Fig. 9: Phase-field scenario and landscapes of free energy density.
a Schematic of the physical processes during SLS, i.e., localized melting, multiple mass transfer paths, and grain boundary migration. Here, the bulk diffusion GB-N represents the path from grain boundary to neck through the bulk, while SF-N presents the path from the surface to neck through the bulk. b Profiles of different OPs across solid-state phases with the corresponding scales. c The landscape of mesoscopic stress-free ftot across the surface and the γ/γ grain boundaries at various temperatures. d The landscape of nanoscopic stress-free ftot across the \(\gamma /{\gamma }^{{\prime} }\) coherent interface at 600 K. Transition path, \({f}_{{{{\rm{ch}}}}}^{\gamma }\), \({f}_{{{{\rm{ch}}}}}^{{\gamma }^{{\prime} }}\), and the energy band of the four-sublattice states \(\{\Delta {f}_{{{{\rm{4sl}}}}}\}=\{{f}_{{{{\rm{4sl}}}}}({Y}^{(s)})-{f}_{{{{\rm{4sl}}}}}({Y}^{(s)}={X}^{{\gamma }^{{\prime} }})\}\) are also denoted. Inset: sublattice sites for the L12 ordering of Fe-Ni. e–f Energy surface of magneto-crystalline anisotropy energy, which alters w.r.t. the sign of anisotropy constant Ku, i.e., (e) the easy-axis anisotropy when Ku > 0 and (f) the easy-plane anisotropy when Ku < 0.
