The Effect of Temperature on Lattice Mechanical Properties of Noble and Transition Metals

A simple pseudopotential model is used for the calculation of the temperature dependence of lattice mechanical properties which also depend on the phonon density of states such as lattice heat capacity C _V , Debye temperature _D, harmonic contribution to free energy, thermal pressure, isothermal bulk modulus corrected to the fourth order, volume thermal expansion coefficient , Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter, and X-ray characteristic temperature _M of Cu, Ag, Au, Ni, Pd, Pt, Rh, and Ir. The contribution of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer-like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings show the ability of our model potential to reproduce wide class of properties in noble and transition metals.     

Temperature variation of the Debye-Waller factors of Ba++ and F− ions in BaF2 powder by x-ray diffraction

The temperature variation of the Debye-Waller factors of Ba⁺⁺ and F⁻ ions in BaF₂ powder has been studied using x-ray powder diffraction over the temperature range 77°–298°K. A continuous flow cryostat has been specially fabricated for this purpose for the YPC 50 NM powder diffractometer available in the department. The Debye-Waller factors of Ba⁺⁺ and F⁻ between room temperature and 879°K have been measured using single crystal neutron diffraction by Cooperet al. Theoretical lattice dynamics shell model calculations using a 7-parameter model in a quasiharmonic approximation have been done over a temperature range 77° to 879°K. The theoretical values have been compared with the present x-ray measurements and the single crystal neutron diffraction values and the results are discussed.     

Pseudopotential study of lattice parameter and heat of formation for substitutional alloys

Ashcroft’s empty core pseudopotential is applied to the substitutional alloy (K-CS) to calculate the heat of formation and lattice parameter over the entire concentration range. At any concentration the defect crystal is considered to be equivalent to a perfect crystal with a modified lattice parameter and the potential parameter for the defect crystal is calculated by using some suitable interpolation formula. The calculated results agree well with the available experimental results.     

The Percolation Transition for the Zero-Temperature Stochastic Ising Model on the Hexagonal Lattice

On the planar hexagonal lattice , we analyze the Markov process whose state (t), in , updates each site v asynchronously in continuous time t0, so that _v (t) agrees with a majority of its (three) neighbors. The initial _v (0)'s are i.i.d. with P[ _v (0)=+1]=p[0,1]. We study, both rigorously and by Monte Carlo simulation, the existence and nature of the percolation transition as t and p1/2. Denoting by ⁺(t,p) the expected size of the plus cluster containing the origin, we (1) prove that ⁺(,1/2)= and (2) study numerically critical exponents associated with the divergence of ⁺(,p) as p1/2. A detailed finite-size scaling analysis suggests that the exponents and of this t= (dependent) percolation model have the same values, 4/3 and 43/18, as standard two-dimensional independent percolation. We also present numerical evidence that the rate at which (t)() as t is exponential.     

On the Lowest Energy Nucleation Path in a Supersaturated Lattice Gas

A lattice gas with non-conserved spin flip dynamics (of both non-Glauber and Glauber types) is considered at TT _c , the critical temperature. For arbitrary supersaturation, S, a general expression for the inverse of the nucleation rate along the lowest energy path is derived. The exponential part is identical to the one by Neves and Schonmann [Commun. Math. Phys. 137:20 (1991)]. The preexponential can be expressed in terms of elliptic theta-functions for small S, and in the limits, respectively, of ST/ or ST/ (– being the nearest-neighbor interaction energy), elementary versions of the general expression are further obtained. The preexponential has a smooth component, as well as small-scale modulations which are approximately periodic in the inverse supersaturation. For ST/, the smooth part is proportional to , in contrast to the zero-T limit where it is linear in S. The latter limit becomes apparent only at extremely low temperatures which are cubic in S.     

On the Diffusion in a Lattice Gas Model: Group-Theoretic Approach

Motivated by some recent results concerning the model of a noninteracting one-dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded, we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation. Closed-form analytic solutions are found.     

Lattice Dynamics of Some Fcc F-Shell Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), phonon density of states, Debye temperature, mode Grüneisen parameters, dynamical elastic constants, Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter and propagation velocities of elastic waves of some fcc f-shell metals La, Yb, Ce, and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the model potential while d- and f-like electron is taken into account by introduction of repulsive short-range Born-Mayer term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The parameter of the potential is evaluated by zero pressure condition. Which is independent of any fitting procedure. An excellent agreement between theoretical investigations and experimental findings prove the ability of the potential for d- and f-shell metals exclusively.     

A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.     

Temperature variation of the Debye-Waller factors of metal and halide ions in CsCl and CsBr powders by X-ray diffraction. I. Debye-Waller factors of Cs+ and Cl− ions in CsCl from room temperature to 90°K

The temperature variation of the Debye-Waller factors of Cs⁺ and Cl⁻ ions in CsCl powder has been studied using X-ray powder diffraction. A continuous flow cryostat has been used to record the diffractograms and the integrated intensities of the Bragg peaks at different temperatures have been obtained. The integrated intensities of the odd and even reflections have been analysed following the structure of the CsCl compound and the Debye-Waller factors of the Cs⁺ and Cl⁻ ions have been estimated. The results have been verified by structure factor least squares refinement. Theoretical shell model lattice dynamical calculations have been done using a 7-parameter model in the harmonic approximation and the values compared with the present X-ray measurements.     

A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.     

On Study of Solutions of Kac-van Moerbeke Lattice and Self-dual Network Equations

The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical computation of travelling wave solutions for differential difference equations, our method obtains exact solutions which have physical relevance.     

Thorium: Phase transformations and equation of state to 300 GPa

Abstract

Equation of state and phase transformations of thorium metal have been investigated to 300 GPa at 300 K in a diamond anvil cell using energy dispersive X-ray diffraction employing synchrotron source. Phase transformations in the 70–100 GPa range indicative of 5f-electron bonding are observed and thorium metal is isostructural with its 4f counterpart cerium at ultra high pressures. The measured static equation of state of thorium to 300GPa (volume fraction V/V _o = 0.40) at 300K is given. At high pressures, the sd to f electronic transfer has significant influence on the measured equation of state of thorium.     

Application of Exp-Function Method to Discrete Nonlinear SchrSdinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.     

Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that in a finite volume the dependence of the ground state on the boundary condition exponentially decays with the distance to the boundary, which implies in particular that the infinite-volume ground state is unique. Also, equivalent forms of boundary conditions for ground states of general finite quantum systems are discussed.On leave from Institute for Information Transmission Problems, Moscow, Russia.     

Extraction of Nuclear Matter Properties from Nuclear Masses by a Model of Equation of State

The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei.It is shown that the volume energy a1 and the nuclear incompressibility Ko depend essentially on μnN - - pZ - 2EN,whereas the symmetry energy J and the density symmetry coefficient L as well as symmetry incompressibility Ks depend essentially on μn - μp,where μp ＝μp - Ec/ Z,μn and μp are the neutron and proton chemical potentials respectively,EN the nuclear energy,and Ec the Coulomb energy.The obtained symmetry energy is J ＝ 28.5 MeV,while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.``     

On the neutron diffraction in crystals in the field of a sound wave

Diffraction of neutrons in crystals under influence of a sound wave is considered. The probability of scattering of neutrons at the elastic interaction with the crystal is calculated. On the contrary, scattering of neutrons by an acoustical phonon has inelastic character. The possibility to control the Debye-Waller factor is shown.     

Extraction of Nuclear Matter Properties from Nuclear Masses by a Model of Equation of State

The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei.It is shown that the volume energy a1 and the nuclear incompressibility Ko depend essentially on μ_nN + μ_pZ - 2E_N,whereas the symmetry energy J and the density symmetry coefficient L as well as symmetry incompressibility Ks depend essentially on μ_n - μ_p,where μ_p ＝μp - ∂E_c/∂Z,μ_n and μ_p are the neutron and proton chemical potentials respectively,E_N the nuclear energy,and E_c the Coulomb energy.The obtained symmetry energy is J ＝ 28.5 MeV,while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.     

Mie-Grüneisen状态方程的物理力学释义

通过建立一种简单的固体一维点阵定容热振动的物理力学模型,完全由力学方程推演出了Mie-Grüneisen形式的固体状态方程,并从力学本质上明确了热压力的物理意义是原子热振动时均值所造成的作用力偏载量。所得Grüneisen系数与频率的关系说明,真实三维晶体的Grüneisen系数与晶体结构相关。在简单立方晶体的情况下,获得了与Dugdale-MacDonald公式形式相同的Grüneisen系数-冷压微分关系式。研究结果证明,在状态方程构建方面,“物理力学”是一种非常有效的研究工具。

     

Application of Exp-Function Method to Discrete Nonlinear Schrödinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrödinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.     

Solution of the Semi-Infinite Toda Lattice for Unbounded Sequences

The semi-infinite Toda lattice is the system of differential equations d _n (t)/dt = _n (t)(b _n+1(t) – b _n (t)), db _n (t)/dt = 2( _n ²(t) – _n–1 ²(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences _n (t), b _n (t) which satisfy the conditions _n (0) = _n ,, b _n (0) = b _n , where _n > 0 and b _n are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences _n and b _n are bounded. When at least one of the known sequences _n and b _n is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences _n and b _n such that the system has a unique solution. The results are illustrated with a typical example where the sequences _i (t), b _i (t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d²/dt ² log h _n = h _n+1 + h _n–1 – 2h _n , n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation.