严格可解四参数双原子分子势函数

提出一个四参数双原子分子势函数,对s波Schrdinger方程进行了严格求解,并采用一个简便的方法考虑了转动修正.该势函数对实验Rydberg-Klein-Rees曲线及振动-转动能级的计算精度远优于常用的Morse势,且将Morse势等势函数作为特例包括于其中. 关键词：     

金和银的晶格反演势的构建及应用

如何确定精确的原子间作用势一直是模拟计算的重要基础问题. 以面心立方金属金和银为对象, 采用第一性原理方法, 分别得到金和银的晶格内聚能-原子距离曲线及基态原子能曲线. 根据陈-莫比乌斯(Chen-Möbius)晶格反演理论和自编程序, 得到了精确的反演对势曲线. 对该曲线进行拟合, 通过比较不同势函数的拟合结果, 提出了双指数型的势函数解析式, 并得到具有全局性且高精度的拟合效果. 为了验证反演势的有效性, 利用反演势结果计算了金和银的声子谱并与Sutton-Chen提出的嵌入原子势和第一性原理计算得到的声子谱做比较. 分析表明, 反演势能够合理反映原子间的相互作用. 最后, 利用得到的结果, 计算了金和银的热膨胀系数和弹性模量等物理量, 计算结果与实验数据基本符合, 表明构建的金和银的反演势是准确有效的.     

硅熔化特性的分子动力学模拟–-不同势函数的对比研究

分别采用Stillinger-Weber (SW)势、修正的成熟原子嵌入模型(MEAM)势、 Tersoff势和HOEP (highly optimized empirical potential)势来描述硅原子间相互作用, 运用分子动力学方法对比模拟研究了四种势函数的硅晶体的体熔化和表面熔化特性. 结果表明: 四种势函数均能反映出硅的热膨胀、高温熔化和熔化时吸热收缩等基本物理规律. 但综合对比发现, Tersoff势和MEAM势相对更适合描述硅的熔化和凝固过程, SW势次之, HOEP势则不适合描述硅的熔化和凝固过程. 关键词： 硅 势函数 熔化 分子动力学     

MEAM势与Tersoff势比较研究——碳化硅熔化与凝固行为

运用分子动力学方法对比模拟研究了碳化硅的体熔化、表面熔化和晶体生长过程.分别采用MEAM 势和Tersoff势两种势函数描述碳化硅.结果表明:体熔化时,两种势函数描述的SiC的原子平均能量、 Lindemann指数和结构有序参数与温度的变化关系相似,但MEAM势对应的体熔点(4250 K)比Tersoff势(4750 K) 的要高.表面熔化时,两种势函数描述的SiC在相同的过热度下熔化速度相近;而在相同的温度条件下,MEAM 作用的SiC表面熔化速度更快.这是由于MEAM势SiC的热力学熔点(3338 K)低于Tersoff势SiC的热力学熔点 (3430 K)的缘故.两种势函数作用的SiC在晶体生长方面差异很大.MEAM势SiC的晶体生长速度与过冷度有关, 过冷度约为400 K时晶体生长速度最快.但Tersoff势SiC晶体却在过冷度为0—1000 K的范围内均不能生长. 综合考虑,MEAM势比Tersoff势能更好地描述碳化硅的熔化和凝固行为.     

Ti2AlNb合金的嵌入原子势

分子动力学模拟是一种行之有效的计算机模拟方法;然而,由于缺少合适的多元合金原子间势,因而限制了分子动力学模拟的应用.多元合金原子间势的开发一直具有挑战性.本文在嵌入原子势模型的框架下,提出一种适用于三元有序合金的原子间势构建方法,并开发了适用于原子尺度力学行为模拟的Ti₂AlNb合金新型原子间势.该势能够很好地再现B2-Ti₂AlNb的弹性常数、未弛豫的空位形成能、置换原子形成能、换位原子形成能、表面能和三种有序构型(B2相、D0₁₉相、O相)在不同体积下的内聚能.为了进一步检验势函数,计算了B2相的E-V曲线,结果与Rose曲线符合得很好;利用分子动力学模拟研究了B2相的熔化转变过程,结果大致反映了实验情况.本文的工作一方面为开发多元合金原子间势提供一种途径,另一方面为模拟计算Ti₂AlNb合金的工作者提供一种选择.     

α-B晶体的Lennard-Jones对势和对势型多体势构建

精确原子间相互作用势函数的建立是分子动力学模拟的核心. 针对α-B晶体(R3m群), 分别构建Lennard-Jones (L-J)型对势和对势型多体势, 这两类势函数的构建仅需考虑晶体的原子平均结合能和几何构型参数. 前者取最近邻原子间距的势函数为最小值; 后者采用负指数(L-J型)函数和分段插值多项式形式来分别构造势函数, 在近邻处为势能极小值, 相邻极小值位置的中点引入势垒. 针对完整的α-B 晶体和偏离完整α-B晶体结构, 首先利用第一性原理计算结果来确定势函数的参数, 然后借助分子动力学的能量最小化方法优化结构, 并对这两类势函数以及Tersoff 势函数进行比较. 结果表明: L-J对势和Tersoff势的结果与α-B晶体构型有较大偏离; 而对势型多体势, 无论初始晶体构型完整与否, 其结果与完整α-B晶体构型比较一致.     

自由能方法与零压下Al的熔化温度

利用自由能方法的分子动力学模拟,计算了零压下Al的熔化温度.在计算液相自由能的过程中,采用勒纳-琼斯(LJ)液体作为参考系统,同时将计算结果与Mei和Davenport等人的计算结果进行了比较,计算结果表明：1)选用LJ参考系统使液相自由能的计算时间节省一半,并且不影响熔化温度的计算结果;2)采用不同的埋入原子势(EAM)的分子动力学模拟计算得到的熔化温度与实验值都存在偏差,而就金属Al而言,采用Cai等人的EAM势的熔化温度的计算结果比Mei和Davenport及Morris等人采用的势模型的结果略有改 关键词： 熔化温度 自由能方法 分子动力学模拟     

自由能方法与零压下Al的熔化温度

利用自由能方法的分子动力学模拟，计算了零压下Al的熔化温度.在计算液相自由能的过程中，采用勒纳-琼斯(LJ)液体作为参考系统，同时将计算结果与Mei和Davenport等人的计算结果进行了比较，计算结果表明：1)选用LJ参考系统使液相自由能的计算时间节省一半，并且不影响熔化温度的计算结果；2)采用不同的埋入原子势(EAM)的分子动力学模拟计算得到的熔化温度与实验值都存在偏差，而就金属Al而言，采用Cai等人的EAM势的熔化温度的计算结果比Mei和Davenport及Morris等人采用的势模型的结果略有改     

铋的固相及液相多相状态方程研究

铋在高温高压下存在一系列复杂相结构,相变伴随着密度、内能等物理性质的改变.采用半经验三项式Helmholtz自由能表达式,构建了铋的五个固相及液相的多相状态方程,其中离子热振动自由能计算基于经典平均场理论给出的平均场势函数模型开展.研究结果表明,状态方程计算给出的铋的相图、等温压缩线、液相的温度-密度曲线以及冲击Hugoniot线等均与实验测量符合较好,故可认为本文构建的铋的多相状态方程具有良好的参数合理性以及模型适用性.     

高压下金属铌熔化曲线的分子动力学模拟

铌作为一种高熔点的金属,广泛应用于制作合金材料. 铌的高温高压熔化曲线对于铌基合金的实际应用具有重要影响,但目前还未被成功研究. 本文中,我们采用铌目前已有的嵌入原子相互作用势函数（EAM）,通过经典的分子动力学方法,模拟了铌的熔化曲线. 两相法和改进Z方法的熔化曲线几乎完全一致,与Z方法的结果稍有差异. 我们也比较了尺寸效应对铌熔化曲线的影响. 我们认为,铌的现有的势函数描述其高压特性时不再适合,后续需要构建精确的温度和压强依赖的相互作用势函数来研究铌的高压特性.     

Pressure effect on the melting point of alkali metals

The mean-square displacement of alkali metals is studied theoretically using our local Heine-Abarenkov-type model potential in the perturbational scheme. The temperature-dependent mean-square displacement of alkali metals decreases as function of the compressed volume. Lindemann's criterion for melting x_m, which is defined as the ratio of two times the root-mean-square displacement to the nearest-neighbour distance, is found to be nearly constant for five alkali metals. The volume effect on the melting temperature of alkali metals is studied by keeping x_m constant. The obtained melting curve increases as function of the compressed volume and are qualitatively in good agreement with the observed tendency for alkali metals.     

Mean square displacements of atoms in cubic metals at melting point

The ratio of the mean square displacement of thermal vibration and the square of interatomic separation at the melting point has been calculated for several cubic metals using the frequency distribution derived from Bhatia's three-force constant model. It is found that this ratio has roughly the same value for metals of certain groups of the periodic table, but exhibits wide variation from one group to another. Lindemann's melting law is shown to be inadequate.We are grateful to the Council of Scientific and Industrial Research and to the University Grants Commission for financial assistance.     

Effect of voids and pressure on melting of nano-particulate and bulk aluminum

Molecular dynamics simulations are performed using isobaric–isoenthalpic (NPH) ensembles to study the effect of internal defects in the form of voids on the melting of bulk and nano-particulate aluminum in the size range of 2–9 nm. The main objectives are to determine the critical interfacial area required to overcome the free energy barrier for the thermodynamic phase transition, and to explore the underlying mechanisms for defect-nucleated melting. The inter-atomic interactions are captured using the Glue potential, which has been validated against the melting temperature and elastic constants for bulk aluminum. A combination of structural and thermodynamic parameters, such as the potential energy, Lindemann index, translational-order parameter, and radial-distribution functions, are employed to characterize the melting process. The study considers a variety of void shapes and sizes, and results are compared with perfect crystals. For nano aluminum particles smaller than 9 nm, the melting temperature is size dependent. The presence of voids does not impact the melting properties due to the dominancy of nucleation at the surface, unless the void size exceeds a critical value beyond which lattice collapse occurs. The critical void size depends on the particle dimension. The effect of pressure on the particulate melting is found to be insignificant in the range of 1–300 atm. The melting behavior of bulk aluminum is also examined as a benchmark. The critical interfacial area required for the solid–liquid phase transition is obtained as a function of the number of atoms considered in the simulation. Imperfections such as voids reduce the melting point. The ratio between the structural and thermodynamic melting points is 1.32. This value is comparable to the ratio of 1.23 for metals like copper.     

New model for tracer-diffusion in amorphous solid

The tracer-diffusion and structure of polymorphic states of amorphous solid is studied by mean of the statistic relaxation technique and simplex analysis. Several different metastable states of amorphous iron have been constructed based on the model containing 2 × 10⁵ atoms. All models have almost the same pair radial distribution functions, but they differ in the potential energy per atom and the density. We found a large number of vacancy-simplexes which varies according to the relaxation and serves as a diffusion vehicle. New diffusion mechanism for tracer-diffusion is found of which the elementary diffusion process likes a collapse of “microscopic bubble” in amorphous matrix. This includes a jump of diffusing atom and the collective movement of a large number of neighboring atoms. The diffusion constant D determined in accordance with considered diffusion mechanism is in reasonable agreement with experimental data. The decrease in diffusion constant D upon thermal annealing is explained by the reducing vacancy-simplex concentration which is caused by both the local atomic rearrangement and the elimination of excess free volume.     

High temperature and pressure thermodynamics of strontium: A macroscopic approach

Close proximity of d-bands (above) to the Fermi level (E _F) makes the heavy alkaline earth metals (Ca, Sr and Ba) fairly sensitive to external influences like temperature and pressure. Softening of some of the phonon modes at high temperatures and/or pressures implies that anharmonic effects can play an important role in determining lattice dynamics and related properties. In the conventional approach, phonon density of states (p-dos) have to be calculated at each volume to compute free energy and thereby the other thermodynamic properties, which is computationally quite demanding. Using an alternative technique, the mean-field potential (MFP) approach was combined with the relatively soft local pseudopotential to obtain the free energy at different temperatures and pressures. The results for phonon frequency shifts at finite temperatures using the MFP approach and those calculated from p-dos within the quasiharmonic approximation are very similar. This validates the use of the MFP approach coupled with the local pseudopotential to estimate vibrational response of the system at high-temperature and high-pressure environments. The present scheme was used to study various thermophysical properties for elemental strontium at elevated temperatures and pressures, including the high-pressure melting curve and temperature along the shock Hugoniot. Computed results are affirmatively compared and analyzed with other reported data. The present scheme completely bypasses traditional cumbersome calculations, and it is computationally convenient yet accurate.     

Model of the change in metal nanostructure at melting

A consequence of the previously proposed physical model of the nanostructure of simple metal liquids is presented. The nanostructure of a dense liquid at the melting temperature is determined by natural unit cells, composed of the central atom and atoms of the first coordination sphere, supplemented with melting vacancies. A method for calculating the concentration of melting vacancies, which explains the corresponding empirical data, is presented and their volume characteristic is estimated for some metals.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

温度对金属纳米线势能分布的影响

采用三维分子动力学模拟方法,以面心立方金属银为研究对象,基于Finnis-Sinclair型嵌入原子法(EAM)多体势,模拟研究了纳米线势能分布特征在常温下及其在不同温度直到熔化过程中的变化,给出了常温及不同温度银纳米线势能分布比例和势能分布函数.结果表明:常温下,纳米线高势能原子比例随纳米线横截面尺寸的减小而增大,势能分布函数曲线各峰位几乎与纳米线横截面尺寸无关;纳米线熔化前的势能分布函数曲线具有多个波峰,随着温度增加,峰数减少且峰位右移;熔化后,多峰特征消失,只有一个宽化的峰.     

Melting evolution and diffusion behavior of vanadium nanoparticles

Molecular dynamics calculations have been performed to study the melting evolution, atomic diffusion and vibrational behavior of bcc metal vanadium nanoparticles with the number of atoms ranging from 537 to 28475 (diameters around 2–9 nm). The interactions between atoms are described using an analytic embedded-atom method. The obtained results reveal that the melting temperatures of nanoparticles are inversely proportional to the reciprocal of the nanoparticle size, and are in good agreement with the predictions of the thermodynamic liquid-drop model. The melting process can be described as occurring in two stages, firstly the stepwise premelting of the surface layer with a thickness of 2–3 times the perfect lattice constant, and then the abrupt overall melting of the whole cluster. The heats of fusion of nanoparticles are also inversely proportional to the reciprocal of the nanoparticle size. The diffusion is mainly localized to the surface layer at low temperatures and increases with the reduction of nanoparticle size, with the temperature being held constant. The radial mean square vibration amplitude (RMSVA) is developed to study the anharmonic effect on surface shells.     

Calculating the melting curves by the thermodynamic data matching method: Platinum-group refractory metals (Ru,Os, and Ir)

A technique for reconstructing thermal properties, including the melting curve, of refractory metals based on the use of experimental data on caloric properties available up to the melting point and some regularities of the Debye–Grüneisen theory has been proposed. The calculation result is the consistent system of high-temperature thermal data, including the thermal expansion coefficient, solid-phase density, and volume jump upon melting. This technique was tried-out on refractory platinum-group metals based on experimental data on the enthalpy of the metals and confirmed by consistency with a thermodynamic calculation using shock-wave experiments and results obtained by the quantum molecular dynamics method.