Size effect on the melting temperature of gold particles

TLDR

Small gold particles exhibit size‑dependent melting temperatures, and two phenomenological models—one describing solid–liquid–vapor equilibrium and another invoking a preexisting liquid layer—have been proposed to explain this behavior. The study derives a new thermodynamic equilibrium expression to enable a clearer comparison between these two models. Using a scanning electron‑diffraction technique on particles as small as 20 Å and accounting for sample size distribution, the authors measured melting points and applied the new equilibrium formulation. Measured melting temperatures agree quantitatively with both models; the first model fits using only bulk gold constants, while the second requires a ~6 Å liquid layer surrounding the solid particle.

Abstract

Recently, small particles have been shown to exhibit a melting temperature which depends on the particle size. The various possible experimental methods have been compared and measurements of the melting points of small gold particles have been made using a scanning electron-diffraction technique. This method was applied to particles having diameters down to 20 \AA{}. Consideration of the size distribution over an entire sample makes it necessary to carry out a careful analysis of the experimental results in order to deduce the melting temperature of particles having a well-defined diameter. The experimental results are quantitatively in good agreement with two phenomenological models. The first model describes the equilibrium condition for a system formed by a solid particle, a liquid particle having the same mass, and their saturating vapor phase. The second model assumes the preexistence of a liquid layer surrounding the solid particle and describes the equilibrium of such a system in the presence of the vapor phase. In order to permit a better comparison between both models, a new expression for the thermodynamic equilibrium condition has been derived in the present work. In the case of the first model, the agreement was obtained using only the physical constants of massive gold. In applying the second model, however, one is compelled to assume the existence of a liquid layer having a thickness of about 6 \AA{}.