Gibbs' rational reconstruction of thermodynamics according to the heuristic tradition of Descartes' analytical method

Lucena, Jojomar; Laranjeiras, Cássio C.; Chiappin, José Raymundo Novaes

doi:10.1590/1806-9126-rbef-2018-0012

Cited by 2 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is confirmed by practically linear graphs of Ф Fe Al 2 5 with correlation coefficients close to 1; these correlation coefficients were obtained during recalculation of compositions of melts for possible presence of mentioned groups (Fig. 3) [24][25][26][27].…”

Section: Obtained Results and Their Analysismentioning

confidence: 66%

Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system

Tolokonnikova¹,

Baisanov²,

Narikbayeva³

et al. 2022

cisisr

View full text Add to dashboard Cite

A theoretically justified method of mathematical description of phase equilibrium lines based on the regularity of the behavior of components along the phase crystallization line has been developed. When analyzing the state diagrams of various systems, a regularity was found in the formation of crystallization fields of phases in the form of a correlation dependence between the osmotic coefficient of the crystallizing component and the ratio of its activity in the liquid and solid phases. The Bjerrum-Guggenheim osmotic coefficient can serve as a measure of the deviation of the energy properties of a real system from the ideal one described by the Schroeder-Le Chatelier equation. Two types of generalized mathematical expression in the form of a modified Schroeder-Le Chatelier equation are proposed for the analytical description of the liquidus and solidus lines of state diagrams of a whole class of systems. These types make it possible to calculate the dependence between the composition and the temperature. Mathematical expressions describing the lines of monovariant phase equilibria are presented on a single analytical basis. Mathematical expressions represent the liquidus and solidus lines of the Fe-Al system for the corresponding elements and compounds using the Schroeder-Le Chatelier equation and the Bjerrum-Guggenheim coefficient (Ф i ). The linear nature of the change in the osmotic coefficient of crystallizing phases (Ф i ) on the ratio of the activity of the components in the ideal liquid and solid phases under the boundary conditions of the formation of crystallization fields of the phases was revealed. The type of change in the Bjerrum-Guggenheim osmotic coefficient depends on the intermolecular interaction of the components in the melt. If only van der Waals forces of interaction between the structural units of the considered component with the second prevail, then a linear relationship is observed. When the formation of various groups from the initial components or the dissociation of a chemical compound takes place in the melt, the osmotic coefficient has a curved dependence.

show abstract

Section: Obtained Results and Their Analysismentioning

confidence: 66%

Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system

Tolokonnikova¹,

Baisanov²,

Narikbayeva³

et al. 2022

cisisr

View full text Add to dashboard Cite

show abstract

“…As soon as the graph is curvilinear, the value of the osmotic coefficient was calculated vie the least squares method for curvilinear relationship. The initial data were processed and the values of osmotic coefficient were obtained in the form of expression (5) [24][25][26]: The obtained results on convergence of the calculated and experimental data are displayed in the Table 6.…”

Section: Research and Resultsmentioning

confidence: 99%

Mathematical description of the lines of monovariant phase equilibria on the MnO-SiO2 phase equilibrium diagram

Tolokonnikova,

Baisanov,

Saulebek

et al. 2023

cisisr

View full text Add to dashboard Cite

When analyzing a number of phase equilibrium diagrams of various types of systems, the regular relationship was found during the formation of phase crystallization fields in the form of a correlation dependence of the osmotic coefficient of a crystallizing component on the ratio of its activity in the liquid and solid phases. The Bjerrum-Guggenheim osmotic coefficient serves as a measure of the deviation of the energy properties of a real system from the ideal one described by the Schroeder-Le Chatelier equation. Mathematical expressions for the liquidus and solidus lines are obtained in the form of semi-empirical dependences on a single analytical basis, which make it possible to calculate the temperature dependence of the composition. Thus, a theoretically substantiated method for the mathematical description of the lines of monovariant phase equilibria has been developed, based on the regularities of the behavior of components in the melt. Mathematical expressions represent the crystallization fields of the phases of the MnO-SiO 2 system for the corresponding components and compounds using the Schroeder-Le Chatelier equation and the correlation dependence of the osmotic coefficient Ф', experimental and calculated data of the Bjerrum-Guggenheim osmotic coefficient (Ф i ) are calculated. The type of variation in the Bjerrum-Guggenheim osmotic coefficient depends on the intermolecular interaction of the components in the melt. If only van der Waals forces of interaction between the components in the melt prevail, then a correlation dependence is observed. When groups from the initial compounds are formed in the melt, or processes of dissociation or, conversely, association occur, the osmotic coefficient is described by a curvilinear dependence. The paper presents mathematical expressions for the fields of crystallization of phases of the MnO-SiO 2 system in the form of semi-empirical dependencies. The nature of the change in the Bjerrum-Guggenheim osmotic coefficient of the crystallizing component depending on the ratio of its activity in the liquid and solid phases is shown.

show abstract

Gibbs' rational reconstruction of thermodynamics according to the heuristic tradition of Descartes' analytical method

Cited by 2 publications

References 9 publications

Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system

Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system

Mathematical description of the lines of monovariant phase equilibria on the MnO-SiO2 phase equilibrium diagram

Contact Info

Product

Resources

About