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First-principles study of the stability of bimetallic PdPt nanoparticles under a finite temperature

To understand the vibrational and configurational entropy effects for the stability of core-shell and solid-solution bimetallic nanoparticles, we theoretically investigated the excess energy of PdPt nanoparticles, adopting the (PdPt)201 model of ca. 2 nm by using the density functional method. The vibrational energy and entropy terms contributed to the total energy of both core-shell and solid-solution nanoparticles. The configurational entropy term was defined only for the solid-solution nanoparticles. Although the absolute values of vibrational energy and entropy terms were much larger than that of configurational entropy term, their contributions were limited in the form of excess free energy due to the small difference between different atomic configurations. The large contribution of configurational entropy term to the excess free energy was clearly confirmed from our first-principles calculations. To estimate the stability of core-shell and solid-solution metal nanoparticles based on the excess energy, the configurational entropy term was the dominant factor.