CaC2–I ($C11_{a}$) Structure : A2B_tI6_139_e_a
| 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:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ca} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} & = & z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{C} \\ \mathbf{B}_{3} & = & -z_{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} & = & -z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{C} \\ \end{array} \]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
- N.–G. Vannerberg, The Crystal Structure of Calcium Carbide III, Acta Chem. Scand. 15, 769–774 (1961), doi:10.3891/acta.chem.scand.15-0769.