一种晶体表面自由能的计算方法

采用“断键模型”计算了立方晶体理想表面的悬键密度，进而计算了其表面自由能(SFE).结 果表明：对于理想(1×1)-(hkl)表面，SFE可以表示为键能、键长和表面方向的函数.该 模型简单地解决了晶体SFE各向异性的理论问题.根据该模型和Wulff定则得出的晶体平衡形 状与理论完全一致；同时，计算结果也表明面心立方和体心立方晶体的平衡形状与其三维第 一布里渊区重合.关键词：表面自由能晶体悬键平衡形状

A theoretical method to calculate the surface free energies of crystals

An ideal density of dangling bonds and the surface free energy (SFE) of (1×1)-(hkl) surface of cubic crystals are calculated by using a broken-bond model. The results show that the SFE(γ) can be expressed as γ=f(hkl)·(E_b/d² ₀) where f(hkl) is a periodically convergent function, E_b and d₀ are respectively the bond energy and the bond length. The f(hkl) is rela ted to the crystal structure. The anisotropy of the SFE and the equilibrium form (EF) of the crystal can be readily determined by using the results. It is found that the EFs of the crystals of fcc and bcc are truncated octahedron and rhombi c dodecahedron, respectively, which are coincident with the corresponding crysta ls' three dimensional first Brillouin zones, respectively.