Surface-directed and bulk spinodal decomposition compete to decide the morphology of bimetallic nanoparticles

An embedded-domain phase-field formalism is used for studying phase transformation pathways in bimetallic nanoparticles (BNPs). Competition of bulk and surface-directed spinodal decomposition processes and their interplay with capillarity are identified as the main determinants of BNP morphology. The former is characterized by an effective bulk driving force $\Delta\tilde{f}$ which increases with decreasing temperature, while the latter manifests itself through a balance of interfacial energies captured by the contact angle $\theta$. The simulated morphologies, namely, core-shell, Janus and inverse core-shell, cluster into distinct regions of the $\Delta\tilde{f}$-$\theta$ space. Variation of $\theta$ with $\Delta\tilde{f}$ in the Ag-Cu alloy system is computed as a function of temperature using a CALPHAD approach in which surface energies are estimated from a modified Butler equation. This $\theta-\Delta\tilde{f}$ trajectory for Ag-Cu, when superimposed on the morphology map, enables the prediction of different morphological transitions as a function of temperature. Therefore, the study establishes a unique thermodynamic framework coupled with phase-field simulations for predicting and tailoring nanoparticle morphology through a variation of processing temperature.