Elastic anisotropy of iron carbides with trigonal-prismatic coordination of C by Fe

• We report four DFT-based Fe–C structures with trigonal prisms of Fe around C.
• A unified setting for Fe3C, Fe5C2 and Fe2C eases comparison of their structures.
• Structurally similar Fe3C, Fe5C2 and Fe2C show a similar elastic anisotropy.
• Fe7C3 is elastically much less anisotropic than Fe3C, Fe5C2 and Fe2C.

Elastic anisotropies obtained by density functional theory (DFT) calculations of four iron carbides exhibiting trigonal prismatic coordination of C by Fe are presented and compared. The elastic anisotropy is considerable for the carbides θ-Fe3C, χ-Fe5C2 and a hypothetical Fe2C with Pbcm symmetry, all with sheet-like arrangement of the trigonal prisms which results in a largely parallel arrangement of the prism axes. It is found that the easy shear which is mainly responsible for the large elastic anisotropy in these carbides occurs in all these three carbides in a plane perpendicular to the average axis of the prisms. In contrast to these three elastically anisotropic carbides, Fe7C3, in which the axes of the trigonal prisms are much more regularly distributed in space, shows a negligible elastic anisotropy.