CaC2–I ($C11_{a}$) Structure : A2B_tI6_139_e_a

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Prototype : C2Ca
AFLOW prototype label : A2B_tI6_139_e_a
Strukturbericht designation : $C11_{a}$
Pearson symbol : tI6
Space group number : 139
Space group symbol : $I4/mmm$
AFLOW prototype command : aflow --proto=A2B_tI6_139_e_a
--params=
$a$,$c/a$,$z_{2}$


  • (Ewald, 1931) designated both CaC2 and MoSi2 as Strukturbericht $C11$. (Smithells,1955) separated them into $C11_{a}$ (CaC2) and $C11_{b}$ (MoSi2, AB2_tI6_139_a_e).
  • This is the stable room–temperature structure for CaC2. There is also a meta–stable room temperature structure CaC2–III (A2B_mC12_12_2i_i), and a low–temperature structure CaC2, which has the ThC2 ($C_{g}$) structure.
  • (von Stackelberg, 1930) describes this structure in a face–centered–tetragonal setting. We follow (Smithells, 1955) and place it in the equivalent body–centered tetragonal setting.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} & = & z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{C} \\ \mathbf{B}_{3} & = & -z_{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} & = & -z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{C} \\ \end{array} \]

References

  • M. von Stackelberg, Die Krystallstruktur des CaC2, Naturwissenschaften 18, 305–306 (1930), doi:10.1007/BF01495090.
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.

Found in

Geometry files


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