Phase Transformations

This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of surfaces and phases of small sizes. Macroscopic and microscopic models are in turn covered with a constant correlation between the two scales. Particular attention has been given to the rigor of mathematical developments.

This fifth volume is devoted to the study of transformations and equilibria between phases. First- and second-order pure phase transformations are presented in detail, just as with the macroscopic and microscopic approaches of phase equilibria.

In the presentation of binary systems, the thermodynamics of azeotropy and demixing are discussed in detail and applied to strictly-regular solutions. Eutectic and peritectic points are examined, as well as the reactions that go with them. The study of ternary systems then introduces the concepts of ternary azeotropes and eutectics.  For each type of solid-liquid system, the interventions of definite compounds with or without congruent melting are taken into account. The particular properties of the different notable points of a diagram are also demonstrated.

Preface xi

Notations and Symbols xv

Chapter 1. Phase Transformations of Pure Substances 1

1.1. Standard state: standard conditions of a transformation 1

1.2. Classification and general properties of phase transformations 2

1.2.1. First-order transformations and the Clapeyron relation  4

1.2.2. Second-order transformations 7

1.3. Liquid–vapor transformations and equilibrium states 16

1.3.1. Method of two equations of state, using the Clapeyron equation  16

1.3.2. Gibbs energy and fugacity method 18

1.3.3. Unique equation of state method  19

1.3.4. The region of the critical point and spinodal decomposition 21

1.3.5. Microscopic modeling  22

1.3.6. Liquid–vapor equilibrium in the presence of an inert gas 26

1.4. Solid–vapor transformations and equilibriums  28

1.4.1. Macroscopic treatment  28

1.4.2. Microscopic treatment  29

1.5. Transformations and solid–liquid equilibria 30

1.5.1. Macroscopic treatment 31

1.5.2. Microscopic treatment 31

1.6. Diagram for the pure substance and properties of the triple point 32

1.7. Allotropic and polymorphic varieties of a solid 35

1.7.1. Enantiotropy 36

1.7.2. Monotropy 39

1.7.3. Transition from enantiotropy to monotropy and vice versa  39

1.8. Mesomorphic states  40

Chapter 2. Properties of Equilibria Between Binary Phases  43

2.1. Classification of equilibria between the phases of binary systems 43

2.2. General properties of two-phase binary systems 45

2.2.1. Equilibrium conditions for two-phase binary systems  45

2.2.2. Conditions of evolution of a two-phase binary system 46

2.3. Graphical representation of two-phase binary systems  47

2.3.1. Gibbs energy graphs 47

2.3.2. Phase diagram in the mono- and bi-phase zones 53

2.3.3. Isobaric cooling curves 63

2.4. Isobaric representation of three-phase binary systems 66

2.4.1. Gibbs energy curve 66

2.4.2. Isobaric phase diagram in tri-phase regions 68

2.4.3. Isobaric cooling curves with tri-phase zones 70

2.5. Isothermal phase diagrams 72

2.6. Composition/composition curves  73

2.7. Activity of the components and consequences of Raoult’s and Henry’s laws 73

Chapter 3. Equilibria Between Binary Condensed Phases 75

3.1. Equilibria between phases of the same nature: liquid–liquid or solid–solid 76

3.1.1. Thermodynamics of demixing 76

3.1.2. Demixing in the case of low reciprocal solubilities 79

3.1.3. Demixing of strictly-regular solutions 81

3.2. Liquid–solid systems 84

3.2.1. Thermodynamics of the equilibria between a liquid phase and a solid phase 86

3.2.2. Isobaric phase diagrams of equilibria between a solid and a liquid  90

3.2.3. Solidus and liquidus in the vicinity of the pure substance 97

3.3. Equilibria between two solids with two polymorphic varieties of the solid  100

3.4. Applications of solid–liquid equilibria 102

3.4.1. Solubility of a solid in a liquid: Schröder–Le Châtelier law 102

3.4.2. Determination of molar mass by cryometry  104

3.5. Membrane equilibria – osmotic pressure 106

3.5.1. Thermodynamics of osmotic pressure 107

3.5.2. Osmotic pressure of infinitely-dilute solutions: the Van ‘t the Hoff law 109

3.5.3. Application of osmotic pressure to the determination of the molar mass of polymers  110

3.5.4. Osmotic pressure of strictly-regular solutions  111

3.5.5. Osmotic pressure and the osmotic coefficient 112

Chapter 4. Equilibria Between Binary Fluid Phases 113

4.1. Thermodynamics of liquid–vapor equilibrium in a binary system 113

4.2. Liquid–vapor equilibrium in perfect solutions far from the critical conditions 117

4.2.1. Partial pressures and total pressure of a perfect solution 118

4.2.2. Isothermal diagram of a perfect solution 119

4.2.3. Isobaric diagram of a perfect solution 120

4.2.4. Phase composition curve  121

4.3. Liquid–gas equilibria in ideal dilute solutions  122

4.4. Diagrams of the liquid–vapor equilibria in real solutions 125

4.4.1. Total miscibility in the liquid phase  125

4.4.2. Partial miscibility in the liquid phase, heteroazeotropes 128

4.5. Thermodynamics of liquid–vapor azeotropy 129

4.5.1. Relation between the pressure of the azeotrope and the activity coefficients of the liquid phase at the azeotropic composition 129

4.5.2. Relation between the activity coefficient and the temperature of the azeotrope 130

4.6. Liquid–vapor equilibria and models of solutions 132

4.6.1. Liquid–vapor equilibria in strictly-regular solutions  132

4.6.2. Liquid–vapor equilibrium in associated solutions  137

4.7. Liquid–vapor equilibria in the critical region 140

4.8. Applications of liquid–vapor equilibria  143

4.8.1. Solubility of a gas in a liquid  143

4.8.2. Determination of molar masses by tonometry  145

4.8.3. Determination of molar masses by ebulliometry  146

4.8.4. Continuous rectification or fractional distillation  149

Chapter 5. Equilibria Between Ternary Fluid Phases  163

5.1. Representation of the composition of ternary systems 163

5.1.1. Symmetrical representation of the Gibbs triangle 163

5.1.2. Dissymmetrical representation of the right triangle 168

5.2. Representation of phase equilibria 169

5.2.1. Isothermal projections 169

5.2.2. Conjugate points and conodes 170

5.2.3. Isopleth sections 171

5.3. Equilibria in liquid phases with miscibility gaps 171

5.3.1. Representation of the miscibility gap 171

5.3.2. Sharing in liquid–liquid systems 173

5.3.3. Application of sharing between two liquids to solvent extraction  177

5.4. Liquid–vapor systems 182

5.4.1. Isothermal and isopleth sections (boiling and dew)  182

5.4.2. Distillation trajectories  184

5.4.3. Systems with two distillation fields  186

5.4.4. Systems with three distillation fields 187

5.5. Examples of applications of ternary diagrams between fluid phases 187

5.5.1. Treatment of argentiferous lead 187

5.5.2. Purity of oil products: aniline point 188

5.5.3. Obtaining concentrated ethyl alcohol 189

Chapter 6. Equilibria Between Condensed Ternary Fluid Phases 191

6.1. Solidification of a ternary system with total miscibility in the liquid state and in the solid state 192

6.2. Solidification of a ternary system with no miscibility and with a ternary eutectic 192

6.2.1. Invariant transformations of a liquid–solid ternary system 193

6.2.2. Representations of the ternary system with no miscibility in the solid state 194

6.2.3. Lowering of the melting point of a binary system by the addition of a component  199

6.2.4. Slope at the ternary eutectic 202

6.3. Ternary systems with partial miscibilities in the solid state and ternary eutectic 204

6.4. Solidification of ternary systems with definite compounds 208

6.4.1. Ternary system with a binary definite compound binary with congruent melting  208

6.4.2. Generalization to the case of a ternary compound and of multiple definite compounds 211

6.4.3. Definite compound with incongruent melting: quasi-peritectic transformation 213

6.5. A peritectic transformation in one binary system and total miscibility in the other two 215

6.6. The ternary peritectic transformation 217

Bibliography 219

Index 221

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