纳米单原子链的热膨胀性质

Thermal expansion of a monatomic nanochain

根据戴逊方程,推导了纳米单原子链的位移-位移Green函数,并得到了声子占有数表象中原子位移与哈密顿的表达式。在这些结果的基础上,应用微扰理论,推导了热膨胀和热膨胀系数的计算公式,并进行了数值计算。研究结果表明,在有限温度下,纳米单原子链中靠近两端的原子间距的热膨胀大于内部的原子间距的热膨胀,而原子链中靠近两端的原子间距的热膨胀系数小于内部的原子间距热膨胀系数。原子链的长度越短,则所有原子间距热膨胀的平均值越大,而原子链的热膨胀系数越小。

Based on Dyson＇s equation, the displacement-displacement Green＇s function of a monatomic nanochain is derived, the formulas of atomic displacement and Hamiltonian in phonon occupation number representation are obtained. On the basis of these results, the formulas of thermal expansion and thermal expansion coefficient are derived with the perturbation theory, and the numerical calculations are carried out. The results show that at finite temperature the thermal expansions for interatomic spacings near the ends of monatomic chain are larger than those in the middle of the monatomic chain, and the thermal expansion coefficients near the ends of monatomic chain are smaller than those in the middle of the monatomic chain. The shorter monatomic chain has a larger mean value of thermal expansions for all interatomic spacings and a smaller thermal expansion coefficient.