Size-, shape- and composition-dependent alloying ability of bimetallic nanoparticles.

Based on the surface-area-difference model, the formation enthalpies and the formation Gibbs free energies of bimetallic nanoparticles are calculated by considering size and shape effects. Composition-critical size diagrams were graphed for bulk immiscible bimetallic nanoparticles with the developed model. The results reveal that both the formation enthalpy and formation Gibbs free energy decrease with the decrease of particle size. The effect of rising temperature is similar to the diminishing of particle size on reducing the formation Gibbs free energy. Contrary to the positive formation enthalpy of the bulk immiscible system, a negative formation enthalpy is obtained when the particles are smaller than a critical size. With the decrease of size, the alloying process first takes place in the dilute solute regions, then broadens to the dense solute regions and finally, particles with all compositions can be alloyed. The composition-critical size diagram is classified into three regions by the critical size curves with shape factors of 1 and 1.49, that is, the non-alloying region, alloying region and possible alloying region. The model predictions correspond well with experimental evidences and computer simulation results for Cu-Ag, Au-Ni, Ag-Pt and Au-Pt systems.