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The effect of misfit on morphology and kinetics of plate shaped precipitates Sagoe-Crentsil, Kwesi Kurentsir 1988

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THE EFFECT OF MISFIT ON MORPHOLOGY AND KINETICS OF PLATE SHAPED PRECIPITATES by KWESI K. SAGOE- CRENTSIL B.Sc (Hons) University of Science and Tech., Ghana, 1978 M.Sc. University of British Columbia, Vancouver, 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Metals and Materials Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1988 ® KWESI K. SAGOE-CRENTSIL, 1988 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. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) ABSTRACT Lattice misfit and its effect on the morphology, interfacial structure and kinetics of plate shaped precipitates are investigated in this study. The 7-Ag2Al phase in the Al-Ag system was used as the reference system and its misfit was controlled by ternary additions of Mg and Cu. The addition of 0.S1 at% Mg was found to increase the misfit from 0.8% for the binary to 1.11%. Cu additions on the other hand, reduced the misfit by 0.38% for Cu concentrations up to 0.51 at%. Electron probe microanalysis showed that the Mg atoms preferentially partition to the 7 phase whereas Cu atoms partition equally between the precipitate and matrix phases. Direct transmission election rnicroscope observations were made on the interface structure in both the equilibrated state and during precipitate dissolution. The interface structure in the ternary Mg alloy consisted of a hexagonal network of partial dislocations which essentially remained the same before and during dissolution. A single array of a/2<110> dislocations was observed in the binary and ternary Cu systems prior to dissolution. This unit array transformed to a stable hexagonal network structure having the equilibrium spacing at the onset of dissolution and remained throughout the period of dissolution. o The thinning and shortening kinetics of the precipitate plates were at least five times slower than the rates for volume diffusion control in all three systems. This interfacial inhibition has further been confirmed by the consistent fall below equilibrium values of the interface concentration as determined from electron probe microanalysis. This suggests the operation of a ledge migration mechanism. A mechanism ii of acquiring ledge/dislocations at the interface is used as a basis to correlate the observed kinetics with misfit and ledge migration at the precipitate-matrix interphase. The mechanism involves co-ordinated motion of sets of dislocations in the network which rids the surface of the highest steps thereby accomplishing dissolution. iii TABLE OF CONTENTS ABSTRACT ..; — ii Table of Contents iv List of Tables . vi List of Figures vii Acknowledgement xi 1. INTRODUCTION 1 1.1 Interface Boundary Structure ... .. 5 1.1.1 Mechanisms of Coherency Loss . 8 1.1.2 Two-Dimensional Conjugate Boundaries. 12 1.1.3 Two-Dimensional Non-Conjugate Boundaries. 14 1.2 Theory of Morphology Development ..... . ...................................—........ 16 1.2.1 Nucleation Theories — 16 1.2.2 Growth Theories 17 1.2.3 Shear Mechanism 23 1.3 Kinetic Theories 23 1.3.1 Volume Diffusion Model 25 1.3.2 Interface Reaction Controlled Kinetics 29 1.3.3 Experimental Observations 30 1.3.4 Ledge Theories 34 1.4 Influence of Trace Elements on Interface Boundary Structure 37 2. AIM OF PRESENT INVESTIGATION 42 3. EXPERIMENTAL 44 3.1 Alloy Preparation 44 3.2 Specimen Preparation 47 3.2.1 TEM/STEM Samples 47 3.2.2 SEM/Electron Probe Samples 48 3.2.3 X-ray Diffractometer Samples 49 3.3 Electron-optics Techniques 49 3.3.1 Burgers Vector Determination 49 3.3.2 Imaging Misfit Dislocations and Moire' Fringes 50 3.3.3 SEM Dissolution Studies 51 3.3.4 Electron Probe Microanalysis: Solute Profiles 52 4. MICROSTRUCTURE CHARACTERIZATION OF THE EQUILIBRATED ALLOYS .. 54 4.1 MicTOStructure - 54 4.1.1 Precipitate Morphology 54 4.1.2 Precipitate Volume Fraction 58 4.1.3. Microstructure 59 4.2 Electron probe Analysis of Solute Concentration 62 4.3 X-Ray Diffractometer Determination of Lattice Parameters 64 4.4 Discussion 68 iv 5. INTERFACE STRUCTURE OF EQUILIBRATED ALLOYS 69 5.1 Description of Equilibrium Interfacial Structure 69 3d*X 13umxy ^^lloy 69 5.1.2 Ternary Cu alloy 82 5.1.3 Ternary Mg alloy 85 5.2 Intersecting Plates - 93 5.3 Overaged Alloys 96 5.4 Misfit Determination - Dislocation Spacing 98 5.5 Misfit Determination - Moire' fringe Spacing 100 5.6 Correlation of Misfit Values 102 5.7 Discussion 102 6. DISSOLUTION STUDIES . 106 6.1 Morphological Changes During Dissolution. 106 6.2 Dislocation Structure at the Phase Interface 108 6.2.1 Broadface Structure 108 6.2.2 Edge Structure 130 6.2.3 Growth Mechanism of 1 precipitates 132 6.2.4 Measurement of Dislocation Spacing During Dissolution 136 6.3 Discussion 137 7. DISSOLUTION KINETICS AND ELECTRON PROBE MICROANALYSIS 141 7.1 Kinetics Results 142 7.1.1 Thinning Results 142 7.1.2 Shortening Kinetics 148 7.1.3 Discussion 152 7.2 Electron probe microanalysis 153 8. DISCUSSION 161 8.1 Morphology and Interface Structure 161 8.2 Kinetics 163 9. CONCLUSIONS 169 REFERENCES 171 APPENDIX 176 v LIST OF TABLES 1. Alloy Composition. 43 2. Precipitate Volume Fraction Detennination 57 3. Results of Microstructure Analysis 58 4. Solute Concentrations from Electron probe and by Calculation. 61 5. Lattice Spacing from Diffractometer Measurements and by Calculation. 66 6. Table of Contrast Analysis of Precipitates 73 7. Calculated Misfit from Dislocation Spacing 99 8. Lattice Mismatch Results 101 9. Misfit During Dissolution from Dislocation Spacing Measurements 136 10. Thinning Kinetics 147 11. Shortening Kinetics 150 12. Election Probe Determination of Interface Composition 156 LIST OF FIGURES 1. Schematic phase diagram illustrating precipitation of one solid phase from another. ...2 2. The Dube morphological classification system, (after Dube*) 4 3. Schematic diagrams of types of interface (a) coherent (b) semicoherent 6 4. Schematic diagram of ledge structure at the edge of a precipitate 19 5. Schematic representation of ledges. 21 6. Composition profiles during dissolution. 26 22 7 Growth kinetics of 1 precipitate, (after Laird and Aaronson ) 31 8. Arrhenius plot of^ h^ffusivities calculated from thickening kinetics of 0' plates. (after Sankaran ) . 32 9. Isoconcentrate contours at the step of a ledge: (a) Jones and Trivedi model (b) Doherty model 38 10. Ag-Al binary diagram, (after Hansen )^ 46 4 11. Microstructure of alloys equilibrated at 418 C for 1.44 x 10 s 55 12. STEM micrographs of (a) binary (b) ternary Mg (c) ternary Cu-III alloys. 57 13. X-ray diffractometer traces of alloys (a) binary (b) ternary Mg (c) ternary Cu-III 66 14. Misfit dislocation structures at the broadface of equilibrated plates 70 15. Misfit dislocations at opposite faces of the broadface 71 16. Dislocation tangles at the broadface of precipitates 72 17. (a) Contrast analysis of a/2-011] misfit dislocations, (b) Contrast analysis using "022] reflection (a) s < 0 (b) s = 0 (c) s > 0 „ 76 18. Fully embedded precipitate showing arrays of misfit dislocations together with corresponding difTraction pattern. 77 19. Enlarged sections of Fig 18 showing details of array 78 20. Misfit dislocation arrays in the ternary Cu system 83 21. Dislocation array conforming to plate curvature 84 v i i 22. Misfit dislocation structures at the broadface of a fully emdedded plate in the ternary Cu system 86 23. Enlargement of a section of Fig. 22 showing dislocation loops 87 24. Misfit dislocation structures in ternary Mg alloy showing one set of partials (a) full plate (b) enlargement of a section of (a) 88 25. Interface structure imaged under different diffracting conditions (a) dislocations (b) Moire' fringes 90 26. Dislocation loops at the broadface of a plate in the ternary Mg system. 92 27. Interfacial dislocations originating from intersecting plates 94 28. Interfacial structure of sample aged at 418° C for 3.6 x 10^  s in (a) binary system (b) ternary Mg system 97 29. Correlation plot for misfit determined from X-ray and Moire' fringe data. 103 30. Plot of dislocation spacing vs ar% Cu in alloy 104 31. Shape changes during plate dissolution. 107 32. Section of 1 precipitate entirely covered by a hexagonal dislocation network. Specimen dissolved at 450° C for 240 s 110 33. Micrograph showing one set of dislocations forming the network structure in Fig. 32 Ill 34. Micrograph showing the effect of changing diffracting conditions on interface structure 112 35. High magnification micrograph and schematic drawings showing one set of dislocations 113 36. Schematic drawings and micrographs separately showing all three sets of dislocations of the network structure 114 37. Micrograph and schematic drawings of interface dislocation structure at the onset of dissolution. 116 38. Enlarged section of micrograph in Fig. 37 117 39. Micrographs and schematic drawings showing the development of the network structure 119 40. Enlarged micrograph showing intersecting dislocations 120 v i i i 41. Contrast reversal of dislocations on changing operating reflection from, +g to -g. 42. Intersection of displacement fringes and dislocations. 123 43. Micrographs and schematic drawings of details of the network structure 124 44. Interface boundary structure (a) before (b) during dissolution in Ternary Mg alloy. 127 45. Close up view of loops at plate edges during dissolution. 128 46. Dark field image of one set of partial dislocations interacting with dislocation loops. 129 47. Precipitate edge structure during dissolution. 131 48. Ledge/dislocations at the edges of the broadface of plate during growth. 133 49. Linear array of ledge/dislocations at the broadface of plate during growth. 133 50. Hexagonal network structure of ledge/dislocations on the broadface of plate during growth 134 51. Schematic illustration of probable mechanism of network formation. 139 52. Plot of precipitate half-thickness vs time 143 53. Parabolic plot of precipitate half-thickness vs time. .„ 144 54. Parabolic plot of precipitate half-thickness vs time for SEM and STEM data. —145 55. Precipitate half-length vs time 149 56. Model prediction of the dependence of the peclet number (p) on saturation 0. ...151 57. Concentration profiles before and after dissolution at 450° C for 600s. ...155 58. Plot of interface composition Cj vs /Dt. 157 59. Plot of concentration, C vs erf [ x/2 /Dt ] 158 60. Schematic drawing of ledge/dislocation nudeation at plate edge 165 61. Schematic representation of dissolution by the movement of ledge/dislocations. 166 62. Boundary conditions used for Model 177 63. Boundary condition applied to precipitate half-tip 178 ix 64. Composition contours at plate tip 179 65. Grid network used for calculation 180 66. Mass balance across interface 184 67. Movement of plate tip with time 186 68. Plot of Dt/h vs normalised height 187 69. Plot of saturation vs interface velocity 188 70. Plot of the peclet number, p vs saturation 189 x ACKNOWLEDGEMENT I would like to express my gratitude to Dr. L C Brown for his guidance and encouragement throughout the course of this work. Thanks are also due to other members of the department and fellow graduate students and friends for help during the preparation of the thesis. The assistance of the staff of the electron-optics lab in particular Miss Mary Mager is very much appreciated. I would especially like to thank my wife Dorcas for her patience and understanding during the entire work. Financial assistance provided by the National Research Council of Canada and the graduate assistantship awarded by the Department of Metals and Materials Engineering are greatfully acknowledged. x i 1. INTRODUCTION Precipitation from supersaturated solid solution is one of the most important reactions in the solid state ttansformation of metals. Its study as a science began with the classical isothermal experiments of Bain. Research along these lines gained prominence with the discovery of Duralumin, the first age-hardenable alloy, at the turn of the century. The reaction has since attained widespread recognition, being responsible for such well known phenomena as precipitation embrittlement and, of course, age-hardening. Precipitation from solid solution has been studied in a large number of systems, from titanium- and nickel-based alloys to ceramics and minerals. The ultimate goal is to suppress or enhance property changes that accompany the reaction. Fundamental studies of the process have not kept pace with commercial exploitation however, and thus aspects of the reaction are still not clear, in particular microstructural stability. The precipitation reaction can occur whenever a single phase material is heated or cooled to a temperature at which a second phase becomes stable. Fig. 1 i.e.. Supersaturated a -* Saturated a + $ The requirement for the reaction is a change in solid solubility with temperature, and thus the new second phase may form in a variety of transformations, such as in the aging, massive or proeutectoid decomposition reactions. Only a few distinct precipitate shapes occur, the most important being allotriomorphs 1 2 Figure 1. Schematic phase diagram illustrating precipitation of one solid phase from another. 3 which form at grain boundaries and Widrnanstatten precipitates which form at grain boundaries or more commonly in grain interiors. The classification of these morphologies 1 2 after Dube and Aaronson is shown in Fig. 2. The first precipitates to form are grain boundary allotriomorphs occuring at boundaries of high misorientation, i.e., high energy boundaries which aid nucleation by heterogeneous nucleation. These allotriomorphs in general have an oblate spheroidal shape being circular in the plane of the grain boundary and having a lens shaped cross section. Consequently precipitates form at lower angle grain boundaries and these are primary and secondary sideplates or sawteeth. The Widrnanstatten structure appears at a later stage in the precipitation reaction. It is mostly identified by the observation of elongated precipitates which grow independently along specific crystallographic directions within a grain in the form of plates, laths and needles. It is common for the plates to form on matrix planes of low index and they are usually associated with a large grain size of the matrix and a fair degree of supersaturation. The sequence of Widrnanstatten precipitation generally begins with the formation of precursor solute-rich clusters termed G.P. zones, followed by one or more transition phases which have the Widrnanstatten morphology. These ultimately transform into the equilibrium phase which also has the Widrnanstatten morphology. The G.P. zones and the transition phases may have perfect crystallographic matching at their interphase boundaries resulting in a low interfacial energy arid hence a larger free energy per atom compared to the equilibrium phase. The form and distribution of G.P. zones and the initial transition phases are responsible for strengthening in age-hardenable systems and this is perhaps the main reason for continued interest in the reaction. Grain Boundary Mlotrlomorphs Widmanstatten Idfomorphs Massive Intra-granular Primary and Secondary Sidedlates Primary and Secondary Sawteeth Morphology / h /\/\ o <8 » ' * — V Figure 2. The Dube morphological classification system, (after Dube ) 5 In the next sections the Widmanstatten precipitation reaction is reviewed with emphasis on the nature of the precipitate boundary. The relation of the boundary structure to morphology and kinetics is then examined and finally the effect of trace elements on Widmanstatten precipitation is reviewed. 1.1 Interface Boundary Structure Interphase boundaries can have one of three basic structures: coherent, semi-coherent or disordered. These structures are first described and then the mechanisms by which coherency is lost, that is the transition from coherency to semi-coherency, are reviewed. Coherent boundaries are characteristic of G.P zones and form with perfect crystallographic matching at the interphase boundary, Fig. 3(a). The mismatch at the boundary is fully accommodated by elastic strains in the matrix and precipitate, depending upon their respective elastic constants. With increasing mismatch, strain energy builds up at die interphase boundary and is relieved by the introduction of misfit compensating dislocations. Such a boundary is termed semicoherent, Fig. 3(b). 3 The degree of misfit may be determined as follows . If a and b correspond to the stress-free lattice parameters in the a-matrix and /3-precipitate, the misfit 8 can be defined as: 5 = 2(a-b)/(a + b) 1.1 The misfit 5 is positive if the misfit strain in the precipitate phase is tensile. The 6 -\ 1 - V— -(a) u — — I B A "IT l_l ' "71 ( r ~ b) B Yl ~ A Figure 3. Schematic diagrams of types of interface (a) coherent (b) semicoherenc 7 3 inter- dislocation spacing (D) at the boundary is given by the Brooks relation, i.e., D = 676 1.2 where, b* is effectively the edge component of the Burgers vector parallel to the interface, and 8 is the degree of mismatch. At increasing values of mismatch, the dislocation spacing is decreased until their cores overlap, and beyond this mismatch, the concept of a dislocation boundary becomes meaningless. For a precipitate and matrix with very different crystal structures, crystallographic planes in the two phases no longer match at the boundary and the interface is incoherent 1.1.1 Mechanisms of Coherency Loss Limited theoretical and experimental work exists concerning the details of coherency loss. When the precipitate size or mismatch is small the misfit is entirely accommodated by a homogeneous elastic strain, which is the lowest energy configuration. In this case the particle is coherent Beyond a certain size, the coherency is lost and the stable state is one in which the misfit is only partly eliminated by extra lattice strain. In the next section the size at which coherency loss occurs is first reviewed and then the mechanisms whereby this takes place are considered. 8 (a) Theory 4 5 Frank and van der Merwe and van der Merwe developed the 6-9 first detailed theory of misfit interfaces. Their theory together with the later ones essentially estimate the way in which the energy of planar interfaces between the crystal 0 6 pairs depends on misfit. Weatherly assumed identical elastic constants for the precipitate and the matrix phases and obtained a critical size, a, for the transformation from a coherent to a dislocation boundary in cube shaped particles as: 2(e$c - ec) (1 - ,) a = u 62(1 + v) 1.3 where, e £ and are the interfacial energies of coherent and semicoherent boundaries respectively, v is Poisson's ratio, and M is shear modulus The transition from coherency to semicoherency may also be based on a stress criterion or on an energy criterion. The stress criterion is based on the theory of elasticity and has been used by Weatherly to calculate the shear stress on the slip planes immediately adjacent to particles. This approach is based on a suggestion by 3 Brooks that coherency loss during growth occurs by the nucleation of small dislocation loops at or in the neighbourhood of the interface. Weatherly then proposed a stress criterion for loss of coherency such that if the shear stress exceeds the theoretical shear stress of the matrix, loop formation is energetically favourable. By assuming that the shear stress for dislocation nucleation in a perfect lattice to be about u/1, Weatherly obtained 9 the critical value of mismatch for a plate shaped particle to be the order of 10%. Brown 7 et al considered the same problem from an energetics point of view. This energy criterion predicts that there is a critical radius, r , below which a dislocation loop is not stable at the surface of a spherical precipitate. rc is given by: b r In 8r 3-2? , r = [ + 1 14 c 16»e(l-*0 b 4(1-where, b = Burgers vector of the dislocation r = radius of precipitate v = Poisson's ratio e = strain equal to 2/3 misfit. 8 9 This approach forms the basis of the Brown-Woolhouse and Ashby-Johnson theories of misfit dislocation nucleation by spherical precipitates. The Brown-Woolhouse theory predicts a critical misfit value of 0.05 above which spontaneous nucleation of dislocations can occur by prismatic punching and condensation' of point defects. The Ashby-Johnson theory gives an upper and a lower critical misfit The upper critical misfit is independent of particle size because the critical nucleation step takes place at the particle surface where the stress is independent of particle size. The lower criterion is similar to the criterion of 7 Brown et al and agrees well with the results of the Brown-Woolhouse theory, (b) Processes of Coherency Loss The mechanisms for the formation of interfacial dislocations have been reviewed by Aaronson et al^ with a later update by Aaronson.^  The following are the main mechanisms suggested: 10 12 (i) Prismatic Loop Punching The punching of prismatic dislocation loops results from high shear stresses due to the strain. The magnitude of stresses involved may be of the order of the theoretical shear stress and this is unlikely to be produced by mismatch alone. Support for this mechanism 8.13 has been obtained during precipitate growth. 1415 (ii) Adsorption of Matrix Dislocations The dislocations involved require adequate mobility in climb, with the elastic interaction between the strain fields of the precipitate and dislocations providing the driving force. Experiments on deformation-induced loss of coherency of Co particles in Cu and of 8 plates in Al-Cu^ show this effect Gleiter^-^ has theoretically analysed this mechanism and shown that when the dislocation encounters the strain field of a precipitate, a dislocation loop is generated at die interface. The sign of the loop is such that the strain Field of the precipitate is cancelled. Based on their experimental findings, Livak and 20 Thomas concluded that loss of coherency in a spinodally decomposed Cu-Ni-Fe alloy occurred by capture of slip dislocations from the matrix and subsequent multiplication by climb of the dislocations at the interfaces to give the observed vertical array. Philips and 14 Livingstone have also theoretically analysed the process of acqusition of climb loops around precipitates. 21 (iii) Nucleation of Dislocation Loops within the Precipitate This mechanism operates by the condensation of excess vacancies or interstitial atoms, depending upon the mismatch, into loops inside the precipitate. These then expand until they encircle the precipitate. 11 (iv) Nucleation at Edges and Comers of Precipitate The driving force for the formation of dislocations by this mechanism is the shear stress. 22 Experimental evidence is given by Laird and Aaronson in their study of 7 plates in an Al-Ag alloy. 1.1.2 Two-Dimensional Conjugate Boundaries, (i) fee-hep Boundaries. The fee-hep interface represents one of the simplest forms of two-dimensional boundaries. In this case a one-to-one correspondence exists between the atomic arrangement on the habit plane and therefore an equilibrium misfit structure should be expected. 23 Laird and Aaronson have outlined a theoretical determination of the most stable dislocation configuration for an fee-hep boundary. They noted that nets made up of two or three sets of edge dislocations are most likely to form. Single dislocation arrays are not likely since they cannot fully accommodate the mismatch. It was shown that the energy of a hexagonal arrangement comprising of three dislocations was somewhat lower than that of a two-dislocation boundary. The spacings of arrays of dislocations comprising two- and three-dislocation networks were given as (b/3)/(2Ae2) and 3b/(2Ae3) respectively, where b is the magnitude of the Burgers vector and Acj is the strain across the boundary. Based on elasticity theory, Laird and Aaronson give expressions for the volume strain and energy per unit area of interface for the precipitate and matrix. 12 The total free energy per unit area was obtained by summing the volume strain energy obtained from elasticity theory and the elastic strain energies. The value of Acj was then obtained by first minimising the total free energy and then solving for Ae.. The chemical energy term was not considered in this analysis. The results of the calculations showed that the values of Ae2 and Ae3 are about 13% and 18% respectively less than the crystallographic strain. This gives a o spacing of 242A for a hexagonal network of three dislocations in edge configuration and with different a/6<112> Burgers vector in the Al-Ag system. The existence of two-dislocation and three-dislocation structures has 23 been observed in several systems. Laird and Aaronson used conventional TEM techniques to study the interfacial structures of 7 (hep) plates precipitated from the a (fee) matrix in an Al-15 wt% Ag alloy. The precipitate habit plane is the close packed {111}^  plane and the orientation relationship is: (lll) a //(0001)7: <110>a//<1120>7 The mismatch in the two lattices is ca. 0.8%. This misfit was found to be compensated for by three principal dislocation arrays. They observed a hexagonal network of three different Burgers vector and also a two-dislocation grid network in support of the theoretical predictions. A linear array having the same Burgers vector was also found to be present (ii) Other Interfaces 24 Philips studied the dislocation structure of spherical Co-rich fee precipitates in a Cu-Co alloy with the orientation relationship: 13 (100)a//(100)Co and [010] ^ /[OlO]^ and a mismatch of 1.7%. The misfit dislocations were of the type a/2<110> in a square or hexagonal network, consistent with the idea that in regions of {111} planes the dislocations may have a hexagonal structure and in regions of {111} and {100} planes, a square array will be preferred. A similar hexagonal dislocation network has been observed 25 by Weatherly and Nicholson . at the interface of ordered spherical 7 particles of {Ni3(Ti,Al)} having an fee structure and a misfit of 0.28% in a Nimonic 80A alloy. 26 Hexagonal misfit structures have also been observed in bec 7 phase precipitated from the bec p" in a Cu-Zn alloy. The two phases are identically oriented with a misfit of about 0.3%. The Burgers vectors are of the type a/2<lll> and a<100> and are aligned along the <112> and <110> directions respectively. The dislocations were in edge configuration. 1.1.3 Two-Dimensional Non-Conjugate Boundaries. Misfit dislocations can also appear at boundaries in which good lattice matching is not initially obvious. This is evidenced in the fee-bee interface bearing die Nishiyama-Wasserman orientation relationship, i.e., (100)bcc//(lll)fcc and [100]bcc//[110]fcc for which the two lattices do not match closely at any boundary orientation. It has been proposed that atomic matching between the {111}^  and UOO^ cc planes are restricted to 27 small diamond shaped regions , by the insertion of monoatomic steps between such regions. This increases the proportion of coherent area to about 25%. The area between the coherent regions then consists of just one more row of atoms in the fee than the 14 bcc lattice. Thus this region becomes partially coherent in the traditional sense when the extra atomic row is recognized as the extra half plane of a misfit dislocation in edge 28 orientation. Computer modelling has been used by Howell et al and Rigsbee and 29 Aaronson to show that partial coherency could be achieved over a wide range of rotations of the fee about the bcc lattice normal to the habit plane. Limited experimental results have so far been obtained to verify 28 these theoretical predictions. Howell et al have shown experimentally an array of misfit dislocations characterising the mismatch between (111)^//(HO)^ planes to be invariably 29 present. This finding is in support of earlier work by Rigsbee and Aaronson in which they observed misfit dislocations at the broadface of ferrite side plates in an Fe-0.6%C-2%Si alloy. There have been a large number of experimental observations showing dislocations on interphase boundaries.^ ^ However, in general, the agreement with the theoretical predictions is at best only semi-quantitative. The reasons for the significant differences between theory and experiment may be due to the fact that theoretical predictions are based upon the assumption that the misfit dislocations are of the lowest energy i.e., the equilibrium structure.^  However this is not the case in general and deviations due to one or more of the following usually characterises observed structures, too large a spacing between adjacent parallel dislocations the network observed is often not the lowest energy type. more than one geometry of dislocation array is present at a given boundary despite the fact that various arrays have different energies. 15 often the Burgers vector of the misfit dislocations is not parallel to the boundary. The basic reasons for these deviations are associated with the specific mechanisms and kinetics of acquiring misfit dislocations. It is often observed that the dislocations nucleated initially are not the lowest energy misfit dislocations but these however usually remain as the stable structure. Although such structures can later 20,32 transform to a more stable configuration, it is likely that the driving force i.e., the misfit energy for conversion to the equilibrium structure, would have been dissipated at the time of formation of the non-equilibrium array. 1.2 Theory of Morphology Development Theories describing morphology development may be classified into three groups: 1. Nucleation Theories 2. Growth Theories 3. Shear Theories. The discussion below follows this sequence but reviews the growth theories in greatest detail since they are the most developed with regards to precipitate morphology. 1.2.1 Nucleation Theories 33 The classical theory of nucleation requires that the nucleus forms with the minimum value of surface energy per unit area of the precipitate. The 16 34 non-classical theory developed by Cahn and Hilliard is based on compositional 35 fluctuations within the matrix. Aaronson and Russel have published a critical review of both theories. Mott and Nabbaro"^  have applied the classical theory of homogeneous nucleation to obtain a dependence of strain energy on the shape of the embryo. They examined the limiting cases of a disc, sphere and needle and suggested that, in general, an ellipsoidal embryo is the most stable shape. Modifications of this 37 38 theory ' have since evolved based on the theory of elasticity and these indicate that oblate ellipsoid morphologies are energetically favourable. 39 The Gibbs-Wulff theorem requires a spherical nucleus shape for a precipitate with isotropic interfacial energy. A low energy interface occurs for particular well-matched planes or directions for precipitates in which the two phases have different crystal structures. It is these facets that determine the shape of the nucleus, and the precipitate correspondingly adopts this shape. For other parts of the interface between the precipitate and the matrix in the required orientation relationship, there is a much poorer atomic fit and a much higher interfacial energy. 1.2.2 Growth Theories Growth theories consider the mobility of different boundaries. Interfaces with good atomic fit have low energies and show a greater reluctance to migration. Migration is therefore, inhibited and the rate of reaction is then controlled by whatever mechanism allows interfacial movement Prominent among these theories is the 17 10,40 ledge mechanism pioneered by Aaronson. The Gibbs-WulfT analysis of nucleation (preceding section) provides the basis of this theory. During nucleation, the facets physically correspond to partially or fully coherent interphase boundaries. Thus according to the theory, a barrier to normal diffusional migration exists on the faceted faces. Such a barrier arises when the precipitate and matrix have different crystal structures. Displacement of the boundary would then involve a change in the order of atom stacking across the boundary. This may only be accomplished by fitting atoms of the migrating phase bound for substitutional sites into interstices of the other phase. This is energetically unfavourable and therefore the boundary remains immobile. Migration of such interfaces can be envisaged as taking place by means of ledges, a familiar phenomenon previously associated with vapour-solid and liquid-solid phase transformations. A schematic diagram of ledges at the tip and broadface of a plate-shaped precipitate is shown in Fig. 4. The source of such ledges is varied. They may be nucleated heterogeneously at edges or at impurity atoms or by precipitate impingement Ledges fall into two main categories. They can be either microscopic ledges which are only a few Angstroms high or macroscopic ledges which are many atom planes high. Macroscopic ledges may be comprised of a large number of monoatomic ledges atop each other in the form of kinks. Ledges found on the interphase boundary have semi-coherent flat faces which enables good atom matching across the interface. However the step faces are Broadface Figure 4- Schematic diagram of ledge structure at the edge of a precipitate. 19 usually considered incoherent This means that atoms leave or enter the precipitate phase only at the step and no passage of solute occurs across the broadface. The growth velocity (G) of the face is determined by the lateral velocity (v), height (h) and spacing (X) of individual steps according to the relation, Fig. 5: G = hv/X 1.5 The edge then moves at a rate controlled by volume diffusion. On this basis, migration can occur at coherent and semicoherent interfaces only with the aid of a ledge and if these ledges are not available in sufficient density, migration is inhibited. It is worth mentioning at this point that the growth or dissolution ledges described above differ from structural ledges which appear at interphases like the fee-bec interface and were described in Section 1.1.3. Much of the discussion on ledges so far has been theoretical in di 42 nature and the experimental evidence for ledge growth is not fully complete. 32 43 Sankaran and Laird and Weatherly have made extensive observations of ledges on 8 plates of the Al-Cu system. A summary of ledge observations has been given by Aaronson.^  There is relatively little direct evidence for the rate of nucleation of ledges 43 and whether in fact they have incoherent edges. Weatherly, for example, shows that the strain fields associated with the edge of a ledge indicate a partially coherent boundary and one that would be immobile. Distinguishing between dislocations and ledges may not be easy. 44 Kang and Laird have suggested that networks are more likely to be preferred by dislocations than by ledges and that arrays of ledges often have irregular spacings. Ledges gure 5. Schematic representation of ledges. 21 are also associated with stronger strain field contrast effects which increases with ledge 45 height Weatherly and Sargent have listed some other characteristic contrast effects associated with ledges. The diffraction contrast observed from ledges depends on the ledge height (h) and the associated misfit (6) and its strain field behaves as a prismatic loop whose Burgers vector (b) is equal to 6h. The thickness differences between regions inside and outside a ledge can be used to estimate its height Ledge heights can be more 46 accurately determined using the displacement fringe technique of Gleiter . The ledge height in this case is calculated according to the relation, h = m sin/3 sin0 1.6 where, m = magnitude of the fringe shift 0 = angle between precipitate interface and the ledge line direction. <p = angle between fringes and the ledge line direction. The use of electron diffraction contrast alone to distinguish between a single macroscopic ledge and an array of closely spaced ledges may not be possible. The heights of nearly monoatomic ledges may be best estimated by convergent beam electron diffraction techniques or by high resolution lattice imaging. The latter technique 47 has been used by Howe to show that the ledges on T plates in the Al-Ag system were either two atom planes high or multiples of two planes and that the edges of ledges appear to be coherent 22 1.2.3 Shear Mechanism The Shear Mechanism is the third principal theory for morphology development It is much less popular than the other two. The theory is based on the minimization of strain energy and involves a non-diffusional, deformation-like process, wherein each solvent atom in the matrix has a predestined site in the precipitate. Displacement of an atom occurs in cooperation with its neighbours. The theory is defended on the basis of the successful application of the phenomenological martensitic theory,^ * which enables the selection of habit planes with minimum interfacial energy, subject to the constraints that the habit plane be unrotated and often undistorted as well. The theory successfully predicts the observed crystallography and 52 surface relief effects in several systems. For example, plate formation in a-f Al-Ag, disordered •• ordered AuCuII5^ and /3-a Cu-Zn.54*5^ The fact that the theory cannot account for needle-shaped precipitates and its other inherent shortcomings have been thoroughly discussed by Aaronson and Lorimer^  1.3 Kinetic Theories In this section theories relevant to the growth and dissolution of Widmanstatten precipitates will be presented. In the case where chemical equilibrium exists between two phases in contact, migration of the interface is controlled by volume diffusion of solute in the matrix phase. Thus the interphase composition is "given by the corresponding phase diagram and local equilibrium conditions are said to prevail. The other case is for a 23 sluggish interface at which the reaction rate is less than that predicted by the local equilibrium model. In reality, however, a mixed control reaction may be expected. This is the case where the boundary composition lies between the two extremes and so part of the driving force of the reaction is used up at the interface and the rest goes to establish a diffusion gradient in the matrix. Volume diffusion kinetics are generally restricted to uniform attachment/detachment of atoms at all points along the interphase boundary. When a precipitate is growing or dissolving by a volume diffusion process, the diffusion field in the matrix adjacent to the precipitate is described by the equation: dC/dt = V(DVC) 1.7 where, C is the concentration of solute in the matrix surrounding the precipitate, and D is the diffusion coefficient of the solute. For the common case where D is a constant, exact solutions have been obtained for growth of a number of simple precipitate shapes. Few exact solutions are available for precipitate dissolution and the stationary interface approximation alone satisfies all the boundary conditions. When D is a function of concentration, Eqn. (1.7) becomes 57-59 non-linear and numerical procedures must be s^ed. 24 Before presenting a few solutions it is first necessary to define the supersaturation parameter, fl J2 = — C p - C 1.8 where the various concentrations are given in Fig. 6, for an alloy equilibrated at T and 8 then heated to T .^ C = the concentration in the matrix at the precipitate:matrix interface, C m = solute concentration in the matrix at infinity, Cp = solute concentration in the precipitate, 1.3.1 Volume Diffusion Model For a planar boundary with constant D growing at diffusion controlled rates, the Dube* and Zener^  solution to Eqn. 1.7 is given as: x = a \/t 1.9 where a is given by: = y/n ( - 4 r ) l / 2 exp( — ) erfc( —%- ) 4D 4D 2 / D 1.10 and X = a/2 / D Shape preserving solutions relating growth rate to supersaturation for most simple morphologies can be obtained from the work of Horvay and Cahn.^  Their generalized 25 Figure 6. Composition profiles during dissolution. 26 solution for ellipsoidal particles is of the form: a = ep[(a,+p)(a2 + p)(a3+p)] l / j F(a„a 2 ,a 3 ) 1.11 where, oo e au FCai.aa.aj) = / , P [ ( a i + M ) ( a 2 + M ) ( a 3 + M ) ] l / j and p is the peclet number given as: p- = pv/2D. 1.12 where v is the instantaneous interface velocity and p has a unit of length. The constants a t , a 2 and a 3 are related to the eccentricity of an ellipsoid such that (ai + p) l / 2:(a 2+p) l / : !:(a 3+p) l / 2 represents the ratio of the three principal axes of the ellipsoid. By selecting specific values of the constants a,, a 2 and a 3 , the growth equations can be obtained for specific shapes. In the case of an oblate spheroid for example, a, =0, a 2 =a and a 3 =a then: S7 = y/p ep (a+p) F(0, a, a) 1.13 Spheroids, cylinders and spheres give a parabolic growth rate due to a changing solute field ahead of the moving interface. Other shapes like parabolic cylinders and paraboloids of revolution migrating by volume diffusion have been shown by 62 61 Ivantsov to give a linear growth rate. Horvay and Cahn generalised Ivantsov's solutions for the growth of elliptical paraboloids, obtaining: 27 = pe p (i+B/ P y/ 2 ; * [|I(B + M ) ] l / 2 1.14 where, [1 + B/p] is the aspect ratio, the precipitate length to thickness ratio and p is the peclet number. This solution assumes a constant isoconcentrate interface composition and does not include surface energy effects, which are particularly significant at small precipitate sizes. In the models of Zener-Hillert^ and Trivedi-Pound^ account is taken of capillarity. of precipitate dissolution. This is so because the diffusion fields adjacent to a growing precipitate and a dissolving precipitate are not identical. A theory for the dissolution of plate shaped precipitates has been developed in the present study. The details of this are presented in the Appendix. The interface stability of growing precipitates has been analysed by Mullins and Sekerka^ and also in the recent work of Langer and Muller- Kjrumbhaar^ All these solutions for growth of a precipitate at constant velocity suffer a common drawback which is yet to be resolved. Eqn. 1.12 i.e., p = pv/2D These solutions for precipitate growth are not applicable to the case gives only the product pv for a given supersaturation and does not yield a specific growth velocity. Since a unique solution is observed experimentally, a number of ad hoc principles have been used in the literature to determine this unique rate e.g. the 28 maximum growth rate equation and maximum rate of entropy production. 1.3.2 Interface Reaction Controlled Kinetics Interface reaction control kinetics occur when the interphase solute concentration falls below equilibrium values and a corresponding drop in interface mobility results. A number of atomic attachment/detachment mechanisms have been proposed to account for the slower kinetics in such cases and mathematical formulations have also 68 been developed to describe them . These formulations are based on a saturation parameter: AC = [ C e - Cj ] 1.15 where AC is the difference in the actual interface concentration, Cj, and the equilibrium interface concentration C . e It is then possible to define a function for the interface velocity (v), which is related to AC by the specific mechanism of atomic attachment/detachment The mechanisms include (a) uniform atomic attachment with v=-k,AC (b) screw dislocation mechanism with 1/2 v=-k2ACJ (c) ledge migration limiting with v=-k3AC expClc/AC) and (d) Ledge 5/6 mechanism, with nucleation limiting, v=-k5(AC) exp(k6/AC). The value of Cj can be obtained by combining the relevant relation above with Eqn. 1.15 which then replaces Cj in Eqn. 1.8. This approach can easily be extended to include curvature effects. The diffusion equation is most conveniently solved numerically under these conditions. 29 Other solutions have been developed to concurrently accommodate volume diffusion and interface reaction control kinetics in a single development simply by allowing the interface composition (C ) to be a variable in the analysis. These include the analytical solutions by Nolfi et al^ and the numerical solutions of Tanzili and Heckel.70 1.3.3 Experimental Observations (i) Ledged Boundaries. Experimental evidence for the existence of ledges on interphase boundaries seems fairly 71 convincing. Their role in migration is still unclear however. The most direct evidence of ledge participation in growth has been provided by the hot-stage TEM studies of Laird 22 and Aaronson on the thickening of 7-Ag2Al plates. Their results, Fig. 7, showed appreciable intervals of time when, in the absence of ledges, no perceptible thickening of the plates occurred. The ledges were also found to move at a constant rate. 72 Observations of the growth rate of isolated ledges have been made on ferrite side-plates using thermionic emission microscopy and on 9 plates in Al-Cu using room 73 temperature TEM techniques. Results of both studies indicate ledges migrate at volume diffusion controlled rates. Diffusion coefficients calculated from the experimentally observed thickening rate using the Jones-Trivedi and Zener-Hillert equations show good agreement 74 with independently measured diffusiviues in Al-Cu , Fig. 8. It therefore appears from these observations that ledges have a disordered structure at the riser and that their migration is controlled by a long range diffusion process. The overall migration rate at the broadface of precipitates has also 30 ZOO 100 D I F F U S I O N C O N T R O L INITIAL THICKNESS 0 20 40 10 «0 100 120 >«0 «0 IM REACTION TIME - SECONOS Figure 7(a). Thickening vs rime plot for a 7 jxrecipitate. Temperature of reaction is 400° C. (after Laird and Aaronson ) 120 200 280 360 REACTION TIME - SECONOS 440 Figure 7(b). Lengthening of a 7 precipitate by means of^ edges. Temperature of reaction is 425° C (after Laird and Aaronson ) 31 l / T * I 0 3 •K' Figure 8. Arrhenius plot of diffy|iviries calculated from thickening kinetics of 9' plates, (after Sankaran ) 32 75 been extensively studied. The results are far from conclusive mainly due to uncertainties surrounding the effect of ledge nucleation and interaction on the kinetics. It has even been contended^ that a ledged boundary may grow faster than a disordered boundary depending on the period at which the kinetics are obtained. Another source of confusion 77-79 in the literature relates to the use of inappropriate kinetic theories. When experimental rates are less than that suggested by volume diffusion kinetics, a ledged boundary is usually inferred. But since the supply of ledges is erratic it may be helpful to monitor ledge migration concurrentiy with boundary kinetics as suggested by Aaronson et al. 8 0 The role of ledges in the migration of plate edges is thus unclear. No single theory has yet been successful in describing such boundaries. The situation arises from a lack of adequate characterisation of the structure of plate edges. Also uncertain are the effects of lattice strain, dislocation pipe diffusion and capillarity on ledges. It may be of interest to note that plate edges are commonly observed to migrate at rates faster than the predictions of the Horvay-Cahn equation. Various explanations have been given for this observed enhanced mobility. Aaronson and 81 Laird suggested the misfit dislocations girdling the plates serve as "collector lines" analogous to the collector plate model for grain boundary allotriomorphs. This model was 82 adopted by the author to explain similar results obtained for the case of Widmanstatten 74 precipitate dissolution. Sankaran, however, attributed the observed enhanced migration to the' coherency stress field around the precipitates. They observed that 6' plates in Al-Cu lengthen more rapidly than volume diffusion control if only their broadfaces were fully coherent, 6' precipitates whose broad faces were partially coherent grew at volume diffusion controlled rates. These discrepancies may well be due to inadequacies in existing models since they do not take individual ledge kinetics into consideration. Theoretical models need also to be developed for the migration of boundaries containing segments of disordered and partially coherent structures. (ii) Electron-probe Studies Electron probe microanalyzer measurements of the solute profiles adjacent to migrating boundaries have been used to determine the nature of the interphase boundary. If the interface concentration values obtained are less than the equilibrium value then this suggests an interface controlled boundary. In a rather definitive experiment, Hall and 83 Haworth observed the dissolution of the 6 phase in Al-5%Cu to be controlled by diffusion in the a-Al matrix. Results of similar studies carried out on Si plates in an 84 Al-0.57%Si alloy gave interphase composition values less than the equilibrium solubility 85 values. Sagoe-Crentsil and Brown, in a recent study, observed lower than equilibrium interface concentrations on the broadface of 7-Ag2Al plates. They showed the existence of a short-circuit path for the solute atoms from the precipitate broadface to the tip on the basis of measured compositional contours around the precipitate phases. The short circuit path was then- shown to be responsible for the observed slower than volume diffusion controlled kinetics at the broadface of the 7 plates. 1.3.4 Ledge Theories The ledge theory attempts to rationalize the low interface mobility from a mechanistic viewpoint The velocity of the step is calculated by solving the steady 34 state diffusion equation in a coordinate system which moves with the step. Two main approaches have been adopted to solve the resulting equations and these are based on the type of boundary conditions imposed on the riser of the ledge. The solution of Jones 86 74 87 and Trivedi and the parallel solutions of Sankaran and of Atkinson will first be 88 reviewed, followed by the model of Doherty and Cantor. The Jones and Trivedi model assumes a constant flux along the riser of the ledge to predict the ledge velocity, v, in terms of the supersaturation 0 given as: p = vh/2D, a(p) is the effective diffusion distance which is numerically evaluated as a function of p, and v is the step velocity and is related to the lateral interface velocity, G, given by Eqn. 1.5 as: = 2 p a(p) 1.16 where, G = hv/X Jones and Trivedi obtain the relationship: / 3 a D 35 where, D = volume diffusivity = solute concentration in the 0 matrix /3a = solute concentration of the j3 matrix at the a / ( a + /3) phase boundary a/3 Ca = solute concentration of the a precipitate at the /3/(a + /3)phase boundary Combining Eqn. 1.5 and 1.17 gives: G = X a Ba a/3 This analysis gives a constant solute field around the ledge at a given supersaturation and hence each ledge could grow at the speed of an isolated ledge if no overlap of diffusion fields occurs. As a result the interface velocity G, remains constant at a constant ledge spacing. Fig. 9(a) shows the model prediction of the solute field ahead of the ledge. Sankaran used a finite difference solution to independently obtain a similar result The Atkinson model is a purely analytical solution. He obtained the following result for p < 0.1 : 2p J2 = —— [ 2.954 - ln p ] 1.19 7T Both the Sankaran and Atkinson solutions give essentially the- same results as the Jones and Trivedi treatment except that at low Peclet numbers the Atkinson analysis gives a 36 growth rate about 3x faster. 88 The Doherty and Cantor model assumes a constant supersaturation along the riser. The large solute flux from the corners of the step due to the point effect of diffusion is eliminated by rapid interfacial diffusion along the riser. The averaged flux at the step then determines the ledge velocity. Their numerical solution gives isoconcentrate contours as shown in Fig. 9(b). The striking difference between the analysis of Doherty and Cantor and that of Jones and Trivedi is that the former predicts a transition from linear to parabolic rates of migration after a given period of time, whilst Jones and Trivedi predict constant growth at all times for values of SI < 0.1. Jones and Trivedi have also investigated the effect of diffusion field overlap from adjacent ledges. The effect of overlapping fields was found to indicate that the merging of ledges is more the rule rather than the exception. There is still a great deal of uncertainty regarding the migrational characteristics of the ledges. Thus the role of ledge parameters like density, height and nucleation rate need to be incorporated in further theoretical models. 1.4 Influence of Trace Elements on Interface Boundary Structure The addition of minor trace elements, up to 0.1 atomic percent, may substantially alter the structure and properties of an alloy. The better known examples are the effects of very small amounts of boron in increasing the hardenability (a) Figure 9. Schematic isoconcenuate contours at the step of a ledge: (a) Jones and Trivedi model (b) Doherry model. 38 of certain steels and the refinement, or modification, of the eutectic structure in cast aluminum-silicon alloys by the addition of as little as 0.001% of sodium. Trace element effects arise because they change the nucleation and/or growth rate of new phases forming during solid state transformations. Trace elements therefore represent a potential mechanism for influencing precipitation in age 89 hardenable alloys. In this regard the aluminum-based alloys have been the most 90 extensively studied with the intent of improving engineering properties like stress corrosion susceptibility and creep resistance of specific alloys. A case in point is the 91 development of the commercial alloy AZ74(7009) which is used for components in several current civil and military aircraft The next section briefly reviews available data on the effects of trace elements with specific reference to aluminium-based alloys. Trace elements are known to influence precipitation in 92 aluminum-copper alloys in two ways . First additions of up to 0.02% of cadmium, indium and magnesium, reduce or inhibit G.P zone formation for considerable periods at ambient temperature. The most commonly accepted explanation for this is that the vacancies needed for the formation of G.P zones are trapped by the impurity atoms in 93 forming impurity-vacancy and impurity-Cu-vacancy clusters . However in cases where the trace elements form part of the G.P zone structure, zones form rapidly since a supply of vacancies is produced by the breakdown of atom-vacancy complexes, eg. Mg in excess of 0.05 at% in Al-Cu-Mg. The second effect of trace elements in the Al-Cu system is to stimulate the formation of 6' plates which then supersede the 9'' phase, thus leading to a finer and more dense distribution of 8' compared with Al-Cu binary alloys. This leads to improvements in mechanical properties. 39 The effect of trace additions on 8 nucleation discussed above has 92 been attributed to one or more of the following reasons: (i) Nucleation of 8' takes place by the coalescence of mobile Cu-impurity-vacancy 94 clusters and the growth of precipitates by the movement of these clusters. (ii) In the presence of impurity elements, vacancies in the quenched Al-Cu alloy condense to form a finer distribution of dislocation loops. An increased density of 8' precipitate can result from this as well as from the impurity atoms keeping vacancies available for diffusion for longer times. (iii) Trace elements modify the a:8' interface giving a better match with the lattice, so that the critical size and energy barrier for nucleation are reduced. Available experimental evidence indicates that the second and third 95 mechanisms are the most likely. Silcock et al obtained evidence for the third mechanism by X-ray diffraction effects, though no direct microscopy work has yet been done. Nuyten^ obtained direct microscopic evidence for the second mechanism and concluded the reason for the increased rate of 8' precipitation is both structural and kinetic. 95 The X-ray observations of Silcock et al require some attention in view of the work being proposed here. They observed that thin 8' plates i.e., less than o 60A , were associated with additional diffraction in the form of slightly elongated spots similar in size to the 8' spots. These have been called P diffractions and represent a structural feature of the same thickness and orientation as the 8' phase and appear at about the same time. They have been interpreted as an interfacial structure at the a-8' 40 interface. Whilst these P diffractions are present, 9' coarsens only slowly. A similar inhibited coarsening effect due to the presence of P diffraction spots has been observed 97 in an Al-Cu-Mg-Ge alloy by Brook and HatL Work carried out on trace element effects on the mobility of boundaries is limited to grain boundaries. The original quantitative analysis by Lucke and 98 99 Detert based on the solute drag effect model has since been extensively modified. The kinetics of interstitial solid solution alloys with substitutional impurities, in particular the Fe-C system, has also received much attention.Much less work has been carried out on the effect of substitutional impurities in substitutional solid solutions. 74 Sankaran determined the effect of Cd, In and Sn on 9' (Al-Cu) precipitation and kinetics. He found that the trace elements reduce the critical diameter of the 6' nuclei by segregating to their edges thereby decreasing the interfacial free energy, but no 102 appreciable effect on precipitate kinetics was observable. Hewitt and Butler have recently shown that the addition Of 0.05% Cd to an Al-3% Cu alloy substantially reduces the 8' dissolution rate and suggest a vacancy interaction mechanism as the probable cause. 2. AIM OF PRESENT INVESTIGATION It has been shown in the preceding sections that our current understanding of Widmanstatten precipitate kinetics and morphology development is quite limited. Specifically, there is the need to develop detailed mathematical theories appropriate to the kinetics of the Widmanstatten boundary, but this would first require a much clearer description of the nature of the moving boundary. Although there exists some data on the interphase kinetics for this purpose, such measurements have been carried out with little or no attention to the structure and mode of migration of the boundaries. The need for a closer study of these boundaries has become particularly needful with the advent of the ledge theory of interphase migration. The present study is an attempt to obtain a better understanding of the dependence of interphase boundary structure and migration kinetics on the misfit between plate-shaped precipitates and the surrounding matrix. The problem of morphology development is also indirectly addressed in this investigation. The focus of this study is to control the mismatch between the precipitate "and the matrix phase of a suitable alloy system. The 7-Ag2Al phase of the Ag-Al system has been extensively studied. It is plate shaped and the dislocation structure of its interphase boundary is well documented. Furthermore the misfit of 0.8% allows a great deal of control in both directions. The 7 phase therefore satisfies the basic requirements needed for this type of investigation. The misfit between two phases may be best controlled by epitaxial 41 42 crystal growth. However the resulting interphase structure may not represent the complex boundaries obtained naturally. Other techniques such as electron/neutron beam irradiation or deformation studies essentially alter the interfacial structure without changing the misfit between the phases involved. Furthermore the resulting interphase boundaries are non-equilibrium structures. For the present study, misfit in the 7-Ag2Al phase is altered by ternary element additions. The ternary elements used are Cu and Mg, selected on the basis of atomic size and their solubilities in the matrix phase. The Cu and Mg atoms are 11% and -10% respectively different in size relative to Ag. The effect of these ternary additions on the mismatch had to be first ascertained. The mismatch in the respective alloy systems was determined by three independent techniques namely (i) X-ray diffractometer measurements, (ii) Moire' fringe spacing measurements and (iii) dislocation spacing measurements. The interphase dislocation structures of equilibrated precipitates and the structures during precipitate dissolution were investigated by conventional Transmission Electron Microscopy (TEM) techniques. This permitted an examination of whether the dislocation structures obtained were equilibrium or non-equilibrium as discussed in Section 1.1.2. Kinetic measurements of plate dissolution were obtained by a combination of Scanning Transmission Electron Microscopy (STEM), Scanning Electon Microscopy (SEM) and Electron Probe Microanalysis (EPMA) techniques. 3. EXPERIMENTAL 3.1 Alloy Preparation The alloys used were prepared by melting weighed amounts of the appropriate elements in a graphite crucible. The elements used were all 99.99% pure except silver which was 99.95% pure. Heating was carried out using a high frequency induction furnace and the alloys were protected from oxidation using an argon atmosphere. A split graphite mould casting produced slabs of dimensions 45mm x 15mm x 100mm. These were then homogenized for one week at 520° C. The alloy compositions were analysed by Cantest Ltd., using atomic absorption spectrophotometry techniques for all elements except Mg. The Mg was analysed using plasma spectroscopy. The compositions were checked in our laboratories for the Ag by gravimetric analysis and by atomic absorption spectroscopy for the Cu. This analysis confirmed the Cantest results to within 0.05%. All analyses were carried out on samples drilled from different parts of the ingot Later scanning of microscopic sections of the alloys in the electron probe microanalyzer showed no significant microsegregation. The compositions of the alloys used are given in Table 1. The Al-Ag binary diagram is shown in Fig. 10. 43 44 Table 1. Alloy Composition. Al - 4.18 ar% Ag Binary alloy Al - 4.10 at% Ag - 0.51 at% Mg Ternary Mg Al - 4.15 at% Ag - 0.06 at% Cu Ternary Cu-I Al - 4.06 at% Ag - 0.12 at% Cu Ternary Cu-II Al - 3.93 at% Ag - 0.51 at% Cu Ternary Cu-III Sections of the ingot one centimetre wide were cold rolled to a 50% reduction. These were then annealed for 1.72 x 10^  s at 520° C and given a further reduction to 1mm thickness to give samples for the SEM and electron probe. Sections of the ingot were cold rolled to foils 0.15-0.20mm thick, to give bulk materials for the TEM and STEM investigations. The foils were then homogenized by annealing at 520° C for 1.72 x 105 s. Because the present investigation combines both TEM and SEM studies, it was important to select one suitable ageing treatment to satisfy the experimental requirements of either technique. The conditions are particularly critical for TEM imaging of the interphase dislocation structures since this technique places a limitation on the precipitate thickness. The SEM and electron probe study requires large precipitates well 45 Figure 10. Ag- Al binary diagram, (after Hansen ) 46 separated from each other in order to eliminate diffusion field overlap. A great deal of effort was therefore expended to obtain an optimum ageing treatment which satisfied both SEM and TEM requirements. Several combinations of ageing temperature and time were initially tried before a suitable choice could be arrived at" Ageing at 418° C was found to give precipitates suitable for both TEM and SEM observations. Electron probe analysis of solute concentration in the matrix of the aged alloy confirmed that equilibrium conditions had been achieved after ageing 4 for 1.44 X 10 s and so this was used for all specimens. 3.2 Specimen Preparation 3.2.1 TEM/STEM Samples The heat treated samples were spark machined to produce 3mm discs and mechanically polished to less than 0.1mm thickness. The samples were electropolished using the standard jet polishing technique. The A-2 reagent was used for all the samples. The solution and conditions of electropolishing were: Polishing solution: Perchloric Acid - 80ml Ethanol - 700ml Distilled Water - 120ml Butyl Cellusolve - 100ml 47 Temperature of solution: - 1 0 ° C Voltage: 20V This technique produced very clean specimens with no preferential etching of the precipitates or of the grain boundaries. Specimens were examined on a 200kV Hitachi H800 electron microscope. The precipitates were on the average 0 .3M m thick with a 20-30M m separation from each other. The foil sections used were normally o about 300A thick. This thickness proved to be very suitable since the interphase structure may be visible only if the ratio of the foil thickness to the precipitate extinction distance (£ ) is greater than 0.25.25 3.2.2 SEM/Electron Probe Samples The aged samples were polished to a 0 . 5M m diamond finish. The individual precipitates used for these studies were selected using the following criteria, in order of priority: 1. large separation from neighbouring precipitates and grain boundaries to avoid impingement of diffusion fields. This condition was often difficult to satisfy for the ternary Mg alloy, 2. large sized precipitates meaning that sectioning had been done close to the centre of the precipitate, 3. perpendicularity to the surface. This was checked by a mild etch using 5% NaOH solution for 20 s, after which the surface was repolished. This procedure was necessary to facilitate later interpretation of the results although it was not possible to satisfy all three requirements in every case. 48 Specimens were observed in a Hitachi S-570 SEM normally at a magnification of up to 20,000% The entire heat schedules involved in this work were carried out in air using horizontal tube furnaces. The length of the hot zone was about 40mm. Temperature control was within ±1°C for prolonged periods, checked periodically using a potentiometer. The transfer time from the furnace to the quenching bath was less than 1.5 s. Solution treatment was carried out at 450° C for varying lengths of time in all cases. 3.2.3 X-ray Diffractometer Samples For the X-ray diffractometer studies, specimens 20mm x 30mm were equilibrated for 1.44 X 10^  s at 418° C then given a 6um diamond polish and examined on a Philips diffractometer using CuKa radiation. 3.3 Electron-optics Techniques 3.3.1 Burgers Vector Determination The conventional method of determining the Burgers vector of dislocations is based on the two beam dynamical approximation which predicts that pure screw dislocations will be invisible when g*.b*=0 and mixed and edge disloaction will be invisible when g\tT=0 and g\b* x u is less than 0.64, where g is the reciprocal lattice vector and u* is the unit tangent vector in the direction of the dislocation. For unambiguous dislocation identification, it is required that the dislocation disappear for at least two non-parallel g* values and throughout a range of values of the deviation 49 parameter, w, for each g\b* =0. When high g values are used, high values of w are needed to produce clear micrographs and under these conditions, the dislocations could be out of contrast Dark field microscopy is often used in determining b" since; (i) even very weak images may be observed (ii) it is easier and quicker to obtain specific two beam conditions (iii) better resolution is possible. However, anomalous invisibility is more of a problem in dark field than in bright field. For low order reflections, the dislocation images change from a dark line in a bright background to a white line in a dark background as w is increased from zero. Thus, for accurate Burgers vector determination, low order reflections and bright field techniques should be used along with a range of w values. A confirmation of Burgers vector analysis can be readily obtained by using the g\b"=2 contrast from a dislocation. It must also be remembered that the diffracting conditions necessary to image interfacial dislocations are very stringent and for good visibility, matrix and precipitate reflections should coincide. 3.3.2 Imaging Misfit Dislocations and Moire' Fringes When the spacing between the dislocations compensating mismatch becomes very small, the individual images overlap and it is often difficult to distinguish between a dislocation array and Moire' fringes. The Moire' fringes form as a result of interference of waves excited in the aF matrix with waves excited in the T. ice hep precipitate phase, since the lattice spacing of the close-packed directions in the two phases are nearly equal. 50 The following techniques were used to separate Moire' fringes and dislocations: 1. The dislocation spacing is independent of the % vector, whereas the Moire* fringe spacing is inversely proportional to the magnitude of %. Thus a higher order reflection produces closely spaced Moire* fringes compared to low order reflections. Since Moire' fringes form due to interference between the main beam and a doubly diffracted beam and since double diffraction is easier in thin specimens, Moire' fringes are imaged best using slightly higher order reflections. Low order reflections on the the other hand give strong dislocation contrast 2. The direction of the dislocation line does not depend upon the diffraction vector g used; g" only determines the visibility of the dislocations. Moire' fringes, on the other hand, show a definite orientation with respect to g\ A parallel Moire' pattern where the two sets of planes differ only in spacing is always normal to the % vector. A rotation Moire' pattern, where the two sets of planes have equal spacing but a slight rotation about an axis normal to the interface, is always parallel to g*. When the Moire' pattern is due to both effects, % will make a definite angle with the fringes depending upon the relative magnitudes of mismatch and twist. 3.3.3 SEM Dissolution Studies In order to study the progressive dissolution of one precipitate it was necessary to examine it at the specimen surface. The SEM was operated at 20kV excitation and images were observed in the secondary electron mode. Measurement of precipitate length was made directly on the monitor 51 of the SEM at a fixed magnification using vernier calipers. A ruled grating standard was employed to calibrate the microscope and the appropriate compensation for magnification was made whenever it became necessary to tilt the specimen for measurements, although this was seldom done. For the thinning kinetics, precipitates were photographed on a Polaroid camera attached to the SEM console. Thickness measurements were obtained directly from the photographs using vernier calipers. The constancy of magnification was confirmed by periodically checking that the distance between reference points on the surface remained constant The effect of surface diffusion particularly during the dissolution experiments was checked by measuring the diffusion profile surrounding partially dissolved precipitates. Repeated measurements were made following successive removal of a 2-3Aim surface layer on a 0.5<x m diamond wheel. No difference between the diffusion fields at the surface and in the interior of the specimen could be observed. 3.3.4 Electron Probe Microanalysis: Solute Profiles The matrix solution concentrations in the aged alloy and solute profiles adjacent to the broadface were obtained through electron probe microanalysis on a Cameca SX-50 machine operating at 20kV. The microprocessor operated stage of the SX-50 gives precise step intervals for solute concentration measurements. Traverses were taken at either lam or • 52 1.5Mm intervals. Each displacement is followed by a stationary spot count of 10 seconds and the resultant counts are registered automatically. Scans were obtained perpendicular to the broadface of precipitates into the matrix until the equilibrium matrix concentration was reached. The measured X-ray intensities were converted to the true mass 104 concentration by applying the PAP correction procedure on line. 4. MICROSTRUCTURE CHARACTERIZATION OF THE EQUILIBRATED ALLOYS 4.1 Microstructure The morphology and microstructure of all five alloys will be discussed in this section. The alloys were in all cases solution heat treated at 520° C for 2.59 x 105 s and aged at 418° C for 1.44 x 104 s in the two phase field. The microstructures of the alloys are shown in Fig. 11. 4.1.1 Precipitate Morphology The morphology of plates in the five alloy systems will be discussed concurrently. The habit planes of precipitates for all five systems were the same as determined by selected area electron diffraction and together with X-ray diffractometer measurements it was confirmed that the plates were indeed the 7 phase. Plates of the binary alloy were nearly always hexagonal in shape, Fig. 12. In a few cases, however, the hexagons were slightly irregular. With the addition of Cu these irregular plates ceased to be present and at the highest Cu content all the plates were perfect hexagons. Adding Mg caused the plates to show significant deviations from hexagonality. The corners of the plates in the ternary Mg alloy were rounded resulting in a rounded hexagon morphology. A few lath morphologies were present in the ternary Mg alloy in addition to the rounded hexagon morphology. These may represent a different phase, possibly the intermetallic Mg3Ag which also has a hexagonal crystal structure and forms 53 Figure 12. STEM micrographs of (a) binary (b) ternary Mg (c) ternary Cu-III alloys. <3> 57 on [111] matrix planes. The lath morphology was not included in this study. 4.1.2 Precipitate Volume Fraction The weight fraction of Ag in the alloys studied was similar ( 3.93 - 4.18 at% Ag ) and they were equilibrated at the same temperature of 418° C. However there is some possibility that the ternary additions of Cu and Mg might change the thermodynamic characteristics of the system. Since one of the primary objectives of this work was to consider only the effect of the misfit between the two phases, it was necessary to ascertain that the levels of ternary elements added were sufficiently low to the extent that the binary Al-Ag phase diagram was applicable to these ternary systems. This would permit the ternary systems to be regarded as pseudo-binary systems. The volume fraction of precipitates in the ternary alloy systems was measured to determine the effect of Cu and Mg additions. The results are shown in Table 2. The volume fraction of precipitates in the five alloys were found to be the same within experimental error. Hence the thermodynamic equivalence of the systems can be safely assumed. 58 Table 2. Precipitate Volume Fraction Determination. Alloy- Volume Fraction(%) Binary 3.8± 0.7 Ternary- Mg 4.2±0.7 Ternary Cu-I 3.7±0.7 Ternary- Cu-Il 3.9± 0.7 Ternary Cu-III 3.510.7 4.1.3. Microstructure SEM microstructures of all alloy systems under investigation were compared on the basis of (i) mean precipitate density (ii) mean precipitate aspect ratio and (iii) mean precipitate diameter. The results of the study are shown in Table 3. 59 Table 3. Results of Microstructure Analysis. Mean Ppte. Mean Ppte. Mean Density Diameter Aspect pxlO 3 (mm) - 2 d Mm Ratio Binary 57 6.7 29 Ternary Mg 184 2.5 10 Ternary Cu-I 55 6.4 27 Ternary Cu-II 51 5.6 22 Ternary Cu-III 39 5.0 16 The distribution of precipitates varies significantly for the alloy systems. Mg additions increase the mean precipitate density by a factor of over 3 in comparison with the binary system. Cu additions progressively decrease the precipitate density. At the maximum Cu content of 0.53 at%, the number is reduced by 30%. However as shown previously in Section 4.1.2, the precipitate volume fraction remains the same in all five systems. Table 3 also gives mean precipitate diameter and aspect ratio for the five alloys studied. Plates of the binary alloy were large and thin with a mean aspect ratio of 29. Adding Cu progressively decreases the precipitate diameter with little 60 effect on the width giving rise to a decrease in aspect ratio. Mg has a large effect on precipitate dimensions with the diameter being decreased by a factor of over 4 times and the width by a factor of almost 2 with an overall decrease in aspect ratio by a factor of almost 2. The differences in microstructure are obviously a result of the added trace elements. As discussed in Section 1.4, trace additions have been shown to 92 enhance precipitation in two ways. First by increasing solute saturation at the ageing temperature and secondly by modifying the interfacial energy between the precipitate and the matrix to produce additional markings on electron diffraction micrographs. No extra spots in the electron diffraction patterns were found in the present work and it appears that neither Mg nor Cu atoms are aiding precipitation through interfacial segregation. In the case of the ternary Mg alloy the higher nucleation rate may 93 be due to the strong interacuon known to exist between Mg atoms and vacancies. Such interactions may result in the formation of solute:vacancy complexes or even solute:solute complexes which then serve as nucleation sites. The higher nucleation rate in this alloy system implies a shortfall of solute atoms during growth of the precipitate phase resulting in a smaller overall size. In summary, while the addition of both Cu and Mg have the effect of reducing the mean precipitate diameter and aspect ratios, the two ternary elements show opposing effects on the density of precipitates. It can also be seen that these variables change progressively with increasing Cu content It is particularly worth noting that the precipitate volume fraction remains unaffected by the ternary element 61 additions. In general however, the effect of Mg in altering the base microstructure appears far more pronounced than the effect of the Cu. 4.2 Electron probe Analysis of Solute Concentration Results of solute concentration measurements in the alloy systems will be discussed in this section. Samples used for this study were equilibrated at 450° C for 240 s, and the concentrations determined by electron probe microanalysis. The matrix concentrations of Ag as well as those of Cu and Mg were determined for each of the alloys. The results are shown in Table 4. 62 Table 4. Solute Concentrations from Electron probe and by Calculation. Alloy Compn. (EPMA) Aged Alloy Matrix Concn. (EPMA) Aged Alloy Ppte. Concn. (Calc.) at.% Ag at.% Ternary aL% Ag aL% Ternary at.% Ag at.% Ternary Binary 4.20 - 2.45 - 51 -Ternary Mg 4.31 0.52 2.62 0.15 39 9.0 Ternary Cu- I 4.17 0.04 2.47 0.03 50 0.3 Ternary Cu- II 4.04 0.12 2.50 0.10 44 0.6 Ternary Cu- III 3.91 0.53 2.42 0.51 45 1.1 Table 4 also gives the solute compositions of the alloy systems as measured on the electron probe. These measured concentrations were used together with prior determined precipitate volume fractions (Table 2) to calculate the Ag and ternary element concentrations in the precipitate phase. Such a calculation is justifiable on the grounds that the crystal structure of the precipitate and matrix phases are both close packed. Direct measurement of precipitate concentrations using the electron probe was not possible since the precipitates were only fractions . of a micron wide in these alloys. The 63 precipitate concentrations thus calculated are shown in Table 4. The accuracy of these calculations was checked for the binary alloy using the Al-Ag phase diagram, Fig. 10. At 418° C the equilibrium concentration in the matrix should be 2.5 at% Ag and this agrees well with the measured value of 2.45 at% Ag. The equilibrium composition of the 7 phase should be 57 at% Ag. The calculated value of 51% is in reasonable agreement with this given the relatively large uncertainty in the volume fraction determination. The ternary Cu alloys all show Ag contents in the matrix comparable to the binary alloy. This is a further indication that Cu additions have little effect on the Al-Ag pseudo-binary phase diagram. The Mg alloy shows a slightly higher Ag content in the matrix indicating a slightly lower volume fraction of precipitate to be expected in this ternary alloy, although the difference would probably not be detectable experimentally. The Ag contents in the 7 phase vary significantly from the binary due to segregation of the ternary elements to be discussed next Partitioning of the ternary element between the matrix and precipitate phases can most readily be understood by comparing ternary element concentration in the initial uniform alloy and in the matrix of the equilibrated alloy. In the Cu ternary alloys, the Cu content in the equilibrated matrix is only a little less than the Cu content in the initial alloy. Noting that the volume fraction of precipitate is only 3.5%, this suggests that nearly all the Cu remains in the a matrix. The Mg alloy, on the other hand, shows a much lower Mg content in the equilibrated matrix than in the initial starting alloy, (0.15 vs 0.52at %). In this case, only 1/3 of the Mg goes into the matrix phase and the remaining 2/3 goes into the 7 64 precipitate. Thus the Mg content in the 1 phase is high and it appears that approximately 20% of the Ag is replaced by Mg. The mode of partioning of the Cu and Mg atoms therefore appears to be distinctly different, in that the Mg atoms have a greater affinity for the Ag-rich precipitate phase, whilst the Cu atoms remain in solution within the Al-rich matrix phase. 4.3 X-Ray Diffractometer Determination of Lattice Parameters The degree of misfit between the precipitate and matrix phases was determined for all five alloys using X-ray diffraction measurements. It proved difficult to obtain adequate diffraction peaks for the 1 precipitate since it represented only 3.5% of the volume of the alloy. Attempts to obtain high angle peaks proved unsuccessful since the peaks were normally too weak to be useful. Thus measurements of d spacing were limited to the low angle {220} peaks of the matrix and {1120} peaks of the precipitate. A large number of counts were recorded from different areas in each sample to ensure that consistent peak positions were obtained and that the peaks were showing the best possible resolution. Fig. 13 shows diffractometer traces for three of the alloys covering the 20 range of interest The binary alloy shows a clear separation for the matrix and precipitate peaks and d values could be accurately calculated. Adding Cu decreases the separation of the peaks and the exact peak position of the precipitate is difficult to calculate "accurately in this case. Mg on the other hand increases the separation of the peaks. 65 220 ZO I 1 1 1 1 67 63 28 (a) 220 i I Z O 67 63 2 e (b) 220 67 63 2 9 (c) Figure 13. X-ray diffraaometer traces of alloys (a) binarv (b) ternary Mg (c) ternary Cu-III. 66 Table 5 gives the d spacing values calculated for the different traces. Table 5. Lattice Spacing from Diffractometer Measurements and by Calculation. XRD Measurement Calculated Alloy d a ±0.002 ±0.002 % Misfit (6) d a Binary 1.431 1.442 0.76 1.430 1.435 Ternary Mg 1.431 1.447 1.11 1.429 1.449 Ternary Cu-I 1.430 1.434 0.42 1.431 1.433 Ternary Cu-II 1.432 1.438 0.42 1.430 1.433 Ternary Cu-III 1.432 1.438 0.42 1.431 1.433 The misfit (5) between the two lattices is calculated from: 6 = 2(dQ - dyMd + d7) 4.1 Comparison of the misfit values clearly indicates that Mg additions 6 7 to the alloy tend to increase the degree of mismatch between the precipitate and matrix phases, whilst Cu additions lower the mismatch. It can be seen that there is a negligible effect on the lattice spacings in the matrix phase due to ternary Cu alloy additions and the measured d spacings for the matrix are all nearly the same. The effect of the trace elements on the precipitate phase is however significant. The Mg addition expands the precipitate lattice whilst the Cu additions reduce the lattice spacing. An approximate lattice spacing calculation was carried out by directly weighting the respective atomic radii with the measured solute concentrations from Table 4. The calculation was carried out for both the matrix and precipitate phases, and the values of d spacings calculated are shown in Table 5. It can be seen that the effect of the ternary additions on the matrix phase is always small, in confirmation with the diffractometer measurements. The corresponding values for the precipitate show a larger variation with ternary alloy addition. The Mg addition increases the d spacing significantly, since the precipitate contains approximately 20 at% Mg and the Mg atom is about '12% larger than the Ag atoms. The Cu additions on the other hand decrease the d spacing only slightly although the Cu atom is 10% smaller than the Ag and Al atoms. This is because the 7 phase contains less than 4% Cu. These variations are in reasonable agreement with the experimental data with the ternary Cu alloy having a slightly lower d spacing than the binary and the ternary Mg alloy having a slightly larger value. However the absolute values of d spacing are somewhat in error presumably because of the simple random solution model used to approximate the structure of the 1 precipitate. 68 4.4 Discussion The Cu and Mg ternary additions have been shown to be significant in altering the shape of the 7 precipitates as well as the precipitate lattice parameter and also the degree of misfit between the matrix and precipitate phases. The X-ray diffraction measurements of lattice parameter as well as the electron probe results have clearly shown that the Mg and Cu atoms partition differently between the precipitate and matrix phases. Nearly 70% of the Mg atoms go into the precipitate phase. The Mg atom is about 12% larger than the Ag atoms of the Ag-rich Ag2Al phase and hence the large Mg concentration in this phase significantly distorts the lattice. This distortion results in an increased mismatch between the matrix and the precipitate, which in turn relaxes the strong crystallographic features of the Ag2Al plates. Plates of the ternary Mg alloy therefore form as rounded hexagons rather than as perfectly shaped hexagons. The misfit associated with the ternary Cu alloys is lower than with the binary system and so correspondingly the plates tended to form as perfect hexagons. These Findings therefore establish a dependence of the shape of the 7 plates on lattice mismatch. Increasing Cu concentration was observed to have very little effect on the plate shapes as well as on the overall precipitate microstructure. This observation enables us to limit further study of the ternary Cu alloys to just the high Cu content alloy. 5. INTERFACE STRUCTURE OF EQUILIBRATED ALLOYS This chapter is concerned with observations of the interface 4 dislocation structure in alloys fully equilibrated for 1.44 x 10 s at 418 C. 5.1 Description of Equilibrium Interfacial Structure 5.1.1 Binary Alloy Fig. 14 shows the misfit dislocation structures at the broadfaces of equilibrated plates in the binary system. The interface consists of a linear dislocation array running parallel to a/2\110-l. This structure was found on nearly all plates examined. The arrays were of considerable regularity and were normally inclined to the plate edge intersecting the foil surface. Dislocations on the opposite faces of the plates generally showed a strong tendency to align vertically or to stay slightly displaced along the entire length of the precipitate, Fig. 15. It was often possible to distinguish between top and bottom dislocations on the basis of contrast differences. Ta. Jes of dislocations were occasionally seen on the broadface of the plates. These either covered the entire surface or were present on sections of the plates, in which case the remaining areas were covered by regular arrays, ln every case plates showed some kind of dislocation structure, typically an arrayed structure and in some few cases there was a combination of arrays and tangles, Fig. 16. A sample result of the contrast analysis to determine the Burgers 69 70 Figure 15. Misfit dislocations at opposite faces of the broadface. Figure 16. Dislocation tangles at the broadface of precipitates. 73 vector is presented in a series of dark field micrographs in Fig. 17(a). This analysis was carried out on the regular dislocation structure. Strong contrast shows for g=(022), (202), (220) and no contrast for g=(311) and (111). The dislocations exhibit double images when g = (022) as shown in Fig. 17(b), taken on a different plate within the same grain. Such double images were more pronounced under exact two beam conditions. Table 6 is a summary of the Burgers vector analysis which shows b = a/2[0ll]. Table 6. Table of Contrast Analysis of Precipitate. \ b a/2[110] a/2[ll0] a/2[101] a/2[10l] a/2[011] a/2[0ll] Zone g \ Axis 202 1 1 0 2 1 1 [111] 022 1 1 1 1 0 2 [111] 220 0 2 1 1 1 1 [111] 111 0 1 1 0 0 1 [121]' 311 1 2 1 2 1 0 [121] 111 0 1 0 1 1 0 [211] In order to unambigously determine the Burgers vector, b, it was also necessary to satisfy the condition that g\n =0, where rT is the unit vector normal to the slip plane. Trace Figure 17(a). Contrast analysis of a/2\011J misfit dislocations. Figure 17(b). Contrast analysis using \022J reflection (a) s < 0 (b) s = 0 (c) s > 0. 76 analysis was carried out to obtain the planes on which the dislocations lay and from this the dislocation line direction could be determined. The line direction of the dislocations in Fig. 17(a) was near \022J . The basic misfit dislocations are therefore of the a/2<110> edge type. These lie in <110> directions normally inclined to the plate edge intersecting the foil, but only occasionally veer from edge to a mixed orientation. Dislocations with mixed orientations are less efficient in misfit compensation since they have a component of Burgers vector perpendicular to the interface plane. Nearly all precipitates observed were sectioned to varying degrees during thinning. It was therefore necessary to investigate whether the intersection of plate edges with the foil surface in any way altered the observed structures. It was fortunate that a few precipitates were found which lay wholly within the foil. This occurred when the foil normal was coincident with a Ul zone axis. By comparing these precipitates with the sectioned precipitates, any effects of edge intersection could be studied. Fig. 18 shows one precipitate lying wholly in the foil. The overall dislocation distribution seems complex. The dislocation structure however is basically the same as observed for the sectioned plates and consists of linear dislocation arrays. All dislocations exhibit b=a/2<110> contrast behaviour. Several groups of dislocations could be identified. Such groups consist of arrays of large numbers of single unit dislocations as shown in the enlarged image of Fig. 19(a). Groups of dislocations continuously branch off into other <110> directions, Fig. 19(b). In the process of branching some arrays appear to deviate from exact <110> directions. The branching dislocations appear to outline regions free of dislocations. 77 Figure 18. Fully embedded precipitate showing arrays of misfit dislocations together with corresponding diffraction pattern. 78 Figure 19(a). Enlarged section of Fig 18 showing details of array. Figure 19(b.c). Enlarged sections of Fig 18 showing details of array. 80 The dislocation contrast varied within a given group. In particular the dislocations immediately adjacent to the dislocation-free areas showed the strongest contrast effects, Fig. 19(b). The strong contrast is characteristic of an aggregate of single dislocations. The rest of the dislocations within a particular group were of uniform contrast and their spacing was also uniform. The sparing of the aggregate of dislocations on the other hand was quite large and uneven, Fig. 19(c). Several fine dislocation loops were observed at regions immediately adjacent to the dislocation-free areas. These loops were much clearer in the ternary Cu system and so will be discussed in the next section. The loops appear to interact with the aggregate of dislocations. The dislocation-free regions were always removed from the precipitate edges and were randomly located on the precipitate broadface. The dislocations appear to have been nucleated in groups at plate edges and to have glided across the broadface. In the process of gliding, portions of the set meander into other <110> directions probably due to stress field interactions from other dislocation groups. The glide process appears to be arrested by the fine dislocation loops since the loops are usually associated with dislocations immediately adjacent to the dislocation-free regions. It may be envisaged that it is the interaction between the loops and the dislocations which prevents the arrays from gliding into the dislocation-free regions. The spacing of the dislocation arrays apart from the dislocation aggregates on the embedded plates was comparable to the spacing of arrays on the sectioned plates. The effect of plate sectioning as a result of the thinning process may therefore not be too significant The common array configuration and spacing characterizing both the sectioned and embedded plates allows the use of the dislocation spacing obtained from sectioned plates for misfit analysis. It also indicates that minimal dislocation 81 rearrangement occurs as a result of thinning during sample preparation. The primary misfit type of dislocation on the broadface are the linear arrays and since these are largely in edge orientation they are also efficient misfit compensators. The regions free of dislocations are likely to be coherent and hence the misfit there is accommodated by lattice strain. In a study of the interfacial structures of 1 plates in an 29 Al-4.2 at% Ag alloy, Laird and Aaronson observed three types of dislocation configuration at the precipitate broadface. The dislocation arrangements included a single array comprising the same Burgers vector, and a hexagonal array of dislocations with three different Burgers vectors. The various configurations were predominantly made up of a/6<112> Shockley partials in principally edge orientation. Howe et al^ "* in a similar study on the T phase of the same system, commonly observed a/6<112> type misfit dislocations as well as a/2<110> unit dislocations, which were much less common. However neither of the two types of dislocations were configured in any definite way. The linear array of unit dislocations observed in the present study-is therefore different from these two previous studies. The difference in the observed structures may be related to the manner of sample preparation in the case of Laird and Aaronson's work. The thin foils used for their study were epitaxially grown and aged in-situ at 350 C and 400 C. Specimens for the present study on the other hand were bulk aged prior to thinning at a slightly higher temperaure of 418 C. The present work is therefore characteristic of the interface structure of the hexagonal plates obtained by nucleation and growth. 82 5.1.2 Ternary Cu alloy The linear dislocation arrays in the ternary Cu system, Fig. 20, were found to be of the same type, i.e., b=a/2<110>, and distribution as those observed in the binary alloy. Comparison of Fig. 20 and Fig. 18 shows the close correspondence between the two structures. In addition to the linear array a large number of dislocation loops were present in the ternary Cu alloy, within both the matrix and precipitate phases. Loops were generally distributed in a random fashion and were oriented in <110> directions. The characteristic "line-of-no-contrast" behaviour of these loops indicate edge dislocations where the extra half plane is normal to the electron beam and b* is parallel to it Individual dislocation lines in the array seem to break up on interacting with the loops but in general neither the dislocation line direction nor the spacing were altered, Fig. 20. It should be emphasized that such loops were seldom observed in the binary alloy. The specific origin of these loops is not certain although they are likely to have formed from vacancy condensation. They are similar to the loops 94 found by of Noble et al in the Al-Cu system. They showed that in the presence of ternary elements, vacancies in the quenched alloy condense to form a fine distribution of vacancy loops. It was found that in a number of plates in the ternary Cu alloy, dislocations parallel to the plate edge embedded in the foil coexisted with the regular array. In cases where the geometry of the plates was not rectangular the array of dislocations conformed to the plate curvature, Fig. 21. The same was true for defects like holes in the plates. Dislocations remained arrayed while conforming to all such morphologies. The other less common features observed in this system, particularly Figure 20. Misfit dislocation array in the ternary Cu system. Figure 21. Dislocation array conforming to plate curvature. 85 dislocation tangles, were similar to those already described for the binary alloy. The process of dislocation nucleation at the plate edge. Fig. 22, and final dislocation distribution across the broadface were also very similar to those of the binary system, as seen in a fully embedded precipitate. The regions free of dislocation arrays in this case however have a regular distribution of dislocation loops, Fig. 23, which were confined to the areas bordering the dislocation free regions. The dislocation loops were seldom observed within the dislocation arrays. The loops were generally aligned in <110> directions. However, the loops in the vicinity of the dislocation-free regions of Fig. 23 were always aligned perpendicular to the adjoining dislocation array. This strong preference of the loops for a specific orientation particularly near the dislocation-free regions indicates that there exist some interaction between the large strain fields at these regions and the dislocation loops. The alignment of the loops is probably an attempt to relieve strain more efficiently. Sectioned plates lying on top of the fully embedded plate in Fig. 22 appear as needles with a strong contrast effect 5.1.3 Ternary Mg alloy The dislocation structure found for precipitates of this alloy was very different from that discussed for the binary and the ternary Cu alloys. The interface structure of these plates consists of arrays of dislocation loops or spirals enveloping the particles as shown in Fig. 24(a). This structure was found in all plates and only slight variations in periodicity exist from plate to plate. For a given plate the array spacing was nearly constant across the entire broadface as well as on the precipitate edges. Identical structures were observed on plates wholly embedded in the matrix and on 86 Figure 22. Misfit dislocation structures at the broadface of a fully emdedded plate in the ternary Cu system. Figure 23. Enlargement of a section of Fig. 22 showing dislocation loops. 88 Figure 24. Misfit dislocation structures in ternary Mg alloy showing one set of partials. (a) full plate (b) enlargement of a section of (a). 89 sectioned plates, indicating the universality of the structure. Loops were always aligned in <110> directions and always showed dotted contrast, i.e., the dislocation line consisted of alternating fine dark and bright spots rather than having a uniform contrast, Fig. 24(b). Images of the dislocation from the top and bottom halves of the precipitate generally overlapped except for areas close to the precipitate edges where the pair was resolvable. Plate distortions, particularly the effects of convexity, seemed to alter the array spacing and direction. The effect was particularly pronounced near the edges of some plates and shows as a reduction in dislocation spacing or as a slight change of dislocation line direction in comparison with the structure at the plate centre. The dislocation images appear to be associated with Moire' fringes. Strong image contrast occurred only for certain reflections, specifically those for which matrix and precipitate spots were coincident Other characteristic parallel Moire' fringe behaviour was also evident For example, the direction of the fringes was nearly always normal to the operating diffraction vector, g, and the direction of the fringe pattern always changed so as to satisfy this condition. In fact dislocation contrast was visible only for 220 / / 1120 reflections. The strong Moire' fringe contrast and the limited diffraction conditions for imaging die dislocations made it impossible to carry out the conventional Burgers vector analysis based on the g*.b*=0 invisibility criterion. The dislocation contrast was best enhanced when kinematic diffracting conditions prevailed, Fig. 25(a). However under dynamical conditions the Moire' fringe contrast seemed to predominate. In certain cases, about 1 specimen tilt from the exact two-beam condition to change the deviation parameter, s, produced a transition, from Moire' fringe to a dislocation structure, Fig. 25(b). Attempts to use the weak beam dark field imaging technique to improve resolution of the interfacial dislocations proved unsuccessful mainly because of the extremely low 90 Figure 25. Interface structure imaged under different diffracting conditions, (a) dislocations (b) Moire' fringes. 91 contrast associated with the images. Pumphrey and Edington^ have made somewhat similar observations on the interface structure of grain boundary nucleated MJ3C« precipitates and were able to distinguish the observed dislocation network from Moire' fringes on the basis of 107 prevailing diffracting conditions. The work of Tholen may also be related to the present findings. Tholen concludes that Moire' fringes and dislocation arrays are indistinguishable for dislocation spacings less than 1/3 the extinction distance^  ). Hirsch et a l ^ have given v a m e s 0I" 155Afor Al and 535Afor Ag. Applying Tholen's 0.3(^ ) criteria to the weighted value for Ag2Al gives a critical extinction distance of 260A. This is much greater than the measured 150A spacing indicating that the dislocations will be quite hard to image in this system. This may perhaps be responsible for the strong Moire' fringe contrast always present in this alloy system under two-beam conditions. The 108 work of Pollard and Nutting on 6' in an Al-4%Cu alloy and the work of Sankaran 32 and Laird on 7j plates in an Al-0.2%Au alloy also showed similar interfacial dislocation structures. Another contrast effect associated with the interface was dislocation loops wrapped around the precipitates. These were not commonly observed. A maximum of three such loops were present on a plate and they were totally absent for most plates. Fig. 26 shows fringes perpendicular to the operating (022) reflection and the loops which lie in the \220J direction. Loops lie in the habit plane of the precipitate and have Burgers vector of the type a/2<110> since they are invisible for g=(lll) and g=(113) and show double images for g=(220). Further, the dislocation images remain the same on changing the value of the operating reflection from g=(220) to g=(220) for 92 Figure 26. Dislocation loops at the broadface of a plate in the ternary Mg system. 93 s>0 indicating that the double images result from dislocations from either side of the precipitate. No direct interaction is apparent between these loops and the network of Shockley partials. The hexagonal network of a/6<112> misfit dislocations on both the broadface and precipitate edge are efficient misfit compensators. It is not exactly clear how the network is generated but it may likely involve the plate edges as nucleation points in a similar fashion to the binary and ternary Cu alloys. The dislocation loops present at the interface do not seem to be involved in misfit compensation. 5.2 Intersecting Plates The effect of intersecting plates on the dislocation array is discussed in this section. Fig. 27(a) shows two plates lying in the (111) plane and joined end-to-end in a ternary Cu alloy. Only the butting edge of the second plate shows in Fig. 27(a) and has a darker contrast. Three distinct groups of dislocations are identifiable. The basic array of a/2<110> type dislocations characteristic of all precipitates are parallel to the plate edge and run along its entire length. A second set of a/2<110> dislocations emanate from the intersecting edge and can be described as intruder dislocations. These dislocations are not confined to the interface although they seem to have been nucleated from the butting edge of the second plate and are seen to be continuous from the interface to the matrix. The dislocations are separately imaged in Fig. 27(b,c) The third type of dislocation was identified as a/6<112> Shockley partials. Stacking fault contrast along the length of the precipitate resulting from this group of dislocations is shown in Fig. 27(d). The partials were present only on intersecting plates 94 Figure 27. Interfacial dislocations originating from intersecting plates (a) intersecting plates (b) linear array. 95 Figure 27. Interfacial dislocations originating from intersecting plates (c) dark field image of intruder dislocations (d) partial dislocations 96 and were not observed on isolated plates. The partials were also associated with fine dislocation loops which perhaps tend to inhibit dislocation glide. The lack of interaction between the partials and the other two types of dislocations i.e., the linear array and the intruder dislocations, indicates that the different types of dislocations may possibly lie on different 111 planes. No fringe reversals were observed to confirm this view. It is evident that both the Shockley partials and intruder dislocations have been nucleated at the intersecting point of the plates, since the plate edge severely distorts the matrix lattice adjacent to it The resulting stress field generates the intruder dislocations. Such dislocations were also observed occasionally in the matrix phase around isolated plate edges again presumably because of the high stress field 5.3 Overaged Alloys Interfacial structures obtained from specimens aged for 3.6 x 10^  s 4 were compared with the regularly aged samples, which had been aged for 1.44 x 10 s. Fewer precipitates were available for observation due to coarsening effects and in almost all cases precipitates were too thick to show any noticeable contrast effects at their interfaces. The microstructure of one of the few precipitates showing contrast effects is shown in Fig. 28(a) for the binary alloy. The nature and type of dislocations on the broadface for the two ageing times are identical and the spacings are also of the same order. Only a few micrographs could be obtained and so it was not possible to carry out a statistical comparison of dislocation spacings. It is however apparent that prolonged ageing has no significant effect on the identity and distribution of misfit structures present Figure 28. Interfacial structure of sample aged at 418 C for 3.6 x 10 s in (a) binary system (b) ternary Mg system. 98 at the broadface. A similar observation has been made by Laird and Aaronson in their study of 7 plates aged at slightly lower temperatures. The equivalent structures for the ternary Cu alloy were very much the same as those of the binary system. The analysis of the ternary Mg alloys aged for longer times also gave identical boundary structures to the regularly aged samples. Fig. 28(b) is a representative micrograph of a prolonged aged ternary Mg alloy. 5.4 Misfit Determination - Dislocation Spacing A linear dislocation array of a/2<110> edge dislocations accommodates misfit on all plates observed in the equilibrated binary systems. The array spacings were found to be quite regular and independent of plate size. A number of measurements of dislocation spacing were made on different plates in the same specimen. The mean dislocation spacing was found for arrays made up of at least eight dislocations and having the same Burgers vector. The variation in spacing in a given array was usually less than 5%. In measuring the spacings, care was taken to include dislocations from only one surface. This condition was easily met for most plates since dislocations from the top and bottom faces were usually found to be aligned vertically on top of each other or the two sets of dislocations were slightly displaced one from another. Measurements were normally carried out on a readily accessible low index orientation although this was limited to one of the following orientations:- 100 , 110 , 111 and 112 for the sake of convenience in subsequent analysis. The regular array was characteristic of over 85% of all plates observed. 99 The actual dislocation spacing (D^ ) was obtained from the observed spacing (DQ) and the angle 0, which is the angle between the normal to the plane of observation and the Burgers vector characteristic of the array. The relation between the two spacings is given by the equation: D d = DQ sintf> 5.1 The calculated values of the actual spacing , , based on several measurements on different grains in different samples are listed on Table 7, together with the standard deviation. Table 7. Calculated Misfit from Dislocation Spacing. Number Dislocation Calculated of Plates 0 Spacing (A) Mismatch (S)% Binary 39 547±132 0.5210.19 Ternary Mg 24 150± 15 1.09±0.12 Ternary Cu-I 38 691± 127 0.41±0.17 Ternary Cu-II 32 554±140 0.52±0.19 Ternary Cu-III 51 464±96 0.62+0.18 The misfit parameter (6) was obtained from Brooks relation given as: 8 = |b |/(Dd) 100 5.2 where, |b | is the magnitude of the Burgers vector of the dislocations, and is the actual dislocation spacing. The Burgers vector used in Eqn. 5.2 was b=a/2<110> for the binary and the ternary Cu alloys and b=a/6<112> for the ternary Mg alloy. The misfit values so determined are shown in Table 7. 5.5 Misfit Determination - Moire* fringe Spacing Moire' fringe contrast has been widely used to determine misfit at interphase boundaries. The fringe spacing is normally unaffected by anomalous absorption effects and hence by small thickness or orientation changes. As already discussed in Section 3.3.2, care has to be taken to distinguish between MoiTe' fringes and dislocations. In the case of the 7-Ag2Al, only parallel Moire' fringe types were present and this was confirmed by the selected area diffraction patterns obtained from these precipitates. The direction of g from the selected area diffraction patterns was nearly always normal to the corresponding fringes. The extent of deviation observed was less than 3 . Distinguishing between dislocations and Moire' fringes was often difficult in the case of the Mg alloy. It appeared that the two patterns were often superimposed but at exact two-beam dynamical conditions the images observed were typical of Moire' fringes. Therefore virtually all images used for Moire' fringe analysis 101 were taken under two-beam dynamical conditions. Fringe spacings were obtained perpendicular to the fringe direction from plates which showed relatively strong fringe contrast and only for fringes resulting from the <220>a//<1120>7 reflections. Spacings were measured directly from micrographs and the results are shown in Table 8. Table 8. Lattice Mismatch Results. Alloy Moire' Fringe 0 Spacing(A) Calculated Mismatch(5)% Moire' Fringe Spacing Dislocation Spacing X-ray Diffractometer Binary 198145 0.7310.14 0.5210.19 0.7610.13 Ternary Mg 150115 1.0910.12 1.0910.12 1.11+0.17 Ternary Cu-III 315+36 0.4510.11 0.62+0.18 0.4210.16 The degree of misfit (6) was subsequently calculated from the relation: 6 = d/D - 5.3 m where. d is the lattice plane spacing of the operating reciprocal • lattice vector, and D is the measured fringe spacing. 102 The calculated misfit values are also shown on Table 8, together with misfit results using the other techniques. 5.6 Correlation of Misfit Values It is now possible to compare misfit values obtained from the X-ray diffraction, dislocation spacing and Moire' fringe spacing measurements for all three alloys. Results of the X-ray diffractometer measurements discussed in Section 4.3 and those from the Moire' fringe spacing are quite consistent The correlation plot of Fig. 29 shows the results of the two techniques to be in good agreement with each other. The misfit values obtained from dislocation spacing for the ternary Cu alloys appear to remain constant with increasing Cu content within experimental error, Fig. 30. In the case of the binary alloy the misfit calculated from dislocation spacing was 0.52%, 33% less than the values obtained by the other two techniques. For the case of the ternary Mg alloy the mismatch was comparable for all three techniques. 5.7 Discussion The linear array of misfit dislocations observed in the binary and ternary Cu systems is not an equilibrium configuration. The misfit in these systems is more efficiently compensated by network structures comprised of either two or three dislocations as discussed in Chapter 2. The observed spacing of the unit dislocations is also not consistent with expected spacings. In particular the mean spacing of the binary 103 Figure 29. Correlation plot for misfit determined from X-ray and Moire' fringe data. 104 1000 • —< a (n fl o CC o o Q 800H B r -e c o n 400H 200 0.0 0.2 0.4 0.6 Cu i n a l l o y 0.8 a t % Figure 30. Plot of dislocation spacing vs at% Cu in alloy. 105 system is larger than predicted and the spacings in the ternary Cu system are generally smaller than the equilibrium spacing for the unit dislocations. The non-equilibrium linear array was also observed on plates embedded in the foil in both the binary and ternary Cu systems. The spacing of these dislocations was identical to the spacings observed on the sectioned plates. The arrays on the embedded plates were confined to the plate edges, however, and there were no dislocations at the plate center. This implies that the plates are under high elastic strain and are therefore far from equilbrium. Failure to attain equilibrium appears to be due to the difficulty in nucleating dislocations. Dislocations initially nucleated at the highly stressed plate edges as observed in these systems would require other dislocations to interact with in order to transform to the expected equilibrium structures. Part of the misfit in these systems must be accommodated elastically. The hexagonal dislocation structure observed in the ternary Mg alloy is an equilibrium configuration and has spacing close to the expected value from the X-ray diffractometer measurements. It appears dislocations are more readily nucleated in this system possibly because of higher stresses due to the large misfit 6. DISSOLUTION STUDIES 6.1 Morphological Changes During Dissolution. The morphological changes during dissolution of the precipitates were studied in samples aged in the bulk prior to thinning. STEM micrographs were obtained from the same area of the thin sample for selected plates after each dissolution run until the precipitate was completely dissolved. The dissolution process was carried out in a tube furnace at 450 C. Fig. 31 shows STEM images of a dissolution sequence in the binary system. (The black spot at the centre of the precipitate is due to an impurity.) Micrographs obtained for the ternary Cu system followed the same pattern as the binary alloy. The plate corners were generally observed to dissolve at a faster rate than the edges, and the edges in turn dissolved faster than the broadface. It seemed that plates with relatively small aspect ratios, i.e., small length/thickness ratios, tended to dissolve more slowly, and the corresponding morphological changes appeared to be more gradual. Even under these circumstances the higher dissolution rates at the plate corners relative to the edges still remained. The initially sharp plate corners became progressively rounded whilst retaining the hexagonal morphology. However the basic hexagonal morphology seems to have been retained right to the end of dissolution. The plate edges thus remained essentially aligned to their respective <110> directions throughout dissolution with all six sides exhibiting uniform dissolution rates. 106 107 t = 19 mins t = 14 mins Figure 31. Shape changes during plate dissolution. 108 The rounded hexagon morphology of precipitates in the ternary Mg system changed in a somewhat similar fashion to the binary and ternary Cu systems during the course of the dissolution process. The plates became more circular as dissolution progressed. The precipitate shapes at the later stages of dissolution in the ternary Mg system were essentially circular and quite different from the starting morphology whereas in the binary and ternary Cu systems the morphology was retained nearly throughout the dissolution process, and not until the very last stages of dissolution did a disc shape evolve. The sequence of shape change appears to be essentially independent of the alloy system and hence of the starting precipitate morphology. The enhanced diffusion at plate corners is clearly a result of the point effect of diffusion. This result confirms earlier work carried out by the author on the morphological changes 82 of 7-Ag2AJ plates during dissolution at several different temperatures. It was demonstrated then that the point effect of diffusion was the dominant factor in dictating the morphological changes during dissolution of these plates. 6.2 Dislocation Structure at the Phase Interface 6.2.1 Broadface Structure (i) Binary Alloy An extremely uniform hexagonal network of dislocations was observed on the broadface of the precipitates during dissolution. This structure was present in all regions of the plate showing dislocation contrast and generally covered the entire 109 broadface. Other types of dislocation configuration were only rarely observed. Fig. 32 shows a sectioned plate uniformly covered by the network structure. An enlarged view of a single set of the dislocations is shown in Fig. 33. Networks were observed to be extremely regular in all cases and the spacing between corresponding sets of dislocations on different plates was virtually constant Imaging the network structure often proved difficult since it tended to be obscured by strong Moire' fringe contrast effects. The masking effect of Moire' fringes was particularly pronounced whenever <1120> precipitate and <220> matrix reflections were operative. Fig. 34(a,b,c) shows Moire' fringe patterns for all three 220 reflections of a <111> zone axis orientation. The corresponding dislocation network structure is shown in Fig. 34(d). The network structure consists basically of three sets of equivalent Shockley partial dislocations having their Burgers vectors at 120 to each other. Fig. 35 is a high magnification micrograph and shows one set of dislocations which consists of extended nodes alternating with contracted nodes. The extended nodes are proof of the existence of stacking faults and demonstrates that the network is indeed made up of partials. Fig 36 is taken at a lower magnification and shows the three sets of dislocations. All three sets have the same node structure as shown in Fig. 36. The nodes occur at the same location in all the micrographs, Point A, foT example, shows the corresponding position of an extended node for all three sets. The dislocations were always aligned in <110> directions. Their extreme periodicity is particularly worth noting. The above characteristics in addition to contrast analysis showed the Burgers vector to be of the a/6<112> type and in predominantly edge orientation. The probability of the network consisting of a unit and two partial dislocations was eliminated on the basis of the equivalence in the contrast features of the three sets of dislocations comprising the Figure 32. Section of 1 precipitate entirely covered by a hexagonal dislocation network. Specimen dissolved at 450 C for 240 s I l l Figure 34. Micrographs showing the effect of changing diffracting conditions on interface structure; (a,b,c) Moire' fringes and (d) dislocation network. 113 114 Figure 36, Schematic drawings and micrographs separately showing all three sets of dislocations of the network structure. 115 network. The nodes at the network also satisfy the condition that lb =0 It was possible to follow the changes in dislocation structure throughout the process of dissolution by observing the structure present at different dissolution times. For this study, bulk samples were aged and solution treated for various times prior to thinning. The initial dissolution stages were found to be the most informative. No appreciable structural changes could be observed after the initial moments of dissolution. Once the network structure was formed, it remained till the end of the dissolution process. It should be recalled that a linear array of unit dislocations was present in the aged samples before dissolution. At the onset of dissolution only a fraction of the broadface had the complete network structure. This can be seen in Fig. 37 for a plate dissolved for 120 s at 450 C. The region close to the lower right hand corner region of the micrograph has been covered by a network structure but the area above that still has a linear array which is characteristic of the equilibrated alloy. The linear array was similar in spacing and Burgers vector to the lineaT array structure observed prior to dissolution. This strongly suggests a transition from the original linear array to the network structure. The transition incorporates a new set of dislocations seen in Fig. 37 as the unevenly spaced dislocations running transverse to the linear array and labelled B. These dislocations show contrast effects characteristic of a/2<110> dislocations. The dislocations also demarcate the region covered by the prior linear array and the transformed section comprising the hexagonal network structures. Fig. 38 is an enlarged section of Fig. 37, clearly showing the two separate regions. It is the interaction between the newly nucleated dislocations and the original dislocations that gives rise to the hexagonal structure. This network structure progressively spreads out until the entire precipitate surface is covered and this structure remains until total dissolution of the 116 Intersected array original array position' Intersecting array (B) Intersecting array (B) Intersected array displaced Hexagonal network Figure 37. Micrograph and schematic drawings of interface dislocation structure at the onset of dissolution. 117 Figure 38. Enlarged section of micrograph in Fig. 37 118 precipitates. The observation that the transition to the network structure is initially localised near plate edges coupled to the fact that the number of newly nucleated intersecting dislocations is high close to the edge of the plate suggest that this is a nucleation site. However, it is also possible for the intersecting dislocations to be direcdy adsorbed from the matrix or precipitate phases from suitably intersecting glide planes. The driving force for such a climb mechanism would be provided by the elastic interaction between the strain fields at the interphase boundary and the intersecting dislocations. The sequence of interaction may be envisaged to proceed in the manner shown in Fig. 39. Once the intersecting dislocation (pq) interacts with the existing linear dislocation array (qr), the latter becomes displaced in the direction of the interacting dislocations (pq). This interaction results in the formation of short segments of dislocations (pr). Such displacements were observed only for isolated intersecting dislocations, usually ahead of the network region. The three resulting dislocations then transform to the equilibrium configuration as shown in Fig. 40. This is due to the line tension acting at the triple points. The dislocation segments may then dissociate to form a network of partials. Certain characteristics of the intersecting dislocations were of particular interest The initial displacement to form the short dislocation segments described above was absent for a couple of the intersecting dislocations. It is assumed that these are yet to interact More important is the contrast effects such dislocations exhibit The contrast of the dislocation is reversed when the operating diffraction vector, g , is changed Figure 39. Micrographs and schematic drawings showing the development of the network structure. Figure 40. Enlarged micrograph showing intersecting dislocations. Figure 41. Contrast reversal of dislocations on changing operating reflection from, +g to -g. 121 from positive to negative or vice-versa as shown in Fig. 41. Such contrast behaviour is 45 typical only of ledges, as shown by Weatherly and Sargent. For the present case it is characteristic only of the intersecting and not the intersected dislocations. The intersecting dislocations are therefore likely to be associated with ledges. Displacement fringes were also observed to be slightly displaced upon intersecting these dislocations. These can be used to determine the height of a ledge. In the present case it was not possible to perform a proper analysis on these dislocation/ledges in order to estimate the ledge height as would have been desired. This is because even the few images of displacement fringes observed on the plates were poor. A rather conservative estimate of the height of the intersecting dislocation in Fig. 42 yielded a value of the order of tens of As. Close observation of the network structure in Fig. 43 reveals another characteristic feature of these structures. Part of the structure shows highly regular hexagons of approximately 220A spacing. This is the region towards the plate edge, i.e., the left-hand comer of the micrograph. As the network structure advances into the plate the spacing of the network component coincident with the intersecting dislocation/ledges becomes progressively larger. Specifically the spacing increments are observed to be in approximate multiples of 2, Fig. 43. The network spacing immediately above the 220A region has an approximate 400A spacing and beyond, a spacing of nearly 900A. Further, the wider the spacing the stronger the contrast associated with the dislocation/ledges. Such contrast effects suggest that the dislocation/ledge height is directly proportional to its spacing and hence the dislocation/ledge height may also be in specific multiples in a similar fashion as the observed multiples in the spacings. It is possible from the above observations, to infer a probable 123 Figure 42. Intersection of displacement fringes and dislocations. 124 Figure 43. Micrographs and schematic drawings of details of the network structure. 125 mechanism underlying dissolution of the precipitates. Foremost, it has to be pointed out that a single mechanism is responsible for the entire dissolution process. This is on the basis of the constancy of the dislocation network structure throughout dissolution with the exception of the very initial stages i.e., prior to the complete formation of the network structure. For the same reason, the a/6<112> Shockley partials are most likely involved in the dissolution process. (ii) Ternary Cu alloy The close identity between the microstructure and interface structures of the ternary Cu alloy and the binary system was found once again during precipitate dissolution. A hexagonal dislocation network consisting of Shockley partials forms on the plates at the onset of dissolution and remains till total dissolution in the same manner as described in the preceding section for the binary system. The conditions and difficulties associated with imaging the network of dislocations as well as their detailed characteristics previously described for the binary alloy were found to be the same for the ternary Cu system. (iii) Ternary Mg. alloy The network structure observed in this system prior to dissolution is identical to the structures of the binary and ternary Cu alloys during dissolution and consists of three equivalent a/6<112> Shockley partials. The hexagonal network structure in the ternary Mg alloy is much finer however. No change in this basic structure was observed during dissolution and it persisted until total dissolution. Despite the stability of the network structure at the interphase boundary a whole new set of unit dislocations 126 also become associated with the boundary as a result of the dissolution process.As discussed in Section 5.1.3. a maximum of three such loops were present on a plate prior to dissolution. Micrographs taken at the earliest stages of dissolution show only a few such dislocations but the number increased progressively with dissolution time. Fig. 44(a) shows the structure at the onset of dissolution while Fig. 44(b) taken at a later stage shows the interface to be completely covered with the dislocations. These dislocations are actually loops, perhaps in a dipole configuration, wrapped around the plates, with only a slight displacement between the top and bottom halves of the loop in most cases. A close look at the plate edges shows details of the dipole loops contouring the edge, Fig. 45. Also for a given plate all the loops had a tendency to lie along a specific <110> direction. The spacing between individual loops was observed to be rather irregular on any given plate. The contrast of the loops was quite uniform with only a slight variation between the top and bottom arms of the loops. Contrast analysis yielded Burgers vectors of the type b~= a/2<110>. Attempts were made to simultaneously image the loops and the hexagonal network structure. The latter by itself was quite difficult to image being regularly obscured by Moire' fringes. Fig. 46 shows a dark field image of one set of partial dislocations interacting with the parallel set of loops. The fact that the dislocation line direction of the partials appears displaced by the loops suggests that these loops are in fact associated with the precipitate-matrix interface. The origin of the loops is likely to be die matrix phase. Such dislocations can readily be adsorbed from the matrix through a climb process as a result of the elastic interaction between the strain fields of the precipitate and the dislocation. The high stress concentration at the plate edge is also 127 Figure 44. Interface boundary structure (a) before and (b) during dissolution in ternary Mg alloy. (Loops : arrowhead) 128 Figure 46. Dark field image of one set of partial dislocations interacting with dislocation loops (arrow-heads) 130 a probable nucleation source for the dislocations. Had the dislocations been nucleated by other known mechanisms, in particular by vacancy loop generation, the corresponding interstitial loops ought also to have been present in the matrix ahead of the precipitate. They also appear to be randomly spaced across the interface but to have the same orientation. It also appears that these loops do not lie exactly in the interface place but close enough to have the effect of their stress field felt at the boundary and hence cause the observed interaction with the network structure. A close look particularly at the plate edges shows that the loops are at a distance away from the plate edge. That being the case, they would have no significant role in either accommodating misfit at the interface or be directly involved in the process of dissolution. The structural pattern of the Shockley partials at the interface and their role during dissolution in this system appear to be identical to those of the binary and ternary Cu systems. 6.2.2 Edge Structure In a few cases it was possible to tilt the 7 plates edge-on so that their edge structure could be examined. The basic dislocation structure was found to be the same as observed for the broadface, being made up of a hexagonal network structure, Fig. 47. In general the mesh size of the network was the same as the broadface but during the initial stages of dissolution the mesh size varied from point to point just as was observed for the broadface at the onset of dissolution. It also appears that the structure at the edge is continuous from the edge to the precipitate broadface. This implies that one single network envelopes the entire precipitate surface. No Burgers vector analysis was carried out on the edge structure because of the restrictions in stage tilting. However, the similarity of the two structures suggest that the edge also consists of three 131 132 sets of Shockley partials at 120 to each other. The entire length of the edge was found to be normally covered by the uniform network structure. 6.2.3 Growth Mechanism of 7 precipitates The results of a limited number of observations made on the dislocation structures on the 7 plates during growth will be discussed in this section. The study was undertaken to see if any significant differences exist between structures observed during dissolution and those occurring during growth. The dislocation configuration observed during growth of the 7 plates at 418 C in the present study was primarily the single array type. The arrays appear to have formed at plate corners or edges and they were usually confined to regions close to these areas. Fewer dislocations were observed in the central region of the plate in the case of arrays nucleated from plate corners, Fig. 48. However those arrays nucleated at plate edges were normally distributed across the entire surface (Fig. 49). The linear array was observed on nearly all plates, and was for the most part very regular. The mean spacing of the regular array was 390A. This spacing was nearly equal to the equilibrium spacing expected for unit a /2<110> dislocations. The contrast effect associated with these arrays suggest that they are probably a few hundred angstroms high. A hexagonal network structure was observed on a few precipitates, Fig. 50. The number of plates displaying the network structure was less than 1% of the total number of plates. The spacing of ledge/dislocations in the network were of the same order as the linear array. These results are in agreement with an earlier study of epitaxially 22 grown 7 plates in an Al-4.2 at% Ag alloy by Laird and Aaronson. Two categories of Figure 49. Linear array of ledge/dislocations at the broadface of plate during growth. 134 Figure 50. Hexagonal network structure of ledge/dislocations on the broadface of plate during growth. 135 dislocation configuration were observed in their study: 1. a hexagonal network with three coplanar Burgers vectors or a two dislocation network with the same kind of Burgers vector, and 2. a single parallel array of dislocations. The work of Laird and Aaronson is the most detailed study on the growth of the 1 plates. However the epitaxially grown thin foils used in their study may not be fully characteristic of bulk conditions. It was therefore necessary to carry out the present experiments on bulk grown precipitates to supplement their observations. The present growth results are in broad agreement with the other 109 75 previous studies of Hren and Thomas and of Howe et al, in particular regarding the presence of a linear array. It is shown here however that growth is accomplished solely by the non-equilibrium linear array rather than by the more stable network configuration as reported by others. The results presented in this section clearly demonstrate that the interphase structures prevalent during precipitate growth are quite different from those observed during dissolution. Growth is accomplished by a linear array of individual ledges which are usually a few hundred angstroms high. Precipitate dissolution on the other hand is achieved by a system of partial dislocations in a hexagonal network configuration. These partials are only a few angstroms high. The only time macroledges are found during dissolution is at the very beginning. These initial ledges are very similar to the ledges found during growth, the height of the ledges being comparable, and their Burgers vector also appearing to be the same. However unlike growth, these ledges break up into a network structure of Shockley partials aided by the existence of a prior array of dislocations which makes it energetically favourable. 136 6.2.4 Measurement of Dislocation Spacing During Dissolution The observed dislocation structures for samples solution treated at o 4 450 C for 1.44 x 10 s were used to determine the misfit during dissolution. The spacings of the dislocations were measured for all three alloys and the misfit was determined using Brooks relation. Details of the procedures involved in this study have already been outlined, see Section 5.3. The results are shown in Table 9. Table 9. Misfit During Dissolution from Dislocation Spacing Measurements. Dislocation 0 Spacing A Calculated Misfit 5% Expected Misfit 8% (Diffractometer) Binary 230 0.72 0.76 Ternary Mg 146 1.13 1.11 Ternary Cu-III 440 0.38 0.42 The network of Shockley partials present during dissolution in the binary and ternary Cu systems is different from the linear array of unit dislocations observed prior to dissolution. The dislocation spacing associated with the two structures is also significantly different The original unit dislocations upon dissociating into partials reduce their spacing by as much as 50% and 40% respectively for the binary and ternary 137 Cu systems. The change in spacing is toward compensating misfit more efficiently. The calculated misfit for the dissolution samples is therefore closer to the expected value particularly in the case of binary systems for which the misfit is within 10% of the expected value as opposed to 35% in the equilibrated alloy. In the binary and ternary Cu systems, the unit dislocations observed prior to dissolution transform to Shockley partials and the dislocation spacing is accordingly adjusted to give an equilibrium sparing. The network in the ternary Mg alloy remains virtually unchanged during dissolution. In general therefore the misfit values obtained during plate dissolution are much closer to their respective equilibrium values. This may be due to the nucleation of new dislocations and the relative ease with which dislocation glide can be accomplished during dissolution. 6.3 Discussion The interface structure has been found to be a stable hexagonal network present during the entire dissolution process except at the very beginning. The Shockley partials forming the network in all three systems have their respective sparing very close to the equilibrium value. In the case of the binary and ternary Cu systems the hexagonal structure appears to originate from interactions between a moving ledge and the prior existing linear array. This is shown schematically in Fig. 51. Fig. 51(a) shows the initial linear array. Ledges could be readily nucleated at the plate edge, Fig. 51(b), and would be similar to the ledges observed during growth. The ledge dissociates into microledges as it moves across the precipitate surface and correspondingly gradually reduces its height. Figs. 51(c,d) until it has swept across the entire surface. The spacings 138 of the microledges left in the trail of the moving ledge were either of unit dimensions or in multiples of 2. The height of the microledges initially appears to be proportional to the ledge spacing but the ledge height gradually becomes uniform and the ledge spacing becomes constant, Fig. 51(e,f). The microledges then interact with the existing linear array and subsequent dissociation of the product of interaction results in the observed network structure. The network structure prior to dissolution in the ternary Mg alloy remains essentially unchanged during dissolution. The extra dislocation loops which are observed during dissolution do not interfere significantly with the existing network structure. 139 Figure 51. Schematic illustration of probable mechanism of network formation. 140 i 7. DISSOLUTION KINETICS AND ELECTRON PROBE MICROANALYSIS Both thinning and shortening kinetics were measured in the present study with the intent of investigating the effect of varying misfit and interfacial structure on the dissolution kinetics of the 1 plates. Measurements were carried out on the SEM and also in the STEM. The STEM measurements were preferred to the SEM but proved quite difficult and time consuming to carry out and only limited results could be obtained with this technique. The basic advantage of using the STEM is that measurements could be carried out on plates wholly submerged in the matrix for the shortening kinetics and it was also easier to tilt specimens to observe the plates edge-on during thinning. STEM imaging was adopted for the verification of the SEM measurements rather than using TEM observations for two reasons. Firstly the thinner sections for TEM imaging were more prone to buckling and secondly by using the relatively thicker sections of up to hum for the STEM imaging, the effect of possible surface diffusion during dissolution was minimized. The results obtained from the SEM were characteristic of plates dissolving at the surface although as will be shown in the next section, comparison of the SEM and the STEM plots showed surface diffusion to be negligible. Measurements of thickness and length of individual plates as a function of dissolution time were obtained for a number of plates at a temperature of 450 C. Dissolution was carried out at progressively longer times with observations being made on the same precipitate. The difficulties associated with the STEM thickness measurements were a result of localized buckling of the sample during quenching. Since samples were quenched after each dissolution run, the orientation characteristics of the plates were 141 142 continuously altered and in this mode it was difficult to align the plates edge-on to the electron beam using the selected area diffraction pattern. Tilting to obtain minimum thickness by direct visual inspection often yielded inconsistent results. However, Considerable effort was made to obtain sample results for the purpose of verifying the SEM data and these have been included in the plots where appropriate. The use of thin foil sections in the STEM for kinetic measurements can be in error if the extent of the diffusion field adjacent to the plate is of the order of the foil thickness. This thin foil effect is negligible in the case of the shortening kinetics and was minimized for the thinning kinetics since plates selected for measurement were nearly always perpendicular to the foil surface. The shortening measurements on fully embedded plates were limited to plates which lay entirely in the matrix. 7.1 Kinetics Results 7.1.1 Thinning Results (i) Binary system Fig. 52 shows a result for the binary alloy plotted as half-thickness against time. It can be seen that the rate decreases with time but when the thickness is plotted against square root of time, a straight line is obtained, Fig. 53. Fig. 54 shows parabolic plots obtained from SEM and STEM measurements which demonstrates that the two measurements are comparable although the SEM data could be more readily obtained. K 0.034 ~\ 1 1 ! | 150 300 450 600 750 T I M E (t, s e c . ) 0.00-J-0 Figure 52. Plot of precipitate half-thickness vs rime. o.l6 0.00 I 1 0 8 12 18 24 30 SQRT-TIME (t, sec.) Figure 53. Parabolic plot of precipitate half-thickness vs time. Figure 54. Parabolic plot of precipitate half-thickness vs time for SEM and STEM data. 146 In general all the thinning results showed such parabolic behaviour with time, and the method of least squares was used to obtain dissolution rates. The mean rate for six —9 experiments was 1.60 ± 0.27 x 10 m/|/s. The linear relation obtained in Fig. 53 suggests that the precipitates dissolve according to the relation a/2 = o/t 7.1 where, a is the thickness of the plate, and a is the parabolic rate constant. In order to obtain a value for the diffusivity (D), the Dube-Zener analysis for the migration of a planar disordered boundary was employed. This yields a parabolic relationship between planar precipitate half-thickness (S) and time (t) i.e., 1/2 S = S -X(Dt) 7.2 where X is given by Eqn. 1.10. The value of the saturation obtained from the Al-Ag phase diagram is 0=0.034. Substituting the appropriate values in Eqn. 7.2 yields a mean -15 2 diffusivity value of 1.71 x 10 m /s. The corresponding literature diffusivity value for the diffusion of Ag in Al at 450 C is 7.15 x 10~1 4 m 2 / s . m The calculated diffusivity value is therefore over 40x slower than the literature value, which strongly suggests an interfacial barrier to atomic migration. 147 (ii) Ternary systems Thinning measurements were carried out for both the ternary Cu and ternary Mg alloys in a similar manner as described for the binary system. The kinetics of both systems follow a parabolic rate law. The mean thinning rates are shown in Table 10 together with the binary results. Table 10 also shows the diffusivities calculated using the Dube-Zener analysis. Table 10. Thinning Kinetics. Experimental Calculated Rate Diffusivity x 10' m/v/s D x 1013 m/s Binary 1.60+0.27 1.71 Ternary Mg 2.1110.31 2.93 Ternary Cu- III 1.4510.29 1.42 The calculated diffusivity values in Table 10 are all much smaller than the literature value for the binary system. It is reasonable to assume that ternary additions do not significantly alter the diffusion coefficient (D) of the system. It is known ^  that the value of D is largely independent of Ag concentration and similarly 148 the effects of Cu and Mg in solid solution in the matrix would be expected to be small. The calculated cuTfusivities are. all at least 20x smaller than the literature value for all three systems. Thus the migration of the broadface appears to be inhibited for all three alloys. Ternary additions do not seem to change the rate controlling mechanism. However, these additions have the effect of altering the kinetics. In particular, Mg additions increase the rate of migration by about 30% whereas the effect of Cu is to decrease it by about 10% in relation to the binary system. The observed kinetics can be directly correlated with the measured misfit in the different alloys. It may be recalled that the extent of mismatch in the three alloys i.e., binary, ternary Mg and ternary Cu alloys, are 0.76%, 1.11% and 0.42% respectively as obtained from the diffractometer measurements. The misfit in the ternary Mg alloy is high. Plates of this system are the least coherent which is the reason why it also exhibits the fastest thinning rates. The binary system with a higher misfit dissolves slightly faster than the ternary Cu system as would be expected. 7.1.2 Shortening Kinetics The shortening results showed linear kinetics for the binary alloy and are shown in Fig. 55. Several measurements of plate length as a function of dissolution time were carried out and the resulting dissolution rate was determined by least square analysis. The mean shortening rate for several experiments was 2.02 ± 0.24 x 10"9 m/s. A computer model was developed to analyse the shortening kinetics. 149 3 . H 3H 1500 TIME (t, sec.) Figure 55. Precipitate half-length vs time. 150 This became necessary since no appropriate model exists in the literature for plate tip 88 dissolution. The model is based on the work of Doherty and Cantor for the growth of a ledge. Details of the mathematical set-up of the model and its verification are presented in the Appendix. The model essentially predicts the dependence of the peclet number p (=vh/2D) on the saturation parameter (0). Fig. 56 gives the relationship between $2 and p. The value of the saturation, Si, obtained from the Al-Ag phase diagram is 0.034, which gives p as 0.015. Substituting for the value of the mean shortening rate and taking the mean half-thickness of the tip, h, equal to 0.15M m, gives -15 2 a diffusivity value of 8.64 x 10 m /s. This value is 8.3x lower than the volume diffusion coefficient Table 11 shows the mean experimental shortening rates for the ternary alloys. The model predictions for the interface diffusivity are also shown for all three alloys. 151 0.05 SATURATION Figure 56. Model prediction of the dependence of the peclet number (p) on saturation 152 Table 11. Shortening Kinetics. Experimental Model Rate Diffusivity x 10' m/s D x 1015 m/s2 Binary 2.0210.24 8.64 Ternary Mg 2.58+0.34 11.04 Ternary Cu- III 1.8310.26 7.84 Volume Diffusivity D = 7.15 x 10 mVs. The model predictions are lower by factors of 6.5 and 9 for the ternary Mg and ternary Cu alloys respectively. These results together with those of the binary system indicate an interfacial barrier to migration. Thus both shortening and thinning kinetics indicate an interfacial barrier to migration in all three alloys. 7.1.3 Discussion The thinning of the precipitates in all three alloys has been shown to follow a parabolic law but at rates slower than expected for dissolution under volume diffusion control. The experimental rates were at least 20x slower than expected. This 153 result is in direct confirmation of earlier findings, in particular those of Sagoe-Crentsil 85 102 and Brown for the thinning of 1 plates and Hewitt and Butler for the thinning of 6' in the Al-Cu system. The thickening of 7 plates have also been shown by Laird and 22 Aaronson to be slower than volume diffusion controlled rates. Such slow kinetics appear to be quite general and may likely be due to interfacial reaction controlled kinetics. As discussed in Section 1.3.2, the most common mechanism suggested for interfacial reaction control is the ledge mechanism. In order to apply this mechanism it is necessary to assume that the ledges are the Shockley partial dislocations observed at all times during o the dissolution process after an initial transient period. The ledge height is about 1.6A o with a spacing of 230A for the binary system. Using equation 1-12 and substituting values for the effective diffusion distance, which was estimated from the work of Laird and Aaronson and the Jones- Trivedi^^ plots, yields a thinning rate of 18.5 x 10~9 m/s. The gradient of the half-thickness against time plot at the early stages is approximately 0.2 x 10 m/s, a value that is nearly two orders of magnitude smaller than the experimental thinning rate. The thinning rates in the ternary systems were also slower by about the same magnitude. Thus the observed dissolution kinetics cannot be explained by a simple ledge mechanism. 7.2 Electron probe microanalysis The results of electron probe determination of the solute profile adjacent to the broadface of dissolving plates are presented in this section. The binary, ternary Mg and ternary Cu alloys were used for this study. The main objective was to investigate the effect of ternary additions on the Ag concentration at the precipitate-matrix interface. Details of the analysis of the measured profiles to calculate the interface 154 composition are presented for the binary system. Only the results are given for the ternary alloys. Fig. 57 shows typical concentration profiles made before and after dissolution at 450° C for 600s The blank profile taken before dissolution shows an apparent increase in Ag content 3.5ym away from the precipitate interface. The electron probe diameter is about 0.15Mm but due to the effective spot size of about 4jum, a fraction of the incident electrons within the matrix, but close to the precipitate phase penetrates into the 7 phase and produces a high Ag La intensity. Several blank profiles were obtained to ascertain the 3.5/um distance because of the difficulty in positioning the electron beam on the precipitate which averaged only about 0.30jum wide. All measurements within the 3.5ym range were ignored in subsequent analysis. The boundary position was taken to be the midpoint of the step in the plot of Ag La intensity against distance. The following assumptions were made in order to simplify analysis of the profiles: 1. The diffusion coefficient of the Al-Ag- ternary solid solution is independent- of concentration at the dissolution temperatures. This has been verified by Heumann and Bohmer^ for the case of the binary system. 2. There is very little movement of the interface relative to the diffusion distance. Kinetic measurements show the displacement to be only about 0.05M m. 3. The diffusion fields from neighbouring precipitates do not overlap; this condition was ensured by the heat treatment and also by obtaining profiles on isolated precipitates. A great deal of effort had to be expended to satisfy this criterion for 155 e -0 4 8 12 16 2 0 2 4 D i s t a n c e f r o m i n t e r f a c e ( x, /um) Figure 57. Concentration profiles before and after dissolution at 450 C for 600s. 156 the ternary Mg alloy. 4. For mathematical convenience, the planar surfaces of the precipitate are assumed to be infinite in extent and to be vertical to the polished surface. Semi-infinite conditions then prevail. For these conditions, the concentration profile ahead of the dissolving plate is given as: Cxt = Cm + ( C i " C m ) [ 1 " erf x / 2 /Dt ] 7.3 The values of the interface concentration Cj and the diffusivity D were obtained from 83 Eqn. 7.3 using the following graphical analysis developed by Hall et al. C m is the solute concentration in the matrix. 1. For three values of x ( x = 4/um, 6um and Hum ) the corresponding experimental values of C x t were obtained from Fig. 58 and were used in 1/2 conjunction with a range of .(Dt) values to solve Eqn. 7.3. The graph of C vs 1/2 1 (Dt) , Fig. 58, consists of three curves which cross at a point conesponding to 1/2 approximate values of C and (Dt) 1 1/2 2. A plot of C x t vs erf [x/2 /Dt] was made using the value of (Dt) obtained from Fig. 58. This is a linear plot which is consistent with Eqn. 7.3, in confirmation of the assumption that the solute profile is indeed volume diffusion-controlled. When extrapolated to erf [x/2 /Dt] = 0 a more accurate value of C is obtained as shown in Fig. 59. Table 12 shows the mean values of Cj and diffusion coefficient determined using this procedure for the three alloys. 158 Figure 59. Plot of concentration, C, vs erf [ x/2 / D t J. 159 Table 12. Electron Probe Determination of Interface Composition. Interface Diffusion Concentration Coefficient C wt% Ag 1 e D x 1014 mVs Binary 14.4 6.13 Ternary Mg 14.8 6.17 Ternary Cu- III 14.3 6.10 Equilibrium Value for C = 15.3 wt% Ag. Literature Value for D = 7.15 x 1 0 ~ 1 4 mVs. Table 12 shows the interface Ag concentrations were all significantly lower than the equilibrium value of 15.3 wt% Ag. The C. values of the binary and ternary Cu alloys are similar and are approximately 1% below the equilibrium value. The ternary Mg alloy is closer to equilibrium but is still 0.5% below the equilibrium value. The deviation of Cj from equilibrium values indicates interface control for the reaction. If indeed the reaction were strictly interface controlled, a varying silver concentration at the phase interphase would occur. No such variation was observed due to the single solution 112 treatment time used. The linear flux model assumes that C. varies linearly with time 160 83 .and would have been quite adequate for such an analysis. However, it has been shown that this model gives C values comparable to the error function analysis adopted here, which assumes a constant value of Cj throughout the dissolution process. The results primarily confirm the kinetics results in establishing the dissolution kinetics at the broadface of the plates to be interface reaction controlled in all three alloy systems. It is also possible to semi-quantitatively relate Cj values of the individual alloys to the respective misfit values and measured dissolution kinetics. The misfit in the ternary Mg alloy is nearly 30% higher than the misfit of the binary system and its broadface dissolves at a rate 25% faster. The probe results show the interface composition in the ternary Mg alloy to be closer to the equilibrium value, i.e., to be significantly less inhibited, than the Cu or binary systems in direct confirmation of the kinetic and misfit observations. The effect of the low misfit in the ternary Cu shows in the broadface dissolution kinetics however the extent of inhibition appears to be comparable with the binary system. Fig. 62 and Table 12 shows that the composition profile adjacent to the broadface of the precipitate follows an error function profile with the diffusion coefficient expected from the literature. The kinetics of dissolution of the broadface are much slower than expected for volume diffusion control. The reasons for this apparent 85 anomaly have been discussed by Sagoe-Crentsil and Brown. They showed that solute is transferred along the interface from the tip and diffuses out uniformly along the broadface so that diffusion distances are comparable at all points along the surface of the precipitate. Thus the composition profile at a given point on the interface is not particularly related to the solute transferred from the precipitate at that point 8. DISCUSSION 8.1 Morphology and Interface Structure The addition of Mg and Cu as ternary elements to the Al-Ag binary system has been shown to have a definite effect on the microstructure. The misfit existing between the 7-Ag2Al precipitate phase and the a matrix is decreased by the addition of Cu and increased by the addition of Mg. The effect of the Mg addition on the microstructure and the interfacial structure is however far more severe and this is because Mg preferentially partitions to the t phase This results in a significant expansion of the precipitate lattice parameter giving rise to an increased mismatch between the precipitate and matrix phases. Cu atoms on the other hand, partition nearly equally between the matrix and precipitate phases. Lutts^ has shown that the Mg atoms have a greater affinity for vacancies than Cu atoms in Al alloys. Vacancies retained by quenching the alloy from the solution treatment temperature are tied up by the Mg atoms producing solute-vacancy complexes which serves as a precursor phase. The precursor phase involving Mg atoms is known to be highly stable especially when the Mg present is in excess of 0.05 wt%. In the ternary Mg alloy, the equilibrium 1 phase may be expected to form directly from the precursor phases by the diffusion of available vacancies which also aid the transport of Mg atoms to the precipitate and thus preferentially partitions the Mg to this phase. This manner of preferential partitioning observed for Mg atoms has been successfully 114 exploited to control misfit and hence precipitate morphology in nickel-base superalloys. In these systems the cumulative effect of all alloying elements on the lattice parameter 161 162 can be accurately predicted from the chemical composition of the 7' phase based on a simple additivity relation. The spacing and configuration of dislocations at the precipitate-matrix interphase are directly related to misfit between the 7 precipitate and the matrix phase. The dislocation spacing is inversely related to the lattice misfit as would be expected and has been confirmed in previous studies. Such a dependence could be observed only during precipitate dissolution and not in the equilibrated alloy for the binary and ternary Cu systems. The equilibrium hexagonal dislocation network also forms only during precipitate dissolution. It appears that the dislocation sources in the binary and ternary Cu systems are initially inhibited and become active only during precipitate dissolution. It is plausible to expect new nucleation sources to be activated during dissolution. The evidence for this is that even in the ternary Mg alloy in which an equilibrium structure exists prior to dissolution, a new set of dislocations appears at the onset of dissolution. The set of newly nucleated dislocations has closely similar characteristics for the three alloy systems, all being the a/2<110> type dislocations nucleated at the plate edge probably as a result of the high stress concentration at such regions. The new set of dislocations interacts with the prior existing array in the case of the binary and ternary Cu systems to produce the equilibrium hexagonal structure in a fashion similar to the mechanism outlined by Whelan"^ 5 for hexagonal network formation. The new set of dislocations remains unreacted in the ternary Mg system since an equilibrium structure already exists at the interphase. 163 The existence of the initial linear dislocation array seems to be a consequence of a favoured nucleation process. Once the energetically unfavourable a/2<110> unit dislocations are nucleated there is no longer any driving force for dislocation rearrangement to an equilibrium configuration. This observation confirms 71 Aaronson's earlier suggestion that the observed interfacial structure may not necessarily be the equiUbrium one but rather the most readily nucleated type. 8.2 Kinetics Dissolution kinetics at the interphase boundary have been shown to be dependent on the degree of misfit between the precipitate and the matrix phases. As would be expected the decrease in coherency caused by Mg additions results in a dissolution rate at the precipitate broadface 30% higher than in the binary system However. Cu additions decrease the dissolution rate only marginally. The increased dissolution rates do indeed appear to be a function of the interphase structure. If the interphase is considered to migrate by a ledge mechanism in which the Shockley partials forming the network structure are associated with ledges, then the dissolution of the precipitate is accomplished by the passage of the ledge/dislocations across the interphase. The rates involved in such isolated events of single ledge/dislocation movement would invariably be related to the spacing and height of the ledges. Such a mechanism has 22 been shown by Laird and Aaronson to be responsible for plate thickening in the Al-Ag system In the case of precipitate dissolution a network structure of Shockley partials covers the entire broadface throughout dissolution. The formation of the 164 network structure at the onset" of dissolution generates a uniformly stepped interface with the spacing of the steps close to the equilibrium spacing. It may therefore be envisaged that the Shockley partials forming the network are associated with ledges. As has been shown in the present study, the spacing of the system of ledge/dislocations remains practically constant as the plate dissolves. These ledge/dislocations must participate in the dissolution process but are not likely to do so by a dislocation climb mechanism since they are primarily in edge orientation and can only glide across the interface. The dissolution of the precipitate plates may therefore involve the sweeping of the ledge/dislocations across the interface. If such a mechanism were to be operative then the plate edge can be envisaged as a probable nucleation site since it is a region of high stress concentration. The plate edge prior to the nucleation of a ledge/dislocation is shown in Fig. 60(a). The nucleation of a new ledge/dislocation on the broadface simultaneously creates a ledge/dislocation at the plate edge also, as shown in Fig. 60{b). The spacing between the newly nucleated ledge and the next ledge thus falls below the equilibrium value. This exerts a force on the adjacent ledge/dislocation which moves to maintain the equilibrium spacing. This process .continues with the other ledge /dislocations moving resulting in a coordinated movement of all the ledge/dislocations. The highest step at the interface is eliminated in the process and dissolution is accomplished as shown schematically in Fig. 61. Hence dissolution occurs progressively with the passage of the three equivalent sets of ledge/dislocations observed at the precipitate/matrix interphase. Some direct evidence for such a coordinated movement has been reported by Laird and 22 Aaronson in their study of the growth of 7-Ag2Al precipitates. They observed uniform periodic movement of sets of dislocations across the precipitate plate during thinning. It must be noted that close similarities exist between Laird and Aaronson's experimental technique and the present study in that their growth studies were carried out on 165 Figure 60. Schematic drawing of ledge/dislocation nucleation at plate edge, (a) before (b) after nucleation 166 Figure 61. Schematic representation of dissolution by the movement of ledge/dislocations. 167 precipitate plates partially dissolved at 450° C and the cooled to a growth temperature between 300 - 425° C. The measured dissolution rates may now be related to this coordinated mechanism of dissolution. If the rate of ledge/dislocation nucleation is regarded as being identical for the three alloy systems then the interphase migration is dependent only on the ledge/dislocation spacing. For example the smaller spacings observed in the ternary Mg alloy gives rise to higher dissolution rates. In general however ledge/dislocation nucleation has been reported to be erratic during precipitate growth J and may therefore contribute much more significantly to the overall boundary migration than the present model indicates if the nucleation behaviour is extended to dissolution. Both the precipitate broadface and edge are envisaged to dissolve by the same mechanism. An attempt to fit the observed kinetics at the broadface to existing ledge theories proved to be unsuccessful, see Section 7.1.3. In general the measured rates at the broadface were at least an order of magnitude lower than rates expected for ledge boundaries. This further shows that the problem of ledge/dislocation nucleation may indeed be relevant to the interphase kinetics and is perhaps the cause for the lack of agreement between theoretical and experimental results. The above mechanism can help to explain the dissolution kinetics of the broadface and the tip. The transfer of Ag from the dissolving precipitate will be controlled by this process. However once the Ag is in the a solid solution normal diffusion processes occur. There is short circuit diffusion at the interface and normal 168 lattice diffusion from the interface into the bulk of the matrix. Thus composition profiles into the matrix from the broadface are characteristic of normal diffusion coefficients. 9. CONCLUSIONS 1. The misfit existing between the 7-Ag2Al precipitate and matrix phases can be altered by ternary element additions. Mg additions were observed to increase the misfit and Cu additions to decrease it 2. Mg additions alter the 7-precipitate morphology to produce rounded hexagons but Cu tends to produce more perfect hexagonal shapes. This can be correlated with the effect of Mg and Cu on the misfit 3. Misfit in the equilibrated binary and ternary Cu alloys is compensated by a linear array of a/2<110> edge dislocations. A hexagonal network of a/6<112> partials compensates misfit in the ternary Mg system 4. At the onset of dissolution, the linear array in the binary and ternary Cu alloys transforms to a hexagonal network. The network structure remains throughout dissolution for all three alloy systems and compensates misfit more efficiently than the linear array. 5. Plate dissolution is initiated by the formation of a network structure in the binary and ternary Cu alloys. The structure is formed by the nucleation of macroledges at at the plate edge which glide across the interface leaving a system of microledges in its trail. These microledges interact with the existing linear array of a/2<110> dislocations to generate the hexagonal network of a/6<112> partials. 6. Plate dissolution after the initial transient period appears to be achieved by a mechanism of co-ordinated motion of sets of dislocations forming the network structure. Growth on the other hand occurs by the passage of individual ledges. 7. Plate thinning was found to be over 40x slower than expected under volume diffusion control for the binary and ternary Cu systems and to be about 25x 169 170 slower for the ternary Mg alloy. The relative faster kinetics of the Mg alloy could be correlated with its higher degree of misfit. 8. A model developed for shortening kinetics shows plate shortening to be inhibited indicating an interfacial reaction there as well. 9. Electron probe niicroanalysis show the binary and ternary Cu alloys to be significantly away from equilibrium. The Mg alloy is closer to equilibrium. Comparision of the electron probe and kinetics data indicate an interfacial short circuit mechanism to be operative. REFERENCES 1. Dube, C. A., Ph.D Thesis, Carnegie Institute of Technology 1948 2. Aaronson, H. I., The Mechanism of Phase Transformation in Metals, Institute of Metals Monograph, 18 , 47 (1956) 3. Brooks, H., in Metal Interfaces (ed. by R. M. Bricks), American Society of Metals Cleveland, Ohio, 20 (1952) 4. Frank, F. C. and van der Merwe, J. H., Proc. Roy. Soc., A198 , 205 (1949) 5. van der Merwe, J. H., J. Appl. Phys., 34 , 117 and 123 (1963) 6. Weatherly G. C . Phil. Mag. A, 17 , 791 (1968) 7. Brown, L. M., Woolhouse, G. R. and Valdre, U., Phil. Mag. A, 17 , 781 (1968) 8. Brown, L. M. and Woolhouse, G. R., Phil. Mag. A, 21 , 329 (1970) 9. Ashby, M. F. and Johnson, L , Phil. Mag. A, 1009 (1969) 10. Aaronson, H. I., Laird, C. and Kinsman, K. R., in Phase Transformations (ed. H. I. Aaronson), American Society of Metals, Metals Park, Ohio, 313, 1970 11. Aaronson, H. I., Jnl. of Microscopy, 102 , 257 (1974) 12. Seitz, F., Rev. Mod. Phys., 79 , 723 (1950) 13. Eikum, A. and Thomas, G , Acta Met., 12 , 537 (1964)' 14. Philips, V. A. and Livingstone, J. D., Phil. Mag. A, 7 , 969 (1962) 15. Matthews, J. W., Klokholm, E , Sadagopan, V., Plaskett T. S. and Mendell, E., Acta Met, 21 , 203 (1973) 16. Humphreys, F. J., Acta Met, 6 , 1069 (1968) 17. Gleiter, H., Acta Met, 15 , 1213 (1967) 18. Gleiter, H., Acta Met, 15 , 1223 (1967) 19. Gleiter, H., Z. Naturforschung, 58 , 101 (1967) 20. Livak, R. J. and Thomas, G., Acta Met, 22 , 589 (1974) 21. Baker, R. G., Brandon, D. G. and Nutting, J., Phil. Mag. A, 4 , 1339 (1959) 22. Laird, C. and Aaronson, H. I., Acta Met, 17 , 505 (1969) 23. Laird, C. and Aaronson, H. I., Acta Met, 15 , 73 (1967) 24. Philips, V. A., Acta Met, 14 , 271 (1966) 171 172 25. Weatherly, G. C. and Nicholson, R. B., Phil Mag., 17 , 801 (1968) 26. Tien, J. K., Shewmon, P. G. and Forster, J. S., Met Trans., 2 , 1193 (1971) 27. Hall, M. G., Aaronson, H. I. and Kinsman, K. R., Surface Science. 31 , 247 (1972) 28. Howell, P. R., Southwick, P. D., Ecob, R. C. and Ricks, R. A.,in Solid-Solid Phase Transformations (ed. Aaronson, H. I., Laughlin, D. E, Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AIME, Warrendale, Pa, 591 (1981) 29. Rigsbee, J. M. and Aaronson, H. I., Acta Met, 27 , 365 (1979) 30. van der Merwe, J. H., in Single Crystal Films (ed. M. H. Francombe and H. Sato) Pergamon Press, Oxford, 139 (1964) 31. Matthews J. W., in Dislocations in Solids (ed. F. R. N. Nabarro) North-Holland Publishing Co., Endhoven, 463 (1979) 32. Sankaran, R., and Laird, C, Acta Met, 22 , 957 (1974) 33. Russel, K. C, in Phase Transformations (ed. Aaronson, H. I)., American Society of Metals, Metals Park, Ohio, 219 (1970) 34. Cahn, J. W. and Hilliard, J. E., Jnl. Chem. Phys., 31 , 688 (1975) 35. Aaronson, H. I. and Russell, K. C, in Solid-Solid Phase Transformation (ed. Aaronson, H. I., Laughlin, D. E., Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AIME, Warrendale, Pa, 371 (1981) 36. Mott, N. F. and Nabarro, F. R. N., Proc. Phys. Soc., 52 , 86 (1940) 37. Eshelby, J. D., Proc. Roy. Soc., A, 421 , 376 (1957) 38. Cahn, J. W., The Mechanism of Phase Transformation in Crystalline Solids, Institute of Metals, London, 1 (1969) 39. Christian, J. W., The Theory of Transformation in Metals and Alloys, Oxford University Press, Oxford, 1965 40. Aaronson, H. I., Decomposition of Austenite by Diffusional Processes, Interscience, J. Wiley, New York, 387 (1962) 41. Howe J. M., Dahmen U. and Gronsky, R., Phil Mag. A, 56 , 31 (1987) 42. Aaronson, H. I., Scripta Met, 11 , 731 (1979) 43. Weatherly, G. C, Acta Met, 19 , 181 (1971) 44. Kang, S. K. and Laird C, Acta Met, 22 , 1481 (1974) 45. Weatherly, G. C. and Sargent, C. M., Phil. Mag. A, 22 , 1049 (1970) 46. Gleiter, H., Acta Met, 17 , 565 (1969) 173 47. Howe, J. M., Aaronson, H. I. and Gronsky, R., Acta Met,, 4 , 649 (1985) 48. Clark, H. M. and Wayman, C. M., in Phase Transformations, American Society of Metals, Metals Park, Ohio, 59 (1970) 49. Wechsler, M. S., Lieberman, D. S. and Reed, T. A., Trans. TMS-AIME, 194 , 1503 (1953) 50. Gaunt, P. and Christian, J. W., Acta Met., 7 , 529 (1953) 51. Gaunt, P. and Christian, J. W., Acta Met, 7 , 534 (1953) 52. Liu, Y. C. and Aaronson, H. I., Acta Met, 18 , 845 (1970) 53. Smith, R. and Bowles, J. S., Acta Met, 8 , 405 (1966) 54. Hunt, A. M. and Pashley, D. W„ Jnl. AusL Inst, of Metals, 8 , 61 (1963) 55. Cornelius, I. and Wayman, C. M, Acta Met., 22 , 291 and 301 (1974) 56. Aaronson, H. I. and Lorimer, G. W., Acta Met, 22 , 291 (1974) 57. Atkinson, C, Acta Met., 16 , 1019 (1968) 58. Atkinson, C, Trans. TMS-AIME, 245 , 801 (1969) 59. Brown, L C, J. Appl. Phys., 40 , 4859 (1969) 60. Zener, C. J., J. Appl. Phys., 20 , 950 (1949) 61. Horvay, G. and Cahn, J. W., Acta Met, 9 , 695 (1961) 62. Ivantsov, V. I., Dokl. Akad. Nauk SSSR, 58 , 567 (1947) 63. Hillert, M., Jernkontorets Ann., 141 , 757 (1957) 64. Trivedi, R. and Pound, G. M., J. Appl. Phys., 40 , 4293 (1969) 65. Mullins, W. W. and Sekerka, R. F., J. Appl. Phys., 34 , 323 (1963) 66. Langer, J. and Muller-Krumbhaar, H., Acta Met, 26 , 1681 (1978) 67. Trivedi, R., in Solid-Solid Phase Transformations (ed. Aaronson, H. I., Laughlin, D. E, Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AiME.Warrendale, Pa, 477 (1981) 68. Aaron, H. B. and Kotler G. R., Met Trans., 2 , 393 (1971) 69. Nolfi, F. V., Shewmon, P. G. and FosterJ. S., Trans. AIME, 245 , 1427 (1969) 70. Tanzili, R. A. and Heckel, R. W., Trans. AIME, 242 , 2313 (1968) 71. Aaronson, H. I., Trans. Indian Inst. Metals, 32 , 1 (1979) 174 72. Kinsman, K. R., Aaronson, H. I. and Eichen E , Met Trans, 6A , 303 (1975) 73. Aaronson, H. I. and Laird, C , Trans TMS-AIME, 242 , 1437 (1968) 74. Sankaran, R., Ph.D. Thesis, University of Pennsylvania, (1973) 75. Howe, J. M., Aaronson H. I. and Gronsky, R., Acta Met, 33 , 649 (1985) 76. Atkinson, C , Kinsman, K. R. and Aaronson, H. I., Scripta Met., 7 , 1105 (1973) 77. Doherty, R. D., Ferrante, M. and Chen, Y. H., Scripta Met, 12 , 885 (1978) 78. Sankaran, R. and Laird, C , Scripta Met., 12 , 887 (1978) 79. Aaronson, H. I., Scripta Met, 11 , 741 (1977) 80. Aaronson, H. I., Lee, J. K. and Russel K. C , in Precipitation Processes in Solids (ed. Russel, K. C. and Aaronson, H. I.) The Metallurgical Society of AIME, Warrendale, Pa., 31 (1976) 81. Aaronson, H. I., and Laird, C , Acta Met,, 22 , 957 (1974) 82. Sagoe-Crentsil, K. K., M.Sc. Thesis, University of British Columbia, Vancouver, (1983) 83. Hall, M. G. and Haworth, C. W., Acta Met., 18 , 331, (1970) 84. Pabi, S. K., Mat Sc. Eng., 43 , 151 (1980) 85. Sagoe-Crentsil. K. K. and Brown L. C , Metall. Trans. A, 15 , 1969 (1980) 86. Jones, G. J. and Trivedi, R., J. Appl. Phys., 42 , 4299 (1971) 87. Atkinson, C , Proc. Roy. Soc. London, A378 , 351 (1981) 88. Doherty, R. D. and Cantor, B., in Solid-Solid Phase Transformations (ed. Aaronson, H. I., Laughlin, D. E. Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AIME, Warrendale, Pa, 547 (1981) 89. Hardy, H. K. and Heal, T. J., Progress in Metal Physics, 5 , 162 (1954) 90. Polmear, I. J., Physics of Materials, University of Melbourne, Melbourne, Australia, 209 (1979) 91. Rosenkranz, W., Aluminum, 39 , 290, 630 and 741 (1963) 92. Brook, G. B., Fulmer Research Institute Special Report, 3 , Fulmer Research Institute, StokePoges , 1 (1965) 93. Hardy, H. K., J. Inst. Metals, 80 , 483 (1951-52) 94. Noble, B., McLaughlin, I. R. and Thompson, G., Acta Met, 18 , 339 (1970) 175 95. Silcock, J. M., Heal, T. J. and Hardy, H. K., J. Inst, Metals., 84 , 23 (1955-56) 96. Nuyten, J. B. M., Acta Met, 15 , 1765 (1967) 97. Brook, G. B. and Hatt B. A., Mechanism of Phase Transformation in Crystalline Solids, Institute of Metals Monograph No. 33, 82 (1969) 98. Lucke, K. and Detert, K., Acta Met, 5 , 628 (1957) 99. Gordon, P. and Vandermeer, R. A„ in Recrystallisation, Grain Growth and Textures, American Society of Metals, Metals Park, Ohio, 205 (1966) 100. Hillert, M., in Solid-Solid Phase Transformations, (ed. Aaronson, H. I., Laughlin, D. E., Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AIME, Warrendale Pa, 789 (1981) 101. Bradley, J. R., Shiflet G. J. and Aaronson, H. I., in Solid-Solid Phase Transformations, (ed. Aaronson, H. [., Laughlin, D. E., Sekerka, R. F. and Wayman, C. M.) Metallurgical Society of AIME, Warrendale, Pa, 819 (1981) 102. Hewitt, P. and Buder, E P., Acta Met, 34 , 1163 (1986) 103. Hansen, M., Constitution of Binary Allovs, 2nd ed. , McGraw-Hill Book Co., New. York, 2 (1958) 104. Pouchou, J-L. and Pichoir, F., La Recherche Aerospatiale, 3 , 167 (1984) 105. Howe, J. M., Aaronson, H. I., and Gronsky, R., Acta Met, 33 , 639 (1985) 106. Pumphrey, P. H. and Edington, J. W., Acta Met, 22 , 89 (1974) 107. Tholen, A. R., Phys. Stat Solid, (A), 2 , 537 (1970) 108. Pollard, G. and Nutting, J., Jnl. of Metals, 93 , 464 (1964-65) 109. Hren, J. A. and Thomas, G., Trans. Metall. Soc. AIME, 227 , 308 (1963) 110. Hirsch, P. B., Howie, A., Nicholson, R. B., Pashley, D. W. and Whelan, J. W.. Electron Microscopy of Thin Crystals, Butterworths, London, 343 (1965) U l . Heumann, von Th. and Bohmer, H. I, Phys. Chem. Solids. 29 . 237 (1967) 112. Abbot, K. and Haworth, C. W„ Acta Met, 21 , 951 (1973) 113. Lutts, A., Acta Met, 9 , 577 (1961) 114. Loomis, W. T.. Freeman J. W. and Sponseller, D. L , Metall Trans., 3 , 989 (1972) 115. Whelan, M. J., Proc. Roy. Soc. A, 249 , 114 (1959) 116. Brown, L. C, Dept. of Metals and Mats. Eng., U. B. C, Private Communication. 117. Murray, W. D. and Landis, F., Trans. ASME, 81 , 106 (1959) APPENDIX Mathematical Model for Tip Dissolution The model developed^ is based on the work of Doherty and 88 Cantor for growth of a ledge. The plate is considered to be of infinite extent in the z-direction. The boundary conditions used are shown in Fig. 62, and are as follows: The tip is considered to be at a fixed concentration and there is no vertical flux on the broad face so that it does not dissolve. The plane y=0 is a plane of symmetry and there are no composition gradients perpendicular to this. Thus it is sufficient to consider one half of the tip, the other half being a minor image. The boundary conditions applied to this half tip are shown in Fig. 63 and the composition contours are shown in Fig. 64. There is a horizontal composition gradient adjacent to the tip and it can therefore move horizontally. The composition gradient is very large at B due to the point effect of diffusion. This would tend to cause the edge B to move more quickly than the rest of the tip and so cause it to change shape. This is avoided by averaging the flux over the tip AB so that all parts of the tip move at the same rate. Fig. 65 shows the 70 x 35 network used. The tip is initially placed at 1 = 35 and moves to the left as dissolution proceeds. The position of the interface shown in Fig. 65 corresponds to an arbitrary time during the dissolution process. The 176 177 t d y " ° Figure 62. Boundary conditions used for Model 178 i Y dy = ° Figure 63. Boundary condition applied to precipitate half-tip 179 Figure 64. Composition contours at plate tip 180 1 2 3 IQIQ+1 IQ+2 68 69 70 ure 65. Grid network used for calculation 181 nearest node on the right side is IQ and the interface is at a distance E from this node. The tip has a height corresponding to the range J = 1 to N. The two-dimensional diffusion equation with concentration independent diffusion coefficients, dC/dt = D(d2C/dx2 + d2C/dy2) 1 can be rewritten in numerical form as: C*(IJ) = C(I,J) + D At/Ax2[C(I+l,J) + C(I-1,J) + C(I,J + 1) + C(I,J-1) - 4C(U)] where, C(IJ) and C*(I,J) are the compositions at node (I,J) at times t and (t + At), respectively, and Ax is the distance between nodes in the network. For stable solutions to this equation with increasing time, it is 117 required that DAt/Ax2 < 1/4. Taking the equality gives C*(I,J) = 1/4[C(I+1,J) + C(I-1,J) + C(I,J+1) + C(LJ-l)] 2 If this equation is applied at all points within the solid solution, the diffusion field at time (t+At) can be determined if the diffusion field at time t is known. To insure that there is no flux normal to the broadface, C(I,N)is taken equal' to C(I,N+1) between I = 1 and IQ - 1. To ensure that the line J = 1 is a line of symmetry, C(I,1) is taken equal to C(I,2) between I = IQ and 70. 182 As rime increases, the diffusion field tends to extend beyond the range of the 70 x 35 matrix used. A simple extrapolation procedure was used to allow for this and was applied to the following nodes 1 = 1 J = N + l , 34 I = 70 J = 1, 34 J = 35 I = 1, 70 The composition is considered to vary exponentially according to the law; C = A exp(bx) 3 adjacent to these points. Therefore on the line 1 = 1 for example, C(l,m) = C(2,m)2/C(3,m) For nodes adjacent to the phase interface, C(IQ,J) with J = l , N, an extrapolation procedure must be used to obtain the concentration. This assumes that the composition profile along the line y = constant close to the phase boundary is given by a polynomial expression of the form: C = A + Bx + Cx2 4 183 If C*(IQ+1J) and C*(IQ + 2,J) are determined at time (t+A't), then C*(I,Q) can be obtained from: C'(IQJ) = 2CA/[(2 + E/Ax)(l + E/Ax)] + 2C*(IQ+1, J)(E/Ax)/[(1 + E/Ax] - C(IQ + 2,J)(E/Ax)/[2 + E/Ax] 5 where E (always negative) is the distance of the phase interface from the IQth node. The composition gradient along the line perpendicular to the phase interface is given by dC/dx = [C*(IQ,J) - C*(IQ + 2),J)]/2Ax - (E + Ax)/Ax2 . [C*(IQ + 2),J) -2C*(IQ + 1,J) + C»(1Q,J)] 6 using the first terms in a Taylor expansion of the composition as a function of distance from the phase interface. The movement of the phase boundary was calculated initially following the approach of Doherty and Cantor and considering only the composition gradients perpendicular to the interface, Eqn. 4. These values were averaged over J = l to N and equated to the mass balance at the interface, Fig. 66, which for dissolution is; -D(dC/dx) = (C - 1) Ax/At 3. with the saturation being given by: Q = 1/C a A second method was also used which made corrections for the flux line trajectories which in general were not perpendicular to the phase boundary. This correction increased the composition gradients and so increased the rate of the boundary movement. However, it was found that this correction was quite small, being typically only 12%. Thus the Figure 66. Mass balance across interface. 185 divergence of the flux lines is not overly important The model was initially checked by applying it to growth of a tip and reasonably good agreement was obtained with the results of Doherty and Cantor for growth under similar conditions. Fig. 67 shows the movement of the tip as a function of time for two different tip heights. The dissolution rate appears to be essentially constant after an initial transient for a given tip height The dissolution rate is slower at the larger value for tip height as would be expected since dispersion of the solute is less effective in this case. If the results are normalised to the ledge height however, and the time is normalised to Dt/h2, then the curves coincide. Fig. 68. Consider the linear portion of this line to have a slope K, then x/h = K . Dt/h2 x/t = v = DK/h or K./2 = vh/2D = p where p is the peclet number. This inter-relationship between v and h has been found by Jones and Trivedi and by 87 Atkinson for growth of a Tedge. Fig. 69 shows the effect of saturation on tip dissolution kinetics. All curves show an initial transient followed by steady state dissolution. The slopes of the straight line regions of Fig. 69 were used to determine the peclet number at different saturation conditions. This plot has practical use since if the saturation is known from the 186 Dt Figure 67. Movement of plate tip with time. 188 Figure 69. Plot of Dt/h vs normalised height for different values of saturation. 189 phase diagram, then the peclet number can be determined and so the tip dissolution velocity can be calculated if the tip half height, h, is known. This plot is shown in the text as Fig. 56. 

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