C2, C3 and ... Nothing Simple
There are many carbides that contain two linked carbon units. CaC2 is one, a simple structure in which the C2 units are close to C22–, like an acetylene (HCCH) with the two hydrogens ripped off as protons. Consistently, the C-C bond length in the C2 units of CaC2 is acetylenic, 1.19 angstroms. There's a drawing of the atomic positions in calcium carbide in another article I've written (Marginalia, July–August 1995). C-C bond lengths in the C2 units of other carbides range remarkably, from 1.19 to 1.48 angstroms, nearly matching the range of C-C bond lengths in organic molecules, from a triple bond to a single bond. This is not an accident.
The final and rare mode of C-C bonding in carbides is a C3 unit. It occurs in Ca3Cl2C3, but I'd rather show you the phantasmagoric Sc3C4 structure of Pöttgen and Jeitschko (Figure 3). Like a smorgasbord of carbon forms in carbides, it has everything—C and C2 and C3 units in a complex arrangement whose repeat unit is Sc30C40, containing 12 C, 2 C2 and 8 C3. It is as if the metal atoms had torn apart a graphite lattice, forming little islands of organic matter in the metal.
Retreating just a bit from this vertiginous edge of complexity, consider Ca4Ni3C5, also made by the Jeitschko group at Münster in Germany. (Wolfgang Jeitschko is responsible for a great fraction of the carbides we have.) Figure 4 shows the one-dimensional Ni3C58– ribbon cut out of the structure. It has vertex-sharing nickel squares, with C2 wingtips. And smack in the middle of each square in this piecewise organic molecule—a square-planar (not tetrahedral) carbon!