Thermodynamic Properties of Solid Ar, Kr, and Xe Based Upon a Short-Range Central Force and the Conventional Perturbation Expansion of the Partition Function

1969 ◽  
Vol 184 (3) ◽  
pp. 968-978 ◽  
Author(s):  
M. L. Klein ◽  
G. K. Horton ◽  
J. L. Feldman
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Short Range ◽  
Perturbation Expansion ◽  
Central Force

KINETIC EQUATION FOR A GAS WITH LONG-RANGE ATTRACTION

1967 ◽  
Vol 45 (11) ◽  
pp. 3555-3567 ◽  
Author(s):  
R. A. Elliott ◽  
Luis de Sobrino
Keyword(s):  
Kinetic Equation ◽  
Long Range ◽  
Short Range ◽  
Kinetic Equations ◽  
Perturbation Expansion ◽  
Interparticle Distance ◽  
Range Interaction ◽  
Short Range Repulsion ◽  
Self Consistent Field ◽  
Range Force

A classical gas whose particles interact through a weak long-range attraction and a strong short-range repulsion is studied. The Liouville equation is solved as an infinite-order perturbation expansion. The terms in this series are classified by Prigogine-type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that, provided the range of the short-range force is much less than the average interparticle distance which, in turn, is much less than the range of the long-range force, the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short-range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from the long-range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations, each of which is valid for a definite range of the parameters of the system.

Thermodynamic properties of pure and dilute alkali cyanides: Short-range-order effects

1985 ◽  
Vol 31 (10) ◽  
pp. 6716-6720 ◽  
Author(s):  
Belita Koiller ◽  
Maria A. Davidovich ◽  
Fritz Lüty
Keyword(s):  
Thermodynamic Properties ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Order Effects

Equilibrium Thermodynamic Properties Behind Strong Shocks in Helium

1968 ◽  
Vol 72 (686) ◽  
pp. 155-159
Author(s):  
M. Lalor ◽  
H. Daneshyar
Keyword(s):  
Mach Number ◽  
Partition Function ◽  
Shock Waves ◽  
Thermodynamic Properties ◽  
Strong Shock ◽  
Equilibrium Thermodynamic ◽  
Ionized Gas ◽  
Number Range ◽  
Shock Mach Number ◽  
Strong Shock Waves

Summary Tables of equilibrium thermodynamic properties of the ionized gas formed behind strong shock waves in Helium are presented, in the Mach number range 10 to 30, for initial pressures of 0-1, 0-5, 1, 5, 10, 50, 100 torr. The effect of the inclusion of the full partition function series is demonstrated in the Mach number range 20 to 30. A numerical solution has been developed such that the only experimental quantities required for its use are the shock Mach number and the pre-shock conditions.

scholarly journals Discriminative interactions between chiral molecules: internal discrimination in 1,2-difluorohydrazine

1985 ◽  
Vol 63 (7) ◽  
pp. 1639-1641 ◽  
Author(s):  
Rudolf Zahradník ◽  
Bohdan Schneider ◽  
Pavel Hobza ◽  
Zdenêk Havlas ◽  
Hanspeter Huber
Keyword(s):  
Thermodynamic Properties ◽  
Quantum Chemical ◽  
Short Range ◽  
Energy Surface ◽  
Saddle Points ◽  
Ideal Gas ◽  
Chiral Molecules ◽  
Standard State ◽  
Transition Complex ◽  
Stable Structures

1,2-Difluorohydrazine represents a model for studying short-range discriminative interactions between two chiral radicals. Possible diastereomeric structures of the system were theoretically investigated by means of nonempirical SCF quantum chemical calculations. Four minima and six saddle points separating them were found on the potential energy surface. All the stable structures and one transition complex were completely optimized. Thermodynamic properties for the equilibrium between the two most stable conformers (meso and chiral) of difluorohydrazine are as follows (in kJ/mol): [Formula: see text], [Formula: see text] (standard state: ideal gas at 101.325 kPa, 298 K).

Studies in jj -coupling - II. Fractional parentage coefficients and the central force energy matrix for equivalent particles

1952 ◽  
Vol 214 (1119) ◽  
pp. 515-530 ◽  
Keyword(s):  
Invariant Theory ◽  
Short Range ◽  
Wave Functions ◽  
Central Force ◽  
Symplectic Groups ◽  
Energy Matrix ◽  
Linear Combinations ◽  
Special Transformation ◽  
Fractional Parentage

Jahn’s method of fractional parentage coefficients is adapted to obtain fully antisymmetric wave functions for the configurations j n of neutrons and protons, where j = 3/2, 5/2, 7/2, and n = 3 and 4. Invariant theory is used to obtain linear combinations of Slater integrals which have special transformation properties with respect to the unitary and symplectic groups. In this way it is shown how the ordering of levels in jj -coupling with short-range central inter­actions is determined by the eigenvalues of Casimir’s operator.

Matrix Description of Some Thermodynamic Properties of Multicomponent Alloys in Explicit Form

2007 ◽  
Vol 268 ◽  
pp. 51-58
Author(s):  
L.I. Erokhin
Keyword(s):  
Thermodynamic Properties ◽  
Explicit Form ◽  
Short Range ◽  
Binary Systems ◽  
Chemical Potential ◽  
Diffusion Processes ◽  
Diffusion Theory ◽  
Multicomponent Systems ◽  
Multicomponent Alloys ◽  
Practical Applications

A matrix method for description of some thermodynamic properties in multicomponent alloys in explicit form has been proposed. It has been found that the method for determining thermodynamic properties from the cross-section data allows to find the contribution of short-range ordering into the thermodynamic state of an imperfect alloy. Diffusion processes in alloys are formed both from purely kinetic migrations of particles and from the system's thermodynamic properties. A consequence of this fact is that the diffusion coefficients D in all systems except for perfect solid solutions include to factors being D = Lg , the second one is the thermodynamic factor directly related to the system's chemical potential. However direct experimental separation of these factors can easily be performed in binary systems only while in triple systems in is highly difficult let alone multicomponent systems. Experimental evaluation of the factors in multicomponent systems from short-range order's parameters [1] would allow to establish a relation between the system's thermodynamic properties which is highly important for further progress in multicomponent diffusion theory and for practical applications.

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