A Cahn-Hilliard approach to modelling phase separation in bimetallic nanoparticles

A ternary system of Cahn-Hilliard equations is used to model phase separation processes in bimetallic nanoparticles. The third component in the ternary system is taken to be vacuum, such that we are able to simulate bimetallic nanoparticles without any need to impose restrictions on the nanoparticle boundary. Strain effects, due to lattice mismatch, are introduced by coupling with the Navier-Lamé equations. The use of this diffuse-interface approach allows the simulation of significantly larger systems than currently feasible with atomistic methods. Particular attention is paid to the core-shell to quasi-Janus particle transition that has been observed in CuAg and other bimetallic nanoparticles of weakly miscible elements. Our simulations are able to capture the various effects seen previously in experimental work and in atomistic simulations. In particular, we observe a transition from core-shell structure to quasi-Janus particle structure as the size of the particles increases. Moreover, it is shown that core-shell particles prevail when the thickness of the shell is small in comparison to the core size. The inclusion of elastic effects into the model further promotes the formation of quasi-Janus particles. The transition from core-shell to quasi-Janus particle structure is, however, also seen in the absence of elastic effects