CaC$_{2}$-I ($C11_{a}$) Structure: A2B_tI6_139_e_a-001
| Prototype | C$_{2}$Ca |
| AFLOW prototype label | A2B_tI6_139_e_a-001 |
| Strukturbericht designation | $C11_{a}$ |
| ICSD | 56164 |
| Pearson symbol | tI6 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A2B_tI6_139_e_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}$ |
Other compounds with this structure
BaC$_{2}$, BaO$_{2}$, CeC$_{2}$, CsO$_{2}$, DyC$_{2}$, ErC$_{2}$, EuC$_{2}$, GdC$_{2}$, HoC$_{2}$, KO$_{2}$, LaC$_{2}$, LuC$_{2}$, NdC$_{2}$, PrC$_{2}$, PuC$_{2}$, RbO$_{2}$, SmC$_{2}$, SrC$_{2}$, SrO$_{2}$, TbC$_{2}$, TmC$_{2}$, UC$_{2}$, YC$_{2}$, YbC$_{2}$
- (Ewald, 1931) designated both CaC$_{2}$ and MoSi$_{2}$ as Strukturbericht $C11$. (Smithells,1955) separated them into $C11_{a}$ (CaC$_{2}$) and $C11_{b}$ (MoSi$_{2}$, AB2_tI6_139_a_e).
- This is the stable room-temperature structure for CaC$_{2}$. At low temperatures it transforms into the ThC$_{2}$ ($C_{g}$) structure. There is also a meta-stable room temperature structure CaC$_{2}$-III (A2B_mC12_12_2i_i).
- (v. 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. (Stackelberg, 1930) gives $a$ = 5.84Å for the face-centered lattice. If we divide this by $\sqrt{2}$ we get $a$ = 3.87Å for the body-centered lattice. The ICSD entry gives $a$ = 3.83, which we attribute to an arithmetic error.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ca I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4e) | C I |
| $\mathbf{B_{3}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | C I |
References
- M. von Stackelberg, Die Krystallstruktur des CaC$_{2}$, Naturwissenschaften 18, 305–306 (1930), doi:10.1007/BF01.
- 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.
Prototype Generator
aflow --proto=A2B_tI6_139_e_a --params=$a,c/a,z_{2}$