Solute interactions in multicomponent solutions

Schuhmann, R.

doi:10.1007/bf02667517

Cited by 24 publications

(19 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If only data for very dilute solutions are available, then Eqs. [19] and [20] are more likely to provide a good extrapolation to higher solute concentrations, although, of course, there will be exceptions.…”

Section: A First-order Formalism-binary Systemsmentioning

confidence: 88%

“…If the following substitutions are made in the binary quadratic formalism: [19] and [20] are thus a modified interaction parameter formalism that is identical to the quadratic formalism and reduces to the Wagner formalism at infinite dilution, but that is consistent with the Gibbs-Duhem Eq.…”

Section: A First-order Formalism-binary Systemsmentioning

confidence: 90%

“…[21] and [22] as there is for Eqs. [19] and [20], which are identical to the quadratic formalism. If only data for very dilute solutions are available, then Eqs.…”

Section: A First-order Formalism-binary Systemsmentioning

confidence: 95%

“…It can be seen that Equations [19] and [20] with ε FeFe ϭ 2.7 provide a very good representation of both ln ␥ Fe and ln ␥ Ni for solute concentrations up to X Fe ϭ 0. 5 Hajra et al [7] propose the use of Eqs.…”

Section: A First-order Formalism-binary Systemsmentioning

confidence: 95%

“…[21] and [22] than by Eqs. [19] and [20] (although neither set of equations is satisfactory; a second-order parameter is required). Based upon this one example, Hajra et al concluded that Eqs.…”

Section: B First-order Formalism-ternary Systemsmentioning

confidence: 98%

See 4 more Smart Citations

The polynomial representation of thermodynamic properties in dilute solutions

Pelton

1997

Metall Mater Trans B

View full text Add to dashboard Cite

Attempts to extend the interaction parameter formalism to higher-order polynomials and to render it thermodynamically consistent at finite solute concentrations have resulted in much confusion. The literature is reviewed with a view to clarifying the issues. The problem is best and most simply resolved through extension of the quadratic formalism, which has a sound theoretical foundation. A new and general set of equations for estimating higher-order parameters from binary parameters is derived. The applicability of using molar ratios rather than mole fractions in the polynomial expansions is discussed. The formation of associate species (such as the formation of ''AlO'' associates in molten Fe) is treated. In such cases of strong solute-solute interactions, the usual practice of expressing the interaction parameters as linear functions of (1/T ) is invalid. Finally, for more concentrated solutions, the advantage of using the Kohler or Toop interpolation models rather than the commonly used Muggianu model is shown.

show abstract

Section: A First-order Formalism-binary Systemsmentioning

confidence: 88%

Section: A First-order Formalism-binary Systemsmentioning

confidence: 90%

“…[21] and [22] as there is for Eqs. [19] and [20], which are identical to the quadratic formalism. If only data for very dilute solutions are available, then Eqs.…”

Section: A First-order Formalism-binary Systemsmentioning

confidence: 95%

Section: A First-order Formalism-binary Systemsmentioning

confidence: 95%

Section: B First-order Formalism-ternary Systemsmentioning

confidence: 98%

See 3 more Smart Citations

The polynomial representation of thermodynamic properties in dilute solutions

Pelton

1997

Metall Mater Trans B

View full text Add to dashboard Cite

show abstract

Representation of thermodynamic properties of multi‐component systems using interaction parameters

Hajra

Frohberg

1989

Steel Research

View full text Add to dashboard Cite

Integral excess free energy of a multi‐component – ternary system has been expressed in terms of the Maclaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction parameters. The partial thermodynamic property of component 1 derived by the use of logarithmic functions together with a geometric progression is presented. The equation is found to be capable of interpreting thermodynamic data over a wide compositional range of the ternary system and is independent of compositional paths. An alternative approach for the determination of generalised relations between interaction parameters to that of Lupis and Elliott has been developed.

show abstract

Representation of thermodynamic properties of quaternary systems using interaction parameters

1997

View full text Add to dashboard Cite

Integral excess free energy of a quaternary system has been expressed in terms of the MacLaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction coefficients. The derivation of the partial functions involves extensive summation of various infinite series pertaining to the first order and quaternary parameters to remove any truncational error. The thermodynamic consistency of the derived partials has been established based on the Gibbs‐Duhem relations. The equations are used to interpret the thermodynamic properties of the Fe‐Cr‐Ni‐N system.

show abstract

Solute interactions in multicomponent solutions

Cited by 24 publications

References 6 publications

The polynomial representation of thermodynamic properties in dilute solutions

The polynomial representation of thermodynamic properties in dilute solutions

Representation of thermodynamic properties of multi‐component systems using interaction parameters

Representation of thermodynamic properties of quaternary systems using interaction parameters

Contact Info

Product

Resources

About