Two-phase equilibrium states in individual Cu-Ni nanoparticles: size, depletion and hysteresis effects.

Aram S Shirinyan

doi:10.3762/bjnano.6.185

Abstract

In isolated bimetallic nanoscale systems the limit amount of matter and surface-induced size effects can change the thermodynamics of first-order phase transformation. In this paper we present theoretical modification of Gibbs free energy concept describing first-order phase transformation of binary alloyed nanoparticles taking into account size effects as well as depletion and hysteresis effects. In such a way the hysteresis in a form of nonsymmetry for forth and back transforming paths takes place; compositional splitting and the loops-like splitted path on the size dependent temperature–composition phase diagram occur. Our calculations for individual Cu–Ni nanoparticle show that one must differentiate the solubility curves and the equilibrium loops (discussed here in term of solidification and melting loops). For the first time we have calculated and present here on the temperature–composition phase diagram the nanomelting loop at the size of 80 nm and the nanosolidification loop at the size of 25 nm for an individual Cu–Ni nanoparticle. So we observe the difference between the size-dependent phase diagram and solubility diagram, between two-phase equilibrium curves and solubility curves; also intersection of nanoliquidus and nanosolidus is available. These findings lead to the necessity to reconsider such basic concepts in materials science as phase diagram and solubility diagram.

Highlights

One of the key questions in nanoscience is related to the problem of equilibrium phase diagrams variation for multicomponent finite systems with size decreasing
The increasing of the sizes leads to the vanishing of hysteresis effect
In general application of the modified Gibbs thermodynamics to free binary nanosystems gives that: i) the solubility curves shift down to lower temperatures, as compared to bulk case, and are the size-dependent; ii) the effective width of the two-phase region on T–X diagram decreases as the size of a bimetallic nanoparticle decreases; iii) nanosolidus and nanoliquidus can overlap and intersect; iv) the forms of the solubility curves on the diagram change; v) solubility limits, eutectic and peritectic points shift in composition and are size-dependent

Summary

Introduction

One of the key questions in nanoscience is related to the problem of equilibrium phase diagrams variation for multicomponent finite systems with size decreasing.

Results

Conclusion