Comparative computations of the lattice energy of sodium chlorate and bromate using explicit minimisation procedures

Two methods are described to evaluate the lattice energies of salts containing polyatomic ions by means of a minimisation procedure. A multipole expansion is used for the electrostatic part of the lattice energy, and the repulsion energy is described within either the simple Born-Mayer scheme or the Huggins and Mayer scheme. The minimum condition for the lattice energy determines the repulsion parameter, whereas the repulsion exponent ρ is either calculated using the experimental compressibility (Method A) or is given a constant value (Method B). Both methods are applied to cubic NaClO₃ and NaBrO₃, where the lattice energies are obtained as a function of the charge of the oxygen atom. The results are very similar indeed suggesting that either approach is satisfactory.     

求解非线性差分方程孤立波解的直接代数法

推广了求解非线性差分方程孤立波解的直接代数法.用此方法研究了Hybrid晶格方程，借助于符号计算Maple,得到它的新孤波解.这种方法也可用于求解其他的差分方程. 关键词： 微分-差分方程 Hybrid晶格方程 行波解 孤     

The direct linearizing transform for the τ function in three-dimensional lattice equations

A connection between the direct linearization and the τ function for solutions of the three-dimensional lattice Toda equation is given. The connection is via a fermionic path integral containing an action defined in terms of the kernel of the linearizing integral transformation for the Toda equation. General properties of the τ function are derived, and some relations with the representation theory of infinite-dimensional Lie algebras are mentioned.     

A minimisation procedure for the calculation of lattice energies of tetragonal,hexagonal and trigonal crystals

This paper generalises the minimisation procedure for the calculation of lattice energies of cubic crystals to the cases of tetragonal, hexagonal, and trigonal crystals. If the repulsion energy is described within the simple Born-Mayer scheme minimisation of the lattice energy with respect to the lattice parameters a and c yields the repulsion parameters. The linear compressibilities obtained either by direct measurement or from the elastic constants of the crystal allow the repulsion exponent ? to be calculated. The application of this method to the tetragonal MgF₂ crystal is demonstrated.     

用拉曼光谱测量离子注入引起的晶格应变

对于10个周期的AlAs/GaAs超晶格和25个周期的GaAs/Ga0.92In0.08As超晶格,在室温下进行0.28 MeV的Zn＋注入,注入剂量为5×1013~5×1014 cm-2。通过拉曼光谱测量,定量地分析了由于离子注入所引起的晶格内应变。实验结果表明：在所选用的注入剂量下,由于离子注入引起的应变小于体材料GaAs的最大非驰豫应变值0.038,说明该注入条件下,注入区的结晶态仍然保持得比较好。在较高注入剂量下应变达到饱和,说明缺陷的产生和复合达到了平衡,从而形成了均衡的应变场分布。     

用拉曼光谱测量离子注入引起的晶格应变

 对于10个周期的AlAs/GaAs超晶格和25个周期的GaAs/Ga0.92In0.08As超晶格,在室温下进行0.28 MeV的Zn＋注入,注入剂量为5×10¹³~5×10¹⁴ cm^-2。通过拉曼光谱测量,定量地分析了由于离子注入所引起的晶格内应变。实验结果表明：在所选用的注入剂量下,由于离子注入引起的应变小于体材料GaAs的最大非驰豫应变值0.038,说明该注入条件下,注入区的结晶态仍然保持得比较好。在较高注入剂量下应变达到饱和,说明缺陷的产生和复合达到了平衡,从而形成了均衡的应变场分布。     

Free energy of a randomly disordered harmonic lattice using the replica trick

The free energy of a lattice dynamical system with random isotopic mass disorder has been obtained employing the replica trick. In the high temperature limit, the expression for the free energy correction reduces to that obtained by Weiss and Maradudin for a linear chain with small mass difference and impurity concentration; in the low temperature limit the expression differ. The merit of the method in incorporating configurational fluctuation effects is discussed.This work has been supported by the Deutsche Forschungsgemeinschaft through SFB 125, Aachen-Jülich-Köln     

Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks.     

由飞行时间质谱峰形获取光解碎片平动能分布

由于在魔角条件下测量的飞行时间（TOF）质谱峰形与光解碎片的角分布无关，因而便于用含待定参数的平动能分布函数去拟合质谱峰形来获取光解碎片的平动能分布.与通常的拟合法不同，提出一种峰形参量法，只需通过测量TOF峰形的半高宽(t^1/2)、四 分之一高宽(t^1/4)和四分之三高宽(t^3/4)，便可借助文中提供 的曲线图或 解析式得出碎片平均平动能，平动能分布特征宽度以及描述实验装置本身的特征峰宽等.处 理过程中，平动能分布及实验装置峰形均采用相应的高斯分布函数描述. 关键词： 魔角 TOF质谱 平动能分布     

Comment on relative ion sputtering yield measurements by integration of secondary ion energy distribution using a retarding-dispersive ion energy analyzer

The location and width of the peak in the sputtered ion energy distributions of W⁺ from the clean surface can be explained by a simple power dependence on energy for the ionization probability. Research sponsored by NASA under Contract/Grant Number NGR 21-002-096     

A standard and direct method to obtain multiple soliton solutions of the nonlinear partial differential equation

In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative equations are investigated by this method and multiple soliton solutions are found.     

Depth-profiling the composition of bimetallic nanoparticles using medium energy ion scattering

The near monolayer depth resolution of medium energy ion scattering is utilized to develop a probe of the depth dependent composition of bimetallic nanoparticles supported on planar oxide supports. The approach fits spectra of scattered ion intensity versus ion energy at well-defined scattering angles taking into account the asymmetric line shape in such spectra and also the depth dependent loss processes encountered by incident ions as they pass through the bimetallic particles.     

Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.     

Relative ion sputtering yield measurements by integration of secondary ion energy distribution using a retarding-dispersive Ion energy analyzer

The application of a retarding-dispersive energy analyzer as the pre-filter of a quadrupole mass analyzer has made it possible to combine a standard high-speed Secondary Ion Mass Spectrometer (SIMS) and a high-resolution secondary-ion energy analyzer into one instrument. Data taken with this instrument indicate the presence of very significant high-energy tails in the energy distribution of all observed secondary ions, even with relatively low (2 keV) primary ion energies. The shape of the energy distribution varies widely from element to element, for atomic compared to molecular species sputtered from a clean metal surface, and depends, for a given species sputtered from a metal surface, on the degree of surface oxidation. The variations established in the present work are large enough to introduce in many cases substantial discrepancies between published values of both relative ion sputtering yields and surface elemental concentrations and values obtained by considering the complete energy distribution. Methods of obtaining accurate secondary ion yields by integrating the energy distribution are discussed. Work performed under the auspices of the Division of Physical Research of the U.S. Energy Research and Development Administration.     

Analytical optimization of the lattice parameter using the binding energy calculated in the quasi-classical approximation

The dependence of the static binding energy of a crystal on the crystal structure as calculated in the initial quasi-classical approximation is shown to allow the equilibrium lattice parameter to be found analytically. The application of this method to boron nitride modifications leads to lattice parameters that coincide with experimental values to within several percent. This method gives lattice parameters of 2.66, 3.49, and 2.44 Å for the BN hexagonal layer and the cubic c-BN and “ideal” wurtzite-like w-BN crystals, respectively. The corresponding binding energies are estimated to be 23.2, 14.1, and 13.6 eV/mol, respectively.