金和银的晶格反演势的构建及应用

Application and foundation on inversion lattice potential of gold and silver

如何确定精确的原子间作用势一直是模拟计算的重要基础问题.以面心立方金属金和银为对象,采用第一性原理方法,分别得到金和银的晶格内聚能-原子距离曲线及基态原子能曲线.根据陈-莫比乌斯(Chen-M?bius)晶格反演理论和自编程序,得到了精确的反演对势曲线.对该曲线进行拟合,通过比较不同势函数的拟合结果,提出了双指数型的势函数解析式,并得到具有全局性且高精度的拟合效果.为了验证反演势的有效性,利用反演势结果计算了金和银的声子谱并与Sutton-Chen提出的嵌入原子势和第一性原理计算得到的声子谱做比较.分析表明,反演势能够合理反映原子间的相互作用.最后,利用得到的结果,计算了金和银的热膨胀系数和弹性模量等物理量,计算结果与实验数据基本符合,表明构建的金和银的反演势是准确有效的.

How to construct an accurate interatomic potential function is an important and basic problem in the simulation procedure. Using first-principles method, the single atom energies in different lattice constants are calculated to achieve the ground state curves of Au and Ag. These energies are calculated in the Perdew and Zunger form of the local- density approximation ultra-soft pseudo potentials. The cut-off energies of the plane wave bases of Au and Ag are set to be 320 eV and 300 eV respectively, which are sufficient for their full converge. The Brillouin zone is all sampled with a 12 × 12 ×12 Monkhorst-Pack mesh of k points for Au and Ag. Allowable error in total energy is smaller than 1 × 10-6 eV per atom. The lattice cohesive energies in different lattice constants are calculated to achieve the lattice energy and atom distance curves after subtracting the value of ground state energy from each of these energy. Then the accurate inversion potential curves are obtained according to the Chen-MSbius inversion theory and self-compiled program. Based on the fitting consequences of inversion potential curves, using different potential function formulas, a double exponential potential function to fit the inversion potential is presented. This function provides the accurate formulas and parameters for the following research. Moreover, the phonon spectra and the densities of states of Au and Ag are calculated respectively by using the inversion potential data, the embedded atom method （EAM） potential theory and first principles method to verify the reliability of the inversion potential. The comparison of the results among the three methods shows that the tendencies of these curves are similar. But they still have some deviations especially in the range of high frequency. However these curves indicate that the inversion potential can reasonably reflect the interaction between atoms. Meanwhile, the inversion potential method has great advantage in calculation quantity compared with the EAM potential method. The inversion method needs less time in calculation. In addition, the thermal expansion coefficients, the elastic moduli and the Grfineisen constants of Au and Ag are also calculated based on the fitting formulas and parameters. The results agree well with the experimental data, which implies that these inversion potentials are effective and accurate.