Magnetic cluster expansion model for bcc-fcc transitions in Fe and Fe-Cr alloys

An ab initio-based magnetic-cluster-expansion treatment developed for body- and face-centered cubic phases of iron and iron-chromium alloys is applied to modeling the $\alpha \text{−}\gamma$ and $\gamma \text{−}\delta$ phase transitions in these materials. The Curie, Néel, and the structural phase-transition temperatures predicted by the model are in good agreement with experimental observations, indicating that it is the thermal excitation of magnetic and phonon degrees of freedom that stabilizes the fcc $\gamma$ phase. The model also describes the occurrence of the $\gamma$ loop in the phase diagram of Fe-Cr alloys for a realistic interval of temperatures and Cr concentrations.

Figure 1

(Color online) The magnetic part of the specific heat for bcc (black circles) and fcc (red circles) iron. Lines are fits to the calculated data, see text.

Figure 2

(Color online) Difference between the free energies of fcc $\gamma \text{-Fe}$ and bcc $\alpha \text{-Fe}$ phases $\Delta F_{tot}=F^{\gamma }-F^{\alpha }$, and its constituent parts plotted (a) for the entire temperature range investigated in this study and (b) for the $\alpha \text{−}\gamma$ transition region.

Figure 3

(Color online) Difference between the free energies of fcc and bcc ${\text{Fe}}_{1-x}{\text{Cr}}_x$ alloys plotted as a function of chromium content $x_{\text{Cr}}$. The predicted $\gamma$ loop is shown in the inset.