Improvement of the Bethe–Peierls approximation to lattice gases

1985 ◽  
Vol 63 (9) ◽  
pp. 1258-1263
Author(s):  
Hiromu Asada
Keyword(s):  
Critical Temperature ◽  
Thermodynamic Properties ◽  
Triangular Lattice ◽  
Lattice Gases ◽  
Nearest Neighbour ◽  
Improved Method ◽  
Self Consistent

The Bethe–Peierls approximation to lattice gases is improved by introducing new self-consistent parameters relating to positional correlation between atoms. The improved method is applied to the triangular lattice with first nearest neighbour attractive interactions. Calculated critical temperature and critical thermodynamic properties show better agreement with the exact ones than those in the normal Bethe–Peierls approximation.

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

Thermodynamic properties of charged ideal spin-1 bosons in a trap under a magnetic field

2014 ◽  
Vol 28 (26) ◽  
pp. 1450206 ◽  
Author(s):  
Yushan Li
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
External Magnetic Field ◽  
Thermodynamic Properties ◽  
Bose Gases ◽  
Spin Factor ◽  
Classical Approximation ◽  
Spinless Case

Thermodynamics of trapped charged ideal spin-1 bosons confined in a magnetic field are investigated within semi-classical approximation and truncated-summation approach. It is shown that the critical temperature increases slightly at the first, and then decreases slowly with increasing external magnetic field. Charged spin-1 Bose gases present a crossover from diamagnetism to paramagnetism as the spin factor increases. Charged spin-1 Bose gases exhibit distinct thermodynamic behaviors from the spinless case.

Thermodynamic Properties of Pure and Mixed Thermal Plasmas Over a Wide Range of Temperature and Pressure

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Omid Askari
Keyword(s):  
Thermodynamic Properties ◽  
Specific Heat ◽  
Fluid Dynamic ◽  
Thermal Plasmas ◽  
Statistical Thermodynamic ◽  
Reference Source ◽  
Degree Of Ionization ◽  
Wide Range ◽  
Self Consistent ◽  
Temperature And Pressure

Chemical composition and thermodynamics properties of different thermal plasmas are calculated in a wide range of temperatures (300–100,000 K) and pressures (10−6–100 atm). The calculation is performed in dissociation and ionization temperature ranges using statistical thermodynamic modeling. The thermodynamic properties considered in this study are enthalpy, entropy, Gibbs free energy, specific heat at constant pressure, specific heat ratio, speed of sound, mean molar mass, and degree of ionization. The calculations have been done for seven pure plasmas such as hydrogen, helium, carbon, nitrogen, oxygen, neon, and argon. In this study, the Debye–Huckel cutoff criterion in conjunction with the Griem’s self-consistent model is applied for terminating the electronic partition function series and to calculate the reduction of the ionization potential. The Rydberg and Ritz extrapolation laws have been used for energy levels which are not observed in tabulated data. Two different methods called complete chemical equilibrium and progressive methods are presented to find the composition of available species. The calculated pure plasma properties are then presented as functions of temperature and pressure, in terms of a new set of thermodynamically self-consistent correlations for efficient use in computational fluid dynamic (CFD) simulations. The results have been shown excellent agreement with literature. The results from pure plasmas as a reliable reference source in conjunction with an alternative method are then used to calculate the thermodynamic properties of any arbitrary plasma mixtures (mixed plasmas) having elemental atoms of H, He, C, N, O, Ne, and Ar in their chemical structure.

Thermodynamic Properties of Antiferromagnetic QuantumXY-Model on the Triangular Lattice

1993 ◽  
Vol 62 (3) ◽  
pp. 880-887 ◽  
Author(s):  
Shigeo Homma ◽  
Hirotsugu Matsuda ◽  
Naofumi Ogita ◽  
Kazuhiro Sano
Keyword(s):  
Thermodynamic Properties ◽  
Triangular Lattice

Thermodynamic Calculation of Phase Equilibria in the Mn-RE (RE=Nd, Gd, Dy) Binary Systems

2017 ◽  
Vol 898 ◽  
pp. 1036-1041
Author(s):  
M.H. Rong ◽  
S.D. Lin ◽  
Jiang Wang ◽  
H.Y. Zhou ◽  
G.H. Rao
Keyword(s):  
Magnetic Properties ◽  
Thermodynamic Properties ◽  
Phase Equilibria ◽  
Thermodynamic Calculation ◽  
Binary Systems ◽  
Ternary Systems ◽  
Experimental Information ◽  
Calphad Method ◽  
Self Consistent ◽  
Ternary Intermetallic Compounds

Ternary intermetallic compounds with rare earth elements and transition metals in the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems show interesting magnetic properties. As key sub-binary systems of the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems, the information of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems are indispensable to explore the RE-Mn-X (X=Si, Ge, Sn etc.) alloys with better magnetic properties. In this work, the experimental data of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems in the published literature were reviewed. Based on the available experimental information, thermodynamic calculation of phase equilibria of the Mn-RE (RE=Nd, Gd, Dy) binary systems was performed using the CALPHAD method. As a result, further experimental investigation and thermodynamic optimization would be still necessary in order to develop the self-consistent and compatible thermodynamic database of the RE-Mn-based alloy systems.

Calculation of Excess Stability Functions of Four Binary Alloys

2021 ◽  
Vol 14 (3) ◽  
pp. 193-200
Keyword(s):  
Thermodynamic Properties ◽  
Concentration Fluctuation ◽  
Ideal Solution ◽  
Nearest Neighbour ◽  
Stability Function ◽  
Stability Functions ◽  
Atomic Correlation ◽  
Neighbour Shell ◽  
The Ideal ◽  
Excess Stability

Abstract: The thermodynamic model based on cluster of two atoms is considered with the view to obtaining Scc(0) and the excess stability function of Scc(0). Concentration-concentration fluctuation; Scc(0) of four binary molten alloys was calculated. The thermodynamic properties of these alloys are evaluated based on cluster of two atoms (A & B) or (B & A). Each system has the view of obtaining concentration-concentration fluctuation; Scc(0) enumerating the low-order atomic correlation in the nearest neighbour shell of liquid binary alloys.The highlights of excess stability functions(ES) of Scc(0) of these alloys were reported. The values of Scc(0) for all these alloys are higher than the ideal solution values. The values of Scc(0) for Bi-Cd alloy is close to the ideal Scc (0). The indication of the excess stability of Scc(0) for some alloys is in support of homocoordination. The Scc(0) and excess stability function of Scc (0) for the four alloys are presented. Keywords: Concentration-concentration fluctuation, Excess stability function, Ordering energy.

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