Solid-Vapor Equilibrium under Conditions of Desolvation of Solid Solutions. Topological Isomorphism with Diagrams of Polymorphic Transformations of Solid Solutions

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Abstract

The article provides a proof of analogues of the three Gibbs-Konovalov laws (Gibbs-Rosebom rules) implemented on solid–vapor phase diagrams in ternary systems under conditions of desolvation of solid solutions in the absence of a liquid phase. The topological isomorphism of the diagrams under consideration with diagrams of polymorphic transformations of solid solutions of binary systems is demonstrated, for which analogues of the Gibbs-Konovalov laws are also obtained. The proof is based on the application of generalized Van der Waals differential equations for phase equilibrium shift, written in the metrics of incomplete and full Gibbs potential of solid phases with variable composition. The applicability of the considered analogues is demonstrated by the examples of a number of model systems. Based on the established patterns for solid solution desolvation diagrams, a method for separation and purification of salt components of solid solutions is proposed.

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N. A. Charykov

East Kazakhstan State Technical University; Saint Petersburg State Technological Institute (Technical University); LETI Electrotechnical University

Author for correspondence.
Email: vvkuznetsov@inbox.ru
Kazakhstan, Ust-Kamenogorsk, 070000; Saint Petersburg, 190013, Russia; Saint Petersburg, 197376, Russia

V. V. Kuznetsov

LETI Electrotechnical University

Email: vvkuznetsov@inbox.ru
Russian Federation, Saint Petersburg, 197376

A. V. Rumyantsev

Saint Petersburg State Technological Institute (Technical University)

Email: vvkuznetsov@inbox.ru
Russian Federation, Saint Petersburg, 190013

V. A. Keskinov

East Kazakhstan State Technical University

Email: vvkuznetsov@inbox.ru
Kazakhstan, Ust-Kamenogorsk, 070000

N. A. Kulenova

East Kazakhstan State Technical University

Email: vvkuznetsov@inbox.ru
Kazakhstan, Ust-Kamenogorsk, 070000

K. N. Semenov

Pavlov Saint Petersburg State University

Email: vvkuznetsov@inbox.ru
Russian Federation, Saint Petersburg, 197022

M. V. Charykova

Saint Petersburg State University

Email: vvkuznetsov@inbox.ru
Russian Federation, Saint Petersburg, 197022

V. P. German

Saint Petersburg State Technological Institute (Technical University)

Email: vvkuznetsov@inbox.ru
Russian Federation, Saint Petersburg, 190013

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2. Fig. 1. Desolvation diagrams of ideal solid solutions on the example of ternary systems PrxNd1 - xCl3 - 6H2O - PrxNd1 - xCl3 - 7H2O - H2O (left) and NixCo1 - xSO4 - 6H2O - NixCo1 - xSO4 - 7H2O - H2O (right) at 25°C. The red colour represents the dependence of the partial pressure of the solvent over saturated liquid solutions (on the solubility diagrams of the corresponding systems).

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3. Fig. 2. Desolvation diagrams of non-ideal (regular) solid solutions on the example of ternary systems NaClxBr1 - x - NaClxBr1 - x - 2H2O - H2O (left) and (C60)x(C70)1 - x - (C60)x(C70)1 - x - 2o-C6H4(CH3)2 - o-C6H4(CH3)2 (right) at 25°C (black lines - calculation of solid solution desolvation diagrams). Red colour represents the dependence of the partial pressure of the solvent over saturated liquid solutions (on the solubility diagrams of the corresponding systems).

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4. Fig. 3. Evolution of solid solution desolvation phase diagrams under the condition that the solvated solid solution is regular and the desolvated solid solution is ideal (black lines - calculation of solid solution desolvation diagrams). W1 is the reduced parameter of the regular solution model.

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5. Fig. 4. Diagrams of polymorphic transformations of solid solutions in the systems (YXEu1 - X)2O3 (left) and (LaXNd1 - X)2O3 (right) (black lines on the equilibria of polymorphic modifications of solid solutions - experimental data of [30-33]).

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6. Fig. 5. Scheme of the processes of salt components separation during solvation-desolvation of solid solutions at increasing-decreasing partial pressure of solvent vapour (blue colour represents compositions of solvated solution, red colour - compositions of desolvated solution (q1 > q2)).

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