A new graph expansion of virial coefficients

It is well known that the virial coefficients of the pressure of thermodynamic systems can be represented in terms of graphs. The existing graph expansions are compared with a new one, the overlap graph expansion. The merits of overlap graphs in general and especially for hard disks and spheres are discussed.     

Exact calculation of one-dimensional irreducible integrals

One-dimensional irreducible integrals (_k) are computed in the form of Mayerf-function polynomials for a general interparticle potential. Obeisance to the exact specification of the irreducible integral definition produces regularities in the interaction of star graphs with the integration process. Tables of _k fork 5 and test solutions are presented.     

Convergence of spherical harmonic expansions for the evaluation of hard-sphere cluster integrals

ForN particles (N>2), by means of a spherical harmonic expansion of Silverstone and Moats, a 3N-dimensional cluster may be reduced to 2N+1 trivial integrals andN–1 interesting integrals. For hard spheres, theN–1 interesting integrals are products of polynomials integrated between binomial bounds. With simple clusters, closed forms are obtained; for more complex clusters, infinite series inl (ofY _lm ) appear. It is here shown for representative cases that these series converge exponentially rapidly, the leading pair of terms accounting for all but a few tenths of a percent of the total cluster integral.     

On the Evaluation of Two-Center Overlap Integrals over Integer and Noninteger -Center Overlap Integrals over Integer and Noninteger n-Slater-Type Orbitals

In this study, two-center overlap integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers in unaligned coordinate systems have been calculated using formulas for overlap integrals in aligned coordinate systems obtained by the author's previous work (T. Ozdogan and M. Orbay, Int. J. Quant. Chem. 87(2002) 15). The obtained results for integer case have been found to be in excellent agreement with the prior literature.On the other hand, to the best of authors knowledge, because of the scarcity of the literatures on the use of noninteger n-STOs in unaligned coordinate systems, the results for noninteger case have been tested with the limit of integer case,and good agreement has been obtained too.     

On the Evaluation of Two-Center Overlap Integrals over Integer and Noninteger n-Slater-Type Orbitals

In this study, two-center overlap integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers in unaligned coordinate systems have been calculated using formulas for overlap integrals in aligned coordinate systems obtained by the author's previous work (T. Özdogan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The obtained results for integer case have been found to be in excellent agreement with the prior literature. On the other hand, to the best of authors knowledge, because of the scarcity of the literatures on the use of noninteger n-STOs in unaligned coordinate systems, the results for noninteger case have been tested with the limit of integer case, and good agreement has been obtained too.     

Explicit and implicit finiteness corrections of virial coefficients

The equation of state of finite systems deviates from thermodynamic limit. The corresponding finiteness corrections of virial coefficients are studied. Most calculations are based on the canonical ensemble with periodic boundary conditions.Explicit andimplicit finiteness corrections occur. They are displayed up to the eighth virial coefficient. These results are applied to hard spheres in one, two, and three dimensions.     

On the computation of molecular auxiliary functions A n and B n

Molecular auxiliary functions A _n (p) and B _n (pt), arising in the Hartree-Fock-Roothaan (HFR) approximation for molecules, Ewald’s crystal lattice theory, electromagnetic stopping theory, and other approximate methods, are evaluated and analysed in the range of 17≤n≤60 and 25≤pt≤60.     

On the absence of intermediate phases in the two-dimensional Coulomb gas

For a simple, continuum two-dimensional Coulomb gas (with soft cutoff), Gallavotti and Nicoló [J. Stat. Phys. 38:133–156 (1985)] have proved the existence of finite coefficients in the Mayer activity expansion up to order 2n below a series of temperature thresholdsT _n =T [1+(2n–1)^–1] (n=1, 2,...). With this in mind they conjectured that an infinite sequence of intermediate, multipole phases appears between the exponentially screened plasma phase aboveT ₁ and the full, unscreened Kosterilitz-Thouless phase belowT T _KT. We demonstrate that Debye-Hückel-Bjerrum theory, as recently investigated ford=2 dimensions, provides a natural and quite probably correct explanation of the pattern of finite Mayer coefficients while indicating the totalabsence of any intermediate phases at nonzero density ; only the KT phase extends to >0.     

On the Calculation of Two-Center Overlap Integrals with STO's Using Zeta-Function Method and Multipole Moments

One electron two-center overlap integrals are re-derived using Barnett's -function method and Guseinov electric-multipole-moments translation technique. To evaluate these integrals a computer program has been constructed. The obtained results are in good agreement with literature.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

Thermodynamic stability of solid and fluid phases in the Si3B3N7 system

We investigate the thermodynamic properties of the ceramic material Si₃B₃N₇ which has so far only been synthesized as an amorphous compound. Using Monte Carlo simulations, we investigate the stability of both solid and fluid phases of Si₃B₃N₇, in order to gain insights into the proper synthetic conditions needed to generate the stable amorphous and crystalline phases of this compound. We study the ternary liquid–gas region of the phase diagram at temperatures above the theoretical glass transition in this system, and construct an approximate ‘metastable’ phase diagram of Si₃B₃N₇. In addition we study the stability of the amorphous and crystalline phases in the solid state against the decomposition into the binary phases h-BN and β-Si₃N₄ as a function of the size of the crystallites involved, and the stability of the melt against evolution of nitrogen as a function of nitrogen pressure.     

Nonlinear optical properties of (B3O7)5- and (B3O6)3- groups

3 O₅ (LBO) crystal has been studied by using the bond valence theory of complex crystals. Chemical bond parameters and linear and nonlinear optical (NLO) properties of each type of constituent chemical bonds are quantitatively determined. Because of the different crystal structure characteristics of LBO from those of β-BaB₂O₄ (BBO), the two anionic groups, (B₃O₇)^5- in LBO and (B₃O₆)^3- in BBO, play different roles in contributions to their own total NLO tensor coefficients of LBO and BBO, respectively. By comparison, we find that planar (B₃O₆)^3- groups are the ideal structure model, leading to little cancellation of contributions of each kind of bond in these groups, and this gives us a useful guide to design new NLO materials in the future. Received: 24 January 1997/Accepted: 27 March 1997     

光学晶体CsLiB6O10与K2Al2B2O7混频性能研究

基于非线性光学晶体的混频理论，利用CsLiB6O10（CLBO）晶体和K2Al2B2O7（KABO）晶体获得了紫外相干光源，详细比较了两种晶体在Ⅰ类相位匹配下的混频性能，包括混频相位匹配角、有效非线性系数、光波走离角、允许角和允许波长等参量．结果表明，KABO晶体比CLBO晶体的有效非线性系数小，其它性能均与CLBO晶体接近．这对于两种晶体用于产生紫外激光的实验研究提供了重要的理论依据．考虑到KABO晶体较好的物化性质以及不潮解这一显著特征，KABO晶体可能是最有希望实现实用化的紫外混频晶体．     

Soft magnetic properties of amorphous Fe52Co34Hf7B6Cu1 alloy treated by pulsed magnetic field and annealing

<正>The crystallization,microstructure,and soft magnetic properties of Fe₅₂Co₃₄Hf₇B₆Cu₁ alloy are studied.Amorphous Fe₅₂Co₃₄Hf₇B₆Cu₁ alloys are first treated by a pulsed magnetic field with a medium frequency,and then annealed at 100℃-400℃for 30 min in a vacuum.The rise in temperature during the treatment by a pulsed magnetic field is measured by a non-contact infrared thermometer.The soft magnetic properties of specimens are measured by a vibrating sample magnetometer（VSM）.The microstructure changes of specimens are observed by a Mossbauer spectroscopy and transmission electron microscope（TEM）.The results show the medium-frequency pulsating magnetic field will promote nanocrystallization of the amorphous alloy with a lower temperature rise.The nanocrystalline phase isα-Fe（Co） with bcc crystal structure,and the grain size is about 10 nm.After vacuum annealing at 100℃for 30 min,scattering nanocrystalline phases become more uniform,the coercive force and the saturation magnetization of the specimens are 41.98 A/m and 185.15 emu/g.