固体的物态方程和高压熔化规律的唯象研究
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摘要
从广义上讲,物态方程(EOS)理论是关于物质系统热力学性质的理论.从狭义上来讲,物态方程是描述处于热力学平衡态的物质系统中压强、温度、体积之间的函数关系.由于固体材料在实际生活和生产中具有广泛的应用,所以固体EOS的研究是基础科学和应用科学中非常重要的领域,对于热力学、统计物理学、凝聚态物理、原子与分子物理、地球物理、天体物理、化学物理等学科具有重要意义.而固体在高温时发生的熔化是日常生活中常见的现象,对于它的研究也是由来已久.本文运用唯象的方法对高温高压的宏观条件下固态物质系统的EOS以及熔化规律作出了较为系统的研究.
前言部分简要地介绍了本文研究工作的缘起、目的和范围,EOS研究的发展简史及其应用学科范围,熔化理论及其目前研究现状,文中所采用的研究方法和手段以及论文的理论意义和实用价值.
第一章,简要介绍了固体的一些基础知识.概括了固体的结构,性质以及物态方程涉及的热力学参量方面的知识,总结了EOS研究中最常用的热力学理论和唯象关系式.
第二章,首先介绍了物态方程的基本理论概要.从固体理论角度给出了固体物态方程的一般形式E=Ec+En和P=Pc+Pn,即晶体系统的能量和压强可以分为的“冷”的和“热”的两部分:冷能冷压和热能热压.分析了固体压缩的微观机理—原子间相互作用势,由此导出了几种不同形式的冷能和冷压;由晶体的自由能出发,给出了热压与热能之间的关系--Grüneisen物态方程.其次,综述了三类典型EOS,即等温EOS P=P(V)、等压EOS V=V(T)和高温EOS P=P(V,T).在本章中,主要做了以下几方面工作:①以NaCl-型结构的晶体为例,比较了离子晶体常用的两种势函数,指出它们之间的内在联系;②根据Grüneisen关系式以及Cui提出的关于Grüneisen参数的表达式,对热压公式进行了修正,将修正后的热压公式用于NaCl等物质,并和其他热压公式进行比较,结果发现我们修正后的公式略有改进;③利用我们得到的热压公式将等温的B-MEOS进行高温修正,得到一个P=P(V,T)关系式,即高温EOS,将其用于考察不同温度压强下的金属Au的状态行为,预期结果和实验结果吻合很好.
第三章,在介绍了熔化理论及其目前研究现状之后,基于著名的Lindemann熔化定律,并结合固体EOS,提出了研究熔点随压强变化规律的一个简单的方法.将其应用到LiF,NaCl和Al等物质,计算结果与可提供的实验数据之间的相对误差很小.另外,对于晶
The theories of equation of state (EOS), in a broad sense, are on the thermodynamic properties of a substance system. In a narrow sense, EOS is on the relationship P=P(V,T) among the pressure P, the volume V and the temperature T of a substance system in thermodynamic equilibrium. With wide applications in actual life and in the production of solid materials, the study of EOS on solids is a very important part of the fields of many basic and application sciences such as thermodynamics, statistical physics, physics of condensed matter, atomic and molecular physics, geophysics, planetary science, chemical physics, etc. Meanwhile, the melting of solids at high temperature is a commonly observed phenomenon in nature, which has been continually investigated for a long time. In this paper, a systematic study of EOS and melting law for solids at high temperatures-high pressures has been made by using phenomenological method.
In the preface, a brief introduction has been made as to the origins, the purposes and the conditional scopes of this work. The history of EOS study and its applications in other subjects, the theory of melting and its investigation at present have also been introduced. The methods and measures used in the paper as well as its theoretical meanings and practical values have also been included in this part.
The first chapter provides the basic knowledge for solids, including their structures and basic properties, and some often-used thermodynamic parameters in the study of EOS. In the second chapter, we first introduced the summary of basic theories of EOS for solids. The general expression of EOS of solids E=Ec+En and P=Pc+Pn are given in the view of solid-state theory. That is, the energies and pressures of the solid substance system can be sorted into cold ones and thermal ones--cold energies (or pressures) and thermal energies (or
前言部分简要地介绍了本文研究工作的缘起、目的和范围,EOS研究的发展简史及其应用学科范围,熔化理论及其目前研究现状,文中所采用的研究方法和手段以及论文的理论意义和实用价值.
第一章,简要介绍了固体的一些基础知识.概括了固体的结构,性质以及物态方程涉及的热力学参量方面的知识,总结了EOS研究中最常用的热力学理论和唯象关系式.
第二章,首先介绍了物态方程的基本理论概要.从固体理论角度给出了固体物态方程的一般形式E=Ec+En和P=Pc+Pn,即晶体系统的能量和压强可以分为的“冷”的和“热”的两部分:冷能冷压和热能热压.分析了固体压缩的微观机理—原子间相互作用势,由此导出了几种不同形式的冷能和冷压;由晶体的自由能出发,给出了热压与热能之间的关系--Grüneisen物态方程.其次,综述了三类典型EOS,即等温EOS P=P(V)、等压EOS V=V(T)和高温EOS P=P(V,T).在本章中,主要做了以下几方面工作:①以NaCl-型结构的晶体为例,比较了离子晶体常用的两种势函数,指出它们之间的内在联系;②根据Grüneisen关系式以及Cui提出的关于Grüneisen参数的表达式,对热压公式进行了修正,将修正后的热压公式用于NaCl等物质,并和其他热压公式进行比较,结果发现我们修正后的公式略有改进;③利用我们得到的热压公式将等温的B-MEOS进行高温修正,得到一个P=P(V,T)关系式,即高温EOS,将其用于考察不同温度压强下的金属Au的状态行为,预期结果和实验结果吻合很好.
第三章,在介绍了熔化理论及其目前研究现状之后,基于著名的Lindemann熔化定律,并结合固体EOS,提出了研究熔点随压强变化规律的一个简单的方法.将其应用到LiF,NaCl和Al等物质,计算结果与可提供的实验数据之间的相对误差很小.另外,对于晶
The theories of equation of state (EOS), in a broad sense, are on the thermodynamic properties of a substance system. In a narrow sense, EOS is on the relationship P=P(V,T) among the pressure P, the volume V and the temperature T of a substance system in thermodynamic equilibrium. With wide applications in actual life and in the production of solid materials, the study of EOS on solids is a very important part of the fields of many basic and application sciences such as thermodynamics, statistical physics, physics of condensed matter, atomic and molecular physics, geophysics, planetary science, chemical physics, etc. Meanwhile, the melting of solids at high temperature is a commonly observed phenomenon in nature, which has been continually investigated for a long time. In this paper, a systematic study of EOS and melting law for solids at high temperatures-high pressures has been made by using phenomenological method.
In the preface, a brief introduction has been made as to the origins, the purposes and the conditional scopes of this work. The history of EOS study and its applications in other subjects, the theory of melting and its investigation at present have also been introduced. The methods and measures used in the paper as well as its theoretical meanings and practical values have also been included in this part.
The first chapter provides the basic knowledge for solids, including their structures and basic properties, and some often-used thermodynamic parameters in the study of EOS. In the second chapter, we first introduced the summary of basic theories of EOS for solids. The general expression of EOS of solids E=Ec+En and P=Pc+Pn are given in the view of solid-state theory. That is, the energies and pressures of the solid substance system can be sorted into cold ones and thermal ones--cold energies (or pressures) and thermal energies (or
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