Chemical Metallurgy, principles and practice, Chiranjib Kumar Gupta

Chiranjib Kumar GuptaChemical Metallurgy

Chemical Metallurgy: Principles and Practice. Chiranjib Kumar GuptaCopyright 2003 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-30376-6

Chiranjib Kumar Gupta

Chemical Metallurgy

Principles and Practice

Author

Dr. Chiranjib Kumar GuptaBhabha Atomic Research CentreMaterials GroupMumbai 400085India

This book was carefully produced. Nevertheless,author and publisher do not warrant the informationcontained therein to be free of errors. Readers areadvised to keep in mind that statements, data,illustrations, procedural details or other items mayinadvertently be inaccurate.

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2003 Wiley-VCH Verlag GmbH & Co. KGaA,WeinheimAll rights reserved (including those of translationinto other languages). No part of this book may bereproduced in any form by photoprinting, microfilm,or any other means nor transmitted or translatedinto a machine language without written permissionfrom the publishers.

Printed in the Federal Republic of GermanyPrinted on acid-free and low chlorine paper

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ISBN 3-527-30376-6

VForeword

Dr. C. K. Gupta is a very distinguished colleague of mine. I have been familiar with his pro-fessional career over a long period. A very large number of research papers, reviews, andseveral books authored by him bear ample testimony to the diverse and wide-ranging con-tributions he has made to date to the field of chemical metallurgy. I was indeed very happyto accept the invitation from him to write a foreword for the present volume entitled, Chemi-cal Metallurgy Principles and Practice, being published by Wiley-VCH Verlag, Germany.

This volume provides in one place a self-contained and adequately detailed coverage ofthe chemical metallurgy of the major metals, common as well as less common. It has beenbrought into being as an exceedingly well-structured treatise. The presentation has beenorganised in seven chapters. The first chapter gives a general appraisal of the whole field ofchemical metallurgy. The coverage also includes a brief account of resources. The next twochapters are devoted to thermodynamics and kinetics and to processing of minerals. Theremaining three chapters deal, respectively, with pyrometallurgy, hydrometallurgy, andelectrometallurgy. The last chapter attends to energy and environmental considerations.Physicochemical principles provided for the various unit operations and description of thekey details of the processes deserve special mention as being among the attractive featuresof this volume. One must also additionally note the emphasis laid on the less commonmetals in the presentation. This is decidedly an additional special feature of the book. Chemi-cal metallurgy of the less common metals described with pertinent principles involved hasnot been done earlier in one place as has been accomplished in this publication. The abun-dance of illustrations and the comprehensive collection of carefully selected references ap-pended to each chapter add to the value and enhance considerably the overall strength ofthe book. On the whole, the presentation displays an imaginative and competent handlingof the subject matter and really reaches out to the readers.

The volume deals with a very wide technical field and will be of interest and relevance tomany disciplines, particularly metallurgy, chemical engineering, and chemistry. It will un-doubtedly be a valuable addition to the list of available books dealing with chemical metal-lurgy. At the same time, this volume will be very useful to professionals working in the areaof extractive and process metallurgy. The present book has had the benefit of Dr. Guptaswide and long-standing experience in the field in full measure and will certainly be greatlyvalued by those to whom it is addressed. I wish this publication all success and hope it willbe as useful as the other books which Dr. Gupta has authored.

India, May 2003 B. BhattacharjeeDirector of Bhabha Atomic Research Centreand Member of Atomic Energy Commission


VII

Preface

As the title, Chemical Metallurgy: Principles and Practice implies, this text blends theorywith practice covering, of course, a good deal of descriptive items on hows and whys ofextraction and processing of metals and materials. While the processes for the extraction ofthe common metals have been provided in sufficient detail, I have tried to go in equaldepth, if not more, to provide focus on the less common metals. I have, however, avoidedlengthy descriptions of current commercial practices as these change rapidly. Rather,selected examples have been presented to illustrate the various principles dealt with in thetext. It is expected the readers will supplement this text with appropriate examples of cur-rent practices. All along I have made an effort to lead the treatment to a point where thereaders will find the transition to more advanced and specialized metallurgical engineeringtextbooks, texts, and monographs with emphasis on chemical metallurgy quite easy.

This book altogether contains seven chapters. In Chapter 1, I have endeavored to organ-ize the text with a view to acquainting the readers with a miscellany of relevant informationand preparing them for going into the contents of the subsequent chapters. Chapter 2 dealswith mineral processing, which usually takes the position as the principal front-end opera-tion in the overall process flowsheet for metal extraction. Chapter 3 pertains to thermo-dynamics and kinetics which provide unequivocally a sound basis for the understanding ofthe processes. The next three chapters delve into pyro-, hydro-, and electro-metallurgy, inthat order. Chapter 7 addresses certain representative issues concerning energy consump-tion and environmental pollution aspects especially pertinent to chemical metallurgyoperations.

It is difficult for an author to praise the virtues of his own book. However, just to say a fewwords, I may add that, as pointed out, I have systematized the organization of the text in thechapters by presenting the process principles first and then following up with process prac-tice. I have in my opinion adopted a lucid style readable, interesting, intelligible, andinformative for a wide and varied audience. It has on the whole been a delightful experi-ence for me to produce and place this book for the readership it will fetch. May I end bysaying that I earnestly believe the book will provide an interesting reading and knowledge,and will certainly be highly successful in putting the readers into the fascinating worldof preparative metallurgy, into the arduous journeys through which different metals andmaterials traverse to come into their useful beings and finally make themselves available inthe service of man. A carefully selected reference list and a good number of clear illustra-tions may be treated as additional features which should not be lost sight of. All thesepresentations have not been carried out without incorporating the backing of the principlesinvolved and this very element should go to provide additional attractions and spice, so tosay, for the book.


VIII

Acknowledgements

For kind permission to use matter of which they hold the copyright, in the preparation ofdiagrams and tables, the author is most grateful to the following:

Academic PressAmerican Institute of Mining, Metallurgical and Petroleum Engrs., Inc.CRC PressElsevier Science PublishersErrol G. Kelly and David G. SpottiswoodFreund Publishing House Ltd.Gordon and Breach Publishers, Inc.Hayes Publishing Co.John Wiley & Sons, Inc.Macmillan Publishing Co.Maxwell Macmillan Canada, Inc.McGraw Hill Publishing Co.Pergamon Press Ltd.Blackwell Science Ltd.ButterworthsThe Society of Chemical IndustryLongmansMcGraw-Hill International Book Company


IX

Appreciation

No reader of this book can fail to recognise how much I owe to others who have written earlierin this field. To the authors and the editors of the references cited in this volume I expressmy heartfelt thanks. A book is very much a team project. I am truly indebted to my colleagues,Tapan Kumar Mukherjee, Ashok Kumar Suri, N. Krishnamurthy, and Pradip Mukhopadhyay,whose counsels I sought and whose opinions and advice, so generously given, have largelydetermined the scope and character of what I have written. All have greatly brought life tothe project in the form of unique insights in chemical metallurgy.

Prof. Kenneth N. Han of South Dakota School of Mines and Prof. Paul Duby of HenryKrumb School of Mines have had occasions to review this work. They provided knowledge,insight, and plain common sense to guide me during the process of development of thiswork. I wish to record my deepest gratitude to them. In the same breath, my deepest appre-ciation goes to Pradeep Mukhopadhyay, who has patiently gone through the writing andspared me in no way to keep mistakes at bay. Despite all the thorough inputs from manyquarters, if errors have still remained they are all my own responsibility, of course, and Ihope readers who find them will communicate them to me or the publisher. This would goa long way to provide a very valuable chance to carry out necessary amendments in thefuture.

It is a pleasure to acknowledge the devoted services of Poonam Khattar, to whom workconnected with the mechanics of manuscript preparation extending to producing com-puter-generated art work has become a labor of love. I also wish to mention Yatin Thakurwho has continued to be associated with me in commendably executing draughtsmanshipduties.

Finally, I express my appreciation to all the members at Wiley-VCH, particularly to ClaudiaBarzen, Maike Petersen, and Martin Ottmar for helping me in many ways right from theinception to the finishing of this publication.

This volume, which is the most significant undertaking in my authorship career in met-allurgical literature, could not have been attempted and brought to completion without theunderstanding and patience of my wife, Chandrima, and my son, Chiradeep. Their sacri-fices were great; my gratitude to them is profound. Throughout the preparation of thisbook, I have derived strength and inspiration from the work and the percepts of my latefather, Probodh Chandra Gupta. It is with a sense of warm affection, great humility, andprofound respect that I am dedicating this work to his memory.

Illustrations may be treated as additional features of the book which should not be lostsight of. I have taken care to see that all these presentations have the backing of the princi-ples involved and this very element should go to provide additional attractions and spice, soto say, for the book.


XI

Contents

Foreword V

Preface VII

Acknowledgements VIII

Appreciation IX

1 Acquaintance 11.1 Introduction 11.2 Materials 41.3 Some Characteristics of Metals 51.3.1 General 51.3.2 Electronic Structure 51.3.3 Crystallography 71.3.3.1 Crystal Systems 81.3.3.2 Metallic Crystal Structures 101.3.4 Alloying 101.3.5 Mechanical Properties 111.3.5.1 Elastic Deformation 111.3.5.2 Plastic Deformation 141.3.5.3 Creep Deformation and Fatigue Deformation 251.3.5.4 Hardness 281.3.5.5 Toughness 301.4 Resources of Metals 311.4.1 General 311.4.2 Earths Crust 321.4.3 Minerals and Ores 351.4.4 Rocks and Ore Deposits 401.4.4.1 Igneous Processes of Rock and Ore Formation 421.4.4.2 Sedimentary Rocks and Sedimentary Processes of Ore Formation 461.4.4.3 Metamorphic Rocks and Ore Processes 501.4.5 Other Resources 511.5 Mineral Properties 531.6 Mining 581.6.1 Surface Mining 59


XII Contents

1.6.2 Underground Mining 591.7 Availability 601.8 Resource Classification 621.9 Minerals Description 621.9.1 Molybdenum 631.9.2 Nickel 661.9.3 Niobium-Tantalum 671.9.4 Rare Earths 681.9.5 Uranium 701.10 Extraction Flowsheets 771.10.1 Features 771.10.2 Process Routes 791.10.3 Process Reactors 811.10.3.1 Heat Sources 841.10.3.1.1 Solid Fuels 901.10.3.1.2 Liquid Fuels 1011.10.3.1.3 Gaseous Fuels 1071.10.3.2 Refractories 1091.10.3.2.1 Classification 1101.10.3.2.2 Physical and Chemical Characteristics 1121.11 Literature 116

2 Mineral Processing 1192.1 Introduction 1192.2 Particles 1202.2.1 Particle Shape 1212.2.1.1 Shape Factor 1212.2.1.2 Qualitative and Quantitative Definitions 1222.2.2 Particle Size 1242.2.2.1 Particle Size Measurement 1252.2.3 Surface 1292.2.3.1 Permeability 1292.2.3.2 Gas Adsorption 1292.3 Comminution 1302.3.1 Fracture of Materials 1312.3.1.1 Fracture Mechanisms 1342.3.2 Energy and Power Requirements 1342.3.2.1 Energy Size Relationship 1352.3.2.2 Bond Law 1352.3.2.3 Crushing Efficiency 1352.3.3 Liberation 1362.3.4 Machine Selection 1382.3.5 Machine Types 1392.3.5.1 Crushers 1402.3.5.2 Grinders 143

XIIIContents

2.3.6 Circuits 1432.3.7 Operational Aspects 1442.4 Mineral Separation 1462.5 Fluid Dynamic Principles 1502.5.1 Particle Settling Phenomena 1512.5.2 Free Settling and Hindered Settling 1552.5.3 Particle Separation 1572.6 Classification 1582.6.1 Classifier Machinery 1592.6.1.1 Mechanical Classifiers 1592.6.1.2 Hydraulic Classifiers 1602.6.1.3 Hydrocyclones 1612.7 Screening 1622.7.1 Passage of Particles 1632.7.2 Ideal and Actual Screens 1632.7.3 Material Balances 1652.7.4 Screen Efficiency and Capacity 1662.7.5 Types of Screens 1672.8 Gravity Concentration 1682.8.1 Gravity Separation Machines 1692.8.1.1 Jigs 1692.8.1.2 Spirals 1712.8.1.3 Tables 1732.8.1.4 Heavy Medium Separators 1752.9 Magnetic Separation 1762.9.1 Magnetic Separators 1792.9.2 Principles 1802.10 Electrostatic Separation 1822.10.1 Electrostatic Separators 1832.11 Flotation 1852.11.1 Principles 1872.11.2 Flotation Chemistry 1922.11.2.1 Surfactants 1932.11.2.1.1 Frothers 1942.11.2.1.2 Collectors 1962.11.2.1.3 Regulators 1992.11.2.2 Sulfide Flotation 2002.11.2.2.1 Principles 2012.11.2.2.2 Examples 2042.11.2.3 Natural Hydrophobicity 2052.11.3 Flotation Systems 2072.11.4 Flotation Machinery 2082.12 Dewatering 2102.12.1 Sedimentation 2102.12.1.1 Coagulation and Flocculation 211

XIV

2.12.1.2 Thickener Machinery 2122.12.2 Filtration 2122.12.3 Thermal Drying 2152.12.4 Evaporation 2162.13 Mineral Processing Flowsheets 2172.14 Literature 222

3 Thermodynamics and Kinetics 2253.1 Introduction (Thermodynamics) 2253.2 Zeroeth Law 2273.3 First Law 2273.4 Thermochemistry 2293.5 Second Law 2353.5.1 Entropy 2363.5.2 Free Energy 2393.6 Third Law 2443.7 Chemical Equilibrium 2473.7.1 Law of Mass Action 2493.7.2 Vant Hoff Isotherm 2563.7.3 Vant Hoff Isochore 2583.7.4 Le Chateliers Principle 2603.8 Free EnergyTemperature Diagrams 2613.8.1 Variation of Free Energy with Temperature 2613.8.2 Ellingham Diagrams 2623.9 Solutions 2693.9.1 Raoults Law 2703.9.2 Henrys Law 2723.9.3 Sieverts Law 2733.9.4 Activity and Activity Coefficient 2733.9.5 Free Energy of Formation of a Solution 2753.9.6 GibbsDuhem Equation 2783.9.7 Ideal Solution 2803.9.8 Nonideal Solutions 2813.9.9 Regular Solution 2833.10 Phases in Equilibria 2843.11 Phase Rule 2873.11.1 Applications 2893.12 Thermodynamic Data Presentation 2923.13 Introduction (Kinetics) 2923.14 Rate of Reaction 2933.15 Homogeneous Reactions 2943.15.1 Rate Equation 2953.15.2 Rate-Controlling Step 2973.15.3 Order of Reaction 2983.15.3.1 First-order Reactions 298

Contents

XV

3.15.3.2 Second-Order Reactions 3003.15.3.3 Consecutive Reactions 3013.15.3.4 Reversible Reactions 3023.15.4 Temperature Effect 3043.16 Heterogeneous Reactions 3053.16.1 Rate Equation 3073.16.2 Types of Reactions 3113.16.3 Heat and Mass Transfer 3113.16.3.1 Conduction 3123.16.3.2 Convection 3153.16.3.3 Radiation 3183.16.3.4 Mass Transfer by Diffusion 3213.16.3.5 Forced Convection 3263.16.4 Dimensionless Groups 3273.16.5 FluidSolid Reactions 3313.16.6 Reactions of Nonporous Particles 3323.16.7 Reactions of Porous Particles 3333.16.8 Reactions Among Solids Through Fluid Intermediates 3343.17 Elements of Process Reactor Design 3353.18 Temperature Effects 3363.19 Catalysis 3373.20 Literature 341

4 Pyrometallurgy 3434.1 Introduction 3434.2 Drying 3434.3 Calcination 3464.4 Roasting 3484.4.1 Thermodynamics 3494.5 Smelting 3534.5.1 Slags 3544.6 Oxide Reduction 3594.6.1 Carbothermy 3604.6.1.1 Iron 3654.6.1.2 Niobium 3694.6.1.3 Tantalum 3724.6.1.4 Magnesium 3734.6.2 Hydrogen Reduction 3734.6.2.1 Tungsten 3744.6.2.2 Molybdenum 3754.6.3 Silicothermy 3774.6.3.1 Pidgeon Process 3774.6.3.2 Ferrovanadium 3794.6.4 Calciothermy 3794.6.4.1 Vanadium 380

Contents

XVI Contents

4.6.4.2 Alloys 3844.6.5 Aluminothermy 3874.6.5.1 Iron 3894.6.5.2 Manganese 3904.6.5.3 Chromium 3914.6.5.4 Niobium 3924.6.5.5 Tantalum 3954.6.5.6 Vanadium 3954.6.5.7 Ferrovanadium and Ferroniobium 3994.7 Halide Processes 3994.7.1 Preparation of Chlorides 4004.7.2 Properties of Chlorides 4084.7.3 Pyrochemical Process 4104.7.4 Preparation of Fluorides 4124.7.5 Reduction of Chlorides 4164.7.6 Reduction of Fluorides 4214.8 Plasma Processes 4274.9 Refining 4284.9.1 MetalSlag Processes 4284.9.1.1 Steel Making 4314.9.1.2 Electroslag Refining 4344.9.2 MetalMetal Processes 4364.9.3 MetalGas Processes 4384.9.3.1 Fractional Distillation 4394.9.3.2 Pyrovacuum Processes for Reactive and Refractory Metals 4414.9.3.3 Chemical Transport Processes 4524.10 Literature 456

5 Hydrometallurgy 4595.1 Introduction 4595.2 Leaching 4625.2.1 Leaching Processes 4665.2.2 Pretreatments 4775.2.3 Leaching Techniques 4795.2.3.1 In-situ/Modified In-situ Leaching 4815.2.3.2 Dump and Heap Leaching 4825.2.3.3 Vat Leaching 4825.2.3.4 Agitation Leaching 4835.2.3.5 Pressure Leaching 4835.2.4 Examples of Leaching Practices 4845.2.4.1 Aluminum Ores 4845.2.4.2 Nickel Ores 4875.2.4.2.1 Nickel Sulfide Concentrates 4875.2.4.3.2 Nickeliferrous Pyrrhotite 4915.2.4.3.3 Lateritic (Oxide) Ores 491

XVII

5.2.4.4 Zinc Ore 4955.2.5 Bacterial Leaching 4965.3 Solution Purification 5005.3.1 Ion Exchange 5005.3.1.1 Ion-Exchange Equilibria 5005.3.1.2 Familiarization 5035.3.1.3 Process Description 5065.3.2 Adsorption on Carbon 5075.3.2.1 Surface and Pore Structure Properties 5075.3.2.2 Mechanism 5085.3.2.3 Preparation 5085.3.2.4 Techniques 5095.3.3 Solvent Extraction 5095.3.3.1 Technical Aspects 5115.3.3.1.1 Extractants 5125.3.3.1.2 Diluents 5155.3.3.1.3 Modifiers 5155.3.3.1.4 Synergists 5155.3.3.2 Solvent Extraction Terminologies 5155.3.3.3 Countercurrent Extraction 5185.3.3.4 Metal Extraction 5205.3.3.5 Solvent Extraction Equipment 5235.3.3.6 Applications 5245.3.3.6.1 Copper 5245.3.3.6.2 ZirconiumHafnium 5265.3.3.6.3 NiobiumTantalum 5275.3.3.6.4 Nuclear Fuel Reprocessing 5295.3.4 Membrane-Based Solvent Extraction 5305.4 Precipitation Processes 5315.4.1 Chemical Precipitation Processes 5335.4.1.1 Hydrolytic and Ionic 5335.4.1.2 Reductive Precipitation Processes 5415.4.1.3 Homogeneous Processes 5415.4.1.4 Heterogeneous Processes 5435.4.2 Uranium 5445.4.3 Titanium 5575.4.4 Tungsten 5585.4.5 Molybdenum 5605.4.6 Precious Metals 5625.4.6.1 Gold 5625.4.7 Dispersed Metals 5675.4.8 Copper 5685.4.9 Manganese Nodules 5695.4.10 Zinc Solution Purification 5725.5 Literature 576

Contents

XVIII Contents

6 Electrometallurgy 5816.1 Introduction 5816.2 Electrical Conductance 5816.2.1 Ionics 5826.3 Electrolytes 5846.3.1 Chemical Behavior 5856.3.1.1 Acids 5856.3.1.2 Bases 5876.3.1.3 Alkalis 5936.3.1.4 Salts 5936.3.1.5 Neutralization and Hydrolysis 5966.3.1.6 Ionization of Water 6006.3.1.7 Buffer Solutions 6036.3.1.8 Solubility Product 6036.3.2 Electrical Behavior 6056.3.2.1 Arrhenius Concept 6056.3.2.2 Conductance 6066.3.2.3 Conductance Measurement 6086.3.2.4 Classification of Electrolytes 6116.3.2.5 Some Properties of Electrolytes 6126.3.2.6 Conductance Variation 6136.3.2.6.1 Ionic Mobilities 6176.3.2.6.2 Equivalent Conductivity for Weak Electrolytes 6206.3.2.6.3 Absolute Ionic Mobility 6216.3.2.6.4 Solubility of Salts 6216.3.2.6.5 Conductance Ratio 6216.3.2.6.6 Conductometric Titrations 6226.4 Galvanics 6246.4.1 Redox Reactions 6246.4.2 Electrochemical Cells, Reactions, and Electromotive Forces 6256.4.3 Cell Electromotive Force 6356.4.4 Standard EMFs and Electrode Potentials 6366.4.4.1 Hydrogen Electrode 6396.4.4.2 Reference Electrodes 6426.4.4.3 Free Energy Changes for Cell Reactions 6426.4.4.4 Electrode Reaction Thermodynamics 6456.4.4.5 Reversible Electrodes and Cells 6496.4.4.6 Applications of Electrochemical Series 6506.4.5 Cell Types 6586.4.5.1 Commercial Galvanic Cells 6646.4.5.1.1 Primary Cells 6646.4.5.1.2 Secondary Cells 6686.5 Electrolytic Cells 6706.5.1 Faradays Laws 6746.5.2 Decomposition Voltage 678

XIX

6.5.3 Polarization and Overvoltage 6816.5.4 Electrode Reactions 6876.5.5 Example of Electrolysis 6896.5.6.1 Electrochemical Separation and Co-deposition 6926.5.6.2 Molten Salt Electrolysis 6946.5.7 Process Classification 6966.6 Technological Aspects 6966.6.1 Electrodes 6966.6.2 Electrolytes 6976.6.3 Current Efficiency 6996.6.4 Energy Efficiency 7016.6.5 Cell Features 7026.6.6 Cell Design Optimization 7066.7 Cell Operation 7076.8 Electrowinning 7096.9 Electrorefining 7156.9.1 Copper 7176.9.2 Vanadium 7206.10 Electroextraction 7216.10.1 Molybdenum Compounds 7216.10.2 Nickel Sulfide 7236.11 Electroleaching 7256.11.1 Electrochemical Aspects 7256.11.2 Process 7266.12 Electrosynthesis 7296.13 Literature 733

7 Energy and Environment 7377.1 Introduction 7377.1.1 General 7377.1.2 Extraction and Process Metallurgy 7407.2 Energy Economy 7407.2.1 Fuel Equivalents 7427.2.2 Mining and Ore Preparation 7437.2.2.1 Energy Conservation 7477.2.3 Reduction and Refining 7487.2.3.1 Improved Process Design 7507.2.3.2 Waste Heat Recovery 7527.2.4 Materials Conservation 7567.2.5 Reclamation and Recycling of Metals 7587.2.5.1 Secondary Metal Production 7617.3 Environmental Impact 7637.3.1 Mining 7657.3.2 Ore Preparation 7667.3.3 Metal Production and Processing 766

Contents

XX Contents

7.3.3.1 Gaseous Effluents 7667.3.3.2 Solid Effluents 7737.3.3.2.1 Dust 7747.3.3.2.2 Solid Wastes 7767.3.4 Secondary Metal Production 7787.4 Hydrometallurgical Processing 7787.4.1 Niobium/Tantalum Metallurgy 7807.4.2 Uranium 7847.5 Literature 789

Subject Index 791

11Acquaintance

1.1Introduction

The subject of metallurgy broadly divides itself into physical metallurgy, mechanical metal-lurgy, chemical metallurgy, mineral dressing, powder metallurgy and engineering metal-lurgy.

Physical metallurgy is concerned with the scientific study of materials. Phase transfor-mations, recovery and recrystallization, precipitation hardening, structureproperty corre-lations, characterization of microstructure by microscopy (optical, electron and field-ion),are some specific examples among the many topics covered under physical metallurgy.

The importance of metals and alloys largely lies in their unique mechanical propertiesinvolving the combination of high strength with the ability to undergo plastic deformation.Their plasticity makes them amenable to various mechanical working methods (drawing,rolling, pressing, forging etc.). Plasticity can make strong materials tough and enable themto endure long service, even under very exacting conditions. Mechanical metallurgy ad-dresses all these aspects of the behaviour of metallic as well as other materials. Testingmechanical properties, establishing relations between these properties of materials andtheir design and selection, assessing and predicting materials performance during serviceare some of the important areas that come under the purview of mechanical metallurgy.This branch also involves with mechanical working of metals and alloys in solid state. Forexample, mention may be made of rolling, forging, drawing and extrusion.

Chemical metallurgy, according to one definition, is the branch of metallurgy that dealswith the extraction of metals from naturally occurring compounds and their refinement tolevels of purity suitable for commercial use. The starting raw materials, however, in manycases are not restricted to naturally occurring compounds. Nor in all cases are the endproducts desired as metals. The chemical treatments quite often depend upon the priorphysical processing to which the relevant materials have been subjected. In acknowledge-ment of these facts it is only proper that both physical and chemical treatments are consid-ered together in the total scheme defined for materials processing. There exist a very largevariety and range of treatments and many possible combinations of these which may beused in chemical metallurgy processes. The chemical metallurgy coverage extends furtherto deal with all the chemical properties of metals, including those pertaining to the forma-tion of alloys by uniting one metal with other metals or nonmetals.


2 1 Acquaintenance

Physical metallurgy has obvious links with mechanical metallurgy. It also has close linkswith chemical metallurgy. It helps in obtaining a scientific understanding of the variouschemical metallurgy processes and can assist in designing new processes or modificationsof existing processes. The linkage between physical metallurgy and chemical metallurgyhas grown with time. This has helped considerably in replacing the empirical or the trialand error mode of development with more logical and science based modes. For example,a newly found ore resource can be studied by such powerful physical metallurgy tools as x-ray diffraction, electron microscopy and electron probe microanalysis, and with the knowl-edge thus gained about the resource, it is possible to make very useful predictions in anumber of fronts. Once the type and the nature of the minerals present in a given resourceare studied and analysed, it is entirely possible to make useful predictions on the process-ing of the resource. Refractory minerals would need highly corrosive leachants and aggres-sive conditions of leaching such as those obtained at elevated temperatures and pressuresas in autoclaves. If the structural features show the substitution of one element at the lat-tice sites of another then separating these elements by physical methods is not possible.

The area of mineral dressing concerns itself with the starting operations and involvescrushing and grinding either for purposes of liberation of the desired substances that arephysically entrapped with others or for making them adoptable for further processes. Onceliberated, they normally go through such physical beneficiation processes as magnetic sepa-ration, electrostatic separation, screening, flotation, to name some, to produce a beneficiatedproduct usually called a concentrate and chemical metallurgy normally takes over fromthen onwards.

Powder metallurgy is concerned with production and processing of powdery forms ofmetals and materials and of solid industrial products therefrom.

Engineering metallurgy mainly deals with the processing of metals and materials in themolten condition. Foundry, metal joining and other related areas appear to come under itscoverage.

These branches, individually as well as collectively, have enabled metallurgy to play a veryimportant role in modern science and technology. The outstanding importance of metalsas constructional materials is, in fact, the reason why metallurgy, by itself, is an extensiveand self-contained subject. It has, however, gone very much beyond the confines of anyrigid classification. On the whole, the subject of metallurgy, besides its own constituentdisciplines, as described herein, draws heavily from a number of others. With inputs fromphysics, chemistry, chemical engineering, instrumentation technology, design engineer-ing and so on, metallurgy today has shaped into a truly multidisciplinary and interdiscipli-nary character.

It is only natural that chemical metallurgy is given a further introductory elaboration atthis beginning stage although a good portion of it will either be repeated or be dealt with ina more detailed way as the text advances in the subsequent chapters.

The extraction of metals fundamentally relies on their availability in nature. Three termsare important while one refers to availability. One is the crustal abundance and the othertwo are the terms: resources and reserves. The average crustal abundance of the most abun-dant metals, aluminum, iron and magnesium, are 8.1%, 5.0% and 2.1% respectively. Amongthe rare metals titanium is the most abundant, constituting 0.53% of the Earths crust. Nometal can be economically extracted from a source in which its concentration is the same

31.1 Introduction

as its crustal abundance. Fortunately, geochemical processes have resulted in significantselective concentration of the elements in certain portions of the Earths crust. These por-tions are called ore reserves or resources, depending on whether their processing is eco-nomical currently or is expected to be so at some future date. With the passage of timemore and more of what are presently considered as resources will become reserves. Highgrade reserves or ore bodies, containing a high concentration of the desired metal, havebeen selectively mined and processed in the past and at the present time there remain veryfew, if any, of such ore bodies. Those presently available are low in grade and complex incomposition. In the future the grade will decrease further and the complexity will increase,making metal recovery from such sources a much more difficult affair.

The poor grade and the complex composition of the ores being processed currently causemineral processing to be a major operation in the metal extraction scheme. Physical andchemical characterization of the minerals becomes very important as these characteristicsdetermine the processing scheme to be used. Magnetic and electrical properties have beenextensively used in mineral beneficiation, using electromagnetic and electrostatic separa-tors. Surface properties of minerals determine the basis for their beneficiation using flota-tion.

The processing of ores or primary resources for metal extraction is constrained by twomajor factors. One is their limited supply and availability and the other is the large energyconsumption involved in their processing. An option to circumvent these constraints is toresort to recycling of metals or secondary resource processing. Recycling of scrap usuallyconsumes only a fraction of the energy needed for metal extraction from the ore. No newore is consumed in recycling and the process causes much less pollution of the environ-ment. These attractive features have generated serious interest in recycling in recent timesand the interest will certainly grow in the days to come. This area has received detailedattention in the chapter on energy and environment.

The route by which an ore ends up as a metal suitable for commercial use is mapped indiagrams known as extraction flowsheets. These comprise a judicious assembly of the unitprocesses that lead to a working scheme. A flowsheet is always amenable for upgradationby improvements both in the unit processes and in their sequencing. The developments inchemical metallurgy pertain to these improvements. Much development can be expected inthe coming decades in chemical metallurgy on account of the efforts needed to extractpurer metals from leaner and more complex ores with minimum energy expenditure, whilecausing minimum environmental pollution. These demands will keep research on im-proved and new extraction processes alive and make extractive metallurgy an importantand dynamic branch of metallurgy, as in the past.

This book Chemical Metallurgy: Principles and Practice contains all together sevenchapters. Chapter 1 embodies a content meant to acquaint the readers on a selection oftopics of considerable relevance to chemical metallurgy. Chapter 2 deals with mineral process-ing, Chapter 3 with thermodynamics and kinetics, Chapter 4 with pyrometallurgy, Chapter5 with hydrometallurgy, Chapter 6 with electrometallurgy, and Chapter 7 with energy andenvironment. The book, as its title implies, presents chemical metallurgy practice manda-torily taking the pertinent principles involved at different stages into account.

4 1 Acquaintenance

1.2Materials

It is a well recognised fact that classification of the vast array of materials is an importantpart of the study of materials. The grouping or classification of materials is to be based ona scheme. Among the different basis of classification schemes known so far the well ac-cepted ones are: (i) nature of atomic bonding, (ii) electrical conductivity, (iii) magnetism.Taking these into account, almost all the major materials can be shown to fall under thefollowing categories: ceramics and glasses, polymers, composites, semiconductors, ther-mocouples, ferroelectrics and piezoelectrics, magnetic materials and metals.

The present writing on classification of materials may additionally be drawn to anotherfundamental aspect and this is about a very well known scheme of classification or a way ofgrouping of elements. It is the periodic classification of elements. Graphical portrayals ofthe periodic classification of elements are familiar as periodic tables. The table representsan arrangement of elements in order of the increasing atomic number in horizontal rows,known as periods. The columns of the table are known as groups. The elements in anygroup have similar chemical properties. Each group is assigned a number, written at thetop of the vertical column. The numbering system used so far has varied since its formalform given from the time of Mendeleev. A numbering uses a combination of roman nu-merals and the letters A or B to label each group while another recommends that the 18groups be numbered consecutively from left to right, 1 to 18. The numbering scheme, thelater one, for the groups will be used in the present text.

The elements in two groups at the far left (1, 2) and the six groups at the far right, asgroup 13 through 18 are called the representative elements or main group elements andthose in the central region labelled as B (312) are the transition elements. The two series,the first one, the lanthanides (cerium, Ce, through lutetium, Lu) are the elements thatfollow lanthanum (La) in period 6, and the second one, the actinides (thorium, Th, throughlawrencium, Lr) are the elements that follow actinium (Ac), in period 7, are known as innertransition elements. These two series of elements do not belong to any of the groups labeledat the top of the table. It is possible in a broad sense to classify elements as metals ornonmetals. The diagonal line or stairway that can be drawn from the left to the lower rightof the periodic table can be looked upon as dividing metals from nonmetals. Elementsbelow and to the left of this line are metals. Included among the metals are (i) all of theelements in group 1 (except H) are known as alkali metals and those in group 2 are knownas alkaline Earth metals; also Al (but not B) in group 13, (ii) all of the transition metals, (iii)the elements to the right of the transition series in groups 13 (Ga, In, Tl), 14 (Sn, Pb), and15 (Bi) (collectively, these elements are called as post-transition metals), and (iv) the lantha-nides and actinides (the inner transition metals). Elements above and to the right of thediagonal line are classified as nonmetals. It may be noted that along the diagonal line in theperiodic table there are several elements that are difficult to classify exclusively as metals ornonmetals. These elements are boron, silicon, germanium, arsenic, antimony, and tellu-rium. Their properties are in between the metallic and nonmetallic classes. They are oftentogether called as metalloids.

51.3Some Characteristics of Metals

1.3.1General

It is obvious from the text described in the last paragraph of the preceding section thatperiodic table is replete with elements that are metals. It turns out that three fourths of allnaturally occurring chemical elements are metals and that each metal occurs in a multi-tude of minerals from which it can be won and put into the service of man. Some membersin the family of metals have been specially classified as rare metals group. The membersbelonging to this family come from almost all the groups of the periodic table. They areclassified into five categories: light rare metals, refractory rare metals, scattered rare metals,rare Earth rare metals and radioactive rare metals (Figure 1.1). It can be seen in this figurethat rhenium figures in two groups. It is a typical scattered metal. However, on account ofits properties, it may also be classified as a refractory metal.

1.3.2Electronic Structure

Detachment of an electron from an atom and taking it into the form of positive ion requiresan expenditure of energy which is the ionization energy or the ionization potential. Thefirst ionization energy is the energy change for removal of the outermost electron from agaseous atom to form a + 1 ion. In general, in the case of the main group elements, ioniza-tion energy decreases moving down in the periodic table and increases going across, al-though there are several exceptions. A consequence of the outer electrons in a metal atombeing quite far from the nucleus is that they are weakly bound to it. This weak binding isreflected in the low values of the ionization energy. This is why metals readily part withtheir valence electrons, playing the role of reducing agents. The magnitude of the ioniza-tion potential can be taken as a measure of the extent of the metallicity of an element. Thesmaller the potential, the easier it is to detach an electron from an atom and the strongerare the metallic properties of the element.

A common feature of metal atoms is that they are generally larger in size in comparisonwith nonmetal atoms. A characteristic of nonmetals is that their atoms have the ability toattach electrons to themselves, leading to the formation of anions. The opposite is true forthe metals and as told they alter to cationic forms when their removable electrons leavethem.

The higher the valency of a metal, the greater will be the number of electrons in theoutermost shell. Now, since the positive charge residing in the nucleus remains unalteredby the removal of electrons, its attractive influence will progressively increase with the re-moval of each successive electron. It follows that when there are a number of electrons inthe outermost shell, the removal of electrons will progressively tend to be more and moredifficult as each electron is taken out.

The larger the atomic volume of an atom, the less strongly will the positively chargednucleus be able to hold the electrons in the outermost or the valency shell. In other words,

1.3 Some Characteristics of Metals

6 1 Acquaintenance

7a

6a

5

4

3

2

1

16

Legend :

1. Light rare metals 2. Refractory rare metals 3. Scattered rare metals 4. Rare earth rare metals 5. Radioactive rare metals

Rare metals

Polonium (14 elements from Th to Lr) Actinides

3

2

Actinium

Radium

3

(14 elements from Ce to Lu) Lanthanides Lanthanum Yttrium Scandium

7 Rhenium

16 Tellurium Selenium

14 Germanium

13 Thallium Indium Gallium

7

6 Tungsten Molybdenum

Rhenium

5 Tanatalum Niobium Vanadium

Hafnium Zirconium 4 Titanium

2 Beryllium

1 Cesium Rubidium Lithium

GroupElements

Figure 1.1 Classification of the rare metals (a = period).

7the more easily will such an atom lose one or more electrons to become an ion. Such is thecase with the atoms of a large number of metals.

Although it is possible, by the loss of several electrons, for certain metal atoms to formpolyvalent cations upto a maximum valency of four (e.g., tin forms the tetravalent stannicion, Sn4+), the formation of polyvalent anions is extremely difficult since for the acquisitionof each additional electron the attractive force exerted by the nucleus on each individualelectron becomes progressively smaller. It is for this reason that the maximum valency fora simple anion is found to be two.

The metallic structure essentially consists of atomic nuclei and associated core electrons,surrounded by a sea of free electrons. The high electrical conductivity of metals is derivedfrom the presence of these free electrons. In addition to high electrical conductivity, the freeelectrons provide the metals with good thermal conductivity as well. The electrical resistiv-ity of a metal increases with temperature.

Metals are noted for their high reflectivity and optical opacity. Both these properties areexplainable in terms of the behaviour of the free electrons. They oscillate in the alternatingelectrical field of the incident light beam, absorbing energy at all wave lengths; this makesthe metals opaque. The oscillating electrons give out light rays and in this way produce thereflected beam, accounting for the high reflectivity.

Metals are immune to radiation damage by ionization. This is also a consequence of thefree electron structure. Fast charged particles and ionizing rays can knock off electronsfrom the atoms they encounter. In metals, the positive vacancies so formed are immedi-ately filled up by the electron gas, leaving no sign of damage apart from a small amount ofheat.

1.3.3Crystallography

All metals in common with many ceramics, some plastics and most minerals, are crystal-line. The crystalline state is one in which the constituent atoms or molecules are arrangedin a regular repetitive and symmetrical pattern in space. The study of the characteristics ofcrystals is known as crystallography. The properties of metals and other crystalline materi-als are greatly dependent on their crystal structures and on the imperfections or crystaldefects that they may contain. A second reason for studying crystal structures is that eachcrystalline substance (elements/compounds) possesses a definite crystal structure. Thus,the crystal structure provides a means of distinguishing between various compounds orelements, even in cases where they are chemically identical. For example, gamma iron andalpha iron are both allotrophic forms of the element iron, and have the same chemicalconstitution but different crystal structures. In the study of crystal structures of metals theunit cell constitutes the basic unit of a crystal structure. A unit cell is a small grouping ofatoms or molecules which, if repeated indefinitely in three dimensions produce a crystal ofmacroscopic dimension. The unit cell, therefore, exhibits all the properties of the largecrystal. Thus, it is only required to known the structure of the unit cell in order to be able tospecify the structure of the whole crystal.


8 1 Acquaintenance

1.3.3.1 Crystal SystemsOne of the concepts in use to specify crystal structures the space lattice or Bravais lattice.There are in all fourteen possible space (or Bravais) lattices.

The points of each of the space lattices can be best addressed by making reference to a setof three coordinate axes which define the directions of the three edges of the unit cell.These edges may or may not be of equal length, and may or may not be inclined at equalangles to one another. On the basis of the lengths of the unit cell edges and their inclinationwith respect to each other it is possible to define seven crystal systems. If these lengths aredenoted by a, b, and c and the interaxial angles are denoted by , , and the crystal systemscan be differentiated in the manner described in Table 1.1.

Space lattices and crystal systems provide only a partial description of the crystal struc-ture of a crystalline material. If the structure is to be fully specified, it is also necessary totake into account the symmetry elements and ultimately determine the pertinent spacegroup. There are in all two hundred and thirty space groups. When the space group as wellas the interatomic distances are known, the crystal structure is completely determined.

a

a

b

Crystallographic elements System

Areas Angles

Examples

Cubic a = b = c = = = 90 CuF2, ZnS, NaCl, Pt, Fe, Diamond, Pb, KCl, Cu, Ag, Au, AgCl, As

Tetragonal a = b c = = = 90 CaWO4, SnO2, Sn, TiO2, PbWO4, PbMO4, CuSO4 5 H2O

Orthorhombic a b c = = = 90 ZnSO4,PbCO3,KNO3,BaSO4, MgSO4 Monoclinic a b c = = 90; 90 Na2SO4 10 H2O CaSO4 2 H2O,

Na2SO4 10 H2O

Triclinic a b c = = 90 CuSO4 5 H2O, H3BO3, K2Cr2O7 Hexagonal a = b c = = 90; = 120 Beryl, Be, graphite Mg Zn Cd, HgS,

Ca; apatite, CuS, pyrrhotite

Rhombohedral a = b = c = = 90 Calcite, magnesite, quartz, ice, Sb, Bi, millerite, cinnabar, corundum

Table 1.1 Crystallographic systems.

9Since the atoms in a crystal are arranged in a regular manner, it is evident that planes canbe defined which will contain many atoms. The simplest of such planes are those definedby any two axes of the coordinate system used to define the crystal system. Other planeswill, of course, be more complex; their occurrence, however, should be obvious. The impor-tance of these planes becomes evident while discussing the features and properties of acrystal such as its orientation, and the twinning and the slip systems associated with it. It is,therefore, important to have some system of nomenclature which will distinguish theseplanes and define their orientation. The system of nomenclature traditionally used is thatof Miller indices. As mentioned earlier, it is convenient to define three coordinate axes todescribe the crystal system. Starting at the intersection of these axes and proceeding alongany one of them, identical points will be encountered at periodic intervals; the smallest ofthese intervals in each direction describes the unit cell. To find out the Miller indices of aplane, it is required first to find its intercepts on the three coordinate axes X, Y, and Z interms of multiples or fractions of the unit cell edge lengths, a, b, and c, the values of whichare known as the lattice parameters. If a plane is parallel to one of the axes, the correspond-ing intercept is considered as infinite. The reciprocals of the values of these three interceptsare then considered, and these reciprocals are reduced to the three smallest integers havingthe same ratio. These integers, written in parenthesis, are the Miller indices of the plane.For purposes of general description, the letters, h, k and l are used to refer to these integers.The Miller indices of the plane would thus be written as (h, k, l). In an example, where aplane intersects the X-axis at four units, the Y-axis at infinity, and the Z-axis at two units, theintercepts are 4, , 2, so that the reciprocals of the intercepts are , 0, ; when multipliedby 4, these give the Miller indices 1, 0 and 2 and the plane is represented as (1 0 2), corre-sponding to (h k l) of the general case. As a consequence of the reduction to the smallestintegers, parallel planes will have the same indices. It may be pointed out that the coordi-nate axes extend to both the positive and the negative directions from the point of theirintersection (which may be taken as the origin), so that negative indices are also possible.

Direction indices are also frequently used in crystallography to specify the direction orthe orientation of a line in the crystal. If a point is moved from the origin (the intersectionof the coordinate axes) to some other position in the crystal by means of translations paral-

Figure 1.2 Miller indices of some important planes.


10 1 Acquaintenance

lel to the coordinate axes, the direction indices of the line connecting the origin and thefinal translated location will be given by the numbers x, y and z, where x is the number ofunits of a that the point moved parallel to the X-axis, y is the number of units of b that thepoint moved parallel to the Y-axis, and z is the number of units of c that the point movedparallel to the Z-axis. The values of x, y, and z are reduced to the simplest integers, and arepresented in square brackets [x y z] to signify that they are direction indices. Figure 1.2shows some of the important crystal planes with their Miller indices. In this figure, the facediagonal of the base of the parallelpiped will have the direction [110], the X-axis will havethe direction [100], and the body diagonal, the direction [111].

1.3.3.2 Metallic Crystal StructuresThe term crystal structure in essence covers all of the descriptive information, such as thecrystal system, the space lattice, the symmetry class, the space group and the lattice param-eters pertaining to the crystal under reference. Most metals are found to have relativelysimple crystal structures: body centered cubic (bcc), face centered cubic (fcc) and hexagonalclose packed (cph) structures. The majority of the metals exhibit one of these three crystalstructures at room temperature. However, some metals do exhibit more complex crystalstructures.

1.3.4Alloying

The unsaturated nature of the metallic bond accounts for several of the typical metallicproperties. It is responsible for the ability of some metals to accept small atoms, as forinstance, carbon, nitrogen and hydrogen, in the interstitial spaces between the metal at-oms. It also accounts for the alloying properties between metals. When two metals such ascopper and nickel are mixed together, each atomic species reacts fairly indifferently to theother, because their atoms are held together by the common free electron cloud to whichboth have contributed. In this way it is possible to form alloys over wide ranges of compo-sition by randomly replacing atoms of one metal by those of another. Such a solid solu-tion is called a substitutional solid solution. For extensive solid solubility to occur, the twometals must be quite similar as defined by HumeRothery rules: (i) less than about 15%difference in atomic radii; (ii) the same crystal structure; (iii) similar electronegativity; and(iv) the same valence. If one or more of these rules get violated, only restricted solid solubil-ity results. For example, in the aluminumsilicon system, the rules (i), (ii) and (iv) areviolated and that explains why aluminum can dissolve not even about 2 atomic percent ofsilicon. In situations where atom sizes of the two components differ greatly, the substitu-tion of a larger atom by a smaller atom at the lattice site of the former may not be energeti-cally stable. In such cases a more stable configuration may be obtained when the smalleratoms place themselves in the interstitial spaces among the adjacent atoms in the hostcrystal lattice. This gives rise to what are known as interstitial solid solutions. Solid solu-tions of this type often constitute very important phases in steels.

11

1.3.5Mechanical Properties

Metals in general possess some characteristic properties. However, many of these proper-ties are not exclusive to metals but are exhibited by some nonmetals as well. Lustre, forexample, is usually taken as characteristic of metals, but it is not their prerogative alone,because nonmetals like iodine and graphite also have a metallic lustre. Again, althoughmetals possess the property of conducting electricity to a remarkable degree, the nonmetalgraphite is used extensively in electrodes in electric furnaces to conduct the current to thecharge or the arc. The exclusivity to metals holds when terms of reference rests on me-chanical properties. Such mechanical properties as malleability and ductility, whilst are nottruly possessed by all metals, are essentially recognised as metallic characteristics.

Mechanical properties per se concerns with the qualities which determine the behaviourof a material towards applied forces. The ability to support weight without rupture or per-manent deformation, to withstand impact without breaking, to be mechanically formedinto different shapes all these depend upon a combination of mechanical properties char-acteristic of metals. Four types of behaviour of a material under stress are very important:linear or elastic behaviour, plastic behaviour, creep behaviour and fatigue behaviour.

1.3.5.1 Elastic DeformationIt is useful to get preliminary learning on the mechanical properties of materials under simplestatic tension. Members of engineering structures are often subjected to steady axial loadsin tension. Moreover, the response of materials subjected to other types of loading also canoften be explained or predicted on the basis of knowledge of their behaviour under simpletension. In addition, such behaviour is usually quite easy to study experimentally.

When a solid bar is loaded axially in tension, it elongates more and more with increasingload. The mechanism by which such elongation occurs can be visualised as a progressiveincrease in the separation of the atoms of the bar in the direction of loading, i.e., in the axialdirection. The displacement of the atoms from their equilibrium positions results in thedevelopment of attractive forces between them; these forces balance the applied load. Thiselementary picture can be considered to be applicable to the initial stages of deformation ofmany types of materials, crystalline as well as amorphous.

If the deformation involves only an increase in the separation of atoms in the direction ofloading by relatively small amounts, the atoms can return to their normal equilibriumpositions when the applied force is withdrawn (i.e., the load is released). In such a situa-tion, the axially loaded bar regains its original size and shape and the deformation is termedelastic deformation. Elastic deformation is reversible.

In the context of elastic deformation two parameters, known as stress and strain respec-tively, are very relevant. Stress is an internal distributed force which is the resultant of allthe interatomic forces that come into play during deformation. In the case of the solid barloaded axially in tension, let the cross sectional area normal to the axial direction be A0.From a macroscopic point of view the stress may be considered to be uniformly distributedon any plane normal to the axis and to be given by A0 where is known as the normalstress. The stress has to balance the applied load, F, and one must, therefore have A0 = For = F/A0. The units of stress are those of force per unit area, i.e., newtons per square


12 1 Acquaintenance

meter (Nm2) or pascals (Pa). The elastic deformation results in an elongation of the barand the elongation per unit length is termed strain. If L0 is the original length of the bar and is its total elongation then the strain, , is given by = /L0. Being the ratio of two lengthsstrain is dimensionless.

As the atoms are pulled apart in the direction of the applied force during elastic deforma-tion, they are simultaneously pulled inwards; as a consequence of this, the longitudinalelongation is accompanied by a lateral contraction. The ratio of unit lateral contraction, orlateral strain, and longitudinal strain is known as Poissons ratio. If the former is denotedby y and the latter by x, then y = x where is Poissons ratio. The negative sign indi-cates that one strain corresponds to contraction and the other to expansion. It is found thatfor most metals the value of Poissons ratio is close to 0.33. If the bar is now assumed to beof square cross section with lateral dimension a, then A0 = a

2 and V0 = L0 a2 where V0 is the

volume of the bar. On being subjected to axial loading its length increases by the amount = x L0 while both of its lateral dimensions decrease by the amount xa. Due to thesedimensional changes the volume of the bar now becomes

= + -

= + -

= + - + - +

0 0

2 20

2 2 2 30

( ) ( ) ( )

(1 ) (1 )

[1 (1 2 ) ( 2 ) ]

x x x

x x

x x x

V a a a aL L

L a

V

Usually x is very small so that the terms containing 2x and

3x can be ignored. The unit

change in volume can then be expressed as:

-

= = -0

0 0(1 2 )x

V VV

V V

The quantity V/V0 remains positive as long as the value of does not exceed 0.5. Inmost situations < 0.5 and thus elongation is accompanied by a dilatation or increase involume.

In order to examine the elastic behaviour of a material in static tension, a uniform bar ofthe material may be loaded slowly and simultaneous observations of load and elongationmade at regular intervals. The load and elongation data so obtained can be converted tostress and strain and plotted in the manner indicated in Figure 1.3 (A). Such a plot is knownas a stress-strain plot. Such plots are usually linear though nonlinear plots may also beobtained in some cases as depicted in Figure 1.3 (B). However, as long as the deformationis elastic, the curve returns to the origin on unloading.

Most engineering materials, particularly metals, follow Hookes law by which it is meantthat they exhibit a linear relationship between elastic stress and strain. This linear relation-ship can be expressed as = E where E is known as the modulus of elasticity. The value ofE, which is given by the slope of the stress-strain plot, is a characteristic of the materialbeing considered and changes from material to material.

The important elastic properties of a material undergoing deformation under static ten-sion are stiffness, elastic strength and resilience. For a material obeying Hookes law, themodulus of elasticity, E (= /), can be taken to be a measure of its stiffness. The elastic

13

strength of such a material is determined by the highest stress upto which its behaviourremains elastic. If the proportionality between stress and strain holds over almost the en-tire elastic range, which is usually the case with most materials, elastic strength corre-sponds to the value of stress which marks the termination of this proportionality and isknown as the proportional limit, PL. The proportional limit can be found experimentallyby obtaining a stressstrain plot and carefully determining the point at which a deviationfrom liner behaviour is first exhibited. The elastic strength of a material is often expressedin terms of another measure, namely, its yield strength which is discussed later in thischapter.

The term elastic limit is mainly a definition. It describes a stress which, if exceeded, willinfluence plastic deformation. Experimentally, the elastic limit is practically unattainablebecause it is a limit. Either it has not been reached or it is overreached. Ideally, the elasticlimit and proportional limit are the same.

The term elastic resilience pertains to the capacity of a material to absorb energy elasti-cally. In the case of a bar elongated elastically in static tension, the energy absorbed by thebar arises from the work done by the applied force. Provided that the deformation is elasticas well as linear in nature, this absorbed energy is stored in the material of the bar in arecoverable form as strain energy which equals the work done by the applied force. If x isthe instantaneous elongation and F(x) is the applied force expressed as a function of x, thestrain energy, U, is given, therefore, by

=

0

( ) dU F x x

since F(x) = A0 and x = L0 so that dx = L0 d , the expression for strain energy becomes

= 0 00

dU A L

Figure 1.3 Elastic stressstrain diagram: (A) linear; (B) nonlinear.


14 1 Acquaintenance

since = /L0. Dividing both sides of this equality by the volume A0 L0, one obtains

= 0 0 0

dU

A L

This expression indicates that U, the strain energy per unit volume is given by the areaunder the stressstrain plot over the strain range = 0 to = . If Hookes law holds, i.e., if = E , it follows that

= =2

0

d2

EU E

It can be easily shown that equivalent expressions for the strain energy per unit volumeare U = /2 and U = 2/2 E. The modulus of elastic resilience, Ur, of a material is definedas the strain energy absorbed per unit volume when it is stressed to its proportional limit.Thus,

= = =

2 2PL PL PL PL

r 2 2 2

EU

E

The shaded area in the stressstrain plot shown in Figure 1.4 is numerically equal to themodulus of resilience. It is to be noted that for a given value of E, Ur directly proportional toPL while for a given value of PL, Ur is inversely proportional to E (stiffness).

1.3.5.2 Plastic DeformationContinuing the discussion on the deformation of a solid bar loaded axially in tension, it isinteresting to consider the phenomena after the limit of elastic deformation is reached. Asthe tension on the bar increases progressively, the atoms are pulled farther and farther apart

Figure 1.4 Linear elastic stress-strain relation.

15

and a point is reached when deformation ceases to be reversible. This marks the end of theelastic range. Elongation no longer involves a simple pulling apart of the atoms from theirequilibrium positions. Irreversible structural changes start occurring. The termination ofthe elastic regime is brought about by one of two possible phenomena: fracture or yielding.

Fracture initiates at some imperfection such as a crack of macroscopic dimensions. Stressconcentration occurs at such imperfections. If the local value of stress at an imperfectionbecomes so large as to exceed the cohesive strength of the material, the atomic bonds inthat region break. As this happens, the imperfection, which was originally confined to amicroscopic region, rapidly spreads across the bar, resulting in complete fracture. If thishappens while the overall deformation is still elastic, the material is said to behave in aperfectly brittle manner. Materials such as some ionic crystals, glass, cast iron etc. tend tobe perfectly brittle. However, generally even such materials undergo some finite, albeitsmall extent of yielding before getting fractured. Some aspects of fracture have been dealtwith in a later chapter.

Yielding is a manifestation of the possibility that some of the atoms (or molecules) in thestressed material may slip to new equilibrium positions due to the distortion produced bythe applied tensile force. The displaced atoms can form new bonds in their newly acquiredequilibrium positions. This permits an elongation over and above that produced by a sim-ple elastic separation of atoms. The material does not get weakened due to the displace-ment of the atoms since they form new bonds. However, these atoms do not have anytendency to return to their original positions. The elongation, therefore, is inelastic, orirrecoverable or irreversible. This type of deformation is known as plastic deformation andmaterials that can undergo significant plastic deformation are termed ductile.

By increasing tension slowly and by taking simultaneous readings of load and elongationat regular intervals a stressstrain plot showing elastic as well as inelastic or plastic rangescan be obtained. Typical stressstrain plots for a perfectly brittle material (only elastic defor-mation), a material of low ductility (only a small amount of plastic deformation) and aductile material (significant plastic deformation) are shown in Figure 1.5 (AC).

The most common mechanism by which yielding occurs in crystalline materials is slip, inwhich two planes of atoms undergo a relative displacement with respect to each other so thatone whole section of the crystal is shifted relative to another. For each crystal structure thereare certain preferred planes on which slop can occur most readily. In general, these preferredplanes are those in which the atoms are the most closely spaced. Since these planes containthe largest number of atoms per unit area, they are also the most widely separated planesbecause the number of atoms per unit volume of the crystal is fixed. Again, for each crystalstructure there are certain directions along which slip can occur most easily. Generally thesedirections of easy slip correspond to those directions in the slip plane along which the atomsare most closely spaced. By way of an example, it may be mentioned that in face centered cubiccrystals the (III) type planes and the [110] type directions are respectively the closed packedplanes and the close packed directions; these are also the preferred slip planes and directions.

In most ductile materials it is found that as yielding progresses, an ever-increasing stressis required to produce further yielding. This is reflected in the stressstrain plot of a ductilematerial (Figure 1.5 C): stress always increases with increasing strain. This is the effect of aphenomenon known as strain hardening or work hardening. Like yielding, strain harden-ing is an important feature of plastic deformation.


16 1 Acquaintenance

In the plastic range of mechanical behaviour the strain has two components. In additionto the irrecoverable plastic strain that results from yielding, there is also a recoverable elas-tic strain component. An elementary explanation for this is presented here. In order toprovide the internal stresses required to balance the externally applied load the atoms mustalways be displaced to a certain extent from their equilibrium positions. With the progressof yielding the atoms get shifted to new equilibrium positions; however, they must moveslightly away from these new positions so that the necessary interatomic forces are gener-ated. Thus in the plastic range two distinct mechanisms elastic and plastic always comeinto play in producing strain and the total strain necessarily has two components. Theelastic component normally continues to increase at a constant rate dictated by Hookeslaw. The plastic component, on the other hand, increases more rapidly with increasingstress. As indicated earlier, elastic strain leads to an increase in volume. This is a conse-quence of the atoms being pulled away from their equilibrium positions. Plastic strain,which involves shifting of atoms to new equilibrium positions, is not accompanied by anysignificant change in volume.

At any given instant the process of yielding is localised at many points which are distrib-uted throughout the material undergoing plastic deformation. The yielding of such a pointis accompanied by a slight reduction in area and a concomitant increase in stress. At thesame time, however, the material undergoes strain hardening and thus becomes capable ofwithstanding the increased stress. The next yielding occurs at a different point. On a mac-roscopic scale, the overall effect of this random yielding is that the strain remains uniformalong the length of the bar. On a microscopic scale there is continued competition between

Figure 1.5 Typical stressstrain diagrams.(A) Brittle material; (B) low ductility material;(C) ductile material.

Fracture Fracture

Fracture

bb

b

(A) (B)

(C)

17

the increased stress due to reduction in area and the increased strength brought about bystrain hardening. The latter more than compensates for the former and the strain remainsessentially uniform.

The rate of strain hardening decreases with increasing strain in many materials. It mayso happen that beyond some value of strain the strengthening due to strain hardening isinsufficient to compensate for the increased stress resulting from area reduction. Whensuch a situation is obtained in some location of the material undergoing plastic deforma-tion, the plastic strain continues to increase there because the rate at which stress increasesis greater than the rate at which strengthening occurs at that location. This localised in-creases in plastic strain takes place with no increase in load. All further elongation occurs atthat location and a neck or constriction starts to form there. With progress of deformationthe rate of strain hardening continues to fall locally and the load bearing area continues todecrease; as a consequence, the load required to bring about further deformation becomessmaller and smaller. This process continues until rupture occurs. The situation describedabove is encountered in many ductile materials and is known as plastic instability. It ischaracterised by a maximum in the load versus elongation curve (Figure 1.6). The condi-tion that has to be satisfied for plastic instability to occur is given by dF = 0, or d ( A) = 0,where A stands for the load bearing area. Since both stress and area are variables, thiscondition can be expressed as

A d + dA = 0

Here the term A d represents the increase in load due to strain hardening and is posi-tive since d is positive; the term dA represents the decrease in load due to area reductionand is negative since dA is negative. Before the maximum load (Fmax in Figure 1.6) is reachedthe absolute value of the first term exceeds that of the second term and dF is positive. At themaximum load these values are equal and dF is zero. After this point the second termdominates and dF becomes negative.

The plastic deformation of a member terminates with its rupture which normally occursat the smallest section of the neck formed due to plastic instability. After being loaded intothe plastic range, if the member is unloaded before plastic instability occurs then the elasticcomponent of the strain can be recovered. This is a consequence of the atoms returning to

Figure 1.6 A load versus elongation diagram for a typical ductile metal, showing plastic instability.


18 1 Acquaintenance

their relevant equilibrium positions. However, the irrecoverable plastic component of thestrain is manifested as a permanent elongation (permanent set) of the member. This isillustrated in the schematic stressstrain plot shown in Figure 1.7. It is to be noted that theunloading line is parallel to the initial elastic loading line. If the member is reloaded afterunloading the atoms are again displaced to the positions that they occupied before unload-ing and further yielding occurs on continued loading. However, as a consequence of thestrain hardening associated with the first loading into the plastic range, the proportionallimit exhibited during the second loading is higher than that exhibited during the firstloading.

In some materials the initiation of yielding takes place abruptly and not in a gradualmanner, with a good amount of plastic deformation occurring without any significant strainhardening, i.e., almost without any increase in stress. In the corresponding stressstrainplot, the point at which yielding commences is called the yield point. While in most metal-lic materials there is a gradual transition from elastic to plastic strain with increasing stress,in some cases, mild steel (which is essentially an ironcarbon alloy containing around0.2% carbon) as for an example, there is a sharp discontinuity in tensile stressstrain curve(Figure 1.8). The material behaves in an elastic manner upto a certain point, A, and thensuddenly yields. Point A is termed the upper yield point. The stress level necessary to con-tinue plastic straining falls to level B, the lower yield stress, and a considerable amount ofplastic strain takes place at this lower level. After this sudden yielding has occurred thestress has to be increased again to bring about further plastic strain, and beyond point C onthe curve normal strain hardening occurs. If the metal is stressed to some point, D, on thecurve and the stress is then removed elastic strain will be recovered along the path DO.Immediate reloading of the test piece will give elastic strain to point D with continuedplastic strain beyond point D, but with no sudden yielding. However, if after stressing to

Figure 1.7 Representation of loading andunloading in the plastic range.

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point D and unloading, the sample is left at ordinary temperatures for about a week beforeretesting (or heated at 100 C for about one hour) it is found that the sudden yield phenom-enon returns. This is termed strain ageing.

It may be pointed out that the term yield point is sometimes erroneously used as a syno-nym for elastic limit and proportional limit. As it has been described in the paragraphsabove it is actually a phenomenon that occurs in only a very small number of cases intensile testing. As it has also been observed in the description that graphically and experi-mentally, it is an anomalous behaviour in which there is a strain occurring with no increasein stress.

The expressions for stress and strain introduced earlier in the context of elastic deforma-tion need some modifications while dealing with plastic deformation. In the elastic rangethe reduction in area and the strain are generally very small. In the plastic range, however,these could be quite large. Stress and strain, when expressed as = F/A0 and = /L0,where A0 and L0 refer to the original dimensions of the member undergoing deformation,are known as nominal or conventional or engineering stress and strain respectively. Asmore appropriate descriptors of the mechanical behaviour of materials terms known astrue stress and true strain will now be introduced.

True stress, , is defined as = F/A where A is the actual area of cross section of themember corresponding to the load F.

True strain differs from nominal strain in that each increment in strain is expressed interms of the actual length of the member at the time of the increment rather than in termsof the increment of the original length. The instantaneous nominal strain is given by

Figure 1.8 Discontinuous yielding.


Str

ess

Strain

A

B C

DUpper yield

point

Lower yieldpoint

OO

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-

= =0

0 0

L L

L L

where L is the instantaneous length. The increment in nominal strain corresponding to aninfinitesimal increase in length, dL, from L to L1 is given by

- - -

= - = - - -1 0 0 1

10 0 0 0

dd

L L L L L L L

L L L L

True strain, , is defined in such a way that the increment resulting from an increase inlength by dL is based on the instantaneous length, L:

=d

dL

L

The total nominal strain, , obtained by integrating the expression for the increment, d,is given by

-

= = 0

0

0 00

dd =

L

L

L LL

L L

which is the same as the expression for the instantaneous nominal strain given earlier. Thetotal true strain, , obtained by integration is

= = = - = 0

00 00

dd ln ln ln

L

L

L LL L

L L

since

-

= = -0

0 01

L L L

L L

true strain can be expressed in terms of nominal strain in the following manner:

= = +0

ln ln (1 )L

L

At large plastic strains, the elastic strain component constitutes only a small fraction ofthe total strain and the volume of the deforming member can be taken to remain essen-tially unchanged so that one has

= =0 0 0V L A L A

or

=0

0

AL

L A

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It follows that = ln A0/A for large plastic strains. The quantity A0/A is a measure of thereduction in area due to deformation. One can define a quantity, the true reduction in area(q), in a manner analogous to the definition of true strain:

= = - = 0 0

0dd lnA A

A A

AAq q

A A

It could be seen that for large plastic strains the true strain and the true reduction in areaare identical.

In Figure 1.9 stressstrain plots of the same material, using nominal and true values, areshown. Corresponding points on the two plots are connected by broken lines. It could benoted that before the maximum load is reached the points on the true stresstrue strainplot are always located to the left of the corresponding points on the nominal stressnomi-nal strain plot. After the maximum load is reached the regime of uniform strain is termi-nated and necking, with the associated localization of strain, starts. Because of the highlocal strains in the neck the true stresstrue strain plot overtakes the nominal stressnomi-nal strain plot in the sense that points on the former are located to the right of the corre-sponding points on the latter. It should be reiterated here that nominal stress and nominalstrain are approximations that are not very inaccurate in the elastic range but become moreand more inaccurate with increasing strain in the plastic range. True stress and true straincorrespond to the correct values in the elastic range as well as in the plastic range until theonset of necking. However, after a neck forms these also have to be regarded as approxima-tions only since neither the stress nor the strain is uniform in any cross section in the neck.Nevertheless, they indicate average values and approximate the true situation better thannominal stress and nominal strain do.

Figure 1.9 Comparison betweennominal and true stressstrain.


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The rate of strain hardening, d/d, at any given value of the true stain is given by theslope of the true stresstrue strain plot at that strain and is called the modulus of strainhardening.

It has been found that in the case of many metals the observed stressstrain data approxi-mately follow the empirical relationship = k1

n (n < 1), where k1 and n are constants thatvary from material to material. Taking logarithms one can write

= + 1log log logk n

A plot of log against log should thus yield a straight line whose slope is n and whichmakes an intercept equal to log k1 on the log axis (at = 1). Thus the constant k1 repre-sents the true stress at unit true strain and is termed the strength coefficient. The exponentn is known as the strain hardening exponent.

It has been seen earlier that the condition for plastic instability can be expressed as

A d + dA = 0

Replacing by and dividing throughout by A, one obtains

= -

d dAA

Assuming that the onset of plastic instability occurs at a fairly large value of plastic strain,one may consider the volume to remain essentially constant, so that A L = A0 L0. Differen-tiation gives

A dL + L dA = 0

or

- = = d d

dA L

A L

Thus it is seen that

=

dd

or

=

dd

This relationship indicates that for plastic instability to occur the modulus of strain hard-ening, i.e., the slope of the true stresstrue strain plot, should be equal to the true stress.This result is independent of any assumed functional relationship between and . If therelationship = k1

n assumed to hold then one obtains

-

= = =

( 1)1 1

d n nn k kd

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so that

= n

This relationship implies that the value of the true strain at which plastic instability setsin, i.e., necking starts to occur, is equal to the strain hardening exponent.

Some of the important inelastic properties of a material undergoing plastic deformationare yield strength, ultimate tensile strength, ductility and toughness.

The yield strength (YS) refers to the stress at which a ductile material commences toyield. It is difficult to detect the beginning of yielding very precisely and it is necessary tospecify a certain measurable extent of yielding as the beginning of yielding. The value ofthe yield strength depends upon the selection of this amount of yielding. The yield strengthcan be determined from the stressstrain plot by following a simple procedure. The speci-fied yield strain is measured along the strain axis and a straight line parallel to elastic part ofthe plot is drawn through the point corresponding to this offset. The stress correspondingto the point at which this straight line intersects the stressstrain plot is the required yieldstress or the offset yield strength which is a measure of the commencement of yielding andof the termination of the elastic range. A very frequently used value of the offset strain is0.2% (Figure 1.10).

In a material exhibiting a distinct yield point, the stress corresponding to the yield pointmay be taken as the yield strength. When both upper and lower yield points occur, gener-ally the stress corresponding to the lower yield point is taken to be the yield strength.

In design, whenever it is intended that a member should be in the elastic range underload, the yield strength is used as the basis for obtaining a design or working stress. Theworking stress, w, is given by w = y/ny where y is the yield strength and ny is an appropri-ate factor of safety. Depending on the application the factor of safety may vary over a widerange, its minimum value being unity. In engineering practice, the yield strength is usuallymeasured in terms of nominal stress.

Figure 1.10 Determination of offsetyield point.


Str

ess

0.002 Offset (0.2 %) Strain

Yield strength

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The ultimate tensile strength (UTS) of a material refers to the maximum nominal stressthat can be sustained by it and corresponds to the maximum load in a tension test. It isgiven by the stress associated with the highest point in a nominal stressnominal stressplot. The ultimate tensile strengths of a ductile and of a brittle material are schematicallyillustrated in Figure 1.11. In the case of the ductile material the nominal stress decreasesafter reaching its maximum value because of necking. For such materials the UTS definesthe onset of plastic instability.

For brittle materials the UTS is generally used as the basis for obtaining the workingstress: w = u/nu where u is the UTS and nu is a factor of safety. The UTS may be used asa basis for arriving at the working stress even for ductile materials in situations where somepermanent deformation is acceptable.

Ductility is one of the very important features of most metals. Two measures of ductilityare obtained from the tension test. These are the percent elongation in a specified length ofthe deforming member at the time of rupture and the percent reduction in area of its small-est cross section at rupture. The percent elongation varies with length on account of thefact that the plastic strain is locally concentrated in the neck region, with relatively littlestrain in other parts of the member. It is, therefore, very much necessary that the length isspecified while quoting the percent elongation. The main use of percent elongation as ameasure of ductility is for comparing the ductilities of materials. The percent reduction inarea can be found by measuring the area of cross section of the member before loading andthe area of cross section of the neck after fracture. If these two are denoted by A0 and Afrespectively, the percent reduction in area can be represented as 100 (A0 Af)/A0. Ductilitycan be expressed in terms of true stress and true strain also. One such measure of ductilitygives the maximum uniform strain and is represented by the true strain at maximum load.

Figure 1.11 Depiction of ultimate tensile strengths of ductile and brittle materials.

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Another measure is the true fracture strain which is expressed in terms of the true reduc-tion in area at fracture and is given by, = q = ln A0/Af, where the subscript f refers tofracture.

The toughness of a material indicates its overall capacity to absorb energy. Just as themodulus of resilience is measured by the strain energy absorbed per unit volume in theelastic range, the modulus of toughness is measured by the strain energy absorbed per unitvolume over the entire range of deformation upto rupture and is given by

= r

0

du

where r is the strain at rupture. The integral represents the total area under the stressstrain plot. If the true stresstrue strain plot is used, this area corresponds to the energy perunit volume pumped into the material at the smallest part of the neck.

The time element has so far remained conspicuously absent. The deformation character-istics is ordinarily considered independent of time. If, however, the rate of straining isvaried over several orders of magnitude, the true stress versus true strain curve may changeas a function of the strain rate, t. A relationship can be used to express at a given strain, in terms of the strain rate, : = k2 ()

m, where k2 is a constant and m is the index ofstrain rate sensitivity. Certain interesting observations ensue from this relationship. If m = 0,the stress is independent of the strain rate and all strain rates yield the same true stressversus true strain behaviour. The value of m is approximately 0.2 for common metals.A material may exhibit superplastic behaviour (deform to several hundred percent of strainwithout necking) if m has a value in range of 0.4 to 0.9. The reason for this is that as soonas necking starts in some region, the strain rate goes up locally; this results in a rapidenhancement in the stress required to cause further deformation in that region. The defor-mation then shifts to another region of the material, where there is no necking. In thisregion the strain rate and hence the stress required for causing deformation are smaller.Some stainless steels and aluminum alloys, with a very fine grain size, show superplasticbehaviour. It is on account of the fact that the value of m for glass approaches unity that aglass blower is able to pull his working material to very long rods without necking. A mate-rial behaves like a viscous liquid when the value of m approaches unity.

The behaviour of materials in static compression is in many ways similar that in statictension described above. There are, however, important differences. Stressstrain diagramsoften differ for tension and compression, a

Chemical Metallurgy, principles and practice, Chiranjib Kumar Gupta

Engineering

Transcript of Chemical Metallurgy, principles and practice, Chiranjib Kumar Gupta