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根据热力学平衡条件,建立了金属纳米晶的相平衡方程.应用Fetch和Wagner的界面膨胀模型以及Smith和其合作者建立的普适状态方程,对纳米晶界面的热力学量进行计算,由此获得金属高温相可在较低的温度下存在的临界尺寸.通过对元素Co的β相（fcc结构）和α相（hcp结构）纳米晶Gibbs自由能的计算表明,β相可在室温存在的临界尺寸和纳米晶界面处的过剩体积（△V）有关.当△V取10％时,β相应在35nm以下稳定存在.与Katakimi的实验较为符合.对影响β-Co稳定性的因素也作了讨论.
Based on the thermodynamic equilibrium conditions, a phase equilibrium equation for metal nanocrystals was established. The thermodynamic quantities at the nanocrystalline interface were calculated using the interface expansion model of Fetch and Wagner and the universal equation of state established by Smith and his collaborators, The critical dimension of high temperature phase can exist at lower temperature.The calculation of the Gibbs free energy of β phase (fcc structure) and α phase (hcp structure) nanocrystals of element Co shows that the critical size of β phase can exist at room temperature And the excess volume (ΔV) at the nanocrystalline interface.When △ V is taken as 10%, β is stable below 35nm, which is in good agreement with Katakimi’s experiment.The factors affecting the stability of β-Co are also discussed .