Se ($A_{k}$) Structure: A_mP64_14_16e

Picture of Structure; Click for Big Picture
Prototype : Se
AFLOW prototype label : A_mP64_14_16e
Strukturbericht designation : $A_{k}$
Pearson symbol : mP64
Space group number : 14
Space group symbol : $\mbox{P2}_{1}\mbox{/c}$
AFLOW prototype command : aflow --proto=A_mP64_14_16e
--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}$


  • We follow Villars (1991) and give this structure the Ak designation. As noted in Villars (1991), the atomic coordinates are not provided in the referenced paper, but were given to the editors by the authors. We use those coordinates. Downs (2003) has the notation gamma-monoclinic selenium is allotrope of cyclo-octaselenium. Despite that, note that this is not what we refer to as $\gamma$–Se.

Simple Monoclinic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ y_{1} \, \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(4e\right) & \mbox{Se I} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{1}\right) \, c \, \cos\beta - x_{1} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{1}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se I} \\ \mathbf{B}_{3} & = &- x_{1} \, \mathbf{a}_{1}- y_{1} \, \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(4e\right) & \mbox{Se I} \\ \mathbf{B}_{4} & = &x_{1} \, \mathbf{a}_{1}+ \left(\frac12 - y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{1}\right) \, c \, \cos\beta + x_{1} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{1}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se I} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ y_{2} \, \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(4e\right) & \mbox{Se II} \\ \mathbf{B}_{6} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{2}\right) \, c \, \cos\beta - x_{2} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se II} \\ \mathbf{B}_{7} & = &- x_{2} \, \mathbf{a}_{1}- y_{2} \, \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(4e\right) & \mbox{Se II} \\ \mathbf{B}_{8} & = &x_{2} \, \mathbf{a}_{1}+ \left(\frac12 - y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{2}\right) \, c \, \cos\beta + x_{2} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se II} \\ \mathbf{B}_{9} & = &x_{3} \, \mathbf{a}_{1}+ y_{3} \, \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(4e\right) & \mbox{Se III} \\ \mathbf{B}_{10} & = &- x_{3} \, \mathbf{a}_{1}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{3}\right) \, c \, \cos\beta - x_{3} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se III} \\ \mathbf{B}_{11} & = &- x_{3} \, \mathbf{a}_{1}- y_{3} \, \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(4e\right) & \mbox{Se III} \\ \mathbf{B}_{12} & = &x_{3} \, \mathbf{a}_{1}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{3}\right) \, c \, \cos\beta + x_{3} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se III} \\ \mathbf{B}_{13} & = &x_{4} \, \mathbf{a}_{1}+ y_{4} \, \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(4e\right) & \mbox{Se IV} \\ \mathbf{B}_{14} & = &- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{4}\right) \, c \, \cos\beta - x_{4} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se IV} \\ \mathbf{B}_{15} & = &- x_{4} \, \mathbf{a}_{1}- y_{4} \, \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(4e\right) & \mbox{Se IV} \\ \mathbf{B}_{16} & = &x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{4}\right) \, c \, \cos\beta + x_{4} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se IV} \\ \mathbf{B}_{17} & = &x_{5} \, \mathbf{a}_{1}+ y_{5} \, \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(4e\right) & \mbox{Se V} \\ \mathbf{B}_{18} & = &- x_{5} \, \mathbf{a}_{1}+ \left(\frac12 + y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{5}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{5}\right) \, c \, \cos\beta - x_{5} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{5}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{5}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se V} \\ \mathbf{B}_{19} & = &- x_{5} \, \mathbf{a}_{1}- y_{5} \, \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(4e\right) & \mbox{Se V} \\ \mathbf{B}_{20} & = &x_{5} \, \mathbf{a}_{1}+ \left(\frac12 - y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{5}\right) \, c \, \cos\beta + x_{5} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{5}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se V} \\ \mathbf{B}_{21} & = &x_{6} \, \mathbf{a}_{1}+ y_{6} \, \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(4e\right) & \mbox{Se VI} \\ \mathbf{B}_{22} & = &- x_{6} \, \mathbf{a}_{1}+ \left(\frac12 + y_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{6}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{6}\right) \, c \, \cos\beta - x_{6} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{6}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{6}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VI} \\ \mathbf{B}_{23} & = &- x_{6} \, \mathbf{a}_{1}- y_{6} \, \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(4e\right) & \mbox{Se VI} \\ \mathbf{B}_{24} & = &x_{6} \, \mathbf{a}_{1}+ \left(\frac12 - y_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{6}\right) \, c \, \cos\beta + x_{6} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{6}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VI} \\ \mathbf{B}_{25} & = &x_{7} \, \mathbf{a}_{1}+ y_{7} \, \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(4e\right) & \mbox{Se VII} \\ \mathbf{B}_{26} & = &- x_{7} \, \mathbf{a}_{1}+ \left(\frac12 + y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{7}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{7}\right) \, c \, \cos\beta - x_{7} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{7}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{7}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VII} \\ \mathbf{B}_{27} & = &- x_{7} \, \mathbf{a}_{1}- y_{7} \, \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(4e\right) & \mbox{Se VII} \\ \mathbf{B}_{28} & = &x_{7} \, \mathbf{a}_{1}+ \left(\frac12 - y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{7}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{7}\right) \, c \, \cos\beta + x_{7} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{7}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{7}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VII} \\ \mathbf{B}_{29} & = &x_{8} \, \mathbf{a}_{1}+ y_{8} \, \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(4e\right) & \mbox{Se VIII} \\ \mathbf{B}_{30} & = &- x_{8} \, \mathbf{a}_{1}+ \left(\frac12 + y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{8}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{8}\right) \, c \, \cos\beta - x_{8} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{8}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{8}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VIII} \\ \mathbf{B}_{31} & = &- x_{8} \, \mathbf{a}_{1}- y_{8} \, \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(4e\right) & \mbox{Se VIII} \\ \mathbf{B}_{32} & = &x_{8} \, \mathbf{a}_{1}+ \left(\frac12 - y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{8}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{8}\right) \, c \, \cos\beta + x_{8} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{8}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{8}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se VIII} \\ \mathbf{B}_{33} & = &x_{9} \, \mathbf{a}_{1}+ y_{9} \, \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(4e\right) & \mbox{Se IX} \\ \mathbf{B}_{34} & = &- x_{9} \, \mathbf{a}_{1}+ \left(\frac12 + y_{9}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{9}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{9}\right) \, c \, \cos\beta - x_{9} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{9}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{9}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se IX} \\ \mathbf{B}_{35} & = &- x_{9} \, \mathbf{a}_{1}- y_{9} \, \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(4e\right) & \mbox{Se IX} \\ \mathbf{B}_{36} & = &x_{9} \, \mathbf{a}_{1}+ \left(\frac12 - y_{9}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{9}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{9}\right) \, c \, \cos\beta + x_{9} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{9}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{9}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se IX} \\ \mathbf{B}_{37} & = &x_{10} \, \mathbf{a}_{1}+ y_{10} \, \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(4e\right) & \mbox{Se X} \\ \mathbf{B}_{38} & = &- x_{10} \, \mathbf{a}_{1}+ \left(\frac12 + y_{10}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{10}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{10}\right) \, c \, \cos\beta - x_{10} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{10}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{10}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se X} \\ \mathbf{B}_{39} & = &- x_{10} \, \mathbf{a}_{1}- y_{10} \, \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(4e\right) & \mbox{Se X} \\ \mathbf{B}_{40} & = &x_{10} \, \mathbf{a}_{1}+ \left(\frac12 - y_{10}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{10}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{10}\right) \, c \, \cos\beta + x_{10} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{10}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{10}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se X} \\ \mathbf{B}_{41} & = &x_{11} \, \mathbf{a}_{1}+ y_{11} \, \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(4e\right) & \mbox{Se XI} \\ \mathbf{B}_{42} & = &- x_{11} \, \mathbf{a}_{1}+ \left(\frac12 + y_{11}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{11}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{11}\right) \, c \, \cos\beta - x_{11} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{11}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{11}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XI} \\ \mathbf{B}_{43} & = &- x_{11} \, \mathbf{a}_{1}- y_{11} \, \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(4e\right) & \mbox{Se XI} \\ \mathbf{B}_{44} & = &x_{11} \, \mathbf{a}_{1}+ \left(\frac12 - y_{11}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{11}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{11}\right) \, c \, \cos\beta + x_{11} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{11}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{11}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XI} \\ \mathbf{B}_{45} & = &x_{12} \, \mathbf{a}_{1}+ y_{12} \, \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(4e\right) & \mbox{Se XII} \\ \mathbf{B}_{46} & = &- x_{12} \, \mathbf{a}_{1}+ \left(\frac12 + y_{12}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{12}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{12}\right) \, c \, \cos\beta - x_{12} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{12}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{12}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XII} \\ \mathbf{B}_{47} & = &- x_{12} \, \mathbf{a}_{1}- y_{12} \, \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(4e\right) & \mbox{Se XII} \\ \mathbf{B}_{48} & = &x_{12} \, \mathbf{a}_{1}+ \left(\frac12 - y_{12}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{12}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{12}\right) \, c \, \cos\beta + x_{12} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{12}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{12}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XII} \\ \mathbf{B}_{49} & = &x_{13} \, \mathbf{a}_{1}+ y_{13} \, \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(4e\right) & \mbox{Se XIII} \\ \mathbf{B}_{50} & = &- x_{13} \, \mathbf{a}_{1}+ \left(\frac12 + y_{13}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{13}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{13}\right) \, c \, \cos\beta - x_{13} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{13}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{13}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XIII} \\ \mathbf{B}_{51} & = &- x_{13} \, \mathbf{a}_{1}- y_{13} \, \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(4e\right) & \mbox{Se XIII} \\ \mathbf{B}_{52} & = &x_{13} \, \mathbf{a}_{1}+ \left(\frac12 - y_{13}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{13}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{13}\right) \, c \, \cos\beta + x_{13} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{13}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{13}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XIII} \\ \mathbf{B}_{53} & = &x_{14} \, \mathbf{a}_{1}+ y_{14} \, \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(4e\right) & \mbox{Se XIV} \\ \mathbf{B}_{54} & = &- x_{14} \, \mathbf{a}_{1}+ \left(\frac12 + y_{14}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{14}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{14}\right) \, c \, \cos\beta - x_{14} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{14}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{14}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XIV} \\ \mathbf{B}_{55} & = &- x_{14} \, \mathbf{a}_{1}- y_{14} \, \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(4e\right) & \mbox{Se XIV} \\ \mathbf{B}_{56} & = &x_{14} \, \mathbf{a}_{1}+ \left(\frac12 - y_{14}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{14}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{14}\right) \, c \, \cos\beta + x_{14} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{14}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{14}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XIV} \\ \mathbf{B}_{57} & = &x_{15} \, \mathbf{a}_{1}+ y_{15} \, \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(4e\right) & \mbox{Se XV} \\ \mathbf{B}_{58} & = &- x_{15} \, \mathbf{a}_{1}+ \left(\frac12 + y_{15}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{15}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{15}\right) \, c \, \cos\beta - x_{15} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{15}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{15}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XV} \\ \mathbf{B}_{59} & = &- x_{15} \, \mathbf{a}_{1}- y_{15} \, \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(4e\right) & \mbox{Se XV} \\ \mathbf{B}_{60} & = &x_{15} \, \mathbf{a}_{1}+ \left(\frac12 - y_{15}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{15}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{15}\right) \, c \, \cos\beta + x_{15} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{15}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{15}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XV} \\ \mathbf{B}_{61} & = &x_{16} \, \mathbf{a}_{1}+ y_{16} \, \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(4e\right) & \mbox{Se XVI} \\ \mathbf{B}_{62} & = &- x_{16} \, \mathbf{a}_{1}+ \left(\frac12 + y_{16}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{16}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 - z_{16}\right) \, c \, \cos\beta - x_{16} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{16}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{16}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XVI} \\ \mathbf{B}_{63} & = &- x_{16} \, \mathbf{a}_{1}- y_{16} \, \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(4e\right) & \mbox{Se XVI} \\ \mathbf{B}_{64} & = &x_{16} \, \mathbf{a}_{1}+ \left(\frac12 - y_{16}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{16}\right) \, \mathbf{a}_{3}& = &\left(\left(\frac12 + z_{16}\right) \, c \, \cos\beta + x_{16} \, a\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{16}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{16}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Se XVI} \\ \end{array} \]

References

  • O. Foss and V. Janickis, X–Ray crystal structure of a new red, monoclinic form of cyclo–octaselenium, Se8, J. Chem. Soc., Chem. Commun. pp. 834–835 (1977), doi:10.1039/C39770000834.
  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 5716.

Geometry files


Prototype Generator

aflow --proto=A_mP64_14_16e --params=

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