KINETICS IN MATERIALS SCIENCE AND ENGINEERING KINETICS IN MATERIALS SCIENCE AND ENGINEERING Dennis W. Readey University Emeritus Professor Colorado School of Mines, Golden, USA Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Cover Image: Courtesy of Jaehyung Lee. From “Vapor Phase Sintering of Hematite in HCl” (PhD Thesis. The Ohio State University, 1984). CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2017 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20160830 International Standard Book Number-13: 978-1-4822-3566-1 (Pack - Book and Ebook) This book contains information obtained from authentic and highly regarded sources. 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Identifiers: LCCN 2016018601| ISBN 9781482235661 (alk. paper) | ISBN 1482235668 (alk. paper) Subjects: LCSH: Materials science. | Chemical processes. | Dynamics. | Diffusion. Classification: LCC TA403.6 .R376 2016 | DDC 620.1/12--dc23 LC record available at https://lccn.loc.gov/2016018601 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To my wife Suzann for her encouragement and patience Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix For the Instructor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii For the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii Section i — introduction to Kinetics Chapter 1. Kinetics and Materials Science and Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Section ii — Reaction Kinetics Chapter 2. Introduction to Kinetic Processes in Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Chapter 3. Second-Order and Multistep Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Chapter 4. Temperature Dependence of the Reaction Rate Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 Chapter 5. Heterogeneous Reactions:Gas–Solid Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Section iii — Phase transformations Chapter 6. Thermodynamics of Surfaces and Interfaces and Some Consequences . . . . . . . . . . . . . . . . . . . . .153 Chapter 7. Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195 vii viii Kinetics in Materials Science and Engineering Section iV — Diffusion with a constant Diffusion coefficient Chapter 8. Fundamentals of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .257 Chapter 9. Atomistics of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275 Chapter 10. Steady-State Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .333 Chapter 11. Solutions to Fick’s Second Law: Infinite and Semi-Infinite Boundary Conditions . . . . . . . . . . . . .381 Chapter 12. Diffusion with Finite Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Section V — Fluxes, Forces, and interdiffusion Chapter 13. Fluxes, Forces, and Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447 Chapter 14. Interdiffusion and Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .479 Chapter 15. Interdiffusion in Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .519 Chapter 16. Spinodal Decomposition Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .563 Appendix I: List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .591 Appendix II: Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .601 Preface T his book is intended to be an undergraduate text for junior- and senior-level students majoring in materials science and engineering (MSE). Most MSE undergraduate programs have a one-semester kinetics course in their curricula that has taken the place of a classical physical chemistry course and one or more courses on materials processing. This book is not intended to be a reference work that summarizes and evaluates all of the reactions and phase transformations of importance in MSE, although some unique topics are presented. Given the breadth of the field today—metals, ceramics, electronic mate- rials, polymers, biomaterials, and composites—it is not feasible to cover all of kinetics. Nevertheless, the book does cover considerably more material than can be covered in a one-semester course and includes approaches and topics that are rarely found elsewhere that might be useful to graduate students, research- ers, and industrial practitioners. One goal of this book is to incorporate important concepts that all students in MSE should be exposed to at some point in their careers based on the author’s personal expe- rience as a student, researcher, practicing engineer, and instructor over a number of years. The primary goal is to develop simple mathematical models, involving process variables such as temperature, pressure, composition, and time, to provide a fundamental model-based understanding of commercially impor- tant materials processes critical to the development, fabrication, and application of materials. In doing so, at the expense of additional equations, most of the mathematical steps necessary to develop a model are explicitly presented so the student, or reader, can follow the text without the absolute necessity of an instructor for interpretation and insertion of the missing steps—frequently the case in many textbooks. This, of course, means more pages to cover a given topic. WHY THIS BOOK There are several reasons why this book was written. First, there is limited textual material for the junior/ senior-level general courses in MSE. There are many introduction to materials, or similarly named, text- books. Most of these texts do not cover the different types of materials equitably, usually reflecting the author’s understandable partiality to a specific material type based on his or her own experience and interests. Unapologetically, some partiality will be found here as well. More importantly, virtually none of introductory texts present kinetics in sufficient depth to be of use in an upper level course. Also, many texts approach important kinetic topics with a black box or “…it can be shown that…” methodology. For example, most introductory texts have sections on solid state diffusion and they tell you that carbon dif- fuses into steel, and its concentration, C, as a function of distance, x, and time, t, is given by  x  C=Cserfc   4Dt  ix