Ca3Al2O6 ($E9_{1}$) Structure: A2B3C6_cP33_221_cd_ag_fh

Picture of Structure; Click for Big Picture
Prototype : Ca3Al2O6
AFLOW prototype label : A2B3C6_cP33_221_cd_ag_fh
Strukturbericht designation : $E9_{1}$
Pearson symbol : cP33
Space group number : 221
Space group symbol : $Pm\bar{3}m$
AFLOW prototype command : aflow --proto=A2B3C6_cP33_221_cd_ag_fh
--params=
$a$,$x_{4}$,$x_{5}$,$x_{6}$


  • (Steele, 1929) do not use the standard Wyckoff position notation to describe the atomic positions, so we use the parameters found in (Herman, 1937). An alternative description of the structure places the O I atoms on the (6e) $(\pm x , 0 , 0) \dots$ site rather than the (6f) site. (Mondal, 1975) reanalyzed this structure and concluded that the true structure was one where the lattice constant was doubled and contained 264 atoms. See the Ca3Al2O6 (A2B3C6_cP264_205_2d_ab2c2d_6d) structure page.

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} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ca I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Al I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Al I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(3c\right) & \mbox{Al I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(3d\right) & \mbox{Al II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(3d\right) & \mbox{Al II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{z}} & \left(3d\right) & \mbox{Al 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}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & -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}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{15} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{16} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{18} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{19} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{20} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{21} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ca II} \\ \mathbf{B}_{22} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & -x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & -x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{26} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{27} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{28} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{29} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{30} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{31} & = & -x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{32} & = & \frac{1}{2} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \mathbf{B}_{33} & = & \frac{1}{2} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(12h\right) & \mbox{O II} \\ \end{array} \]

References

  • F. A. Steele and W. P. Davey, The Crystal Structure of Tricalcium Aluminate, J. Am. Chem. Soc. 51, 2283–2293 (1929), doi:10.1021/ja01383a001.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II, 1928–1932 (Akademsiche Verlagsgesellschaft M. B. H, Leipzig, 1937).

Found in

  • P. Mondal and J. W. Jeffery, The crystal structure of tricalcium aluminate, Ca3Al2O6, Acta Crystallogr. Sect. B Struct. Sci. 31, 689–697 (1975), doi:10.1107/S0567740875003639.

Geometry files


Prototype Generator

aflow --proto=A2B3C6_cP33_221_cd_ag_fh --params=

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