Polycrystalline elastic constants of in situ cementite (Fe3C)

By extrapolation, we estimated cementiteʹs elastic constants. Altogether, we studied seven Fe–C binary alloys varying from 0 to 17.3 at% carbon. Thus, we measured hypoeutectoid, near-eutectoid, and hypereutectoid alloys. Using the hypereutectoid compositions, for cementite, we report a complete set of quasiisotropic (polycrystal) elastic constants. To correct for texture, we used a Voigt–Reuss–Hill averaging method. Surprisingly, for the dilatational modes, cementiteʹs elastic constants differ little from those of b.c.c. iron and are about 10% higher for a shear mode such as the Young modulus. This stiffening indicates a tendency toward Fe–C covalent bonding. The decrease in Poisson ratio supports covalent bonding, but the small decrease indicates smaller covalent-bonding effects than expected by Pauling. Against ten previous Young modulus reports, we find cementite stiffer than α-iron, almost 10% in the Young modulus. Our results support Paulingʹs suggested Fe–C bonding over Petchʹs suggested Fe–Fe bonding. We compare our results with those from recent ab initio calculations, which make very different predictions, which suggests that cementite occurs in at least two crystal structures, a suggestion made at least twice previously. Our derived Debye temperature TD = 501 K differs considerably from previous reports. Within measurement errors, our bulk modulus agrees with three recent geophysical measurements.