【作者】 谢传梅；

【导师】 陈立溁；

【作者基本信息】 安徽师范大学 ， 原子与分子物理， 2004， 硕士

【摘要】 相图研究是基础科学和应用材料科学中非常重要的领域。相图主要研究处于平衡状态或准平衡状态下,物质的组分、物相和外界条件的关系。获得了某种材料的相图，就很容易探索和了解该材料的组分、结构和性能之间关系的规律，这就是相图研究的意义所在。本文用一种唯象的理论模型，即Collins模型研究相图，对实际的相图研究具有一定的理论指导意义。第一章，给出了与相图相关的一些基本概念和理论，介绍了当前相图计算的进展情况，讨论了二维相变存在的可能性，并介绍了Collins模型系统的建立及其相变理论的发展与研究动态。第二章，假设二维Collins模型系统中有a、b、c三种组元，写出了该二维三元替换式L-J系统的自由能和Gibbs函数的表达式。首先利用Largrange不定乘子法，由热力学理论和相平衡的稳定性条件，得到了决定该二维三元替换式L-J系统的固?液两相平衡曲线方程的表达式，给定势参数后，得到了典型的三元系统固液相图（如，匀晶相图）的水平截面图和竖直截面图。接着，利用相似的方法，得到了决定二维三元替换式L-J系统的三相平衡曲线方程的表达式，给定势参数后，得到了三元系统中的由两固相与一液相形成的三相平衡相图，即结三角。所得的相图与实际情形十分相似。第三章，影响相图的参数有温度、约化压强和势参数三类。为进一步研究约化压强p和势参数对相图的影响，首先讨论了在温度和势参数不变的情况下，约化压强p对匀晶相图的水平截面图、竖直截面图以及代表三相（如两固相一液相）平衡区域的结三角的影响，即研究当约化压强p增大或减小时，系统的结构、相变温度、相图的共存区域等的变化规律；接着，讨论了固定温度和约化压强时，改变一组势参数比的值对匀晶相图的水平截面图的影响。结果发现，系统的结构、相变点的位置及相图的形状等都会随着各种参数的变化而发生一定变化。结束语中，就Collins模型在二维系统中的应用给予总结与展望。我们相信，Collins模型是一个简单而又形象化的模型，对人们理解物质内部结构和理论计算相图具有一定的启发作用。更多还原

【Abstract】 Phase Diagram Study is an important branch in the field of the basic and the applied science. The main study of the Phase Diagram is the relationships between the matter’s components and its phases with the outside conditions. Obtaining a phase diagram of a matter, the relationships between the matter’s components, structure and capabilities can be easily got, which is just the place where Phase Diagram Study shows very important meaning. This paper entirely uses a theoretical model –Collins model–to calculate and study phase diagrams, which has some theoretical meaning to the practice.The first chapter gives some basic conceptions and theories according to phase diagrams, introduces the current progresses of the calculation of phase diagrams, and discusses the probabilities of the existing phase transitions in the two dimensions (2D), and then introduces the establishment of the Collins model as well as its development and study trends. The second chapter supposes three components a，b and c in the 2D system ,writes out the expressions of the free energy and the Gibbs functions of the 2D alternative ternary L-J system. Firstly, by using the Largrange indeterminate multiplier method, and according to the thermodynamic conditions describing the coexistence of two phases and the stability conditions of Equilibrium State, the equations describing the solid-liquid phase diagram equilibrium curves of the 2D alternative ternary system are obtained. Given a group of the attractive interactions’ values, the isothermal sectional diagrams and the vertical sectional diagrams of the typical phase diagram of the ternary system (e.g. the “even crystal” type) are obtained. Then using the similar method , the equations describing the three phases (e.g. one liquid phase and two solid phases) equilibrium curves of the 2D alternative ternary system are obtained. Given a group of the attractive interactions’ values, the phase diagrams that representing the equilibrium of one liquid phase and two solid phases, i.e. the knot triangles, are got, which are similar to the practice.The third chapter. There are three kinds of parameters that influence phase diagram, i.e., the <WP=8>temperature, the normalized pressure and the attractive interactions between atoms. For further researching the influence on the phase transition curves by these parameters, the first discussions are made about the normalized pressure’s influence (fixing the temperature and the attractive interactions parameters) on the isothermal sectional and vertical sectional diagrams of the “even crystal” type ternary system, as well as on the knot triangles representing the equilibrium of one liquid phase and two solid phases. Then another discussion is made about the influence (fixing the temperature and the normalized pressure) of the changed attractive interactions parameters on the isothermal sectional diagrams of the “even crystal” type ternary system.The results show that the lattice structure, the normalized temperature of the phase transition and the coexistence area of the phase diagram changed with the variety of the given parameters in certain regularity.In the end, we make a summary of our work and give the prospects for the 2D Collins model. We believe that the Collins model is a simple but visual model, which can enlighten people well on the understandings of the matter’s intetior structure and the phase diagram’ theorectical calculation.更多还原