Introduction to Phase Diagrams in Materials Science and Engineering

188 Pages·2019·18.681 MB·English

by  Hiroyasu Saka

11368_9789811203701_TP.indd 1 8/8/19 5:28 PM
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World Scientific
11368_9789811203701_TP.indd 2 8/8/19 5:28 PM
Published in 2019 by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Control Number: 2019948668
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Originally published in Japanese as 坂公恭『材料系の状態図入門』
(Zairyoukei no Joutaizu Nyumon)
This English translation is published by arrangement with
Asakura Publishing Company Ltd., Tokyo, Japan.
INTRODUCTION TO PHASE DIAGRAMS IN MATERIALS SCIENCE
AND ENGINEERING
Copyright © 2012 by Hiroyasu Saka
All rights reserved.
ISBN 978-981-120-370-1
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/11368#t=suppl
Printed in Singapore
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v
Preface
Phase diagrams are a MUST for materials scientists and engineers (MSEs).
However, understanding phase diagrams is a hard task for most MSEs. The
audience of this book is two-fold. The first group is young MSEs, who
start learning phase diagrams and are supposed to become specialists as
MSEs. The other group are those who were trained in fields other than
materialsscienceandengineeringbutengageinresearchand/ordevelopment
of materials after they are employed.
For the first group it is crucial to get accustomed to handling “diagrams
(oftenverycomplex)”of“phasediagram”,whichtheyhadnevercomeacross
in their previous career. The second group must cope with phase diagrams
byliterally“on-the-jobtraining”. Inthisbooktheessenceofphasediagrams
is presented in a reader-friendly manner.
Phase diagram is based on thermodynamics, or rather thermodynamics
itself. Therefore, phasediagramistobetaughtbasedonthermodynamicsin
principle. However, for both beginners and on-the-job trainees this teaching
method is too difficult a task. Elements of thermodynamics necessary to
understand phase diagrams is briefly described in Chapter 3, however, this
chapter can be skipped, since it is not necessarily crucial in order to master
phase diagrams.
Ternary phase diagrams in Chapter 4 is far more complex than binary
phase diagram. For this reason, a ternary phase diagram is nowadays less
andlesstaught. However, inceramicsandsemiconductorstheternaryphase
diagrams become more and more important. Recent software provides nec-
essary information to handle ternary phase diagrams. However, needless
to say, without fundamental knowledge of ternary phase diagrams it is
August27,2019 10:57 ws-book961x669 IntroductiontoPhaseDiagramsinMaterialsScienceandEngineering 11368-main pagevi
vi Introduction to Phase Diagrams in Materials Science and Engineering
impossible to understand ternary phase diagrams correctly. In this book
ternary phase diagrams are presented in a completely original way, with
many diagrams in full colour. This book is expected to be a bible for MSEs.
Hiroyasu Saka
Nagoya, Japan
August 2019
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vii
Contents
Preface v
1. Equilibrium Phase Diagrams 1
1.1 General Theory . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Metallography and phase diagram . . . . . . . . . . 1
1.1.2 Terminology . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Phase rule of Gibbs . . . . . . . . . . . . . . . . . . 10
1.2 Binary Alloys in Equilibrium State . . . . . . . . . . . . . . 14
1.2.1 How to express . . . . . . . . . . . . . . . . . . . . . 14
1.2.2 Isomorphous (complete) solid solution . . . . . . . . 18
1.2.3 Eutectic alloy . . . . . . . . . . . . . . . . . . . . . 21
1.2.4 Eutectoid reaction . . . . . . . . . . . . . . . . . . . 31
1.2.5 Other eutectic-type invariant reactions . . . . . . . 33
1.2.6 Peritectic reaction . . . . . . . . . . . . . . . . . . . 33
1.2.7 Other peritectic-type invariant reactions. . . . . . . 36
1.2.8 Phase diagram containing an intermediate phase . . 37
1.2.9 Two-phase separation versus ordering . . . . . . . . 38
1.2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . 40
1.3 Deviation from Equilibrium in Natural Cooling of Binary
Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.3.1 Isomorphous (complete) solid solution . . . . . . . . 46
1.3.2 Eutectic alloy . . . . . . . . . . . . . . . . . . . . . 48
1.3.3 Peritectic alloy . . . . . . . . . . . . . . . . . . . . . 48
2. Heat Treatment of Alloys 51
2.1 Aging and Precipitation in Aluminum Alloys . . . . . . . . 52
2.1.1 Explanation based on phase diagram . . . . . . . . 52
2.1.2 Morphology of precipitates, structure of interfaces . 53
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viii Introduction to Phase Diagrams in Materials Science and Engineering
2.1.3 Sequenceofprecipitation, G.P.zoneandmetastable
precipitates . . . . . . . . . . . . . . . . . . . . . . . 56
2.1.4 Reversion . . . . . . . . . . . . . . . . . . . . . . . . 59
2.1.5 Precipitation hardening . . . . . . . . . . . . . . . . 59
2.1.6 Spinodal decomposition . . . . . . . . . . . . . . . . 62
2.2 Heat Treatment in Steels . . . . . . . . . . . . . . . . . . . . 66
2.2.1 Fe-C phase diagram . . . . . . . . . . . . . . . . . . 66
2.2.2 Quenching and martensite . . . . . . . . . . . . . . 69
2.2.3 Other martensitic transformations . . . . . . . . . . 77
2.2.4 Tempering of martensite,
Temperature-time-transformation (TTT) diagram,
Continuous cooling transformation (CCT) diagram 81
2.2.5 Improvement of hardenability of steel . . . . . . . . 88
2.2.6 Case hardening . . . . . . . . . . . . . . . . . . . . . 89
3. Thermodynamics of Binary Phase Diagrams 92
3.1 Equilibrium Between Different Phases . . . . . . . . . . . . 92
3.1.1 Chemical potential . . . . . . . . . . . . . . . . . . . 92
3.1.2 Simple phase diagram and free energy . . . . . . . . 97
3.1.3 Free energy of substitutional solid solution . . . . . 99
3.1.4 Free energy of a liquid . . . . . . . . . . . . . . . . . 110
3.2 Thermodynamics of Nucleation . . . . . . . . . . . . . . . . 112
3.2.1 Spinodal decomposition . . . . . . . . . . . . . . . . 112
3.2.2 Homogeneous nucleation . . . . . . . . . . . . . . . 114
3.2.3 Heterogeneous nucleation . . . . . . . . . . . . . . . 116
3.2.4 Precipitation of intermediate phases . . . . . . . . . 118
3.2.5 Martensitic transformation . . . . . . . . . . . . . . 119
4. Ternary Phase Diagram 121
4.1 Fundamentals of Ternary Phase Diagrams . . . . . . . . . . 121
4.1.1 How to represent — The Gibbs triangle . . . . . . . 121
4.1.2 Tie-lines and lever principle . . . . . . . . . . . . . . 122
4.1.3 Phase rule in the ternary system . . . . . . . . . . . 125
4.1.4 Space diagram and sectional diagram . . . . . . . . 125
4.2 Relatively Simple Ternary Systems . . . . . . . . . . . . . . 128
4.2.1 Solidification of an isomorphous (complete) ternary
solid solution . . . . . . . . . . . . . . . . . . . . . . 128
4.2.2 Simple eutectic system . . . . . . . . . . . . . . . . 129
4.2.3 Simple peritectic system . . . . . . . . . . . . . . . 138
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Contents ix
4.3 Complex Ternary Systems . . . . . . . . . . . . . . . . . . . 144
4.3.1 Ternary eutectic system (Class I) . . . . . . . . . . 144
4.3.2 Peritecto-eutectic system (Class II) . . . . . . . . . 152
4.3.3 Peritecto-eutectic system (Class III) . . . . . . . . . 157
4.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . 166
4.4 Ternary Systems Containing Intermetallic Compound. . . . 168
4.4.1 Quasi-binary system . . . . . . . . . . . . . . . . . . 168
4.4.2 Quasi-binary systems are not formed . . . . . . . . 168
Appendix: Conversion of indices between
three and four indices in HCP 171
Index 173