Principles of Classical Thermodynamics: Applied to Materials Science

✍ Scribed by Didier De Fontaine

• Publisher: World Scientific Publishing Co
• Year: 2019
• Tongue: English
• Leaves: 390
• Edition: 1
• Category: Library

✦ Synopsis

The aim of this book is to present Classical Thermodynamics in a unified way, from the most fundamental principles to non-uniform systems, thereby requiring the introduction of coarse graining methods, leading for instance to phase field methods. Solutions thermodynamics and temperature–concentration phase diagrams are covered, plus also a brief introduction to statistical thermodynamics and topological disorder. The Landau theory is included along with a general treatment of multicomponent instabilities in various types of thermodynamic applications, including phase separation and order disorder transitions. Nucleation theory and spinodal decomposition are presented as extreme cases of a single approach involving the all-important role of fluctuations.

In this way, it is hoped that this coverage will reconcile in a unified manner techniques generally presented separately in physics and materials texts.

Readership: Students and professionals in solid state physics and materials science.

✦ Table of Contents

Contents
Foreword
1 Introduction
References
I Basic Thermodynamics
2 Thermodynamic Systems
2.1 Types of work
2.2 Types of equilibria
2.3 Types of evolution
Irreversible process
Quasi-static process
Reversible process
2.4 Types of partitions
Adiabatic partition
Diathermic partition
Permeable partition
2.5 Types of Systems
Isolated system
Adiabatic system
Closed system
Open system
2.6 Reservoirs, Probes
2.7 Simple Systems
References
3 Fundamental Laws
3.1 Zeroth Law
3.2 First Law
3.3 Second Law
3.4 Fundamental Energy Differential
Important caveat
3.5 Mathematical Interlude
Types of differentials
Cyclic partial formula
Differential forms
3.6 Thermodynamic Integration
Examples
Principle of Increase of Entropy
Clausius Theorem
“Chemical Work”
4 Thermodynamic Equilibria
4.1 Euler Integration
4.2 Gibbs–Duhem
4.3 Legendre Transformation
Examples
4.4 Maxwell Relations
4.5 Evolution Criteria
4.6 Phase Equilibrium
4.7 Chemical Potentials
References
5 Ideal Gases
5.1 Definition
5.2 Entropy of an Ideal Gas
Example
5.3 Reversible Adiabats
5.4 Chemical Potential of an Ideal Gas
6 Single-Component Equilibrium
6.1 Phase Transformations
6.2 Derivatives and Discontinuities
6.3 P–V–T Equation of State
6.4 Clapeyron–Clausius Equation
References
7 Solutions
7.1 Chemical Potentials in Solutions
Fugacity of a Real Gas
Mixture of Real Gases
Mixture of Condensable Substances
7.2 Henry and Raoult Laws
7.3 Gibbs–Helmholtz Equation
7.4 Quantities of Mixing
Examples
Volume of Mixing
Enthalpy of Mixing
Entropy of Mixing
Gibbs Energy of Mixing
7.5 Intercept Rule
7.6 Independent Variables
7.7 Qualitative Discussion of Mixing
Ideal Behavior
“Real” Behavior
7.8 Example: Mixing of Hard Spheres
7.9 Barycentric Coordinates
7.10 Regular Solution Model
References
8 Introduction to Statistical Mechanics
8.1 Reminder of Basic Results
8.2 Statistical Interpretation
Averages
Adiabatic systems
Optimal Distribution
Correspondence with Classical Thermodynamics
Discussion
8.3 The Third Law of Thermodynamics
8.4 The Unattainability of Absolute Zero
References
II Materials Applications
9 Temperature-Composition Phase Diagrams
9.1 Binary Systems
One Free Energy Curve
Dilute solutions
Two Free Energy Curves
Three Free Energy Curves
More Free Energy Curves
9.2 Multicomponent Systems
Ternary Systems
Quaternary Systems
9.3 Experimental Determination
9.4 Computation of Phase Diagrams
Calphad Method
First Principles Calculations
Trial Calculation of the Cd-Mg Phase Diagram
9.5 Phase Diagrams and the Third Law
References
10 Topological Disorder
10.1 Glass Thermodynamics
10.2 A Little Geometry
10.3 Random Close Packing
Entropy-driven Transformations
10.4 Amorphization Criteria
Clustering and Ordering
Number of Components
High-entropy alloys
References
11 Chemical Reactions
11.1 One Chemical Reaction
Mass Action Law
Equilibrium Constant
11.2 Several Chemical Reactions
11.3 Multi-Phase Equilibrium
11.4 Phase Rule
Constraints on Initial Amounts
Electroneutrality
11.5 Ellingham Diagrams
12 Point Defect Equilibrium
12.1 General Definitions
Constituents
Unit Cell
Building Unit
Structure Elements
Electronic Defects
Point Imperfections
12.2 Electrochemical Reactions
Mass Balance Constraint
Site Ratio Constraint
Electroneutrality Constraint
12.3 Examples
Intrinsic Electronic Defects
Schottky Defects
Frenkel Defects
Off-Stoichiometric Compounds
References
13 Interfaces
13.1 The Gibbs Stratagem
13.2 Interfacial Equilibrium
13.3 Gibbs Adsorption Isotherm
13.4 Intersection of Interfaces
References
14 Non-Uniform Systems
14.1 Coarse Graining
14.2 Square-Gradient Approximation
References
15 Landau Theory
15.1 Ordering
15.2 Concentration Waves
15.3 Landau Approach
Second-order transition
Asymmetric first-order transition
Symmetric first-order transition
Order Parameter Plots
15.4 Generalized Bragg–Williams Method
Generalized regular solution
Taylor’s expansion
Fourier expansion
Symmetry of V(h)
Special points
15.5 Landau–Lifshitz Rules
15.6 Discussion of the Landau Theory
Energy and constitutive expressions
15.7 Critical Exponents
Coexistence curve
Susceptibility
References
16 Thermodynamic Stability of Crystals
16.1 Transformation Mode
16.2 Multivariable Instabilities
Quadratic Forms
Linear Stability Conditions
Multicomponent Compositional Instabilities
16.3 Tensor Formalism
Definitions
Cubic Symmetry
16.4 Physical properties
Application to Ferroelectricity
Landau, Lifshitz, Ginzburg Formulation
The Ferroelectric Transition
One-Dimensional, Second-Order Case
One-Dimensional, First-Order case
Cubic Crystals, Second-Order Case
References
17 Nucleation and Growth
17.1 Statistics of Embryo Formation
17.2 Creating an Embryo
17.3 Work of Formation of a Nucleus
17.4 Single-component System
17.5 Multicomponent System
17.6 Growth of a New Phase
References
18 Kinetic Aspects
18.1 The Spinodal Concept
18.2 The Kinetic Equation
18.3 Linear Solution
Example
18.4 The Non–Linear Equation
18.5 General Quantitative Theory
References
19 Summary and Conclusion
References
A Pfaffian Differential Forms
Example
General method of integration
Integration along a path
Reference
B The Second Law and the TdS Derivation
C Euler’s Theorem on Homogeneous Functions
D Constrained Extrema and Lagrange Multipliers
Direct Method
Method of Lagrange Multipliers
References
E Jacobians in Thermodynamics
Property 1
Property 2
Property 3
Property 4
Property 5
Property 6
Property 7
Example
F The Third Law in Statistical Mechanics
G Proof of Triangle Equalities
Reference
H Variational Calculus
References
I Discrete Lattice Fourier Series
Discrete Fourier Transform
Lattice Delta Function
Plancherel and Parseval Theorems
Convolution Theorem
Diagonalization of Quadratic Forms
J Symmetry of Tensors
Voigt notation
Crystal Symmetry
References
K Diagonalization of Quadratic Forms
Eigenvalues and Eigenvectors
Gaussian Reduction Algorithm
Jacobi Formulation
Index