应用于金属固体的四参数通用状态方程

提出一种能精确考虑固体结合能的四参数通用状态方程, 并且在高压和膨胀区域都具有正确的行为, 不会出现物理上不正确的振荡现象. 新方程可以将Vinet方程和普遍化Lennard-Jones (GLJ) 方程作为特例包括于其中. 将新方程与文献中的典型方程应用于32种金属固体, 结果表明新方程在给出正确结合能数据的同时, 能够很好的拟合实验压缩数据. 结果还表明, 多数金属的相互作用具有短程相互作用的性质, 但是结合能较大相互作用的强度较强.     

4种等温物态方程适用性的比较研究

 通过分析现有文献,认为4种两参数的物态方程在高压物理研究中较为流行,它们是Vinet、Baonza、Morse和Born-Meyer（BM）方程。将这4种方程用于拟合50种材料的实验压缩数据,得出了零压下压缩模量及其一阶压力导数的优化取值,并计算了4种方程的平均压力误差。结果表明,Morse方程的精度最高,对50种材料的平均拟合误差为0.557 6%;BM方程次之,平均误差为0.615 1%;Vinet和Baonza方程的误差大一些,分别为0.788 9%和0.833 3%。对8种典型材料计算了压力误差随压强变化的曲线,所得结果与平均误差的趋势一致,也是Morse方程的精度最高。在宽广压力范围的高压物态方程研究中,推荐使用Morse方程。     

氮化硅α，β和γ相的解析状态方程和热物理性质

对固体通用状态方程考虑热效应的Einstein模型进行修正，提出一种利用参考温度下的实验数据计算绝对零度下物质参数的方法，并用于Baonza方程以考虑热效应.结果表明，对于Baonza方程，零温下的参数可以解析地求解出来，常用的热物理量也可以推出解析表达式.将得出的公式用于研究氮化硅α，β和γ相的热物理性质.通过对文献的分析确定了这三种相的方程参数，计算的体积随压强变化和热膨胀系数随温度变化的结果与实验数据符合很好.     

γ-Ce中的高压纵波声子模软化和状态方程描述

利用同步辐射角散X射线衍射技术测量了室温条件下0---0.74 GPa 压力范围内Ce的等温压缩线.发现γ-Ce的室温等温压缩线呈外凸形, 这是由其纵波声子模软化所致.利用超声测量得到的体弹性模量随压力变化的规律, 对实验所得到的压力与体积数据, 用二阶和三阶Murnaghan 方程、 二阶和三阶Birch 方程、 三阶Xu方程以及二阶Vinet方程进行比较, 并且对这些状态方程得到的体弹性模量随压力的变化规律与超声实验的结果相对比, 发现三阶Murnaghan 方程和三阶Xu方程对γ-Ce最适用.     

碱金属卤化物键长、德拜温度和热膨胀系数的温度效应

以碱金属卤化物为研究对象,根据局域键平均近似方法,从热膨胀系数的定义出发,建立热膨胀系数和键长的温度效应函数表达式。定量获取碱金属卤化物的键长、刚性因子、德拜温度和热膨胀系数。结果表明：①碱金属卤化物的热膨胀系数与结合能成反比;②同类碱金属卤化物中,从氟碱化物到碘碱化物德拜温度逐渐减小而热膨胀系数逐渐增大;③碱金属卤化物的键长在其德拜温度的三分之一处,由非线性转变为线性热伸长。     

两种状态方程参数的计算

在一定程度上,状态方程的形式与外推数据的置信度有直接影响,对于在高压下发生反应的材料,通过外推方式计算其未反应状态具有一定的意义。依据由Vinet以及Parsafar和Mason(简称P-M)等人提出的两种统一状态方程,对以其为等温压缩线的完全状态方程进行了研究。根据对热力学状态量的分析,从热压系数和定容比热入手,对完全状态方程的建立进行了讨论,给出了在已知物质等温线条件下构成状态方程的方法,并推导了Vinet和P-M两种表达式的完全状态方程形式。以几种材料为例,通过实验测量的冲击绝热线和有关参数,采用最小二乘法,对其状态方程进行了拟合。结果表明,由冲击绝热线拟合的状态方程与实验结果相吻合。     

对爱因斯坦模型的修正及考虑热效应的三个通用状态方程

 对固体考虑热效应的爱因斯坦模型进行了修正。指出考虑热效应的通用状态方程中不应该包含零点振动项，方程参数不应该直接取为参考温度下的实验值V_R，B_R，B′_R和γ^G_R，而应该取为零温下的数值V₀，B₀，B′₀和γ^G₀；提出了一种从V_R，B_R，B′_R和γ^G_R求解V₀，B₀，B′₀和γ^G₀的方法。将提出的方法应用于三个典型的通用状态方程，包括Baonza、mMNH和Vinet方程。数值结果表明，利用相同的实验参数对三个方程解出的参数，以及预测的零压和低压下的热物理性质差异很小，而且都与实验数据符合很好。这些结果表明，在零压和低压下预测热物理性质的精确度不足以用来判断各种通用状态方程的适用性。     

广义Morse流体解析状态方程及对氮的应用

 根据Ross变分微扰理论以及硬球流体Percus-Yevick（PY） 径向分布函数表达式,建立了广义Morse势流体的解析状态方程。与模拟结果的比较一方面证实了广义Morse 势模型的合理性;另一方面表明了解析Ross变分微扰理论的精度相当或略好于非解析的Weeks-Chandler-Anderson （mWCA）理论,而优于复杂的优化超网络链积分方程理论（RHNC）。该解析状态方程被应用于拟合处于环境温度和压强小于1 GPa情形流体氮的实验数据,所得到的势能参数被用于预测高温高密度情形氮流体的压强,预测结果证实,该解析状态方程可以很好地适用于较宽的压强和温度范围。     

静高压加载下LY12铝的超声测量与等温状态方程

 利用“脉冲回波重合法”测量了多晶LY12铝在流体静压加载下的纵波与横波声速随压力的变化。并根据较低压力（<0.5 GPa）下的超声测量数据所确定的零压弹性模量及其对压力的偏导数,导出了LY12铝的Murnaghan、Birch-Murnaghan、Vinet三种不同形式的等温状态方程,发现由超声测量数据导出的Vinet 状态方程能很好地描述面心立方（fcc）结构的铝与铝合金在较高压力（约200 GPa）下的压缩特性。此外,由超声数据计算了LY12铝在室温常压条件下的Debye温度为430.97 K、热力学Grüneisen系数为2.025、平均声模Grüneisen系数为2 379。     

一种计算固体冷能、冷压和结合能的新方法

 给出了利用Hugoniot参数计算材料冷能、冷压和结合能的一种新方法，对52种纯元素单质固体材料的计算表明，该方法的计算误差较小，对计算碱金属等外层电子数较少的材料效果尤佳。利用文中给出的冷能、冷压公式，计算出的铝、铜、银和锌等材料的冲击绝热线与实验数据符合得非常好。     

The Test and Comparison of Three Equations of State for Solids

Vinet equation, Couchman-Reynolds equation and Birch equation are tested and compared by using the data of compressibility for 29 kinds of metals and 9 alkali halide compounds. The rerrults show that the Vinet equation is the best one among three equations, and its universality is very prominent.     

考虑热效应的Vinet状态方程及其应用

 基于爱因斯坦模型将Vinet等人提出的关于金属固体的通用物态方程推广到包括热效应。采用最近邻普遍化Lennard-Jones势描述金属离子之间的有效配对相互作用,将每个离子的势能展开为离子位移的二阶泰勒级数,从而推导出爱因斯坦温度和Grüneisen常数的解析表达式,该表达式只与体积有关而与温度无关。推广方程包括的7个参数只有5个是独立的,在高于德拜温度时,只需要4个参数。对典型金属及两种非金属材料计算的结果与实验符合得很好。     

Equation of state for solids considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state(EOS) in wide ranges of pressure and temperature is constructed within the MieGrneisen-Debye framework.Instead of the popular Birch-Murnaghan and Vinet EOS,we employ a five-parameter cold energy expression to represent the static EOS term,which can correctly produce cohesive energy without any spurious oscillations in the extreme compression and expansion regions.We developed a Pad’e approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in the low temperature region.The anharmonic effect is taken into account by using a semi-empirical approach.Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature,and tends to ideal-gas limitation at high temperature,which is physically correct.Besides,based on this approach,the anharmonic thermal pressure can be expressed in the Gru¨neisen form,which is convenient for applications.The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions,and the results are very satisfactory as compared with the experimental data.     

Equation of state for solids with considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state (EOS) in wide ranges of pressure and temperature is constructed within the Mie-Grüneisen-Debye framework. Instead of the popular Birch-Murnaghan and Vinet EOS, we employ a five-parameter cold energy expression to represent the static EOS term, which can correctly produce cohesive energy without any spurious oscillations in extreme compression and expansion region. We developed a Padé approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in low temperature region. The anharmonic effect is taken into account by using a semi-empirical approach. Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature, and tends to ideal-gas limitation at high temperature, which is physically correct. Besides, based on this approach, the anharmonic thermal pressure can be expressed in the Grüneisen form, which is convenient for applications. The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions, and the results are very satisfactory as compared with the experimental data.     

Two universal equations of state for solids satisfying the limiting condition at high pressure

In this paper it is shown that the relationship of bulk modulus with pressure, B=f(P), should be linear both at low and high-pressure limiting conditions. Because most of present equations of state (EOS) for solids cannot satisfy such linear relationship at high pressure, a new function f(P) is proposed to satisfy the linearity. By integrating the bulk modulus, an EOS with three parameters and satisfying the quantum-statistics limitation is derived. It is shown that the EOS can be reduced to two-parameter EOS approximately satisfying the limiting condition. By applying the two EOSs and other three typical EOSs to 50 materials, it is concluded that for materials at low and middle-pressure regimes, the limiting condition does not operate, the Baonza EOS gives the best results, but it cannot provide analytic expression for cohesive energy. The Vinet and our second EOSs are slightly inferior, both EOSs can provide analytic expression for cohesive energy, and for materials at high-pressure regimes our second EOS gives the best results. The Holzapfel and our first EOSs give the worst results, although they strictly satisfy the limiting condition. For practical applications, the limiting condition is not important because it only operates as V→0.     

Structure and melting of Morse solids

Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of the Morse pair potential. The structural properties of the liquid and solid phases vary significantly with the range. The longer range, softer potentials are associated with increased densities and cohesive energies in both the solid and liquid phases. The extent of local disorder associated with lattice sites in the solid phase, as measured by the Lindemann and bond orientational order parameters, increases with increasing range of the pair potential.     

氢化氙离子XeH+基态X1S+解析势能函数的变分研究

采用双原子分子离子XY+的能量自洽法(Energy-consistent -method for ion XY+, ECMI)研究了氢化氙离子XeH+基态X1S+的解析势能函数,并与解析形式的Morse势和Huxley- Murrell-Sorbie（HMS）势、耦合电子对方法(coupled electron pair approximation method, CEPA)的结果和基于实验的Rydberg-Klein-Ress（RKR）数据进行了比较。结果表明,由ECMI方法得到的解析势能函数ECMI势明显优于Morse势和HMS势,与理论方法的结果和RKR数据符合得很好,并能得到CEPA和RKR非法缺乏的离解区和渐近区的势能数据以及正确的离解极限,而正确的全程势能数据对研究各种散射问题都是非常必要的。     

氢化氙离子XeH+基态X1S+解析势能函数的变分研究

采用双原子分子离子XY+的能量自洽法(Energy-consistent -method for ion XY+, ECMI)研究了氢化氙离子XeH+基态X1S+的解析势能函数,并与解析形式的Morse势和Huxley- Murrell-Sorbie（HMS）势、耦合电子对方法(coupled electron pair approximation method, CEPA)的结果和基于实验的Rydberg-Klein-Ress（RKR）数据进行了比较。结果表明,由ECMI方法得到的解析势能函数ECMI势明显优于Morse势和HMS势,与理论方法的结果和RKR数据符合得很好,并能得到CEPA和RKR非法缺乏的离解区和渐近区的势能数据以及正确的离解极限,而正确的全程势能数据对研究各种散射问题都是非常必要的。