An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

A SAFT model for associating Lennard-Jones chain mixtures

The recently proposed equation of state of statistical associated fluid theory (SAFT) is extended to associating Lennard-Jones (LJ) chain mixtures. In this extension, a new radial distribution function (RDF) for LJ mixtures is derived around the LJ potential size (σ _ij ). The RDF expression is completely analytical and real. Comparisons with computer simulation data under various conditions indicate that the RDF is very accurate up to its first peak. The new RDF, together with a previously established equation of state for LJ mixtures, is employed to study LJ chain mixtures by combining with Wertheim's first-order perturbation theory. The resulting equation of state is tested satisfactorily against computer simulation data for both non-associating and associating LJ chain mixtures, with a performance similar to its predecessors for pure LJ chains and LJ mixtures. The SAFT model is uniquely featured by being totally mixing-rule free and by being adjustable at both chain bonding and association sites. Moreover, the SAFT model is formulated very generally, so that it is applicable to both homonuclear and heteronuclear chain mixtures.     

Phonon dispersion of d and f shell metals: A dynamical treatment

The effective pair potential is written as the sum of s-s, d-d, s-d, f-f and s-f contributions. The free electron part of the pair potential is obtained in second-order perturbation theory using rational dielectric function (RDF) in conjunction with Heine-Abarenkov model pseudopotential (HAMP). The exchange-correlation corrections due to Taylor are inherent to RDF. The overlap between d states and f states on different ions and the effect of sd and hybridization are included in an approximate manner, as has been suggested by Wills and Harrison [Phys. Rev. B 28 (1983) 4363], and Harrison [ibid., 550]. An approximate temperature dependence has been included in the effective potential through an asymptotic factor. The ion-ion interaction so defined is used to calculate the phonon dispersion curves for hcp metals Tb and Ho. The calculated phonon frequencies are found to be real and in reasonably good agreement with the neutron inelastic scattering measurements which establishes the validity of the effective pair potential for rare earths.     

Characterizing auditory neurons using the Wigner and Rihacek distributions: a comparison

Because of their dynamic properties, most sounds can best be characterized in the combined frequency-time (FT) domain. Powerful frequency-time characterizations are the Wigner distribution function (WDF) and the Rihacek energy density function (RDF). In the present paper several new concepts are introduced such as using the WDF to characterize the tuning of auditory neurons under wideband noise stimulation and a new method to quantify phase lock of auditory neurons to a wideband noise. No appreciable differences were found between the WDF and RDF in narrow-band signal representations. However, the differences between the WDF and RDF increase as the bandwidth of the signal increases. When signals are buried in uncorrelated background noise, the average FT function of these signals may be obtained through averaging the FT functions for each signal plus noise segment. The WDF takes at least a factor 2 more in time to compute than the RDF. The FT functions can be used to characterize (linear) filters by averaging FT functions of input-noise segments that precede threshold crossings of the filter's output signal. Both the WDF and the RDF were used to characterize auditory neurons from the midbrain in anurans; the WDF always had a smaller bandwidth than the RDF. By comparing the spectrum of the reverse correlation function and the average spectrum of the noise segments preceding the spikes, a quantification of the amount of phase lock of the auditory neuron to the noise is obtained.     

Correlation functions for diatomic symmetric molecules from the RISM equation

Using the solution of the RISM equation for diatomic symmetric molecules outlined in a previous paper, the site-site radial distribution function (RDF) is calculated and compared with the Monte Carlo results and the numerical RDF of Lowden and Chandler. The RDF calculated here and the numerical RDF of Lowden and Chandler agree well at intermediate and high densities. At low density, however, both have systematic errors. The agreement between the RDF calculated here and the Monte Carlo results suggests that a simplified formulation of the RISM solution may serve well as a reference system in a perturbation theory for diatomic fluids.     

取向对径向分布函数的影响

依据实验结果导出的径向分布函数（ＲＤＦ），因实验测量和数据处理误差引入的误差称作“误差畸变”，如峰形宽化，峰面积改变，峰位移动以及假峰出现等。ＲＤＦ是建立在非晶材料结构各向同性和均匀性假设基础上的。因此当非晶材料存在取向各向异性时，其ＲＤＦ出现一种比误差畸变更为严重的“取向畸变”，它将导致ＲＤＦ的解释出现严重错误。讨论了这种“取向畸变”特征。 关键词：     

磁场对水系统内能影响的MC计算机模拟方法研究

用Monte-Carlo计算机模拟方法,通过对一个含有64个水分子的三维体系在磁场作用时内能变化的计算,定量评估了磁场强度及温度对磁处理效应的影响。研究发现:水的内能与外加磁场强度的关系曲线是一条多极值曲线;水-水径向分布函数伴峰的高度与磁感应强度也具有多极值特征;计算机模拟结果与实验结果基本一致,计算机模拟确实是从分子水平研究磁处理机理的有效方法。     

Radial-distribution function by EXAFS: Asymmetry in metallic glasses

Summary The authors discuss the information on the radial-distribution function (RDF) obtainable from EXAFS as compared with X-ray diffraction. The cases of Gaussian and non-Gaussian RDFs are illustrated showing how the Fourier transform (FT) of the experimental spectrum is connected with the RDF parameters in the two cases. The evidence of an asymmetric RDF in a metal glass, Fe₈₀B₂₀, is presented and discussed in detail. Paper presented at the Workshop on ?EXAFS Data Analysis in Disordered Systems?, held in Parma, October 5–7, 1981.     

Study of structural transition of nickel metal under temperature

A molecular dynamics (MD) simulation study has been performed to investigate the structural transition of nickel metal using Pak–Doyama potential. The local atomic structure was analyzed through the radial distribution function (RDF), coordination number distribution, simplex statistics and three-dimensional visualization. It was shown that the splitting of the second peak of RDF appears when the liquid transforms to amorphous solid. This feature originated from the transformation of simplexes from strongly to weakly distorted tetrahedron type. We found that the liquid state contains a significant number of nanocrystal nuclei which strongly depend on the temperature and MD time steps. Accordingly, the simulation shows that the crystallization originated from expanding of nanocrystal nucleation process. The thermodynamic properties are also estimated through the dependence of mean-squared displacement on the MD time steps.     

Analytical expressions for the correlation function of a hard sphere dimer fluid

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.     

Theoretical and analytical radial distribution function for dense fluids

The ‘identical particles in quasi-mean potential energy field’ assumption was used to derive the approximate theoretical and analytical radial distribution function (RDF) for dense fluids through solving the two-body Schrödinger equation and using the first-order perturbation method. The theoretical and analytical expressions of RDF can save much computation time in calculating the thermodynamics properties of fluids and may make the statistical mechanics theories comparable with the equation of state method that is currently widely used in physics, chemistry and technology. The calculated properties for argon by this RDF fit well with the experimental data of reference over a very wide range of conditions, including dense fluids (liquid phase and dense gas), critical point, and dilute gas, in which the pair potential and the Axilrod-Teller three body interaction were considered. The extensive practical application of this model for science and technology needs further investigation.     

Cooling rate effects on structure and thermodynamics of amorphous nanoparticles

Cooling rate effects on structure and thermodynamics of amorphous nanoparticles were studied in a spherical model using Molecular Dynamics (MD) method. The good equilibrium melts are cooling down by three different cooling rates in order to observe the cooling rate effects. We find that cooling rate effects on thermodynamic quantities such as potential energy and surface energy are more pronounced than those for static quantities. Microstructure of amorphous nanoparticles is analyzed via radial distribution function (RDF) and coordination number distributions. Relatively weak cooling rate effects on such quantities are found. Microstructure of surface and core of amorphous nanoparticles are analyzed.     

The deposition of Fe or Co clusters on Cu substrate by molecular dynamic simulation

A molecular dynamic method is used to simulate the film growth process of Fe or Co clusters depositing on Cu substrate with low energy. The tight-binding (TB-SMA) many-body potential is used to simulate the interaction between atoms. The effects of different incident energies and/or substrate temperatures on the surface roughness, layer coverage function, radial distribution function (RDF), and residual stress are investigated. From the simulation results, as the substrate temperature and/or incident energy is increased, the surface roughness of the grown film could be reduced, and the interface intermixing is increased. Also, as compared to Co–Cu system, Fe–Cu system has better surface roughness, less interface intermixing, and similar radial distribution function as well as average stresses.     

用X射线异常色散效应测定二元非晶合金Fe82B18偏径向分布函数方法的简化

本文采用Mo,Cu,Co三种不同波长的X射线辐射,测定了Fe₈₂B₁₈二元非晶合金的径向分布函数。比较了不同波长辐射对测定径向分布函数的影响。应用X射线异常色散方法计算了Fe₈₂B₁₈二元非晶合金的偏径向分布函数。在计算时略去了B-B原子对对径向分布函数的贡献,因而简化了计算过程,并相对提高了计算精度。所得结果与国际上使用同类方法或其它方法的结果相近。 关键词：     

Theoretical and analytical Radial Distribution Function for non-polar mixtures

The theoretical and analytical Radial Distribution Function (RDF) for non-polar mixtures is presented, and the estimation methods of model parameters (such as the minimum molecular diameter d_ii, mean calibration factor of volume β_V and mean free path of relative motion λ_r,ij) are discussed. The calculated thermodynamic properties for H_e-H₂ fluid mixtures by this RDF fit well with that of MC simulations and classical results from the Yukawa-type EOS, in which the Double Yukawa (DY) potential was used and the quantum effect was considered. Compared with the semi-empirical RDF expressions in references, the advantage of this theoretical and analytical RDF is that it can be used for all kinds of potential functions of non-polar molecules, and it covers a very wide range of temperatures and densities. The extensive practical application of this RDF for chemistry, physics and technology needs further investigation.     

Kinematic theory of diffraction by matter of any kind and the theory of liquids

An expression for the intensity function scattered coherently by an arbitrarily distorted lattice has been derived which degenerates under well-defined conditions to the well-known formulae valid for crystals, liquids and gases or amorphous substances. A new method for the analysis of the radial distribution function (RDF) of simple liquids has been suggested. RDF curves for liquid argon near the triple point have been analysed to obtain the distance statistics of neighbours and their coordination numbers. Using the first-neighbour statistics an expression for the partition function for matter of any kind and, in particular, for simple liquids has been deduced.     

非晶态物质径向分布函数的微机程序X－RDF（Ⅲ）

报导了一个通用性好,可信度高的径向分布函数程序,它可以根据X射线衍射数据计算实验径向分布函数,也可根据模型结构计算理论径向分布函数,还可给出结构参数。     

A molecular dynamics study of the effect of Coulomb Buckingham Potential on equilibrium structural properties of calcium titanate perovskite

The demand on new and highly efficient energy conversion systems and many other advanced applications have suggested perovskites to be important future candidate materials. Though a lot of work has been done to understand and model their structure and properties, further investigation is still needed. Consequently, the development and enhancement of computational methods including molecular dynamics and quantum chemical calculations is one of the main issues regarding the understanding and optimization of perovskites. In this work, Coulomb Buckingham interatomic potential function is investigated to analyze the structure of Calcium Titanate CaTiO₃ through the application of Molecular Dynamics via LAMMPS open source code. The results are compared with the results of other potential functions representations, namely Vashishta-Rahman (VR) and Lennard-Jones (LJ) potentials. The understanding of the effect of potential representation on structural properties would lead to deduction of mechanical and thermal properties and to building a platform for adapting the different types of oxide perovskites, or even nonorganic halide perovskites, to enhance their technological aspects. The VR interaction potential was previously proven to be the most effective for describing the phase changes of perovskites and to match the experimental observations. It was also proven in previous studies that the radial distribution function (RDF) undergoes essential changes when replacing LJ with VR. According to the findings of this study, Buckingham potential is shown to produce much closer results to VR than LJ of the radial distribution function.     

不同势函数状态方程湿空气性质的模拟研究

本文从L-J维里状态方程、L-J径向状态方程,TIP4P维里状态方程以及TIP4P径向状态方程四种模型出发,利用分子动力学模拟技术,进行了湿空气性质的研究.对不同状态方程的模拟结果的稳定性进行了探讨,发现径向状态方程的稳定性要好于维里状态方程,最后采用径向分布方程及TIP4P模型,模拟了湿空气的性质,结果表明湿空气在低温、高压和高含湿量下,其性质不再接近于理想气体的性质.     

Structural study of highly dispersed cerium dioxides

Cerium dioxide samples of different dispersivity, obtained by different methods, have been investigated by X-ray diffraction (XRD) analysis, full-profile analysis of diffraction patterns, calculation of radial distribution function (RDF) of electron density, and extended X-ray absorption fine-structure (EXAFS) spectroscopy. According to the XRD data, the samples studied can be identified in the fluorite structure with conventional unit-cell parameters. However, the local structure of highly dispersed samples, determined by the RDF and EXAFS methods, changes: the coordination spheres for the Ce-O distances are represented by two distances.