Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Mo纳米薄膜热力学性质的分子动力学模拟

采用改进嵌入原子法(MAEAM),通过经典的分子动力学(MD)模拟计算了高熔点过渡金属体心立方(bcc) Mo块体Gibbs自由能和表面能. 对于纳米薄膜的热力学数据,比如Gibbs自由能等,可以看成是薄膜内部原子和表面原子两部分数据之和,然后根据薄膜的体表原子之比就可以直接计算出总的自由能,并由此可以得到热力学性质与薄膜尺寸及温度的定量关系式. 分别计算了bcc Mo块体及其纳米尺寸薄膜的自由能和热容,结果表明,Mo纳米薄膜的热力学性质具有尺寸效应,并且在薄膜尺寸小于15—20nm时,这种效应变得非常明 关键词： 改进嵌入原子法 Mo纳米薄膜 表面自由能 热容     

Dimension spectrum of axiom a diffeomorphisms. I. The Bowen-Margulis measure

We compute the dimension spectrumf() of the singularity sets of the Bowen-Margulis measure defined on a two-dimensional compact manifold and invariant with respect to aC ² Axiom A diffeomorphism. It is proved thatf is the Legendre-Fenchel transform of a free energy function which is real analytic (linear in the degenerate case). The functionf is also real analytic on its definition domain (defined in one point in the degenerate case) and is related to the Hausdorff dimensions of Gibbs measures singular with respect to each other and whose supports are the singularity sets, and we decompose these sets.     

Dimension spectrum of axiom a diffeomorphisms. II. Gibbs measures

We compute the dimension spectrumf() of the singularity sets of a Gibbs measure defined on a two-dimensional compact manifold and invariant with respect to aC ² Axiom A diffeomorphism. This case is the generalization of the case where the measure studied is the Bowen-Margulis measure—the one that realizes the topological entropy. We obtain similar results; for example, the functionf is the Legendre-Fenchel transform of a free energy function which is real analytic (linear in the degenerate case). The functionf is also real analytic on its definition domain (defined in one point in the degenerate case) and is related to the Hausdorff dimensions of Gibbs measures singular with respect to each other and whose supports are the singularity sets, and we finally decompose these sets.     

Conformal invariance in incommensurate phases

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f _–A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.     

Study of surface cell Madelung constant and surface free energy of nanosized crystal grain

Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO₂ and the surface electrostatic energy(absolute value) of nanosized-crystal-grain α -Al₂O₃ are found to be the biggest among all the crystal grains including those of other species.     

Quantum corrections to thermodynamics of polar hard sphere fluids

The quantum corrections to the thermodynamic properties of polar hard sphere fluids and fluid mixtures are estimated taking into account the influence of dipole and quadrupole moments. Expressions are given for the second virial coefficient, free energy and pressure and results are given for different values ofμ* andϑ*. The first order quantum correction arises due to the translational contribution only. The quantum effect increases with density,μ* andϑ*. Numerical results are also estimated for binary mixtures of (i) hard spheres and dipole hard spheres and (ii) hard spheres and quadrupole hard spheres. The ‘excess’ free energy for dipole hard sphere binary mixture is also reported. It is found that the ‘excess’ quantum effect depends on the concentration and the particle diameter ratio and increases with increase ofμ* andϑ*.     

The effect of repulsive interactions on Bose-Einstein condensation

One-dimensional Bose gases that interact via a repulsive two-body interaction and show Bose-Einstein condensation at the free level are studied. It is shown that the introduction of this interaction, however small, destroys the condensate. It is also shown that the free energy of an interacting Bose gas does not depend on the boundary conditions(including attractive boundary conditions) in the van der Waals limit.     

The thermodynamic functions of ferroelectric and paraelectric SbSI

A first-principle method is used to calculate phonon density of states, Helmholtz free energy, internal energy, and entropy for ferroelectric and paraelectric SbSI. Theoretical phase transition temperature was obtained using the difference of the Helmholtz free energy, internal energy, and entropy term between ferroelectric and paraelectric phases on temperature. The obtained value is in reasonable agreement with the experimental second-order phase transition temperature T_c2 = 233 K.     

Theoretical prediction of linear free energy relationships using proton nucleomers

Values of σ and σ⁺, for use in linear free energy relationships, are determined for para hydrogen atoms having nuclear charges other than 1 (nucleomers). Hammett ρ values for a variety of free energies of activation, reaction, and other extrathermodynamic properties (e.g., vibrational frequencies) are computed therefrom and compared to those computed using typical para functional groups. The nucleomer correlations show excellent qualitative agreement with standard correlations but the quantitative agreement is less good, typically underestimating the standard ρ‐value by 10–60%. Copyright © 2007 John Wiley & Sons, Ltd.     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

Free energy reaction root mapping of alanine tripeptide in water

ABSTRACT

We have investigated the free energy surface of alanine tripeptide in water. To elucidate the secondary structure of the amide chain, information on the free energy surface with explicit water at room temperature, and the multidimensional reaction coordinates are required. We studied the minimum free energy paths (MFEPs) connecting reactants, transition structures (TS) and products. To solve this problem, we used the free energy reaction root mapping (FERRMap) method. This is an automated search method to find MFEPs by using umbrella integration and the scaled hypersphere search method. We calculated the four-dimensional free energy surface for alanine tripeptide in water using FERRMap and found 61 equilibrium structures (EQ) connected by 133 TS points. After elucidating the MFEP network, we analysed the structures of the EQ points and the MFEPs connecting beta-sheet structures and beta-turn structures or left-handed helix structures.     

A superconductor with 4-fermion attraction weakly perturbed by magnetic impurities

A superconductor with 4-fermion attraction, considered by Maćkowiak and Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic interaction V between conduction fermions and localized distinguishable spin 1/2 magnetic impurities. V has the form of a reduced s-d interaction. An upper and lower bound to the system’s free energy density f(H, β) is derived and the two bounds are shown to coalesce in the thermodynamic limit. The resulting mean-field equations for the gap Δ and a parameter y, characterizing the impurity subsystem are solved and the solution minimizing f is found for various values of magnetic coupling constant g and impurity concentration. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Quantum corrections to the thermodynamic properties of a two-dimensional fluid with hard-core potential

A simple theory, based on the physical interpretation of the reciprocal of activity, is developed to evaluate the thermodynamic properties of a two-dimensional fluid in the semi-classical limit. The theory is applied to calculate the quantum corrections to the equation of state and excess free energy of two-dimensional fluids, whose molecules interactvia hard-disc and square-well potential. It is found that the quantum effect increases with the increase of density and decrease of temperature.     

Directed polymers in a random environment: Some results on fluctuations

We consider a polymer model on ℤ ₊ ^d where to each edgee is associated a random variable v(e). A polymer configuration is represented by a directed pathr and has a weight exp[-β ∑ _e ∈r ν(e)], withβ=1/T the inverse temperature. We extend some rigorous results that have been obtained for the ground state of this model to finite temperatures. In particular we obtain some upper and lower bounds on sample-to-sample free energy fluctuations, and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations     

Disorder in liquid Cu–Pd alloys

The disorder in thermodynamic and microscopic structure of liquid Cu–Pd alloy at 1350?K has been studied using regular associated solution model. For this, we have calculated free energy of mixing (G_M ), activity (a), concentration fluctuation in long wavelength limit [S_CC (0)] and chemical short-range order parameter (α ₁) of liquid Cu–Pd alloy at 1350?K. The energetic and structural asymmetry of liquid Cu–Pd alloys has been successfully explained on the basis of regular associated solution model.     

Experimental Evidence of Parametric Instabilities in an Unmagnetized Plasma Subjected to a Strong H.F. Electric Field

Experimental evidence of parametric excitation, by an intense external H.F. field, of an electron surface mode and an ion wave is presented. The pumping electromagnetic energy density is equal to or slightly larger than the thermal energy density of the electrons. The value of f_pc/f₀ (electron plasma frequency/external field frequency) is that for an electron surface wave. Depending on the pressure and field intensity, this decay instability can lead to three types of low frequency oscillations, with frequencies close to the ion plasma frequency. Two of these are described by Aliev and Silin's intense field theory: one is the volume ion plasma oscillation and the other a surface ion plasma oscillation. The third corresponds to no known ion eigenmode. Several other features of the theory by Aliev and co-workers are also confirmed experimentally, such as the harmonic excitation of the instability (nf₀ ≈ f_pe/√2, where n is an integer), the instability amplitude as a function of f_pe/f₀ (above threshold conditions), the value of the mismatch parameter as a function of field strength and ion mass, and the existence of a fine structure corresponding to the symmetric and antisymmetric electron surface oscillations. Even at high pump field strengths, the decay products are nearly monochromatic i.e. the plasma does not become turbulent.     

On the study of fluid structure of tetrahydrofuran-n-butyric acid mixture by dielectric studies

The Kirkwood correlation factors g^eff and g_f, excess permittivity ε^E and excess free energy F^E of mixing for the binary mixture of n-butyric acid with tetrahydrofuran (THF) were calculated from the experimental dielectric data obtained at temperatures 303, 308, 313 and 318 K over the entire composition range. The value of g^eff decreases with increase in acid concentration and g_f is found to be greater than unity. At higher temperature, two maxima and two minima have been obtained for ε^E and F^E, respectively. These parameters are analyzed to obtain information about the complex formation through H-bond and dipolar orientation.