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1.
In honor of Baxter's sixtieth birthday, we would like to review some of his work on the free energy of the chiral Potts model. In spite of the enormous complexity and difficulty of the problem, Baxter, using functional relations was able to calculate not only the free energy, but also the interfacial tension. We here show that the integral for the free energy simplifies in the superintegrable case and is identical to his earlier results using entirely different approaches. His calculations are extended to include other regions. We also attempt to clarify some of his reasoning as several steps may be mysterious at first glance. 相似文献
2.
R. J. Baxter 《Journal of statistical physics》2003,112(1-2):1-26
In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice inversion relation method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site T
pq
of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of T
pq
. In terms of the t
p
,t
q
variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a (2N–1)-dimensional lattice (for N>2). The function T
pq
is meromorphic on this surface: we obtain the orders of all the zeros and poles. For N odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For N even, this method does not give the orders uniquely, but leaves only [(N+4)/4] parameters to be determined. 相似文献
3.
Nils Brinkmann Gabriel Micard Yvonne Schiele Giso Hahn Barbara Terheiden 《固体物理学:研究快报》2013,7(5):322-325
For the first time we present a free energy loss analysis (FELA) of heterojunction silicon solar cells (HSSC) to study the influence of the intrinsic buffer layer thickness (tbuffer) on the solar cell efficiency (η). The main advantage of the FELA is that the impact of various loss mechanisms can be directly expressed in absolute percentage of η. Furthermore, it is possible to extract the magnitude of every loss for each region of the solar cell. All quantities required to perform the FELA are obtained by the simulation software AFORS‐HET. The FELA yields an optimum efficiency of 21.24% for tbuffer ≈ 5 nm. The efficiency drop for tbuffer £ 5 nm is ascribed to a lower maximum usable generated power ΦG(22.84% @ 2 nm, 23.98% @ 5 nm). Lower efficiencies for tbuffer ³ 5 nm are attributed to the increased transport loss of holes in the intrinsic buffer layer (0.05% @ 2 nm, 0.65% 8 nm). The η values yielded by the FELA are in agreement with the ones calculated by AFORS‐HET, demonstrating the applicability of the FELA to the HSSC concept. Therewith, we demonstrate that the FELA can be employed to obtain a deeper understanding of the HSSC concept. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
An energy model for the melt of bulk metallic glass (BMG) with clusters was established, the Gibbs free energy and interfacial energy for the Zr-Al-Ni ternary alloy melt with Zr2Ni clusters were calculated, and the effects of the clusters on the Gibbs free energy, interfacial energy and nucleation rate were analyzed. The results showed that the existence of the clusters in the Zr-Al-Ni ternary alloy melt enables the Gibbs free energy to decrease in the composition range where bulk metallic glass forms easily, makes the interfacial energy increase and changes the distribution of the interfacial energy with the alloy composition. Because of the clusters in the melt, the Gibbs free energy of the Zr66Al8Ni26 alloy melt decreases about 0.3-1 kJ/mol and the interfacial energy between the melt and crystal nucleus increases about 0.016 J/m2. The nucleation rate of the undercooled Zr66Al8Ni26 alloy melt decreases evidently under the influence of the clusters on Gibbs free energy and the interfacial energy, and the maximum of the nucleation rate in the melt with the Zr2Ni clusters is only about 107 mol-1·s-1. 相似文献
5.
水和氢气、氧气在同等条件下(一个大气压,温度为25度)互相转变时自由能是相同的;同等条件下水变水蒸气时的汽化潜热和水蒸气变为水时的凝结热是相同的。利用一个刚性的绝热的容器,在海拔零米处电解水,利用氢气和氧气的混合密度小于空气密度的特点,携带一定质量的物体到数千米的高空。点燃混合气体,生成高温水蒸气。通过这个过程分析,将发现两部分能量多出。 相似文献
6.
We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain TT
c
, H0. The analysis is based on numerical data obtained through the Truncated Free Fermion Space Approach. We determine the discontinuities across the Yang–Lee and Langer branch cuts. We confirm the standard analyticity assumptions and propose extended analyticity; roughly speaking, the latter states that the Yang–Lee branching point is the nearest singularity under Langer's branch cut. We support the extended analyticity by evaluating numerically the associated extended dispersion relation. 相似文献
7.
In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density. 相似文献
8.
In the light of φ-mapping method and topological current theory, the effect of disclination lines on the free energy density of nematic liquid crystals is studied. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclination lines. The other is the saddle-splay energy density, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2 when the Jacobian determinant of the director field does not vanish at the singularities of the director field. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e., the disclination strengthes. When the Jacobian determinant vanishes, the generation, annihilation, intersection, splitting and merging processes of the saddle-splay energy density are detailed in the neighborhoods of the limit points and bifurcation points, respectively. It is shown that the disclination line with high topological quantum number is unstable and will evolve to the low topological quantum number states through the splitting process. 相似文献
9.
Giuseppe Albertini 《Journal of statistical physics》1998,90(3-4):853-871
The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative. 相似文献
10.
Gavin E. Crooks 《Journal of statistical physics》1998,90(5-6):1481-1487
An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that the system's dynamics is Markovian and microscopically reversible. 相似文献
11.
The kinetic coefficient, , is the constant of proportionality between the velocity of a solid-liquid interface and the interface undercooling. The value of and its anisotropy are critical parameters in phase field modeling of dendritic solidification. In this paper we review several different molecular dynamics simulation methods which have been proposed to compute the kinetic coefficient. Techniques based on forced velocity simulations, free solidification simulations and fluctuation analyses are discussed and compared. In addition, a model of crystalline growth kinetics due to Broughton, Gilmer and Jackson will be compared with available atomistic simulation data. 相似文献
12.
We show that a precise assessment of free energy estimates in Monte Carlo simulations of lattice models is possible by using cluster variation approximations in conjunction with the local states approximations proposed by Meirovitch. The local states method (LSM) utilizes entropy expressions which recently have been shown to correspond to a converging sequence of upper bounds on the thermodynamic limit entropy density (i.e., entropy per lattice site), whereas the cluster variation method (CVM) supplies formulas that in some cases have been proven to be, and in other cases are believed to be, lower bounds. We have investigated CVM-LSM combinations numerically in Monte Carlo simulations of the two-dimensional Ising model and the two-dimensional five-states ferromagnetic Potts model. Even in the critical region the combination of upper and lower bounds enables an accurate and reliable estimation of the free energy from data of a single run. CVM entropy approximations are therefore useful in Monte Carlo simulation studies and in establishing the reliability of results from local states methods. 相似文献
13.
FAN Hong-Yi TANG Xu-Bing 《理论物理通讯》2006,46(8)
For the first time, we derive the dispersion energy for a molecule which involves the anisotropic dipole interaction by virtue of the invariant eigen-operator method, which greatly simplifies the usual calculation if one uses the Schr(o)dinger equation. 相似文献
14.
David M. Saylor Adam Morawiec Brent L. Adams Gregory S. Rohrer 《Interface Science》2000,8(2-3):131-140
Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the 3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes. 相似文献
15.
Experimental methods for the determination of anisotropy in crystal-melt interfacial energy are explored. Equilibrium shape measurements of liquid droplets entrained in single-phase solid are utilized and results are reported for an Al-Cu and an Al-Si alloy. The grain boundary groove method for determination of interfacial energy anisotropy is also examined. A complete coupled-groove solution is presented for a general tilt-boundary groove. The effects of various physical parameters, including interface energy anisotropy, on the groove shape are discussed. 相似文献
16.
The interfacial free energy of a two-dimensional Ising model is calculated by using various renormalization group schemes. The results obtained are quantitatively consistent with known exact results. In addition, a general discussion of various drawbacks within different renormalization group approximations is given. The best result are obtained with the 4×4 finite cluster approximation, while the Migdal-Kadanoff approximation seems to be inherently unsuitable for calculation of interfacial properties. 相似文献
17.
Sujitkumar Bontapalle Upendra Natarajan 《Journal of Macromolecular Science: Physics》2013,52(7):1282-1302
A molecular model for the free energy of a confined system of diblock copolymer chains within a 2D slit with the interior surfaces having end-tethered chains is presented, based on a combined lattice and scaling theory approach. The thermodynamics of a model system, based on a constrained minimization of free energy, is explored as a function of the intermolecular energy parameters for interaction between the segments of block copolymer chains, end-tethered chains, and the surfaces. The effects of chain length and the block length ratio are investigated over a wide range of values. The results obtained are qualitative in nature; however, the model can be implemented to real systems provided appropriate parameterization of the model parameters to real systems can be performed. The phase diagrams obtained here provide ways for designing thermodynamically stable systems within the physical parametric variable space. 相似文献
18.
At first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable, which is conjugate to an order parameter for the transition. This result is proved at low temperature for lattice models with finite range interaction and two periodic ground-states, under the only condition that they satisfy the Peierls condition.Supported by Fonds National Suisse de la Recherche Scientifique. 相似文献
19.
We study the Raman spectra of Bi4GeO12 crystal at different temperatures, as well as its melt. The structure characters of the single crystal, melt and growth solid-liquid boundary layer of BGO are investigated by their high-temperature Raman spectra for the first time. The rule of structure change of BGO crystal with increasing temperature is analysed. The results show that there exists [GeO4] polyhedral structure and Bi ion independently in BGO melt. The bridge bonds Bi-O-Bi and Bi-O-Ge appear in the crystal and at the boundary layer, but disappear in the melt. The structure of the growth solid-liquid boundary layer is similar to that of BGO crystal. In the melt, the long-range order structure of the crystal disappears. The thickness of the growth solid-liquid boundary layer of BGO crystal is about 50 μm. 相似文献
20.
The dynamics of dislocation-free crystal facets is examined in the context of grain boundary grooves at the junction between two crystallites of a solid and the liquid phase. The geometry and thermal conditions of grain boundary grooves allow a detailed analysis of facet morphology during solidification in terms of the nucleation and spreading rates of elementary crystal planes. Observations on the freezing of water in a two-dimensional cell reveal several dynamical features which are treated by the theory. Additional observations provide indications for the stiffness and premelting of grain boundaries. 相似文献