Thermodynamic Equilibrium and Stability of Materials

✍ Scribed by Long-Qing Chen

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 464
• Category: Library

✦ Synopsis

This is a textbook on thermodynamics of materials for junior/senior undergraduate students and first-year graduate students as well as a reference book for researchers who would like to refresh their understanding of thermodynamics.

The textbook employs a plain language to explain the thermodynamic concepts and quantities. It embraces the mathematical beauty and rigor of Gibbs thermodynamics through the fundamental equation of thermodynamics from which all thermodynamic properties of a material can be derived. However, a reader with basic first-year undergraduate calculus skills will be able to get through the book without difficulty. One unique feature of this textbook is the descriptions of the step-by-step procedures for computing all the thermodynamic properties from the fundamental equation of thermodynamics and all the thermodynamic energies from a set of common, experimentally measurable thermodynamic properties, supplemented with ample numerical examples.

Another unique feature of this textbook is its emphasis on the concept of chemical potential and its applications to phase equilibria in single component systems and binary solutions, chemical reaction equilibria, and lattice and electronic defects in crystals. The concept of chemical potential is introduced at the very beginning of the book together with temperature and pressure. It avoids or minimizes the use of terms such as molar Gibbs free energy, partial molar Gibbs free energy, or Gibbs potential because molar Gibbs free energy or partial molar Gibbs free energy is precisely the chemical potential of a material or a component. It is the chemical potential that determines the stability of chemical species, compounds, and phases and their tendency to chemically react to form new species, transform to new physical state, and migrate from one spatial location to another. Therefore, it is the chemical potential differences or gradients that drive essentially all materials processes of interest. 

A reader after finishing reading the book is expected to not only achieve a high-level fundamental understanding of thermodynamics but also acquire the analytical skills of applying thermodynamics to determining materials equilibrium and driving forces for materials processes.

✦ Table of Contents

Preface
Contents
About the author
1 Thermodynamic System and Its Quantification
1.1 Introduction
1.2 Thermodynamic Systems
1.3 Thermodynamic Variables
1.3.1 Internal Energy
1.3.2 Entropy
1.3.3 Volume
1.3.4 Amount of Chemical Substance
1.3.5 Potentials Within a System
1.4 Densities
1.5 Extensive and Intensive Variables
1.6 Conjugate Variable Pairs
1.7 Classical, Statistical, and Nonequilibrium Thermodynamics
1.8 Exercises
2 First and Second Laws of Thermodynamics
2.1 Thermodynamic States and State Variables
2.2 Thermodynamic Processes
2.2.1 Spontaneous, or Natural, or Irreversible Processes
2.2.2 Reversible Processes
2.3 Thermodynamic Systems
2.4 First Law of Thermodynamics
2.4.1 First Law of Thermodynamics for Isolated Systems
2.4.2 First Law of Thermodynamics for Closed Systems
2.4.3 First Law of Thermodynamics for Reversible Processes in Open Systems
2.5 Second Law of Thermodynamics
2.5.1 Quantifying Second Law of Thermodynamics
2.5.2 Isolated Systems
2.5.3 Constant Entropy Processes in a Closed System
2.5.4 Constant Entropy and Constant Volume Processes in a Closed System
2.5.5 Constant Temperature and Constant Volume Processes in a Closed System
2.5.6 Constant Entropy and Pressure Processes in a Closed System
2.5.7 Constant Temperature and Pressure Processes in a Closed System
2.5.8 Open Systems
2.6 Summary on First and Second Laws of Thermodynamics
2.7 Examples
2.8 Exercises
3 Fundamental Equation of Thermodynamics
3.1 Differential Form of Fundamental Equation of Thermodynamics
3.2 Integrated Form of Fundamental Equation of Thermodynamics
3.3 Equations of States
3.4 Independent Variables
3.5 Alternative Forms of Fundamental Equation of Thermodynamics
3.6 Differential Forms of Alternative Fundamental Equations of Thermodynamics
3.7 Interpretation of Fundamental Equation of Thermodynamics
3.8 Gibbs–Duhem Relation
3.9 Entropic Representation of Fundamental Equation of Thermodynamics
3.10 Fundamental Equations of Thermodynamics Including Irreversible Internal Processes
3.11 General Forms of Fundamental Equations of Thermodynamics
3.12 Legendre Transforms
3.13 Examples
3.14 Exercises
4 Introduction to Statistical Thermodynamics
4.1 Macrostates and Microstates
4.2 Statistical Interpretation of Entropy and Boltzmann Equation
4.3 Ensembles
4.4 Partition Functions and Fundamental Equation of Thermodynamics
4.5 Entropy and Microstate Probabilities
4.6 Examples
4.7 Exercises
5 From Fundamental Equations to Thermodynamic Properties
5.1 First Derivatives of Thermodynamic Energy Functions
5.2 Second Derivatives of Energy Functions
5.2.1 Heat Capacity or Thermal Capacitance
5.2.2 Compressibility or Mechanical Susceptibility and Modulus
5.2.3 Chemical Capacitance
5.2.4 Electric Capacitance
5.3 Volume Thermal Expansion Coefficient
5.4 Thermal, Mechanical, Electric, and Magnetic Effects of Homogeneous Crystals
5.5 Principal Properties
5.6 Coupled Properties
5.7 Summary Comments on Relationships Between Derivatives and Properties.
5.8 Examples
5.9 Exercises
6 Relations Among Thermodynamic Properties
6.1 Maxwell Relations
6.2 A Few Useful Strategies for Deriving Property Relations
6.3 Examples of Applying Maxwell Relations
6.3.1 Barocaloric Effect
6.3.2 Isothermal Volume Dependence of Entropy
6.3.3 Joule Expansion Effect
6.3.4 Joule–Thomson Expansion Effect
6.3.5 Grüneisen Parameter
6.3.6 Property Relations Between Coupled Properties in Crystals
6.4 Summary Comments on Relationships Between Coupled Properties
6.5 Examples
6.6 Exercises
7 Equilibrium and Stability
7.1 Maximum Entropy Principle
7.2 Minimum Internal Energy Principle
7.3 Minimum Enthalpy Principle
7.4 Minimum Helmholtz Free Energy Principle
7.5 Minimum Gibbs Free Energy Principle
7.6 Equilibrium Conditions for Potentials
7.7 General Equilibrium Conditions for Potentials
7.8 Thermodynamic Fields
7.9 Thermodynamic Stability Criteria
7.10 Exercises
8 Thermodynamic Calculations of Materials Processes
8.1 Changes in Thermodynamic Properties with Temperature at Constant Volume
8.2 Changes in Thermodynamic Properties with Temperature at Constant Pressure
8.3 Changes in Thermodynamic Properties with Volume at Constant Temperature
8.4 Changes in Thermodynamic Properties with Pressure at Constant Temperature
8.5 Changes in Thermodynamic Properties with Both Temperature and Volume
8.6 Changes in Thermodynamic Properties with Both Temperature and Pressure
8.7 Changes in Thermodynamic Properties for Phase Transitions
8.8 Changes in Thermodynamic Properties for Chemical Reactions
8.9 Examples
8.10 Exercises
9 Construction of Fundamental Equation of Thermodynamics
9.1 Choice of Fundamental Equation of Thermodynamics
9.2 Molar Helmholtz Free Energy as a Function of Temperature and Molar Volume
9.3 Chemical Potential as a Function of Temperature and Pressure
9.4 Chemical Potential as a Function of Temperature Involving Phase Changes
9.5 Reference States
9.5.1 Reference State for Molar Helmholtz Free Energy at 0 K
9.5.2 Reference State for Chemical Potential at 298 K and 1 bar
9.6 Fundamental Equations with Multiphysics Effects
9.6.1 Chemogravitational Potential
9.6.2 Electrochemical Potential
9.6.3 Chemical Potential Including Surface Effects
9.7 Examples
9.8 Exercises
10 Chemical Potentials of Gases, Electrons, Crystals, and Defects
10.1 Chemical Potential of Ideal Gases
10.1.1 Standard State, Activity, and Fugacity
10.1.2 Chemogravitational Potential of Ideal Gases
10.2 Chemical Potentials of Electrons and Holes
10.2.1 Electrons in Metals
10.2.2 Electrons and Holes in Semiconductors and Insulators
10.2.3 Electrochemical Potential of Electrons
10.2.4 Chemical Potentials of Electrons in Trapped Electronic States of Dopants or Impurities
10.3 Chemical Potentials of Einstein and Debye Crystals
10.4 Chemical Potentials of Atomic Defects
10.4.1 Chemical Potentials of Vacancies in Elemental Crystals
10.4.2 Chemical Potentials of Interstitials
10.4.3 Chemical Potential of Frenkel Defects
10.4.4 Chemical Potential of Schottky Defects
10.4.5 Chemical Potentials of Neutral Dopants
10.5 Examples
10.6 Exercises
11 Phase Equilibria of Single-Component Materials
11.1 General Temperature and Pressure Dependencies of Chemical Potential
11.2 Thermodynamic Driving Force for Phase Transition
11.3 Temperature and Pressure Dependences of Driving Force
11.4 Classification and Order of Phase Transitions
11.5 Temperature–Pressure Phase Diagram
11.6 Gibbs Phase Rule
11.7 Clapeyron Equation
11.8 Clausius–Clapeyron Equation and Vapor Pressure of Condensed Phase
11.9 Size Effect on Phase Transition Temperature
11.10 Landau Theory of Phase Transitions
11.11 Examples
11.12 Exercises
12 Chemical Potentials of Solutions
12.1 Representation of Chemical Composition
12.2 Fundamental Equation of Thermodynamics of a Multicomponent Solution
12.3 Chemical Potential as Fundamental Equation for a Multicomponent System
12.4 Chemical Potential of a Mixture of Pure Components
12.5 Chemical Potential of a Component in a Multicomponent Solution
12.6 Chemical Potential of Homogeneous Solution from Component Chemical Potentials
12.7 Obtaining Chemical Potentials of Components from Chemical Potential of Solution
12.8 Chemical Potential of a Uniform Solution at a Fixed Composition
12.9 Gibbs–Duhem Equation for Multicomponent Systems
12.10 Thermodynamic Stability of a Solution and Thermodynamic Factor
12.11 Lever Rule
12.12 Chemical Potential Change of Solution Formation from Pure Components
12.13 Chemical Potential Change for Adding Pure Components into a Solution
12.14 Chemical Potential Change of Adding a Solution into Another Solution
12.15 Driving Force for Precipitation in a Solution
12.16 Chemical Potential of a Two-Phase Mixture
12.17 Stability at 0 K (Convex Hull)
12.18 Chemical Potentials of Ideal Gas Mixtures
12.19 Relation Between Activity of a Component in Solution and Its Vapor Pressure
12.20 Raoult’s Law and Henry’s Law
12.21 Chemical Potentials of Ideal Solutions
12.22 Chemical Potentials of Regular Solutions
12.23 Flory–Huggins Model of Polymer Solutions,
12.24 Redlich–Kister Expansion for Chemical Potential of a Solution
12.25 Osmotic Pressure
12.26 Chemomechanical Potentials of Components in a Solution
12.27 Electrochemical Potentials of Components in a Solution
12.28 Particle Size Dependence of Solubility
12.29 Interfacial Segregation
12.30 Examples
12.31 Exercises
13 Chemical Phase Equilibria and Phase Diagrams
13.1 Equilibrium States from Chemical Potentials Versus Composition
13.2 Examples of Model Phase Diagrams
13.3 Number of Degrees of Freedom—Gibbs Phase Rule
13.4 Phase Fractions—Lever Rule
13.5 Estimates of Activity Coefficients in Binary Systems
13.6 Calculations of Simple Phase Diagrams
13.7 Exercises
14 Chemical Reaction Equilibria
14.1 Reaction Equilibrium
14.2 Graphical Representation of Oxidation Reactions—Ellingham Diagram
14.2.1 O2 Scale
14.2.2 H2/H2O Scale
14.2.3 CO/CO2 Scale
14.3 Example
14.4 Exercises
15 Energy Conversions and Electrochemistry
15.1 Maximum Work Theorem
15.2 Theoretical Efficiencies of Thermal Devices
15.3 Voltage Derived from Light-Excited Electron–Hole Pairs: Photovoltaic Effect
15.4 Electrochemical Reactions and Energy Conversion
15.4.1 Electrode Reactions and Electrode Potentials
15.4.2 Standard Hydrogen Electrode (SHE) and Standard Electrode Potential
15.4.3 Cell Reactions and Cell Voltage
15.4.4 Standard Cell Voltage from Standard Electrode Potentials
15.4.5 Temperature Dependence of Cell Voltage
15.4.6 Voltage Derived from Chemical Composition Difference
15.4.7 Voltage Derived from Partial Pressure Difference
15.5 Exercises
Index