(x_{34} \, a + z_{34} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{34} \, b \, \mathbf{\hat{y}}+ z_{34} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si X} \\ \mathbf{B}_{68} & =& \left(x_{34} + y_{34}\right) \, \mathbf{a}_{1} + \left(x_{34} - y_{34}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{34}\right) \, \mathbf{a}_{3}& =& \left(x_{34} \, a + \left(\frac12 + z_{34}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{34} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{34}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si X} \\ \mathbf{B}_{69} & =& \left(x_{35} - y_{35}\right) \, \mathbf{a}_{1} + \left(x_{35} + y_{35}\right) \, \mathbf{a}_{2} + z_{35} \, \mathbf{a}_{3}& =& \left(x_{35} \, a + z_{35} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{35} \, b \, \mathbf{\hat{y}}+ z_{35} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si XI} \\ \mathbf{B}_{70} & =& \left(x_{35} + y_{35}\right) \, \mathbf{a}_{1} + \left(x_{35} - y_{35}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{35}\right) \, \mathbf{a}_{3}& =& \left(x_{35} \, a + \left(\frac12 + z_{35}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{35} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{35}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si XI} \\ \mathbf{B}_{71} & =& \left(x_{36} - y_{36}\right) \, \mathbf{a}_{1} + \left(x_{36} + y_{36}\right) \, \mathbf{a}_{2} + z_{36} \, \mathbf{a}_{3}& =& \left(x_{36} \, a + z_{36} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{36} \, b \, \mathbf{\hat{y}}+ z_{36} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si XII} \\ \mathbf{B}_{72} & =& \left(x_{36} + y_{36}\right) \, \mathbf{a}_{1} + \left(x_{36} - y_{36}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{36}\right) \, \mathbf{a}_{3}& =& \left(x_{36} \, a + \left(\frac12 + z_{36}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{36} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{36}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Si XII} \\ \end{array} \]

References

  • W. A. Dollase and W. H. Baur, The superstructure of meteoritic low tridymite solved by computer simulation, Am. Mineral. 61, 971–978 (1976).

Geometry files


Prototype Generator

aflow --proto=A2B_mC144_9_24a_12a --params=

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