含杂质一维原子链热导Monte Carlo模拟

Monte Carlo Simulation of Thermal Conduction in One-Dimensional Doped-Chains

在弹性碰撞模型基础上,采用Monte Carlo随机抽样计算方法,并考虑局部温度控制局部碰撞顺序,我们研究掺杂对一维原子链热导的影响.对等质量一维原子链的热导模拟结果显示出一个非常稳定的平衡态,呈现出一个近似的温度梯度分布,满足Fourier定律.当链中含单个杂质时,杂质质量和位置都会使整个链的温度分布发生改变,杂质附近的温度振荡幅度最大,而且杂质质量相差越大,杂质附近的温度振荡幅度越大,杂质原子附近因巨大的热运动差异会导致断裂发生.链上原子质量无序分布时,无序度越大,高温端的端口处温度差越大,越容易发生断裂,而且无序度δ>1.0,链的中部虽有较大振荡,但仍呈现线性分布,满足Fourier定律.

On the base of the elastic collision model, we investigate the influence of doping on the thermal conduction in one-dimensional chain, by using Monte Carlo stochastic sampling numerical method and considering the local colliding order controlled by the stochastic sampling according to the probability determined by the local temperature. The results of simulating equal mass one-dimensional chain shows that its temperature profile presents a temperature gradient, and there is a steady equilibrium state. It satisfies Fourier law. After doping a different atom in chain, the mass and position of the doped-atom causes a fully different T - x profile on whole chain. The amplitude of increasing temperature around the doped-atom slowly increases with the increase of the difference between doped-atom＇ s mass and chain-atom＇ s mass. The mass difference is larger and the oscillating amplitude of temperature around the doped-atom is larger. Thus enough large temperature difference causes the enough thermal dynamic difference leading to break around doped-atom. When the distribution of mass in chain is in disorder, the results show that the degree of disorder is much larger, the temperature difference at the left tip of chain is larger and it is easier to break. Furthermore, when the disorder 8 is larger 1. 0, the middle part of disorder-chain still has a gradient linear distribution and satisfies Fourier law, although the temperature oscillation is much larger with the increase of disorder degree.