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

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 sheetlike 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.