# Phase Equilibria

### Basic Principles, Applications, Experimental Techniques

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Phase Equilibria: Basic Principles, Applications, Experimental Techniques presents an analytical treatment in the study of the theories and principles of phase equilibria. The book is organized to afford a deep and thorough understanding of such subjects as the method of species model systems; condensed phase-vapor phase equilibria and vapor transport reactions; zone refining techniques; and nonstoichiometry. Physicists, physical chemists, engineers, and materials scientists will find the book a good reference material.

## Table of Contents

Contents

Preface

Acknowledgments

1. Some Preliminary Remarks and Observations

2. Thermodynamics and the Phase Rule

3. Definition of Terms and Concepts

A. Introduction

B. Systems

C. Phases

D. The Limits Imposed by an Experimental Situation

E. The Component, Species, and Mole Terms

F. Defining the Number of Components Present

G. Chemical, Compound, Substance and Constituent

4. The Thermodynamic Basis of the Phase Rule

A. Introduction

B. The Phase Rule and Its Basis

C. Choice of Systems and the Reduced Phase Rule

D. The Vapor Pressure, the Evaporation Rate and the Reduced Phase Rule

E. The Time Factor in a Non-Time-Dependent Science

5. Systems of One Component—Temperature Effects

A. Introduction

B. The Analytical Description of Univariance

C. Univariant Equilibria Involving Solids and Gases

D. Univariant Equilibria Involving Liquids and Gases

E. Univariant Equilibria Involving Solids and Liquids

F. Further Aspects of Univariant Systems

G. Metastability in One-Component Systems

H. Structure Changes in Unary Systems

6. Systems of One Component—Pressure Effects and the Continuous Nature of Metastability

A. Metastable-to-Stable Transformations with Increasing Pressure

B. Solid Phases That Do Not Exhibit Stable Solid-Vapor Equilibria at Any Temperature: Monotropes

7. Complex Metastability in One-Component Systems

A. Systems with Solid-Vapor Univariance

B. Stable High-Pressure Systems

8. Other Aspects of One-Component Behavior

A. The Effects of Inert Gas Pressures on the Vapor Pressure of Single-Component Solids or Liquids

B. The Effect of Surface Tension on the Vapor Pressure of a Single Component

9. Enthalpy and Entropy Diagrams of State for Unary Systems

A. Introduction

B. Enthalpie Relationships and the Enthalpy Diagrams of State

C. Entropie Relationships and Entropy Diagrams of State

10. Multicomponent Systems, Homogeneous Systems, and the Equilibrium Constant

A. Introduction

B. The Species and the Homogeneous Equilibrium Constant

C. Standard States and Their Significance

D. The Homogeneous Equilibrium Constant in Terms of Mole Fractions

E. The Variation of Equilibrium Constant with Temperature

11. Multicomponent Systems, the Equilibrium Constant, and Heterogeneous Systems

A. Introduction

B. The Chemical Potential for Components and Species

C. Equilibrium Constants in Terms of Partial Molar Quantities

12. The Thermodynamic Parameters-Fugacity and Activity

A. Introduction

B. Rationale for a Thermodynamic Approach to the Treatment of Real Systems

C. The Fugacity, Standard States, and Free Energy Relations

D. Thermodynamic Concentrations-The Activity

13. Two-Component Systems-Systems in Which One Phase Is Pure and in Which Species and Component Mole Terms Are Equivalent-Simple Eutectic Interactions

A. Introduction

B. The Analytical Expression of Univariance in a Simple Eutectic Interaction

C. An Alternative Derivation of Univariant Equations for Eutectic Systems

14. Graphical Representations of Simple Eutectic Interactions

A. Introduction

B. The Phase Diagram-A Qualitative View

C. The Lever Arm Principle

D. Specifics of Application of the Lever Arm Principle

15. Eutectic Systems Continued—The Parameter ΔHfusion/Tmelting and Its Influence on the Contour of Eutectic Liquidus Curves

A. Introduction

B. Theoretical Analysis

C. Application of the ΔΗΑ/ΤA Principle to Real Systems

D. Pseudobinary Systems

16. Eutectic Interactions Continued—The Effects of Homogeneous Equilibria on Liquidus Contours

A. Introduction

B. Dissociation of One of the Liquid-Phase Species

C. Solution for the AB Liquidus Curve

D. The Liquidus for the Nondissociating Component

17. Common Species Effects in Simple Eutectic Systems

A. Introduction

B. The Liquidus Curve for AB

C. The Liquidus for B

18. Eutectic Interactions Continued—The Effects of Association on Liquidus Contours

A. Introduction

B. The A Liquidus

C. The Liquidus for the Component B

19. Eutectic Interactions Continued—Effects of End Member Species Interactions on Liquidus Contours

A. Introduction

B. Solution of the A Liquidus,

C. Solution of the B Liquidus,

20. Eutectic Interactions Continued—Effects of Complete Dissociation on Liquidus Contours

A. Introduction

B. The AB Liquidus

C. The B Liquidus

21. Eutectic Interactions Continued—Graphical Description of the Results of Chapters 16-20

A. Introduction

B. Test Cases

C. Dissociation of a Pseudounary Component in the System AB-C

D. Dissociation with a Common Species Effect

E. Association of One of the Liquid-Phase Species

F. Reaction between Liquid-Phase Species

G. Effects of Complete Dissociation on Liquidus Contours

22. Eutectic Interactions Continued—Single Compound Formation in Binary Systems and Coordinate Transformations

A. Introduction

B. A Single Compound Is Generated

C. Scaling Factors and Coordinate Transformations

D. Examination of Solubility Curves in Systems Exhibiting Compound Formation

23. Eutectic Interactions Continued—Multiple Compound Formation in Binary Systems and Coordinate Transformations in Multiple Compound Systems

A. Introduction

B. Two Compounds Are Generated

24. Eutectic Interactions Continued—p-T-Mx Representations and Phase Changes

A. Introduction

B. The Τ-p-Μx Diagram of State

C. Phase Changes—A Second Quadruple Point

25. Eutectic Interactions Continued—Intermediate Compound Instability—Incongruently Melting Compounds

A. Introduction

B. The Intermediate Compound AxBy Melts Incongruently

C. The Three-Dimensional Model of Incongruently Melting Systems

D. The Effect of Pressure When the S-L Slope of the Intermediate Incongruently Melting Compound Is Positive

26. Liquid Immiscibility in Eutectic Systems

A. Introduction

B. The Miscibility Gap Is Confined to the Liquid Regions

C. The T-p-Μx Representation of the Eutectic System Showing Liquid Phase Immiscibility

D. The Intersection of a Miscibility Gap with the Liquidus Regions

E. The T-p-Μχ Representation of the MG Intersecting a Liquidus

27. Systems Exhibiting Solid Solubility—Ascending Solid Solutions

A. Introduction

B. The Analytical Description of Univariance for Ascending Solid Solutions

C. The Graphical Representation of Ascending Solid Solutions

D. The Purification of Materials

E. The General Experimental Approach to the Resolution of Solid Solution Diagrams

F. The Space Model for Solid Solution Systems

28. Solid Solutions Continued—Graphical Representation of Idealized Systems and Some Comment on Real Systems

A. Introduction

B. Temperature—Composition Diagrams for Cases I-XIV

C. Real Systems

29. Solid Solutions Continued—Complete Liquid Phase Dissociation and Minimum Type Solid Solutions

A. Introduction

B. The Qualitative Aspects of Fig. 1

C. Complete Dissociation in Solid Solution Systems

D. Case I—Dimer-Monomer Behavior

E. Case II

F. The Case Where Both Components Are Dimers in the Solid

G. Space Models

30. Hypothetical Examples Using the Equations of Chapter 29

A. Introduction

B. Some Hypothetical Examples

C. The System Na2C03-K2C0-A Comparison between Experimental and Theoretical Solidus and Liquidus Curves

31. Condensed-Vapor Phase Binary Diagrams

A. Introduction

B. Boiling and Sublimation Point Diagrams(Constant Pressure Diagrams)

C. Constant Temperature Condensed-Vapor Phase Diagrams

D. Some Hypothetical Examples of Maximum Type S-V Equilibria in Isothermal Diagrams

E. Isothermal Distillations

F. Isobaric Distillations

32. Condensed-Vapor Phase Binary Diagrams Continued—Incongruently Vaporizing Systems

A. Introduction

B. Vaporous Curves in Isothermal Diagrams

C. Immiscible Solid-Vapor Systems Exhibiting Congruently Vaporizing Compounds

D. Immiscible Solid-Vapor Systems Containing Incongruently Vaporizing Compounds

E. Hydrate Systems

F. Further Remarks on the Regions of Variable Composition

G. Deliquescence and Efflorescence of Hydrate Systems

H. Efflorescence and Deliquescence in Aqueous Systems Not Generating Hydrates

I. The Variation of p with T of Isothermally Invariant Incongruently Vaporizing Systems

33. Limited Solid Solubility

A. Introduction

B. Limited Solubility Systems Exhibiting a Eutectic

C. The Case Where Limited Solubility Occurs below the Solidus

D. Three-Dimensional Representations

of Limited Solid Solubility Systems

34. Three-Component Systems

A. Introduction

B. Representation of Three-Component Condensed-Phase Equilibria

C. Simple Ternary Eutectic Interactions

D. Ternary Diagrams for Systems in Which Binary Congruently Melting Compounds Are Formed

E. Ternary Diagrams for Systems in Which Binary Congruently Melting Compounds Occur,One of Whose Eutectic Extensions Generates a Ternary Peritectic

F. Ternary Systems in Which Incongruently Melting Binary Compounds Are Present

G. Ternary Compound Formation—Congruently Melting Ternary Compounds

H. Ternary Compound Formation—An Incongruently Melting Ternary Compound Is Present

I. Isothermal Sections for Selected Ternary Systems

J. Systems Exhibiting Solid Solubility

35. Three-Component Solid-Vapor Equilibria—Chemical Vapor Transport Reactions

A. Introduction

B. Disproportionation Processes

36. Experimental Techniques

A. Introduction

B. Pressure Measurements

C. Measurement of Thermal Anomalies

D. Other Useful Tools

Appendix: References and Additional Remarks for Chapters 1-36, General Bibliography

Subject Index

## Product details

- No. of pages: 560
- Language: English
- Copyright: © Academic Press 1970
- Published: January 1, 1970
- Imprint: Academic Press
- eBook ISBN: 9781483265841