KClO3 ($G0_{6}$) Structure: ABC3_mP10_11_e_e_ef

Picture of Structure; Click for Big Picture
Prototype : KClO3
AFLOW prototype label : ABC3_mP10_11_e_e_ef
Strukturbericht designation : $G0_{6}$
Pearson symbol : mP10
Space group number : 11
Space group symbol : $\mbox{P2}_{1}\mbox{/m}$
AFLOW prototype command : aflow --proto=ABC3_mP10_11_e_e_ef
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


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} + \frac14 \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Cl} \\ \mathbf{B}_{2} & =& - x_{1} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{1} \, \mathbf{a}_{3}& =& - \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Cl} \\ \mathbf{B}_{3} & =& x_{2} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{K} \\ \mathbf{B}_{4} & =& - x_{2} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{2} \, \mathbf{a}_{3}& =& - \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{K} \\ \mathbf{B}_{5} & =& x_{3} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O I} \\ \mathbf{B}_{6} & =& - x_{3} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O I} \\ \mathbf{B}_{7} & =& 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(4f\right) & \mbox{O II} \\ \mathbf{B}_{8} & =& - x_{4} \, \mathbf{a}_{1} + \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{9} & =& - 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(4f\right) & \mbox{O II} \\ \mathbf{B}_{10} & =& x_{4} \, \mathbf{a}_{1} + \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O II} \\ \end{array} \]

References

  • J. Danielsen, A. Hazell, and F. K. Larsen, The Structure of Potassium Chlorate at 77 and 298 K, Acta Crystallogr. Sect. B Struct. Sci. 37, 913–915 (1981), doi:10.1107/S0567740881004573.

Geometry files


Prototype Generator

aflow --proto=ABC3_mP10_11_e_e_ef --params=

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