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Part One The Phase Rule,Its Deduction and Application 3

Chapter 1 The Phase Rule,Its Deduction and Application 3

1.1 Why do We Discuss the Phase Rule at First 3

1.2 Different Methods for Deducing the Phase Rule:The Method of Gibbs Himself,Gibbs-Roozeboom's Method and the Method of Gibbs Free Energy Minimization 4

1.3 Determination of the Number of Independent Components by Brink-ley's Method 14

1.4 Some Remarks on the Application of the Phase Rule 25

References-1 28

Summary of Part One 28

Part Two The Boundary Theory of Isobaric Phase Diagrams and Its Application 31

Chapter 2 The Boundary Theory of Isobaric Phase Diagrams—Rules for Phase Diagram Construction 31

2.1 Introduction 31

2.2 Several Basic Concepts for Underlying the Phase Diagram 32

2.3 The Theorem of the Corresponding Relationship between the Total Nu-mber of All the Different Phases in NPRs Ф and the Dimensions of the Phase Boundary R1 in Phase Diagrams,and Its Theoretical Deduction 38

2.4 The Theorem of the Corresponding Relationship(TCR)is an Indepen-dent Theorem,Not a Variant of the Phase Rule 41

2.5 Corollaries of TCR for Isobaric Phase Diagrams 44

2.6 The Relationship between the Dimensions of the Phase Boundary R1 and the Dimensions of the Boundary Rí for Isobaric Multiconponent Phase Diagrams 48

2.7 The Summary of the Boundary Theory of Isobaric Phase Diagrams 4858

References-2 59

Chapter 3 Application of the Boundary Theory to Unary,Binary and Ternary Phase Diagrams 61

Comparison of the Boundary Theory Application and Palatnik-Landau's Contact Rule of Phase Regions 61

3.1 Determination of Phase Assemblages of NPRs and the Characteristics of Their Boundaries by the Boundary Theory 61

3.2 Application of the Boundary Theory to Unary Phase Diagrams 63

3.3 Application of the Boundary Theory to Binary Phase Diagrams 64

3.4 Application of the Boundary Theory to Ternary Phase Diagrams 68

3.5 Explanation of Rhines'Ten Empirical Rules for Constructing Complicated Ternary Phase Diagrams with the Bounary Theory 82

3.6 Comparison of the Boundary Theory and the P-L's Contact Rule of Phase Regions 85

References-3 91

Chapter 4 The Application of the Boundary Theory of Phase Diag-rams to the Quaternary and Higher Number Component Phase Diagrams 92

4.1 Introduction 92

4.2 The Relationship among NPRs and their Boundaries in a Typical,Iso-baric,Quaternary Phase Diagram 92

4.3 During Temperature Decreasing,Some Cases of Variations of the NPRs and their Boundaries,May be Encountered for Several Types of Quaternary Isobaric Phase Diagrams 94

4.4 The Isobaric Quinary Phase Diagrams 106

4.5 Conclusion 106

References-4 106

Chapter 5 The Boundary Theory in Construction of Multicompo-nent Isothermal Sections 107

5.1 The Relationship among Neighboring Phase Regions(NPRs)and Th-eir Boundaries in Isobaric Isothermal Multicomponent Sections 107

5.2 The Non-Contact Phase Regions and the Boundaries between Them 110

5.3 Construction of an Isothermal Quinary Section,with Limited Information 112

5.4 The Method of Constructing an Isothermal Eight-Component Section 116

5.5 Summary of Using the Boundary Theory Method 121

References-5 121

Chapter 6 The Boundary Theory of Multicomponent Isobaric Isopleth Sections 122

6.1 Introduction 122

6.2 The Characteristics of Boundaries in Isopleth Sections for the Case of N≥2 and R1≥1 123

6.3 The Characteristics of Boundaries in the Isopleth Section for the Case of N≥2,R1=0,there is no Invariant Phase Transition between the two NPRs 126

6.4 The Case of N≥2,R1=0,there is an Invariant Phase Transition between the two NPRs.In this Case,there may be a Boundary Line or a Boundary Point between two NPRs 127

6.5 Example 129

6.6 The Theory of Two-Dimensional Sections of Isobaric Multicomponent Phase Diagrams 132

References-6 134

Chapter 7 The Application of the Boundary Theory to Isobaric Phase Diagrams 135

7.1 Brief Review of the Application for the Boundary Theory 135

7.2 The Analysis of the Fe-Cr-C Isopleth Section 135

7.3 The Application of the Boundary Theory to Phase Diagram Calculation 138

7.4 The Application of the Boundary Theory to Phase Diagram Assessment 145

7.5 The Application of the Boundary Theory to Phase Diagram Determination 149

7.6 The Application of the Boundary Theory to Phase Diagram Education 152

References-7 152

Summary of Part Two 153

Part Three The Boundary Theory and Calculation of High Pressure Phase Diagrams 157

Chapter 8 The Boundary Theory for p--T-xi Multicomponent Phase Diagrams 157

8.1 Introduction 157

8.2 The Theorem of Corresponding Relationship for p-T-xi Multicomponent Phase Diagrams and Its Corollaries 158

8.3 The Relationship between Rí and R1 in p-T-xi Multicomponent Phase Diagrams 160

8.4 The Relationship among NPRs and Their Boundaries for the p-T-x Binary Phase Diagrams 167

8.5 Relationship among NPRs and their Boundaries for the p-T-xi Ternary Phase Diagram 168

8.6 The Application of Boundary Theory for Quaternary p-T-xi Phase Diagrams 170

8.7 The Reliability of the Boundary Theory of Multicomponent p-T-xi Phase Diagrams 171

References-8 171

Chapter 9 The Calculation of Unary High-Pressure Phase Diagra-ms and the Boundary Theory of p-T Phase Diagrams of Multicomponent Systems 173

9.1 Introduction 173

9.2 Calculation of Uuary p-T Diagrams 174

9.3 The Boundary Theory of p-T Phase Diagrams of Multiconponent Systems without Composition Variable 176

Referenees-9 177

Chapter 10 Calculation of Binary High-Pressure Phase Diagrams 178

10.1 Principles for the Calculation of Binary Phase Diagrams at Elevated Pressures 178

10.2 Calculation of the Standard Molar Gibbs Free Energy for the Pure Components 180

10.3 Calculation of Activity Coefficients γi(T,p0,xi)of the i-th Component in the Equilibrium Phases 181

10.4 Partial Molar Volumes 183

10.5 Some Remarks on the Values of α andβ 186

10.6 Example-Calculation of the Cd-Pb Phase Diagram at High Pressure 187

References-10 194

Chapter 11 The Calculation of High-Pressure Ternary Phase Dia-grams 196

11.1 The Characteristics of the Boundaries of the High-Pressure Ternary Phase Diagrams,and the Basic Equations for Their Calculation 196

11.2 The Treatment of Thermodynamic Parameters for Ternary Systems at High Pressure 201

11.3 Verification of the Estimation Method for the Excess Molar Volume by Experiment 204

11.4 The Calculation of High-Pressure Phase Diagrams of Cd-Pb-Sn and Cd-Sn-Zn Systems 206

11.5 Verification of Calculated High-Pressure Ternary Phase Diagrams through Experimental Determination 219

11.6 The Comparison between the Methods of Experimental Determina-tion and Thermodynamic Calculation of High Pressure Phase Diagrams 221

References-11 223

Summary of Part Three 224

References of This Book 226

Important Symbols 230

Index 232

Annex 234