Sodium Chlorate (NaClO3, $G3$) Structure: ABC3_cP20_198_a_a_b

Picture of Structure; Click for Big Picture
Prototype : NaClO3
AFLOW prototype label : ABC3_cP20_198_a_a_b
Strukturbericht designation : $G3$
Pearson symbol : cP20
Space group number : 198
Space group symbol : $P2_{1}3$
AFLOW prototype command : aflow --proto=ABC3_cP20_198_a_a_b
--params=
$a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • NaBrO3

Simple Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & a \, \mathbf{\hat{z}} \\ \end{array} \]

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} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cl} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cl} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cl} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cl} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Na} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Na} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Na} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Na} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{13} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{16} & = & -z_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{17} & = & y_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{18} & = & -y_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{O} \\ \end{array} \]

References

  • G. N. Ramachandran and K. S. Chandrasekaran, The absolute configuration of sodium chlorate, Acta Cryst. 10, 671–675 (1957), doi:10.1107/S0365110X57002327.

Found in

  • A. A. Kaminskii, S. N. Bagayev, J. Hulliger, H. Eichler, J. Findeisen, and R. Macdonald, Acentric cubic NaClO3–a new crystal for Raman lasers, Appl. Phys. B 67, 157–162 (1998), doi:10.1007/s003400050487.

Geometry files


Prototype Generator

aflow --proto=ABC3_cP20_198_a_a_b --params=

Species:

Running:

Output: