Anomalous elastic hardening in Fe-Co alloys at high temperature

The elastic moduli of ${\mathrm{Fe}}_{1-c}{\mathrm{Co}}_c$ ($c\le 0.2$) alloys are found to decrease strongly with increasing temperature, but show very weak alloying effects for both low-temperature ferromagnetic and high-temperature paramagnetic states. For temperatures slightly below and around the Curie temperature of Fe, Co addition significantly increases the elastic moduli. The variation of the tetragonal shear elastic constant upon 20% Co addition increases from a small negative value to more than 135% as the temperature rises from 0 to 1200 K. The expected elastic softening in the case of Al doping is not confirmed. Both anomalous trends are ascribed to the interplay between intrinsic chemical effects, magnetism, and temperature.

Figure 1

Changes (in %) of the bulk (upper panel), shear (middle panel) and Young's (lower panel) moduli of Fe-Co relative to those of pure Fe at 0 K as a function of temperature and Co concentration.

Figure 2

Changes (in %) of the tetragonal shear elastic constant $C^{\prime }$ of Fe-Co and Fe-Al relative to those of pure Fe at 0 K as a function of temperature and Co and Al concentration.

Figure 3

Total and partial ($e_g$ and $t_{2g}$) density of states of nonmagnetic (NM, upper panel), ferromagnetic (FM, middle panel), and paramagnetic (PM, lower panel) Fe in the bcc lattice. The dashed lines mark the Fermi level $E_{\mathrm{F}}$. For NM, the occupation number is shown on the right axis. For NM and PM, only one spin channel is shown.