Baddeleyite (ZrO2, $C43$) Structure: A2B_mP12_14_2e_e

Picture of Structure; Click for Big Picture
Prototype : ZrO2
AFLOW prototype label : A2B_mP12_14_2e_e
Strukturbericht designation : $C43$
Pearson symbol : mP12
Space group number : 14
Space group symbol : $\mbox{P2}_{1}\mbox{/c}$
AFLOW prototype command : aflow --proto=A2B_mP12_14_2e_e
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • HfO2, CoSb2, Ag2Te

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{O 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{O 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{O 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{O 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{O 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{O 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{O 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{O 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{Zr} \\ \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{Zr} \\ \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{Zr} \\ \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{Zr} \\ \end{array} \]

References

  • C. J. Howard, R. J. Hill, and B. E. Reichert, Structures of ZrO2 polymorphs at room temperature by high–resolution neutron powder diffraction, Acta Crystallogr. Sect. B Struct. Sci. 44, 116–120 (1988), doi:10.1107/S0108768187010279.

Geometry files


Prototype Generator

aflow --proto=A2B_mP12_14_2e_e --params=

Species:

Running:

Output: