Po ($A19$) Structure: A_mC12_5_3c

Picture of Structure; Click for Big Picture
Prototype : Po
AFLOW prototype label : A_mC12_5_3c
Strukturbericht designation : $A19$
Pearson symbol : mC12
Space group number : 5
Space group symbol : $\mbox{C2}$
AFLOW prototype command : aflow --proto=A_mC12_5_3c
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


  • This was the original determination of the structure of Po, and given the Strukturbericht designation A19. (Gottfried, 1938, 4-5). Eventually it was determined that the sample used here was a mixture of $\alpha$–Po (Ah) and $\beta$–Po (Ai) (Donohue, 1982, 390). We retain the A19 page for historical interest.

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+ \left(x_{1} + y_{1}\right) \, \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(4c\right) & \mbox{Po I} \\ \mathbf{B}_{2} & =&- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}+ \left(y_{1} - x_{1}\right) \, \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(4c\right) & \mbox{Po I} \\ \mathbf{B}_{3} & =&\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+ \left(x_{2} + y_{2}\right) \, \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(4c\right) & \mbox{Po II} \\ \mathbf{B}_{4} & =&- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+ \left(y_{2} - x_{2}\right) \, \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(4c\right) & \mbox{Po II} \\ \mathbf{B}_{5} & =&\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} + y_{3}\right) \, \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(4c\right) & \mbox{Po III} \\ \mathbf{B}_{6} & =&- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} - x_{3}\right) \, \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(4c\right) & \mbox{Po III} \\ \end{array} \]

References

  • M. A. Rollier, S. B. Hendricks, and L. R. Maxwell, The Crystal Structure of Polonium by Electron Diffraction, J. Chem. Phys. 4, 648–652 (1936), doi:10.1063/1.1749762.
  • C. Gottfried, Strukturbericht Band IV, 1936 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1938).
  • J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982).

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=A_mC12_5_3c --params=

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