  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.
