【作者】 王苍龙；

【导师】 段文山；

【作者基本信息】 西北师范大学 ， 理论物理， 2009， 硕士

【摘要】 二十世纪90年代兴起的纳米科学技术为人们能制造出用于在原子尺度上研究材料特性的实验设备提供技术指导。同时,计算方法的巨大变革衍生出了便于理论工作者在该尺度上探索真实滑动体系的新技术——分子动力学技术。这种实验和计算上的进步进一步激发了人们用简单的数学模型来探索复杂体系的浓厚兴趣。在众多模型中,Frenkel-Kontorova(FK)模型便是成功地描述和解释有关复杂摩擦体系的动力学特性的模型之一。本论文研究了作为上层的正方形晶格和作为下层的正方形基低间存在任意错合角θ,外界驱动力沿任意角度α驱动时,二维FK模型的动力学行为及摩擦特性。本文第一章概述了纳米摩擦学的发展历史及应用前景。第二章我们主要介绍纳米摩擦学的理论研究技术——分子动力学技术。实践证明该技术能有效地用来研究纳米结构及探索微观现象的新规律。因而受到人们越来越广泛的关注,并成功地应用于包括纳米摩擦学在内的许多微观研究领域中。第三章基于分子动力学(molecular dynamics)模拟技术,主要介绍了二维FK模型在纳米摩擦学领域中的应用。我们的数值模拟结果表明:系统的静摩擦力与系统的重要参数有关,如改变系统的硬度(stiffness)、系统的公度和不公度、系统的错合角θ,外界驱动力的方向α以及原子间的强度系数K等都可改变系统的静摩擦力。本文第四章展望了我们在纳米摩擦学领域中的后续工作。更多还原

【Abstract】 Over the last decade, remarkable developments in nanotechnology have provided the possibility to build experimental devices which are able to perform analysis on materials at the atomic-scale. Simultaneously, tremendous advances in computing methodology (molecular dynamics techniques, MDT) have supplied very detailed information on the atomic scale for realistic sliding system. The accelerations in experiments and computations have deeply stimulated the search and implementation of simpler mathematical model such as the Frenkel-Kontorova (FK) model. The model of friction is capable of describing and interpreting the main features of the complicated dynamics involved.In this dissertation, we study the dynamical behavior of a two-dimensional FK model with a square symmetry potential for a square lattice layer driven by an external driving force with an arbitrary directionαand an arbitrary misfit angle 9 between upper and lower layer. There are four chapters in the dissertation. The paper is organized as following: in chapter I, the development and prosperity of the nano-tribology is briefly introduced. In the theoretical simulations of the nano-tribology, one of the most important techniques called the MDT will be reviewed in chapter II. It is verified that the technique is effective and coherent in the study of the nanostructure. So, many physicists pay more and more attention on it. In chapter III, by using the MDT, the application of the two dimensional FK model in the nano-tribolody will be presented. With regards to the static friction force, the results show that the parameters of the system, such as the effective elastic constant, the commensurate and incommensurate structures of the system, the misfit angleα, the direction of external driving forceθand the interatomic stiffness strength K can affect the static friction force of the system. In the future, we will focus on the study of quantum behaviors of the FK model. These works are shown in chapter IV.更多还原