com The Physics of Phase Transitions www. Meijer The Physics of Phase Transitions Concepts and Applications Translated from the French by S. Schnur With 180 Figures Second Revised Edition ABC www.com Pierre Papon Paul H. Meijer Jacques Leblond Catholic University of America École Supérieure Department of Physics de Physique et de Chimie Industrielles Washington, DC 20064, USA de Paris (ESPCI) E-mail: MEIJER@cua.edu Laboratoire de Physique Thermique 10 rue Vauquelin Translator 75005 Paris, France S.
Schnur E-mail: pierre.fr Concepts Unlimited 6009 Lincolnwood Court Burke, VA 22015-3012, USA Translation from the French language edition of Physique des transitions de phases, concepts et applica- tions by Pierre Papon, Jacques Leblond and Paul H. Meijer, Second Edition c 2002 Editions Dunod, Paris, France This work has been published with the help of the French Ministère de la Culture – Centre national du livre Library of Congress Control Number: 2006923230 ISBN-10 3-540-33389-4 2nd Edition Springer Berlin Heidelberg New York ISBN-13 978-3-540-33389-0 2nd Edition Springer Berlin Heidelberg New York ISBN-10 3-540-43236-1 1st Edition Springer Berlin Heidelberg New York ISBN-13 978-3-540-43236-4 1st Edition Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer.
Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and techbooks using a Springer LATEX macro package Cover design: 2nd Editon, eStudio Calamar, Pau/Spain Printed on acid-free paper SPIN: 11735984 56/techbooks 543210 www.com Foreword We learned in school that matter exists in three forms: solid, liquid and gas, as well as other more subtle things such as the fact that “evaporation produces cold.” The science of the states of matter was born in the 19th century.
It has now grown enormously in two directions: (1) The transitions have multiplied: first between a solid and a solid, particu- larly for metallurgists. Then for magnetism, illustrated in France by Louis Néel, and ferroelectricity. In addition, the extraordinary phenomenon of superconductivity in certain metals appeared at the beginning of the 20th century. And other superfluids were recognized later: helium 4, helium 3, the matter constituting atomic nuclei and neutron stars.
There is now a real zoology of transitions, but we know how to classify them based on Landau’s superb idea. (2) Our profound view of the mechanisms has evolved: in particular, the very universal properties of fluctuations near a critical point – described by Kadanoff’s qualitative analysis and specified by an extraordinary theo- retical tool: the renormalization group. Without exaggerating, we can say that our view of condensed matter has undergone two revolutions in the 20th century: first, the introduction of quantum physics in 1930, then the recognition of “self-similar” structures and the resulting scaling laws around 1970. It would be naı̈ve to make too much of these advances: despite all of this sophistication, we are still very unsure about certain points – for example, the mechanism governing superconducting oxides or the laws of the glass transi- tion.
However, a body of doctrines has been formed, and it is an important element of scientific culture in the 21st century. This knowledge is generally expressed solely in works dedicated to only one sector. The great merit of the book by Drs. Papon, Leblond and Meijer is to offer a global introduction, accessible to students of physics entering graduate school.
I notice with pleasure the addenda of this new edition on Bose-Einstein condensates, on colloids, etc. The panorama is broad and www.com VI Foreword will stimulate the interest of the young public targeted here: this book should guide them soundly. I wish it great success. de Gennes January 2006 www.com Preface to the Second Edition This book takes up and expands upon our teachings on thermodynamics and the physics of condensed matter at the School of Industrial Physics and Chemistry and Diplôme d’Etudes Approfondies in Paris and at the Catholic University of America in Washington D.
It is intended for graduate stu- dents, students in engineering schools, and doctoral students. Researchers and industrial engineers will also find syntheses in an important and constantly evolving field of materials science. The book treats the major classes of phase transitions in fluids and solids: vaporization, solidification, magnetic transitions, critical phenomena, etc. In the first two chapters, we give a general description of the phenomena, and we dedicate the next six chapters to the study of a specific transition by explaining its characteristics, experimental methods for investigating it, and the principal theoretical models that allow its prediction.
The major classes of application of phase transitions used in industry are also reported. The last three chapters are specifically dedicated to the role of microstructures and nanostructures, transitions in thin films, and finally, phase transitions in large natural and technical systems. Our approach is essentially thermodynamic and assumes familiarity with the basic concepts and methods of thermody- namics and statistical physics. Exercises and their solutions are given, as well as a bibliography.
In this second edition, we have taken into account new de- velopments which came up in the states of matter physics, in particular in the domain of nanomaterials and atomic Bose-Einstein condensates where progress is accelerating. We have also improved the presentation of several chapters by bringing better information on some phase transition mechanisms and by illustrating them with new application examples. Finally, we would we like to thank J. Leoni who assisted in the prepara- tion of the manuscript and the drawings and diagrams and Dr.
Schnur who put much effort into translating the book as well as Dr. Meyer from Springer-Verlag who provided helpeful advice in publishing the book. We are also grateful to our colleague Prof. Nishinari, from Osaka City University, for his valuable comments on our manuscript.
Paris, France Pierre Papon Paris, France Jacques Leblond Washington, D. Meijer January, 2006 www.com Contents 1 Thermodynamics and Statistical Mechanics of Phase Transitions .1 What is a Phase Transition? .2 Thermodynamic Description of Phase Transitions .1 Stability and Transition – Gibbs–Duhem Criterion .3 Thermodynamic Classification of Phase Transitions .3 General Principles of Methods of Investigating Phase Transitions .1 Calculation of Thermodynamic Potentials and Quantities .2 Equation of State .3 Dynamic Aspects – Fluctuations .4 The Broad Categories of Phase Transitions .1 Transitions with a Change in Structure .2 Transitions with No Change in Structure .3 Non-Equilibrium Transitions .5 The Major Experimental Methods for Investigation of Phase Transitions .6 The Broad Categories of Applications of Phase Transitions .7 Historical Aspect: from the Ceramics of Antiquity to Nanotechnologies. 35 2 Dynamics of Phase Transitions .1 A Large Variety of Mechanisms .1 The Diffusion Phenomenon – Fick’s Law .2 Diffusion Coefficient and Activation Energy .3 Nucleation of a New Phase .5 Global Phase Transformation – Avrami Model .1 Thermodynamics of Spinodal Decomposition .2 Experimental Demonstration – Limitation of the Model 61 2.1 Dynamics of a Structural Transition – The Soft Mode .2 Percolation and Gelation .6 Dynamics of Phase Transitions and Properties of Materials. 75 3 Phase Transitions in Liquids and Solids: Solidification and Melting .2 Characterization of the Phenomena .3 Delays in the Transition: Supercooling–Superheating .4 Methods of Observation and Measurement .1 The Lindemann Model .2 The Role of Defects .3 Melting and Surface of Materials .1 Theoretical Approach to Crystallization with Intermolecular Potentials .2 Case of Colloids .3 Crystallization and Melting of Polymers .5 Crystallization, Melting, and Interface .2 Size Effect on Small Particles .3 The Special Case of Ice .6 Very Numerous Applications .1 Melting – Solidification in Metallurgy .2 Molding of Polymers .3 Production of Sintered Ceramics.
121 4 Phase Transitions in Fluids .1 The Approach with Equations of State .2 The Liquid–Gas Transition in Simple Liquids .1 Van der Waals Equation of State .2 The Law of Corresponding States .3 Behavior Near the Critical Point .3 Thermodynamic Conditions of Equilibrium .1 Liquid–Gas Equilibrium .com Contents XI 4.3 Clausius–Clapeyron and Ehrenfest Equations .4 Main Classes of Equations of State for Fluids .2 One–Component Fluids .3 Variants of the van der Waals Equation .5 Metastable States: Undercooling and Overheating .1 Returning to Metastability .2 Drops and Bubbles Formation .6 Simulation of Phase Transitions .3 Monte Carlo Method .7 Mixture of Two Components .1 Conditions of Phase Equilibrium in a Binary Mixture .2 Systems in the Vicinity of a Critical Point .3 Equation of State of Mixtures .4 Mixtures of Polymers or Linear Molecules .5 Binary Mixtures far from the Critical Point. 159 5 The Glass Transition .2 The Glass Transition .2 Behavior of the Viscosity .3 Relaxation and Other Time Behaviors .3 The Structure of Glasses .1 Mode Coupling Theory .3 Models for Biological Systems. 185 6 Gelation and Transitions in Biopolymers .1 The Gel State and Gelation .1 Characterization of a Gel .2 The Different Types of Gels .2 Properties of Gels .3 A Model For Gelation: Percolation .1 The Percolation Model .1 An Important Gel: Gelatin .3 Modeling of the Coil ⇔ Helix Transition .com XII Contents 6.5 Main Applications of Gels and Gelation. 209 7 Transitions and Collective Phenomena in Solids.1 Transitions with Common Characteristics .2 The Order–Disorder Transition in Alloys .1 Characterization of Magnetic States .2 The Molecular Field Model .2 The Broad Categories of Ferroelectrics .3 Theoretical Models – the Landau Model .6 Universality of Critical Phenomena .1 Critical Exponents and Scaling Laws .2 Renormalization Group Theory.
245 8 Collective Phenomena in Liquids: Liquid Crystals and Superfluidity .1 Partially Ordered Liquid Phases .2 Definition of Order in the Liquid Crystal State .3 Classification of Mesomorphic Phases .4 The Nematic Phase and its Properties .5 The Many Applications of Liquid Crystals .6 Mesomorphic Phases in Biology .2 Superfluidity of Helium .2 Superfluidity in Helium 3. 301 9 Microstructures, Nanostructures and Phase Transitions .1 The Importance of the Microscopic Approach .2 Microstructures in Solids .1 Solidification and Formation of Microstructures .2 A Typical Example: The Martensitic Transformation .3 Singular Phases: The Quasicrystals .4 The Special Case of Sintering in Ceramics .com Contents XIII 9.5 Microstructures in Ferromagnetic, Ferroelectric, and Superconducting Phases .3 Microstructures in Fluid Phases .4 Microstructure, Nanostructures, and Their Implications in Materials Technology. 329 10 Transitions in Thin Films .1 Monolayers at the Air–Water Interface .1 The Role of Surfactants .2 Examples of Molecules Forming Monolayers .3 Preparation and Thermodynamics Study of Monolayers .4 Phase Diagram of a Monolayer .2 Monolayer on the Surface of a Solid .3 Melting and Vitification of Thin Films. 345 11 Phase Transitions under Extreme Conditions and in Large Natural and Technical Systems .1 Phase Transitions under Extreme Conditions .2 Equations of State and Phase Transitions under Extreme Conditions .4 The Plasma State .5 Bose–Einstein Condensates at Extremely Low Temperature .2 The Role of Phase Transitions in the Ocean–Atmosphere System .1 Stability of an Atmosphere Saturated with Water Vapor .2 Thermodynamic Behavior of Humid Air .3 Formation of Ice in the Atmosphere – Melting of Ice and Climate .3 Phase Transitions in Technical Systems .1 Vaporization in Heat Engines .2 The Cavitation Phenomenon .4 Phase Transitions and Energy Storage.
374 Answers to Problems. Conditions for Phase Equilibrium .com XIV Contents B. Percus–Yevick Equation. Renormalization Group Theory .