Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A_mC12_5_3c-001

This structure originally had the label A_mC12_5_3c. Calls to that address will be redirected here.

If you are using this page, please cite:
M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)

Links to this page

https://aflow.org/p/FECP
or https://aflow.org/p/A_mC12_5_3c-001
or PDF Version

$A19$ Po Structure (Obsolete): A_mC12_5_3c-001

Picture of Structure; Click for Big Picture
Prototype Po
AFLOW prototype label A_mC12_5_3c-001
Strukturbericht designation $A19$
ICSD 31684
Pearson symbol mC12
Space group number 5
Space group symbol $C2$
AFLOW prototype command aflow --proto=A_mC12_5_3c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$

  • This was the original determination of the structure of Po, given the Strukturbericht designation $A19$ by (Gottfried, 1938, 4-5). Eventually it was found that the sample used here was a mixture of $\alpha$–Po ($A_h$) and $\beta$–Po ($A_i$) (Donohue, 1982, 390). We retain the $A19$ page for historical interest.
  • The ICSD entry uses polonium coordinates that are slightly different from the ones we use. Both sets are published in (Rollier, 1936).

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po I
$\mathbf{B_{2}}$ = $- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ = $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po I
$\mathbf{B_{3}}$ = $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po II
$\mathbf{B_{4}}$ = $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ = $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po II
$\mathbf{B_{5}}$ = $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po III
$\mathbf{B_{6}}$ = $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4c) Po III

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 and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).

Found in

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

Prototype Generator

aflow --proto=A_mC12_5_3c --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$

Species:

Running:

Output: