論文重點由Kubo理論中已知金屬奈米粒子系統下，其費米能量附近形成不連續狀態，我們假設為等能階分佈，利用等能階理論模擬中代入不同能階間隙與能階數目n於方程式中，得理論曲線，並了解n與能階間隙對平衡位置的影響。實驗中由熱蒸鍍法所製成的奈米粉粒，利用X光變溫架設量測，溫度範圍由14K~300K，藉由繞射峰的變化與實驗修正後，觀察粒徑及熱膨脹係數的改變；在實驗上我們發現4nm金粉粒與4nm鉛粉粒均有熱縮現象，其轉折發生位置與理論擬合相當近似，故我們可由等能階模型來解釋奈米粉粒的熱縮的原因及估算轉折發生位置，其中能階間隙的實驗值亦與Kubo理論估算符合。 We consider the effect of valence electron potential on the equilibrium lattice separation in nanoparticles systems having discrete electronic energy levels and the attractive binding energy Ue of thermally excited valence electrons embedded in a caubic lattice of ions, where the energy of nth level above Fermi energy, can be taken to be Dn(T)=a/d3 , where a depends on the distribution of the level. The variation of the attractive binding energy with unit cell parameter R(T) shows a minimum occurs at Tmin , indicating that the effect on the lattice parameter are different for temperatures below and above Tmin. This crossover from a postive thermal expansion to negative thermal expansion can then be anticipated at Tmin Our lattice temperature depentent experiment of 4 nm Au and Pb particles can be reasonably well fitted by the effect of valence electron potential on the equilibrium lattice separstion, with a weakly temperature dependent level spacing.
