Chemical Thermodynamics in Materials Science
Taishi Matsushita
•Kusuhiro Mukai
Chemical Thermodynamics in Materials Science
From Basics to Practical Applications
123
Taishi Matsushita
Department of Materials and Manufacturing, School of Engineering
Jönköping University Jönköping
Sweden
Kusuhiro Mukai
Kyushu Institute of Technology Kitakyushu
Japan
ISBN 978-981-13-0404-0 ISBN 978-981-13-0405-7 (eBook)
https://doi.org/10.1007/978-981-13-0405-7
Library of Congress Control Number: 2018940878
© Springer Nature Singapore Pte Ltd. 2018
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Preface
This book, Chemical Thermodynamics in Materials Science, was originally developed as course material at the School of Engineering, Jönköping University, Sweden, based on a book written by one of the authors (KM) in 1992 (the English title of which is ‘How to Utilize Chemical Thermodynamics’; Kyoritsu Shuppan Co., Ltd., Tokyo).
Although the Japanese book was widely accepted by many students and researchers, a quarter of a century has passed, and in the intervening time, the author has received many comments and much input from readers. This volume retains the contents of its predecessor, but manyflaws have been corrected and new chapters added. Specifically, the chapter on entropy has been significantly revised, and the sections on the Carnot cycle and basic concepts of statistical thermody- namics have been added. In addition, thermodynamic calculation software packages such as Thermo-Calc have become more widely used in recent years, and so a chapter on the basics of computational thermodynamics has also been added.
The above-mentioned Japanese book assumes that readers have a basic knowledge of thermodynamics (beginning with the practical applications of the van’t Hoff isotherm), but the structure of this book has been changed extensively so that readers can learn thermodynamics step by step, from beginning to end. Here, many schematic diagrams and examples are presented to facilitate understanding of peculiar concepts in thermodynamics.
Through our teaching activities, we realised that one difficulty experienced by those beginning to study thermodynamics is the symbols used in books, as different texts on thermodynamics use different symbols for the same concepts, or the same symbol for different concepts. This creates confusion for beginners, and so in this book the symbols used are those recommended by the International Union of Pure and Applied Chemistry (IUPAC).
In order to improve metallurgical processes by applying knowledge of thermo- dynamics and assessing the calculation results of thermodynamic software pack- ages, a systematic and correct understanding of thermodynamics is required.
However, books from which one can learn thermodynamics from the basic to advanced levels are rarely published. This book bridges the gap between the basic
v
elements of thermodynamics, which are covered in general books on the subject, and their applications, which are partially discussed within specialised texts written for a specific field.
This book is written with a focus on learning reliable, applied skills using easy-to-understand explanations and in-depth descriptions and schematic diagrams.
It can be used to teach the basics of chemical thermodynamics and their applica- tions to beginners, but can also be used by advanced readers (postgraduate students/researchers) to learn or refresh the basic concepts of the subject.
We hope that this book helps you to understand and utilise in practice the basic elements of chemical thermodynamics.
Jönköping, Sweden Taishi Matsushita
Associate Professor, Jönköping University, Sweden
Fukuoka, Japan May 2018
Kusuhiro Mukai Professor Emeritus, Kyushu Institute of Technology, Japan
vi Preface
Contents
1 Introduction . . . 1
2 Symbols and Glossary. . . 5
2.1 Symbols. . . 5
2.2 Glossary. . . 8
2.3 Equilibrium State . . . 13
References . . . 16
3 The First Law of Thermodynamics. . . 17
3.1 The First Law of Thermodynamics. . . 17
3.2 Internal Energy, U . . . 17
3.3 The Nature of Internal Energy . . . 21
3.4 Summary . . . 22
Reference. . . 22
4 Enthalpy,H . . . 23
4.1 Enthalpy, H, and Heat Capacities. . . 23
4.2 Definition of Enthalpy, H ¼ 0 . . . 26
4.3 Heat of Reaction,DrH. . . 26
4.4 Influence of Temperature on the Heat of Reaction (Kirchhoff’s Law). . . 27
4.5 Temperature Dependence of Enthalpy, H . . . 28
4.6 Enthalpy of Formation (Heat of Formation) . . . 30
4.7 Hess’s Law. . . 33
4.8 Summary . . . 34
5 The Second Law of Thermodynamics. . . 37
5.1 Expressing the Second Law of Thermodynamics. . . 37
5.2 Reversible and Irreversible Processes . . . 40
vii
5.3 Carnot Engine (Carnot Cycle) . . . 41
5.4 Mathematical Expression of the Second Law of Thermodynamics as Regards Entropy. . . 48
5.5 Summary . . . 52
6 Entropy,S. . . 53
6.1 The Microscopic Perspective on Entropy . . . 53
6.2 Calculation of Entropy . . . 55
6.2.1 Entropy Change During the Isothermal Expansion of Gas . . . 55
6.2.2 Temperature Dependence of Entropy, S. . . 56
6.3 Macroscopic and Microscopic Perspectives on Entropy. . . 58
6.3.1 Macroscopic Perspective. . . 58
6.3.2 Microscopic Perspective . . . 60
6.4 Summary . . . 62
7 Equilibrium Conditions. . . 63
7.1 Closed Systems. . . 63
7.1.1 General Conditions for Equilibrium for Closed Systems . . . 63
7.1.2 Criterion for Equilibrium for a Closed System at Constant U and V ðdU ¼ 0; dV ¼ 0Þ . . . 65
7.1.3 Criterion for Equilibrium for a Closed System at Constant S and V ðdS ¼ 0; dV ¼ 0Þ. . . 65
7.1.4 Criterion for Equilibrium for a Closed System at Constant T and V ðdT ¼ 0; dV ¼ 0Þ. . . 65
7.1.5 Criterion for Equilibrium for a Closed System at Constant T and P ðdT ¼ 0; dP ¼ 0Þ. . . 66
7.1.6 Basic Equations that Are True for a Closed System in Equilibrium . . . 68
7.2 Open Systems. . . 71
7.2.1 Basic Equations for Homogeneous Open Systems and Chemical Potential . . . 71
7.2.2 The Gibbs-Duhem Equation . . . 73
7.3 Isolated and Heterogeneous Systems . . . 74
7.3.1 Criterion for Equilibrium for an Isolated Heterogeneous System . . . 74
7.3.2 The Influence of Temperature and Pressure on Melting Phenomena (The Clausius-Clapeyron Equation). . . 79
7.3.3 The Influence of Temperature and Pressure on the Conditions for Diamond Synthesis . . . 82
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7.4 Chemical Equilibrium . . . 86
7.5 The Phase Rule. . . 89
7.5.1 Systems in Which no Chemical Reaction Occurs . . . . 89
7.5.2 Systems in Which Chemical Reactions Occur . . . 91
7.6 Summary . . . 99
References . . . 101
8 Chemical Potential and Activity . . . 103
8.1 Chemical Potential and the Concentration of an Ideal Mixture . . . 103
8.1.1 Ideal Gases . . . 104
8.1.2 Ideal Solutions. . . 107
8.2 Chemical Potential and Concentration of a Non-ideal Mixture . . . 112
8.2.1 Non-ideal Gases and Fugacity. . . 112
8.2.2 Non-ideal Solutions and Activity. . . 116
8.2.3 Choice of Standard Conditions and Unit of Concentration. . . 117
8.3 Determining Activity—Measurement Methods . . . 129
8.3.1 Electromotive Force Measurement. . . 130
8.3.2 Using an Oxygen Concentration Cell Consisting of Solid Electrolyte. . . 131
8.3.3 Vapour-Pressure Measurement. . . 131
8.3.4 Measurement of Partition Constants. . . 133
8.3.5 Osmotic Pressure Measurement. . . 134
8.3.6 Other Methods. . . 136
8.4 Determining Activity—Calculation Methods. . . 136
8.4.1 Calculation of Activity Using Equilibrium Phase Diagrams. . . 136
8.4.2 Calculating Activity Using the Gibbs-Duhem Equation . . . 142
8.4.3 Calculating Activity Using the Heat of Mixing. . . 145
8.4.4 Activity of Multicomponent Solutions . . . 147
8.5 Summary . . . 151
8.5.1 Chemical Potential and Fugacity/Activity. . . 151
8.5.2 Activity Measurements . . . 152
8.5.3 Activity Calculation . . . 153
8.5.4 Types of Solution, Heat of Mixing, DmixH, and Entropy of Mixing, DmixS. . . 155
Reference. . . 155
9 Partial Molar Quantities and Excess Quantities . . . 157
9.1 Partial Molar and Integral Quantities . . . 157
9.2 Excess Quantities . . . 159
Contents ix
9.3 Partial Molar, Integral, and Excess Quantities
of Enthalpy and Entropy . . . 160
9.4 Calculation of Partial Molar Quantities. . . 162
9.5 Summary . . . 163
10 Gibbs Energy Change,DG, and Standard Gibbs Energy Change,DG. . . 165
10.1 The van’t Hoff Isotherm . . . 165
10.2 The van’t Hoff Isotherm for Different Systems . . . 166
10.2.1 Liquid Phases (Reaction in a Solution) . . . 167
10.2.2 Gas Phases. . . 168
10.2.3 Gas, Solid, and Liquid Phases. . . 171
10.2.4 Solid and Liquid Phases . . . 179
10.3 Calculating the Standard Gibbs Energy Change,DG, of Reactions . . . 188
10.3.1 Using the Free-Energy Function and Enthalpy . . . 188
10.3.2 Using Standard Gibbs Energy of Formation, DfGi . . . 191
10.3.3 Using Heat Capacity. . . 198
10.4 The Relationship Between Equilibrium Constant, Temperature, and Pressure. . . 204
10.4.1 Temperature Dependence of the Equilibrium Constant. . . 205
10.4.2 Pressure Dependence of the Equilibrium Constant. . . 206
10.5 Ellingham Diagram. . . 208
10.5.1 Obtaining the Dissociation Pressure of Oxygen . . . 208
10.5.2 Equilibrium Between COCO2 and MeO2 . . . 211
10.5.3 Equilibria Between H2H2O and MeO2, S2 and MeS2, and H2H2S and MeS2 . . . 214
10.6 Summary . . . 217
11 Introduction to Computational Thermodynamics . . . 219
11.1 Introduction . . . 219
11.2 Binary Isomorphous Phase Diagrams . . . 220
11.3 Binary Systems—Other Types of Phase Diagram . . . 221
11.4 Phase Diagrams of Multicomponent Systems . . . 222
11.5 Gibbs Energy of a Regular Solution. . . 222
11.6 General Form of Gibbs Energy . . . 225
11.7 The Sublattice Model . . . 225
11.8 Multicomponent Systems. . . 227
11.9 Other Models . . . 227
11.10 Summary . . . 228
Reference. . . 229
x Contents
12 Books, Databases, and Software . . . 231
12.1 Further Reading (in Roughly Ascending Order of Difficulty). . . 231
12.2 Thermodynamic Data Books . . . 232
12.2.1 Data Books . . . 232
12.2.2 General Materials/Substances . . . 232
12.2.3 Metals and Oxides . . . 233
12.3 Thermodynamic Databases and Software . . . 233
13 Thermodynamic Data. . . 235
13.1 Standard Gibbs Energy of Formation (Data as a Function of Temperature) . . . 235
13.2 Interaction Parameters (Data for Normal Steel). . . 245
References . . . 257
Index . . . 259
Contents xi
