Solid solubility limit in alloying nanoparticles

In order to gain a better thermodynamic understanding of the phase diagram of alloying nanoparticles, we establish a size-dependent solid solubility model of binary metallic systems to elucidate the anomalous solid solubility in nanometre-sized alloying particles. It is found that a diameter of 20 nm seems a threshold value of the size of alloying nanoparticles for the unusual solid solubility, i.e. the solubility is greatly promoted with decreasing grain size when the size of alloying nanoparticles is less than 20 nm. Taking the Pb-Sn system as an example, we show that the theoretical predictions are consistent with experimental data.