Matrix Representation of Thermodynamic Properties of Multicomponent Systems

1962 ◽  
Vol 37 (6) ◽  
pp. 1192-1199 ◽  
Author(s):  
Robert R. V. Wiederkehr
Keyword(s):  
Thermodynamic Properties ◽  
Matrix Representation ◽  
Multicomponent Systems

scholarly journals Comparative analyses of thermodynamic properties assessments, performed by geometric models: Application to the Ni-Bi-Zn system

2013 ◽  
Vol 49 (3) ◽  
pp. 347-352 ◽  
Author(s):  
V. Gandova ◽  
G. Vassilev
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Thermodynamic Properties ◽  
Wide Temperature Range ◽  
Excess Energy ◽  
Energy Calculation ◽  
Thermochemical Properties ◽  
Multicomponent Systems ◽  
Ternary Interaction ◽  
Geometric Models

The thermochemical properties of metals and alloys are essential for the chemists to invent and improve metallurgical and materials? design processes. However, the properties of multicomponent systems are still scarcely known due to experimental difficulties and the large number of related systems. Thus, the modelling of some thermodynamic properties would be advantageous when experimental data are missing. Considering mentioned facts, geometric models to estimate some thermodynamic properties for the liquid phase of the Ni-Bi-Zn systems. The calculations have been performed in a wide temperature range (1000-2000 K). Ternary interaction parameters for the liquid phase allowing molar Gibbs excess energy calculation have been determined.

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.

The statistical thermodynamics of multicomponent systems

1951 ◽  
Vol 205 (1081) ◽  
pp. 247-269 ◽  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Potential Energy ◽  
Multicomponent Systems ◽  
Reference Species ◽  
Two Phase ◽  
Energy Of Mixing ◽  
Volume Of Mixing ◽  
Two Component Systems ◽  
Free Energy Of Mixing

This paper describes a new statistical approach to the theory of multicomponent systems. A ‘conformal solution’ is defined as one satisfying the following conditions: (i) The mutual potential energy of a molecule of species L r and one of species L s at a distance ρ is given by the expression u rs (ρ) = f rs u 00 ( g rs ρ ), where u 00 is the mutual potential energy of two molecules of some reference species L 0 at a distance ρ , and f rs and g rs are constants depending only on the chemical nature of L r and L s . (ii) If L 0 is taken to be one of the components of the solution, then f rs and g rs are close to unity for every pair of components. (iii) The constant g rs equals ½( g rr + g ss ). From these assumptions it is possible to calculate rigorously the thermodynamic properties of a conformal solution in terms of those of the components and their interaction constants. The non-ideal free energy of mixing is given by the equation ∆* G = E 0 ƩƩ rs x r x s d rs , where E 0 equals RT minus the latent heat of vaporization of L 0 , x r is the mole fraction of L r and d rs denotes 2 f rs — f rr — f ss . This equation resembles that defining a regular solution, with the important difference that E 0 is a measurable function of T and p , which makes it possible to relate the free energy, entropy, heat and volume of mixing to the thermodynamic properties of the reference species; and the predicted relationships between these quantities agree well with available data on non-polar solutions. The theory makes no appeal to a lattice model or any other model of the liquid state, and can therefore be applied both to liquids and to imperfect gases, and to two-phase two-component systems near the critical point.

The Thermodynamic Database for the Development of Modern Lead-Free Solders

2007 ◽  
Vol 263 ◽  
pp. 99-104 ◽  
Author(s):  
A. Kroupa ◽  
J. Vízdal
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Database ◽  
Lead Free ◽  
Multicomponent Systems ◽  
The Creation ◽  
Lead Free Solders

The methods for the modeling of thermodynamic properties of multicomponent systems are described here. The rules for the creation of a consistent database for multicomponent systems are described generally and documented on the Thermodynamic Database for Lead-free Solders developed in the scope of COST 531 Action. The reassessment of the Sb-Sn system is shown as an example, illustrating the application of consistency rules.

Matrix Representation of Thermodynamics of Multicomponent Systems

1962 ◽  
Vol 30 (4) ◽  
pp. 282-284
Author(s):  
Philip Joseph Carroll ◽  
Joseph John Kyame
Keyword(s):  
Matrix Representation ◽  
Multicomponent Systems
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