Interfaces in Materials Atomic Structure, Thermodynamics and Kinetics of Solid-Vapor, Solid-Liquid and Solid-Solid Interfaces

by Howe, James M.

• ISBN13: 9780471138303
• ISBN10: 0471138304
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-02-27
• Publisher: Wiley-Interscience

Summary

A thorough exploration of the atomic structures and properties of the essential engineering interfaces-an invaluable resource for students, teachers, and professionalsThe most up-to-date, accessible guide to solid-vapor, solid-liquid, and solid-solid phase transformations, this innovative book contains the only unified treatment of these three central engineering interfaces. Employing a simple nearest-neighbor broken-bond model, Interfaces in Materials focuses on metal alloys in a straightforward approach that can be easily extended to all types of interfaces and materials. Enhanced with nearly 300 illustrations, along with extensive references and suggestions for further reading, this book provides: A simple, cohesive approach to understanding the atomic structure and properties of interfaces formed between solid, liquid, and vapor phases Self-contained discussions of each interface-allowing separate study of each phase transformation A comparative look at the different interfaces, including atomic structure and crystallography; anisotropy, roughening, and melting; interfacial stability and segregation; continuous and ledge growth models; and atomistic modeling An analysis of nearest-neighbor broken-bond results against thermodynamic and kinetic descriptions of the interfaces Problem sets at the end of each chapter, emphasizing the key concepts detailed in the text Spanning the fields of chemical, electrical and computer engineering, materials science, solid-state physics, and microscopy, Interfaces in Materials bridges a major gap in the literature of surface and interface science.

Author Biography

JAMES M. HOWE, PhD, is Associate Professor of Materials Science and Engineering at the University of Virginia. He is the recipient of numerous honors and awards for his research on transformation interfaces and electron microscopy, and his articles have appeared in such journals as Philosophical Magazine A, Acta Metallurgica et Materialia, and Ultramicroscopy.

Table of Contents

Preface	xiii	(2)
Acknowledgments	xv	(2)
Symbols	xvii
1 INTRODUCTORY MATERIAL	1	(44)
1 Atomic Bonding	3	(14)
1.1 Interatomic Potential and Binding Energy	3	(4)
1.2 Correlation of Binding Energy and Interatomic Potential with Physical Properties	7	(6)
1.2.1 Interatomic Potential, Binding Energy and Enthalpy of Sublimation	7	(1)
1.2.2 Interatomic Potential and Theoretical Strength	7	(4)
1.2.3 Interatomic Potential and Vibrational Frequency	11	(2)
1.3 Embedded Atom, Monte Carlo and Molecular Dynamics Calculations	13	(2)
1.4 Problems	15	(2)
2 Regular Solution (Qausi-Chemical) Model	17	(28)
2.1 The Gibbs Free Energy of Binary Solutions	17	(2)
2.2 Ideal Solutions	19	(1)
2.3 Chemical Potential	20	(2)
2.4 Regular Solutions	22	(4)
2.5 Systems with a Miscibility Gap	26	(2)
2.6 Ordered Alloys	28	(4)
2.7 Effect of Temperature on Solid Solubility	32	(2)
2.8 Calculation of Regular Solution Constant and EAB from Phase Diagrams	34	(3)
2.9 Generality of the Regular Solution Model	37	(1)
2.10 Problems	38	(4)
Part I References and Additional Reading	42	(3)
II SOLID-VAPOR INTERFACES	45	(156)
3 Surfaces Energy	47	(24)
3.1 Definition of Surface Energy and Thermodynamic Functions	47	(6)
3.2 Correlation of Solid Surface Energy with Physical Properties	53	(2)
3.3 Calculation of Surface Energy Using a Nearest Neighbor Broken-Bond Model	55	(5)
3.4 The y Plot	60	(3)
3.5 The Wulff Plot and Wulff Construction	63	(6)
3.5.1 Wulff Plot	63	(1)
3.5.2 Wulff Consturction	63	(6)
3.6 Problems	69	(2)
4 Surface Structure	71	(56)
4.1 Terrace-Ledge-Kink Model of Surfaces	71	(4)
4.2 Surface Defects and Surface Roughening	75	(11)
4.2.1 Analytical Treatment of Terrace and Ledge Roughening	78	(5)
4.2.2 Computer Calculation of the Equilibrium Structure of Crystal Surfaces	83	(3)
4.3 Surface Crystallography	86	(4)
4.4 Surface Relaxation and Reconstruction	90	(10)
4.5 Phase Transformations and Surface Melting	100	(12)
4.5.1 Surface Phase Transformations	102	(7)
4.5.2 Surface Melting	109	(3)
4.6 Particle Size, Surface Stress and Stability	112	(11)
4.7 Problems	123	(4)
5 Crystal Growth from the Vapor	127	(23)
5.1 Continuous Growth	127	(1)
5.2 Growth of Vicinal Surfaces	127	(22)
5.2.1 Sources of Ledges (Steps)	129	(1)
5.2.2 Two-Dimensional Nucleation and Growth	129	(4)
5.2.3 Surface Diffusion	133	(4)
5.2.4 Crystal Growth by Ledge Motion	137	(4)
5.2.5 Crystal Growth by Screw Dislocations	141	(3)
5.2.6 Comparison with Experiment	144	(5)
5.3 Problems	149	(1)
6 Thermodynamics of Multicomponent Systems and Surface Segregation	150	(26)
6.1 Binary Systems--The Surface Excess	150	(2)
6.2 Gibb's Equation	152	(3)
6.3 Adsorption Isotherms	155	(1)
6.4 Surface Segregation	156	(12)
6.5 Alloy Surface Phase Transformations	168	(5)
6.6 Problems	173	(3)
7 Surface Films	176	(25)
7.1 Contact Angle, Wetting, Interfacial Energy and Work of Adhesion	176	(5)
7.2 Epitaxial Layers	181	(10)
7.2.1 Lattice Mismatch	183	(2)
7.2.2 Elastic Strain Energy	185	(1)
7.2.3 Stability of Heteroepitaxial Layers	185	(4)
7.2.4 Epitaxy Between Different Crystal Structures	189	(2)
7.3 Problems	191	(3)
Part II References and Additional Reading	194	(7)
III SOLID--LIQUID INTERFACES	201	(94)
8 Liquids	203	(16)
8.1 The Structure of Liquids	203	(7)
8.2 Properties of Liquids	210	(8)
8.2.1 Surface Energy of Liquids	210	(1)
8.2.2 Segregation in Liquids	210	(4)
8.2.3 Thickness of Liquid--Vapor Interface	214	(4)
8.3 Problems	218	(1)
9 Interfacial Structure and Energy	219	(37)
9.1 Solid/Liquid Interfacial Energy	219	(5)
9.2 Atomic Structure of the Solid--Liquid Interface	224	(12)
9.2.1 Spaepen's Model	224	(9)
9.2.2 Computer Models	233	(3)
9.3 Anisotropy of Solid--Liquid Interfacial Energy	236	(6)
9.4 Interfacial Roughening	242	(11)
9.4.1 Jackson's Parameter	242	(4)
9.4.2 Kinetic Roughening	246	(7)
9.5 Problems	253	(3)
10 Crystal Growth from the Liquid	256	(13)
10.1 Continuous Growth	256	(2)
10.2 Lateral Growth	258	(5)
10.2.1 Ledge Velocity	258	(1)
10.2.2 Two-Dimensional Nucleation Rate	259	(1)
10.2.3 Mononuclear Growth Rate	260	(1)
10.2.4 Polynuclear Growth Rate	261	(1)
10.2.5 Screw Dislocation Growth	262	(1)
10.3 Comparison with Experiment	263	(5)
10.4 Problems	268	(1)
11 Solute Partitioning and Morphological Stability	269	(21)
11.1 Plane-Front Solidification of Pure Substances	270	(4)
11.1.1 Temperature Gradient and Interface Morphology	270	(4)
11.1.2 Heat Flow	274	(1)
11.2 Plane-Front Solidification of Single-Phase Alloys	274	(14)
11.2.1 Equilibrium Partition Ratio	274	(4)
11.2.2 Solute Redistribution During Solidification	278	(2)
11.2.3 Constitutional Supercooling and Cell Formation	280	(2)
11.2.4 Morphological (Mullins-Sekerka) Stability Theory	282	(6)
11.3 Problems	288	(2)
Part III References and Additional Reading	290	(5)
IV SOLID--SOLID INTERFACES	295	(196)
12 Introduction to Solid--Solid Interfaces	297	(10)
12.1 Types of Solid--Solid Interfaces	298	(1)
12.2 Atomic Matching at Solid--Solid Interfaces	299	(7)
12.3 Problem	306	(1)
13 Structure and Energy of Homophase Interfaces	307	(70)
13.1 Grain Boundary Energy	307	(2)
13.2 Grain Boundary Structure	309	(62)
13.2.1 Dislocation Models	309	(16)
Symmetrical Tilt Grain Boundary	309	(6)
Asymmetrical Tilt Grain Boundary	315	(2)
Twist Grain Boundary	317	(2)
Degrees of Freedom of a General Grain Boundary	319	(3)
Frank's Formula for the Dislocation Content of a Boundary	322	(3)
13.2.2 O-Lattice Formulation	325	(6)
13.2.3 Coincident Site and Displacement Shift Complete Lattices	331	(15)
Coincident Site Lattice	333	(4)
Displacement Shift Complete Lattice	337	(4)
Structure and Properties of Grain and Interphase Boundary Line Defects	341	(5)
13.2.4 Atomistic Modeling of Grain Boundary Structure and Energy	346	(9)
Structural (Polyhedral) Unit Model	347	(2)
Structure--Energy Correlation	349	(6)
13.2.5 Stacking Faults and Twin Boundaries	355	(3)
13.2.6 Roughening, Phase Transformations and Melting	358	(2)
13.2.7 TLK Model of Grain Boundary Motion	360	(5)
13.2.8 Segregation to Grain Boundaries	365	(6)
13.3 Problems	371	(6)
14 Structure and Energy of Heterophase Interfaces	377	(71)
14.1 Interphase Boundary Energy	378	(1)
14.2 Coherent Interphase Boundary Structure and Energy	379	(15)
14.2.1 Becker Model	379	(1)
14.2.2 Cahn-Hilliard (Gradient Energy) Model	380	(6)
14.2.3 Discrete Lattice Plane Model	386	(8)
14.3 Roughening and Phase Transformations at Interphase Boundaries	394	(6)
14.4 Antiphase Boundaries	400	(6)
14.5 Semicoherent Interphase Boundaries	406	(17)
14.5.1 Geometry of Semicoherent Interfaces	408	(2)
14.5.2 Energy of Semicoherent Interfaces	410	(5)
14.5.3 Incoherent Interfaces	415	(1)
14.5.4 Comparison of the Compositional and Structural Components of the Interphase Boundary Energy	416	(3)
14.5.5 Atomistic Modeling of Semicoherent Interphase Boundaries	419	(4)
14.6 Interfaces Between Phases with Different Bravais Lattices	423	(14)
14.6.1 Orientation Relationships at Heterophase Interfaces	424	(4)
14.6.2 High-Index Heterophase Interfaces	428	(7)
14.6.3 Atomistic Calculations	435	(2)
14.7 Terrace-Ledge-Kink Structure of Interphase Boundaries	437	(5)
14.8 Problems	442	(6)
15 Growth of Solid-Solid Heterophase Interfaces	448	(22)
15.1 Diffusion Versus Interface-Controlled Growth	448	(3)
15.2 Continuous Growth of Planar Interface	451	(1)
15.3 Diffusion-Controlled Lenghthening of Plates or Needles	452	(1)
15.4 Growth by Ledges	453	(7)
15.5 Ledge Interactions	460	(2)
15.6 Growth by Kinks in Ledges	462	(1)
15.7 Comparison with Experiment	463	(5)
15.8 Problems	468	(2)
16 Morphological Stability and Segregation	470	(12)
16.1 Morphological Stability	470	(5)
16.2 Segregation to Heterophase Interfaces	475	(5)
16.3 Problems	480	(2)
Part IV References and Additional Reading	482	(9)
Appendix A. Fundamental Constants and Conversion Factors	491	(1)
Appendix B. Physical Data of the Elements	492	(5)
Appendix C. Surface Data from Alonso and March	497	(3)
Appendix D. Circle Patterns for Constructing Interfaces	500	(5)
Index	505