The Representation of Thermodynamic Properties in Multicomponent Alloys

1982 ◽  
Vol 19 ◽  
Author(s):  
I. Ansara
Keyword(s):  
Thermodynamic Properties ◽  
Binary Systems ◽  
Theoretical Models ◽  
Higher Order ◽  
Interaction Parameters ◽  
Experimental Measurements ◽  
Multicomponent Systems ◽  
Multicomponent Alloys ◽  
Summation Methods ◽  
Different Types

ABSTRACTIn addition to theoretical models which have been developped to interpret the interactions in metallic systems, polynomials of different types have been used to represent the thermodynamic properties of solution phases. Ternary and higher order systems have been described by adding the properties of the limiting binary systems, using various summation methods ; interaction parameters specific to the multicomponent systems can be derived from sufficiently precise experimental measurements.

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.

Numerical Prediction of the Thermodynamic Properties of Ternary Al-Ni-Pd Alloys

2016 ◽  
Vol 35 (1) ◽  
pp. 37-45
Author(s):  
Maryana Zagula-Yavorska ◽  
Jolanta Romanowska ◽  
Sławomir Kotowski ◽  
Jan Sieniawski
Keyword(s):  
Thermodynamic Properties ◽  
Ternary System ◽  
Boundary Conditions ◽  
Mole Fraction ◽  
Thermodynamic Functions ◽  
Binary Systems ◽  
Interaction Parameters ◽  
Ternary Interaction ◽  
The Third ◽  
Gibbs Triangle

AbstractThermodynamic properties of ternary Al-Ni-Pd system, such as exGAlNPd, µAl(AlNiPd),µNi(AlNiPd) and µPd(AlNiPd) at 1,373 K, were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting exGAlNiPd values was regarded as calculation of values of the exG function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of exG on all legs of the triangle are known (exGAlNi, exGAlPd, exGNiPd). This approach is contrary to finding a function value outside a certain area, if the function value inside this area is known. exG and LAl,Ni,Pd ternary interaction parameters in the Muggianu extension of the Redlich–Kister formalism were calculated numerically using the Excel program and Solver. The accepted values of the third component xx differed from 0.01 to 0.1 mole fraction. Values of LAlNiPd parameters in the Redlich–Kister formula are different for different xx values, but values of thermodynamic functions: exGAlNiPd, µAl(AlNiPd), µNi(AlNiPd) and µPd(AlNiPd) do not differ significantly for different xx values. The choice of xx value does not influence the accuracy of calculations.

Vapour-Liquid Equilibria and Excess Thermodynamic Properties in Binary Systems of Cyclopentanone + Chloroalkanes in View of the Disquac and Unifac Group Contribution Models Extention

2008 ◽  
Vol 59 (5) ◽  
Author(s):  
Alexandru Birhala ◽  
Dana Dragoescu ◽  
Mariana Teodorescu
Keyword(s):  
Binary Systems ◽  
Excess Enthalpy ◽  
Group Contribution ◽  
Excess Properties ◽  
Structural Effects ◽  
Liquid Equilibrium ◽  
Excess Thermodynamic Properties ◽  
Different Types ◽  
Thermodynamic Excess Properties ◽  
Thermodynamic Excess

The data available in the literature and our recent data on vapour�liquid equilibrium (VLE), excess Gibbs energy, GE, and excess enthalpy, HE, for the homologous series of cyclopentanone + chloroalkane mixtures are examined in terms of the predictive group contribution models DISQUAC and UNIFAC. In our treatment, we present also how the structural effects and different types of molecular interactions are reflected by the thermodynamic excess properties of the mentioned series mixtures.

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Higher Order Language: Risk, Promotive, and Risk-Based Protective Associations with Youth Offending

2021 ◽  
pp. 001112872110077
Author(s):  
Stavroola A. S. Anderson ◽  
David J. Hawes ◽  
Pamela C. Snow
Keyword(s):  
Oral Language ◽  
Figurative Language ◽  
Protective Factor ◽  
Language Skills ◽  
Theoretical Models ◽  
Higher Order ◽  
Protective Effects ◽  
Youth Offenders ◽  
Order Language ◽  
Nonverbal Skills

Research has implicated oral language deficits as risk factors for antisocial behavior. The aim of this study was to investigate the relationship between higher order language skills and youth offending through a risk, promotive and risk-based protective factor paradigm. In a sample of adolescent males ( n = 130; 13 to 20 years; 62% youth offenders) skills in understanding ambiguity, making inferences, and understanding figurative language were demonstrated to have risk and promotive effects in association with youth offending. Figurative language also met criteria for having risk-based protective effects for youth at high offending risk due to poor nonverbal skills. Conceptualization of higher order language skills through this paradigm promotes a broader frame of reference for considering theoretical models and practical interventions.

Viscosity of the binary systems 2-methyl-2-propanol with n-alkanes at T=(303.15, 308.15, 313.15, 318.15 and 323.15)K: Prediction and correlation – New UNIFAC–VISCO interaction parameters

2010 ◽  
Vol 299 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Emila M. Živković ◽  
Mirjana Lj. Kijevčanin ◽  
Ivona R. Radović ◽  
Slobodan P. Šerbanović ◽  
Bojan D. Djordjević
Keyword(s):  
Binary Systems ◽  
Interaction Parameters
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