NaNbO3 Structure : ABC3_oP40_17_abcd_2e_abcd4e

Picture of Structure; Click for Big Picture
Prototype : NaNbO3
AFLOW prototype label : ABC3_oP40_17_abcd_2e_abcd4e
Strukturbericht designation : None
Pearson symbol : oP40
Space group number : 17
Space group symbol : $P222_{1}$
AFLOW prototype command : aflow --proto=ABC3_oP40_17_abcd_2e_abcd4e
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$y_{5}$,$y_{6}$,$y_{7}$,$y_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$


  • (Downs, 2003) identifies this as a possible polymorph of Lueshite.
  • If the AFLOW parameters are set to ––params=$a$, $1$, $\sqrt{8}$, $1/2$, $0$, $0$, $1/2$, $1/2$, $0$, $0$, $1/2$, $0$, $0$, $3/8$, $1/2$, $1/2$, $3/8$, $1/4$, $1/4$, $3/8$, $3/4$, $1/4$, $3/8$, $1/4$, $3/4$, $3/8$, $3/4$, $3/4$, $3/8$ then the structure is equivalent to Cubic Perovskite $E2_{1}$.

Simple Orthorhombic primitive vectors:

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

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}a \, \mathbf{\hat{x}} & \left(2a\right) & \mbox{Na I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Na I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} & = & x_{2}a \, \mathbf{\hat{x}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} & \left(2b\right) & \mbox{Na II} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Na II} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} & \left(2b\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & y_{5} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{5}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Na III} \\ \mathbf{B}_{10} & = & -y_{5} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{5}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Na III} \\ \mathbf{B}_{11} & = & y_{6} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{O III} \\ \mathbf{B}_{12} & = & -y_{6} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{6}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{O III} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Na IV} \\ \mathbf{B}_{14} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Na IV} \\ \mathbf{B}_{15} & = & \frac{1}{2} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{O IV} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{O IV} \\ \mathbf{B}_{17} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb I} \\ \mathbf{B}_{18} & = & -x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb I} \\ \mathbf{B}_{19} & = & -x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb I} \\ \mathbf{B}_{20} & = & x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb I} \\ \mathbf{B}_{21} & = & x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb II} \\ \mathbf{B}_{22} & = & -x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb II} \\ \mathbf{B}_{23} & = & -x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb II} \\ \mathbf{B}_{24} & = & x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Nb II} \\ \mathbf{B}_{25} & = & x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O V} \\ \mathbf{B}_{26} & = & -x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O V} \\ \mathbf{B}_{27} & = & -x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O V} \\ \mathbf{B}_{28} & = & x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O V} \\ \mathbf{B}_{29} & = & x_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VI} \\ \mathbf{B}_{30} & = & -x_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VI} \\ \mathbf{B}_{31} & = & -x_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{12}\right) \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{12}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VI} \\ \mathbf{B}_{32} & = & x_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}}-z_{12}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VI} \\ \mathbf{B}_{33} & = & x_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VII} \\ \mathbf{B}_{34} & = & -x_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VII} \\ \mathbf{B}_{35} & = & -x_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{13}\right) \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{13}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VII} \\ \mathbf{B}_{36} & = & x_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}}-z_{13}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VII} \\ \mathbf{B}_{37} & = & x_{14} \, \mathbf{a}_{1} + y_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VIII} \\ \mathbf{B}_{38} & = & -x_{14} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VIII} \\ \mathbf{B}_{39} & = & -x_{14} \, \mathbf{a}_{1} + y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{14}\right) \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{14}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VIII} \\ \mathbf{B}_{40} & = & x_{14} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}}-z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O VIII} \\ \end{array} \]

References

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=ABC3_oP40_17_abcd_2e_abcd4e --params=

Species:

Running:

Output: