Materials Thermodynamics
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More About This Title Materials Thermodynamics


A timely, applications-driven text in thermodynamics

Materials Thermodynamics provides both students and professionals with the in-depth explanation they need to prepare for the real-world application of thermodynamic tools. Based upon an actual graduate course taught by the authors, this class-tested text covers the subject with a broader, more industry-oriented lens than can be found in any other resource available. This modern approach:

  • Reflects changes rapidly occurring in society at large—from the impact of computers on the teaching of thermodynamics in materials science and engineering university programs to the use of approximations of higher order than the usual Bragg-Williams in solution-phase modeling

  • Makes students aware of the practical problems in using thermodynamics

  • Emphasizes that the calculation of the position of phase and chemical equilibrium in complex systems, even when properly defined, is not easy

  • Relegates concepts like equilibrium constants, activity coefficients, free energy functions, and Gibbs-Duhem integrations to a relatively minor role

  • Includes problems and exercises, as well as a solutions manual

This authoritative text is designed for students and professionals in materials science and engineering, particularly those in physical metallurgy, metallic materials, alloy design and processing, corrosion, oxidation, coatings, and high-temperature alloys.


Y. Austin Chang is Wisconsin Distinguished Professor Emeritus in the Department of Materials Science and Engineering at the University of Wisconsin–Madison. He is a member of the National Academy of Engineering, Foreign Member of the Chinese Academy of Sciences, and the recipient of many honors and awards, including the J. Willard Gibbs Award, the Gold Medal, and A. E. White Distinguished Teacher Award of ASM International, and the W. Hume-Rothery Award, John Bardeen Award, and the Educator Award, all awarded by The Minerals, Metals and Materials Society (TMS).

W. Alan Oates is a recipient of several awards, including the W. Hume-Rothery Award of TMS.¿Since 1992, Oates has held the position of Honorary Professor at the Science Research Institute, University of Salford, England.



Quantities, Units, Nomenclature.

1 Review of Fundamentals.

1.1 Systems, Surroundings and Work.

1.2 Thermodynamic Properties.

1.3 The Laws of Thermodynamics.

1.4 The Fundamental Equation.

1.5 Other Thermodynamic Functions.

1.6 Equilibrium State.


2 Thermodynamics of Unary Systems.

2.1 Standard State Properties.

2.2 The Effect of Pressure.

2.3 The Gibbs-Duhem Equation.

2.4 Experimental Methods.


3 Calculation of the Thermodynamic Properties of Unary Systems.

3.1 Constant-Pressure/Constant-Volume Conversions.

3.2 Excitations in Gases.

3.3 Excitations in Pure Solids.

3.4 The Thermodynamic Properties of a Pure Solid.


4 Phase Equilibria in Unary Systems.

4.1 The Thermodynamic Condition for Phase Equilibrium.

4.2 Phase Changes.

4.3 Stability and Critical Phenomena.

4.4 Gibb's Phase Rule.


5 Thermodynamics of Binary Solutions I: Basic Theory and Application to Gas Mixtures.

5.1 Expressing Composition.

5.2 Total (Integral) and Partial Molar Quantities.

5.3 Application to Gas Mixtures.


6 Thermodynamics of Binary Solutions II: Theory and Experimental Methods.

6.1 Ideal Solutions.

6.2 Experimental Methods.


7 Thermodynamics of Binary Solutions III: Experimental Results and Their Analytical Representation.

7.1 Some Experimental Results.

7.2 Analytical Representation of Results for Liquid or Solid Solutions.


8 Two-Phase Equilibrium I: Theory.

8.1 Introduction.

8.2 Criterion for Phase Equilibrium Between Two Specified Phases.

8.3 Gibb's Phase Rule.


9 Two-Phase Equilibrium II: Example Calculations.


10 Binary Phase Diagrams: Temperature-Composition Diagrams.

10.1 True Phase Diagrams.

10.2 T-xi Phase Diagrams for Strictly Regular Solutions.

10.3 Polymorphism.


11 Binary Phase Diagrams: Temperature-Chemical Potential Diagrams.

11.1 Some General Points.


12 Phase Diagram Topology.

12.1 Gibbs's Phase Rule.

12.2 Combinatorial Analysis.

12.3 Schreinemaker’s Rules.

12.4 The Gibbs-Konovalov Equations.


13 Solution Phase Models I: Configurational Entropies.

13.1 Substitutional Solutions.

13.2 Intermediate Phases.

13.3 Interstitial Solutions.


14 Solution Phase Models II: The Configurational Energy.

14.1 Pair Interaction Model.

14.2 Cluster Model.


15 Solution Models III: The Configurational Free Energy.

15.1 Helmholtz Energy Minimization.

15.2 Critical Temperature for Order/Disorder.


16 Solution Models IV: The Total Gibbs Energy.

16.1 Atomic Size Mismatch Contributions.

16.2 Contributions from Thermal Excitations.

16.3 The Total Gibbs Energy in Empirical Model Calculations.


17 Chemical Equilibria I: Single Chemical Reaction Equations.

17.1 Introduction.

17.2 The Empirical Equilibrium Constant.

17.3 The Standard Equilibrium Constant.

17.4 Calculating the Equilibrium Position.

17.5 Application of the Phase Rule.


18 Chemical Equilibria II: Complex Gas Equilibria.

18.1 The Importance of System Definition.

18.2 Calculation of Chemical Equilibrium.

18.3 Evaluation of Elemental Chemical Potentials in Complex Gas Mixtures.

18.4 Application of the Phase Rule.


19 Chemical Equilibria Between Gaseous and Condensed Phases I.

19.1 Graphical Presentation of Standard Thermochemical Data.

19.2 Ellingham Diagrams.


20 Chemical Equilibria Between Gaseous and Condensed Phases II.

20.1 Subsidiary Scales on Ellingham Diagrams.

20.2 System Definition.


21 Thermodynamics of Ternary Systems.

21.1 Analytical Representation of Thermodynamic Properties.

21.2 Phase Equilibria.


22 Generalized Phase Diagrams for Ternary Systems.

22.1 System Definition.


Appendix A: Some Linearized Standard Gibbs Energies of Formation.

Appendix B: Some Useful Calculus.