Coesite (SiO2) Structure: A2B_mC48_15_ae3f_2f

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_mC48_15_ae3f_2f
Strukturbericht designation : None
Pearson symbol : mC48
Space group number : 15
Space group symbol : $\mbox{C2/c}$
AFLOW prototype command : aflow --proto=A2B_mC48_15_ae3f_2f
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


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{O I} \\ \mathbf{B}_{2} & = & \frac12 \, \mathbf{a}_{3}& = & \frac12 \, c \, \cos\beta \, \mathbf{\hat{x}} + \frac12 \, c \, \sin\beta \mathbf{\hat{z}} & \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{3} & =& - y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& = &\frac14 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{4} & =& y_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& = &\frac34 \, c \, \cos\beta \, \mathbf{\hat{x}}- y_{2} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\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(8f\right) & \mbox{O III} \\ \mathbf{B}_{6} & =&- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} - x_{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(8f\right) & \mbox{O III} \\ \mathbf{B}_{7} & =&\left(y_{3} - x_{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(8f\right) & \mbox{O III} \\ \mathbf{B}_{8} & =&\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(8f\right) & \mbox{O III} \\ \mathbf{B}_{9} & =&\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(8f\right) & \mbox{O IV} \\ \mathbf{B}_{10} & =&- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+ \left(y_{4} - x_{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(8f\right) & \mbox{O IV} \\ \mathbf{B}_{11} & =&\left(y_{4} - x_{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(8f\right) & \mbox{O IV} \\ \mathbf{B}_{12} & =&\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(8f\right) & \mbox{O IV} \\ \mathbf{B}_{13} & =&\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(8f\right) & \mbox{O V} \\ \mathbf{B}_{14} & =&- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+ \left(y_{5} - x_{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(8f\right) & \mbox{O V} \\ \mathbf{B}_{15} & =&\left(y_{5} - x_{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(8f\right) & \mbox{O V} \\ \mathbf{B}_{16} & =&\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(8f\right) & \mbox{O V} \\ \mathbf{B}_{17} & =&\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(8f\right) & \mbox{Si I} \\ \mathbf{B}_{18} & =&- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+ \left(y_{6} - x_{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(8f\right) & \mbox{Si I} \\ \mathbf{B}_{19} & =&\left(y_{6} - x_{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(8f\right) & \mbox{Si I} \\ \mathbf{B}_{20} & =&\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(8f\right) & \mbox{Si I} \\ \mathbf{B}_{21} & =&\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{Si II} \\ \mathbf{B}_{22} & =&- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+ \left(y_{7} - x_{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(8f\right) & \mbox{Si II} \\ \mathbf{B}_{23} & =&\left(y_{7} - x_{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{Si II} \\ \mathbf{B}_{24} & =&\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(8f\right) & \mbox{Si II} \\ \end{array} \]

References

  • L. Levien and C. T. Prewitt, High–pressure crystal structure and compressibility of coesite, Am. Mineral. 66, 324–333 (1981).

Geometry files


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