  The nickel--carbon system has received increased attention over the past
years due to the relevance of nickel as a catalyst for carbon nanotube and
graphene growth, where Nickel carbide intermediates may be involved or carbide
interface layers form in the end. Nickel--carbon composite thin films
comprising Ni$_3$C are especially interesting in mechanical sensing
applications. Due to the meta-stability of nickel carbides, formation
conditions and the coupling between mechanical and electrical properties are
not yet well understood. Using first-principles electronic structure methods,
we calculated the elastic properties of Ni$_3$C, Ni$_2$C and NiC, as well as
changes in electronic properties under mechanical strain. We observe that the
electronic density of states around the Fermi level does not change under the
considered strains of up to 1%, which correspond to stresses up to 3GPa.
Relative changes in conductivity of Ni$_3$C range up to maximum values of about
10%.
