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Sintering and its enhancement in ferrous powder compacts Subrahmanyam, Gowri 1991

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S I N T E R I N G A N D ITS E N H A N C E M E N T I N F E R R O U S P O W D E R C O M P A C T S By Gowri Subrahmanyam M. Engg. (Metallurgical Eng.) Indian Institute of Science, Bangalore, INDIA, 1982. A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S M E T A L S A N D M A T E R I A L S E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A April 1991 © Gowri Subrahmanyam, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Department DE-6 (2/88) ABSTRACT Sintering maps have been developed for pure iron compacts. The maps have been drawn as a function of various sintering parameters such as particle size, green density, time and temperature. Two sets of diagrams have been drawn to define the sintering kinetics, namely, the field map and the neck growth/shrinkage map. A new and simple method has been developed to construct the field maps, which define the dominant mechanisms of mass transport that contribute to neck growth under a given set of conditions of sintering. Shrinkage maps, which show how far the neck is growing or give % linear shrinkage for a given neck size and temperature, are generated by numerically integrating, the sum of the contributions to neck growth from the different mechanisms of transport. The model developed is based on ideal geometry and does not take into account complex phenomena such as grain growth, pore coalescence or pore growth. The sintering equations and diagrams that have been developed for pure iron compacts have been used effectively in the present study to predict and analyze the results of experiments involving various attempts to enhance sintering in such compacts. Small additions of a selected group of elements were made to iron compacts in an attempt to provide activation of solid state sintering similar to that which is obtained when tungsten powder compacts are doped with nickel. A few of the dopants used with iron compacts produced a small increase in shrinkage and densification for a given set of sintering conditions. Based on the present results and on the several studies of tungsten - nickel compacts which are reported in the literature, a new theory of dopant activated sintering has been proposed. Consistent with this model, it is suggested that certain criteria must be met by the dopant-base metal combination if activated sintering is to be ii observed. Sintering enhancement based on ferrite stabilization in two systems, iron - phosphorus and iron - silicon has been studied. This approach to solid state sintering enhancement proved to be highly effective and it is believed to have important practical applications in the P / M parts industry. The results of these experiments were consistent with predic-tions based on the sintering theory and maps appropriate to the conditions of sintering employed. in Table of Contents A B S T R A C T i i Table of Contents iv List of Tables x List of Figures x i i List of Symbols xx Acknowledgement x x i i i 1 I N T R O D U C T I O N 1 1.1 INTRODUCTION TO SOLID STATE SINTERING MODELS 2 1.1.1 The Driving Force 2 1.1.2 Mechanisms of Mass Transport 4 1.1.3 Sintering Equations for a Pair of Spheres 6 1.1.4 Sintering Equations for Irregular Arrays of Contacting Spheres . . 7 1.1.5 Sintering Equations for Ideal Compacts 8 1.2 STAGES OF SINTERING AND SINTERING RATE EQUATIONS . . . 9 1.2.1 Stage 0 : Adhesion 9 1.2.2 Stage 1 : Initial Stage of Sintering 10 1.2.3 Stages 2 and 3 : Intermediate and Final Stages of Sintering. . . . 14 1.3 SINTERING DIAGRAMS 17 iv 1.4 INTRODUCTION TO SOLID STATE SINTERING ENHANCEMENT . 20 1.4.1 Enhanced Sintering 22 1.4.2 Methods of Enhancing Sintering 22 1.4.3 Activated Sintering of Tungsten Powder : Literature Review . . . 24 1.4.4 Activated Sintering in Other Systems 28 1.5 THEORIES OF ACTIVATED SINTERING 28 1.5.1 Solution Precipitation Theory of Brophy 29 1.5.2 Modified Surface Theory of Toth and Lockington 30 1.5.3 Electronic Configuration Theory of Samsonov 31 1.5.4 Enhanced Diffusion Theory 31 1.5.5 Summary of the Theories 34 1.6 CRITERIA FOR THE SELECTION OF AN ACTIVATOR 35 2 O B J E C T I V E S O F T H E P R E S E N T I N V E S T I G A T I O N 37 3 C O N S T R U C T I O N A N D A N A L Y S I S O F S I N T E R I N G D I A G R A M S F O R I R O N C O M P A C T S 39 3.1 AIM AND DESCRIPTION OF THE PROBLEM • . . 39 3.2 SIMPLIFIED METHOD OF ESTABLISHING A FIELD MAP 40 3.2.1 Construction of Field Maps 44 3.2.2 Observations 48 3.3 SINTERING DIAGRAMS FOR A PAIR OF IRON SPHERES 55 3.3.1 Calculations 55 3.3.2 Experimental Verification of Neck Growth 66 3.4 SINTERING DIAGRAMS FOR COMPACTS OF IRON 75 3.4.1 The Geometry of Compacts 75 3.4.2 Calculations 83 v 3.4.3 Effect of Changing Diffusion Coefficients 92 3.4.4 Incorporation of Grain Growth in Sintering Equations 98 3.4.5 Experimental Verification 101 3.5 LIMITATIONS OF T H E IDEAL SPHERICAL PARTICLE M O D E L . . 105 3.5.1 Assumptions About Neck and Pore Geometry 106 3.5.2 Influence of Powder and Process Variables 107 3.6 SINTERING BEHAVIOR O F C O M M E R C I A L IRON P O W D E R C O M -PACTS 110 3.6.1 Adapting the "Theoretical" Model to Real Compacts 110 3.6.2 Experimental Verification of Shrinkage in Real Compacts 110 3.7 SUMMARY 112 4 D O P A N T - A C T I V A T E D SINTERING 118 4.1 AIM-AND DESCRIPTION OF T H E S T U D Y 119 4.2 MATERIALS AND E X P E R I M E N T A L PROCEDURES 120 4.2.1 Dopant Selection 120 4.2.2 Blending of Dopants with Iron Powder 127 4.2.3 Compacting and Sintering 134 4.2.4 Sintering Shrinkage and Weight Changes 135 4.3 RESULTS AND DISCUSSION 135 4.3.1 Pure Iron Compacts 135 4.3.2 Doped Compacts 141 4.4 ANALYSIS OF A C T I V A T E D SINTERING IN T U N G S T E N - NICKEL . 159 4.4.1 Sintering of Pure Tungsten Powder 160 Analysis of Field Maps for the Sintering of Pure W . . . 160 Analysis of Flux of Matter Arriving at the Neck 164 v i 4.4.2 Role of Nickel in Activated Sintering of Tungsten 167 Significance of Number of Monolayers of Nickel 167 State of Dispersion of Nickel in Tungsten - Nickel . . . . 168 Enhancement of Mass Transport in Tungsten - Nickel . . 178 4.5 PROPOSED THEORY OF ACTIVATED SINTERING 179 4.5.1 Suggested Model 179 4.5.2 Support For The Suggested Model 184 4.6 CRITERIA FOR THE SELECTION OF AN ACTIVATOR 187 4.7 ANALYSIS OF ACTIVATED SINTERING IN FERROUS SYSTEMS . . 191 4.7.1 Introduction 191 4.7.2 Comparison of Activated Sintering in Ferrous and W - Ni system 192 4.8 SUMMARY 194 5 F E R R I T E S T A B I L I Z A T I O N E N H A N C E D S I N T E R I N G 197 5.1 SELECTION OF THE SYSTEMS FOR STUDIES OF FSES 198 5.2 AIM AND DESCRIPTION OF THE PROBLEM 201 5.3 PREVIOUS STUDIES OF Fe - P AND Fe - Si COMPACTS 203 5.3.1 System Fe - P 203 5.3.2 System : Fe - Si 205 5.4 MATERIALS AND EXPERIMENTAL PROCEDURES 214 5.4.1 System : Fe - P 214 Preparation of Prealloyed FeP powder 214 Compaction of the Prealloyed Powders 216 Sintering Conditions and Temperature 216 Shrinkage Measurements 216 5.4.2 System : Fe - Si 216 vii Preparation of Powders for Studying the Progress of Al-loying 217 Compaction of the Mixed Powders 217 Sintering Conditions and Temperatures 218 5.4.3 Preparation of Powders for Prediction of Shrinkage in a FeSi. . . 218 Preparation of Prealloyed Powders 218 Compaction of the Prealloyed Powders 218 Sintering Conditions and Temperature of Sintering . . . 218 Shrinkage Measurements 219 5.5 RESULTS OF FSES IN Fe - P COMPACTS 219 5.5.1 Shrinkage and Densification 219 5.5.2 Metallographic Observations 224 5.6 ANALYSIS OF THE RESULTS 232 5.6.1 Pure Iron 232 5.6.2 Predictions of Sintering Shrinkage in Fe - P Compacts 234 5.6.3 Comparison of Experimental and Theoretical Predictions 235 5.7 RESULTS OF FSES IN Fe-Si COMPACTS 238 5.7.1 Progress of Alloying : Microstructural Examination 238 5.7.2 Progress of Alloying : Dimensional Changes .' 250 5.7.3 Results of Shrinkage in Prealloyed Powders 262 5.8 ANALYSIS OF FSES IN Fe - Si COMPACTS 262 5.8.1 Mixed Powder Compacts 262 5.8.2 Prealloyed Powder 266 5.9 DISCUSSION 270 5.10 EFFECT OF BOTH P AND Si ON SINTERING 279 5.11 SUMMARY 280 vm 6 S U M M A R Y A N D C O N C L U S I O N S 281 7 S U G G E S T I O N S F O R F U T U R E W O R K 286 B i b l i o g r a p h y 287 ix List of Tables 1.1 Paths of Different Mechanisms of Mass Transport 5 3.1 Material Constants for Iron Used in the Predictions 43 3.2 Contributions to Neck Growth Rate from Different Mechanisms of Trans-port in a Pair of Iron Spheres 44 3.3 Contributions to Neck Growth Rate from Different Mechanisms of Trans-port in an Iron Compact 45 3.4 Material Constants for Copper Used in the Predictions 47 3.5 Diffusion Coefficients of Fe at 800 - 1200 °C 57 3.6 Comparison of Experimental and Theoretical Values of (x/a) 68 3.7 Characteristics of GS6 Carbonyl Powder used in this Study 102 3.8 Shrinkage Results of Carbonyl Compacts 105 3.9 Characteristics of Atomet 28 Iron Powder used in this Study I l l 3.10 Shrinkage Results of Atomet 28 Powder Compacts Sintered for 20 Minutes. 112 4.1 Additions to Pure Carbonyl Iron Powder Compacts. 121 4.2 Description of Additive Powders 128 4.3 Data for Fe Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. . . . 136 4.4 Data for C Loss in Fe Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes at 900 °C 141 4.5 Data For Fe - B Compacts Sintered in a Flow of H 2 - Ar mixture for 20 Minutes , 145 4.6 Data for Fe - Ge Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. 147 x 4.7 Data For Fe - Ti Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. 150 4.8 Data for Fe - W Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. 152 4.9 Data for Fe - 0.3 Cr Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes 154 4.10 Data for Fe - 0.3 Ni Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. 155 4.11 Data for Fe - 0.3 Ag Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. 158 4.12 Material Constants for Tungsten used in the Calculations 161 4.13 Diffusion Coefficients of W at 1000 - 1400 °C 161 4.14 Summary of Parameters of Activated Sintering in W - Ni used by Different Investigators 168 4.15 Factors Important for the Selection of an Activator 190 4.16 Comparison of the Factors Important for the Selection of an Activator. . 195 5.1 Diffusion Data for the Lattice Diffusion of Phosphorus in Iron 199 5.2 Data.for Fe-P Compacts Sintered in a Flow of H 2 - Ar for 60 Minutes. . . 222 5.3 Mean Ferrite Grain Diameter for Fe and Fe - P Sintered Compacts which remained Ferritic throughout the Sintering Cycle of 60 minutes 232 5.4 Data for Fe - 2.8 Si ( a ) Compacts Sintered in a Flow of H 2 - Ar for 60 Minutes 264 5.5 Data for Volume Diffusion Coefficients of iron in a - FeSi Alloy available in Literature 268 5.6 Linear Shrinkage of a Fe - 3 %Si Compact Sintered for One Hour 278 xi List of Figures 1.1 Idealized section of a two particle model (a) without penetration (b) with centre approach 3 1.2 ( a ) Progress of neck growth ( b ) Paths of different mechanisms of transport. 5 1.3 Geometry during Stage 1 sintering 13 1.4 Pore shape in the intermediate and final stages of sintering - Coble's model 15 1.5 Geometry of Stages 2 and 3 of sintering - Ashby's model 18 1.6 Sintering diagram of copper spheres of 57 /xm radius 19 1.7 Effect of doping on shrinkage rate of W compacts 21 1.8 Sintering results of Ni coated W compacts 25 1.9 Influence of additive coating thickness on sintering shrinkage of W compacts 27 1.10 Solution precipitation theory of Brophy et al 30 1.11 Enhanced diffusion model of Gessinger and Fischmeister 32 1.12 Geometric model of German's heterodiffusion controlled activated sintering 33 1.13 Ideal Phase Diagram of an activator 36 3.1 Schematic representation of a Field Map 42 3.2 Construction of Field Maps for Copper spheres : ( a )(2DBSBIDsb~s) vs. (T/TM) ( b ) (2Dv/Ds6s) vs. (T/TM) 49 3.2 ( c ) log (xKl 3/K2 2) vs. log(x/a) ( d ) log (K1 3/K2 2) V S . log(x/a). . . . 50 3.2 ( e ) log(x/a) vs. (T/TM) 51 3.3 Demonstration of plotting the boundary for Copper spheres 52 xii 3.4 Effect of particle size on the shift in (a) [S/V] interface (b) [B/V] interface for Copper spheres 54 3.5 Construction of Field Maps for Iron spheres : ( a ) log (2DB&B/DSSS) vs. (T/TM) ( b ) (2DV/DSSS) vs. (T/TM) 58 3.5 ( c ) log (xK13/K22) vs. log(x/a) ( d ) log (K,3/K22) V S . log(x/a). . . . 59 3.5 (e) log(x/a) vs. ( T / T M ) 60 3.6 Effect of particle size on the shift in ( a ) [S/V] interface ( b ) [B/V] interface in Iron spheres . 61 3.7 Field Maps for pair of Iron spheres in initial contact ( a ) 75 /xm ( b ) 10 /xm. 62 3.8 Neck growth for a pair of Iron spheres : (x/a) vs. (T/TM) 63 3.9 Individual contribution of surface, volume and boundary diffusion to (x/a) ( sintered for one hour ) for a pair of spheres ( a ) 75 / i m ( b ) 10 / i m . . . 64 3.10 % Linear shrinkage vs. (T/TM) for a pair of Iron spheres ( a ) 75 /xm ( b )~10 /xm 65 3.11 Distribution of spherical Fe powder : as received 67 3.12 Progress of neck growth in Spheromet iron powder sintered at 900 °C : ( a ) 10 minutes ( b ) 60 minutes . 69 3.12 ( b ) 60 minutes 70 3.12 ( c ) 600 minutes 71 3.13 Progress of neck growth in Spheromet iron powder sintered at 1100 °C : ( a ) 60 minutes 72 3.13 ( b ) 600 minutes 73 3.14 (x/a) vs. time of sintering in Spheromet iron powder sintered at 900 and 1100 °C 74 3.15 Variation of relative density with the compaction pressure, P 76 3.16 Average contact area between particles as a function of relative density. . 78 xiii 3.17 Densely packed planar array of pressed Copper spheres 79 3.18 Theoretical plot of init ial (^); vs. relative density 82 3.19 Field Maps for a compact of 75 % relative density ( a ) 75 pm ( b ) 34 pm. 84 3.19 ( c ) 10 / im particles 85 3.20 Field Maps for a compact of 90 % relative density ( a ) 75 pm ( b ) 34 pm particles 87 3.20 ( c ) 10 |tm particles 88 3.21 (x/a) vs. (T/TM) for a compact of 75 % relative density a = 75 pm. . . . 89 3.22 Individual contributions to (^) ( sintered for one hour ) in compacts of 75 % relative density by surface, volume and boundary diffusion ( a ) 75 pm ( b ) 10 pm 90 3.23 Individual contributions to (^) ( sintered for one hour ) in compacts of 80 % relative density by surface, volume and boundary diffusion ( a ) 75 pm ( b ) " 10 A*m 91 3.24 Calculated % linear shrinkage vs. (T/TM) for a compact of 75 % relative density a = 75pm 93 3.25 Calculated % linear shrinkage vs. (T/TM) in a compact of ( a ) 75 % relative density ( b ) 90 % relative density 94 3.26 Calculated % linear shrinkage vs. (T/TM) for a = 75 pm in ( a ) 80 % relative density ( b ) 90 % relative density 95 3.27 Calculated % linear shrinkage ( sintered for one hour ) vs. (T/TM) for a = 75 pm for relative densities of 75, 80, 90 % 96 3.28 Calculated % linear shrinkage ( sintered for one hour ) vs. (T/TM) for relative densities of 75 and 90 % 97 3.29 Effect of Increasing Diffusion Coefficients ( a ) Surface 99 3.29 ( b ) Boundary diffusion ( c ) Volume diffusion. 100 xiv 3.30 Distribution of GS6 Iron powder particles 103 3.31 Comparison of experimental shrinkage with the predicted values as a func-tion of temperature of sintering in GS6 powder compacts sintered for 20 minutes 104 3.32 SEM Photomicrograph of Atomet 28 iron powder particles 113 3.33 Comparison of experimental shrinkage with theoretical predictions as a function of temperature of sintering in Atomet 28 iron compacts sintered for one hour 114 4.1 Phase diagrams of the binary systems considered ( a ) Fe - Si [94] 122 4.1 ( b ) Fe - B [94] 123 4.1 ( c ) Fe - Ge [94] ( d ) Fe - Ti [94] 124 4.1 ( e ) Fe - W [94] ( f ) Fe - Pd [94] 125 4.1 ( g ) J e - Cr [94] ( h ) Fe - Ni [94] 126 4.2 Shape and size distribution of additive powder particles ( a ) B 129 4.2 ( b ) T i H 2 130 4.2 ( c ) Si 131 4.2 ( d ) W 132 4.2 ( e ) Pd 133 4.3 Sample dimensions used in the experiments - ASTM E8 61T Specification. 134 4.4 Linear shrinkage of Fe powder sintered for 20 minutes 137 4.5 Relative sintered densities Fe powder sintered for 20 minutes 138 4.6 Effect of B additions on linear shrinkage in Fe - B compacts sintered in a flow of Ar - H 2 atmosphere for 20 minutes. 142 4.7 Microstructure of Fe - 0.1 B compact sintered for 20 Minutes at (a) 850 °C143 4.7 ( b ) 1000 °C 144 xv 4.8 Microstructure of Fe - 0.1 Si compact sintered at 850 °C for 20 Minutes. 146 4.9 Microstructure of Fe - 0.1 Ge compact sintered at 800 °C for 20 Minutes. 148 4.10 Effect of Ti additions on linear shrinkage of Fe - Ti compacts sintered in a flow of Ar - H.2 atmosphere for 20 minutes 149 4.11 Microstructure of Fe - 0.1 Ti compact sintered at 850 °C for 20 Minutes. 151 4.12 Microstructure of Fe - W compacts sintered at 850 °C 153 4.13 Microstructure of compacts sintered at 850 °C showing unreacted additive particles : ( a ) Pd 156 4.13 ( b ) Cr 157 4.14 Field map for W spheres of diameter ( a ) 100 /xm (b) 20 /xm 162 4.14 (c) 0.56 /xm 163 4.15 Linear shrinkage as a function of Ni content - Brophy and German . . . . 169 4.16 Phase Diagram of W - Ni, 170 4.17 EPMA Results of Ylasseri and Tikkanen 172 4.18 Conditions of Wetting 175 4.19 The appaerance in three dimension of a minor phase occurring at grain edges 176 4.20 Schematic representation of the activated sintering mechanism 181 4.21 Field map for Iron compacts of 75 % relative density. 193 5.1 Fe - P Phase Diagram 200 5.2 Experimental results of Fe - P compacts - Lindskog et al 206 5.3 Experimental results of dimensional changes - Weglinski et al 207 5.4 Effect of silicon admixture on shrinkage - Rutkowski and Weglinski. . . . 209 5.5 Effect of ferrosilicon admixture on shrinkage - Jang et al.. ." 210 5.6 Effect of silicon admixture on shrinkage - Jang et al.. . : 211 xvi 5.7 Isothermal dilatometer data for Fe - 3wt. % Si compacts - Qu et al 213 5.8 Gamma loop portion of Iron - Phosphorus Phase Diagram 215 5.9 Experimental linear shrinkage vs. % Phosphorus in compacts sintered for one hour 220 5.10 Densification parameter ( D.P. ) vs.% Phosphorus in compacts sintered for one hour 221 5.11 Plot of linear shrinkage vs. proportion of ferrite at various sintering tem-peratures 223 5.12 Microstructure of a Fe - 0.45 P compact sintered for one hour at ( a ) 900 °C225 5.12 ( b ) 1100 °C 226 5.12 ( c ) 1200 °C 227 5.12 ( d ) 1350 °C 228 5.13 Microstructure of a Fe - 0.93P compact sintered for one hour ( a ) 1200 °C229 5.13 ( b )"l350 °C 230 5.13 ( c ) Fe - 0.2P sintered for one hour at 1350 °C 231 5.14 Comparison of experimental shrinkage with theoretical predictions as a function of temperature of sintering in Atomet 28 iron compacts sintered for one hour 233 5.15 Linear shrinkage vs. %P calculated from sintering equations ( theoretical ).236 5.16 Comparison of linear shrinkage ( obtained from experiment and theoretical calculations ) vs. % Phosphorus 237 5.17 SEM Photographs of a as pressed compact of ( a ) FeSi 239 5.17 ( b ) FeSiNa 2C0 3 240 5.18 Microstructure of a Fe - 3Si compact sintered at 850 °C for ( a ) 10 minutes.241 5.18 ( b ) 60 minutes 242 5.18 ( c ) 100 minutes 243 xvii 5.18 ( d ) 1000 minutes 244 5.19 Microstructure of a FeSiNa 2C0 3 compact sintered at 850 °C for ( a ) 10 minutes.245 5.19 ( b ) 60 minutes 246 5.19 ( c ) 60 minutes 247 5.19 ( d ) 500 minutes 248 5.20 Microstructure of a Fe - 3Si compact sintered at 950 °C for ( a ) 10 minutes. 251 5.20 ( b ) 60 minutes 252 5.21 Microstructure of a FeSiNa 2C0 3 compacts sintered at 950 °C for ( a ) 10 minutes : shows the new phases formed 253 5.21 ( b ) 60 minutes 254 5.21 ( c ) 1000 minutes 255 5.22 SEM Microstructure and the corresponding X-Ray map of a Fe - 3Si com-pacts sintered at 1000 °C for ( a ) 10 minutes 256 5.22 ( b )"60 minutes 257 5.23 Dimensional variation in compact sintered for various times at ( a ) 850 °C259 5.23 ( b ) 950 °C 260 5.23 ( c ) 1000 °C 261 5.24 % Linear shrinkage as a function of temperature in a prealloyed a - FeSi alloy sintered for one hour 263 5.25 Theoretical full green and sintered density as a function of silicon content. 267 5.26 Theoretical predictions of linear shrinkage in a prealloyed compact sintered for one hour 269 5.27 Comparison of linear shrinkage observed in the present study with that of values reported in the literature t . 272 5.28 Microstructure of Fe - 0.35P compacts etched with Oberhoffer's reagent. 273 5.28 Microstructure of Fe - 0.48P compacts etched with Oberhoffer's reagent. 274 xviii 5.28 Microstructure of Fe - 0.2P compacts etched with Oberhoffer's reagent. . 275 xix List of Symbols A C - excess vacancy concentration in the neck region A P - decrease in vapor pressure in the neck region Po — vapor pressure on a fiat surface Co - vacancy concentration under a flat surface C - concentration, w/o Ds - surface diffusion coefficient, m2/s Dos ~ P r e - exponential for surface diffusion, m2/s Djg - grain boundary diffusion coefficient, m 2/s DOB _ pre - exponential for grain boundary diffusion, m2/s " Dy - lattice diffusion coefficient, m2/s Doy ~ P r e - exponential for lattice diffusion, m2/s Do - theoretical density, g/cm3 D; - initial density of the compact, g/cm3 D r - relative density Ds - sintered density of the compact, g/cm3 F - 7s^ / kT, m G 0 _ initial grain size, /xm G - grain size, fxm K i , K2 and K 3 ~ curvature differences which drive diffusive fluxes, m~T L - edge length of a grain, fim N - dislocation density, m~ 2 xx p - porosity P - applied pressure, M N / m 2 ^ [p] - rate of pore shrinkage Py - vapor pressure, N/m 2 Qs - activation energy for surface diffusion, kJ/mole QB ~ activation energy for grain boundary diffusion, kJ/mole Qv ~ activation energy for lattice diffusion, kJ/mole Z - coordination number R - universal gas constant, 8.31 J/mole T - temperature, °C TH, T / T M - homologous temperature T M - melting temperature, °C V - volume, m 3 a - particle radius, /xm b - burgers vector, m / - volume fraction of pores h - one half of the approach of particle centres, / im k - Boltzmann's constant, 1.38 x l O " 2 3 J / K I - initial length, / im If - length at zero porosity, /xm It - length at any instant of time, /xm c, m, n - constants C , M , N - constants r - radius of pore, /xm x x i t - time of sintering, minutes x -- radius of neck between two particles, ^m Xi -- initial contact neck radius of a green compact, /xm x/a - normalised neck radius (x/a)i -- normalised initial neck radius for a green compact, /xm x - neck growth rate, m/s xf ' - final value of x when 100 % density is reached, /xm 8 -- film.thickness, /xm SB -- effective grain boundary thickness, /xm Ss -- effective surface thickness, /xm (SI/I) -- linear shrinkage 7 " surface tension of solid, J /m 2 IB -- grain boundary free energy, J /m 2 75 - surface free energy, J /m 2 A* " - shear modulas, N/m 2 ft -- atomic or molecular volume, m 3 4> -- dihedral angle, degrees p • - radius of curvature of the neck, /xm a stress acting in the neck area, MPa 6 contact angle, degrees t complex geometry factor X X I I Acknowledgement I would like to express my sincere gratitude to my research supervisor Pro-fessor J. A. H. Lund for his advice, encouragement and guidance throughout the course of this project. It is my privilege to be associated with such a kind and helpful person. I would also like to extend my gratitude to Professor A. C. D. Chaklader for his involvement in the project. Thanks are also extended to other committee members for critically reviewing the manuscript and making many useful suggestions. The assistance provided by Professor R.G. Butters, Mr. P. Musil and other technical staff members of the Department is gratefully acknowledged. My sincere thanks to Mr. K. Mukunthan for his constant encouragement, help and moral support. Spontaneous help and useful suggestions by Mr. Bernardo Hernandez Morales are sincerely appreciated. There are no words to describe the indebtness I owe to the members of my family without whose sacrifices nothing would have been possible. I acknowledge with thanks the financial support provided by A L C A N Canada and the Natural Sciences and Engineering Research Council of Canada. xxiii Chapter 1 I N T R O D U C T I O N A wide range of machine parts is commercially mass produced from metal and alloy powders by a sequence of compacting and sintering operations. The required shape is first obtained by compacting loose powders in a die. The resulting "green" compact is typically 75 to 90 per cent of solid density ( 25 to 10 per cent pores by volume ), and has enough strength to permit some handling when it is ejected from the die. In order to develop the required mechanical, magnetic, electrical or other properties, the parts must be "sintered", i.e., heated to a temperature at which strongly bonded bridges or necks are established at powder particle contacts through diffusional or other processes. Frequently it is desirable to control the sintering process such that very lit-tle change occurs in the density of the compact, i.e., the dimensions and shape olthe as-pressed parts are maintained. In other applications, where property requirements ne-cessitate that the pore content he reduced to a very low level, sintering conditions are chosen to produce densification ( shrinkage ). Most pressed and sintered parts are made from iron powders and blends of powders based on iron. In some systems, e.g. iron-copper, it is possible to sinter under conditions where a wetting liquid phase forms. In such cases, dimensions change rapidly and it is difficult to avoid shape distortion during sintering. The work of this thesis deals with the more important case of solid state sintering, applied to ferrous powder compacts. The driving force for sintering is the reduction in the system free energy, manifested by the elimination of surface area. Sintering kinetics depend on a number of important 1 2 physical and process variables. The effect of each one of these variables has been system-atically studied in the past, and qualitative trends have been established. Even though some equations describing the process of sintering were derived long ago, there has been very little attempt to use these equations to determine the mechanisms of material trans-port, or to predict quantitatively the influence of such important parameters as sintering temperature, time, particle size, and initial green density. This chapter examines the theoretical approach to the solid state sintering of metals, and describes how the theory can be applied to the construction of sintering maps for model ferrous compacts. 1.1 I N T R O D U C T I O N T O SOLID S T A T E SINTERING M O D E L S 1.1.1 The Driving Force Sintering classically involves mass transport which is driven by surface tension ( or cap-illary ) stresses. These stresses arise from the geometry of the inner and the outer boundaries of the particles in contact. The simplest example is sintering of a pair of spheres of equal size for which the geometry is shown in Figure 1.1. The most important parameters to describe the course of sintering, particularly in the initial stage of sintering, are the radius of the neck x and the approach of particle centres 2h ( which is taken as a measure of shrinkage ). The equations for x and 2h are derived with many simplifying assumptions. Once the neck is formed the neck has a different radius of curvature p compared to the particle surface. The radii of curvatures p and a have opposite signs with respect to the solid surfaces. The stress acting in the neck area, defined as <r, is given by the Laplace equation 3 Figure 1.1: Idealized section of a two particle model : x is the neck radius, p is the radius of curvature and a is the particle radius : ( a ) without penetration ( b ) with centre approach. 4 Since p is <C x this is simplified to <r = - l (1.1) P where 7 is the surface tension of solid. The negative sign indicates that the stress in the neck area is tensile. Thus under a concave surface like the neck tensile stresses exist and under a convex surface compressive stresses are present. Applying the Gibbs -Thompson equation, due to this stress there is a difference in vapor pressure and vacancy concentration between the neck and the surfaces of the particles approximated by A C _ A P _ 7 0 ~~C% ~ ~h\ ~ ~RTp where A C is the excess vacancy concentration in the neck region, Cl is the molecular volume of solid, A P is the decrease in vapor pressure in the neck region, P 0 , Co are the vapor pressure and vacancy concentration on a flat surface. 1.1.2 Mechanisms of Mass Transport The stress in the neck area given by Equation 1.1 can induce mass transport by plastic deformation ( if the stresses created during sintering are large ), by evaporation and condensation (. due to gradients in vapor pressure ) or atomic movement by surface, volume or boundary diffusion ( due to the gradient of vacancy concentration ). Methods of mass transport other than plastic flow are illustrated in Figure 1.2 and listed in Table 1.1. The several sources from which the material diffuses to the neck, listed in Table 1.1 are the particle surface, volume and grain boundaries ( particularly the boundary formed at the interparticle contact ). Surface diffusion ( Mechanism 1 ) contributes to substantial mass transport and hence neck growth, but cannot contribute to densification or shrinkage. Similarly movement of mass from surfaces to the neck by lattice diffusion or sublimation ( Mechanisms 2 and 5 Figure 1.2: ( a ) Progress of neck growth ( b ) Paths of different mechanisms of transport. Table 1.1: Paths of Different Mechanisms of Mass Transport. Mechanism Transport Sources of Sink of No path matter matter 1 Surface diffusion Surface Neck 2 Lattice diffusion Surface Neck 3 Vapor transport Surface Neck 4 Boundary diffusion Grain boundary Neck 5 Lattice diffusion Grain boundary Neck 6 Lattice diffusion Dislocations Neck 6 3 ) does not cause shrinkage, but causes only neck growth and pore rounding. On the other hand volume and boundary diffusion, involving material which is removed from the particle contacts ( Mechanisms 4 to 6 ), contribute to both shrinkage and densification. Figure 1.1 represents the section along the line between the particle centres, and it illustrates the two extreme cases of neck formation ( a ) without approach between the centres and ( b ) with maximum penetration. 1.1.3 Sintering Equations for a P a i r of Spheres The general relationship between neck geometry and time for a single transport mecha-nism and for two equal sized spheres initially in point contact has been derived by several workers [1-10] and can be summarized as \aj am v ' where x is the neck radius, a is the particle radius, t is the time of sintering and C = f(T). The constants n, m , and C have been shown to have values characteristic of the vari-ous transport mechanisms. Following the suggestions of Kuczynski [1], it was customary for many years to fit the experimentally observed sintering rates to the rate equations derived from theoretical models of each of the several mechanisms to determine which mechanism contributed predominantly to sintering i n a given material. However, only in rare cases does a single mechanism contribute to sintering. Even in experiments involving spheres, there is a high probability that the sintering behavior cannot be unambiguously interpreted in terms of a single mechanism. Two or more mechanisms operating simul-taneously can give a reasonably straight line on log(neck size or shrinkage) vs. log(time) plots with a slope close to one of the individual expected values. The problem of how to deal with two or more simultaneous mechanisms has been studied by several authors 7 [2,3,4,5]. Johnson [5] was the first to show that sintering of two spheres could be cal-culated under simultaneous surface, volume and grain boundary diffusion by adding the individual contributions to the rate as previously suggested by Rockland [6]. A graphical method was adopted by Johnson and Cutler [7] to relate sintering shrink-age, radius of curvature of the neck surface p, the contact radius x and the area of cross section A across which diffusion takes place. For derivation of sintering equations most authors [1,8,9,10] have assumed a circular arc for the neck contour and also have set 2h, the penetration depth, equal to the radius of curvature of the neck p. German and Munir [11] assumed a hyperbolic cosine function instead of a circular arc for the neck contour. Swinkels and Ashby [12] used an elliptical contour and modified the equations accordingly. Since the exact contour is not known, the simple case of a circular arc is used in most cases. 1.1 .4 S i n t e r i n g E q u a t i o n s f o r I r r e g u l a r A r r a y s o f C o n t a c t i n g S p h e r e s Exner [13] has surveyed the sintering behavior of irregular ( non-close packed ) arrays of three or more loose spherical particles, including linear, planar and three dimensional arrays. In all cases the geometry of neck growth is complicated by the fact that rearrange-ment of particles occurs by the rotational or gliding movement of particles relative to one another. The reasons for rearrangement are unsymmetric neck formation and induced stresses. Asymmetric necks form due to asymmetric contact geometry and asymmetric packing of particles. No equations have been suggested to describe this type of sintering. Eadie et al. [14] developed a model to predict the shrinkage rate during the initial stage of sintering of a line of spheres. The model can be applied to predict the shrinkage rate of a planar aggregate of equal sized spheres. But to do so, the initial packing density and the number of contacts per sphere has to be known. In practice the maximum packing that is obtained with monosized spheres is found to be 64 % of the available 8 space and the average number of contacts per particle is 4.5 ( two particles share each contact point and therefore the total number of contacts is 9 ) . As the aggregate is sintered the number of contacts increases. 1.1.5 Sintering Equations for Ideal Compacts The neck growth equations can be used to derive equations for the shrinkage of model compacts of monosized spherical particles. In the derivation it is always assumed that the coordination number i.e. the number of contacts or necks per particle remains constant during sintering. As noted in the previous section, this assumption is not valid for loose powder arrays because particles rotate and the coordination number increases as sintering progresses. In pressed compacts, however, the spheres are constrained from rotating and a constant maximum number of contacts for a given density can be assumed. A close packing of spheres fills 74 % of space and the average coordination number is 12. A compact of perfectly uniform spheres ( an ideal compact ) init ial ly follows the same shrinkage equations as two spheres in contact, if the sintering mechanism is volume and or grain boundary diffusion. After a certain amount of shrinkage has taken place in the compact the individual necks begin to impinge on each other and the shrinkage rate drops below that predicted for a pair of spheres. As for a pair of spheres, the relationship between linear shrinkage and time is generalized by the equation compacts for which sintering equations of the form of Equation 1.3 have been derived. For example, the process of compaction causes init ial contact areas to be established by plastic flow at interparticle contacts. Moreover the metal powders used are not of uniform (1.3) where I is the init ial length. A typical ( real ) metal powder compact of practical interest deviates from the model 9 size, are seldom spherical, and may have irregular and oxidized surfaces. Attempts to cope with these deviations from the above models are discussed in a later section of the thesis. 1.2 STAGES OF SINTERING AND SINTERING RATE EQUATIONS It is conventional to think of sintering to occur in three overlapping ( sequential ) stages. In addition to this, sometimes a fourth stage ( adhesion or zero stage ) is included. 1.2.1 Stage 0 : Adhesion When two particles are placed in contact with each other interatomic forces, Van der Waals in character, act between them drawing them together. A small contact area is established. If they are absolutely clean an upper limit for the radius of the contact is given by Easterling and Tholen [15] When the contacts are not perfectly clean, the Van der Waals forces act to produce a smaller contact radius given by ( dirty surface approximation ) [15] (1.4) where 7 e / / = 27 s - 7 5 ,75 is the surface free, energy, 7^ is the grain boundary energy and fi is the shear modulus. Since (f) is inversely proportional to a, adhesion plays a more important role when sintering very fine powders e.g. powders with submicron size particles. 10 1.2.2 Stage 1 : Initial Stage of Sintering True sintering starts with the formation of solid cohesively bonded necks at interparticle contacts. The precise mechanism by which neck formation is nucleated is poorly under-stood. Since there is in general a crystallographic misorientation between the grains in the particles on either side of a contact, each neck formed contains a grain boundary. Stage 1 refers to the early progress of neck growth during which the individual particles are still distinguishable. In the case of an aggregate of particles, stage 1 typically extends until a sintered density of ~ 85 % of solid is achieved. Many studies have been devoted to the study of sintering mechanisms in the first stage. Equation 1.2 was proposed by Kuczynski [1] to represent the kinetics for a pair of spheres. Equations derived by other workers differ essentially in the values of the constants. For the present purpose the rate equations which will be used to describe the contribution of each participating mechanism of neck growth in the first stage are taken from the published reports of Ashby [16], which in turn were obtained by him from earlier literature and in some cases modified by him. (a) Pair of spheres Sintering is driven by the vapor pressure or concentration gradients which arises from the difference of curvature of solid surfaces in the region of the interparticle contacts. Consider a pair of equal sized spheres in contact. Figure 1.2 shows successive positions of the growing neck and describes the mass transport paths for the six different mechanisms of sintering listed in 1.1. The radius of curvature of the neck is p. This radius is found from the geometry [1] shown in Figure 1.1 and is given by 11 Since i < a in most cases, p is simplified to (x2/2a). The curvature difference from the surface of a particle to the neck is given by K . - f i . i ^ U - E ) (,6) \p x a) V a) and from the grain boundary ( inside the neck ) to the neck is In the initial stages the magnitudes of K\ and K2 are nearly the same and as x ap-proaches a, they begin to differ. (b) Aggregate of spheres The equations of curvature can be applied to the sintering of aggregates with ap-propriate modifications. The sintering equations will be the same as those for a pair of spheres except that after a certain amount of sintering has taken place, the necks in the aggregate begin to interfere with each other and there is a limiting or maximum (^ ) value. Figure 1.3 shows the geometry during stage 1 of sintering. When the neck size is small, the curvature difference for surface diffusion is given by \p x a J The curvature difference becomes zero when the pore becomes spherical or cylindrical and the neck radius at which it becomes zero is a function of pore fraction / . If the initial density of the compact of particles is Di and the theoretical density of the material is D0 then the volume fraction of pores is given by = Do - Pj  f D0 12 Assuming three pores per particle the radius of the spherical pore is given by (|)3o. Thus K\ becomes zero when where Xf is the value of a; at which 100 % density is reached. Thus the curvature difference for diffusion from surface source is modified to incorporate the volume fraction of pores / in an aggregate as [16] = + '-jJ] (1.8) \P x a) y X f - (LyaJ where Xf is the hmiting value of (^ ) equal to 0.74. In other words K 1 = ( i _ i + H ) ( I _ _ i ) \p x a/ \ ma) where m = 1 for pair of spheres Tn = Xf - 3 a for an aggregate of spheres, and K2 remains the same as before. Once Ki and K2 are identified for the given cases the sintering equations are defined for the six different mechanisms considered. 1. surface diffusion from surface sources [1,4] xx = 2Ds6sFKl (1.10) 2. lattice diffusion from surface sources [1,4] s 2 = 2DvFKl (1.11) Figure 1.3: Geometry during Stage 1 sintering [16]. 3. vapor transport from surface sources [8] 4. boundary transport from sources on the grain boundary [5] ADB8BFKl XA = X 5. lattice diffusion from sources on the grain boundary [4] x5 = ADvFKl 6. lattice diffusion from dislocation sources [16] ie = ^K2Nx2DvF (K2 - f-^-) 9 V 2-ytaJ 14 F = jQ/kT and the meanings of the symbols used above are referred in the lists of symbols in the beginning of the thesis. If the mechanisms are taken to be independent, the net sintering rate in Stage 1 is given by summing the individual contributions i.e. 1.2.3 Stages 2 and 3 : Intermediate and F i n a l Stages of Sintering. Although most studies of sintering mechanisms are confined to the initial stages, there is practical interest in the later stages where significant additional changes take place in the density and properties of the sintered aggregate. Theoretical treatment is complicated, however, by grain growth and the formation of isolated pores, the effects of which compete with densification. Coble [17,18] has attempted to analyze sintering kinetics for the later stages. He con-siders a sintered compact as an aggregate of grains each of the same size and having the form of a tetrakaidecahedron. The porosity in stage 2 consists of interconnected cylinders along the grain edges as shown in Figure 1.4. The transition to stage 3 involves constric-tion of these cylindrical channels to form closed pores at the grain corners. Pore surfaces are the vacancy sources and grain boundaries are the vacancy sink. Two mechanisms, volume and grain boundary are responsible for densification and pore shrinkage. Assuming the process to be controlled by grain boundary diffusion, the rate of pore shrinkage is given by [17] (1.16) t = l,6 (1.17) 15 Figure 1.4: Pore shape in the intermediate and final stages ( a ) Intermediate stage : dark grains adopt a shape of tetrakaidecahedron, enclosing white pore channels at grain edges ( b ) Final stages : pores are at corners [17]. 16 where L is the edge length of the tetrakaidecahedron at time = t. For the case of volume diffusion the equation is given by <i NDyjfl Jt\P\ ~ R T L 3 where N is a numerical constant. These equations cannot be used without knowing the variation of L with t\ i.e. the effect of grain growth must be included. Assuming grain size to change with time as G3 = At and approximating G3 = L3, we get d NDvlVl It [p] = --Mkf- ( L 1 8 ) - W I = J ™ B * 5 ( L 1 9 ) dtm AthT The value of A is a function of temperature. The equations involve the rate of change of volume fraction of pores and not the length of the specimens. However, porosity in the compact is simply related to the linear shrinkage as Spores P ~ '• Knatier Spores If lt is the specimen length at time t and If is the length at zero porosity, then provided that the shrinkage is isotropic. For the final stage of sintering the pore is assumed to be spherical and isolated and the porosity is given by _ 7r(r) 3  P ~ y/2L3 where r is the radius of the pore and L is as before the edge length of tetrakaidecahedron. The rate of pore shrinkage is given by dp Air d 3 8TvDv"fCl Tt  = TTr r>  = kf 17 However, this neglects the possibility that pores may coarsen ( some grow at the expense of others ) and that gas trapped in the closed pores acts to oppose the surface tension stress. Ashby [16] treated stages 2/3 together. Figure 1.5 represents the geometry of stages 2 and 3 with pore radius p2 given by p2 = Xf - x. The sintering rate due to boundary and volume diffusion as solved by Ashby [16] is given by xB = —DB8BFKl I \ ) 16 3 \ l o g e ( ^ ) - f j xv = —xDyFKl ( \ ) where K3 is the curvature difference for diffusion in the stages 2 and 3 given by Net sintering rate in the second stage is given by the sum of the two xnet = xB +xv (1-20) Ashby made no attempt to include the effects "of grain growth in his sintering equations. 1.3 SINTERING DIAGRAMS Based first on the two sphere model, Ashby [16,19] developed the construction and use of sintering diagrams. The two major assumptions made for the construction are that sintering occurs in the absence of an applied stress and that pores contain no gas other than the vapor of the metal being sintered. These plots, also referred to as sintering maps, are used as an aid in sintering and represent a powerful tool in choosing the conditions of sintering. Later sections describe in detail the mathematics and the construction of sintering diagrams. 18 \ Figure 1.5: Geometry of stages 2 and 3 [16]. All six major transport mechanisms indicated in Figure 1.2 are considered. In its simplest form the sintering diagram consists of fields or regimes of neck size and tem-perature within which one particular mechanism is contributing most to the transport of mass to the neck. Superimposed on these fields are lines which represent the rates of sintering that all mechanisms acting together produce. Ashby [16,12] developed two kinds of diagrams: 1. Plots of contours of constant sintering rate. The diagram reveals how fast a neck is growing under given conditions. 2. Plots of contours of constant sintering time, which reveal the neck size after a given sintering time t. These diagrams are the most useful for practical purposes. Figure 1.6 shows a typical sintering diagram for a pair of copper spheres of 57fim radius. 19 For sintering aggregates Ashby [19] has also developed density diagrams in which relative density is plotted against homologous temperature. Maugis [20] has extended the Ashby's sintering diagram to the hot pressing of metal powders. TEMPERATURE °C 300 tSO 600 750 900 1050 3«10"5 10-5 E Q < CL 3«10"6 § - 10"6 " ' " o ~ <K bli vo HOMOLOGOUS TEMPERATURE T/T M Figure 1.6: Sintering diagram of copper spheres of 57 fim radius [16]. The boundaries between fields on a sintering map are established by equating pairs of rate equations and solving for neck size (|) as a function of temperature ( or homologous temperature T/TM )> since at such boundaries two mechanisms contribute equally to the sintering rate. This is a very useful plot particularly in choosing appropriate conditions of temperature and time for densification, as not all mechanisms of transport lead to densification. The contours of constant time are found by numerical computation of integral of the sum of the rates, appropriate to each stage, with respect to time. The approximate nature of available sintering rate equations and the questionable 20 accuracy of much of the published diffusion data which are used to construct the sintering diagrams make them intrinsically imprecise. Most of the published theory is based on ideal spherical particles of a single element. Ashby [16,19] has verified the theory in few cases. 1.4 I N T R O D U C T I O N T O S O L I D S T A T E S I N T E R I N G E N H A N C E M E N T The term enhanced sintering refers to any special approach aimed at improving the sintering rate of a powder compact at a given temperature, or improving the sintered properties obtainable under normal sintering conditions, or reducing the temperature of sintering. The enhancement may be due to changes in the surface properties, modification of grain boundary structure, or promotion of a normally dormant mechanism of mass transport. Activated sintering is the term used to describe a special case of solid state enhanced sintering which involves minor dopant additions to the base metal powder. One of the most dramatic examples of activated sintering is that of tungsten powders to which certain transition elements are added in small concentrations. Figure 1.7 shows the sintering shrinkage of 0.56 ^m W powder compacts with and without Ni additions [21]. It is evident that shrinkage at 1000 and 1100 °C is much higher for the doped material. Additions of Ni, Pd or Pt have all been found to lower the sintering temperature necessary for substantial densification from 2800 °C to below 1100 °C. Introducing a second phase addition which results in a wetting liquid phase is also a form of enhanced sintering. A major difference between liquid phase and activated sintering is in the amount of second phase present at the sintering temperature, typically liquid phase sintering is associated with a much larger volume fraction of second phase. The present study concentrates on solid state sintering only. 21 TIME (min) Figure 1.7: Effect of doping on shrinkage Rate of W compacts [21]. 22 1.4.1 Enhanced Sintering Sintering is accompanied by a reduction of surface area of the assembly of particles. The driving force for sintering is the reduction in the system free energy, manifested by decreased surface curvature and elimination of surface area. Sintering kinetics are dominated by the sharp curvature gradients located near the interparticle necks. In the previous section it was shown that solid state sintering involves transport of atoms to and across the contact points between the particles in a powder compact. To provide enhanced sintering one has to increase the driving force for sintering. 1.4.2 Methods of Enhancing Sintering There are several suggested approaches to enhance the solid state sintering rate of a metal powder aggregate. 1. Decreasing the particle size - This increases the specific surface area and thus provides a greater driving force for sintering. Rhines et al. [22] discussed this effect in terms of the increased number of interparticle contacts as the particle size decreases. 2. Inhibiting grain growth - Steps can be taken to ensure that pores remain intercon-nected by grain boundaries; Stages 2 and 3 of sintering will be enhanced. 3. Mechanical activation of powder by milling [23,24,25]. Mechanical milling may increase the density of dislocations and may increase surface energy appreciably. Dislocations act as sinks for vacancies and thus facilitate mass transport to necks by lattice diffusion. 4. Cycling the sintering temperature through a phase transformation [26,27,28,29]. Thermal cycling generates internal stresses and excess vacancy during sintering 23 cycle, which may increase sintering rates. There are claims that this is effective in sintering both iron and titanium alloys, but the evidence is questionable. Lund and Macquistan [30] found no effect for iron compacts, and Cizeron and Lacombe [31] and Hausner [32] observed a negative effect of cycling. 5. Adding suitable reactive gases to the sintering furnace atmosphere [33,34]. For Fe [35], halogens and halides have been used with apparent success. Modest improve-ments in strength and ductility were reported and were attributed to pore shape changes associated with evaporation and condensation of iron chloride. One dis-advantage of using a halide atmosphere is its corrosive effect on furnace heating elements. This approach is not considered to be practical. 6. Prior oxidation of powder or compacts [36,37,38]. Sintering enhancement from this source has been attributed to the higher activity of the newly formed surface following the dissociation or reduction of oxide. A critical oxide film thickness of the order of 50 — 70wn is reported [39] for a beneficial effect on the sintering of copper and iron powder compacts. 7. Activated sintering in which small amounts of second element ( dopant ) are added to the base powder. Sintering is in the solid state. Activators can be introduced by (a) mixing activator powder with the matrix powder (b) coating the powder with a uniform layer of the activator e.g. by plating (c) chemical reduction of a salt of the activator which has been admixed with the base metal powder. 24 1.4.3 Act ivated Sintering of Tungsten Powder : Literature Review The earliest report on the activated solid state sintering of tungsten powder was by Agte [40]. He first observed the effect of Ni as an activator during the sintering of mixed W -Ni powder compacts at temperatures as low as 900 °C ( i.e. 0.32 TM )• Vacek [41] later demonstrated the phenomenon with other additives to tungsten. The first detailed investigation in which W was sintered with the aid of dopants was done by Brophy et al. [42]. They observed a final density of 90% of theoretical after 30 minutes at 1100 °C in a compact of only 53 % starting density. Their data for Ni - coated H2 reduced W powder of 0.56 ^m diameter sintered at 1000 °C are shown in Figure 1.8. The sintering rate was observed to be inversely proportional to tungsten particle size. Densification was observed in two stages. The second stage (slower) was found to begin with the onset of grain growth. From the determination of the amount of Ni required to attain full activation of sintering Brophy [42] concluded that a "monoatomic" layer of Ni is required assuming the activator is evenly distributed on the entire surface of the W particles. There was no direct experimental evidence for the distribution of Ni on the surfaces. The activation energy for the sintering process was calculated by Brophy et al. as 284 kJ/mole. Hayden and Brophy [43] studied the influence of each of the elements Ru, Rh, Pt, Ni and Pd in W powder compacts and again established an optimum content of each activator equivalent to an assumed uniform layer thickness. Further work was done by Ylasseri and Tikkanen [44], Schintlemeister and Richter [45], and Skhorokhod and Paninchkina [46] on the Ni activated sintering of W. A series of experiments was done by Samsonov and Yakovlev [47] in an attempt to determine the characteristics which provide activated sintering. They found that additions of elements to the left of W in the periodic table i.e Ti , Hf, Ta, Cr, Nb showed 25 07 OlO 05 -<| o 02 <U g 01 x z £ 3> 005 a < UJ z " ' .002 001 0 0 0 5 002 005 OlO 0 2 0 5 10 2 0 WEIGHT PERCENT NICKEL Figure 1.8: Sintering Results of Ni coated 0.56 fim. W sintered at 1000°C [42]. no activation effect whereas additions from the right of W in the transition series resulted in positive activation. Based on these observations they related activation to the different "d" electron structure of W and the activator. Toth and Lockington [48] introduced the activator as a halide which was reduced to metal before sintering of the W powder ( 3.8 fim ) at 1000 °C. In the first series of tests activator concentration was varied ( Ni from 0.0054% to 0.865% and Pd from 0.545% to 1.75% ) to determine the optimum activator content needed to give maximum linear shrinkage. The optimum concentration of activator was found to be 0.130% for Ni and 0.317% for Pd. The optima reported by Brophy and colleagues [42] are 0.12% and 0.25% for Ni and Pd respectively. Unlike Brophy et al [42] Toth and Lockington observed a decrease in shrinkage rate beyond the optimum concentration. At the optimum con-centration shrinkage rate was more pronounced in the case of Pd than Ni i.e. Pd was a stronger activator than Ni. From a second series of isothermal sintering tests at the t O MIN : T 1 lOOCC 26 optimum activator concentration, the activation energy was found to be 211 kJ/mole which corresponds to the estimated value of surface self diffusion in tungsten. Electron microprobe analysis on the fracture surface revealed the presence of Ni. Gessinger and Fischmeister [21] introduced 0.5% nickel to tungsten powder compacts in three different ways; i.e. by evaporation, chemical solution and reduction and elemental blending. Some experimental results on activated sintering of Gessinger and Fischmeister are shown in Figure 1.7. Regardless of the W powder particle size ( 0.5 /im, 50 /im ) or the mode of addition of nickel, no continuous layer of Ni was observed. They measured the contact angle of solid Ni on W by evaporating Ni onto a flat W surface and heating at 1200 °C. The contact angle measured from SEM photographs was 35° i.e., Ni did not wet the W surface completely. The microstructures indicated that Ni had diffused into the tungsten grain boundaries. The effect of various transition metal additions on the sintering of 10 /im W powder in the temperature range of 900 - 1400 °C was analyzed by German and Munir [49]. The equivalent of approximately four atomic monolayers of Pd on W surfaces was found to give the optimal enhancement. In effectiveness as activator, Pd was first followed by Ni, Co, Pt and Fe. Each addition was made in the form of soluble nitrates and chlorides. Figure 1.9 shows results obtained for sintering temperatures of 1200 and 1300 °C using compacts of green density 43 % of solid. The activation energy for densification was determined to be 430 to 450 kJ/mole, which is consistent with a grain boundary diffusion process. German and Ham [50] reported that Pd provides the best enhancement of the sin-tering shrinkage of W when present in a quantity equivalent to four monolayers. No experimental evidence was provided that the activator was continuous, however. Ger-man and Li [51] demonstrated that if grain growth occurs during sintering it decreases the sintering shrinkage, and therefore the sintered strength. 27 Figure 1.9: Influence of additive coating thickness on W shrinkage enhancement for Ni, Pd and Pt sintered at 1200 and 1300 °C [49]. 28 The degree of shrinkage enhancement is very dependent on the particle size, clearly being greater for fine powders. Shrinkage is also shown to be dependent on the method of addition of the activator although this effect is less well established. Brophy [42] concluded that maximum shrinkage is achieved when small quantities are applied as surface coatings on the tungsten powder. Kim, Kim and Moon [52] found however that Ni when added as salt ( and reduced ) gives only slightly more activation than when added by mechanical mixing. Shrinkage is also dependent on the amount of activator. 1.4.4 Activated Sintering in Other Systems Activated sintering has been observed in other systems; for example Nb with Fe, Co, Ni, Pd and Pt [53], Hf with Co, Ni, Pd and Pt [54], Ta with Ni, Pd and Pt [55], Re with Pd and Pt [56], Cr with Pd, Ni [57,58], Mo with Ni [59,60,61,62]. The kinetics and mechanisms of sintering of Mo with Ni additions were studied by Smith [59]. The sintering rate was found to be two orders of magnitude higher than for pure Mo at a temperature of 1200 °C. Lejbrandt and Rutkowski [60] observed a similar effect. Rapid grain growth accompanies the activated sintering of Mo treated with Ni additions. Zovas and German [63] added fine dispersions of Si0 2 to control the grain growth and to thereby increase the overall sintering kinetics. 1.5 THEORIES OF A C T I V A T E D SINTERING As discussed above, very small additions of Ni and other transition elements are enough to activate sintering of W at temperatures far below the conventional sintering temperature. Although the effect is well known, interpretation of the process occurring during sintering varies considerably. 29 A number of mechanisms of activation have been proposed and are discussed in de-tail below using W-Ni as the prototype system. It should be noted that none of these proposals provide a totally satisfactory explanation for the role of the activator during the initial stages where a considerable amount of densification takes place. The accepted dominant low temperature sintering mechanism for pure tungsten is grain boundary self diffusion with a reported activation energy of 440 kJ/mole. The activation energy for W activated with Ni was found to be 280 kJ/mole by Brophy et al. [42]. Therefore they concluded that the mechanisms involving self diffusional transport in tungsten could be neglected in trying to explain activated sintering ( in tungsten ) by transition metal additives. 1.5.1 Solution Precipitation Theory of Brophy Brophy et al. [42] proposed a model in which nickel is a continuous film on tungsten surfaces and at contacts. The model proposed for the activating effect in the initial stage of sintering is shown schematically in Figure 1.10. Here the tungsten particles have been approximated to spheres with a nickel film of thickness (S/2). Volume diffusion of W on or through this Ni film is proposed to be the cause of densification. Basically the suggested mechanism of densification resembles the liquid phase sintering model of Kingery [64] with the Ni film playing the role of a completely wetting phase. The driving force is supplied by the surface energy of the "carrier" phase nickel. Although the centre to centre distance between the particles would decrease and shrinkage is expected, the model does not produce the kind of neck generally observed [1] shown in Figure 1.1 when two particles sinter. On the basis of linear shrinkage measurements as a function of Ni content, particle size, time and temperature, Brophy et al. [42] obtained : 30 The rate controlling step is believed to be the dissolution of tungsten in the nickel layer. Figure 1.10: Solution Reprecipitation Model of Brophy et al [42]. 1.5.2 M o d i f i e d Surface Theory of Toth and Lockington Toth and Lockington [48] proposed that the surface of tungsten particle was modified by the presence of nickel. Since the shrinkage rate was found to depend on the activator content, Toth and Lockington [48] ruled out the possibility of a phase boundary reaction ( dissolution ) as the rate controlling step of densification as suggested by Brophy [42]. A general analysis of the possible mechanisms is made which suggests that the movement of the tungsten atoms takes place through a series of steps in which surface diffusion is the key step. There are two weaknesses in the model: 31 1. Surface diffusion does not produce shrinkage in powder aggregates as discussed previously. 2. It is not indicated why Ni should increase the surface diffusivity of W. 1.5.3 Electronic Configurat ion Theory of Samsonov Samsonov and Yakovlev [53] ascribe activated sintering to the transfer of electrons from Ni to unlocalized electron orbitals in W, which facilitates diffusion. The activation occurs with the dissolution of the base metal into the activator layer with the net result of intermediate electron bonding between the two metals. Enhanced mass flow is attributed to the lowered average bond energy and hence lower process activation energy, as electron concentration in the layer controls the bond energy. It is argued that sintering is enhanced with the completion of a "d" subshell in the added transition metal. Unfortunately this suggestion was advanced without any geometrical model of the transport process involved. 1.5.4 Enhanced Diffusion Theory Ylasseri and Tikkanen [44] and Schintlemeister and Richter [45] postulated that sintering in the case of a trace addition was increased due to enhanced diffusion through a layer of activator at the interparticle contacts. Gessinger and Fischmeister [21] found that the contact angle between Ni and W was around 35°, which implied the need to revise Brophy's [42] assumption of a completely wetting carrier phase. The model is based on the diffusion of Ni over the W surface at the beginning of sintering and subsequent enrichment of Ni along the grain boundary at interparticle contacts. The Ni does not form a continuous film on W. Densification proceeds by the transport of W atoms from the boundary as shown in Figure 1.11 to the 32 surface region outside the contact zone but inside the Ni ring, under the influence of a chemical potential gradient set up by the capillary force. Figure 1.11: Enhanced diffusion model of Gessinger and Fischmeister [21]. The equation for shrinkage rate, a slight modification of that given by Brophy [42] and Kingery [64] is given by where £ is a complex term incorporating geometric parameters and interfacial energies. The activation of sintering is considered in two ways. 1. Formation of a thin film of Ni at the interparticle contacts through which W diffuses similar to Brophy et al [42]. 2. Grain boundary self diffusion enhancement by Ni as an impurity in a W grain akT (1.21) dt boundary. 33 Since a continuous layer of Ni was never observed directly and since Ni in grain boundaries was observed [48], Gessinger and Fischmeister [21] attributed at least some of the observed activation to the second suggestion i.e enhancement of grain boundary self diffusion in tungsten. The authors declined to be conclusive about which of the models is dominant. Subsequently German [65] developed a quantitative model for enhanced sintering of refractory metals, assuming activator - enriched interparticle grain boundaries. In this model the additive which is depicted as a layer shown in Figure 1.12 is seen as providing an easier path for grain boundary diffusion of W. The theory is questionable, since in the assumed geometry of the contacts there is no neck or grain boundary in the tungsten. The quantitative calculations of German apply the Engel - Brewer [66] theory. Activator Figure 1.12: Geometric model of heterodiffusion controlled activated sintering -Schematic Diagram [61]. The Engel - Brewer theory predicts the activation energy for the diffusion of refractory metals through various additive layers. The Engel - Brewer theory and its application 34 to activated sintering is discussed in later sections. This quantitative model was tested for the molybdenum - nickel system. The experimental shrinkage was found to be in agreement with the predicted values. 1.5.5 Summary of the Theories In spite of considerable past work on activated sintering, particularly in the W-Ni system, a consistent theory has not been evolved and a physical understanding of the process is lacking. The proposed theories are based on surface diffusion enhancement [48], solution -reprecipitation [42], electronic configuration [53] and enhanced grain boundary self diffu-sion [21,44,45,65]. For solution - reprecipitation, unipolar solubility was thought to be a dominant effect. Accordingly this led to a kinetic model analogous to liquid phase sinter-ing. However subsequent observations by Gessinger and Fischmeister [21] discounted this approach in favour of conventional solid state self diffusional arguments. Samsonov and Yakovlev [53] used electronic configuration stability to try to explain activated sintering. Models in which the activator is assumed to be present as a continuous film at in-terparticle contacts seem to have been most widely used. The following questions arise from this prior body of work: 1. How can a film of activator influence surface / boundary / volume self diffusion coefficients? 2. There is no direct evidence of the existence of interparticle films of the additive. How valid is the assumption? 3. What is the physical significance of a "monolayer" of Ni as a diffusion path?. Why should there be an optimum amount of activator? 35 4. If a continuous film is to form along the entire grain boundary, must not the dihedral angle be zero? It has not been demonstrated to be so in W - Ni alloys. 5. Why is activated sintering apparently observed only in fine particle compacts? 1.6 C R I T E R I A F O R T H E S E L E C T I O N O F A N A C T I V A T O R It has been proposed by others that activated sintering occurs when the additive remains segregated at the particle contacts or at the grain boundary and when an "optimum" amount of activator is present. German [67] has proposed criteria for selecting an activa-tor based on certain phase diagram features. For a generalized presentation an element " A " (activator) is to be added to a base "B" powder to enhance the sintering of the latter. The first of German's criteria refers to the solubility relationship between the two components. The activator must have solubility for the base material to have favorable diffusion. The reverse solubility of A in B should be low if an activator film is to be maintained. Mathematically this can be expressed as (solubility of B in A / solubility of A in B) > 1. The second requirement according to German [67] is the segregation of the additive to the interparticle contacts during sintering. A decreasing solidus and liquidus as A is alloyed with B is said to favour such segregation. This idea follows from the work of Burton and Machlin [68]. Gibbs [69] predicted that equihbrium concentration at an alloy surface is not identical to its bulk composition and that one component may segregate to the surface. This phenomenon is referred to as surface segregation. Burton and Machlin [68] suggested that surface segregation is related to equilibrium distribution of a solute in an alloy to its liquid. They postulate that segregation will occur on the solid surface if and only if distribution occurs in the solid - liquid equihbrium so that the liquid is richer 36 in solute than the solid phase. This is the basis of zone refining to produce ultra high purity solids. Accordingly, they predicted that in dilute binary alloys if the separation between the solidus and the liquidus is large, surface segregation will occur. These criteria were brought together in the form of an ideal phase diagram as shown in Figure 1.13 which exhibits the required solubility and segregation criteria. These features are observed in several systems which exhibit activated sintering such as W - Ni, W -Pd, Mo - Ni, Cr - Ni, Mo - Pt, etc.. temperature large melting difference high solubility decreasing liquidus & solidus liquid phase .activated low solubility criteria solubility segregation diffusion Figure 1.13: Ideal Phase Diagram of an Activator [67]. The criteria for choosing an enhancer in the case of liquid phase enhanced sintering are also satisfied by the same phase diagram features. Both liquid phase and activated sintering rely on the presence of a second phase in sintering, though the mechanism of densification is different. Chapter 2 O B J E C T I V E S O F T H E P R E S E N T I N V E S T I G A T I O N It has been shown in the preceding section that our current understanding of the mech-anism of activated sintering is quite limited. However, if the process can be applied to more commonly used materials like Fe it will be beneficial from both economic and practical points of view. Ferrous sintered materials provide the largest class of powder metallurgy commercial products. A typical sintering temperature range is 1100-1200 °C. While some sintering enhancement in these materials has been reportedly obtained by several techniques, there has been no success with activated sintering analogous to W -Ni. In fact, the literature reveals that there have been few deliberate efforts to improve the solid state sintering of ferrous compacts. Prior work has concentrated on enhancement by liquid phase sintering, i.e. by the use of low temperature melting additives. One of the objectives of the present work is to find ways to improve the kinetics of solid state sintering in ferrous systems. One focus is on the identification of potential activators for ferrous systems and on an explanation of the phenomenon of activation in terms of its applicability to other systems in which it has been observed. To be able to analyze activated sintering it is first necessary to characterize the solid state sintering of iron through appropriate models and sintering maps. The existing models of sintering for ideal particle arrays need to be applied to the special case of iron powder compacts. Models then need to be modified and developed for real compacts i.e. they must incorporate the complex effects of particle shape, size distribution, surface 37 38 morphology, prior compaction and other factors which are ignored in the classical theories of solid state sintering. Sintering diagrams which have been developed for certain arrays of spherical particles are very useful in choosing sintering conditions, and in identifying the dominant mechanism of sintering. The specific development of these diagrams for iron powders, their modification to take material variables into account and their application to actual sintering are needed and will be attempted. For the process of activated sintering of iron with dopants, it is necessary to predict and test what additives might be effective based on available and proposed theories of the phenomenon. No attempts or successes of activated sintering with iron powders have previously been reported. The higher self diffusivity of Fe in the bcc ferrite form than that in the fee austenite form at a given temperature is well known and established. Therefore, there exists the potential for enhancement of sintering in ferrous systems by adding elements to Fe which dissolve and stabilize the a phase at typical or lower sintering temperatures. This ap-proach has been little used or recognized by previous investigators or in the ferrous P / M industry. It should be possible to model this form of sintering enhancement and to pre-dict systems and sintering conditions which are potentially useful. The predictions can then be tested experimentally. Two cases of ferrite stabilization can be distinguished, one involving a prealloyed material in which only sintering is involved, and a second in which mixed powders are used and in which alloying by interdiffusion must precede or accom-pany sintering. Once again it may be possible to treat these cases both experimentally and theoretically. Chapter 3 CONSTRUCTION AND ANALYSIS OF SINTERING DIAGRAMS FOR IRON COMPACTS 3.1 AIM AND DESCRIPTION OF THE PROBLEM Many experimental results for the sintering of Fe powder are available in the literature. However, there are no theoretical predictions of sintering behavior for iron in the form of published calculations or sintering diagrams. Even though in their present state of development sintering maps have some limitations, they can be useful in establishing the effects of many sintering variables on the sintering kinetics of compacts. Accordingly, the present study was initiated to develop appropriate field maps and shrinkage plots for iron from which it would be possible to develop quantitative relationships between sintering behavior and such variables as initial packing density, particle size and temperature. With this goal, on the basis of the analysis of driving forces and transport phenomena, linear shrinkage and neck growth rate equations for a compact are derived for model systems, using the first principles of sintering. These equations are then used for the construction of sintering diagrams. In the earlier work on sintering diagrams [16,19], aggregates of spheres were considered which were packed densely, but with point contacts to one another. In practical sintering studies a different contact geometry is of greater importance, i.e. the geometry which is formed by deformation during pressing of the powders. In the production of powder metallurgy parts sintering is almost always preceded by cold pressing. Only occasionally 39 40 there has been any mention of pressing which may influence the kinetics of sintering [10,70,71]. Exner [13] found an empirical relationship between applied pressure P and contact neck radius x; after pressing and has indicated that by using this geometric factor Xi, the sintering equations might be modified for a pressed compact. The present study on Fe compacts incorporates the effect of initial density ( instead of pressing pressure ) on the sintering kinetics. No prior attempt to use this approach is reported in the literature. In the case of a pair of spheres it is easy to measure (^ ) as a function of time t of sintering at a given temperature T and hence to conduct verification of the theoretical models from a sintering diagram. But in the case of a compact, it is only practical to measure linear shrinkage or density rather than the neck radius and the equations have therefore been modified to predict linear shrinkage % ( j ) to obtain a plot of % (j) versus (ft)-3.2 S I M P L I F I E D M E T H O D O F E S T A B L I S H I N G A F I E L D M A P Field maps are useful tools to predict trends associated with large changes in sintering conditions of different materials. A schematic example of such a map is shown in Figure 3.1. The fields are bounded by lines which are the locus of the points at which two mech-anisms are calculated to contribute equally to mass flow. The following section shows how the basic map can be constructed with a minimum of computational effort when certain relationships among the sintering equations are recognized. The practical method of constructing the map as suggested by Ashby [19] is laborious and time consuming. The simplified method of construction of field maps developed in the present work is applicable to rows, aggregates and compacts of particles. For metals under sintering conditions of practical interest the contributions to neck growth ( beyond adhesion ) are 41 made by the different transport mechanisms listed in Table 1.1. However, the magni-tudes of x from various mechanisms, calculated for copper and iron pairs of spheres and compacts, indicate that major contributions are from three mechanisms, namely surface diffusion from surface sources and volume and boundary diffusion from boundary sources. The calculated results of x for iron are listed in Tables 3.2 and 3.3. The material con-stants used for iron in these calculations are tabulated in Table 3.1 and were taken from the reports of Ashby [19]. The values of material constants and properties were carefully selected by Ashby from published values. The contribution from x6 ( from mechanism 6 ) was not included as the data were insufficient. However, Ashby [16] calculated this contribution to be negligible in silver, copper and tungsten. It is seen that the contribution from evaporation and condensation, i 3 , is very low as expected and so this mechanism is also not included in calculations. For a compact, the contribution from lattice diffusion from a surface source is less than one tenth of that due to the lattice diffusion from boundary sources. Since in a field map only the x values are compared this mechanism need not be considered. The symbols and equations used for different stages are given in Chapter 1. 42 1-3 BOUNDARY MECHANISM 3 DOMINATES MECHANISM 1 DOMINATES 2-3 BOUNDARY 1-2 BOUNDARY MECHANISM 2 DOMINATES HOMOLOGOUS TEMPERATURE (T/Tm) Figure 3.1: Schematic representation of a Field Map : Mechanisms 1, 2, 3 could be Boundary, Surface and Volume diffusion respectively as observed for many metals. 43 Table 3.1: Material Constants For Iron Used in the Predictions. PROPERTY a Iron 7 Iron Source Atomic Volume Q(m3) 1.18 x 10" -29 1.21 x 10 -29 Melting Point TM(K) 1810 1810 Surface Energy 7s(rn?) 2.10 2 [72] Effective boundary thickness SB (m) 5.12 xlO" -10 5.12 xlO -10 Effective surface thickness Ss (m) T 3.0 x lO-10 3.0 xlO" 10 Pre - Exp, lattice diffusion £W(§~) 1.9 x 10" 04 1.8 x 10" -04 [73] Activ. Energy, lattice diffusion Qv(jjtfe) 239 270 [73] Pre - Exp, boundary diffusion SBD0B(J^) 1.12 x 10 -12 7.5 x 10" -04 [74] Activ. Energy, boundary diffusion QB(^I^) 174 159 [74] Pre - Exp, surface diffusion D0sSs(j~) 2.5 x 10--09 1.1 x 10--10 [75] Activ. Energy, surface diffusion Qsim^) 232 220 [75] " value is taken to be that of Ag, Cu and W * value is taken to be that of Cu and is close to that of Ag and W 44 Table 3.2: Contributions to Neck Growth Rate x (m/s) From Different Mechanisms of Transport in a Pair of Iron Spheres. Particle size = 75 fim ( A ) xx x2 0.4 0.403 xlfJ--08 0.363 x l O " 1 2 0.10 x l O " 2 8 0.28 x lO-09 0.73 xio-12 0.50 0.72 xicr 06 0.821 x l O " 0 9 0.23 x l O - 2 3 0.73 xio- 07 0.164x10- 08 0.60 0.1026 xlO -02 0.136 x l O - 0 6 0.846 x l O - 2 0 0.288 xlO -05 0.273 xlO" -06 0.70 0.465 xlO--02 0.25 x l O " 0 6 0.28 x l O - 1 7 0.105 xlO -04 0.511 xirj--06 0.80 0.55 xifr 01 0.541 x l O - 0 5 0.214 x l O " 1 5 0.61 xlO" 04 0.109 xlO -04 0.90 .0.376 0.582 x l O - 0 4 0.611 x l O " 1 4 0.235 xlO -03 0.116 xlO -03 1.00 0.171 0.385 x l O - 0 3 0.877 x l O - 1 3 0.685 xlO -03 0.769 xlO -03 3.2.1 Construction of Field Maps The boundaries between fields on a sintering map are established by equating pairs of rate equations. At such boundaries two mechanisms contribute equally to the sintering rate. Equating i i and i 4 from Equations 1.10 and 1.13 (see p. 12) and rearranging gives iff - % <31» ZUBOB XKI which defines the interface [S/B] between the surface-diffusion dominated field and the grain boundary-diffusion dominated field. Similarly, from i\ and x5 ( Equations 1.10 and 45 Table 3.3: Contributions to Neck Growth Rate x (m/s) Different Mechanisms in an Iron Compact of 90 % Initial Relative Density. Particle size = 75 fim Xy x2 x3 0.40 0.23 x lO" 18 0.52 x l O " 1 9 0.32 x l O - 3 2 0.89 xlO" 17 0.56 xlO- 18 0.50 0.46 x i r r 15 0.13 x l O " 1 5 0.86 x l O ' 2 7 0.24 xlO" 14 0.14 xlO" 14 0.60 0.68 x i r r 13 0.22 x l O " 1 3 0.33 x l O - 2 3 0.10 xlO-12 0.24 xlO" 12 0.70 0.35 x lO" 12 0.47 x l O " 1 3 0.13 x l O ' 2 0 0.40 xlO" 12 0.51 xlO" 12 0.80 0.40E xlO -11 0.97 x l O " 1 2 0.97 x l O - 1 9 0.23 xlO" 11 0.10 xlO" -10 0.90 0.26 xlO-10 0.10 x l O " 1 0 0.27 x l O " 1 7 0.86 xlO" -11 0.11 xlO--09 1.00 0.12 xlO" 09 0.66 x l O " 1 0 0.37 x l O - 1 8 0.24 xlO--10 0.72 xlO" -09 Particle size = 10 fim 0.40 0.99 xlO" -16 0.29 x H T 1 7 0.23 x l O " 3 1 0.38 x lO' -14 0.31 xlO--16 0.50 0.19 xl0~ -12 0.72 x - 1 4 0.64 x l O - 2 6 0.10 x lO --11 0.78 xlO" -13 0.60 0.29 xlO" -10 0.12 x l O " 1 1 0.25 x l O " 2 2 0.42 xlO" -10 0.13 xlO" -10 0.70 0.14 xlO" -09 0.26 x l O - 1 1 0.10 x l O " 1 9 0.16 xlO" -09 0.28 xlO" -10 0.80 0.17 xlO" -08 0.55 x K T 1 0 0.73 x l O " 1 8 0.95 xlO" -09 0.59 xlO' -09 0.90 0.11 xlO--07 0.57xKT°9 0.20 x l O - 1 6 0.36 xlO" -08 0.62 xlO -08 1.00 0.50 xlO" -07 0.37.xlO - 0 8 0.28 x l O " 1 5 0.10 xlO" -07 0.40 xlO -07 46 1.14 ) (see p. 12) we obtain r'sOs J^2 D,8, K?2 2D, K l ' ( 3 2 ) which describes the Une [S/V] separating the fields dominated by surface diffusion and volume diffusion, respectively. From xA and x5 (Equations 1.13 and 1.14) (see p. 13) M£ = 1 (3.3) L>va a which defines the interface [B/V] between the grain boundary and volume diffusion fields. In stages 2 and 3 where only boundary and volume diffusion are operative by equating the rate equations, [B/V] interface is found to have the same relationship as Equation 3.3. -Several characteristics of Equations 3.1 through 3.3 provide the basis for the simple method proposed here to construct field maps. The case of copper spheres will be used for illustration. Relevant data were obtained from Ashby [19] and are listed in Table 3.4. Some of the salient characteristics of these equations can be identified as follows: 1. In each of the equations, the left hand side is a function of temperature but not of neck geometry. Thus plots of the logarithm of the left hand side vs. T [ or (-r^ ) ] are 'master' plots for a given material. The plots of Equation 3.1 and Equation 3.2 are applicable to any particle size or density of packing. Examples are shown for copper spheres in Figure 3.2 ( a ) and ( b ). 2. In each equation, the right hand side is a function of neck geometry only and not of temperature. Plots of the logarithm of the right hand side against logarithm of (^ ) as shown in Figure 3.2 ( c ) and ( d ) are therefore truly 'master' curves since they are applicable to any material. The plot is not needed for Equation 3.3 wherein the right hand side is simply (^). Table 3.4: Material Constants For Copper U s i ed in the Predictions. PROPERTY Copper Source Atomic Volume fi(m3) 1.18 x lCr 2 9 Melting Point T M ( K ) 1356 Surface Energy 75(7^2) 1.72 [72] Effective boundary thickness 63 (m) 5.12 x l O - 1 0 Effective surface thickness Ss (m) 3.0 x l O " 1 0 Pre - Exp, lattice diffusion Dov(f^) 6.2 x IO" 0 5 [76] Activ. Energy, lattice diffusion Qv{jjfi£fe) 207 [76] Pre - Exp, boundary diffusion SBD0B(J^:) 5.12 x l f r 1 5 [19] Activ. Energy, boundary diffusion QB(^~[^) 105 [19] Pre - Exp, surface diffusion Dosf>s{i^:) 6.0 x I O - 1 0 [77] Activ. Energy, surface diffusion Qs(jl^u) 205 [77] 48 3. In order to develop the field map, it is only necessary to plot log(^) vs. T or (^)-To establish the different field interfaces it is necessary then to find, from the plots just described, corresponding values of log(^) and ( ^ ) for equal values of the left hand and right hand side of equations 3.1 through 3.3. This is shown in Figure 3.3. Thus for points on the [S/B] interface of the field map for copper spheres from Figures 3.2 ( a ) and ( c ) equal values of the ordinate are found. For an equal value of 1 on the y axis of Figure 3.3, log(x/a) = -0.92 corresponding to a homologous temperature (T/TM) of 0.673 and for an equal value of 2 on the y axis, log(x/a) = -1.74 for a corresponding (T/T^f) of 0.582. The procedure is repeated to obtain a continuous log(x/a) vs. (T/T^f) curve. The [B/V] boundary is given immediately by Figure 3.2 ( e ), since this plot is already one of log(^) vs. (^)-This represents an easy and neat method for construction of a boundary map which does not involve the many calculations outlined in [12]. Further, the sintering rate equations are reduced to such a form that it is possible to predict easily the effect of changing particle size, pore fraction, ratio of diffusion coefficients etc. on the field maps and the dominating mechanism of transport. 3.2.2 Observations Several interesting observations were made during the construction of the field map. For example, the effects of changing the material geometry or conditions of sintering are readily predicted from Equations 3.1 through 3.3 and the plots obtained from them. The boundary between surface diffusion and grain boundary diffusion [S/B] is independent of the particle radius a, so that the triple point ( point at which all three mechanisms con-tribute simultaneously and equally to the neck growth ) moves along the curve of [S/B] when a varies. As a increases surface diffusion decreases in favour of volume diffusion. 4 9 ;ure 3.2: ( c )log(xK1 3/K2 2) vs. log{x/a) (d)log (KX 3IK2 2) vs. log{ 51 Figure 3.2: ( e ) log(x/a) vs. (T/TM) (calculated from DBSBIDVO) : Plot is the locus of points at which boundary and volume diffusion contribute equally to neck growth. H O M O L O G O U S T E M P E R A T U R E ( T / T M ) Figure 3.3: Demonstration of plotting the boundary for Copper spheres 53 This influence of radius is in accordance with Herrings scaling law [78] which predicts the effect of changing particle size on the time of sintering. It is thus easily seen, for example, that: 1. The [S/B] field boundary position is independent of particle size. This follows from Equation 3.1. A further simplification arises in Equation 3.1, for which the right hand side can be written as Ki2 xK22 (3.4) xKxz x2Kx3 From Equations 1.5 and 1.7 it is found that x 2x(a — x) 2a xK2 = - _ i = _ L _ ^ - l = 3 p X* X x K i = (He _ 3 + (i--?-) V x a J \ ma/ Thus, xKi and xK2 and the right hand side of Equation 3.1 are all functions of (f) and not of particle size alone. 2. The [S/V] interface moves to higher (^ ) values as particle size decreases ( see Figure 3.4 ). The shift in [S/V] interface can be easily calculated and predicted. 3. The [B/V] boundary location is strongly affected by particle size. For a given (^ ) value Equation 3.3 shows that the boundary will move to higher (-f^) as particle size decreases. These effects [(2) and (3)] are shown in Figure 3.4 for copper spheres. 54 -2 AA AA AA A3. A 41.8 -0.« -0.4 4)2 0 log(i/<0 (a) 0 -2 - f - — i 1 1 1 1 1 1 1 1 1 1 i i r ~ 0.7 0.74 0.78 0.82 OM 0.9 0.94 0.98 HOMOLOGOUS TEMPERATURE (T/TM) (b) Figure 3.4: Effect of particle size on the shift in (a) [S/V] interface (b) [B/V] interface for Copper spheres. 55 4. As pore fraction / = ( 1 - pTei ) of the powder aggregate rises, both the [S/B] and [S/V] interface move to lower (^ ) levels. [B/V] is not affected, as seen by Equation 3.3. 5. It is important to note that field boundary locations are determined by ratios of the different self diffusion coefficients, and not by the individual coefficients. Thus a change in sintering conditions which affects diffusion coefficients in similar proportions will not strongly influence the field boundaries on the sintering map. This accounts for the observation that the [S/V] boundary map is horizontal on the sintering map for packed copper spheres, since D$ and Dy have similar temperature dependence according to the values obtained from the literature [16]. This form of graphical representation to obtain the field or boundary map is essen-tial in understanding the influence of both geometrical and material properties in the sintering process. Establishing these graphs for all important materials provides ready means of obtaining knowledge about the dominant mechanism of sintering under different conditions. 3.3 S I N T E R I N G D I A G R A M S F O R A P A I R O F I R O N S P H E R E S 3.3.1 Calculat ions Following the procedure discussed before in Section 3.2 for the construction of sintering diagrams, maps were developed for pure iron. The graphical basis for constructing field maps for iron is shown in Figures 3.5 ( a ) to ( e ). Figure 3.5 ( a ) and ( b ) describe the variation of log of left hand side of Equations 3.1 and 3.2. This is independent of particle size a and therefore can be used as a master plot for future calculations. Figure 3.5 ( c ) and ( d ) represent the log of right hand side 56 of Equations 3.1 and 3.2. While the plot in Figure 3.5 ( c ) is independent of particle size, the plot in Figure 3.5 ( d ) is strongly dependent on a. The effect of changing the particle size on the shift in the boundary interfaces [S/V] and [B/V] is given in Figure 3.6. There is a phase transformation in iron at 912 °C, and since material properties, in particular diffusion coefficients, ( Table 3.5 ), are different for the alpha and gamma phase, a discontinuity is observed in neck growth plots and field maps at T = O.Q5TM-The material constants of Table 3.1 were used in all calculations in the present work. Predicted field maps for a pair of iron spheres are shown in Figures 3.7 ( a ) and ( b ). For calculating plots of neck growth, the starting value of (^ ) was taken as 0.01 ( ascribable to adhesion in stage 0 ). A simple computer program was developed to calculate (^ ) vs. (Y^) from the sintering equations, with the results shown in Figure 3.8. The individual contribution to (^ ) by surface, volume and boundary diffusion is given in Figure 3.9. The linear shrinkage calculated for a pair of spheres of 75 and 10 fim is given in Figure 3.10. The combination of Figures 3.7 and 3.8 for a given particle size constitutes a complete sintering "diagram" for a pair of iron spheres. Ashby [16] superimposed the two plots of field maps and neck growth. However this practice is avoided in the present work because it can be confusing. The field map ( e.g. Figure 3.7 ) indicates regimes of neck size and temperature where one transport mechanism is dominant, but in fact several mechanisms contribute to the actual values of (^) which are given from plots such as Figure 3.8. Sintering maps have been constructed for other metals by Ashby. The maps of most common metals like Ag, Cu, Ni, W and stainless steels all exhibit a field diagram domi-nated by surface, volume and grain boundary diffusion transport. In the case of iron the rates of sintering and field interface change sharply at the phase boundaries. Table 3.5: Diffusion Coefficients of Fe at 800 - 1200 °C. Temperature ( T / T M ) Diffusion Coefficients (m2/s) °C Surface Boundary Lattice 800 ( 0.6) 4.18 x l 0 ~ 1 2 7.34 x l O " 1 2 4.35 x l O - 1 6 900 (0.65) 3.84 x l O " 1 0 3.87 x l O - 1 1 4.23 x l O - 1 5 "912(a) (0.655) 4.88 x l O " 1 0 4.64 x l O - 1 1 5.47 x l O " 1 5 912(7) (0.655) 7.33 xlO"" 1 1 1.42 x l O " 1 1 2.2 x K T 1 6 1000 (0.7) 3.44 x l O - 1 0 4.33 x l O " 1 1 1.48 x K T 1 5 1100 (0.76) 1.56 x l O " 0 9 1.29 x l O - 1 0 9.51 x l O " 1 5 1200 (0.81) 5.79 x l O " 0 9 3.3 x l O " 1 0 . 4.742 x l O ~ 1 4 58 Figure 3.5: Construction of Field maps for iron spheres : ( a ) log (2DBSB/Ds6S) VS. (T/TM) ( b ) (2Dy/DSSS) vs. (T/TM). 59 Figure 3.5: ( c ) log [xK^/K^) vs. log(x/a) ( d ) log [K^IK22) vs. log{x/a). 60 Figure 3.5: ( e )log(x/a) vs. (T/TM) (calculated from DB8B/Dva) : Plot is the locus of points at which boundary and volume diffusion contribute equally to neck growth. 61 10 logixla) (a) 0.4 0.6 0.8 1 HOMOLOGOUS TEMPERATURE (T/TM) (b) Figure 3.6: Effect of particle size on the shift in ( a ) [S/V] interface ( b ) [B/V] interface in Iron spheres. 62 H o 0 -a 1 -0.2 •0.3 -0.4 -0.5 -0.6 -0.7 -0.1 -0.9 -I -1.1 -1.2 -1.3 •1.4 -1.5 -1.6 1.7 -1.1 -1.9 -2 VOLUME 0.4 0.4 VOLUME SURFACE PAIR OF SPHERES « - 751 ' 0 6 OS H O M O L O G O U S T E M P E R A T U R E (T/TM) (a) VOLUME BOUNDARY V O L U M E SURFACE PAIR OF SPHERES 1 = 10 microns 0.6 0.8 H O M O L O G O U S T E M P E R A T U R E (T/TM) (b) Figure 3.7: Field Maps for pair of Iron spheres in initial contact ( a ) 75 fim ( b ) 10 fim. 63 Tamparatur* C <3 H " S i o JO 1537 PAIR OF SPHERES a = 75 microns • O.Olhr + O.lhr O lhr A lOhn HOMOLOGOUS TEMPERATURE (T/TM) (a ) Twnpwatur* *C 1537 PAIR OF SPHERES a = 10 microns • O.Olhr * O.lhr O lhr & lOhn HOMOLOGOUS TEMPERATURE (T/TM) (b) Figure 3.8: Neck growth for a pair of Iron spheres : log(^) vs. ( ^ ) ( a ) 75 fim ( b ) 10 fim : all mechanisms added together. 64 Figure 3.9: Individual contribution of surface, volume and boundary diffusion to (x/a) ( sintered for one hour ) for a pair of spheres ( a.) 75 /xm ( b ) 10 /xm. 65 HOMOLOGOUS TEMPERATURE {T/TM) ( b ) Figure 3.10: % Linear shrinkage vs. (T/TM) f°r a Pa^T of I r o n spheres ( a ) 75 fim ( b ) 10 fim. 66 3.3.2 Experimental Verification of Neck Growth In order to evaluate the agreement between model predictions and experiments, spher-ical powders were sintered. With the irregular non-spherical powders normally used in the powder metallurgy industry, it would not be possible to observe neck growth quan-titatively. The Spheromet iron powder supplied by Quebec Metal Powders, having the following composition 0.06 % C, 0.013 % Si was used in the experiments. The iron powder was screened to a narrow range of particle size ( > 45 fim and < 63 fim ) and sprinkled on a quartz substrate to obtain a single layer. It was found to be difficult to secure close-packed arrays of particles in such a layer. Care was taken to ensure that at least some groups of particles were touching each other. Each powder layer was sintered at 900 or at 1100 °C in a flowing mixture of Hydrogen and Argon (1:1) for sintering times up to 10 hours. The sintered specimen was gold coated for examination in the scanning electron microscope. Neck Size Measurements The average diameter of a group of particles from many measurements ( about 50 ) was found to be 56.5 fim. Because observations are made normal to a single plane of particles, it is reasonable to assume that sintered necks are seen in full profile; i.e. that the true neck diameters and curvatures are seen in the microscope. Figure 3.11 shows the micrograph of as received Spheromet iron powder. Figures 3.12 and 3.13 show the progress of neck growth at 900 and 1100 °C. Measure-ments of necks were made at each neck for each time and temperature of sintering using a large number of SEM photographs, and the average value of (^) was recorded. The neck radius at contacts between particles having different diameters was not included in the determination of average neck size. The measured necks in each case were found to 67 Figure 3.11: Distribution of spherical Fe powder : as received. 68 be of uniform size. Experimental Results and Observations Table 3.6 summarizes the experimental and theoretical values of (x/a) for the conditions of sintering used. The low values of standard deviation from the measured (x/a) indicates that necks were quite uniform in size. Table 3.6: Comparison of Experimental and Theoretical Values of (x/a). TEMPERATURE in °C TIME hours (x/a) Standard Deviation theoretical Experimental 900 0.1 0.169 0.159 0.003 1 0.224 0.217 0.014 -• 10 0.294 0.282 0.0047 1100 0.1 0.195 0.182 0.001 1 0.256 0.248 0.04 10 0.336 0.318 0.02 Figure 3.14 is a plot of neck growth versus time, in which experimental and calculated values are compared. As expected, (^ ) increases fairly rapidly initially and more gradually at longer times. In the initial stage surface diffusion dominates and contributes to rapid mass transport ( neck growth ). As the neck grows the curvature gradients diminish, so that the driving force for sintering decreases. 69 Figure 3.12: Progress of neck growth in Spheromet iron powder sintered at 900 °C ( a ) 6 minutes. Figure 3.12: ( b ) 60 minutes. 71 Figure 3.12: ( c ) 600 minutes. 72 Figure 3.13: Progress of neck growth in Spheromet iron powder sintered at 1100 °C ( a ) 60 minutes . Figure 3.13: ( b ) 600 minutes. 74 0.05 H 200 400 Time (min) Figure 3.14: (x/a) vs. time of sintering in Spheromet iron powder sintered at 900 and 1100 °C. 75 3.4 SINTERING D I A G R A M S F O R C O M P A C T S OF IRON 3.4.1 The Geometry of Compacts The model of a pair of spheres can be extended to an array of particles or an aggregate of spheres or a compact, if all the particles have the same size and the arrangement is perfectly regular. In an aggregate of loosely packed random powders, there is no regular packing and therefore a sintering equation cannot be derived. In the more practical case of compacts made by the application of pressure to powders in a die, the particles become deformed but the array wi l l be relatively regular if mono-sized particles are involved. It is possible to calculate the pore fraction, but in extending the model to a compact, the init ial geometry at particle contacts must be known i n addition to pore fraction. This init ial contact radius, defined as x^, is a function of applied pressure P, i.e., green density is a function of compaction pressure. Therefore, the process of compaction must be examined first. Many studies of powder compaction have been made, most of them concerned with the relationship between the applied pressure P and relative density Dr. Of the numerous empirical formulae suggested, the most accepted one is given by [79] as where i f is a compaction constant and is principally a measure of the ability of the material to deform. The compaction behavior may also be described by expressions of the form [80] p/p0 = exp(-PjA) D-D0 = BP2 D-DQ = <7P ( I / J ) 76 where the subscript 0 refers to conditions at zero pressure, and D is the density, P is the applied pressure, p is the porosity and A, B and C are constants. Experimental data for an iron powder are given in Figure 3.15 [81]. The curve exhibits three characteristic C O M P A C T I O N P R E S S U R E , N/mm2 Figure 3.15: Variation of In (jzjj) with compaction pressure, P for Atomet 28 Fe powder [81]. regions, also observed by other investigators for a variety of materials. The three regions relate to three different stages of compaction. stage 1 : at low pressure, a certain amount of individual particle movement (sliding) occurs, before interparticle bonding becomes appreciable. This is called "transi-tional restacking" [82]. Less than 5% increase in density typically results from this source. stage 2 : elastic and plastic deformation occurs at the contact between particles. Some density increase occurs due to ability of particles to fill space more efficiently. There may be some cold welding occurring at contacts. 77 stage 3 : bulk compression and deformation of the particles takes place in this stage. The size of contacts is established, and the densification of the aggregate depends on the plastic deformation properties of the material being compacted. Fischmeister et al. [83] studied the development of contact facets between particles during compaction of spherical bronze powder. It was found that the number of contacts per particle gradually changed from 7.3 in the uncompacted stage to about 12 at 97 % theoretical density. The contact number is reported to change rapidly towards the end of densification. Fischmeister and Arzt [84], developed a model for describing the packing behavior of random arrays of spherical particles based on the above study of particle deformation during compaction. Using the Random Design Packing ( RDP ) theory [85], the increase in both the average size and number of contact facets was calculated. The density of the compact is determined by the amount of particle flattening which can be characterized by the average contact area and average coordination number, obtained from metallography. Figure 3.16 gives the result of their study. Kakar and Chaklader [86] modelled the deformation of spheres in a compact and verified the model experimentally. The change in contact area was related to the bulk density for different methods of packing, i.e., cubic, orthorhombic, rhombohedral and body centered cubic. In their study the coordination number Z was kept constant. In reality Z varies continuously as deformation takes place. Exner et al. [87,88] made model experiments in which a regular planar arrangement of uniform size particles was deformed between two punches. Figure 3.17 reveals the contacts formed on pressing these particles. They described the geometry of the contact by two new parameters, namely X{ the radius of the pressed contact and the radius 78 10 • o 0-8 0 RELATIVE DENSITY Figure 3.16: Average contact area between particles vs. relative density for spherical bronze powder [84]. of curvature of the particle surface adjacent to the neck. In addition to their experi-mental results they fitted a polynomial of fifth order to express the dependence of these Moon et al [89] derived a theoretical equation for the relationship between green density and contact area from geometrical considerations. Their theoretical calculations agreed very well with the experimental findings in pressed copper powder compacts. The relationship between contact area characteristics (|)t- and the relative density DT for B C C packing is given by parameters on the pressing pressure P as Xi = 103.9P - 308P2 + 400P3 - H O P 4 - 120P5 r,- = 31.26 - 11.5P + 385P2 - 1000P3 + 1440P4 - 820P5. a (3.5) 79 Figure 3.17: Densely packed planar array of Copper spheres pressed at 200 MN/m2 (a) as pressed (b) pressed and sintered at 1300 K for 10 minutes [13]. 80 and that for FCC is given by (-); = DT^ (0.905 - 1.417(1 - Dry) (3.6) where x is the contact radius and a is the initial particle radius. Basis of Calculations In the present study, predictions are made for compacted powder aggregates in which contacts ( necks ) are present at the onset of sintering. The initial condition of the compact could be specified by pressing pressure P or the green density. If the pressing pressure is used in the prediction, the empirical relationship of initial neck geometry as proposed by Exner [13] could be used. However the specific empirical relationships he derived are based on experimental results for copper. Since the deformation and strain hardening behavior of different materials are different, the Exner [13] relationship cannot be confidently used for Fe. Further, the empirical relations do not contain an a ( particle radius ) term; i.e., the equations are the same for all particle sizes. While x± becomes zero at P — 0, r; does not, but has a constant value of 31.6, the physical meaning of which is hard to imagine. The term r; will have a finite value at P = 0 which should be related to the particle size a. The derivation of Moon [89] based on geometrical calculations, is used in preference to estimate the initial neck size in this work. This equation eliminates the influence of material properties on the compaction behavior as the geometry is calculated from green density. Three initial green densities are used for the calculations in the study, namely 75, 80 and 90 % of theoretical density. In more advanced stages of compaction bulk deformation takes place and the particles lose their sphericity. This affects the value of particle radius used in the calculations, but in a complex way. The effect has been ignored in the present work since densities higher than 90 % of solid are not included. The change in a, the 81 particle radius, for various densities were calculated by Kakar and Chaklader [90] and the change in a from 74 - 90 % theoretical density calculated from their work is found to be 2.07 %. The following values have been used as the initial values (-){ for compacts of defined densities Dr = 0.75 : (l)i = 0.0136 Dr = 0.80 : (f )i = 0.0822 Dr = 0.90 : (f )i = 0.2561 These values are obtained from the plot of (^); vs. green density in Figure 3.18, which was drawn using equation 3.6. The equations for curvature and the sintering rate equations are essentially unchanged except for the introduction of Xi at the appropriate places. From the geometrical relation-ship and simplifications the equations of sintering are denned as before by the following equations of curvature. (x - Xi2) P = 4(a - (x - x^) The driving force for surface diffusion becomes zero when the pores become cylindrical or spherical. The value of (^) at which the pores become spherical in a compact is given by a simple relation [16] xf ~ x = I 3 I a where Xf = 0.74 a, the final neck radius when full density is reached. Thus it is seen that the driving force K\ becomes zero at different (^ ) for different pore fractions. Even when K\ becomes zero K2 contributes to neck growth and shrinkage until Kz becomes dominant. Since K2 and K$ are independent of pore fraction, the transition from Stage 1 to Stages 2 and 3 is found to occur at the same constant value of (^ ) = 0.41. 82 Figure 3.18: Theoretical plot of initial (^)j vs. relative density. 83 This transition value of (^ ) can also be calculated by equating K2 and K3 2(a — x) — x 2 X2 Xf — x x2 - A.22ax + 1.58a2 = 0 x - = 0.41 a Once the conditions are known, the diagram is constructed by integration of the sum of x with respect to time as described before. In the present study, Ashby's equations were used for all stages of sintering. An analytical solution of these equations does not exist, and so numerical methods were used. For solving this numerically, the fourth order Runge - Kutta method was used. This is an approximate solution with good error control. It must be recognized that the compacts discussed in this section are still geometrically ideal. Sintering diagrams for such compacts may require modification if they are to be applied to predictions of sintering behavior in real compacts made from particles of unequal size, non - spherical shape or with rough surfaces. Consideration of the effects of these and other variables follows in section 3.5. 3 . 4 . 2 C a l c u l a t i o n s Field maps The calculated field maps for a compact of relative theoretical density of 75 % for particle radii of 75 /xm , 34 /xm and 10 /xm are given in Figures 3.19 ( a ), ( b ) and ( c ). With coarser particles, it is seen that volume diffusion is dominant at higher temperatures and neck size. At finer particle size, grain boundary diffusion is seen to be a major contributor to sintering over a wide range of temperature and neck growth. For all particle sizes, surface diffusion is seen to be prevalent throughout the temperature regime of sintering. 84 Figure 3.19: Field maps for a compact of 75 % relative density ( a ) 75 /xm ( b ) 34 /xm. 85 Figure 3.19: ( c )10 fim particles. 86 The field map for a compact is obviously a function of initial pore fraction or green density, as this affects the neck size when the sintering process is started. The initial changes the boundary field by virtue of altering the driving force equations. Figures 3.20 ( a ) and ( b ) and ( c ) are the field maps for three particle sizes namely 75 /xm, 34 /xm and 10 /xm and an initial relative density of 90 %. These may be compared with Figures 3.19 ( a ) and ( c ) which are for a relative density of 75 %. The region of domination by grain boundary transport at temperatures close to the ferrite to austenite transformation is extended as the relative density is decreased. Neck Growth and Shrinkage The calculated neck growth plots for a compact of relative density of 75 % for particle size 75 /xm is given in Figure 3.21. Contributions to (^ ) for each of the three major transport mechanisms in compacts of relative density 75 and 80 % theoretical were calculated as a function of (^ ) for particle sizes of 75 and 10 /xm and are plotted in Figures 3.22 and 3.23. For compaction of coarse powder ( 75 /xm particles ) and green density of 75 % solid ( f = 0.25 ), surface diffusion dominates neck growth at all sintering temperatures. However, for fine powder ( 10 /xm particles ) both boundary and volume diffusion become important at homologous temperatures TH > 0.75. For compacts pressed to a higher green density ( f = 0.2 ) surface diffusion is less dominant as the source of neck growth during sintering. Two of the solid state diffusional transport mechanisms cause shrinkage as well as neck growth in compacts. This shrinkage has considerable practical interest in ferrous P / M and is experimentally much more directly measured than neck radius. Accordingly, calculations of linear shrinkage vs. (T/TM) provide a valuable additional type of sintering diagram. No such diagrams have been reported for iron. 87 H o i -2 3 H 4 5 -6 -7 8 •9 H I I -2 3 -4 -5 -6 -7 -8 9 •2 VOLUME BOUNDARY VOLUME SECOND STAGE BOUNDARY SURFACE COMPACT f= 0.1 a = 75 micron* 0.4 —f— 0.6 —r~ 0.8 T H -O 0 --0.1 --0.2 --0.3 --0.4 --0.5 --0.6 --0.7 --0.8 --0.9 --1 --1.1 --1.2 --1.3 --1.4 --1.5 --1.6 --1.7 --1.8 --1.9 --2 -• 0.< HOMOLOGOUS TEMPERATURE (T/TM) (a) BOUNDARY VOLUME BOUNDARY VOLUME SECOND STAGE SURFACE COMPACT f= 0.1 a = 34 microns —r -0.6 0.8 HOMOLOGOUS TEMPERATURE (T/TM) /(b) Figure 3.20: Field Maps for a compact of 90 % relative density ( a ) 75 fim ( b ) 34 fim particles. 88 <3 0 •0.1 -0.2 -0.3 H -0.4 -0.5 •0.6 --0.7 --0.8 --0.9 --1 -11 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7 -1.8 H -1.9 -2 0. BOUNDARY SECOND STAGE VOLUME SURFACE COMPACT f= 0.1 a = 10 microns —r-0.6 —r-• 0.8 HOMOLOGOUS TEMPERATURE (T/TM) CO Figure 3.20: ( c ) 10 /xm particles. H O M O L O G O U S T E M P E R A T U R E (T/TM)-Figure 3.21: (x/a) vs. (T/TM) for a compact of 75 % relative density a = 75 /xm. 90 Figure 3.22: Individual contributions to (|) ( sintered for one hour ) in compacts of 75 % relative density by surface, volume and boundary diffusion ( a ) 75 /xm ( b ) 10 /xm. 91 0 •0.1 --0.2 --0.3 --0.4 -OJ --0.6 -0.7 -0.8 -0.9 -1.1 -1.2 -1.3 -1.4 -M " -1.6 -1.7 -i -1.8 -1.9 -2 0.4 COMPACT f= 0.2 » = 75 microns • SURFACE + BOUNDARY o VOLUME 0.6 0.8 HOMOLOGOUS TEMPERATURE (T/T„) (a) 0.6 0.8 H O M O L O G O U S T E M P E R A T U R E (T/TM) (b) Figure 3.23: Individual contributions to ) ( sintered for one hour ) in compacts of 80 % relative density by surface, volume and boundary diffusion ( a ) 75 fim ( b ) 10 fim. 92 The shrinkage values are calculated from transformations of (^ ) equations to equiva-lent (y) using the definition of shrinkage and the geometry of the neck according to 61 —p x2 I a Aa2 However, since surface diffusion does not contribute to shrinkage, i s is subtracted from the total x in calculating (j). Calculated plots of linear shrinkage vs. ( ^ ) for ideal compacts are given as Figures 3.24 to 3.28 inclusive. Figures 3.24 shows the effect of sintering time. The powerful effect on shrinkage of decreasing particle radius from 75 to 10 /zm is seen in Figure 3.25. Finally, the effect of pressing compacts to higher density is seen in Figures 3.26 to 3.28. At a higher green density such as 90 % of solid, which is achievable in commercial ferrous P / M practice, negligible shrinkage is predicted to occur when 75 iim compacts are sintered for one hour at 0.8Xjvf ( 1175 °C ). This is consistent with the experience of the P / M industry. 3.4.3 Effect of Changing Diffusion Coefficients There are limited data in the literature for self diffusion in iron, and reported values of activation energies and diffusion coefficients are in some disagreement. There is a large body of quantitative data on the lattice diffusion coefficients but relatively very little on grain boundary and surface diffusion. This is particularly true of surface dif-fusion, which is sensitive to surface topology and atmosphere. The prominent reason is difficulty in controlling the atmosphere or surface structure. The variable in this case is the adsorption of solute originally dissolved in the crystal or from the ambient gas present. Adsorbed impurities, in particular, have been found to have very important and sometimes spectacular effects on the diffusion coefficient. Accordingly, an examination has been made of the sensitivity of the sintering diagrams 93 Temperature C 450 3.4 3.2 2.8 H 2.6 2.4 2.2 H 2 1.8 1.6 -1.4 -1.2 -1 -0.8 0.6 0.4 0.2 0 800 I 1175 1537 0.4 COMPACT f = 0.25 a = 75 microns • O.Olhr + O.lhr o lhr lOhrs 06 0.8 H O M O L O G O U S T E M P E R A T U R E (T/TM) Figure 3.24: Calculated % linear shrinkage vs. (T/TM) for a compact of 75 % relative density a = 75tim. 94 Figure 3.25: Calculated % linear shrinkage vs. (T/TM) for a compact of 90 % relative density. = 75 fim and 10 fim in a T«mp«ratur« C UJ O < S ac < UJ 6? UJ O 5 <* x < UJ S <-j 3.2 3 2.8 -2.6 -2.4 2.2 2 1.8 1.6 1.4 i l I -0.6 -0.4 -02 -0 0.4 4S0 3.4 ii' -3 -2.8 -2.6 2.4 22 2 t.8 H 1.6 1.4 12 H 1 0.8 0.6 -0.4 -0.2 0 0.4 MM _ J 1537 COMPACT 1. 02 a • 75 microns • O.OItu-+ O.lhr H O M O L O G O U S T E M P E R A T U R E (T/TM) (a) Tcmparatur* C 800 1175 1537 COMPACT f= 0.1 a = 75 microns • O.Olhr + O.lhr o lbr A lflhrs 0.6 H O M O L O G O U S T E M P E R A T U R E (T/TM) (b) Figure 3^26: Calculated % linear shrinkage vs. (T/TM) for a = 75 in ( a ) 80 relative density ( b ) 90 % relative density. ^ 1 Temperature C 450 800 1175 H O M O L O G O U S T E M P E R A T U R E (T/TM) Figure 3.27: Calculated % linear shrinkage ( sintered for one hour ) vs. (T/TM a = 75 fim for relative densities of 75, 80, 90 %. 97 H O M O L O G O U S T E M P E R A T U R E (T/TM). Figure 3.28: Calculated % linear shrinkage ( sintered for one hour ) vs. relative densities of 75 and 90 %. (T/TM) for 98 for iron powder to the values of the diffusion coefficients used in the mass transport equations. Figures 3.29 ( a ), ( b ) and ( c ) are sintering diagrams for a = 34 fim which show the combined contributions of surface, boundary and volume diffusion to neck growth. The lower curves on each plot are calculated from the diffusion data in Table 3.5. The upper three curves in Figure 3.29 ( a ) are the predicted result of an increase in the surface diffusion coefficient by factors of 10, 100 and 1000, while not changing other diffusion coefficients. Similarly the curves in Figure 3.29 ( b ) show the effect of increasing only the boundary diffusion coefficient by the same ratios. Figure 3.29 ( c ) shows the result of similar changes to the volume diffusion coefficient only. At low homologous temperatures, the amount of neck growth is least sensitive to changes in the lattice diffusion coefficient, and most sensitive to changes in surface diffu-sion coefficient. At high temperatures, increasing the volume diffusion coefficient has a greater effect on neck growth than has a comparable increase in the grain boundary diffu-sion rate. The boundary maps are constructed by equating the ratio of contribution to x by different mechanisms. Thus, when diffusion coefficients are increased, the magnitudes of is increase in the same proportion. Therefore, the respective regions of dominant diffusion mechanism will be extended by the increase in the individual coefficients. 3.4 .4 Incorporation of Grain Growth in Sintering Equations The present model assumes no grain growth or particle size variation. The incorporation of grain growth in the pore shrinkage equations was described in Section 1.2.3 ( see p. 14 ). Grain growth is often assumed to follow the law GN - GQ = At where n = 2orS 99 Figure 3.29: x/a vs. T/TM for pair of Iron spheres a = 34 fim : Effect of increasing diffusion coefficient by 10, 100 and 1000 times (a.) Surface diffusion. Figure 3.29: ( b ) Boundary diffusion ( c ) Volume diffusion. 101 and since the initial grain size Go <C G, Gn = At. That is the variation of grain size with time should be known for incorporating the effect of G in shrinkage equations. Further the value of A has to be known and A is found to be a function of sintering temperature. Therefore, the incorporation of these in the model has to be supported by substantial amount of experimental results of grain growth which itself is a function of starting geometry, particle size and green density. If we assume the grain growth to occur when a compact reaches a particular density, the diagrams developed in this study help one to read out the temperature and time of sintering that a compact of given density and particle size will exhibit grain growth. 3.4.5 Exper imenta l Verif ication In order to verify the theory developed in the present work, spherical powders of uniform size are required. A Carbonyl iron powder namely GS6 supplied by the GAF corporation, USA, was selected in this study. The characteristics of the powder are shown in Table 3.7. The morphology and distribution of the powder is shown in Figure 3.30. The powders were pressed into tensile shaped compacts. The relative green density of the compacts were found to be approximately 75 % on pressing at a pressure of 386 MPa. The specimens were sintered at temperatures of 800 - 1000 °G for 20 minutes in a flowing H2 and Ar atmosphere. The temperature was measured to an accuracy of ± 5 °C. Table 3.8 gives the experimental results of shrinkage in the sintered powder compacts. Also included in the table are the theoretically predicted shrinkage values for the corre-sponding temperature and density. Figure 3.31 shows the comparison between the model prediction and the experimental values. A detailed discussion of the results of Carbonyl powder compacts is included in Chapter 4. Table 3.7: Characteristics of GS6 Carbonyl Powder used in this Stu' Supplier : GAF Corporation, USA Description : Reduced Powders Batch Number : Mix No 87 Apparent Density : 1.2 - 2.2 g/cm3 Tap Density : 2.2 - 3.2 g/cm3 Average particle size : 3 - 5 fim Chemical Analysis ( weight % ) Carbon - 0.10 max Silicon -0.082 Sulphur - 0.006 Oxygen - 0.30 max Nitrogen - 0.10 max Figure 3.30: Distribution of GS6 Iron powder particles. 104 8 Figure 3.31: Comparison of experimental shrinkage with the predicted values as a func-tion of temperature of sintering in GS6 powder compacts sintered for 20 minutes. 105 Table 3.8: Shrinkage Results of Carbonyl Compacts. Temperature °C % Weight Loss Density (gm/cm3) Before | After % Shrinkage Experimental | Theoretical GS6 powder compacts 700 -0.22 5.81 5.82 0.33 0.94 750 -0.22 5.84 5.97 1.79 2.256 850 -0.33 5.7 6.53 5.11 5.3 900 -0.32 5.77 6.68 6.237 7.16 950 -0.44 5.78 6.07 3.4 5.467 3.5 LIMITATIONS OF THE IDEAL SPHERICAL PARTICLE MODEL In a real compact there are many variables which are ignored in the above model, but which are characteristic of any P M processes, e.g., particle shape and size distribution, surface morphology of particles, deformation during compaction, number of contacts ( coordination number ), pore distribution etc.. All of these factors may influence sin-tering kinetics. In the development of the model for the prediction of shrinkage charac-teristics, many simplifying assumptions are made which can lead to errors in predictions made from the model. An attempt is made in this section to identify various sources of error, and to evaluate the problems associated with application of the "ideal model" to the prediction of shrinkage in real compacts. For the purpose of discussion this is divided into two sections. The first section relates to the changes in geometry and struc-ture which are assumed to accompany sintering, the second relates to the influence of 1 0 6 material properties and the effect of processing parameters on the sintering kinetics. 3.5.1 Assumptions A b o u t Neck and Pore Geometry In the derivation of the theoretical equations for two particle models, the neck geometry was described by a circle and other approximations and simplifications were made in the derivation of curvature equations. The exact nature of the neck contour is not yet known. A few attempts have been made to replace the circular approximation by another geometry. German and Munir [11] assumed a catenary contour and Ashby and Swinkels [12] assumed an elliptical one. Since until now no exact description of the neck contour is available, the circular contour appears to remain the most reasonable. The neck contour becomes complex when the shape and size of the particles are not uniform; i.e., the calculations of neck contour and shrinkage kinetics become complex when the starting geometry is not symmetrical and spherical. Gessinger et al. [92] have shown that in this case the neck growth also becomes asymmetrical and that particles can rotate with respect to each other. Rearrangement of particles and the rotation of particles in groups of three or more spheres was analyzed by Exner [13]. Ross et al. [93] applied a computer simulation procedure to study the effects of packing geometry on the sintering of powder compacts comprised of uniform, randomly - packed spheres, and density < 6 6 . 5 % of solids. Compacts of practical interest are made by pressing to densities much higher than this ( typically > 8 0 % of solid ). In such compacts, rearrangement and rotation at contacts are constrained and can probably be ignored. Attention has been focussed on Stage 1 of sintering because certain features in Stages 2 and 3 are not well defined. The second stage does not lend itself conveniently to modelling due mainly to the uncertainty introduced by grain growth. The transition from Stage 1 to Stage 2 where the pores have become cylindrical is also not clearly demarcated, but is considered to begin when the sintered density reaches about 8 5 % of 107 theoretical. The third stage begins around 95 - 98 % of theoretical density [9], which is outside the range of common practical interest. In the intermediate and final stages of sintering, grain growth during sintering causes boundaries to migrate which results in a decrease in the rate of densification. The grain growth process is complex and the kinetics depend not only on material properties like diffusion coefficients but also on other parameters like initial particle size, distribution and arrangement. Impurities can also have a large effect on grain growth even if present in small quantities. In addition to grain growth there have been instances in which pore growth has been observed. Coble's [9] model discussed in Chapter 1 (see p. 14) does not take any effect of pore growth into account. In the final stages of sintering the gases entrapped in the remaining pores may pre-vent full densification. The pores shrink to minimize the surface area, but as they do so the gas pressure inside them will tend to increase. Therefore, three more variables should probably be incorporated in the densification equation; namely outward diffusion of entrapped gases, grain growth and pore growth. At present we are not able to charac-terize these effects with adequate rigor to justify their inclusion in the sintering models. Moreover, their effect is most important at densities beyond those of normal interest in the P M industry. 3.5.2 Influence of Powder and Process Variables The sintering behavior of a compact is influenced by such powder characteristics as particle shape, size and distribution, the roughness of particle surfaces, and the presence of oxide on particle surfaces. The effect of these parameters is difficult to characterize and is probably impossible to quantify. Powders produced by different methods do show different shrinkage behavior. Most commercially made iron powders have particle shapes which are far from regular, and the particles have irregular surfaces. Shapes which deviate 108 from spherical may lead to asymmetrical neck growth. Also, irregularities in packing will lead to an additional uncertainty in the neck growth kinetics. The presence of an oxide film on the surfaces may prevent or alter the bonding of particle contacts. Also impurity elements or chemical additives can influence the nature of neck growth through their effect on surface energies and self diffusion coefficients. It is difficult to assess the effect of each of these on the shrinkage behavior quantita-tively and to introduce the necessary modifications in the ideal model. The transport phenomena dominating at any instant during sintering depend on a great variety of factors in addition to the characteristics of the powder; e.g., starting density of the compacts, sintering time and temperatures, and sintering atmosphere. Properties of powders important with respect to consolidation are particle size dis-tribution, particle shape, surface conditions and presence of oxide film, metallic contam-ination and additives. Particle size distribution affects both compaction and sintering. There are large variations in both the size and shape typical of particles in commercial powders. Thus the contacts can have a wide range of radii. Further the local curvature and curvature gradients at necks which are the driving force for mass transport can be much more variable and complex than calculated for the model case from Equation 1.5. However, considering single fraction of pure powder, for spherical powders, the radius of the neck formed on pressing can be estimated using the theoretical/empirical equations listed before. The case of angular powder is complex and the contact geometry is gener-ally irregular. The size of the neck on pressing depends on the shape and distribution of powder and also on the packing geometry. The geometry is extremely complex and can-not be defined for irregularly packed arrangements of irregular particles of uneven size. More experimental data on the cold pressed compact as a function of applied pressure and particle geometry is needed. Another important factor may be the breaking of the oxide layer on pressing and its influence on sintering. Due to the interaction between 109 surface irregularities on particle surfaces when they are pressed together, the interparti-cle contacts in green compacts are typically discontinuous and have contact pores. The effect of this on the sintering diagrams can be ignored because of their small size and their location on the grain boundary at interparticle contacts, these contact pores can be expected to close rapidly and disappear due to grainboundary and lattice diffusion. Surface conditions of powder is known to play an important role in the sintering characteristics of powders, since factors such as vapor pressure, surface tension, atomic mobility are all affected by the presence of oxide film and other contaminants. During sintering of metals oxygen is probably the major source of contamination. Little quan-titative information is available in the case of powders. However, in the case of iron powders since a reducing atmosphere is used during processing this may not affect the sintering kinetics. Surface contaminants other than oxygen may also affect the sintering kinetics. Also, if there is a mixture of different elements of powders, the sintering kinetics may be altered depending upon the ease of homogenization and alloying. The additives or dopants may alter the mass transport kinetics resulting in fast/slow sintering kinetics. Owing to so many added complications in real compacts, the spherical model cannot be directly utilized for any quantitative predictions. However the spherical model is the ideal staring point for the development of quantitative models in real compacts. Thus any study on the spherical model is a great step towards that direction. 110 3.6 SINTERING B E H A V I O R OF C O M M E R C I A L IRON P O W D E R C O M -P A C T S 3.6.1 Adapting the "Theoretical" Model to Real Compacts In applying the ideal model to real compacts for any quantitative predictions extreme caution is required. In this work it is proposed that some simple modification of the ideal models can make them applicable to real compacts, but owing to the many dependent parameters the models must be applied with great caution when attempts are made at quantitative predictions. As a first approximation, the model can be modified to real compacts by assuming the particles to be spherical and calculating an "equivalent" particle diameter from values such as projected cross sectional area or particle volume. Also, in commercial powders, the sieve analysis permits a mean particle size to be calculated from the size distribution curve. Hence, for particles exhibiting low aspect ratio, averaging the particle size in terms of an equivalent spherical diameter and using that for quantitative predictions may be justifiable. 3.6.2 Experimental Verification of Shrinkage in Real Compacts Studies have been made of the sintering behavior of compacts made from a commercial atomized sponge iron powder Atomet 28. Some characteristics of this powder are given in Table 3.9. The average particle size from the sieve analysis is found to be 68 /xm diameter. Figure 3.32 shows the shape and size distribution of loose Atomet 28 powder. The powders were compacted at 386 Mpa pressure into a cylindrical shape with di-mensions of 10 mm diameter and 4 mm height. The compacts, initially of approximately 75 % theoretical density, were sintered in an inductively heated furnace for 60 minutes Table 3.9: Characteristics of Atomet 28 Iron Powder used in this Stu Supplier : Quebec Metal Powder Limited Description : Atomized/reduced Batch Number : Lot No 9707 Apparent Density : 2.8 g/cm3 Flow Rate 27 sec/50 grams Screen Analysis ( Tyler Mesh ) Mesh size Microns % minus 140 106 27.8 200 75 23.9 230 63 8.00 325 45 12.5 325 45 ' 22.6 Chemical Analysis ( weight %.) Carbon - 0.02 Silicon - 0.013 Sulphur - 0.015 Oxygen - 0.18 as received 112 at temperatures between 900 and 1350 °C in a flowing H2 and Ar atmosphere. Theoretical predictions of linear shrinkage for a particle size of a = 34 fim is compared with experimental results in Table 3.10 and Figure 3.33. Table 3.10: Shrinkage Results of Atomet 28 Powder Compacts Sintered for 20 Minutes. Temperature Density J Ctrl'* % linear Shrinkage °c Green Sintered Experimental Theoretical 900 5.91 5.94 0.51 0.67 1100 5.84 5.89 0.93 0.94 1200 5.66 5.82 1.15 1.26 1350 5.81 6.27 2.34 3.67 Good agreement between the model prediction and experiment at T < 1200 °C is seen. At the highest temperature, the theory predicts substantially more shrinkage than was observed. This is probably attributable to grain growth, and the resulting migration of boundaries away from necks during sintering. The decrease in both boundary and lattice diffusion which is expected to result from grain growth is not taken in to account in the model. 3.7 SUMMARY A model has been developed to predict the dominant mechanism of transport and shrink-age characteristics of iron compacts during sintering. The results are presented in the form of sintering diagrams. The diagrams are constructed using existing equations in the 113 Figure 3.32: SEM Photomicrograph of Atomet 28 iron powder particles. 114 TEMPERATURE (°C) Figure 3.33:- Comparison of experimental shrinkage with theoretical predictions as a function of temperature of sintering in Atomet 28 iron compacts sintered for one hour. 115 literature and therefore retain their inherent limitations. The main mass transport mechanisms for the sintering of iron compacts as seen from the boundary maps are surface and volume diffusion under practical sintering conditions. From the examination of the particle size dependence of shrinkage it is seen that sintering kinetics is strongly enhanced by a decrease in particle size. The predictions also indicate that initial density affects the linear shrinkage significantly. Pressing decreases the porosity and increases the initial contact areas between the particles. Shrinkage is greater, the smaller the compacting pressure i.e., the lower the initial green density. At higher green density the neck contacts are larger but the neck growth rate and hence sintering shrinkage is reduced. With increasing relative density the driving force for sintering decreases and hence there is less sintering shrinkage with increase in green density. The temperature at which sintering takes place strongly affects the material transport in iron compacts. Sintering Fe powder in the a ( < 912 °C for pure iron ) range results in higher densification than sintering in the 7 range for a given temperature. This is because of the comparatively lower values of the self diffusion coefficients for 7 iron ( refer Table 3.5 ). The activation energy for grain boundary diffusion in 7 iron is slightly lower than that in a iron, while the activation energy for volume diffusion is considerably higher. In fact, the volume diffusion coefficient drops in value abruptly by more than 2 orders of magnitude at the transition temperature. Since the sintering rate is dependent on the respective diffusion coefficient, a marked drop in the sintering rate at the transformation temperature is expected and is observed in all the plots. The extent of drop in the individual cases are quite evident from Figures 3.8 to 3.10 in pairs of spheres and Figures 3.22 to 3.29 for compacts. Also a finer powder shows a sharper decrease in shrinkage values at the a —> 7 transformation. The model predictions had been tested in a few cases. In the initial stage of sintering, 116 as mentioned earlier, it is convenient to measure the neck growth kinetics (^ ) and in a pair of spheres. Accordingly neck growth studies were made in spherical spheromet iron powders. Comparison of experimental measurements with the predictions shown in Figure 3.14 and 3.15 reveals a reasonably good agreement. This also suggests that the material constants used in the calculations are fairly accurate. The lattice and grain boundary diffusion coefficients used in the present calculations are comparable to the values reported in Literature. The surface diffusion coefficient is sensitive to atmosphere and the values used here were obtained in vacuum ( 1.0 x l O - 0 6 Pa) [75]. Sintering of spheromet powders were performed in a hydrogen atmosphere, the reduction of the oxide film on the surface should present a clean surface for diffusion during sintering. Therefore the use of the same surface diffusion coefficient is probably justified. The theoretical prediction of the "ideal" model is tested experimentally with the spherical Carbonyl powder compacts. More details on the shrinkage of these compacts are discussed in Chapter 4. The predictions in the case of a commercial iron powder compacts ( for a commonly used Atomet 28 powder ) are in reasonable agreement except at high temperatures. Both in the Carbonyl as well as in Atomet 28 iron powder at higher temperatures the theory predicts a significantly higher value than experimentally observed shrinkage. A possible reason for this is that at that temperature of sintering the compacts are at the second stage and the equations used for predictions are simplified ones. In the present study the rate equations proposed by Ashby [19] were used. Ashby's model does not include the effect of grain growth in the sintering equations. Therefore the theory overestimates the shrinkage rates and hence shrinkage values. The equation of Coble's ( Equation Nos. 1.17 - 1.19 ) (see p. 14) should give a slightly better prediction, but again certain assumptions about grain size and growth kinetics have to be made which may offset the accuracy. Accurate predictions for the second and third stage require rigorous 117 experimental results and refined models. The good agreement between the experimental and predicted values in the neck growth kinetics for a pair of spheres and shrinkage values in the Carbonyl ideal com-pacts and Atomet non-ideal compacts demonstrates the applicability of the developed models for quantitative predictions. C h a p t e r 4 D O P A N T - A C T I V A T E D S I N T E R I N G Powder processing is a viable industrial manufacturing approach for several materials and components. Inherently this technique depends on a sintering cycle and techniques aimed at enhancing the sintering process are thus important. Lower temperatures facil-itate furnace design and reduce energy consumption. Even though the P / M process is considered energy efficient because it produces components to final tolerances without machining operations, substantial further energy and cost savings could be made by re-ducing the sintering temperatures. Estimates indicate that for ferrous parts a decrease in sintering temperature of 100 °C would reduce energy consumption by 20 % and furnace cost by a factor of two. Small additions of certain transition elements have been shown to enhance dramati-cally the solid state sintering ( referred to as activated sintering ) of tungsten powders, as discussed in Section 1.4 (see p. 20). At temperatures of 1000 - 1400 °C, corresponding to homologous temperatures of 0.35 - 0.45, the addition of as little as 0.1 wt. % of nickel allowed 0.56 /xm tungsten powder compacts to be sintered to high relative density. This dopant-activated sintering approach has been suggested for ferrous powder com-pacts, but there is no reported evidence that it has ever been successfully applied. Prior attempts have generally involved relatively coarse iron powders ( > 30 /xm ), compacted to high initial green densities and sintered at homologous temperatures of 0.70 to 0.75. Even if there had been activation of sintering due to additives, it would have been almost impossible to isolate it from other phenomena under these conditions. 118 119 4.1 A I M A N D D E S C R I P T I O N O F T H E S T U D Y The principle of activated sintering has not been applied previously to ferrous powder compacts. The aim of the present study is to determine if the process of activated sintering can in fact be extended to ferrous systems. One aspect of the present study, therefore is a search for elements which might activate sintering of iron. In this study it was decided to use fine iron powders with lower compact densities and lower sintering temperatures than those typical of ferrous P / M and of any prior reported work. It is believed that this work represents the first attempt to study activation of sintering in iron under conditions reasonably comparable to those used in the well documented work with nickel-doped tungsten powder. When the present experiments were initiated, criteria suggested by German [67], as discussed in Section 1.6 (see p. 35), were used as a guide for selecting candidate activators ( dopants ). Other criteria specific to ferrous-base systems were also considered. Several additives were identified for this study, the success of each additive as a potential candidate was based on the measurements of linear shrinkage. The initial experimental results with iron were inconclusive. Accordingly, it was decided to reexamine critically existing models for activated sintering in the tungsten -nickel system. There is no satisfactory qualitative description of the process of activated sintering in the literature. One of the reasons claimed for higher shrinkage in W - Ni is increased grain boundary diffusion due to the presence of additive elements in the grain boundary. Using the developed model for the construction of sintering diagrams, the process of activation in the W - Ni system is analyzed in the present study for a qualitative and if possible quantitative description of the process. Based on the analysis, a new model can be proposed. The shrinkage results of these compacts are compared to explain the phenomenon of 120 activation in ferrous compacts. An attempt is made to develop dopant selection criteria and to consider more thoroughly the practical potential of applying activated sintering to ferrous as well as other systems. The order of presentation in this chapter reflects the above chronology. 4.2 M A T E R I A L S A N D E X P E R I M E N T A L P R O C E D U R E S 4.2.1 Dopant Selection The additives and concentrations listed in Table 4.1 were used in these experiments. Some were chosen on the basis of the criteria described in section 1.6 (see p. 35). However, there are no published reports of successful activation in ferrous compacts and an exploratory set of other elements was therefore used. Phase diagrams for the relevant binary systems [94] are given in Figures 4 .1 (a ) to ( h ) . In principle, high solid solubility of dopant in the base metal would be undesirable, since the small addition might be consumed before performing its desired function. How-ever, if the interdiffusion of dopant into base metal is very slow, the dopant may provide at least a transient effect. Of the dopants tried : • Most have significant solid solubility in iron at 0.65 T M , 900 °C ( Si, Ge, Ni, Cr, W ); but would be expected to dissolve very slowly at this temperature or lower. • Some ( Ti, Pd ) have appreciable solid solubility for iron; others ( B, Si, Ge ) dissolve very little at 0.65 Tjf. • The melting points range from substantially higher than iron ( W , Ti, Pd, B ), through similar to iron ( Si, Ni ) to lower than iron ( Ge, Ag ). 121 Table 4.1: Additions to Pure Carbonyl Iron Powder Compacts. Additive Concentrations Tjif A used wt % (K) Boron 0.1, 0.3, 0.5 2303 Silicon 0.1, 0.3, 0.5 1683 Germanium 0.1, 0.3, 0.5 1210 Nickel 0.3 1730 Chromium 0.3 2148 Tungsten 0.1, 0.3, 0.5 3683 Titanium 0.1, 0.3, 0.5 1941 Palladium 0.3 1825 Silver 0.3 1234 122 Atomic Percenloge Silicon 30 4 0 50 60 70 Weight Percenloge Silicon 80 90 Si Figure 4.1: Phase diagrams of the binary systems considered ( a ) Fe - Si [94]. 123 Atomic Percentage Boron 70 8 0 90 0.008 0.016 0.024 Weight % B 3 0 4 0 5 0 6 0 7 0 Weight Percentage Boron 8 0 9 0 B Figure 4.1: ( b ) Fe - B [94]. Atomic Percentage Titanium 40 50 €0 •OOOI" 5 0 0 30 4 0 Weight Pe: 50 6 0 7 0 8 0 9 0 Ti centoge Titanium ure 4.1: ( c ) Fe - Ge [94] ( d ) Fe - Ti [94]. °c 1800 3200F 1700 SOOOF 1600 2e<X>F 1500 2600F 1400 2500F 1300 2300F 1 0 Atomic Percentage Tungsten 20 30 4 0 5 0 6 0 70 9 0 1200 21O0F I lOOt 1900F }• 1000 ITOOF 900 I600F 800 • / / / 1 L / 1 46 0 I 1641 ±7* i 68.5 99.2 J \ 1536 533 «3 - . 29.3 :554 ±6* |l3.2% / 35.5 (a Fe) e -.1394" / / / 1060120* / I l .912" I s—j-1 • t' ! 1! 10 20 30 40 50 60 70 Weight Percentage Tungsten 80 90 W 1600 -itcmic Percentage Pnllaa'um 20 30 "0 50 60 70 80 90 Fe 30 40 50 60 70 Weight Percentage Pollodium 80 90 Pd Figure 4.1: ( e ) Fe - W [94] ( f ) Fe - Pd [94]. 1800 3000F 1600 2 0 O O F 1400 2«0OF 1200 2000F 1000 I 6 0 0 F 800 770*^  I200F 600 K)OOF Atomic Percentage Chromium 400 • L. — 1538* : i 3 9 f . . . . 15 2 16*. IX | (a-F e,Cr) (r-F«) L L9I2-- 8 5 I - . - 7 1 Cu*« 821'. 46 cr ] ... S S s > \ ) 475* N Fe 10 20 30 40 50 60 70 80 90- Cr Weight Percentage Chromium Figure 4.1: ( g ) Fe - Cr [94] ( h ) Fe - N i [94]. 127 German suggested that boron, silicon and titanium were potential activators for iron, but no actual attempts to use them for the purpose are reported in the literature. Based on reported observations in the W - Ni system, the concentrations of dopants added were at levels chosen to ensure that all iron surfaces would be covered by at least one atom layer of dopant if the dopant was spread uniformly over such surfaces. 4.2.2 B lending of Dopants w i t h Iron Powder A Carbonyl iron powder designated as GS6, described in Table 3.7 was used for all blends in this study. The shape and size distributions of the particles are revealed in Figure 3.30 For a few experiments a much coarser iron powder, Atomet 28, was used. Character-istics of this powder, a typical moulding grade, were described in section 3.6 (see p. 110), Table 3.9 (see p. I l l ) , and the highly irregular particle shape is shown in Figure 3.32 (see p. 113). The description of the additives is given in Table 4.2. Blending of iron powder and additive powders was done in a laboratory mixer for 30 minutes. Because some additional oxidation of the iron powder particles could have been caused in this operation, pure iron powder was also similarly treated before being used to make undoped compacts. As can be seen from Table 4.2, the additive powders were typically of larger average particle size than the finer iron, in several cases as coarse as 44 fim in diameter. While it would have favoured more intimate mixing of iron and dopant, attempts to match their particle size was not made because there is unavoidable oxidation of particles and this becomes a serious problem as powder size decreases. In the hydrogen atmosphere and at the relatively low sintering temperature used in this study, the oxides of most of the additives are thermodynamically stable. 128 Table 4.2: Description of Additive Powders. Additive Description and Particle size and Powder Source Shape Boron Crystalline, Pure All < 44 /xm Chemonics Limited, USA Figure 4.2 ( a ) Silicon Electronic grade, 99.99 Si All < 44 fim Source unknown Figure 4.2 ( c ) Titanium added as Titanium Hydride Figure 4.2 ( b ) Germanium 99.99 Ge crushed from pieces All < 44 fim Research Organic and Inorganic Company, USA. Tungsten Commercial Purity All < 44 fim Fischer Scientific Company, USA Figure 4.2 ( d ) Palladium added as PdCl2 All < 44 fim Ventron Alpha Products, USA Figure 4.2 ( e ) Nickel Commercial Purity All < 100 mesh Electronic Space Products, USA Coarse Silver Added as Silver Nitrate in solution 129 Figure 4.2: Shape and size distribution of additive powder particles ( a ) B . 130 Figure 4.2: ( b ) T i H 2 . Figure 4.2: ( c ) Si. 132 Figure 4.2: ( d ) W. Figure 4.2: ( e ) Pd. 134 4.2.3 Compacting and Sintering Powders were compacted to obtain a tensile shaped compacts. This facilitates the mea-surement of shrinkage and tensile strength on the same sample. Tensile test-bar compacts were made to ASTM E8 61T specifications by pressing powders in a floating die set at 365 MPa. Transverse shape and dimensions of the green compacts are shown in Figure 4.3. The variation in the thickness of the specimens was ± 0.20mm. Die parts were lubricated periodically, but no admixed lubricant was employed. Figure 4.3: Sample dimensions used in the experiments - ASTM E8 61T Specification. Compacts were placed in a wire sling and sintered, three or four at a time, at tem-peratures up to 1000 °C, in a tube furnace. The heating rate was rapid, approximately 600 °C per minute, to the sintering temperature. A flow of dry hydrogen and argon, 135 mixed in equal proportions by volume, was passed through the furnace tube. Tempera-ture variation within and between specimens were less than ± 5 °C. Specimen - mounted thermocouples were used for calibration runs. Of the specimens sintered together in the sling, one was a pure iron compact ( to provide a reference standard for the run ) and the others were compacts containing different levels of one of the dopants or same quantity of different dopants. The sling and specimens were rapidly drawn from the hot zone to the cold zone of the furnace tube after sintering. 4.2.4 Sintering Shrinkage and Weight Changes Powder compacts do not shrink isotropically when sintered. In the present work, all green compacts were made at the same pressure, were of closely similar average density and were of the same width and length. Changes in dimensions on sintering, while not isotropic, were reproducible in each dimension. Compact dimensions were measured accurately in all three dimensions using a digital vernier caliper. Density was calculated from the weight and volume of the compact. Compacts were weighed before and after sintering. Both density and length changes were recorded. 4.3 RESULTS A N D DISCUSSION 4.3.1 Pure Iron Compacts Results for the sintering of pure iron compacts based on Carbonyl GS6 iron powder are summarized in Table 4.3. The data for linear shrinkage, 51/7, are plotted against sintering temperatures in Figure 4.4 and a similar plot of relative sintered density values is presented as Figure 4.5. Table 4.3: Data for Fe Comp acts Sintered in a Flow of H 2 - Ar for 20 Minutes. Green Density Temp % Shrinkage Sint. Density Meas (gm/cm3) Rel % °C Expt Sint (gm/cm3) Rel % 5.84 74.14 650 0.17 5.89 74.81 5.81 73.8 700 0.33 5.82 73.96 5.77 73.3 700 0.32 5.93 75.34 5.84 74.18 750 1.79 5.97 75.86 5.69 72.24 800 5.11 6.53 82.98 5.81 73.8 .800 4.38 6.46 82.08 -5.70 72.43 800 6.03 6.83 86.78 5.76 73.22 800 6.91 6.77 86.08 5.78 73.49 850 7.52 7.19 91.34 5.8 73.7 850 •7.86 7.17 91.1 5.72 72.68 850 7.85 6.74 85.64 5.68 72.17 900 8.03 7.00 88.95 6.07 77.1 900 8.65 7.38 93.78 5.76 73.19 900 6.24 6.68 84.89 5.63 71.53 950 5.99 6.68 84.87 5.78 73.49 950 6.36 6.83 86.79 5.78 73.37 1000 1.67 6.08 77.2 137 n 10 9 8 7 6 5 4 3 2 1 0 -- alpha • gamma - • • • - • • • • • - • - • - • • • i i I I i i i i i i i i 700 800 900 1000 TEMPERATUTRE (°C) Figure 4.4: Linear shrinkage of Fe powder sintered for 20 minutes. 138 100 98 96 alpha gamma 94 - • 92 — • 90 • H r—( 88 -00 • • 86 • • W • • Q 84 W • > 82 • H 80 < — s 78 H 76 • • 74 • 72 i i i i i • I l l 1 1 700 800 900 1000 TEMPERATUTRE <°C) Figure 4.5: Relative sintered densities Fe powder sintered for 20 minutes. 139 There was a large scatter in both the sintering shrinkage results and the correspond-ing density values for a given sintering temperature, as seen in Table 4.3 and Figures 4.4 and 4.5. It is evident from the data, however, that shrinkage was at a maximum around 900 °C. This is attributed to the increase in self diffusivity in alpha - iron as the temperature increases and the decrease in diffusivity after the transformation to gamma - iron at 912 °C. Fine Carbonyl powders have poor flow properties. Although care was taken to fill the die cavity uniformly, there were gradients in the loose packed mass which translated into green density gradients. Because of the shape of compacts, the gradients were greater along the length of the compact. Only average densities were measured and reported. The aforementioned density gradients were partly a consequence of the highly elon-gated shape of the compacts, which made it more difficult to fill the compacting die uniformly in the long dimension. However, this large dimension was also beneficial, since it allowed sintering shrinkage to be determined with considerable precision. The large scatter seen in the data of Table 4.3 for shrinkage at a given sintering temperature requires explanation. Each of the pure iron specimens was sintered in a different run, with a different group of "companion" compacts in the same sintering sling. These groups of iron and doped compacts were prepared at various times during the course of the study. Although the conditions of compaction and sintering were kept as constant as practicable, several sources of variation in the sintering behavior can be expected. Variation in green density, as discussed above, may introduce some scatter in shrinkage. Some series of specimens were compacted immediately after mixing the component powders, while some were compacted after a lapse of hours or days. Similarly, some green compacts were sintered immediately after pressing, others after a substantial time of delay. Powders or compacts which were held longer in the laboratory atmosphere could be expected to experience more oxidation. The presence of oxygen in iron compacts 140 has been reported to impart a slight but positive influence on sintering kinetics. Weight loss on sintering at 900 °C in hydrogen was typically 0.4 wt. % for pure iron compacts. Such losses are generally associated with the reduction of iron oxide on particle surfaces. However chemical analysis ( Table 4.4 ) revealed that there was carbon loss as well. Compacts thus experience deoxidation and decarburisation in the reactions : 2 FeO + C -» 2 Fe + C 0 2 FeO + H 2 Fe + H 2 0 2 H 2 0 + C -* C 0 2 + 2 H 2 Since the degree of decarburisation depends to some extent on the amount of iron oxide initially present, the scatter in the results for pure iron compacts may be partially attributable to the aforementioned differences in the times of exposure of powders and compacts to the atmosphere before sintering. Pure iron 'compacts were placed adjacent to doped compacts in the sintering sling. While the external atmosphere was maintained reasonably constant, the local sinter-ing atmosphere may have been contaminated by the products of reaction between the sintering atmosphere and all compacts in the sling. Tensile test results for sintered compacts showed a very large scatter. This is at-tributed to packing and density gradients along the length of the green compacts. Failure in tension is initiated where the density is lower than elsewhere; that is, where the ef-fective load carrying cross section area is most reduced. Tensile strength is based on the cross sectional area under load. Large scatter in this property is therefore not surprising. Consequently tensile tests were not performed on most of the samples. 141 Table 4.4: Data for C Loss in Fe Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes at 900 °C. % Carbon as received : 0.10 % C Fe arbon af1 Fe - B ;er sinten Fe - Si mg in cor Fe - Ti npacts Fe - Cr 0.019 0.017 0.014 0.010 0.016 4.3.2 Doped Compacts Referring to Table 4.3 at 850 and 900 °C, the linear shrinkage of pure iron compacts was rapid and extensive. Some compacts achieved densities as high as 94 % of theoretical. It is therefore clear that at these temperatures additives were not necessary to obtain substantial sintering shrinkage in the pure iron compacts pressed from 3 fim powders. Nevertheless, by comparing the shrinkage of doped specimens to that of a pure iron specimen from the same sintering run ( i.e., prepared identically in the same sling ) evidence of activation due to the dopants could be distinguished. Table 4.5 and Figure 4.6 show the effect of addition of boron to iron. Boron is seen to activate sintering in both alpha and gamma phase and it shows a consistent trend with increasing boron content. Metallographic observations of the Fe - 0.1B compact sintered at 850 °C and sintered for 20 minutes indicate that B has reacted with iron, probably forming a boride phase. Compacts sintered at 1000 °C show no trace of ( Figure 4.7 ( b ) ) boride phase or unreacted boron indicating that boron has redistributed itself uniformly throughout the compact. Preliminary experiments with Fe - 0.3 % Si indicated no activating effect on sintering. 142 gamma o + I CARBONYL Fe + B COMPACT PF = 0.23 sint. time 2 0 min A Fe • Fe + 0.1%B + Fe + 0.3%B o Fe + 0.5%B 800 900 1 1000 T E M P E R A T U T R E (°C) Figure 4.6: Effect of B additions on linear shrinkage in Fe - B compacts sintered in a flow of Ar - H 2 atmosphere for 20 minutes. 143 Figure 4.7: Microstructure of Fe - 0.1 B compact sintered for 20 Minutes at (a) 850 °C. Figure 4.7: ( b ) 1000 °C. 145 Table 4.5: Data For Fe - B Compacts Sintered in a Flow of H 2 - Ar mixture for 20 Minutes. Temperature Shrinkage as a function of % B added °C 0.0 0.1 0.3 0.5 850 5.01 5.61 5.79 6.14 900 6.24 6.91 7 7.1 950 3.4 3.48 3.72 3.98 SEM metallography, Figure 4.8, of the specimens revealed that alloying had not taken place in the Fe - Si compacts, thus preventing the dopant from having an influence on sintering. The oxide film on silicon particles remained stable throughout the compaction and sintering stages, prevented contact between iron and silicon. In later work, described in Chapter 5, alloying between iron and silicon was found to be enhanced by small additions of a flux, sodium carbonate. The compacts used in the later study had been pressed from coarser iron powders and at high pressures. Attempts to use the carbonate to promote alloying in Carbonyl iron - silicon compacts were made in the present study. No evidence of alloying was seen at the temperatures used. It is concluded that the relatively low compaction pressure used for the fine powder compacts did not provide a good mechanical contact between iron and silicon. As seen from the data in Table 4.6, germanium added in quantities of 0.1 to 0.5 wt. % 146 147 Table 4.6: Data for Fe - Ge Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. Ge % Green Density Temp % Shrinkage Sint. Density (gm/cm3) Rel % °C Expt (gm/cm 3) Rel % 0 5.77 73.3 700 0.32 5.93 75.4 5.81 73.8 800 4.38 6.46 82.1 5.8 73.7 900 7.86 7.17 91.1 0.1 5.71 72.55 700 0.28 6.12 77.75 5.74 72.87 800 4.35 6.52 82.84 5.6 71.13 900 7.86 7.00 88.94 0.3 5.66 71.92 700 0.30 5.94 75.43 5.80 73.7 800 4.25 6.52 82.984 5.76 73.16 900 7.74 7.16 90.96 0.5 5.8 73.67 700 0.300 5.86 74.34 5.77 73.55 800 4.67 6.53 82.94 5.81 73.77 900 7.51 7.06 89.69 did not result in any enhancement of the sintering of pure iron compacts. Germanium, like silicon has high affinity for oxygen and its oxide is not easily reduced under the conditions of sintering. Metallographic observation of the Fe - Ge compacts indeed showed the presence of unreacted germanium ( Figure 4.9 ) in the sintered microstructure. Ti has also been suggested as a potent sintering enhancener for Fe [95]. Ti in this study was introduced as T i H 2 . T i H 2 loses its H 2 around 400 °C, and therefore acts as an additional source of H 2 during sintering. Figure 4.10 and Table 4.7 reveal the effect of additions of Ti to Carbonyl powder. Titanium is seen to improve to a small degree the 148 Figure 4 . 9 : Microstructure of Fe - 0.1 Ge compact sintered at 800 °C for 20 Minutes. 1 4 9 + A gamma CARBONYL Fe+Ti COMPACT PF = 0.23 sint. time 20 min A Fe • Fe + 0.1%Ti + Fe + 0.3% Ti o Fe + 0.5% Ti l 1000 T E M P E R A T U T R E <°C) Figure 4.10: Effect of Ti additions on linear shrinkage of Fe -flow of Ar - H 2 atmosphere for 20 minutes. Ti compacts sintered in a 150 sintered density of iron compacts, but much less than boron. Metallographic observations indicate that the original titanium particles are replaced by a new phase ( Figure 4.11 ). Table 4.7: Data For Fe - Ti Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. Temperature Shrinkage as a function of % Ti added °C 0.0 0.1 0.3 0.5 850 5.01 5.61 5.3 5.3 900 6.24 6.43 6.5 6.6 950 3.4 4.01 3.72 4.2 Additions of 0.1, 0.3, 0.5 % of W and Cr and 0.3 % of Pd and Ni were made to Fe pow-der to find their effect on shrinkage. All transition elements except Ni produced a small amount of activation. Compacts containing nickel gave a negative effect. Even though the starting densities of nickel containing compacts was low, the resultant shrinkage and density were less than in the other high density iron compacts. The shrinkage results of these compacts have been compiled in Tables 4.8 to 4.10. In compacts containing W as additive, no unreacted tungsten was detected and the microstructure showed the uniform structure seen in Figure 4.12. Metallographic observations in compacts contain-ing palladium and chromium additives revealed the unreacted particles of the additives ( Figures 4.13 ( a ) and ( b ) ). Silver was added as silver nitrate in two different ways. In the wet mix method, silver 151 4.11: Microstructure of Fe - 0.1 Ti compact sintered at 850 °C for 20 Minutes. 152 Table 4.8: Data for Fe - W Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. % w Green Density Temp % Shrinkage Sint. Density (gm/cm3) Rel % °C Expt (gm/cm3) Rel % 0 5.76 73.2 800 6.9 6.77 86.08 5.78 73.5 850 7.52 7.2 91.34 6.06 77.1 900 8.65 7.38 93.78 5.78 73.5 950 6.36 6.83 86.79 0.1 5.76 73.2 800 7.01 6.92 87.88 5.77 73.3 850 8.64 7.45 94.66 5.75 73.05 900 8.66 7.28 92.41 5.72 72.6 950 6.5 7.25 92.08 0.3 5.80 73.73 800 6.84 6.85 86.97 5.78 73.4 850 8.73 7.46 94.82 5.76 73.16 900 8.42 7.39 93.86 5.76 73.23 950 6.56 6.73 85.45 0.5 5.80 73.73 800 6.46 7.05 89.63 5.69 72.32 850 8.63 7.42 94.23 6.03 76.4 900 8.35 7.25 92.15 5.77 73.33 950 6.56 7.21 91.61 Figure 4.12: Microstructure of Fe - W compacts sintered at 850 °C. 154 Table 4.9: Data for Fe - 0.3 Cr Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes Additive Green Density Temp % Shrinkage Sint. Density (gm/cm3) Rel % °C Expt (gm/cm3) Rel % Fe 5.70 72.4 800 6.03 6.51 82.78 5.72 72.7 850 7.85 6.74 85.64 5.68 72.2 900 8.03 7.00 88.95 5.63 71.5 950 5.99 6.68 84.87 Cr 5.78 73.54 800 5.74 6.83 86.78 5.83 74.0 850 8.48 7.23 91.86 5.83 74.0 900 7.97 7.3 92.75 5.83 74.08 950 7.16 7.26 92.20 155 Table 4.10: Data for Fe - 0.3 Ni Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. Additive Green Density Temp % Shrinkage Sint. Density (gm/cm3) Rel % °c Expt (gm/cm3) Rel % Fe 5.77 73.30 800 6.90 6.75 85.76 5.78 73.40 850 7.52 7.19 91.35 5.76 73.8 900 8.65 7.38 93.77 5.78 73.44 950 6.36 6.83 86.78 Ni 5.34 67.78 800 4.86 6.11 77.63 5.3 67.27 850 7.32 6.46 82.11 5.24 66.56 900 5.6 5.83 74.1 5.26 66.77 950 3.59 5.80 73.75 156 157 Figure 4.13: ( b ) Cr. 158 Table 4.11: Data for Fe - 0.3 Ag Compacts Sintered in a Flow of H 2 - Ar for 20 Minutes. Additive Green Density Temp % Shrinkage Sint. Density (gm/cm 3) Rel % °C Expt (gm/cm3) Rel % Fe 5.75 73.1 700 0.68 5.82 73.89 5.75 73.1 800 2.56 6.1 77.52 Wet Mix 5.64 71.64 700 0.90 5.90 74.9 5.72 72.63 800 2.77 6.33 80.44 Dry Mix 5.67 72.1 700 0.97 5.84 74.23 5.71 72.57 800 2.82 6.10 77.5 nitrate was dissolved in ethyl alcohol first and then iron powder was added. This mixture was then dried at a low temperature of 100 °C. In the dry mix method, silver nitrate was added to iron powder and then blended. Compacts prepared by the wet mix method yielded a higher linear shrinkage than pure iron compacts ( Table 4.11 ). In the case, of several of the additives, metallography revealed that there had been little or no reaction or alloying between the iron and dopant particles, thus precluding any beneficial effect on sintering at iron - iron contacts. The problem is believed to be oxidation of the surfaces of the additive particles, and the inability of such oxides to be reduced to metal or to be otherwise dispersed under the conditions of sintering. It was hoped that difficulty might be overcome in the case of Si, Ge and Cr by using freshly ground particles which would be fairly slow to oxidize at 20 °C. Titanium was added as the dihydride, which decomposes above 400 °C to yield fresh metal surfaces. The less reactive elements nickel, tungsten and palladium have oxides which reduce 159 to metal in hydrogen at the sintering temperatures. At the low concentrations in which they were used in iron compacts, much of each of these additives would have to be dispersed through the iron particles to ensure that all surfaces were coated. However, metallography indicated that such coating was minimal for these dopants. This suggests that their dispersion was less favorable than that obtained for nickel activated sintering of tungsten. Boron, unlike all the other additives in this study was found to be fully dispersed throughout compacts after sintering at 1000 °C. The absence of well defined activated sintering in ferrous compacts compared to the tungsten system necessitates the analysis of activated sintering. 4.4 A N A L Y S I S O F A C T I V A T E D S I N T E R I N G I N T U N G S T E N - N I C K E L Theories for the activated sintering of tungsten powder by nickel and other additives were reviewed in Section 1.5 (see p. 28). The several models that have been advanced are in substantial disagreement with each other. Differences derive from the totally different assumptions that are made about how the additive is distributed among and between the tungsten particles during sintering, and this determines the mass transport mechanisms and paths involved in densification. In this section, the approaches described in Chapter 3 will be applied to an examina-tion of the sintering of tungsten powder, with particular interest in the temperature range at which activated sintering has been observed. Previous geometric models of activation will then be critically reviewed, in order to provide a basis for selecting or developing a theory which is consistent with the available facts and observations. 160 4.4.1 Sintering of Pure Tungsten Powder Analysis of Field Maps for the Sintering of Pure W With reference to Figure 1.2 ( b ) (see p. 5) the three principal mass transport mechanisms for the sintering of pure tungsten powder are those involving self diffusion at external surfaces, along grain boundaries at the neck and through the lattice from grain boundaries ( paths 1, 4, and 5 in Figure 1.2 ). As in the case of iron, negligible contributions to neck growth and shrinkage are provided by the other transport mechanisms. Based on the properties of tungsten which are compiled in Table 4.12, field maps were generated for compacts of different particle size using the short method of construction developed in Chapter 3. The maps are shown in Figures 4 .14 ( a ) to ( c ). It is seen that • at all homologous temperatures of interest, surface diffusion is the dominant mech-anism of neck growth up to a neck radius ratio of ( x/a ) of 0.25. • for TJ J < 0.5 ( where activation is effective ), sintering shrinkage is strongly domi-nated by grain boundary diffusion at x/a > 0 . 2 5 . From the data on material constants in Table 4.12, calculations were made of the diffusion coefficients for surface, boundary and volume diffusion in tungsten at temper-atures in the range of 1000 - 1400 °C. The results, which are compared in Table 4.13, confirm that volume self - diffusion will be of no consequence to neck growth or shrinkage at these temperatures. The absolute value of the surface diffusion coefficient in the range of 1200 - 1400 °C is notably high. Growth and rounding of necks can be expected to proceed relatively fast in compacts of 0.56 /xm particles even at these low sintering temperatures. It is seen from Figure 4.14 (c) that, for very fine particles, surface and grain bound-ary diffusion are the dominant transport mechanisms at all temperatures. As proved 161 Table 4.12: Material Constants for Tungsten used in the Calculations. PROPERTY VALUES SOURCE Atomic Volume fi(m3) 1.59 x IO" 2 9 Melting Point T m (K) 3683 Surface Energy -J,{^) 2.65 [72] Effective boundary thickness SB (m) 5.48 x l O - 1 0 Effective surface thickness SS (m) 3.0 x l O - 1 0 Pre - Exp, lattice diffusion Dov(-^) 5.6 x IO" 0 4 [96] Activ. Energy, lattice diffusion Qvijj^,) 585 [96] Pre - Exp, boundary diffusion ^D^^—) 5.48 x 10-1 3 [97] Activ. Energy, boundary diffusion Qbijfi^) 378 [97] Pre - Exp, surface diffusion D,6s(j£;) 2.55 x 10~13 [98] Activ. Energy, surface diffusion Qsi^ie) 326 [98] Table 4.13: Diffusion Coefficients of W at 1000 - 1400 °C. Temperature ( T/TM ) Diffusion Coefficients — sec °C Surface Boundary Lattice 1000 ( 0.35 ) 3.51 x l O - 1 7 3.08 x l 0 ~ 1 9 5.39 x l O - 2 8 1100 ( 0.37 ) 3.32 x l O - 1 6 4.15 x l 0 ~ 1 8 3.0 x l O ' 2 6 1200 ( 0.4 ) 2.31 x l O " 1 5 3.94 x l O " 1 7 9.8 x l O " 2 5 1300 ( 0.43 ) 1.25 x l O " 1 4 2.8 x l 0 ~ 1 6 2.05 x l O " 2 3 1400 ( 0.45 ) 5.57 x l O " 1 4 1.58 x l O " 1 5 2.98 x l O - 2 2 162 Figure 4 .14: Field map for W spheres of diameter ( a ) 100 fim (b) 20 fim. 163 o -0.1 -0.2 h -0.3 -0.4 -•0.5 --o.a --0.7 --0.8 •0.9 H -1 -1.1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7 -1.8 -1.9 -2 BOUNDARY SURFACE 0.4 0.6 0.8 H O M O L O G O U S T E M P E R A T U R E ( T / T M ) Figure 4.14: (c) 0.56 fim. 164 previously, the surface to grain boundary field interface does not change position with changing particle size, but the surface to volume field interface and the grain boundary to volume diffusion interface shift to lower temperatures as the particle size increases. Thus, for larger particle radius spheres, all three mechanisms are seen to contribute at a high sintering temperature. At the low temperature and small particle size where the activation effect has been observed, the dominant mechanisms predicted are boundary and surface diffusion. Moreover, the addition of nickel is unlikely to alter this latter pre-diction because there is no reason to expect that the presence of nickel can significantly influence transport of tungsten atoms by volume self-diffusion. Analys is of F l u x of M a t t e r A r r i v i n g at the Neck A field boundary is the locus of points at which two transport mechanisms contribute equally to the flux of matter arriving at the neck. Thus by changing the values of x for one transport mechanism the boundary can be shifted. Considering Equation 1.10 (see p. 12), xs is increased if either the surface diffusion coefficient Ds, or surface energy 7s, or the driving force for the process is increased by the presence of Ni. There are experimental reports that Ds is increased by the presence of Ni. The possibility of some increase in the surface energy, though anticipated, is not given a serious consideration in this study as the increase would have to be considerable to account for the kind of activation seen in W - Ni. . Moreover, the increase of Ds due to nickel does not in itself contribute to activated sintering because surface diffusion is not expected to contribute to shrinkage. Considering Equation 1.13 (see p. 13) for XB, the rate is influenced by any one or combination of the three terms DB,SB, 1B- Many solute species in metals have been shown to segregate at grain boundaries. The presence of impurities at the grain boundary increases the effective width SB- In quantitative studies of intergranular diffusion only 165 the product DB$B is determined and it is not easy to say whether the impurity has the greatest effect on the grain boundary width or the actual diffusion coefficient. In general, due to segregation at the boundary, both 7# and Dg are reported to decrease [100]. Finally considering Equation 1.14 (see p. 13) for xy, the rate can be increased only by increasing Dy. The diffusion coefficients for pure tungsten in the temperature range of activated sin-tering is compiled in Table 4.13. It is observed that grain boundary diffusion coefficients are of the same order as lattice diffusion. These values were calculated using the data reported in Table 4.12. At a temperature of 1200 °C ( ^ = 0.4 ) for x/a = 0.01; i.e. at the start of Stage 1, xs : xB : xv = 0.2373 x IO" 0 2 : 0.1624 x IO" 0 5 : 0.742 x 10~12 The predicted boundary and lattice contributions are both extremely small. Shrinkage of compacts which are sintered at 1000 - 1400 °C can only be expected if the relevant diffusion coefficients or the driving force due to the curvature difference can be markedly increased by the presence of an activator. Thus, the dopant must reduce substantially the activation energy for diffusion. In order to make xy > i 5 , o r x j g > i s the volume diffusion flux has to be increased by a factor of at least 1014 times and boundary diffusion flux by a factor of 1007 times. This is possible by decreasing the activation energy for the process i.e., by increasing the corresponding self diffusion coefficient of W. Table 4.12 shows that W has a very high activation energy for the volume self-diffusion process. The reported activation energy values observed during sintering of nickel activated tungsten are in the range of 220 - 300 kJ/mole. These are less than half the activation energy for volume self diffusion ( 585 kJ/mole ) in tungsten and less or of the same order as that of boundary or surface self diffusion in pure tungsten ( 378 kJ/mole for boundary 166 and 326 kJ/mole for surface diffusion ). It is likely that any one of surface, boundary or volume diffusion is altered by the presence of Ni. Surface diffusion even if affected does not contribute by itself to the shrinkage. Computations of the new diffusion coefficients from the reported activation energy of 300 kJ/mole for activated sintering in the W - Ni system, shows that the volume diffusion coefficient is far higher than the corresponding boundary diffusion coefficient at all temperatures. As a first approximation, the effect of changing the diffusion coefficient on the shrinkage can be estimated from the following simplified equations of the form of Equation 1.3 (see p. 8), {DB) 81 1 " SI , n s Thus at 1200 °C, the effect of the increase in the diffusion coefficient ( correspond-ing to an activation energy of 300 kJ/mole, D s = 1.93 x l O " 1 4 , D B = 2.3 x l O - 1 4 , Dy = 1.27 X l O - 1 4 ) , keeping all other parameters constant, increases the percentage shrinkage by 1004 times that for the case of volume diffusion and 8.3 times for the bound-ary diffusion over that of shrinkage of a pure W compact. Hence, it is logical to conclude that the grain boundary diffusion is influenced by the presence of Ni. It is seen that pre-dicted shrinkage is very large when volume diffusion coefficient is changed and is more realistic when the boundary diffusion coefficient is changed. A similar analysis on the reported results of Gessinger and Fischmeister [21] ( Figure 1.7, see p. 21 ) shows that shrinkage is increased by 12.6 times ( corresponding to an increase in boundary diffusion coefficient of 2000 times ) by the presence of nickel over that of pure tungsten. 167 4.4.2 Role of Nickel in Activated Sintering of Tungsten The theories of activated sintering in W - Ni were described in Chapter 1 (see p. 28), with the indication that the most widely accepted theory is the enhancement of grain boundary diffusion of W due to the presence of Ni along the boundary. In order to develop a model for the process of activation in W - Ni system, two important questions must first be answered. • What is the significance of a "monolayer" of additive as suggested by earlier workers. Is there a minimum quantity of the additive needed to cause enhanced shrinkage? • How is the additive distributed and how does it influence the transport of W? In this section a critical review of published results with reference to the above points is made and an appropriately modified model is proposed. Significance of Number of Monolayers of Nickel Table 4.14 is a summary of data from the work of prior investigators of W - Ni in which pronounced activation was observed. While the number of "equivalent" monolayers and the particle sizes were different, strong activation was found. It is significant to note that enhancement due to nickel was largely independent of how the nickel was introduced, which suggests that it was rapidly redistributed during sintering. Referring to Figures 4.15 ( a ) and ( b ) which show the dependence of linear shrinkage upon Ni content for various sintering times at 1000 °C [43], 1200 and 1300 °C [49], it is seen that the process is independent of Ni content over a large range beyond that equivalent to one monolayer. The monolayers are calculated theoretically from the weight % of the additive assuming it to be distributed uniformly and continuously on the surface of the tungsten particles. This assumption may be valid when the particles are pre 168 Table 4.14: Summary of Parameters of Activated Sintering in W - Ni used by Different Investigators. a Wt No. of Sintering Method of fim % Ni Monolayers Temp. °C Addition Source 0.56 0.12 1 900 - 1100 N i N 0 3 aq. soln. Brophy et al. [43] 3.3 0.1 8.8 850 - 1200 Impregnation of Halide Toth et al. [48] 0.5 0.5 - 1000 - 1100 N i N 0 3 aq. soln. Gessinger et al. [21] 0.6 0.1 ~ 1 1000 » German [49] 0.5 - 4 1000 - 1400 » German et al. [61] Equivalent monolayers calculated theoretically - coated with" nickel or if the additive initially diffuses rapidly over the surface of the particle to cover them uniformly. Calculation of the number of monolayers is dependent on the particle radius, thus making the critical amount of additive different for different particle sizes. State of Dispersion of Nicke l in Tungsten - Nicke l The W - Ni equihbrium phase diagram is shown in Figure 4.16. Under conditions where effective activation of sintering has been found in W - Ni, dopant after sintering was so thoroughly dispersed that the distribution could not be determined unambiguously by conventional imaging techniques in the microscope. Several investigators reported high concentrations of nickel at grain boundaries. However, the observations did not make it possible to distinguish between ( a ) discrete nickel films between tungsten grains, or ( b ) segregation of nickel as an impurity at tungsten grain boundaries. Figure 4.15: Linear shrinkage as a function of Ni content [43,49]. 170 1600 MOO u 3 a v E— 1200 4 1000 -j 800 800-j 400 A 200 Atomic Percent Tungsten 10 20 30 40 SO 60 70 80 90 100 (Ni) •1S10*C 3tt*C N •» Tr»Mform«Uo 399/ ~i8.0 -1S00*C 0 10 20 30 40 30 SO 70 Ni Weight Percent Tungsten 80 98.7J • • I • • 90 100 Figure 4.16: Phase Diagram of W - N i . 171 At higher levels of nickel than those needed for optimum activation, Ylasseri and Tikkanen [44] were able to observe in the electron beam microprobe the presence of a tungsten-saturated nickel phase in the microstructure. Their photomicrographs ( Figures 4.17 ) indicate wetting of solid tungsten surfaces by the nickel phase. However, there was no evidence that the grain boundaries at tungsten particle contacts had been penetrated by a film of nickel. In developing theoretical models for the activated sintering of tungsten by nickel, different investigators have made different assumptions about the state of dispersion of nickel and its consequent effects on mass transport of tungsten. These are summarized below. For brevity, the nickel rich solid solution ( gamma ) is referred to simply as "nickel" in the discussion. 1. Brophy et al. [42] assumed that nickel was present as a continuous film on tung-sten surfaces, precluding the formation of grain boundaries or necks at tungsten - tungsten particle contacts. The physical situation described in Figure 1.10 (see p. 30) led to a solution - reprecipitation model of activated sintering. 2. Toth and Lockington [48] assumed that continuous nickel films were present on tungsten surfaces, but that nickel was also present as an impurity in the tungsten grain boundaries. Activation was attributed to enhanced diffusion of tungsten atoms at the "nickel modified" tungsten surfaces. 3. Gessinger and Fischmeister [21] concluded that solid nickel is only partially wetting with respect to tungsten surfaces, and is present as shown in Figure 1.11 (see p. 32) as "islands" ( at A ) and as "pendular rings" at the contact between tungsten particles ( at B ). The tungsten grain boundaries contain nickel as an impurity, but are not wetted by nickel. Thus necks are assumed to exist both in tungsten 172 Figure 4.17: EPMA Results of Ylasseri and Tikkanen [44]. 173 and in nickel, as seen in Figure 1.11. Activation was associated with enhanced grain boundary self-diffusion in the tungsten. 4. German [61] used the physical model shown in Figure 1.12 (see p. 33). He accepted the Gessinger and Fischmeister observation that nickel does not completely wet tungsten surfaces, but assumed that nickel was present at tungsten contacts in the form of a film and that a solution - reprecipitation process was responsible for transport of tungsten. It should be noted that tungsten reportedly dissolves 0.3 wt. % nickel at temperatures in the range of 800 - 1500 °C ( Figure 4.16 ). Since effective activation is obtained at concentrations lower than this, there is the possibility that the dopant is dissolved during sintering and that only surface or grain boundary enrichment are involved in sintering activation. Toth and Lockington [48] seemed to suggest this in referring to "modified" surfaces of tungsten due to nickel. Several of these physical models involve the requirement that solid tungsten surfaces and grain boundaries are wetted by solid nickel or the nickel - tungsten phase ( 7 ). Wetting is defined by the geometry shown in Figures 4.18 ( a ) and ( b ). For complete wetting of tungsten surfaces by nickel, i.e. for 6 = 0, 7 w ^ 7 N i + 7w-Ni ( 4 1 ) For complete penetration of tungsten grain boundaries by Ni, the dihedral angle <j> must be zero or T^w-Ni — 2^ww (4-2) Dihedral angle is very sensitive to the ratio of 7 W W / 7 W N ; . The lower the dihedral angle, the more energetically favorable is it for nickel to remain at the boundary. For a dihedral angle of 60° or less, penetration of nickel can occur along the three grain edges 174 of the tungsten phase ( Figure 4.19 ), but the complete penetration of nickel into the tungsten grain boundaries requires (j> to be zero. It is found that for metals the grain boundary energy fww is about one third of the solid - vapor surface energy *yw [99] Tww — 3^w (4-3) The condition for grain boundary wetting then becomes 7w-Ni — Q^W (4-4) For a zero contact angle ( Equation 4.1 ) we now have 7N i < ^ 7 W (4-5) Values reported for 7 W and 7N ; [99] are 2.68 and 1.73 J /m 2 respectively which establishes the condition" that 6 = 0 when <p = 0 from Equation 4.5. However, it does not follow that 0 = 0 when 6 = 0. Using the reported surface energy values for 7 N ; and 7 W we have from equation 4.1 that 7 w . N i <0.95 J/m2 (4.6) for 6 = 0. If 6 = 35° as reported by Gessinger and Fischmeister [21], then 7w-Ni = 7 w - 7 N i c o s 0 = 1.236 J /m 2 For grain boundary wetting it would follow from Equation 4.2 that ~fww must be > 2.53 J /m 2 . Clearly this is an unreasonably high value of grain boundary energy. Using instead the <a) (b) Figure 4.18: Conditions of Wetting. 176 Figure 4.19: The appearance in three dimension of a minor phase occurring at grain edges [101]. 177 expected value of 1/3 7 W , we find cos (j) 7 W W ^ W N i ^w ^TwNi 2.68 6(1.263) Therefore <f> = 70°. On this basis alone it is possible to reject the physical model assumed by German et al. [61] and Brophy et al. [42] which requires that <f) = 0 even when there is only partial wetting of the tungsten surfaces. In the case of the W - Ni system, this would appear to be impossible. Further, with the geometry of Brophy et al. [42], there is a neck only in the nickel phase during sintering, and this neck would tend to assume a relatively large diameter ( ancl low curvature ) even before there has been much transport of tungsten atoms from the particle. Since the surface energy of nickel is much lower than that of tungsten, it follows that the capillary stress provided by nickel is much lower than that of tungsten at a neck. The Toth and Lockington [48] model is based on the assumption of a continuous nickel film on the tungsten surfaces, although the authors do not refer to wetting. Since their model of activated sintering involves only surface diffusion, an increase in the capillary driving force due to the activator is not required. Therefore it does not matter whether the nickel layer wets the tungsten, so much as it is required that a continuous monolayer of nickel atoms be present to provide a "modified" surface on which tungsten atoms can diffuse more readily. The model of Gessinger and Fischmeister [21] assumes partial wetting of tungsten by nickel. 178 Enhancement of Mass Transport in Tungsten - N i c k e l The activated sintering theories of Brophy et al. [42] and of German et al. [51] depend on the volume diffusion of tungsten through a dopant layer i.e., a diffusion path different from any of those involved in the solid state sintering of a single component. Since it has been shown above that <f> > 0 in W - Ni, a continuous layer of nickel cannot form at boundaries, both of these models will be rejected. In the Toth and Lockington theory, the distribution of activator is plausible. However, the mass transport process which is said to be activated by nickel is surface diffusion of tungsten. The major weakness of the model is that it is normally assumed that surface diffusion cannot produce shrinkage ( densification ) of a compact, yet it is shrinkage which is used as the principal indicator of activated sintering. In the Gessinger and Fischmeister model [21], shrinkage in W - Ni is due to grain boundary diffusion, the same as for pure tungsten. According to the authors, nickel enhances this transport in one or both of two ways : 1. by introducing an extra capillary stress at the contacts, which increases the driving force for grain boundary diffusion ( i.e., thermodynamic effect ); 2. by entering tungsten grain boundaries as an impurity and somehow increasing the grain boundary self - diffusivity ( i.e., kinetic effect ). In fact, the presence of an impurity at the grain boundary might be expected to impede grain boundary self-diffusion rather than to enhance it as assumed by Gessinger and Fischmeister [21]. 1 7 9 4.5 P R O P O S E D T H E O R Y O F A C T I V A T E D S I N T E R I N G 4.5.1 Suggested Model It was shown in the previous section that nickel does not wet tungsten particles completely i.e., 8 ^ 0 and therefore the dihedral angle <f> cannot be zero. From this it can be inferred that necks form and grow between the tungsten grains by self diffusion of tungsten to cause shrinkage. The presence of nickel somehow influences the driving force or the rate of transport of tungsten to the growing neck. In this section a simple model is proposed which is qualitative and which is not fundamentally different from the model for regular solid state sintering of metals. Based on the model and its analysis, criteria for the selection of systems for activated sintering and the potential activator for a given base material are proposed. The model is derived from the fundamentals of the sintering theory. In Chapter 1 it was pointed out that the transport of matter to the neck is provided by different diffusion mechanisms. It was also shown that in the initial stage of sintering when the radii of curvature between the two particles ( Figure 1.1 , see p. 3 ) are small, the resulting stress, given by Equation 1.1, is high. The high free energy at the neck surface reflects the accumulation of vacancies beneath the surface. Under the vacancy gradient, atoms diffuse towards the particle necks of high curvature while vacancies diffuse in the opposite direction. It has been observed that mass transport occurs through vacancy diffusion and that the grain boundary acts as a vacancy sink. A higher vacancy concentration in the neck area leads to a greater movement of atoms to the neck from the surface, volume and boundary regions. Based on this concept a new theory is proposed to explain activated sintering in the W - Ni system. Nickel is usually added as pure nickel or a nickel salt either as a coating or in powder form. Even if nickel is added as elemental particulate metal, Vacek [102,103] suggested 180 from his diffusion experiments that nickel diffuses rapidly over the surface of tungsten particles. By pressing a porous nickel compact against a porous tungsten compact and heating at 1300 °C, he found that interdiffusion was extensive and that nickel had pen-etrated further into the tungsten compact than had tungsten into the nickel compact. This was unexpected, since W has much more solubility in Ni than has Ni in W, and the lattice diffusion of W into Ni is expected to be very much faster than the diffusion of nickel into tungsten. Since both compacts were porous at the beginning Vacek [102,103] concluded that surface diffusion rather than volume diffusion was responsible for the deep penetration of Ni into the W compact. It is suggested here that the addition of nickel to tungsten compacts imparts activation of sintering by causing extra vacancies to be generated under the tungsten neck surfaces due to ( a ) the large difference in the relative intrinsic diffusion coefficients of W in Ni and Ni in W and ( b ) the low solubility of Ni in W compared to that of W in Ni. The activation of sintering is then the result of an increased driving force. This is schematically represented in Figure 4.20. The duration of this activation effect is the duration of an effective inter-diffusion flux. When the nickel at necks become saturated with W, the sintering rate will be essentially that experienced by pure tungsten for the same neck geometry. When the diffusion coefficients between the two components are unequal, two con-nected but distinguishable, vacancy fluxes are possible in any powder compacts. First there is that already described for pure metal which is associated with curvature gradi-ents. The second arises from the Kirkendall effect where the flux of atoms of each species across the interface at the neck is not equal. In the case of W - Ni, as discussed later, diffusion is highly unidirectional from W into Ni or the Ni rich solid solution. Thus, a vacancy rich region exists within the W at the W - Ni interface due to more diffusion of atoms from the tungsten side to the nickel side. Thus the total number of vacancies 181 Increased vacancy ctracentratioo as a result of W diffusion Into Ni solution increased vacancy concen tattoo accelerates material transport Figure 4.20: Schematic representation of the activated sintering mechanism. 182 leaving the neck surface/sec at any instant is the sum of those that diffuse under the effect of the curvature gradient and those due to excess vacancy concentration as a result of W diffusion into Ni. If we assume that all vacancies that are formed at the neck sur-face are annihilated at the grain boundary, the main influence of the increased vacancy concentration is to accelerate material transport as diffusion takes place by reverse flux of vacancies. This flux steadily and rapidly decreases with sintering time and that is probably why the effect of activated sintering in most cases is observed only in the early period of sintering. Diffusion data for the W - Ni binary system indeed indicate that the volume diffu-sion of tungsten into nickel is relatively rapid [104,105] compared to the volume diffusion of nickel into tungsten. These intrinsic diffusion data can also be calculated using the method of Srikrishnan and Ficalora [106], as discussed in the next section. This calcula-tion shows that the activation energy for the diffusion of tungsten into a layer of nickel is 310 kJ/mole while that for the diffusion of nickel into tungsten is 507.7 kJ/mole. The self diffusion coefficient of W at 1300 °C is reported to be ~ 10 - 1 8 cm2/sec while that of W in Ni is about IO - 1 0 cm2/sec [107]. Thus the predicted flux of tungsten atoms into nickel is much higher than that in the reverse direction. This creates an excess vacancy concen-tration gradient on the tungsten side of the neck regions which in turn drives additional transport of tungsten to the neck region. The vacancies reaching the grain boundary are either diffused out by the grain boundary diffusion or simply collapse. The tungsten par-ticle centers approach each other i.e., there is linear shrinkage. Since the grain boundary acts as an effective sink for vacancies it appears that it is grain boundary self-diffusion of tungsten which is influenced. The activation energy for the volume self diffusion in tungsten is very high ( 585 kJ/mole ) and transport along the grain boundary is clearly favoured. Using the values of activation energy for tungsten listed in Table 4.12 and the results of Gessinger and Fischmeister [21], the change in the activation energy which is 183 required to account for the observed increase of 800 and 2000 times in the self-diffusion coefficient at 1100 and 1200 °C, is calculated to be 307 and 291 kJ/mole if grain bound-ary transport is favoured. This is well within the range of reported activation energy values for activated sintering in the W - Ni system. The corresponding values for volume diffusion are found to be 514 and 498 kJ/mole respectively. Based on the above observations one can argue that the activation energy values determined experimentally by various investigators are probably correct. They all he in the same range. However, the interpretation of the data by different workers is quite different from that which is advanced here. Thus, according to the new concept, any binary system in which there is a wide gap between the intrinsic diffusion coefficients of the base metal and the additive such that ^Base in Additive ^Additive in Base •^ ••^ Base in Additive ^ ^-E . Additive in Base is a potential candidate for activated sintering. The directional mass flow of B into A is also favoured by a large difference in the mutual solid solubilities. The activation energy for each of the diffusing species is further related to the melting point of that species. In general the higher the melting point the higher is the activation energy. Thus one criterion for a system to exhibit activated sintering is related to the melting temperature and activation energy for self diffusion. It is not enough for the above criterion to be satisfied if there is no solid solubility of B in A. Thus conditions favouring solid solubility should be satisfied, e.g., small difference in the atomic radii, valence and crystal structure. Also, in order to have a high concentration gradient at the start of sintering, the additive should be introduced as the pure element. Both wetting and dihedral angles are functions of surface energy/surface tension /in-terfacial energy. In general surface energy is high for metals with high melting point. The 184 relative difference in melting points of the base and the additive is thus likely to reduce or modify the interfacial energy favorably. The model proposed here is not much depen-dent on the specific state of dispersion of the additive, although a uniform distribution is needed. As long as 6 ^ 0 and <p ^ 0 the tendency will be for the additive to be concentrated at the neck region. Therefore conditions for'wetting can be ignored as they were in the earlier proposed models. The condition 8 = 0 may not be harmful, but if <p = 0, the presence of a film along the boundary may alter the sintering kinetics and damage the mechanical properties. If the additive is present as a substitutional impurity along the grain boundary, it can plug channels of high diffusivity in the grain boundary so that the effective cross section area for rapid diffusion is decreased. Thus the criteria to be considered for activated sintering include relative melting points, atomic radii, degree of mutual solubility and relative position in the periodic table. 4.5.2 Support For The Suggested Model In the equihbrium diagram for the W - Ni system the solubility of tungsten in nickel is seen to be much higher than that of nickel in tungsten. For example, at 800 °C, 32 wt. % of tungsten dissolves in nickel but only 0.3 wt. % of nickel is soluble in tungsten. Cobalt dissolves 35 wt. % of tungsten at the eutectic temperature of 1465 °C• The solubility declines rapidly below 1100 °C and is only about 3 wt. % at 400 °C. Tungsten, however, dissolves only 0.3 wt. % cobalt at 1690 °C, a solubility which remains practically unchanged with temperature. The Fe - W equihbrium diagram shows that tungsten dissolves only about 0.8 wt. % 185 iron at 1640 °C and this solubility changes very little below and above this temperature. On the other hand, 6 wt. % of tungsten dissolves into iron at 600 °C and 32.5 wt. % is soluble at 1600 °C. As noted above, the additive should be introduced in the pure form rather than as an alloy to maximize concentration gradient, which is the driving force for diffusion. The importance of this is quite clearly brought out in the experiments of Thummler [102]. Thummler studied the effect of solid solution forming foreign atoms on sintering. He studied two different cases, • a solid solution that pre-existed before sintering. Systems studied were Fe - Sn, Fe - Mo, Fe - Ni and Cu - Sn with solute concentration of 0 to 1 % by weight. • solutions formed only during sintering. Systems studied involved pure metal elec-trodeposited on a base metal rod; e.g. Fe/[Ni deposit]/Fe, Co/[Ni deposit]/Co, Ag/[Cu~deposit]/Ag. In the first case Thummler [102] found either a negative effect or no effect on sinter-ing. However, in the second case he found a very strong positive effect on the sintering behavior. He attributed these results to the formation of vacancies during diffusion on the one side. The atomic radius difference favouring high solid solubility according to Hume-Rothery [108] is < 15 % which is not very restrictive. Agte and Vacek [109] observed a marked increase in the rate of sintering of tungsten and molybdenum as a result of very small additions of nickel, iron or cobalt. These authors also made a systematic study on the effect of atomic radius r of the added atoms and showed that the activation energy for sintering was small when AT- = r — r0 — 0 and increased rapidly with A r . The above two criteria help to choose a system or an additive for a given base metal, but the success of activation also depends on the relative magnitudes of the coefficients 186 of inter - diffusion. This is the most important criterion to be satisfied. Diffusion data are often not to be found in the literature for systems of interest. However, it is possible to calculate the activation energy for the transport of base material ( W ) through an additive layer ( Ni, Co, Fe etc., ) from the respective self-diffusion coefficients using Srikrishnan's model [106]. Comparison of this value for different additives to a given base metal should indicate their effectiveness. Calculation of Activation Energy for Diffusion through the Additive Layer The basis for the calculation of activation energy according to Srikrishnan's [106] ap-proach is the Engel Brewer theory [66]. The number of "d" electrons is correlated with the activation energy for diffusion. [110]. This can be accomplished by one of two ap-proaches. The process can be described by the diffusion of W metal in either a pure additive layer (tracer diffusion) or in an alloy of the additive and base metal (alloy diffu-sion). The activation energy for diffusion can be written in terms of the sum of the energy to create a vacancy in the additive layer EVA and that required to accomplish a jump from a site occupied by the metal atom, i.e., EM. Thus Q = E\ + EM (4.7) where Q is the activation energy for diffusion. Experimental observations have demon-strated that for close packed structures the energy of formation of a vacancy is 0.57 times the activation energy for self diffusion [111]. Therefore the equation can be rewritten as Q = 0 . 5 7 Q f + 0 . 4 3 [ ( Q f + Qf?)/2] (4.8) where Q s^  and Qj° are the activation energy for self diffusion for the metal M and the additive A respectively. is modified by the structure of the additive layer. The degree to which Qfj* is modified can be calculated by first determining the number of "d" 187 electrons associated with M . The Engel Brewer theory [66] provides such information. Using the periodic correlation between the number of " d " electron and the diffusional activation energy a modified Q value is obtained. For B C C structures, the relationship defining the overall Q is Q = 0.55Qf + 0A5[(QSMD + QsAD)/2] (4.9) This approach of Srikrishnan and Ficalora [106] covers only transition metals and alloys. The value of pre-exponential factor has been normalised to unity and therefore one can make comparison of the activation energy data alone. The values of D0 listed for these elements in their paper shows that Do does not appreciably differ from the original value by the presence of an additive layer. German [49] has used this approach in the case of activated sintering of molybdenum, and to a lesser extent in tungsten. He correlated the experimentally determined shrinkage of a powder compacts with that of the calculated activation energy. He also reports that experimental and calculated values of the activation energy agree within experimental errors. The activation energy for volume diffusion of W through a layer of N i , calculated using the above model, is 310 kJ/mole. This is in good agreement with the reported values for activated sintering in W - N i system in the literature. 4.6 C R I T E R I A F O R T H E S E L E C T I O N O F A N A C T I V A T O R Section 1.6 (see p. 35) summarized German's criteria [67] for the selection of an activator. In general it is agreed that activated sintering occurs when the additive has a high solubility for the base metal and when it remains segregated at the grain boundaries of the base metal. The first of German's criteria [67] is the solubility relationship between the additive A and the base metal B . The additive must have a high solubility for the base metal, 188 and the reverse solubility of A in B should be low. Low solubility of A in B minimizes the amount of additive needed to achieve activated sintering. The solubility of A in B increases diffusional homogenization and will consume the additive requiring a larger concentration to maintain a persistent effect. In a system in which the base metal has a high solubility for the additive there would be swelling by the creation of pores. It is obvious, therefore, that to obtain densification the additive should have a low solubility in the base metal. The solubility ratio of additives ( ratio of solubility of W in Additive to solubility of Additive in W ) at 1200 °C for the commonly added elements has been estimated roughly from the relevant phase diagrams Pd : 320 Ni : 400 Co : 420 Fe : 120 Pt : 20 Ru : 13 Comparing the results of German [61] shown in Figure 1.9 (see p. 27) it is seen that shrinkage is not simply related to this solubility criteria alone. Segregation of solute at solvent grain boundaries was related by German to the phase diagram features. The kind of segregation that is revealed by the phase diagram is that which occurs during solidification, and it is highly unlikely that the same feature can be extrapolated to solid state sintering phenomena although German did so. In general, the relative size and valency difference between the solvent and solute atoms are important factors in determining the magnitude of grain boundary segregation. Segregation is favoured whenever the size difference between the component atoms is large. Data for 189 systems based on W are shown in Table 4.15. Based on size factor alone, and assuming there are no differences in valence, Ni, Co or Cr should segregate more than Pd. Yet Pd is a strong activator compared to Cr or Co. It is suggested here that the most important criterion is the ability of the additive to reduce the activation energy for diffusion of the base metal below that for corresponding self diffusion. Using the model of Srikrishnan and Ficalora [106] it is possible to estimate the activation energy for the diffusion of tungsten through transition metal additives. As a first approximation it can be said that if the difference between the activation energies for volume diffusion in the base metal and in the additive is high, the potential for reducing the activation energy for volume self diffusion of the base metal is high. Further, the difference between the melting points of the base metal and additive should be high to facihtate low temperature sintering of the base metal, thus maintaining the dopant at a high homologous temperature. It should be mentioned here that this calculated activation energy IS NOT the activation energy for the process of activated sintering ( as is assumed incorrectly by German [51] ), but is only a criterion for selection of a dopant. The above factors are tabulated for tungsten-based systems in Table 4.15. The values of material constants are taken from Metals Handbook while the activation energies are taken from the published reports of Srikrishnan and Ficalora [106]. Looking at the Table 4.15 and comparing the important parameters in the W - Ni system, it can be said that for the process of activation the additive and the base metal should have a low r-factor to facilitate solid solution formation, high M.Pt-factor and high A.E-factor. Thus it is possible to list the order of effectiveness of various additives according to the three factors. Solubility criterion : Co > Ni> Pd > Fe > Pt Radius factor : Pd > Pt > Co > Fe > Ni 190 Table 4.15: Factors Important for the Selection of an Activator. Additive W Pd Co ' Fe Ni Pt R u r- factor % A r = ^-=^ 4.38 8.03 • 9.49 0.73 7.30 M.Pt-factor AT T M ( B ) - T M ( A ) 0.50 0.52 0.51 0.53 0.44 0.314 A.E-Factor AAE =  A E b a e a b E a 0.54 0.52 0.51 0.52 0.51 0.4 ^ ( 1000 - 1400 °C ) Additive 0.35 - 0.45 0.70 - 0.90 0.72 - 0.95 0.70 - 0.93 0.74 - 0.97 0.62 - 0.81 0.50 - 0.66 191 A.E.-Factor : Pd > Ni > Co > Pt > Fe According to the literature [43] the order of effectiveness is : Pd > Ni > Co > Pt > Fe. Thus good correlation is seen between activation and the criteria indicated. The additive should reduce the activation energy for the diffusion of base metal through it, in addition to having a considerable solubility for the base metal. In general activated sintering is carried out at homologous temperature of ( 0.4 - 0.5 ) of the base metal. If the sintering temperature is very low the sintering kinetics are slow. The additive should be a fairly low melting element with a M.Pt. ratio with the base metal of ( 0.50 - 0.55 ) that is to say that there should be a large difference in the melting points. Thus during sintering additive is maintained at a fairly high homologous temperature of ( 0.75 - 0.90 ) with respect to the sintering temperature and therefore the diffusion kinetics are faster. In actual practice for metals, the melting point, related to bond strength, bears a close relationship to surface energy. Finally the additive should have a low r-factor. 4.7 ANALYSIS OF A C T I V A T E D SINTERING IN F E R R O U S S Y S T E M S 4.7.1 Introduction The analysis of activated sintering for the W - Ni system as discussed in the previous section shows that there are a number of additives to tungsten which satisfy criteria consistent with the revised model of the present work, and which do indeed provide sintering enhancement. In the present study, the effect of a number of additives on the sintering of fine Carbonyl Fe powder has been studied. The results show that B, Ti and a few transition 192 element increase the shrinkage rate of ferrous compacts. However, the degree of activation is modest compared to that reported for W - Ni compacts. One reason for this is that in the case of W - Ni system, the particle size of the base metal powder was very much smaller than that of the iron powder used here. However, the homologous temperatures used with W - Ni was much lower than that used for ferrous compacts in the present work. Comparison between the tungsten-base and iron-base systems may suggest other reasons for the smaller amount of activation seen in the ferrous compacts. 4.7.2 Compar ison of Act ivated Sintering in Ferrous and W - N i system The dominant mechanisms of transport in iron and tungsten are grain boundary and surface diffusion as shown in Figure 4.21. Even at the lowest temperature of 800 °C used for all systems except for Fe - Ag in the present study, the homologous temperature T/TM is 0.62. At this temperature substantial shrinkage is predicted to occur in the fine iron powder compacts of this study. In contrast to this, the lowest T/TM of sintering for the W - Ni system is 0.34 ( 1000 °C ). Even at this low homologous temperature high sintering shrinkage was seen in W - Ni; This can be attributed to the fact that the nickel additive was at the relatively high homologous temperature of 0.75 when sintering was at 1000 °C. In the case of experiments with iron compacts, all additives that were tried had melting point comparable to that of iron or higher. Thus the additives were not at high homologous temperature in the experiments. In order to bring about activation, the additive must be capable of reducing the activation energy substantially for volume diffusion. The most commonly added elements to ferrous compacts come from the transition group series. The model of Srikrishnan and Ficalora applied to these transition elements show that except for Ag all other additives give comparable activation energy for the process ( Table 4.16 ). The additives all have 193 Figure 4.21: Field map for Iron compacts of 75 % relative density. 194 the same or higher intrinsic diffusion coefficients in both the alpha and gamma iron. Thus it is seen that transition elements other than Ag and Au are not predicted to activate sintering in ferrous systems under the conditions of the present study. Even these two additives are not expected to produce substantial shrinkage as the A.E. factor is calculated to be small. In fact, the addition of silver as silver nitrate to the Carbonyl powder and sintered at temperatures 700 and 800 °C produced little if any activation. Addition of gold on the other hand will permit a slightly higher temperature of sintering. The very high cost of this additive makes its use impractical and this material was not tried in the present study. Among the other additives from group 3, 4, and 5, namely B, Al , Ge and Si, B was found to be the best in terms of the sintering shrinkage. B in the compacts was found to be redistributed uniformly at the sintering temperatures unlike most of the other additives. Some of the additive did not react with or spread throughout the iron powder particles, and any potential beneficial effect was probably missed in these cases. The reactive nature of both iron and the additive powders in ferrous compacts does not favour diffusion between them, as they are separated by oxide films. This film on the additive particle in particular is not easily reducible, unlike the situation in the tungsten - additive systems under practical sintering conditions. 4.8 SUMMARY Published studies show that the addition of certain transition elements Ni, Pd, Pt have all been found to increase the sintering kinetics of W powder compacts at low homologous temperatures. Additions of several elements were made to see if there was similar effects in ferrous compacts. A fine Carbonyl iron powder of average radius 3 fim was used in the study. Several 195 Table 4.16: Comparison of the Factors Important for the Selection of an Activator. Additive r-factor % Ar = RB M.Pt-factor TM(B) A.E-Factor AAE = AEBAEABEA ^ ( 800 - 1000 °C ) Additive Fe 1 1 0.6 - 0.7 Cr 0.79 -0.19 -0.39 0.50 - 0.59 w .. 8.73 -1.03 -1.43 0.30 - 0.35 Ni 1.59 0.044 -0.168 0.62 - 0.73 Ti . 18.25 -0.072 -0.06 0.55 - 0.66 Ag 14.29 0.318 0.164 0.87 - 1.03 B 84.13 -0.47 - 0.47 - 0.55 Si 6.35 0.07 - 0.64 - 0.75 196 additives, B, Si, Ge, Ti, W, Pd, Ag were introduced in small quantities and compacts were sintered in a reducing atmosphere of hydrogen and argon at a relatively low temper-ature ( T / T M = 0.6 - 0.7 ). In the temperature range fine pure iron powder compacts experienced a large linear shrinkage, of the order of 7 %. A comparison of the important parameters of the W - Ni system and Fe - X systems has been made. The analysis indicates that for the sintering conditions used commer-cially, and in the present study on ferrous compacts, there is no additive which adequately can meet the set of conditions ( criteria ) required. That is, activated sintering of iron to theoretical density is impracticable. Therefore, for ferrous compacts other techniques and means of enhancing solid state sintering should be developed. One such promising approach is Ferrite Stabilization Enhanced Sintering as discussed in the following chapter. Chapter 5 FERRITE STABILIZATION ENHANCED SINTERING At the temperature used for sintering of ferrous powder metallurgy compacts; i.e., 1100 to 1350 °C, iron is austenitic. Furthermore, the alloying elements most commonly used for improving the strength and other properties of ferrous compacts are carbon, copper and nickel. These are all also austenite stabilizers. As discussed in Chapter 3, self-diffusion rates are much higher in ferritic than in austenitic steels at a given temperature, reflecting the lower activation energies of the relevant mass transport processes i n the body-centered cubic lattice. Thus one approach to enhanced solid state sintering i n ferrous materials, other than dopant activated sin-tering, is to choose compositions and sintering temperatures where the alloy is ferritic ( or largely ferritic ) in structure, to benefit at least i n principle from the higher rates of mass transport. The potential sintering benefits of this approach have been recognized by previous investigators, although there appears to be no recognized example of its successful ap-plication. German [112] suggested the term "phase stabilization enhancement" which is modified in the present work to the more specific "ferrite stabilization enhancement of sintering", hereafter abbreviated as F S E S . In activated sintering the additive element is relatively inert with respect to its re-action with the base metal, and the shrinkage is independent of concentration of the additive ( beyond an optimum amount corresponding to a few monolayers ). B y con-trast, in F S E S , the added element alloys with the base metal to homogenize the structure 197 198 and the shrinkage is a function of the concentration ( weight % added element ) and the amount of phases present for given sintering conditions. Depending on the concentration of the added element and the relative ease of mutual diffusion between the base and the added element, two kinds of FSES can be envisaged, one involving true FSES where enhanced sintering takes place and the other involving sintering and alloying. In the former case shrinkage is a result of sintering only and in the later case shrinkage is a combination of sintering and homogenization through diffusion. 5.1 S E L E C T I O N O F T H E S Y S T E M S F O R S T U D I E S O F F S E S A limited number of elements with significant solid solubility in iron stabilize the body-centered cubic ( a ) ferrite structure at all temperatures below the solidus. In the case of powder compacts made from binary mixtures, two processes occur simultaneously on heating, namely: ( a ) sintering, the initiation and growth of "necks" at interparticle contacts, and ( b ) alloying. Both processes are necessary to develop the final properties desired in the parts. Both involve mass transport by diffusion driven by vacancy or composition gradients. Thus, in a mixed powder ferrous compact, the alloying element must alloy readily with iron at the sintering temperature and also must provide properties desired in the sintered compacts. Both alloying by interdiffusion and sintering by self-diffusion are promoted by a-stabilizing elements such as phosphorus, silicon, vanadium, molybdenum and chromium. Of these elements, P and Si have proved to be of commercial importance. They also exhibit the characteristics of the two types of FSES mentioned in the previous section. Therefore P and Si have been chosen in this study. The phase diagram Figure 5.1 of binary Fe - P shows that only 0.65 wt. % phos-phorus dissolved in iron renders it ferritic at all solid state temperatures. Phosphorus is 199 Table 5.1: Diffusion Data for the Lattice Diffusion of Phosphorus in Iron. Inter Diffusion Data Source Phosphorus in a Iron 700 - 850 °C [113] D 0 = 7.1 x l O " 3 ( cm2/sec ) G> = 40 ( kCal/mole ) [113] Calculated D at 900 °C = 2.5 x l O " 1 0 ( cm2/sec ) Calculated D at 1200 °C = 8.24 x l 0 ~ 9 ( cm2/sec ) Phosphorus in 7 Iron 950 - 1200 °C [113] D 0 = 1.1 x l0~ 2 ( cm2/sec ) Qv = 43.7 ( kCal/mole ) [113] Calculated D at 950 °C = 1.55 x l O ~ 1 0 ( cm2/sec ) "Calculated D at 1200 °C = 3.28 x l 0 ~ 9 ( cm2/sec ) easily introduced into iron powder compacts as the pure element or as an iron phosphide (FesP) and oxidation is not a problem under normal sintering conditions. Interdiffusion coefficients for phosphorus in iron are high, ( Table 5.1 ) and alloying in mixed powder compacts is thus very rapid at temperatures of interest. This ensures that the achieve-ment of a ferritic structure occurs early in the sintering period. Moreover, phosphorus is an effective solid - solution strengthened Silicon stabilizes the a phase in the same manner as Phosphorus ( Figure 4.1 ( a ) ) and is also a strong solid - solution strengthener. FeSi alloys have commercial applica-tions particularly in soft magnetic parts. It is thus another potential example of FSES. Conventionally silicon is added as pure silicon or ferrosilicon powder to achieve a desired " o p Atomic Percentage Phosphorus . - j r . 10 20 30 40 50 60 70 80 IfoUO j 2800F 1500 esoF 4 0 0 f l h Fe 10 20 30 4 0 5 0 60 70 Weight Percentage Phosphorus 80 9 0 ure 5.1: Equilibrium Phase Diagram for binary Fe - P system [94]. 201 final alloy composition. Alloying in Fe-Si mixed powder, unlike that of Fe - P and Fe - FeaP mixtures is not accomplished easily. Moreover, alloying is made difficult by the presence of the oxide film on the surface of the silicon particles. This oxide film interferes with neck formation and alloying by diffusion. Si02 is reduced only in reducing atmo-spheres of very low dew point and at high sintering temperatures. Thus, in commercial practice, sintering of Fe - Si compacts is performed at high temperatures ( > 1200 °C ) in a very dry reducing atmosphere. It is seen from the phase diagram ( Figure 4.1 ( a ) ) that to obtain a fully ferritic structure in Fe-Si system, the silicon content should be > 2%. Commercial Fe-Si alloys contain 3 - 6 wt. % silicon. 5.2 AIM AND DESCRIPTION OF THE PROBLEM The present study is undertaken to test and predict the applicability of FSES to com-mercial ferrous compacts. Two strong a stabilizers were chosen for this study, namely phosphorus and silicon as discussed above. Although both are a stabilizers the two systems are not identical. Silicon is added in higher concentrations than phosphorus in commercial applications. The P content is low ( < 0.65 wt % ) whereas in Fe-Si, silicon is commonly > 3 wt %. Diffusion of P into Fe is very rapid which leads to rapid alloying and homogenization of the structure. The observed shrinkage is solely due to sintering effects. Further, P at such low levels has little effect on the diffusion or other physical properties of the homogenized Fe-P alloy. On the other hand in the Fe - Si system, diffusion of silicon into iron is observed to be slow. Further the theoretical density of the FeSi alloy changes during homogenization as do the activation energies of the various self-diffusion processes. In this case sintering involves dimensional changes from different sources. 202 The self-diffusion coefficient of iron in the ferrite phase is greater than in the austenite phase, so that when austenite transforms to ferrite it is evident that sintering shrinkage will become faster. Therefore the shrinkage of a compact containing phosphorus should be much higher than for pure iron compacts at normal sintering temperatures. The shrinkage of a compact containing varying amounts of phosphorus can be expected to be related to the amount of ferrite present at a given temperature, as predicted from the phase diagram. Experiments were planned to evaluate the shrinkage as a function of phosphorus content and temperature to obtain varying distributions of ferrite and austenite and to relate this to the observed shrinkage. Based on the above proposition that stabilizing the a phase increases the sintering shrinkage, and as the amount of ferrite increases the net shrinkage increases, an attempt has been made in this study to theoretically predict the shrinkage as a function of fer-rite content in the microstructure and to compare this with the experimental results. Theoretical predictions were made using the developed quantitative model for compacts described in section 3. In the case of FSES in FeSi, a commercial composition, namely a Fe-3% Si, is chosen to model and to predict the shrinkage of the a - FeSi alloy. Prealloyed powders are seldom used in the production of FeSi parts because of their hardness and poor compactibility and their high cost. Instead a mixed powder is used. In the mixed FeSi powder compacts, the addition of silicon changes the theoretical solid green density from 7.87 (gm/cm3) for pure Fe to 7.354 (gm/cm3) for a 3 wt. % silicon mixture. It is apparent that the compact when sintered will undergo a substantial decrease in solid volume as a result of alloying. Since the shrinkage due to alloying is expected to be more than that due to sintering, it becomes necessary to follow the progress of both alloying and sintering. For FSES to be reahzed, it is obvious that the alloy has to be at least partially ferrite. Experiments 203 were planned in this study to follow the progress of alloying through microstructural and dimensional changes at low temperatures and to measure shrinkage in fully prealloyed a - FeSi compacts to compare with theoretical predictions for the alloy. Predictions of shrinkage due to sintering both in Fe-P and in Fe-Si systems have not been made before. In particular the concept of FSES, correlating the amount of ferrite with the shrinkage observed, has not been previously attempted. 5.3 P R E V I O U S STUDIES OF Fe - P A N D Fe - Si C O M P A C T S 5.3.1 System Fe - P Phosphorus has been added beneficially to ferrous P / M for several decades, the earliest studies being attributed to Lenel [114]. Levels of up to 1 wt. % are used commercially. In conventional ingot-metallurgy steel, phosphorus is considered a harmful element to which several types ..of embrittlement are attributed. Far from causing embrittlement in P / M steels, however, phosphorus provides significantly enhanced room temperature ductility [114]. This apparent discrepancy is probably attributable to the difference in the way phosphorus segregates in the two processes. Due to the nature of the liquidus - solidus region in the F e - P phase diagram at low P concentrations, severe macro-segregation of phosphorus occurs during the freezing of a large ingot. Subsequent working and heat treatment of the steel does not produce homogenization and therefore the scale of segregation is too large. Some regions are sufficiently rich in phosphorus that an iron phosphide is present. The compound will be located at the ferrite grainboundary at ordinary temperatures, where it produces embrittlement. In contrast, phosphorus in a mixed powder compact is never segregated over distances exceeding a few microns and sintering permits a homogeneous alloy to be attained readily. Grain boundary segregation of phosphorus can be expected but apparently does not cause 204 embrittlement, as discussed in a later section. Several prior studies of the sintering of binary Fe - P compacts are reported in the literature: Lindskog et al. [115] describe the sintering behavior and properties of a wide range of Fe - P and Fe - P - C compacts, containing up to 1.2 wt. % phosphorus and made from mixtures of powders of pure iron and an iron phosphide, Fe3P ( referred to also as 'fer-rophosphorus' ). Some of their results are shown in Figure 5.2. Sintering was performed at temperatures from 900 to 1250 °C. The iron powders used were of average particle di-ameter in the range of 50-100 /xm, typical of those used for P / M parts manufacture. Both an atomized and a milled sponge iron powder were used. The authors attributed most of the sintering shrinkage to the formation of a transient liquid phase at temperatures above the Fe - P eutectic temperature of 1050 °C. This conclusion was based on two sets of observations: ( a ) major shrinkage of compacts was observed only when sintering was above 1050 °C, and ( b ) the amount of shrinkage at 1120 °C increased with increasing phosphorus content, particularly above 0.3 wt. % phosphorus. They presented no direct evidence that liquid phase had formed, however. Lindskog [116] subsequently reported observations of the microstructure of compacts containing 1.5 wt. % phosphorus which were quenched from a sintering temperature of 1200 °C after very short times at temperature. He showed that liquid phase was formed and it was quickly eliminated by continuing homogenization of the compact. He did not discuss the effect of the transient liquid on dimensions or density of the compacts. Weghnski and Kaczmar [117] conducted similar studies on compacts pressed to rel-atively high green densities. Phosphorus was again added as Fe3P, in concentrations up to 2.0 wt. %. Density and shrinkage data are given in Figure 5.3 for compacts sin-tered at 1177 °C. These authors also concluded that liquid phase sintering contributed importantly to the shrinkage observed. Based on metallographic studies, they further 205 concluded that the maximum solid solubility of phosphorus in ferrite was 0.8 wt. %, con-siderably higher than the 0.6 wt. % previously reported and shown in the phase diagram of Figure 5.1. This does not appear to have been confirmed by other workers. Observations of the intergranular fractures of Fe - P compacts which had been sintered at 1100 and 1200 °C led Hwang and German [118] to conclude that a liquid layer was present along the grain boundaries during sintering. A similar conclusion was reached by Crowson and Burlingame [119] who had, however, used a much higher sintering tem-perature of 1350 °C. Although several of these previous investigators of the sintering of Fe - P acknowl-edged the possible beneficial effect of ferrite stabilization, none concluded that FSES was a major contributor to the dimensional changes and density increase which they had ob-served. Moreover, their experiments were not designed to reveal the effect of the amount of ferritic phase present during sintering. 5.3.2 System : Fe - Si The main applications of Fe - Si materials are in soft magnetic parts where the principal property requirements are high flux density, high permeability, high electrical resistivity and low coercive force. Addition of silicon to iron increases both permeability and resistivity. The addition also causes solution hardening and embrittlement. Wrought Fe-Si alloys containing > 4.5 % Si are difficult to roll. Thus sheet material is limited to < 4.5 wt. % Si. By using powder metallurgy techniques, materials with higher silicon contents can be easily produced and at a lower cost. P / M FeSi materials are produced by pressing and sintering. The starting materials may be prealloyed powder or mixtures of iron powder with silicon or ferrosilicon of varying silicon contents. Conventional 'sintering' ( neck growth ) may occur long before 206 0 2 0.4 0.6 PHOSPHORUS CONTENT. % Figure 5.2: Shrinkage vs. %.P for compacts pressed at 589 Mpa from Fe-Fe3P mixed powder compacts sintered for 1 hour at 1120 °C in cracked Ammonia [115]. 207 Figure 5.3: Shrinkage and density data for Fe - Fe3P mixed powder compacts sintered for 2 hrs at 1177 °C in H2 [117]. Green density ~ 7.1 (gm/cm3) ( 91 % of solid ). 208 alloying can be distinguished, especially at low temperatures. At high temperatures ( e.g., > 1200 °C ) neck growth and alloying are superimposed. Several papers have been published covering production and magnetic properties of P / M FeSi materials. A very limited number of publications describe observations of the alloying, course of alloying and dimensional or microstructural changes during the sintering of mixed iron and silicon compacts. Rutkowsi and Weglinski [120] reported the effect of silicon, introduced as the element and as ferrosilicon, on physical properties like density, strength and magnetic properties of compacts made from a coarse iron powder ( Hoganas ASC 100.29 ). They found that silicon added in the form of the pure element ( 3 - 5 wt. % ) produced optimum properties. Shrinkage in these compacts was observed for composition silicon content > 2 wt. % Si, when sintered at 1177 °C for two hours in an atmosphere of dry hydrogen. This is shown in Figure 5.4. The microstructure was homogeneous. By contrast, Jang et al. [121] found that the addition of silicon in the form of in-termetalhcs yielded optimum properties. They prepared the FeSi material by varying both the starting iron powder ( Hoganas ASC 100.29, WP 150 Mannesmann, and RZ type DV 160 ) and the way silicon was added ( as elemental powder milled and screened to < 63 fim, as FeSi50 powder prepared from an FeSi melt and screened, or as - atom-ized FeSi30 powder as supplied by Hoganas ) to obtain an optimal production process. From their observations of mechanical and magnetic properties, of all the combinations they tried, they found that the addition of FeSi30 to ASC 100.29 resulted in better properties and therefore conducted later experiments on this material. They added sil-icon as FeSi30 ( up to 6 wt. % silicon ) and sintered in a dry atmosphere of hydrogen ( dew point -20 °C ). To study the sintering process at various temperatures, they sintered samples contain-ing 6 wt. % silicon for different times and evaluated the properties. As can be seen from 209 Figure 5.4: Effect of silicon admixture on shrinkage in a Fe - Si mixed powder compacts sintered for 2 hrs at 1177 "Cm H2 [120]. 210 Figure 5.5, sintering at 1050 °C produced no dimensional change. In the first 30 minutes of sintering at 1150 °C slight shrinkage was observed which was followed by expansion and then gradual shrinkage. They attributed the expansion to the diffusion of silicon into the iron matrix ( due to lower density of FeSi solid solution compared with Fe/FeSi30 powder mixture from which it forms ) and due to Kirkendall porosity. Rapid shrinkage Figure 5.5: Dimensional change of FeSi samples ( ASC 100 4- FeSi30 ) as a function of sintering time at various temperatures [121]. Green density ~ 6.6 (gm/cm3). seen at 1250 °C is associated with the formation of a liquid phase at that temperature. They also reported that materials sintered with elemental silicon showed different sintering behavior ( Figure 5.6 ) from those sintered with FeSi30. The high shrinkage, low compactibility, and excessive tool wear made this a poor choice according to their observations. A significant amount of work on the sintering of fluxed compacts has been reported 211 Figure 5.6: Dimensional change of FeSi samples ( ASC 100 + 6 wt % Si ) as a function of sintering time at various temperatures [121]. Green density ~ 5.88 ( gm/cm 3 ). 212 by Tanaka et al. [122]. Small amounts of sodium or potassium carbonate in FeSi powder blends ( Atomet 28 iron powder ) have been found to enhance markedly the alloying which takes place in compacts sintered at temperatures in the low range of 800 - 1100 °C. An external furnace atmosphere of inert gas rather than a dry reducing atmosphere was used for studying the sintering of fluxed compacts. Alloying was found to be initiated at temperatures as low as 800 °C and after 100 minutes at 1100 °C was much more advanced than in hydrogen-sintered flux-free compacts. Enhancement of alloying is believed to be associated with the removal of oxide from silicon particle surfaces by reaction with the carbonate to form a liquid or partially liquid silicate glass within the pores of the compact. Qu, Lund and Gowri [123] also studied the sintering and alloying behavior using SEM and dilatometry on two binary compositions : Fe-3 wt % Si ( Atomet 28 iron powder mixed with elemental silicon ), Fe - 3 wt % Fe3P ( 0.46 P Ancorsteel 45P mixture : as supplied ) and one ternary : Fe - 3 wt % Si - 3 wt % Fe3P. In the ternary compact it was found that both phosphorus and silicon behaved synergistically to enhance alloying and therefore sintering. In the binary Fe - Si system metallography supplemented by the dilatometer results provided an insight into the progress of alloying. Figure 5.7 shows the isothermal dilatometer results of Qu et al. [123]. Sintering at 950 °C produced no net dilatation or contraction. During 60 minutes at 1000 °C a small dilatation was observed. Microscopy revealed that reaction or interdiffusion at FeSi contacts, new phases were formed at the sites of silicon particles ( corresponding to the £ phase at 70 at.% silicon ). Holding at 1060 °C, the compact was observed to expand first and then contract. At this stage, original silicon particles were seen to be replaced by silicon saturated a phase. At 1100 °C continuous shrinkage of the compact was seen, and after 60 minutes silicon was found to be in solution in iron but not quite homogeneously distributed. Figure 5.7: Isothermal dilatometer data for Fe -in the range of 950 - 1100 °C [123]. 3 wt. % Si compacts held at temperatures 214 5.4 M A T E R I A L S A N D E X P E R I M E N T A L P R O C E D U R E S 5.4.1 System : Fe - P In order to provide a comprehensive set of different ferrite - austenite proportions during sintering, twenty experimental combinations of composition and sintering temperature were selected. These are shown in Figure 5.8, which reproduces the gamma-loop part of the Fe - P phase diagram. Compositions ranged from 0 to 0.93 wt. % phosphorus, and sintering temperatures ranged from 900 - 1350 °C. Atomized / reduced iron powder, Atomet 28, was used in the experiments for both the Fe - P and Fe - Si systems. Char-acteristics of the iron powder are given in Table 3.9, and the shape and size distribution are revealed in Figure 3.32. Atomet 28 powder is widely used in ferrous P / M industry, and is typical of the powders used in previous reported studies of Fe - P. Preparation of Prealloyed FeP powder Prealloyed powders were used to eliminate liquid phase sintering. Five alloys composi-tions shown in Figure 5.8 were used to obtain different amounts of ferrite during sintering. Atomet 28 iron powder and phosphorous were used in preparation of the prealloy. Weighed quantities of amorphous red P and iron powders were blended for 10 minutes in a laboratory type mixer. The powders were sealed in an evacuated quartz tube and homogeneously heated for 11 hours at 850 °C. The spongy product of this operation was manually crushed with mortar and pestle and ground lightly to pass a 140 mesh screen. The average particle size of the powder was roughly estimated as 68 ^m. Chemical analysis confirmed that there was no gradient of P content within a batch of alloy powder. The following compositions were used ( chemically analyzed ) in the experiments, 0, 0.20, 0.35, 0.48 and 0.93 wt % P. 215 Figure 5.8: Gamma loop portion of Iron - Phosphorus Phase Diagram [94]. Small squares identify compositions and sintering temperatures used in this study. 216 Compaction of the Prealloyed Powders The prealloyed powders were compacted with die lubrication only at pressures of 310 — 440 MPa ( lower for P free materials ) to obtain cylindrical specimens of 10 mm diameter and 3 - 4 mm height. The targeted green density was 5.9 ( gm/cm3 ) ( 75 % of solid Sintering Conditions and Temperature Sintering was carried out in an induction-heated susceptor furnace for 60 minutes at temperatures between 900 - 1350 °C. The sintering atmosphere was a flowing mixture approximately 0.75 //min. Shrinkage Measurements Dimensions of all compacts were taken before and after sintering. Linear shrinkage values based on the changes in the height, were measured. The densification parameter, defined where D0 is the theoretical solid density and D{ is the initial green density and D, is the sintered density of the compacts, was also used in the analysis of sintering behavior. 5.4.2 System : Fe - Si In order to characterize the FSES in FeSi compacts, two sets of experiments are required. In the first set, the progress of alloying in a mixed powder compact is monitored with the density ); actual values ranged from 5.7 - 6.1 ( gm/cm3 ) as tabulated in a later section. of roughly equal volume proportions of dry hydrogen and argon. The flow rate was by 217 corresponding dimensional changes. In the second set, actual shrinkage of a fully alloyed a-FeSi alloy is measured. Accordingly, experiments were planned as detailed below. Preparation of Powders for Studying the Progress of Alloying In previous studies at The University of British Colombia by Tanaka et al.. [124], it was established that small amounts of sodium or potassium carbonate in FeSi powder compacts, markedly enhanced the alloying which takes place between iron and silicon, even at relatively low temperatures of 800 - 1100 °C in an inert gas atmosphere. Addition of 0.4 weight % of sodium carbonate was found to give optimum mechanical properties. The same approach was used in this study. Weighed quantities of iron, silicon and sodium carbonate ( corresponding to a compo-sition of Fe - 3Si - 0.4Na2CO3 ) were mixed for half an hour in a laboratory mixer. Silicon and sodium carbonate have a lower density than iron, and therefore rotating was needed to ensure a fairly uniform distribution. The silicon powder < 44 fim ( same powder as was used in the activated sintering studies ), was used in the study. Sodium carbonate was a very fine powder supplied as monohydrate sodium carbonate. The carbonate loses all its moisture, at temperatures > 100 °C. Mixed iron - silicon and pure iron powder compacts were also prepared in the same manner for direct comparison. It was obvious that silicon would not alloy under the conditions used for sintering. Compaction of the Mixed Powders The powders were pressed to a cylindrical shape of 10 mm diameter and 3-4 mm height to an approximate green density of 75 % of theoretical. No lubricant was used. Silicon reduces the compressibility of the iron powder and therefore these specimens had to be pressed at a higher pressure, close to 600 MPa, to obtain the targeted density. 218 Sintering Conditions and Temperatures The compacts were enclosed in a quartz tube of 11 mm diameter and about 4 inch long, packed with Ti turnings ( to remove oxygen ) at both ends and sealed under a slight positive pressure of argon. Sintering was carried out in a box-type furnace at temperatures of 850 and 950 °C for varying times of 10 to 1000 minutes. The specimens were air cooled. 5.4.3 Preparation of Powders for Prediction of Shrinkage in a FeSi. Preparation of Prealloyed Powders In order to isolate the true FSES in FeSi, prealloyed powders were made. Ferrosilicon powder ( 75 % ) crushed to 44 fim was mixed with iron powder for 10 minutes, sealed in a quartz tube and heated at 1100 °C for 16 hours in a box type furnace to give a final composition of Fe(3%)Si. The product was crushed and sieved to pass a 140 mesh screen. Batches of powders were sent for chemical analysis. The composition was found to be uniform at 2.8 wt % silicon. Compaction of the Prealloyed Powders The prealloyed powders were compacted with die lubrication only at a pressure of ap-proximately 600 MPa to obtain cylindrical specimens of 10 mm diameter and 3 - 4 mm in height. Sintering Conditions and Temperature of Sintering The compacts were sintered at temperatures of 900, 1000, 1100 and 1200 °C in an induction heated furnace in a flowing atmosphere of hydrogen and argon ( 50 : 50 ) for a period of one hour. The estimated flow rate was 0.75 Z/min. 219 Shrinkage Measurements Shrinkage was measured by the changes in the linear dimensions, before and after sinter-ing, using a digital vernier caliper. 5.5 R E S U L T S O F F S E S I N Fe - P C O M P A C T S 5.5.1 Shrinkage and Densification Linear shrinkage values were derived from changes in the height of compacts. Experi-mental shrinkage data are plotted as a function of phosphorus content of the compact in Figure 5.9. It is seen that % linear shrinkage increases with increase in % phospho-rus added. Density and densification parameters were calculated from measurements of diameter, height and weight of green and sintered compacts. In figure 5.10 the densi-fication parameter is plotted against % phosphorus. The trend to greater densification at higher phosphorus levels parallels the shrinkage behavior. Although alloys with >0.3 wt % phosphorus are fully ferritic at 1350 °C according to the phase diagram, there was a substantial increase in sintering densification at this temperature as the phosphorus content was increased from 0.35 to 0.93 wt% phosphorus. Shrinkage and densification data are compiled in Table 5.2. For a given sintering temperature, shrinkage and densification increased with increasing amounts of ferrite present. This trend, which indicates clearly that FSES is involved in these experiments, is shown in Figure 5.11. For specimens sintered at 900 °C and for those of 0.2 wt % phosphorus content, shrinkage was not isotropic, and there was a greater fractional decrease in height than in diameter. For other conditions, volume shrinkage was approximately three times the linear shrinkage. Chemical analyses revealed that there had been no loss of phosphorus during sintering. 220 Figure 5.9: Experimental linear shrinkage vs. % Phosphorus in compacts sintered for one hour. 221 Figure 5.10: Densification parameter ( D.P. ) vs.% Phosphorus in compacts sintered for one hour. 222 Table 5.2: Data for Fe-P Compacts Sintered in a Flow of H 2 - Ar for 60 Minutes. % p Green Density Temp % a % Shrinkage Sint. Density Densification Meas ( ^ ) Rel % °C Phase Expt Theo Sint Rel % Parameter 0 5.91 75.1 900 100 0.51 0.67 5.94 75.4 0.015 5.84 74.2 1100 0 0.93 0.94 5.89 74.8 0.046 5.66 71.9 1200 0 1.15 1.26 5.82 73.9 0.072 5.81 73.8 1350 0 2.34 3.67 6.27 79.7 0.23 0.2 6.12 77.7 900 100 0.5 0.67 6.15 78.1 0.016 6.08 77.2 1100 0 0.83 0.94 6.14 78 0.03 6.09 77.3 1200 0 1.24 1.26 6.16 78.3 0.04 6.12 77.7 1350 49 2.76 4.85 6.77 86 0.37 0.35 5.84 74.2 900 100 0.56 0.67 5.85 74.3 0.001 5.83 74 1100 19 1.27 1.09 5.93 75.3 0.05 5.89 74.8 1200 22 .2.35 1.89 6.29 79.9 0.2 5.81 73.8 1350 100 3.48 6.1 6.66 86.6 0.41 0.48 5.95 75.6 900 100 0.93 0.67 5.96 75.7 0.004 5.85 74.3 1100 54 1.8 1.73 6.11 77.6 0.12 5.93 75.3 1200 63 2.58 3.06 6.48 82.3 0.28 5.96 75.7 1350 100 4.39 6.1 6.88 87.5 0.48 0.93 5.76 73.2 900 100 0.93 0.67 5.79 73.6 0.015 5.76 73.1 1100 100 1.9 2.57 6.13 77.8 0.17 5.78 73.14 1200 100 3.3 4.14 6.51 82.7 0.35 5.73 72.8 1350 100 5.3 6.1 7.08 90 0.63 223 Figure 5.11: Plot of linear shrinkage vs. proportion of ferrite at various sintering tem-peratures. 224 5.5.2 Metallographic Observations Optical metallography on sections of sintered compacts is shown in Figures 5.12 and 5.13. In all compacts which were sintered at 900 °C, and all those which contained 0.93 wt.% phosphorus, the structure remained ferritic throughout the full cycle of heating, sintering and cooling. In those cases, therefore, the grain size observed at room temperature is representative of that which prevailed after one hour at the sintering temperature. In all other cases, there was at least some austenite present when sintering was in progress, and the final structure observed included the product of transformation of that austenite to ferrite. A Wild-Leitz Image Analysis system was employed to measure the ferrite grain diam-eter. Table 5.3 contains the results of ferrite grain size measurements on specimens which remained ferritic. The grain size of compacts sintered at 900 °C showed no dependence on phosphorus content over the full range, and was roughly half the average diameter of the particles used to make the compacts. On the other hand, the grain size of the compacts containing 0.93 % phosphorus increased with the sintering temperature. At the highest temperature, the grains grew to a diameter double that of the original powder particles. The photomicrographs of Figures 5.12 through 5.13 also reveal changes in the size, shape and density of pores which resulted from sintering. It is quite obvious that voids are fewer in number as the temperature is increased and the average grain size is somewhat larger. At 0.93 % phosphorus and with fully a-phase alloy, the pores are seen to be quite coarse and are isolated leading to excessive grain growth. 225 Figure 5.12: Microstructure of a Fe - 0.45P compact sintered for one hour at ( a ) 900 °C - dark phase represents the pores in the ferrite matrix. Magnification : X 200. 226 Figure 5.12: ( b ) 1100 °C, Magnification : X 200. 227 Figure 5.12: ( c ) 1200 °C, Magnification : X 200. 228 Figure 5.12: ( d ) 1350 °C, Magnification : X 200. 229 Figure 5.13: Microstructure of a Fe - 0.93P compact sintered for one hour at ( a ) 1200 °C - To indicate the extent of grain growth, Magnification : X 200. F i g u r e 5.13: ( b ) 1350 °C. 231 232 Table 5.3: Mean Ferrite Grain Diameter for Fe and Fe - P Sintered Compacts which remained Ferritic throughout the Sintering Cycle of 60 minutes. % p Grain Size in /xm at Temperatures (°C) Phase present 900 1100 1200 1350 during sintering 0 37.7 These specimens underwent 7 0.2 37.4 a —> 7 and 7 —> a: transformation 7 0.35 39.0 on heating and cooling. Ferrite a + 7 0.48 36.9 grain size at 20°C is not representative a + 7 0.93 35.1 51.1 56.7 134.0 a 5.6 A N A L Y S I S O F T H E R E S U L T S 5.6.1 P u r e Iron Compacts made from Atomet 28 powders represent the non-ideal or real compacts dis-cussed in Section 3.5-3.6 (see p. 110). The powders are not spherical or uniform in size. In order to apply the developed "ideal model" to such real compacts, it was suggested earlier in this work that an equivalent spherical diameter can be used in the calcula-tions. The average particle size from the sieve analysis was found to be 68 fim diameter. The experimental results of pure iron ( 0 % P ) can therefore be used to evaluate the applicability of the model to real compacts. Theoretical predictions of linear shrinkage for a particle size of a = 34 fim are com-pared with the experimental results in Table 5.2 and Figure 5.14. Good agreement between the model prediction and experiment at temperatures < 1200 °C is seen. Therefore it can be inferred that the use of an average particle size for 233 TEMPERATURE (°C) I Figure 5.14: Comparison of experimental shrinkage with theoretical predictions as a function of temperature of sintering in Atomet 28 iron compacts sintered for one hour. 234 quantitative prediction in real compacts is a reasonable approximation. At the highest temperature, the theory predicts substantially more shrinkage than was observed. This is probably attributable to grain growth, and the resulting migration of boundaries away from necks during sintering. The decrease in both boundary and lattice diffusion contri-butions resulting from grain growth is not taken into account in the model calculations. 5.6.2 Predictions of Sintering Shrinkage in Fe - P Compacts Using the sintering equations and the appropriate materials constants and properties of ferrite and austenite, Table 3.1 [16,19], predictions were made of the linear shrinkage of alloy compacts. For compacts sintered within the gamma loop, the phase distribution was assumed to be random. The following additional assumptions were made for the analysis. 1. Shrinkage is attributed entirely to grain boundary self-diffusion and lattice self-diffusion ( with grain boundaries as vacancy sinks ) acting simultaneously. 2. In the two-phase structure, necks are within either the ferrite or austenite phase and the proportion of the two types of necks are the same as the proportion by volume of the two phases in the microstructure. 3. Shrinkage at necks is additive in both ferrite and austenite. 4. The phase diagram of Figure 5.1 correctly describes the phases present for a given set of sintering conditions. 5. Phosphorous contents of up to 0.93 wt % do not affect such properties as the activation energies for grain boundary and lattice diffusion or the surface energy. 6. Compacts consist of uniformly packed spheres 68 fim in diameter. Following Moon and Kim [89], the effect of compacting to 75 % of solid density is to give an initial 235 neck radius : particle radius ratio (^), of 0.0137, which is taken into account in the calculation of shrinkage from sintering equations. The predictions of shrinkage based on these assumptions are contained in Table 5.2 and Figures 5.15 and 5.16. Agreement between theory and experiment is reasonably good for sintering temperatures up to 1200 °C. As was the case for pure iron compacts, the sintering equations predicted considerably more shrinkage at 1350 °C than was observed. When correlated with the phase diagram ( Figure 5.11 ), they reveal the effect of FSES i.e., for a given sintering temperature the predicted shrinkage increases as the relative proportion of ferrite increases. All alloys at 900 °C and those containing > wt. %0.93 P at 1350 °C are fully ferritic. The theory predicts that there will be no effect of phosphorus content on shrinkage in these ranges. 5.6.3 Comparison of Exper imenta l and Theoretical Predict ions Experimental shrinkage data is plotted against the phosphorous content of compacts in Figure 5.9. There is a qualitative agreement with the theoretical predictions shown in Figures 5.15 and 5.16 ( < 1200 °C ). Moreover, considering the number of assumptions and the reliability of material data used for predictions, even the qualitative agreement is fairly good. Theoretically beyond a certain % P, depending on temperature, ( the maximum solubility of P in a - Fe, as seen from the phase diagram ) the shrinkage should essentially remain the same. However a slight deviation is observed in the experimental results. Pure Fe at 900 °C and at 0.2 P are not expected to show any difference in their shrinkage characteristics, as the phase diagram indicates that the alloy is fully ferritic at that temperature. The results also published [125] clearly indicate that it is possible to model shrinkage in a FeP compact, on the basis of ferrite stabilization. 236 Figure 5.15: Linear shrinkage vs. %P calculated from sintering equations ( theoretical ). 237 Figure 5.16: Comparison of linear shrinkage ( obtained from experiment and theoretical calculations ) vs. % Phosphorus. 238 5.7 R E S U L T S O F F S E S I N Fe-Si C O M P A C T S Shrinkage during sintering of Fe-Si alloys is much larger than conventional ferrous sintered alloys. This has always been attributed to the alpha stabilizing effect of silicon. However, unlike the Fe-P system, the alpha phase is not stabilized readily. A longer time at a higher temperature is needed to achieve complete homogenization following which the shrinkage rate becomes that of solid state sintering. Two sets of experiments were done in the present study to isolate the effects of alloying from those of enhanced sintering. The following sections discuss the experimental observations. 5.7.1 Progress of A l l o y i n g : Micros t ruc tura l Examinat ion In order to interpret the dimensional change during sintering of mixed FeSi powder com-pacts, the progress of alloying has to be monitored. The pressed compacts were sintered at temperatures of 850, 950 and 1000 °C for various lengths of time in a pure argon atmosphere. The sintered specimens were then mounted and polished for observation by SEM. Figure 5.17 shows SEM photos of as-pressed FeSi and FeSiNa2C03 samples. Consid-erable fragmentation of the brittle silicon particles has occurred during compaction. Figures 5.18 ( a ) to ( d ) are a series of photomicrographs from FeSi compacts sintered at 850 °C for times up to 1000 minutes. Figures 5.19 ( a ) to ( d ) reveal the microstructures of similar compacts containing Na 2 C0 3 . Without carbonate addition, silicon does not seem to have reacted with the iron as can be seen in Figure 5.18 ( a ) to ( d ) even after 1000 minutes. In contrast to this, in compacts containing Na 2 C0 3 , alloying of silicon with iron at 850 °C is seen to be initiated at sintering times > 10 minutes. A new phase was observed to form where there was silicon originally. This phase was found to be homogeneous. Seven point analyses Figure 5.17: SEM Photographs of a as pressed compact of ( a ) FeSi. 240 Figure 5.17: ( b ) FeSiNa 2C0 3. 241 Figure 5.18: Microstructure of a Fe - 3Si compact sintered at 850 °C for ( a ) 10 minutes. 242 Figure 5.18: ( b ) 60 minutes. 243 Figure 5.18: ( c ) 100 minutes. 244 Figure 5.18: ( d ) 1000 minutes. 245 Figure 5.19: Microstructure of a FeSiNa 2C0 3 compact sintered at 850 °C for ( a ) 10 minutes. 246 004561 £0KV 50 um Figure 5.19: ( b ) 60 minutes : x indicates the new phase formed. 247 Figure 5.19: ( c ) Same as ( b ) : Enlarged view of the new phase formed, the numbers mark the place where E D X analysis was performed. 248 Figure 5.19: ( d ) 500 minutes. 249 by EDX ( Energy Dispersive X-Ray ) ( Figure 5.19 ( c ) ) revealed the composition of the new phase to be 25.7 atom % Si ( 17 weight % ). This corresponds to the terminal solid solubility of silicon in iron at 850 °C i.e., the phase is the silicon saturated a phase. Reaction of iron and silicon and diffusion of iron into the intermediate phases in the Fe - Si system is thus seen to be faster in compacts containing carbonate additions. Even at the low temperature of 850 °C and short time intervals, alloying of silicon had progressed beyond the formation of the intermediate phases indicated in the phase diagram. Analysis of the original iron regions, immediately adjacent to ( within 10 /xm ) the iron rich phase which had replaced the silicon particles revealed that there had been almost no flux of silicon into the iron particles. Thus diffusion was highly unidirectional. The above observations are consistent with the diffusion of iron and silicon into and within those alloyed regions which originated as pure silicon particles. There had been almost no diffusion of silicon into the pure iron particles. Metallographic sections of samples confirmed that silicon remained intact and no silicon had been dissolved in the matrix (Figures 5.18 and 5.20 ). The following published diffusion data provide a partial explanation for this behavior. For Fe into Si at 1000 °C D = 2.3 x l O " 6 cm2/sec [126] at 1100 °C D = 4.1 x l 0 ~ 6 cm2/sec [126] For Si into a-Fe at 1100 °C D = 3.1 x l 0 ~ 9 cm2/sec [127] at 1200 °C D = 1.2 x l O " 8 cm2/sec [128] For Si into 7-Fe at 1206 °C = 4.0 x l O - 1 0 cm2/sec. After sintering for 500 minutes or longer at 850 °C ( Figure 5.19 ( d ) ) much wider distribution of silicon had occurred. Analysis by EDX at different places showed that the compacts were approaching homogeneity with respect to silicon composition in the flux doped specimens. 250 At a slightly higher temperature of sintering, ( 950 °C ), and without carbonate present, silicon does not appear to have reacted with iron after 10 or 60 minutes as seen in Figures 5.20 ( a ) and ( b ). But when carbonate was present, even after 10 minutes of sintering at 950 °C there was extensive alloying. The silicon-rich solid solution re-gions, which were initiated at silicon particles, now occupy a substantial fraction of the microstructure ( Figures 5.21 ( a ) and ( b ) ). The diffusion zones around the particles are much larger than in compacts sintered at 850 °C. After 1000 minutes at 950 °C ( Figure 5.21 ( c ) ), a homogeneous structure was obtained in the flux - bearing com-pacts: i.e., E D X analysis showed silicon in the bulk of the sample to be uniform. From the long time taken for homogenization beyond that needed to first convert silicon to sat-urated a-solid solution, it can be inferred that diffusion of iron into the iron rich-phase is slow. It can also, be inferred therefore that the carbonate addition is very effective in the initiation of alloying and formation of silicon rich phases early in the alloying process. In order to establish clearly if alloying had started at 1000 °C in Fe-Si ( without carbonates ) several experiments were performed. It is clear from Figures 5.22 ( a ) and ( b ), that silicon did not show any reaction with iron. In a separate study by Qu et al. [123] high density Fe - 3Si compacts did not show any tendency to alloy even in a hydrogen atmosphere when sintered for an hour at 1000 °C. 5.7.2 Progress of A l l o y i n g : Dimensional Changes Sintering shrinkage in a one component system has been dealt with in the previous chap-ters. It is easy to interpret the dimensional changes in such a case. In a mixed powder compact, such as in Fe-Si, complicated dimensional changes occur during sintering. In mixed powder compacts at suitable sintering temperatures, interdiffusional mass trans-port and reaction between particles proceed until alloy equilibrium is established. Interim Figure 5.20: Microstructure of a Fe - 3Si compact sintered at 950 °C for ( a ) 10 minutes. 094735 X 6 J | 5 0 u m Figure 5.20: ( b ) 60 minutes. 253 Figure 5.21: Microstructure of a FeSiNa 2C0 3 compacts sintered at 950 °C for ( a ) 10 minutes : shows the new phases formed. 254 Figure 5.21: ( b ) 60 minutes. F i g u r e 5.21: ( c ) 1000 minutes . 256 Figure 5.22: SEM Microstructure and the corresponding X-Ray map of a Fe - 3Si com-pacts sintered at 1000 °C for ( a ) 10 minutes. 257 Figure 5.22: ( b ) 60 minutes. 258 or final products of alloying may occupy more or less solid volume than the original com-ponents, and dimensional changes can result. For example, 100 grams of green Fe-3Si compacts contain 12.3 cm3 of iron and 1.3 cm3 of silicon, for a total of 13.6 cm3 of solid. After homogenization, the density of the alloy is 7.71 gm/cm3 and the volume of solid is therefore 13.0 cm3. On this basis, contraction of the compact might be expected to result from alloying. When sintering the mixed powder the problem is further complicated by the Kirkendall effect. The origin of the effect is that the diffusion of one element ( gen-erally the low melting metal ) into the other ( higher melting metal ) is more rapid than the reverse process, creating new pores and causing expansion. The measured values of dimensions are a cumulative effect of all these phenomena. It is difficult to separate the effect of each of the components. During sintering of the mixed FeSi compacts in the present study, it was observed that those containing sodium carbonates underwent considerable changes in dimension. The values are plotted as a function of sintering time for temperatures of 850, 950 and 1000 °C in Figures 5.23 ( a ), ( b ) and ( c ), respectively. Pure iron compacts were also sintered to compare the results directly, but since the same pressing pressure was used for making the compacts, they were found to have higher green density than those containing silicon. Therefore, the shrinkage values for pure iron are not plotted in these figures. In all the plots, it is seen that compacts with no carbonates showed less dimensional change than those containing carbonate. Referring to the corresponding microstruc-ture shown in the previous subsection, the differences can be explained on the basis of progress in alloying. In compacts mixed with sodium carbonate, even at the lowest time of sintering alloying is seen to be in progress. The dimensional change is very large in the beginning and is fairly gradual at the later stages of sintering. The FeSi compacts, on the other hand, showed a minor expansion in the earlier stages before beginning to 259 5.23: Dimensional variation in compact sintered for various times at ( a ) 850 °C. Figure 5.23: ( b ) 950 °C. 261 Figure 5.23: ( c ) 1000 °C. 262 exhibit shrinkage. 5.7.3 Results of Shrinkage in Prealloyed Powders In the present study prealloyed powders were prepared specifically to demonstrate the true FSES in a-stabilized FeSi alloy. The Fe - 2.8Si compacts were sintered at temper-atures between 900 and 1200 °C for a constant sintering time of 60 minutes. Since the starting structure is a homogeneous a-phase alloy, shrinkage or dimension changes are solely due to the sintering enhancement because of FSES. The shrinkage measurements made on the prealloyed compacts are compiled and listed in Table 5.4. Linear shrink-age plotted as a function of sintering temperature for a constant time of sintering of 60 minutes is shown in Figure 5.24. It is seen from the Figure that shrinkage increases with increase in temperature as expected. 5.8 ANALYSIS OF FSES IN Fe - Si C O M P A C T S 5.8.1 Mixed Powder Compacts Sintering can be complicated by concurrent processes such as phase formation/transformation reaction and all these may affect the shrinkage events. With prolonged heating the system homogenizes to form a single phase. Alloying does not seem to be initiated in the pure Fe+Si system under any of the conditions of sintering used in this study. The addition of the fluxing agent, sodium carbonate, is highly effective in initiating the alloying process. The shrinkage in the fluxed compacts is very high and it may be due to a compound formation and is very gradual with further progress of alloying. In the case of powder mixtures of two elements, if the alloying proceeds through the formation of intermetallic compounds as in the case of FeSi, the direction of diffusion of 263 Figure 5.24: % Linear shrinkage as a function of temperature in a prealloyed a - FeSi alloy sintered for one hour. 264 Table 5.4: Data for Fe - 2.8 Si ( a ) Compacts Sintered in a Flow of H 2 - Ar for 60 Minutes Temp Green Density % Shrinkage Sint. Density Densification °C Meas (gm/ cm3) Rel % Sint (gm/cm3) Rel % Parameter 900 - 5.74 73.0 0.31 5.75 73.0 0.26 950 5.72 72.6 0.57 5.76 73.1 1.96 1000 5.7 72.5 0.69 5.74 73.0 2.02 1200 5.91 75.2 1.43 6.14 78.1 12.57 265 the individual element is important. If the higher density metal ( for example iron ) dif-fuses to the lighter metal ( for example silicon ), a considerable shrinkage can be expected in the compacts. This is because silicon occupies more volume than the higher density phases which form from it. Since Fe and Si particles are in contact the compact expe-riences shrinkage. Further variation in the density occurs gradually. Therefore the first compound which forms produces the major change in dimension during homogenization. In the present study it was shown that diffusion is from iron to silicon via a compound formation. The compound formed is Fe - 25.7 atom %, reported to have a density of 4.2 gm/cm3. Therefore during the initial stages of sintering the dimensions plotted will show a strong time-dependence, as observed. Further, shrinkage due to further homogenization, i.e., the formation of a solid solution, is very gradual and slow. In mixed powder compacts, as explained before, two different phenomena occur which independently affect the dimensions. One of them is shrinkage caused by sintering phe-nomena, and the other is dimensional change caused by alloying. The homogenization process may be characterized by diffusional porosity leading to swelling of compacts. It is not possible at this time to predict the rate of homogenization, or the degree of homog-enization and the corresponding microstructural development or vice versa. However, it is possible to evaluate the amount of shrinkage that alloying can produce. Using the density of iron as 7.88 gm/cm3 and a reported density of 7.65 gm/cm3 for a solid Fe-4.0wt % Si [126] alloy as basis, the theoretical density of the alloyed compacts was estimated as a function of silicon content. The theoretical green density ( density of the compacts containing 3 % elemental silicon mixed with the matrix iron powder and pressed to full density ) was also calculated as a function of silicon content. Figure 5.25 represents the results of the calculations. It is apparent from these plots that the volume of the solids in a compact, undergoes a substantial decrease as a result of alloying. For example, for a 3 % silicon compact sintered to homogeneity, a decrease of 5.1 % in 266 solid volume is predicted from the two plots of Figure 5.25. This corresponds to a linear shrinkage of 1.7 % due to alloying alone. Referring to the results of the present study indicated in Figure 5.23, the amount of shrinkage in the compacts indicate the extent of alloying. Alloying is not complete at temperatures of 850 and 950 °C in compacts containing N a 2 C 0 3 as observed from metallography or microstructures. The shrinkage experienced by flux - free compacts is very much less, as expected from the much lower extent of alloying. 5.8.2 Preal loyed Powder When the starting powders were prealloyed, sintering shrinkage could be totally at-tributed to sintering phenomena, as activated by the alpha stabilizing effect of silicon. However, comparing the values of shrinkage obtained for a fully alpha Fe-P alloy listed in Table 5.2 with that of FeSi reveals that the effect of stabilized alpha is not the same. Colombia et al. [129] used a grain boundary grooving technique to determine the transport mechanism in Fe-3Si % strip. They found that the mass transport was mainly due to volume diffusion, with a calculated self - diffusion coefficient of iron in Fe-Si alloys in the temperature range of 1092 - 1300 °C given by, D = 0.15 exp(-198 ± 26/RT), cm2 s"1 The value of activation energy, Q (kJ/mole), agrees reasonably well with others existing in the literature, as shown in Table 5.5, leading to the conclusion that in FeSi the matter transport is predominantly through volume diffusion. From measurements of grain boundary kinetics at 950 °C in 3 % SiFe, Mills et al. [130] showed that surface diffusion is two orders of magnitude slower in the alloy than in the pure metal. The activation energy for surface diffusion reported in the literature for 267 Figure 5.25: Theoretical full green and sintered density as a function of silicon content. 268 Table 5.5: Data for Volume Diffusion Coefficients of iron in a - FeSi Al loy available in Literature. Si % D 0 (cm 2/sec) Q (kJ/mole) Source 3.8 2.3 222 ± 15 [131] 3.0 0.44 218 ± 15 [132] 3.5 4.3 237 ± 25 [133] 3.0 0.29 199 ± 26 [129] 3.0 0.2 207 ± 15 [134] diffusion of iron i n FeSi is 253 kJ/mole and D 0 is 1.0 x l O 5 cm 2 /sec [135]. This is higher than the corresponding activation energy for pure iron reported in the literature. Corresponding values for grain boundary diffusion are unavailable i n the literature. The only value so far found is suspect as the units of Do do not match wi th the reported values. The values reported are Q = 126.35 kJ /mole and 2D6 = 2.7 x l O 7 cm 2 /sec. The units of 2D<5 should be in cm 3 /sec. O n the basis of these reported values of activation energies and D 0 for surface and volume diffusion mechanisms, and neglecting the contribution from grain boundary dif-fusion, theoretical predictions were made using the quantitative model developed for compacts. Figure 5.26 represents the results of the calculations, which compare reason-ably well with the experimental results for prealloyed compacts plotted i n Figure 5.24. The shrinkage obtained in the case of fully alpha FeSi alloy is seen to be much lower than that obtained in a fully alpha FeP alloy for the same temperatures of sintering. However, the predicted values cannot be taken as absolute values of shrinkage as they 269 2.1 TEMPERATURE <°C) Figure 5.26: Theoretical predictions of linear shrinkage in a prealloyed compact sintered for one hour. 270 do not take an important mechanism ( grain boundary ) of transport into consideration. The analyses thus gives only a very rough qualitative estimate of the shrinkage. 5.9 DISCUSSION Fe - P The results in Table 5.2 and Figure 5.11 reveal a close correlation between sintering shrinkage and the proportion of ferrite in Fe - P compacts. Therefore, there is, strong evidence that FSES is the dominant source of sintering enhancement, as predicted. Shrinkage data for 1100 °C and 1200 °C in this study compare closely with those reported for Fe - P compacts by Lindskog et al. [115] at 1120 °C Figure 5.2 and by Weglinski and Kaczmar [117] at 1177 °C Figure 5.3. In these prior studies, compacts were made from blends of iron and Fe3P powders. As the figures reveal, there was a marked increase in the sintering shrinkage as the phosphorus content was increased above 0.3 % P. In both published works, the authors attribute much of the large observed shrinkage to the influence of a liquid phase formed on heating the mixed Fe - Fe3P compacts above the eutectic temperature of 1050 °C, and it is doubtful that the phosphide would persist to the eutectic temperature at conventional heating rates. Studies by Qu et al. [123] have shown that phosphorus was transferred rapidly to iron during the heating of Fe - Fe3P compacts, and that when the temperature reached 1050 °C, there was no possibility of forming a liquid phase. No liquid phase could have been involved in the present experiments because prealloyed powder was used, yet the amount of sintering shrinkage observed was at least comparable to that reported by previous workers with Fe - Fe3P blends as shown in Figure 5.27. The difference between the present results and those of Lindskog et al. and Kaczmar et al. can be explained by several possibilities. Both the earlier authors had used higher density compacts and a much coarser powder. However, 271 there is a good qualitative agreement in terms of the trend of the plots. Addition of P causes grain growth. This has been reported by previous investigators also [136,117]. Larger grains are preferred in the magnetic applications of Fe - P alloys because there is a corresponding increase in the magnetic permeability and improved coercive force. At the sintering temperature, those specimens which were of mixed structure con-tained phosphorus concentration gradients because the ferrite grains were richer in phos-phorus than the austenite grains. Since the compacts were cooled rapidly after sinter-ing, phosphorus gradients were mostly retained to room temperature. Oberhoffer's etch ( 30 g FeCl 3, 1 g CuCl 2 , 0.5 g SnCl 2, 50 ml HCl, 500 ml ethyl alcohol and 500 ml dis-tilled water ) was used to reveal these gradients, and the relative amounts, grain size and distribution of ferrite and austenite at the sintering temperature. Photomicrographs of etched specimens are given in Figures 5.28 ( a ), ( b ) and ( c ). Due to the differ-ence in P content between the ferrite phase ( high P content ) and the austenite phase ( low P content ) these regions show up as light and dark areas respectively when etched. The amounts of phases were evaluated using the Image Analyser mentioned before. The amounts of phases are seen to be in the expected range. It should be mentioned that the theoretical analysis is made with the assumption that impurities do not affect the % ferrite or austenite. . It is possible for impurities, in particular carbon, to have a significant effect on the amount of austenite. Thus the benefit of higher diffusion and shrinkage in Fe - P compacts may be restricted to low carbon powders. The powder used in the present study has a fairly low carbon content ( 0.02 % specified by the supplier ). An increase in phosphorus content beyond that necessary to give a fully ferritic struc-ture produced additional sintering shrinkage and densification. This was particularly evident at 1350 °C. It is possible that dissolved phosphorus lowers the activation energy for lattice or grain boundary self-diffusion in ferrite. There is published evidence [137] 272 Figure 5.27: Comparison of linear shrinkage observed in the present study with that of values reported in the literature ( a ) Lindskog et al. [115] ( b ) Weglinski et al. [117]. 273 Figure 5.28: Microstructure of Fe - P compacts sintered in the two phase region ( a ) Fe - 0.35P at 1100 °C : Etched with Oberhoffer's Reagent. Expected amount offer-rite from phase diagram : 19.00 %; Calculated value from microstructure ( approximate ) : 17.01 %, Magnification : X 200. dark phase represents the porosity, grey phase repre-sents the austenite and light phase represents the ferrite. 2 7 4 Figure 5 . 2 8 : ( b ) Microstructure of Fe - 0 . 4 8 P compacts sintered in the two phase region 1 2 0 0 °C : Etched with Oberhoffer's Reagent. Expected amount of ferrite from phase diagram : 2 2 %; Calculated value from microstructure ( approximate ) : 2 7 . 0 6 % , Magnification : X 2 0 0 . 275 Figure 5.28: ( c ) Microstructure of Fe - 0.2P compacts sintered in the two phase region 1350 °C : Etched with Oberhoffer's Reagent. Expected amount of ferrite from phase diagram : 49 %; Calculated value from microstructure : 34.5 %, Magnification : X 200. 276 that phosphorus segregates at a-phase grain boundaries, causing embrittlement. In the present calculation the diffusion coefficients are assumed to be the same as that of self -diffusion coefficients of pure iron. At the highest temperature of sintering ( 1350 °C ) and for the alloy of highest phosphorus content ( 0.93 wt % ), the sintering theory predicted substantially more shrinkage due to FSES than was observed. Some of the discrepancy may be attributed to the appreciable ferrite grain growth which occurred under these conditions. By the end of the sintering cycle, the grain size was such as to isolate many pores from the grain boundaries and to preclude further pore shrinkage. The present results are reasonably consistent with a simple model in which necks are assumed to exist in either the ferrite or the austenite phase, and in which sintering shrinkage at the various necks is additive. Enhancement results when there are more necks in ferrite because mass transport rates are much higher in body-centered cubic phase. German [112] offers an additional suggestion that in mixed ferrite - austenite structures, contributions to FSES may be provided by ( a ) resistance to grain growth and ( b ) interphase boundaries acting as good vacancy sinks. Since the greatest shrinkage and densification were shown by compacts which were fully ferritic, these other contributions to enhancement would appear to be of secondary importance. The absolute densification provided by FSES is worthy of note. Even though a rela-tively coarse moulding grade iron powder was used in this work, appreciable densification was possible without resorting to liquid phase. Fe - Si FeSi parts are normally made from mixtures of iron and silicon powders. These parts experience a large shrinkage during sintering and often this has been attributed almost 277 totally to the a-phase stabilizing effect of the silicon. SEM observations and analyses of FeSi mixed powder compacts indicate that there is highly directional interdiffusion of iron into silicon when such iron compacts are sintered. A phase identifiable as the iron rich a - solid solution in the Fe - Si system was formed at locations originally occupied by silicon particles. Enhancement of alloying in the initial stage was effectively provided by the addition of a flux, sodium carbonate. Tanaka et al. [124] speculated that this enhancement was due to the removal of the oxide layer from silicon particles. A model based on the present work and results, to interpret the role of carbonate in aiding the alloying process is proposed. Results incorporated in the model include weight loss, microstructure and differential thermal analysis of powder samples based on both Atomet 28 and Spheromet powders. Experimental results of carbonate containing iron and iron - silicon powders are not discussed here as it may be out of context. Metallographic observations indicate that directional diffusion of iron is favoured at the onset of alloying. However, iron has almost no solid solubility in silicon, and two intermetallic compounds must form in succession before the iron rich a-solid solution can be generated. The results of Qu et al. [123] indicate that the kinetics of diffusion of iron and silicon into and through the intermetallic remain more favorable at the sintering temperature than those of the diffusion of silicon into iron. The a-phase solid solution which forms is ferritic at all sintering temperatures, whereas the adjacent unalloyed iron is austenitic at T > 912 °C. Since diffusion - rates are much higher in the BCC ferritic structure at a given temperature, unidirectional interdiffusion at this interface remains in effect. The experimental results in the present study indicate that the expected enhancement of sintering also occurs, but that the effect is overshadowed by phenomena which accom-pany the alloying process. Alloying itself produces considerable shrinkage as revealed by 278 both theoretical and the experimental plots. A recent study was reported by Qu et al. [138] involving mixed FeSiP ternary powder compacts which were sintered for one hour at 1100 °C. Shrinkage results are reproduced in Table 5.6. Comparing the linear shrinkage expected due to alloying, it is once again evident that the alloying process dominates in contributing to net shrinkage. Table 5.6: Linear Shrinkage of a Fe - 3 %Si Compact Sintered for One Hour [138]. % Si % shrinkage % shrinkage Experimental due to alloying ( theoretical ) 1.0 0.797 0.687 2.0 1.388 1. 368 3.0 1.83 1.704 4.0 2.44 2.75 5.0 3.1066 3.43 6.0 3.6566 4.11 The present results also indicate that the additive effect of alpha stabilization in the case of FeSi is not realized until the alloying is complete. Metallography indicates that homogenization proceeds first through the formation of the various intermediate phases in Fe - Si. The a-phase does not become homogeneous until a later stage. Therefore, the positive effect of a-phase stabilization does not occur until the alloying is complete, or largely so. Typically the homogenization event dominates the diffusional flow during mixed powder phase sintering. After homogenization, densification events then become active. 279 Once the homogenization is complete, shrinkage is due to solid state sintering, en-hanced by the stabilized alpha phase. Since the activation energies for various mecha-nisms of mass transport are seen to be increased in the alpha alloy, the shrinkage is not very high as seen from the results of prealloyed powder compacts. Thus it can be said that the major contributor to shrinkage in the mixed FeSi compacts is alloying. When the alloy is fully homogeneous the compacts sinter due to enhanced mass transport in the stabilized a-phase compacts. 5.10 E F F E C T O F B O T H P A N D Si O N S I N T E R I N G Since both P and Si stabilize a-phase structure, a study of the combined effect of both elements on the sintering and alloying behavior of iron compacts was made using dilatom-etry and scanning electron microscopy. Experiments were made on Fe - 3 Si - 3 Fe3P compacts of high density. The iron powder used was a Ancorsteel 45P powder, a mixture of as supplied 3 wt. % Fe3P powder with an atomized iron powder, and this was blended with 3 wt. % silicon powder. In this ternary alloy it was found that P and Si behaved synergistically [138]. P strongly enhanced the alloying which took place between iron and silicon at temperatures in the range of 900 - 1100 °C. According to Fe - P phase diagram the Fe - 0.45P alloy is partially austenitic between 930 and 1300 °C. Since silicon is a strong alpha stabilizer, dissolution of silicon in the F e - P alloy would be expected to contract the gamma loop portion of the phase diagram. Thus the ternary alloy is expected to be 100 % ferritic at all solid state temperatures. Alloying with silicon, on the other hand, greatly enhanced the sintering ( neck growth and shrinkage ) of Fe - P by rendering the alloy fully ferritic at all temperatures and thereby promoting high rates of self-diffusion in the alloy. No attempt was made to predict shrinkage or dimensional change from the sintering 28-0 theory, because it was not possible to find reliable values of the materials constant relevant to the ternary system. 5.11 SUMMARY In order to test the concept of FSES, two typical ferrous systems, Fe - P and Fe - Si were chosen. Both P and Si are a-phase stabilizing agents, but are effective in different quantities ( 0.9% P max and 3% Si ). Whereas in the case of Fe - P, the additive rapidly alloys with iron, thus imparting the advantages of a ferrite stabilized phase almost instantly. The diffusion and homogenization of Si with iron is slow. Using the quantitative model developed in the present work both Fe - P and Fe - Si have been modelled and verified for the FSES effect. Chapter 6 S U M M A R Y A N D C O N C L U S I O N S 1. Using simple ideal models of solid state sintering, predictions have been made of the sintering behavior of iron powder compacts. It was found that, in common with the sintering of other metal powders, the dominant mechanisms of mass transport in the sintering of iron powder compacts are surface, grain boundary and lattice self-diffusion. 2. Sintering maps and diagrams have been derived for iron powder compacts. A discontinuity in such diagrams is predicted to occur at the alpha —• gamma trans-formation temperature of 912 °C and is associated with marked differences between the self-diffusion coefficients of alpha and gamma iron. 3. A new and simple graphical method has been developed to construct the field maps. The method is applicable to the sintering of any material. 4. For practical reasons, the neck growth rate equations are translated into shrinkage equations and maps are drawn. These maps give directly the shrinkage of a compact of a given starting density and particle size at any given time and temperature of sintering. 5. The sintering equations are reduced to such a form that it is easy to predict the effect of changing the important process parameters of sintering namely the initial particle size and green density, diffusion coefficients, time and temperature on the sintering maps. 281 282 6. The sintering model used for predictive purposes in the present study involved a number of simplifying assumptions particularly in the second and third stages of sintering where the geometry of compacts becomes more complex. Also the concurrent grain growth, pore coalescence and growth and pore closure, all provide additional complications. Extensive theoretical and experimental work in this area is recommended. 7. The sintering maps that were constructed for pure iron compacts were verified for two specific cases, ( a ) neck growth in compacts made from the spherical particles of Spheromet iron powder, ( b ) linear shrinkage of compacts made from fine spherical particles of Carbonyl iron powder. In both cases there was reasonably good agreement between experiment and the theoretical predictions. 8. An attempt was made to extend the ideal model to real compacts by using an av-erage particle size. Experiments with compacts made from non spherical particles of Atomet 28 iron powder were conducted. There was a good agreement between the predicted and experimental shrinkage of such compacts for sintering at tem-peratures up to 1200 °C. At higher temperatures the experimental shrinkage was lower than that predicted from the theory and this was attributed to the effect of appreciable austenite grain growth during sintering. 9. Elemental additions of boron, titanium, silicon, tungsten, palladium, silver, nickel, chromium and germanium were made at low concentrations to iron powder com-pacts in an attempt to obtain the type of activation of sintering which is observed when small amounts of nickel are added to tungsten powder compacts. Only boron, 283 and titanium to some extent were seen to activate sintering in these compacts. The results have been analyzed and compared with the published results of tungsten -nickel. 10. A new model has been proposed to account for dopant activated sintering of base metal compacts. The proposed theory involves important contributions from inter-diffusion between the base metal and the activating species and is quite different from the models suggested previously by other investigators to account for activated sintering in tungsten - nickel and similar systems. 11. Consistent with the proposed model for activated sintering, criteria have been de-veloped for the selection of appropriate combinations of base metal and activator species. Specifically, if there is a large difference in interdiffusion coefficients and melting points between the base metal and the additive and if atomic radius dif-ference is high, activated sintering is predicted to occur. 12. In the case of iron powder compacts the model for activated sintering and the cri-teria based on that model, suggest that only silver of the several elemental dopants that were tried in the present work can be expected to provide significant activation of sintering. Whereas for tungsten powder compacts, it has been both predicted and observed that a substantial number of elements will provide activation of sin-tering. Very few elements of practical significance are predicted to provide similar activation in iron powder compacts. It is therefore suggested that activated sin-tering is not a useful technique to employ for the enhancement of sintering in real ferrous powder compacts. 13. It is predicted from the sintering theory that for a given temperature, ferrous com-pacts which are largely ferritic in structure will sinter more rapidly than those 284 which are largely austenitic in structure. This follows because self-diffusion rates in ferrite are higher than in austenite. It should therefore be possible to enhance the sintering of ferrous compacts by adding ferrite stabilizers such as phosphorus and silicon. In the present work, two binary alloys, iron - phosphorus and iron - silicon were used to investigate the practical feasibility of ferrite stabilization enhance-ment of sintering ( FSES ) and to establish whether the amount of enhancement was predictable from the sintering theory. 14. Using prealloyed iron - phosphorus powder compacts, it was possible by varying both the phosphorus content and the sintering temperature, to vary over the full range the relative proportions of ferrite and austenite in the microstructure of com-pacts during sintering. It was found that sintering shrinkage was greatly enhanced by increasing proportions of the ferrite phase. Moreover, the results were reasonably predictable using a model in which the necks are assumed to be present in either ferrite or austenite and that shrinkage at the various necks is linearly additive. 15. Studies of iron - phosphorus compacts were carried out using the relatively coarse iron powders which are typical of the P / M parts industry. The strong enhancement provided by phosphorus is therefore of practical as well as theoretical interest. Previous investigators of iron - phosphorus alloy compacts have attributed the large observed shrinkage to the presence of a transient liquid phase during sintering. The present work however, has clearly established that FSES can account for all the enhancement of sintering and therefore for the shrinkage observed. 16. Iron - silicon powder compacts were made from mixtures of the elemental powders. Because of the tenacious oxide film on the silicon powder particles and because of the relatively low rates of interdiffusion of silicon in iron, alloying at conventional sintering temperatures was relatively slow. Moreover, the redistribution of mass 285 which accompanied the process of alloying in this system itself caused the compacts to shrink. Additional shrinkage due to FSES was also observed but did not take place until alloying between iron and silicon was complete. 17. Alloying between iron and silicon in the mixed powder compacts was aided by the addition of a small amount of sodium carbonate to the original powder mixture. The effect of the carbonate was to react with oxide on the silicon particles to form a low melting glassy phase which did not interfere with the alloying between iron and silicon. 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