Phase equilibrium in small-sized solid alloys and controlling factors

为了了解纳米级固体合金颗粒的相平衡，有必要弄清楚相互溶解度增强的原因。在此前提下，用固体合金颗粒在Au-Ge体系中研究了溶解度极限随尺寸的变化。结果表明，当颗粒尺寸大于20nm时，固相溶解度的增强并不明显，但随着颗粒尺寸的减小，固相溶解度的增强变得明显，最终在直径小于几nm的颗粒中形成非晶相而不是结晶固溶体。结果表明，与金在锗中的溶解度相比，随着颗粒尺寸的减小，金在Au中的溶解度大大提高。然后对这些实验结果进行理论分析。基于纳米颗粒的德拜温度比块状材料低10-30%的事实，从理论上研究了纳米颗粒弹性常数的降低对固体溶解度极限提高的影响方式和影响程度。在实际应用中，采用正则解近似法计算了体系的吉布斯自由能，并在相互作用参数中加入了弹性能项。在计算中，弹性常数的值由块状材料的100%改为50%。结果表明，在Au-Ge体系中实验观察到，弹性常数的减小会导致固体溶解度的显著提高。由此得出，弹性性能在决定纳米级固体合金颗粒的相平衡中起着至关重要的作用。

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.