Phase equilibrium in small-sized solid alloys and controlling factors

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In order to understand the phase equilibrium in nm-sized solid alloy particles, it is essential to make clear the cause of the enhancement of the mutual solubility. Based upon this premise, changes in the solubility limit with size have been studied using solid alloy particles in the Au-Ge system. It was found that the enhancement of the mutual solid solubility was not so significant when the size of particles was above around 20nm, but, it became remarkable with decreasing size of particles and eventually in particles smaller than a few nm in diameter an amorphous phase formed instead of crystalline solid solutions. It was noted that the Ge solubility in Au was much more enhanced with decreasing size of particles as compared to the Au solubility in Ge. These experimental results were then subjected to a theoretical analysis. Based upon the fact that the Debye temperature of nm-sized particles is lower by 10-30% than that of bulk materials, it was theoretically studied how and to what extent the decrease in the elastic constant in nm-sized particles may affect the increase in the solid solubility limit. Practically, the Gibbs free energy of the system was calculated using the regular solution approximation, and in the calculation an elastic energy term was integrated into the interaction parameter. In the calculation, the value of the elastic constant was changed from 100% to 50% of the value for bulk materials. As a result, it turned out that the decrease in the elastic constant could cause a significant enhancement of the solid solubility which was experimentally observed in the Au-Ge system. It is then concluded that the elastic property plays an essential role in determining the phase equilibrium in nm-sized solid alloy particles.