CHEMISTRY AND PHYSICS OF MECHANICAL HARDNESS John J. Gilman A JOHN WILEY & SONS, INC., PUBLICATION CHEMISTRY AND PHYSICS OF MECHANICAL HARDNESS CHEMISTRY AND PHYSICS OF MECHANICAL HARDNESS John J. Gilman A JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. 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Strength of materials. I. Title. TA418.42.G55 2009 620.1′126–dc22 2008038594 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 TABLE OF CONTENTS Preface xi 1 Introduction 1 1.1 Why Hardness Matters (A Short History) 1 1.2 Purpose of This Book 5 1.3 The Nature of Hardness 7 References 10 2 Indentation 11 2.1 Introduction 11 2.2 The Chin-Gilman Parameter 14 2.3 What Does Indentation Hardness Measure? 14 2.4 Indentation Size Effect 20 2.5 Indentation Size (From Macro to Nano) 22 2.6 Indentation vs. Scratch Hardness 23 2.7 Blunt or Soft Indenters 24 2.8 Anisotropy 24 2.9 Indenter and Specimen Surfaces 25 References 25 3 Chemical Bonding 27 3.1 Forms of Bonding 27 3.2 Atoms 28 3.3 State Symmetries 29 3.4 Molecular Bonding (Hydrogen) 31 3.5 Covalent Bonds 36 3.6 Bonding in Solids 41 3.6.1 Ionic Bonding 41 3.6.2 Metallic Bonding 43 3.6.3 Covalent Crystals 44 3.7 Electrodynamic Bonding 45 3.8 Polarizability 47 References 48 v vi TABLE OF CONTENTS 4 Plastic Deformation 51 4.1 Introduction 51 4.2 Dislocation Movement 52 4.3 Importance of Symmetry 55 4.4 Local Inelastic Shearing of Atoms 56 4.5 Dislocation Multiplication 57 4.6 Individual Dislocation Velocities (Microscopic Distances) 59 4.7 Viscous Drag 60 4.7.1 Pure Metals 61 4.7.2 Covalent Crystals 62 4.8 Deformation-Softening and Elastic Relaxation 62 4.9 Macroscopic Plastic Deformation 63 References 64 5 Covalent Semiconductors 67 5.1 Introduction 67 5.2 Octahedral Shear Stiffness 69 5.3 Chemical Bonds and Dislocation Mobility 71 5.4 Behavior of Kinks 75 5.5 Effect of Polarity 77 5.6 Photoplasticity 79 5.7 Surface Environments 80 5.8 Effect of Temperature 80 5.9 Doping Effects 80 References 81 6 Simple Metals and Alloys 83 6.1 Intrinsic Behavior 83 6.2 Extrinsic Sources of Plastic Resistance 85 6.2.1 Deformation-Hardening 85 6.2.2 Impurity Atoms (Alloying) 87 6.2.3 Precipitates (Clusters, Needles, and Platelets) 89 6.2.4 Grain-Boundaries 90 6.2.5 Surface Films (Such as Oxides) 94 6.2.6 Magnetic Domain Walls 95 6.2.7 Ferroelectric Domain-Walls 96 6.2.8 Twin Boundaries 96 References 96 7 Transition Metals 99 7.1 Introduction 99 7.2 Rare Earth Metals 101 References 101 TABLE OF CONTENTS vii 8 Intermetallic Compounds 103 8.1 Introduction 103 8.2 Crystal Structures 104 8.2.1 Sigma Phase 104 8.2.2 Laves Phases 105 8.2.3 Ni3Al 107 8.3 Calculated Hardness of NiAl 112 8.4 Superconducting Intermetallic Compounds 113 8.5 Transition Metal Compounds 115 References 116 9 Ionic Crystals 119 9.1 Alkali Halides 119 9.2 Glide in the NaCl Structure 120 9.3 Alkali Halide Alloys 123 9.4 Glide in CsCl Structure 124 9.5 Effect of Imputities 124 9.6 Alkaline Earth Fluorides 126 9.7 Alkaline Earth Sulfi des 128 9.8 Photomechanical Effects 128 9.9 Effects of Applied Electric Fields 129 9.10 Magneto-Plasticity 129 References 129 10 Metal-Metalloids (Hard Metals) 131 10.1 Introduction 131 10.2 Carbides 132 10.3 Tungsten Carbide 134 10.4 Borides 136 10.5 Titanium Diboride 137 10.6 Rare Metal Diborides 138 10.7 Hexaborides 138 10.8 Boron Carbide (Carbon Quasi-Hexaboride) 140 10.9 Nitrides 141 References 141 11 Oxides 143 11.1 Introduction 143 11.2 Silicates 143 11.2.1 Quartz 144 11.2.2 Hydrolytic Catalysis 146 11.2.3 Talc 146 11.3 Cubic Oxides 147 11.3.1 Alkaline Earth Oxides 147 viii TABLE OF CONTENTS 11.3.2 Perovskites 148 11.3.3 Garnets 150 11.3.3.1 (Y3Al5O12)—YAG 151 11.4 Hexagonal (Rhombohedral) Oxides 152 11.4.1 Aluminum Oxide (Sapphire) 152 11.4.2 Hexaboron Oxide 153 11.5 Comparison of Transition Metal Oxides with “Hard Metals” 155 References 156 12 Molecular Crystals 157 12.1 Introduction 157 12.2 Anthracene 158 12.3 Sucrose 159 12.4 Amino Acids 159 12.5 Protein Crystals 160 12.6 Energetic Crystals (Explosives) 161 12.7 Commentary 161 References 161 13 Polymers 163 13.1 Introduction 163 13.2 Thermosetting Resins (Phenolic and Epoxide) 164 13.3 Thermoplastic Polymers 165 13.4 Mechanisms of Inelastic Plasticity 166 13.5 “Natural” Polymers (Plants) 166 13.6 “Natural” Polymers (Animals) 168 References 168 14 Glasses 171 14.1 Introduction 171 14.2 Inorganic Glasses 172 14.3 Metallic Glasses 176 14.3.1 Hardness—Shear Modulus Relationship 177 14.3.2 Stable Compositions 180 References 180 15 Hot Hardness 183 15.1 Introduction 183 15.2 Nickel Aluminide versus Oxides 184 15.3 Other Hard Compounds 184 15.4 Metals 185 TABLE OF CONTENTS ix 15.5 Intermetallic Compounds 187 References 187 16 Chemical Hardness 189 16.1 Introduction 189 16.2 Defi nition of Chemical Hardness 190 16.3 Physical (Mechanical) Hardness 192 16.4 Hardness and Electronic Stability 193 16.5 Chemical and Elastic Hardness (Stiffness) 194 16.6 Band Gap Density and Polarizability 194 16.7 Compression Induced Structure Changes 195 16.8 Summary 196 References 196 17 “Superhard” Materials 197 17.1 Introduction 197 17.2 Principles for High Hardness 197 17.3 Friction at High Loads 198 17.4 Superhard Materials 199 References 200 Index 203 PREFACE For the structural applications of materials, there is no more useful measurable property than mechanical hardness. It quickly and conveniently probes the strengths of materials at various scales of aggregation. Firstly, it does this at the human scale (Brinell hardness — millimeters to centimeters). Secondly, it does so at a microscopic scale (Vickers microhardness — 1 to 100 microns). And thirdly, it does so at a “ nanoscale ” (nanoindentation — 10 to 1000 nanometers). For millenia, hardness has been used to characterize materials; for example, to describe various kinds of wood ranging from soft balsa wood to hard maple and ironwood. Mineralogists have used it to characterize differing rocks, and gemologists for the description of gems. Ceramists and metallurgists depend on it for classifying their multitude of products. Hardness does not produce a complete characterization of the strengths of materials, but it does sort them in a general way, so it is very useful for “ quality control ” ; for the development of new materials; and for developing prototypes of devices and processes. Furthermore, mechanical hardness is closely related to chemical hardness, which is a measure of chemical bond stability (reactivity). In the case of metals the connection is somewhat indirect, but nevertheless exists. The principal intention of the present book is to connect mechanical hardness numbers with the physics of chemical bonds in simple, but defi nite (quantitative) ways. This has not been done very effectively in the past because the atomic processes involved had not been fully identifi ed.