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Effect of stress in chemical diffusion Behera, Saroj Kumar 1968

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THE EFFECT OF STRESS IN CHEMICAL DIFFUSION . by SAROJ KUMAR BEHERA B.Sc.(Hons.), Utkal University, India, 1962 B.E., Indian I n s t i t u t e of Science, India, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept this thesis as conforming to the required standard ' THE UNIVERSITY OF BRITISH COLUMBIA May, 1968 In presenting this thesis in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and Study. I further agree that permission for extensive copying of this thesis for s c h o l a r l y purposes may be granted by the Head of my Department or by h.iis representatives. It is understood that copying or p u b l i c a t i o n of this thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Metallurgy  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date June 3, 1968 S u p e r v i s o r : Dr. L. C. Brown i ABSTRACT Diffusion has been studied i n a range of systems having intermediate phases i n the d i f f u s i o n zone. I t has been found that i n some systems (Ag-Sb, Ag-Se, Ni-Sb, Cu-Se and Cu-Sb) the d i f f u s i o n rates are very sensitive to compressive stress, with a load of 100 psi making a s i g n i f i c a n t difference to the width of the d i f f u s i o n zone. In other systems (Cu-Zn, Cu-Sn and Al-Zr) stresses up to the maximum of 1500 p s i had no effect on the d i f f u s i o n rate. The growth rates of a l l phases i n the pressure sensitive systems were found to be parabolic with time indicating d i f f u s i o n control. In Cu-Se and Cu-Sb there was a nucleation time at the beginning of d i f f u s i o n . However, growth of the phases i n these systems was also found to be parabolic once this effect was accounted for. The effect of compressive stress was, generally, to increase the growth rate of one of the intermetallic phases. In Ag-Sb,- Ag-Se and Cu-Sb, there was a l i m i t i n g stress above which growth rates of the i n t e r -mediate phases were constant. Such a l i m i t i n g stress was not observed i n Ni-Sb and Cu-Se and the growth rates of the Ni_Sb_ and Cu^Se phases i n these systems increased apparently l i n e a r l y with applied stress. In experiments i n which d i f f u s i o n took place at low stress following an i n i t i a l high stress anneal, i t was generally found that the growth rate cha r a c t e r i s t i c of the new stress was attained after long times of d i f f u s i o n . In Cu-Se and Cu-Sb however, i t was found that the stress-sensitive phases disappeared on ageing, although a f i n i t e growth was observed i n the normal growth experiments. From the existing knowledge of d i f f u s i o n theories, this particular phenomenon could not be explained. However, i t i s thought that this may possibly be due to a s i g n i f i c a n t decrease i n s p e c i f i c volume on formation of these phases. Non-appearance of certain stable phases predicted from the phase diagram has been attributed to their small d i f f u s i o n c o e f f i c i e n t s . Hydrostatic tests were carried out to see i f there was any difference i n growth rates between un i a x i a l compressive stress and t r i a x i a l hydrostatic pressure. I t was found i n general that the growth rate under hydrostatic pressure was very similar to that for a compressive test of zero p s i , indicating that applying a hydrostatic pressure does not have any effect on the growth rate and that only compressive loading i s of any significance. A l l the stress-sensitive systems investigated showed a very large Kirkendall effect. The tungsten markers interfered with d i f f u s i o n and the width of the d i f f u s i o n zone adjacent to the markers was less than elsewhere. This gave r i s e to ledges of the pure metals with the tungsten wires being at the top of the ledges. The development of ledges was much greater i n pressure sensitive systems than i n other systems and could be attributed to slow l a t e r a l d i f f u s i o n due to the lack of compressive stress i n this d i r e c t i o n . The experimental results can be explained on the basis of porosity which forms at a single interface i n these systems owing to the large Kirkendall effect. This decreases the effective cross-sectional area of d i f f u s i o n and so reduces the width of the d i f f u s i o n zone. The effect of i i i compressive stress i s to decrease the amount of porosity and hence increase the e f f e c t i v e interface area and the atomic flux into the d i f f u s i o n zone. The l i m i t i n g stress observed i n Ag-Sb, Ag-Se and Cu-Sb was thus attributed to the complete absence of porosity i n the d i f f u s i o n zone. In Ni-Sb and Cu-Se i t i s believed that the pressure sensitive phases have very high growth rates and the maximum stress of 1500 p s i was i n s u f f i c i e n t to obtain a good interface. A l l the other results can be explained s a t i s f a c t o r i l y by the mechanism suggested. ACKNOWLEDGEMENT The author would l i k e to express his sincere gratitude to his research director, Dr. L.C. Brown, for the advice and assistance given throughout the period of study and during the preparation of this thesis. The author wishes to thank other members of the faculty and fellow graduate students of the Department of Metallurgy for many useful discussions. Thanks are also extended to the members of the technical s t a f f whose help was readily available to the author. Financial grants i n the form of NRC Grant No. A - 2459 and a National Research Council fellowship are gratefully acknowledged. TABLE OF CONTENTS Page CHAPTER I 1.1 Introduction 1.1.1 General 1 1.1.2 Significance of the Study 1 1.2 Review of Previous Work 2 1.3 Theory of Diffusion 1.3.1 Atomic Mechanisms for Diffusion 9 1.3.2 Kirkendall Effect 10 1.3.3 Vacancy Di s t r i b u t i o n i n the Diffusion Zone 11 1.3.4 Kirkendall Porosity 12 1.3.5 Mathematics of Diffusion 16 1.3.6 Diffusion i n Ionic Compounds 20 1.4 Effect of Pressure on Multiphase Diffusion 1.4.1 Possible Effects 22 1.4.2 Effect of Pressure on Diffusion Coefficients 22 1.4.3 Effect of Pressure on Equilibrium Composition 25 1.4.4 Relative Significance of the Effect of Pressure on Diffusion Coefficient and on Phase Boundary Composition 28 1.4.5 Effect of Pressure on Kirkendall Porosity 30 CHAPTER I I EXPERIMENTAL PROCEDURE 2.1 Choice of Systems 33 2.2 Apparatus 33 2.3 Materials and Specimen Preparation 35 v i Page 2.4 Experimental Procedure 36 CHAPTER I I I EXPERIMENTAL RESULTS 3.1 I n i t i a l Experiments . . 40 3.2 Silver-Antimony System 3.2.1 The Phase Diagram 40 3.2.2 I d e n t i f i c a t i o n of the Phase 42 3.2.3 Effect of Stress on Diffusion 45 3.2.4 Kinetics 45 3.2.5 Hydrostatic Test 50 3.2.6 Kirkendall Experiments 54 3.2.7 Discussion 58 3.3 Silver-Selenium System 3.3.1 The Phase Diagram 60 3.3.2 I d e n t i f i c a t i o n of the Phase 62 3.3.3 Effect of Stress on Diffusion 62 3.3.4 Kinetics 62 3.3.5 Kirkendall Experiment 62 3.3.6 Discussion 67 3.4 Nickel-Antimony System 3.4.1 The Phase Diagram 68 3.4.2 I d e n t i f i c a t i o n of the Phases 68 3.4.3 Effect of Stress on Diffusion ....... 74 3.4.4 Kinetics 74 3.4.5 Kirkendall Experiment 80 3.4.6. Discussion 80 v i i Page 3.5. Copper-Selenium System 3.5.1 The Phase Diagram 88 3.5.2 I d e n t i f i c a t i o n of the Phases 88 3.5.3 Effect of Stress on Diffusion 90 3.5.4 Kinetics .. 90 3.5.5 Hydrostatic Test . 100 3.5.6 Kirkendall Test . . 103 3.5.7 Discussion 103 3.6 Copper-Antimony System 3.6.1 The Phase Diagram .. 107 3.6.2 I d e n t i f i c a t i o n of the Phases 107 3.6.3 Effect of Stress on Diffusion 107 3.6.4 Kinetics I l l 3.6.5 Hydrostatic Test 119 3.6.6 Kirkendall Test 119 3.6.7 Discussion 123 CHAPTER IV SUMMARY AND CONCLUSIONS 4.1 Relative Variations of Diffusion Coefficients and Phase Boundary Composition 128 4.2 Effect of Pressure on Diffusion Coefficient .. 129 4.3 Effect of Stress on Kirkendall Porosity 131 4.4 Growth Kinetics .. 134 4.5 Restricted Diffusion i n Cu-Sb and Cu-Se 135 4.6 Diffusion Coefficient and Non-Appearance of Stable Phases . 139 4.7 Conclusions 142 V l l l Page Appendix 143 Bibliography 155 i x LIST OF FIGURES Page 1. Effect of Pressure on Diffusion i n Al-Fe and Al-Ni 3 2. Effect of Pressure on Diffusion i n U-Al, a-Brass/y-Brass and Cu-Sb 5 3. Effect of Pressure on Diffusion i n Cu-Te 7 4. Calculated Concentration P r o f i l e s Showing Deviation from Parabolic Behaviour „ 13 5. Distr i b u t i o n of Vacancies i n the Diffusion Zone 13 6. Schematic Representation of the Diffusion P r o f i l e for Different Systems . 17 7. Schematic Representation of Concentration P r o f i l e s for Two Cases of Intermetallic Diffusion 19 8. Schematic Representation of Diffusion i n Ag-S 21 9. Schematic Representation of Changes i n Free Energy Diagram with Pressure 26 10. Apparatus for Carrying out Diffusion Under Compressive Stress 34 11. Apparatus for Hydrostatic Experiments 39 12. Phase Diagram of Ag-Sb System 41 13. Electron Microprobe Traverse of Ag-Sb Diffusion Couple .. 44 14. Photomicrographs of Diffusion Zone i n Ag-Sb at Different Stresses 46 15. Effect of Stress on Diffusion i n Ag-Sb 47 16. Growth of Ag3Sb at 350°C 48 17. Effect of Stress on Growth Rates of Ag3Sb at 350°C 49 o 18. Growth of Ag^Sb at 350 C when Pressure i s Changed During the Diffusion Anneal 51 19. Parabolic Plot of the Results i n Fig. 18 52 20. Growth of Ag^Sb at 350°C Under Hydrostatic Pressure 53 X Page-21. Photomicrographs of K i r k e n d a l l Marker Experiments i n Ag-Sb 55 22. Photomicrograph of K i r k e n d a l l Experiment i n Ag-Sb w i t h D i f f e r e n t Marker Diameters 56 23. Photomicrograph of K i r k e n d a l l Experiment i n Cu/a-Brass w i t h D i f f e r e n t Marker Diameters 57 24. Phase Diagram of Ag-Se 61 25. E l e c t r o n Probe Traverse of Ag-Se D i f f u s i o n Couple 63 26. E f f e c t of Stress on D i f f u s i o n i n Ag-Se 64 o 27. Growth of Ag 2Se at 350 C 65 28. Micrograph of K i r k e n d a l l Experiment i n Ag-Se 66 29. Phase Diagram of Ni-Sb 69 30. E l e c t r o n Probe Traverse f o r Ni-Sb D i f f u s i o n Couple .... 73 o 31. Photomicrographs of D i f f u s i o n Zone i n Ni-Sb at 350 C at D i f f e r e n t Stresses 75 32. E f f e c t of Stress on D i f f u s i o n i n Ni-Sb 76 o 33. Growth of the I n t e r m e t a l l i c Phases i n Ni-Sb at 400 C and 200 p s i 77 34. Growth of the I n t e r m e t a l l i c Phases i n Ni-Sb at 400°C and 500 p s i „ 78 35. E f f e c t of Stress on Growth Rate of N i Sb 2 at 400°C 79 36. Growth of Ni Sb at 400°C when Pressure i s Changed During the ^ D i f f u s i o n Anneal 81 37. P a r a b o l i c P l o t of the Results of F i g . 36 82 38. Micrographs of K i r k e n d a l l Experiment i n Ni-Sb 83 39. Schematic Representation of D i f f u s i o n Around the K i r k e n d a l l Markers i n Ni-Sb 85 40. E l e c t r o n Probe Traverse of Cu-Se D i f f u s i o n Couple 89 o 41. E f f e c t of Stress on D i f f u s i o n i n Cu-Se at 170 C 91 x i Page 42. Growth of Cu^Se at 170°C at Different Stresses 92 o 43. Growth of Cu Se 9 at 170 C at Different Stresses 93 3 Z 44. Eff ect of Stress on Incubation Time for Cu^Se 95 45. Parabolic Growth Plot for Cu2Se and Cu-Se? at 1709C and 50 p s i 7. .7 96 46. Parabolic Growth Plot for Cu Se and Cu3Se„ at 170°C and 1000 p s i ... 7 97 47. Effect of Stress on Growth Rates of Cu2Se and Cu3Se- at 170°C 98 48. Graph Showing Results of Zero Pressure Diffusion Following a High Pressure Anneal at 170 C 99 49. Graph Showing Results of Diffusion at 120 p s i following a High Pressure Anneal at 170°C 101 50. Growth of Cu2Se and C^Se, at 170°C under Hydrostatic Pressure 102 51. Photomicrograph of Kinkendall Experiment i n Cu-Se .... 104 52. Schematic Representation of the Dependence of Con-centration Gradient on the Thickness of C^Se 105 53. Phase Diagram of Cu-Sb 108 54. Electron Probe Traverse i n Cu-Sb Diffusion Couple .... 109 55. Photomicrograph of Diffusion Zone i n Cu-Sb at 390°C at Different Pressures 110 56. Effect of Pressure on Diffusion i n Cu-Sb at 390°C 112 o 57. Growth of Cu Sb at 390 C 113 58. Growth of Cu Sb at 390°C 114 59. Effect of Stress on Incubation Time for Cu-,Sb 115 60. Parabolic Plot for the Growth of CUoSb and Cu Sb at 390°C and 50 p s i 1 7 116 61. Parabolic Plot for the Growth of Cu~Sb and Cu2Sb at 390°C and 400 p s i . ........7.. 117 62. Effect of Stress on the Growth Rates of Cu>.Sb and Cu2Sb at 390°C 7 118 x i i Page 63. Graphs Showing Results of Zero Pressure Diffusion Following a High Pressure Anneal 120 64. Growth of Cu-Sb and Cu2Sb at 390°C and Under Hydrostatic Pressure 121 65. Microphotograph of Kirkendall Marker Experiment i n Cu-Sb at 390°C 122 o 66. Micrographs of Marker Experiments Annealed at 390 C for Different Times 124 67. Photomicrographs.of Marker Experiment i n Cu-Sb at 390°C with Different Size Markers .. 125 68. Growth of Cu_Sb and Cu-,Sb at 390°C and 850 psi 126 x i i i LIST OF TABLES Page 1. Changes i n Diffusion Coefficients with Pressure 24 2. Specific Volumes of Intermediate Phases i n Ag-Sb 43 3. C h a r a c t e r i s t i c s of Intermediate Phases i n Ni-Sb 70 4. X-Ray Data for Ni 5Sb. 72 5. ' u ' Factors and Changes i n Diffusion Coefficient with Pressure for Stress Sensitive Phases 130 6. Energy of Formation, Crystal Structure, and changes i n Specific Volume for Intermediate Phases i n Stress-Sensitive Systems 137 7. Diffusion Coefficients for the Stress-Sensitive Phases . 140 CHAPTER I INTRODUCTION 1.1.1 GENERAL The formation and growth of intermetallic phases i n d i f f u s i o n couples i s of considerable significance to metallurgists interested i n d i f f u s i o n bonding, especially i n the cladding of fu e l elements for nuclear reactors and i n the galvanizing and aluminising processes. The strength of the d i f f u s i o n bonded materials w i l l be dependent on the thickness of the intermediate phases that form during d i f f u s i o n and on the nature of the 1 2 interface. Early experiments on the Al-Ni and Al-Fe systems indicated that maximum strength i s obtained at an optimum thickness of the d i f f u s i o n zone and that pressure on the weld can be used to optimise the thickness of 3 the d i f f u s i o n zone. Observations i n Al-U indicated that a non-defective interface can be obtained on application of pressure. 1.1.2 SIGNIFICANCE OF THE STUDY The widths of the intermediate phases formed during d i f f u s i o n have been found to be very sensitive to applied pressures sometimes as low as 100 p s i . In some systems e.g. Al-Ni"'" and a-Brass/y-Brass^ the thickness of the d i f f u s i o n zone decreased with increasing pressure whereas 3 A 5 6 i n others e.g. Al-U , Cu-Sb ' and Cu-Te the width of the d i f f u s i o n zone increased. The present investigation was undertaken with a view to determining the generality of the effect of pressure on chemical d i f f u s i o n and to making a detailed examination of the influence of compressive stress and hydrostatic pressure i n those systems which are stress sensitive. 2 The aim of the investigation was to permit the prediction of the effect of stress on other systems. 1.2 REVIEW OF THE PREVIOUS WORK Most experiments on the effect of pressure on d i f f u s i o n have been carried out by pressing a specimen into a die, the specimen being i n contact with the die walls to r e s t r i c t creep, thereby giving semi-hydrostatic conditions. 2 In the Al-Fe system , an increase i n the thickness of the di f f u s i o n zone with increasing pressure was observed, with, for example, no di f f u s i o n being observed below 16,000 p s i for a one hour anneal at 525°C whereas at 40,000 p s i a zone 55y i n width was obtained. (Fig. 1 (a)). 1 8 In Ni-Al ' , two phases Ni-Al-(g) and Ni-Al-(y) appeared at zero pressure. The thickness of both the phases was progressively reduced with increasing pressure (Fig. 1 (b,c)). According to Storchheim, a pressure of 25,000 p s i at 500°C reduced the thickness of the d i f f u s i o n zone by 50 pet, with the Ni^Al phase disappearing between 22,000-40,000 p s i and the whole d i f f u s i o n zone disappearing at 68,000 p s i . Castleman and 8 o Seigle found that at 600 C the d i f f u s i o n c o e f f i c i e n t of the Ni^ A l - phase decreased by 27 pet on application of a pressure of 10,000 p s i ; the acti v a t i o n energy increased by 200 cal/mol. Simple calculation shows that the energy required to create one mole of vacant l a t t i c e s i t e s i n N i - A ^ under a pressure of 10,000 psi w i l l be approximately 120 c a l . Hence the decrease i n the thickness of the Ni-Al- phase with increasing pressure i s due mainly to the decrease i n the d i f f u s i o n c o e f f i c i e n t i n N i - A l - . Fig. 1 The effect of pressure on d i f f u s i o n i n Al-Fe and Al-Ni 4 In cx-Brass/y-Brass couples the thickness of the B-phase formed during d i f f u s i o n was reduced by 20 pet at a pressure of 20,000 p s i ^ . This again has been explained as being due to the decrease of the d i f f u s i o n c o e f f i c i e n t with pressure. 3 9 In the Al-U system several investigators ' have found that the 9 width of the UAl- phase increases with pressure. Le C l a i r e and Bear have observed that two phases, UAl- and UA1-, were present i n the d i f f u s i o n zone and that the r e l a t i v e amount of UAl- appeared to increase with pressure. 3 This has been contradicted by Castleman who found that only the UAl.- layer grew to a substantial thickness and that UA1_ appeared infrequently. A multiphase zone was also observed with no d e f i n i t e boundary. He observed that the rate of formation of UAl- at 520°C was 75 pet faster at a pressure of 20,000 psi as compared with a pressure of 2,500 p s i . The thickness of UAl- approached an asymptotic value as the pressure was increased to 20,000 p s i and the d i f f u s i o n zone became more sound on increasing pressure. I t has been suggested that the increase i n the width of the d i f f u s i o n zone i s due to the closure of the Kirkendall pores with pressure. This w i l l be discussed i n more,detail i n section (1.4.4). In Cu-Sb the effect of pressure i s greater than i n the systems 4 5 described previously. According to Heumann ' only one phase, Cu-Sb(y), appeared i n the d i f f u s i o n zone at a stress of 495 p s i , but above a pressure of 850 psi two phases ,Cu_Sb("y) and Cu^Sbdc), were present. I f a d i f f u s i o n couple containing both Cu-Sb and Cu-Sb was annealed at low stress levels the Cu-Sb grew at the expense of the Cu-Sb, whereas i f a higher pressure was used the reverse phenomenon occurred. This i s shown i n f i g . 2 (c). From these measurements they concluded that the Cu-Sb can grow only above a 5 C u - S b 1 3 5 7 9 / T i m e i n / h r . ( c ) F i g . 2 P r e s s u r e e f f e c t ( a ) i n U - A l , (b ) a - B r a s s / y - B r a s s a n d ( c ) t h e e f f e c t o f c h a n g i n g p r e s s u r e d u r i n g d i f f u s i o n a n n e a l i n C u - S b 6 pressure around 570 p s i ; below this pressure not only was growth impeded but the phase disappeared. They also observed that the Cu-Sb required an incubation period of approximately one hour after which I t grew at a much faster rate than Cu.Sb. Heumann gave a tentative explanation of this effect based on the formation of Kirkendall porosity at the d i f f u s i o n i n t e r -face. Diffusion i n the Cu-Te system^ showed marked s e n s i t i v i t y to uni-a x i a l compressive stress, with a stress of 20 p s i making a s i g n i f i c a n t difference to the width of the d i f f u s i o n zone. On annealing at 250°C under zero stress, two phases, Cu^Te. and CuTe, were present i n the d i f f u s i o n zone. The t h i r d stable phase ,Cu-Te,appeared under compressive loading and i t s thickness increased apparently l i n e a r l y with increasing stress. The thickness of the Cu^ Te.. appeared to increase with stress up to 400 p s i and then decreased whilst the thickness of CuTe decreased progressively with stress. The effects of stress on CuTe and Cu^Te^ were, however, small compared to the effect on Cu-Te. These results are shown i n f i g . 3 (a). As the pressure varied from 0 to 1,500 p s i , the thickness of Cu-Te increased from zero to 86 pet of the t o t a l width of the d i f f u s i o n zone. Growth of the phases Cu^Te. and CuTe was parabolic with time indicating a volume d i f f u s i o n controlled mechanism. The results for growth of Cu.Te showed considerable scatter and i t was not possible to decide whether growth was controlled by d i f f u s i o n or by interface reaction (linear growth). Diffusion couples with a wide band of Cu-Te were prepared by d i f f u s i n g at 250°C at a stress of 500 p s i . After 48 hours the load was removed and d i f f u s i o n was allowed to proceed at zero stress. The results are shown i n f i g . 3 (b). I t i s observed that the Cu.Te zone becomes progressively thinner with 250°C, 11 hr. 6 (Brown et. a l . ) - T o t a l s 0 -^ ^ ^ ^ Cu_Te Cu.Te-^<<^~?^~^~^r-*—~_—* 4 3 _ _ _ 4 j ^ _ ^ L _ A | CuTe 'O 250 500 7jfo 1000 1250 1500 Stress i n p s i (a) 0 4 8 12 16 /Time in/hr« (b) Fig. 3 (a) Effect of stress on d i f f u s i o n i n Cu-Te at 250°C and (b) Shrinkage of Cu-Te at 250°C and zero stress. Original couple was annealed for 48 hrs. at 250°C and 500 p s i . 8 increasing time and disappears within 16 hours, whereas Cu^Te^ and to a lesser extent CuTe grow at the expense of Cu.Te. These experiments show that Ct^Te i s not stable at zero stress i n a k i n e t i c system. In this case also the effect of stress has been tentatively explained to be due to incipient Kirkendall porosity. p 10 Experiments on Cu-Ag two phase couples by Lindemer and Guy » have shown that d i f f u s i o n i s increased by orders of magnitude when a pressure of 1,000 p s i i s employed as compared to d i f f u s i o n under zero pressure. The application of pressure has been shown to produce successful bonding plus d i f f u s i o n i n Al-Zr, Cu-Pt and ternary Cu-Ni-Zr couples under experimental conditions which f a i l e d to produce a successful d i f f u s i o n zone i n the absence of pressure. In summary,two types of systems reacting d i f f e r e n t l y to increasing 1 8 pressure have been observed. The effect of pressure on Ni-Al ' and a-Brass/y-Brass^ which show a decrease i n the d i f f u s i o n zone thickness can be ra t i o n a l i s e d by considering the decrease i n the d i f f u s i o n c o e f f i c i e n t with pressure. The increase i n the width of the d i f f u s i o n zone with 3 9 2 4 5 6 pressure i n the U-Al ' , Al-Fe , Cu-Sb ' and Cu-Te systems cannot be rationalised by either changes i n d i f f u s i o n c o e f f i c i e n t or changes i n the equilibrium concentrations at the phase boundary. The explanation given by most workers i s the formation of Kirkendall porosity during d i f f u s i o n which i s affected by the application of pressure i n such a manner as to give an apparent increase i n the d i f f u s i o n c o e f f i c i e n t . 9 1.3 THEORY OF DIFFUSION 1.3.1 ATOMIC MECHANISMS FOR DIFFUSION A variety of mechanisms have been proposed to explain the di f f u s i o n process. The interchange mechanism involving correlated rotation of two or more atoms about a common centre i s associated with large distortions and does not take place to any extent. The i n t e r s t i t i a l mechanism involves the motion of an atom from one i n t e r s t i t i a l s i t e to another and i s applicable to systems with open structures and to atoms of small atomic r a d i i . The most probable mechanism for close-packed l a t t i c e s i s the vacancy mechanism, i n which atom movement takes place by interchange of vacancy-atom positions. Short-circuit d i f f u s i o n mechanisms (grain boundary d i f f u s i o n and disloc a t i o n pipe diffusion)are s i g n i f i c a n t only at low temperatures. On re l a t i n g the macroscopic d i f f u s i o n c o e f f i c i e n t to the atomic 13 jump mechanism by random walk theory , the following relations are obtained: 2 D = a X T ( i n t e r s t i t i a l ) 2 (1.1) D = a A T Nv (vacancy) where D = macroscopic d i f f u s i o n c o e f f i c i e n t . a = constant characteristic of the c r y s t a l structure. X = l a t t i c e parameter. T = jump frequency Nv = equilibrium vacancy concentration i n atom f r a c t i o n . Substituting expressions for T and Nv i n eq. (1.1) gives: 10 D = - i A 2, exp (^) exp (- ||&) for i n t e r s t i t i a l d i f f u s i o n (1.2) D = -r A v exp (-ASf + AS; for vacancy d i f f u s i o n where v = v i b r a t i o n a l frequency of atoms i n the c r y s t a l . ASf, AS. m = entropies of formation and migration of the defect. AH f, AFL-j = enthalpies of formation and migration of the defect. The term i n the square bracket i s temperature independent and i s generally represented as Do, .1.3.2 KIRKENDALL EFFECT 14 The o r i g i n a l experiments of Smigelkas and Kirkendall on marker movement i n the Cu/a-Brass system and further analysis by Darken''""' indicate that different species have different d i f f u s i o n coefficients and that i n e r t markers move towards that side of the couple with the faster d i f f u s i n g species. In the Cu/a-Brass system zinc has a higher d i f f u s i o n c o e f f i c i e n t than copper. Since each atom which moves i n one particular d i r e c t i o n causes a vacancy to move i n the opposite d i r e c t i o n , there w i l l be a net flow of vacancies from copper towards brass, equal at any point to the difference between the zinc and copper fluxes. The required net transfer of atoms towards the copper i s much greater than could be effected by the number of vacancies which are i n thermodynamic equilibrium, so that some sources of vacancies must be operating i n the copper. Also the excess vacancies i n the brass side must disappear i n some way i f brass i s to shrink and the markers are to move towards the brass side of the couple. 11 Possible sources of vacancies are grain boundaries, climbing edge 16 17 dislocations , moving jogs . Possible sinks for vacancies are the reversed dislocation movements, formation of faulted d i s l o c a t i o n loops and stacking f a u l t tetrahedra by collapse of vacancy clusters, and the formation of pores. In this thesis most attention w i l l be given to the development of porosity. However, before going on to the d e t a i l s of sources and sinks for vacancies i t i s necessary to establish the vacancy d i s t r i b u t i o n i n the d i f f u s i o n zone. 1.3.3 VACANCY DISTRIBUTION IN THE DIFFUSION ZONE The phenomenological model of the Kirkendall effect developed 15 18 by Darken and Hartley and Crank used widely i n d i f f u s i o n analysis assumes a) conservation of l a t t i c e s i t e s and b) that vacancies are maintained, everywhere,in equilibrium. Observations of porosity i n the 19-23 d i f f u s i o n zone, deformation markings on the surface of specimens and 23 24 different rates of marker movement at different points of the couple ' , a l l suggest a non-equilibrium vacancy d i s t r i b u t i o n i n the d i f f u s i o n zone. 23 26 27 This has been analysed by Seitz ' , B a l l u f f i and Fara and recently by 90 Schlipf . B a l l u f f i and Fara considered d i f f u s i o n i n a substit u t i o n a l a l l o y containing vacancies }and developed equations to represent d i f f u s i o n of the two substit u t i o n a l species i n terms of the concentration gradient, d i f f u s i o n c o e f f i c i e n t s , vacancy l i f e time and the mass flow vel o c i t y which was assumed to be due only to sources and sinks for vacancies i n different parts of the d i f f u s i o n zone. Numerical solutions of their equations are shown i n f i g . 4 and 5 and were evaluated assuming that essentially a single species was di f f u s i n g and that the vacancy l i f e time was small and constant. T i s the r e l a t i v e vacancy l i f e t i m e and i s given by Nvt x = — , where N„ = vacancy concentration. t = t o t a l d i f f u s i o n time. T = vacancy l i f e t i m e and R i s the r e l a t i v e excess vacancy concentration and i s given by R - *Z- 1, N° v where N° = the equilibrium vacancy concentration. Fig. 4 shows that composition p r o f i l e s show marked deviation from parabolic behaviour at small x i . e . for small d i f f u s i o n time (t<<T)but approach the parabolic case as the d i f f u s i o n time increases. In F i g . 5 i t can be seen that the maximum vacancy supersaturation and subsaturation expressed i n terms of R decreases as the d i f f u s i o n zone widens and d i f f u s i o n progresses. 1.3.4 KIRKENDALL POROSITY Fig. 5 shows a region of vacancy supersaturation on that side of the d i f f u s i o n couple having the faster d i f f u s i n g species. This vacancy supersaturation can result i n the development of pores which move out as di f f u s i o n proceeds. Porosity has been found i n many systems such as _ ...29 . . 29 r ...23,29,30 _ A,31,32 _,„29,30 ... . 29,30 Fe-Ni , Ag-Au. , Cu-Ni , Cu-Al , Ag-Pd , Ni-Au and XA 23 31 32 Cu/a-Brass ' ' ' The amount of porosity varies from system to system, generally increasing with increasing d i f f u s i o n time and becoming greater the larger the concentration gradient. 13 -.8 -.4 0 .4 .8 X = X/2/Dt Fig. 4 Diffusion penetration curves as a function of X and x. ( B a l l u f f i and Fara27) Pi .04 .02 0 -.02 -.04 -.06 h * T = 0.3 S*T = 1.2 = 19.2 » For para-bo l i c growth - i i i i 1.6 0 -.8 X = X/2/Dt -1.6 F i g . 5 The r e l a t i v e excess vacancy concen-t r a t i o n , R, as a function of x a n d T-( B a l l u f f i and Fara 2 7) 14 THEORIES OF KIRKENDALL POROSITY Supersaturation of vacancies leads to the formation of voids. The excess vacancy concentration N v needed to nucleate a spherical void of radius ' r ' i s given by the Gibbs-Thomson r e l a t i o n l n ^ - = T^T- (1.3) „o NkTr N v where N° = equilibrium vacancy concentration, k = Boltzmann's constant. T = absolute temperature, s = surface energy. N = atomic density. Vacancies may condense to form voids i n a perfect l a t t i c e i f N* 33 3 — 3 1 i s of the order of 100 or greater i f a c r i t i c a l radius of 10 cm i s N° v assumed for the nuclei. This number i s very high and homogeneous nucleation rarely takes place. The supersaturation necessary w i l l be much less i f heterogeneous nucleation i s considered, the nucleation s i t e s being small voids, cracks 35 36 36 37 and foreign p a r t i c l e s (observed i n Cu/a-Brass ' and Cu-Ni ). B a l l u f f i has shown that a maximum vacancy supersaturation of only 1 pet i s necessary for the heterogeneous nucleation of voids, i n agreement with the experimental 36 results i n Cu-Ni . Assuming 1 pet vacancy supersaturation, Seitz has shown that nuclei of radius of the order of 1,000 atomic distances w i l l be effe c t i v e for the growth of voids. He has also concluded from the 23 32 results of Barnes and Buckle and B l i n that between a thi r d and a half of the vacancy current i s transferred to pores and this has been observed 34 i n Cu/a-Brass 15 19 Brlnkman has taken into account the p o s s i b i l i t y of a change i n the potential energy i n the region around a void upon absorption of a vacancy when a stress f i e l d i s present. He has shown that a stress equivalent to the y i e l d stress of the material w i l l develop i n the di f f u s i o n zone i f i t i s assumed that only 1 pet of the vacancies are i n t e r -acting with dislocations. In the presence of a.stress f i e l d 'F' the 19 Gibbs-Thomscn equation i s given by Nv In N° v 2 5 3 F (3F - % r 4(X + 2y) W i r where A and y are Lame's constants. /NkT (1.4) 4 I f F i s taken to be of the order of 1.5 x 10 p s i , this quantity -3 changes sign when r = 10 cm. for Cu. Thus, once nuclei of this size are formed, no excess vacancy concentration i s necessary for their growth 19 i f a stress f i e l d of s u f f i c i e n t strength i s present. Brinkman suggests that these nuclei may form by a process of f i s s u r i n g a t the interface between the portion of the d i f f u s i o n zone undergoing p l a s t i c deformation under the stress f i e l d and the region outside the d i f f u s i o n zone which i s free of stress. Porosity formed during the d i f f u s i o n process can act as an obstruction to d i f f u s i o n by decreasing the cross-sectional area, p a r t i c u l a r l y when a substantial f r a c t i o n of the area i s covered by voids. This i s important i n the present work and w i l l be discussed i n more d e t a i l i n a later section. 16 1.3.5 MATHEMATICS OF DIFFUSION Fick's f i r s t law i s given by J = - D ^ (1.5) where J = flux/unit volume/unit time. D = d i f f u s i o n c o e f f i c i e n t concentration gradient. 6c. 6 x Fick's second law i s given by |£ = J- ( D i £ ) (1.6) 6 t 6 x 6 x For the semi-infinite single phase d i f f u s i o n couple shown i n f i g . 6 (a), eq. (1.6) can be transformed to give a d i f f u s i o n equation i n a single variable, X = — . This can then be integrated twice assuming D to /t be constant to give the solution, X c l " co So = h 1 - erf 2vu5" (1.7) X _ 2 e n dn, X 2 where erf ( ) i s the Gaussian error function defined by erf x = — 2v_) /n" o In systems with m i s c i b i l i t y gaps between the various stable phases, discontinuities occur i n the concentration vs distance p r o f i l e across the two phase regions, as shown i n f i g . 6 (b). Diffusion within the various phases i s quite normal and as i n single phase systems, the p r o f i l e can be drawn i n X-space to eliminate x and t as independent variables. This means that the phase boundaries or discontinuities occur at constant values for X and so the motion of the phase boundary i s parabolic with time. If i t can be assumed that the di f f u s i o n c o e f f i c i e n t i n an intermetallic phase i s independent of concentration, then the composition F i g . 6 Schematic representation of d i f f u s i o n p r o f i l e (a) for a.system with complete s o l i d s o l u b i l i t y (b) for a syst)em having one intermediate phase. 18 p r o f i l e i n that phase i s a portion of an error function. For the simple case where there i s no s o l i d solution i n the terminal phases, the p r o f i l e shown i n f i g . 6 (b) i s given by: c = <_1 c _, erf c . erf 2VTJ a l a 2 erf erf c . - c _ yA yB a l a 2 erf erf 2VTJ 2VTJ erf 2/5" 2VTJ 2VT. where and are the growth constants at the A/y and y/B interfaces respectively and D i s the d i f f u s i o n c o e f f i c i e n t of the y-phase. (1.8) By considering the mass balance across the phase interfaces i . e . taking the motion of phase boundary to be controlled by the fl u x down the concentration gradient, values of and a_ are given by: ( CA " CyA ) T al = ( cyA " CyB ) E > i S e X p (" a l 2 / 4 D ) a l a 2 erf erf — 2vTJ 2v_) and ( CyB " CB> T U 2 " " 2 ( CyA ~ CyB ^ (~ 2 ) erf 2/5 erf 2v/fj ( 1 . 9 ) In the case where the intermetallic compound occurs at 50 at pet and has an equal composition range on either side of stoichiometry i . e . c _. - c_ = c. - c . , a- = - a, = a and c„ = 0, eq. (1.9) can be written as: y B B A yA 2 1 B n /?T (c . - c _)D'S exp (- a /4D) CYB ~Y ' a = —^ ^ - (1.10) 2 erf 2/5 19 Eq. (1.10) shows cl e a r l y that as the composition range of the int e r m e t a l l i c compound tends to zero, the growth rate of the phase w i l l become very small. The analysis obtained above can be extended to cases where more than one intermetallic phase appears i n the d i f f u s i o n zone. Growth of a l l phases w i l l be parabolic with time i f d i f f u s i o n controlled with the growth rate of any intermediate phase depending on factors such as the d i f f u s i o n c o e f f i c i e n t within the phase and i n the adjoining phases, the homogeneity range of the phase and the concentration range of the adjacent two phase 38 regions. Baird has suggested that i n int e r m e t a l l i c compounds with a very low homogeneity range, large growth rates are possible because of the thermodynamic factors which give extremely large d i f f u s i o n coefficients within the phases. In systems showing only one intermetallic phase and no s o l i d 39 s o l u b i l i t y the growth rate i s given by „ (c - c.) (c- - c„) <*i = 2 0 , ~ ^vH £ _ x (1.11) 1 (c. - c )(c- - C - + c. - c ) 1 o j _ 1 o i f a linear concentration p r o f i l e within the phase i s assumed as shown i n f i g . 7 (a), c 3 Phase 1 Phase 2 («; »+<— «J c i l 1 1 2 l C l C o 1 o (a) '1 - x -v Fig. 7 Schematic composition p r o f i l e s for two cases of intermetallic d i f f u s i o n 20 The same analysis can be extended to systems showing more than one intermetallic phase and no s o l i d s o l u b i l i t y . Assuming a linear concentration gradient within the phases, the concentration gradients i n phases 1 and 2 are given by: (1.12) 6c, _ c4 " °3 6 X 1 " ? 2 " ?3 6c, °2 " C l and — ) = — 6x - _ Considering the mass balance at £- gives d.„ . c, - c_ ( c c - c.) — 7 — = -D.. — > - -D. — 5 4' dt 1 6x 1 1 _2 _ _ C4 " C3 and hence a-(a- - a.) = -2D. (1.13) 3 2 3 1 c c -c, 5 4 a l _ a3 since - = — , .„ = — and 5- = — /t 2 /_" 3 /t" Similarly, the mass balance at £^ gives "1< _ " ° 2 > * 2 D 2 " c f ^ T 1 ^-14> 1- o a^, a. and a- can be found by determining the Matano interface i n the composition p r o f i l e and the d i f f u s i o n coefficients i n the phases can be calculated from eqs. (1.13) and (1.14). 40 1.3.6 DIFFUSION IN IONIC COMPOUNDS In multiphase d i f f u s i o n involving growth of ionic compounds, the kinetics of the process w i l l be controlled either by d i f f u s i o n of ions through the intermediate phase or by phase boundary reactions including transport through the space charged boundary layer. Diffusion i n i o n i c crystals takes place by the movement of defects. In ioni c c r y s t a l s 3 d e v i a t i o n from stoichiometry takes place by 21 the formation of cation vacancies or i n t e r s t i t i a l s , or anion vacancies. To maintain e l e c t r i c a l n eutrality s i m i l a r number^ of electrons or holes must be formed. Diffusion i n non-stoichiometric compounds takes place by a movement of ions which i s always coupled with a flow of electrons or holes to maintain e l e c t r i c a l neutrality at every point i n the di f f u s i o n zone. Electrons can diffuse much faster than ions but are constrained to move i n step with the ions and merely have the effect of doubling or t r i p l i n g the ion d i f f u s i o n c o e f f i c i e n t . The nature of the diff u s i n g species can be determined by Kirkendall marker experiments. For example.in Ag„S s i l v e r ions are the Ag Ag2S S Ag + + e -»• Ag ->• Ag + + e S + 2 e = S ~ 2Ag + + S " = Ag.S Fig. 8 Schematic representation of d i f f u s i o n i n Ag-S diffusing species^"*". S i l v e r atoms ionize at the Ag/Ag2S boundary to give Ag + ions plus electrons. These diffuse through the Ag2S phase to the Ag2S/S boundary where chemical reaction takes place to form Ag2S and thus give r i s e to an increase i n the thickness of the di f f u s i o n zone. Since Ag + ions are diffu s i n g i n Ag„S, Kirkendall markers w i l l remain at the Ag/Ag»S interface. 22 1.4 EFFECT OF PRESSURE ON MULTIPHASE DIFFUSION 1.4.1 POSSIBLE EFFECTS Pressure or u n i a x i a l stress can affect the width of the d i f f u s i o n zone by one or more of the following processes; a) Alteration of the d i f f u s i o n c o e f f i c i e n t . b) Alteration of the equilibrium compositions of the phases. c) Changing the conditions for the formation of Kirkendall porosity thereby affecting the d i f f u s i o n kinetics of the system. The r e l a t i v e significance of each of these processes w i l l be discussed i n turn. 1.4.2 EFFECT OF PRESSURE ON DIFFUSION COEFFICIENT The effect of hydrostatic pressure on d i f f u s i o n has been the 42 43 subject of increasing attention during the past decade ' . I t i s now well established that the s e l f d i f f u s i o n c o e f f i c i e n t of an element i s 44 45 reduced by hydrostatic pressure ' and that the anisotropy of the s e l f 46 d i f f u s i o n c o e f f i c i e n t i s reduced i n non-cubic metals such as zinc The d i f f u s i o n coefficient, D, i s given by eq. (1.1) and(1.2) i n page 10 . The effect of pressure on D w i l l be a combined effect on the equilibrium defect concentration and on the jump frequency. Taking logarithms of eq. (1.2) and d i f f e r e n t i a t i n g with respect to pressure gives: 23 and 6 In D 6P 6 In D 6P _1_ r_SAH__. ,6 In D0. " kT 6P _, 6P \ for i n t e r s t i t i a l d i f f u s i o n (1.15) ____ kT V 6P ; T ^ 6P ; T 6 In D ^ 6P \ for vacancy d i f f u s i o n The terms i n D- (i.e. v, X, AS m, AS^) do not vary with pressure unless high pressures are used and hence 6 In D, 6P 0 Terms (~^) have the dimensions of volume and are called the T act i v a t i o n volumes , i.e SAH 6P (^_ni) = V m i s the activation volume for migration of the defect and (^^) = i s the activation volume for the formation of the vacancy. 6P Integrating eq. (1.15) gives: D(P) = D(o) exp (- ^ ) D(P) = D(o) exp for i n t e r s t i t i a l d i f f u s i o n -P(V m + V f) (1.16) kT for vacancy d i f f u s i o n where D(P) and D(o) are the d i f f u s i o n coefficients at pressures P and zero, respectively. For i n t e r s t i t i a l d i f f u s i o n the effect of pressure i s to make i t more d i f f i c u l t for an atom to jump from one atom s i t e to the next. This effect i s quite small, t y p i c a l l y giving 0-10 pet reduction i n the d i f f u s i o n 5 43 c o e f f i c i e n t at 7 x 10 p s i . In the case of vacancy d i f f u s i o n where both formation and migration of vacancies are affected the o v e r a l l effect of 24 TABLE I D(P)/D(o) FOR VARIOUS MATERIALS AT T/Tm = 0.5 AND P = 10,000 psi 3 Material V Q i n A° /atom T m i n °K T i n °K D(P)/D(o) i n pet . 1C. 047 1233.5 611.75 88.4 Ag 15.2 Pb 21.6 4 8 610.4 305.2 70.3 49 Ag-Zn(27 pet) 8.9 1023.0 511.5 91.6 (solidus) L i 6.0 5 0 553.0 276.5 89.7 Na 20.5 4 4 370.6 185.3 57.6 P(white) 49.8 4 3 317.4 158.7 20.9 25 pressure on d i f f u s i o n rates i s much higher. Values of j? have been ° D(o) calculated at 10,000 p s i at T/Tm = 0.5 and are shown i n Table 1 . A l l the experiments described above refer to tracer s e l f - d i f f u s i o n . No work has been carried out on the effect of pressure on the chemical d i f f u s i o n . However, i t i s believed that effects of similar magnitude to s e l f d i f f u s i o n would be observed. 1.4.3 EFFECT OF PRESSURE ON EQUILIBRIUM COMPOSITION Pressure can affect the d i f f u s i o n characteristics i n multiphase systems by changing the composition range or the s t a b i l i t y of the phases, thereby changing the d i f f u s i o n p r o f i l e of the system. Extensive research has been carried out on the effect of pressure on the temperature of polymorphic transformation and melting point of pure metals. On the other hand research on phase e q u i l i b r i a i n multicomponent system has been .. ,51,52 very limited The effect of pressure on the phase diagram depends on the molar volumes of the intermetallic phases and the terminal phases. A schematic representation of the effect of pressure on phase e q u i l i b r i a i s given i n f i g . 9 (a). The a, y and 3 phases are i n thermodynamic equilibrium at temperature T i n f i g . 9 (b). In case 1, where V^ > V^ > V., application of pressure increases the composition range of the 3-phase and decreases that of the y-phase. In case 2, where V^ > V_ > V , the composition range of y increases whereas that of a i s decreased. In general, i t i s observed that pressure increases the f i e l d of s t a b i l i t y of the phase with lower molar volume. This concept can be developed quantitatively by thermodynamic analysis'^"'"^ as follows: 26 0 p s i under pressure > V > V Y a (a) Free energy diagrams at temp. 'T' showing v a r i a t i o n of composition with pressure when the s p e c i f i c volumes are d i f f e r e n t l y related. V^, Vg, and V are the molar volumes of the" respectively. 6 and y phases (case 3) 27 In binary systems the boundaries and c r i t i c a l points for two and three phase e q u i l i b r i a can be described mathematically by relationships obtained by equating the chemical potentials or p a r t i a l molar free energies of both components at the phase boundaries i . e . (refer to the a/y phase boundary i n f i g . 9 (b)). F. 011 = 7 ° ! A 1 c A I c a y y a (1.17) «* Vic " Vic ay ya , ~ <5F where F. = F - c •_— A 6c 6F ( 1 - 1 8 ) and F B = F + (1 - c ) ^ F = free energy of the a l l o y , c = composition. Equation (1.17) can be differentiated with respect to pressure, and using eq. (1.18) the change i n equilibrium composition with pressure can be formulated and i s given by: dc 1 - c 6F Y _ = • AV | • (r~- | T 1 dP c - c 'c 6c 1 c ya ay ay Y a where AVI = V aI - (1 - c )V Y | - c V Y I 1 c 1 c ay A 1 c ay B 1 c ay ay ya ya (1.19) a i with V = molar volume of the a-phase at composition c 1 c c ay _ ay _ ' V Y| , V Y| = p a r t i a l molar volumes of A and B at composition A 'c ' B 'c ya ya c. i ya' The term AV| essentially represents the difference i n the ay molar volumes of the a-phase and the yphase. I f suitable thermodynamic and volumetric data are available eq. (1.19) can be integrated to obtain c (T,P). ya 28 In the special case where there i s no terminal s o l i d solution and i n which the y-phase has a low range of composition on either side of 50 at pet, eq. (1.19) can be modified to g i v e ^ dc (1 - 2c )(1 - c ) ya _ ya ya dP dc RT c ya I i - ( 2 C Y B ' 1 ) C Y 3 V A " V A A A 1 c ya_ (1.20) dP R T ( 1 - V V - V Y| B B 'c A^» ^B = m ° l a r volumes of A and B respectively I t i s important to note that the effect of pressure, on equilibrium composition i s characterised by the molar volumes of the phases i n equilibrium. Thus the compositional f i e l d of the y-phase w i l l expand dc dc with pressure i f ya i s negative and yg i s positive and hence depends dP dP on the sum of the volumetric terms i n eq. (1.20) being positive. In iron-base alloys which show a y-loop, hydrostatic pressure expands the y-loop by increasing the s t a b i l i t y of the denser f.c.c. phase at the r . , -I j . . 51-58 expense of the less dense b.c.c. a-phase 1.4.4 RELATIVE SIGNIFICANCE OF EFFECT OF PRESSURE ON DIFFUSION COEFFICIENT AND PHASE BOUNDARY COMPOSITION 59 Castleman has discussed the r e l a t i v e importance of changes i n d i f f u s i o n c o e f f i c i e n t and changes i n phase boundary composition i n systems showing an intermediate phase (y) and no s o l i d s o l u b i l i t y . The d i f f u s i o n p r o f i l e i s given by eq. (1.10) i n page 18. 29 Di f f e r e n t i a t i n g eq. (1.10) with respect to pressure and rearranging gives: ,1 da. , ,1 dD, . 1 d CyA 1 d c Y B , ... ( a ^ } = + y ( c ~ T ~ ^ P } ( 1 ' 2 1 ) yA Y B C Y A where y = ^ 2~ (1-22) CY A ( 1 + |>> " C Y B ( 1 " Equation (1.21) implies that a value of \i>>h w i l l cause pressure induced concentration changes to outweigh any effect resulting from pressure induced d i f f u s i v i t y changes on the growth kinetics of the intermediate phase; i f y<<*_ the s i t u a t i o n i s reversed. 59 Castleman has calculated the change i n composition with hydrostatic pressures up to 7.4 x 10^ p s i using a s i m p l i f i e d version of eq. (1.19) [page 27j » with the assumptions that the free energy curves are essent i a l l y parts of c i r c l e s and that the shapes of these curves do not change with pressure, being merely raised to higher values on application of pressure. His calculations show that the s h i f t s i n composition are very small and do not exceed 0.1 pet of the o r i g i n a l value unless a pressure 3 induced free energy increase of over 600 cal/g atom (25,000 cm atm.) i s postulated i . e . a molar volume change of 5cc i s assumed which i s very high for the systems studied. Using these values, calculating the factor 'y' and determining -^) from experiment, one can calculate the contribution of the change i n the d i f f u s i o n c o e f f i c i e n t to the growth rate. Castleman has calculated these factors and found that for the Ni-Al system i s negative indicating a decrease i n the d i f f u s i o n c o e f f i c i e n t and that the contribution from this factor i s much higher than that due to concentration 30 changes with pressure. Hence he rati o n a l i s e s the decrease i n the thickness g of the Ni.Al- layer with pressure to be due to a decrease i n the d i f f u s i o n c o e f f i c i e n t . However,in U-Al i n which the width of the UAl^ layer increases with pressure 3, a similar calculation suggests a positive — indicating an apparent increase i n the d i f f u s i o n c o e f f i c i e n t , the term due to concentration changes being negligible. This i s i n contradiction with the observation that the d i f f u s i o n c o e f f i c i e n t generally decreases with increasing pressure. An alternative explanation of the pressure effect i n U-Al w i l l be discussed i n the next section. The effect of pressure on the d i f f u s i o n c o e f f i c i e n t i s approximately one order of magnitude greater than the effect due to the equilibrium concentration change. Consequently a pressure induced change i n i n t e r f a c i a l concentration i s not important unless the function y i s at least greater than f i v e and probably greater than f i f t y . I t may, therefore, be concluded that the main effect of pressure w i l l be due to apparant variations of the d i f f u s i o n c o e f f i c i e n t . 1.4.5 EFFECT OF PRESSURE ON KIRKENDALL POROSITY The third possible factor that may be sensitive to pressure i s the Kirkendall porosity. Study of the Kirkendall effect under hydrostatic pressures of large magnitude (7.7 x 10"* psi) i n In-TJ.^ and Fe-V^ "*" did 62 not show any porosity i n the d i f f u s i o n zone. Geguzin has observed that the amount of Kirkendall porosity decreases with increasing pressure - i n the Cu/a-Brass system porosity completely disappeared above 145 psi and i n the 36 Cu-Ni system no porosity was observed above 1420 p s i . Barnes and Mazey have studied the effect of pressure i n the Cu-Ni system i n d e t a i l . They 31 observed that a hydrostatic pressure of 1300 psi at 1000°C prevents the formation of voids, and that a pressure of 2300 p s i eliminates voids previously formed by a 4 hour 1000°C anneal i n vacuo. The large difference i n these two pressures indicates that the pressure of 1300 p s i does not merely collapse voids which form early i n the anneal. The voids retained an approximately spherical shape during their regression suggesting that the collapse was by a d i f f u s i o n a l process rather than a deformation process. They explain their results by assuming a hydrostatic stress condition and introducing a term PV i n the Gibbs-Thomson equation (eq. (1.3) on page 14), PV being the extra work done i n forming a void of volume V against the external pressure P. Hence^eq. (1.3) i s modified to kTN In — = — + P (1.23) N° v Their calculations indicate that the c r i t i c a l r a d i i i n the Cu-Ni system are, r (1300 psi) = 2.8 x 10~ 5 cm. c r (0 psi) = 1.2 x 10~ 5 cm. c Hence^ucleation of pores at high pressures i s more d i f f i c u l t than at low pressures. The porosity developed i n single phase systems can be quite extensive i f there i s a s i g n i f i c a n t difference i n the d i f f u s i o n rates of the two species. In Ag-Au, for example, approximately 40 pet of the cross-30 sectional area of the d i f f u s i o n couple i s taken up by pores . This extensive porosity can s i g n i f i c a n t l y hinder d i f f u s i o n and lead to a noticeable decrease i n the width of the d i f f u s i o n zone. 32 In multiphase systems the effect can be much greater, since i n some intermetallic compounds essentially only one component i s d i f f u s i n g . This means that the necessary vacancy fl u x has the same magnitude as the d i f f u s i o n f l u x and also that the vacancies w i l l condense out at one plane i n the d i f f u s i o n zone. Hence i n such systems there w i l l be a strong tendency for porosity to interfere with the d i f f u s i o n f l u x . Application of an external pressure to the system w i l l prevent pores being formed and so give a wider d i f f u s i o n zone. The stresses required for this are expected to be comparable to those i n a single phase system and would generally be less than 2500 p s i . This explanation has been used to explain the results on A 5 6 3 systems l i k e Cu-Sb ' , Cu-Te and U-Al already discussed i n pages 4-6' A l l these systems have a large Kirkendall effect and so w i l l have the large vacancy fl u x necessary to develop extensive porosity. I f this explanation i s correct, one would expect the pressure induced increase i n layer growth to disappear once the pressure i s s u f f i c i e n t l y great to eliminate the macroscopic defects. CHAPTER I I EXPERIMENTAL' 2.1 CHOICE OF SYSTEMS The object of this work was to study the effect of stress on multiphase d i f f u s i o n i n a range of systems. The systems selected for this study were determined by the following factors. 1. Materials undergoing rapid oxidation are d i f f i c u l t to handle i n the apparatus used 2. Systems should be such as to y i e l d a measurable d i f f u s i o n zone at r e l a t i v e l y low temperatures 3. The materials should not creep i n the course of a di f f u s i o n anneal. The systems studied were Cu-Zn, Cu-Sn, Zn-Se, Zn-Sb, Ag-Te, Al-Ag-Sb, Ag-Se, Ni-Sb, Cu-Sb, and Cu-Se. 2.2 APPARATUS The apparatus used for preparing d i f f u s i o n couples under an applied stress i s shown i n f i g . 10. A uni a x i a l compressive load was applied to the system through a simple lever bar. A stainless s t e e l (316) rod activated by a lever arm lay inside a stainless s t e e l tube. The d i f f u s i o n couple lay on top of the steel rod i n a specimen holder and stress was applied to the couple between the rod and a plug welded into the centre of the tube. To ensure a uniform stress across the couple a hemispherical boss and cup were used to transmit the load to the di f f u s i o n couple. A 400 w. tube furnace with a uniform hot zone 3" long s l i d around the stainless s t e e l tube, and maintained the assembly 34 Furnace Thermocouple Well Welded Steel Plug Pressure Transmitting Boss Specimen Holder Diffusion Couple Stainless Steel Furnace Tube Stainless Steel-Rod Fig. 10 Apparatus for carrying out d i f f u s i o n under compressive Stress 35 at the desired temperature. A thermocouple situated 1/2" from the specimen operated a proportional temperature controller which maintained the specimen temperature constant to ± 2°C. A clearance of 1/16" between the specimen holder and the specimen was maintained to ensure a uniaxial compressive load. The pressure applied had a repr o d u c i b i l i t y of ± 10 p s i , the main source of error being i n the measurement of specimen dimensions. Error due to f r i c t i o n was avoided i n the design of the apparatus. The apparatus was designed to be used at 600°C with a stress of up to 10,000 p s i . The lever bar was calibrated for a specimen size of 0.5" i n diameter. 2.3 MATERIALS AND SPECIMEN PREPARATION The materials used were supplied by Western Alloys and Metals Ltd. (Cu), Cominco (Ag and Zn), International Nickel Company (Ni), Wah-Chang Corp. (Zr), Fairmount Chemical Co. Inc. (Sb and Se), Vulcan Detinning div. (Sn) and were of the following purity: Cu 99.92 pet. Ag 99.95 pet. Ni 99.92 pet. Sb 99.8 pet. Se 99.99 pet. Zn 99.99 pet. Zr 99.99 pet. Sn 99.95 pet. Copper, s i l v e r , and zirconium discs were cut from bar stock whereas ni c k e l specimens were spark-machined from nickel plates. Zinc and t i n specimens were cut from cast bars. Antimony was melted i n a plumbago crucible at 675°C and cast into preheated (600°C) graphite slab moulds to give a f l a t slab of 6" x 1" x 1/4" dimensions. The slabs o were annealed at 500 C for 8 hrs. and 0.5" diameter specimens were spark-machined from the slabs. Selenium was also melted i n a plumbago crucible at 250°C and cast into 0.5" dia. bars i n a pyrex glass mould. On s o l i d i f i c a t i o n the selenium had a glassy structure and was amorphous. This could not be used for d i f f u s i o n experiments since i t crept badly at 50°C and 100 p s i . The cast bars i n glass moulds were , o therefore,heat treated at 200 C for 2-3 hrs to obtain the c r y s t a l l i n e form of selenium. Specimens were then cut from the bars with a jeweller's saw. 2.4 EXPERIMENTAL PROCEDURE Specimens 0.5" i n diameter by approximately 1/4" i n thickness were ground f l a t to 3/0 emery paper, and washed i n soap, water and acetone. Ultrasonic cleaning was used for a f i n a l cleaning step i n i n i t i a l experiments but was omitted i n l a t e r experiments since i t did not affect the width of the d i f f u s i o n zone. The specimens were inserted and removed from the pressure apparatus with the furnace at operating temperature. I t took the specimens only 2 minutes to reach d i f f u s i o n temperature - a time small compared with the d i f f u s i o n times. Stress was applied immediately after the specimens were introduced. A l l di f f u s i o n experiments were carried out i n a hydrogen atmosphere. Following the d i f f u s i o n anneal, the specimens were mounted i n cold mount and ground on a belt grinder so that a section through the diameter was being examined. The section was then ground to 3/0 emery paper, polished and etched. 37 The following etchants were used; Cu-Sb Cu-Se Etchants K 2Cr 20_ NaCl H„SO. (cone) I 4 I H_0 2 gm. 1.5 gm. 8 ml. 100 ml. Ag-Sb Ag-Se 1 part 6 gm. 20cc. NaCl(sat. soln) 12 cc. K 2Cr-0 7 H 2S0 4 ,.H20 5 parts Chromic Acid 2C l H 2 ° Ni-Sb F e C l 3 HCl(Conc) Ethyl Alcohol 300 cc. 40 gm 380 cc. 5 gm. 2 cc. 99 cc. The phase layers were measured using a F i l a r eye-piece with 10-15 readings being taken for each specimen and the average thickness being calculated. About half the experiments were repeated and the re p r o d u c i b i l i t y was always found to be within - 20y. The average value was used for pl o t t i n g the graphs. The phases i n the d i f f u s i o n zone were i d e n t i f i e d by both electron probe analysis and x-ray d i f f r a c t i o n . Specimens were prepared for electron probe analysis by polishing with ly diamond paste. An e l e c t r o s t a t i c a l l y focused electron 38 probe with a take-off angle of 12-deg and a spot diameter of less than 10p was used. Values of X-ray intensity were converted to weight percent using 63 the matrix absorption correction method of Castaing and Descamps and the 64 fluorescent correction procedure of Birks For X-ray determination of d-spacings for the in t e r m e t a l l i c s , specimens with a thick d i f f u s i o n zone were broken and the intermetallic layers were f i l e d to give a fine powder. Care was taken not to mix the phases when more than one phase was present i n the d i f f u s i o n zone. A diffractometer trace of the powder was made using a Norelco X-ray diffractometer with Cu-K_. radiation. The 29 values corresponding to the d i f f r a c t i o n peaks were compared with standard ASTM cards to id e n t i f y the phases. To investigate the Kirkendall effect, d i f f u s i o n couples were prepared with 0.001" tungsten wire markers i n the d i f f u s i o n zone. The wires were pressed into the d u c t i l e part of the sample (Cu, Ag, Ni) and the surface ground on 3/0 emergy paper prior to assembling i n order to give completely f l a t interfaces. Hydrostatic tests were carried out i n a ste e l pressure vessel connected to a hydrogen gas cylinder by a pressure tube. The specimens were prebonded under compressive stress and were then inserted into the pressure vessel containing Dow Corning F-1-0173 s i l i c o n e o i l . The pressure transmitting tube was screwed on t i g h t l y to the pressure vessel which was then inserted into the furnace. The required temperature was attained within 10 minutes and the required pressure was applied by a regulator. The assembly i s shown i n f i g . 11. 39 Stainless Steel Pressure Tube Bench Furnace Copper washer to maintain pressure Stainless Steel pressure vessel with Silicone O i l specimen Stainless Ste"B± Furnace Tube gas Cylinder with pres-sure gauge Fig. 11 Apparatus for Hydrostatic Experiments 40 CHAPTER I I I  EXPERIMENTAL RESULTS 3.1. PRELIMINARY STUDIES I n i t i a l s t u d i e s on the Cu-Zn, Cu-Sn and A l - Z r systems d i d not show any e f f e c t of s t r e s s over the range of 0-1500 p s i . The Zn-Se and Zn-Sb systems d i d not give a uniform d i f f u s i o n zone - the i n t e r m e t a l l i c compound formed only on c e r t a i n grains of z i n c i n d i c a t i n g a p o s s i b l e o r i e n t a t i o n dependence. In Ag-Te, s i g n i f i c a n t g r a i n boundary d i f f u s i o n made measurements of the d i f f u s i o n zone d i f f i c u l t . A marked s t r e s s s e n s i t i v i t y , however, was observed i n Ag-Te, Zn-Sb and Zn-Se, although i t was not p o s s i b l e to study i t q u a n t i t a t i v e l y because of the nature of the d i f f u s i o n zones. Extensive work was c a r r i e d out i n Ag-Sb, Ag-Se, Ni-Sb, Cu-Se and Cu-Sb. These systems showed a uniform d i f f u s i o n zone c o n s i s t i n g of one or more i n t e r m e t a l l i c compounds. The r e s u l t s on Ag-Sb and Ag-Se w i l l be presented f i r s t i n t h i s chapter, s i n c e these systems showed only one i n t e r m e t a l l i c compound. These w i l l be followed by r e s u l t s i n Ni-Sb, Cu-Se and Cu-Sb which had two or three phases i n the d i f f u s i o n zone. 3.2 SILVER - ANTIMONY SYSTEM 3.2.1 ,THE PHASE DIAGRAM The phase diagram of the Ag-Sb system i s shown i n f i g . 12. I t i s observed that there i s only s l i g h t , s o l u b i l i t y of antimony i n s i l v e r and no s o l i d s o l u b i l i t y of s i l v e r i n antimony. There are two s t a b l e intermediate phases - . (8.8 - 16.3 wt % Sb) and Ag-Sb (23 - 27 wt % Sb). The .-phase, s t a b l e below 702°C, i s a 3/2 e l e c t r o n compound having an h.c.p. s t r u c t u r e ^ 66 with a = 2.955A 0 and c = 4.788A 0 . The Ag-Sb phase, s t a b l e below 558°C5is F i g . 12 Phase diagram of the Ag-Sb system (Hansen ) 42 & Ilk electron compound having an orthorhomic (Cu„Ti type) structure with 68 J a = 5.99A°, b = 5.24A° and c = 4.85A° Specific volumes,defined as the volume of one gram of the material, were calculated for both stable phases from density or l a t t i c e parameters obtained from the l i t e r a t u r e and are shown i n table 2 . I t i s observed that s i l v e r and antimony undergo a contraction of 6.1 pet when 0 tepcX reacting to form the Ag-Sb phase and a .very plight o:cpanoion (0,4 pet) when forming the .-phase. This would suggest that application of pressure would f a c i l i t a t e the formation of Ag-Sb over the .-phase. 3.2.2 IDENTIFICATION OF THE PHASE Diffusion couples of Ag-Sb annealed at 350°C and 400°C produced very uniform d i f f u s i o n zones containing only one intermediate phase. The phase was i d e n t i f i e d by electron probe microanalysis and by X-ray d i f f r a c t i o n as Ag-Sb. The probe traverse i s shown i n f i g . 13 and the X-ray data are given i n Appendix 1 . There appeared to be no concentration gradient within the intermetallic phase and no terminal s o l i d s o l u b i l i t y could be observed i n the s i l v e r or i n the antimony. According to the phase diagram s i l v e r can take up to 6.5 pet Sb i n s o l i d solution at 350°C. However the s o l i d solution d i f f u s i o n rate of antimony i n s i l v e r at this temperature w i l l be very small compared with the d i f f u s i o n rate i n the Ag-Sb. Hence there w i l l be some s o l i d s o l u b i l i t y of antimony i n s i l v e r , but the d i f f u s i o n distance w i l l be so small i t w i l l not appear i n the probe traverse. The second phase (?) was not observed i n any of the d i f f u s i o n experiments. 43 TABLE 2 SPECIFIC VOLUMES OF INTERMEDIATE PHASES IN Ag-Sb Phase Q -phase Ag-Sb Volume of Ag reacting to 0.07152 cc. 0.07152 form 1 g. of the compound Volume of Sb reacting to 0.02875 cc. 0.03776 form 1 g. of the compound. Total volume of Ag and Sb 0.10027 cc. 0.1093 reactant. Specific volume of the 0.09982 cc/gm 0.1026 6 9 phase. Net change i n the volume -Q. 35 % -6.11 % during reaction (pet). O-rj-O-O o Sb Ag3Sb 23.0% {jO^t^jjXUXQ-^j^j^y^C Sb Ag e—©—e—®-e-100 200 300 400 500 ^ 409 7_J 0 7UU Distance i n y Fig. 13 Electron probe traverse of Ag-Sb d i f f u s i o n couple aged for 25 hrs. at 350°C and 300 p s i . Probe traverse made using Sb - L radiation. 45 3.2.3 EFFECT OF STRESS ON DIFFUSION A p p l i c a t i o n of a s t r e s s made a s i g n i f i c a n t d i f f e r e n c e to the width of the d i f f u s i o n zone i n t h i s system. Photomicrographs of the d i f f u s i o n zone at d i f f e r e n t s t r e s s e s are shown i n f i g . 14. F i g . 15 shows the thickness of the Ag-Sb as a f u n c t i o n of s t r e s s at 350 C and 400 C. I t was observed that at 350°C the thickness of the d i f f u s i o n zone increased wi i n c r e a s i n g s t r e s s - from 250y at 0 p s i to 400y at 800 p s i , w h i l s t beyond 800 p s i no v a r i a t i o n i n the width of the d i f f u s i o n zone was n o t i c e d . This would mean that there i s an apparent i n c r e a s e i n the d i f f u s i o n c o e f f i c i e n t by 150 pet when the s t r e s s i s increased from zero to 800 p s i . S i m i l a r behaviour was observed at 400°C, the r a t e of increase of the width of the d i f f u s i o n zone w i t h s t r e s s being higher than that at the lower temperature, i n d i c a t i n g that the s t r e s s e f f e c t i s not c h a r a c t e r i s t i c of j u s t one tempera ture. I t was a l s o observed that the l i m i t i n g s t r e s s beyond which the d i f f u s i o n width was constant seemed to be higher at higher temperatures. 3.2.4 KINETICS Curves showing the growth of Ag-Sb at various s t r e s s e s are shown i n f i g . ;. 16^ . . In every case growth was p a r a b o l i c i n d i c a t i n g a mechanism c o n t r o l l e d by d i f f u s i o n . The k i n e t i c curves a l l pass through the o r i g i n i n d i c a t i n g that delayed n u c l e a t i o n of the Ag^Sb phase was not r e s p o n s i b l e f o r the s t r e s s e f f e c t and that i t was a r e a l growth e f f e c t . The growth r a t e a i n cm//sec i s p l o t t e d as a f u n c t i o n of s t r e s s i n f i g . 17 and i t can be seen that i t increases by a f a c t o r of 1.6 on going from zero to 800 p s i . A s e r i e s of t e s t s were c a r r i e d out i n which d i f f u s i o n was F i g - M Photomicrographs of the d i f f u s i o n zone i n Ag-Sb annealed at 350°C f o r 25 h r s . at v a r i o u s pressures. 50 x. -p-47 800 h Stress i n p s i F i g . 15 Graph of the thickness of Ag-Sb as a f u n c t i o n of s t r e s s f o l l o w i n g d i f f u s i o n f o r 25 hr s . at 350°C and 400°C 48 16.0 15.0 50 allowed to take place at low pressure following an i n i t i a l high pressure d i f f u s i o n anneal. Specimens were i n i t i a l l y diffused at 350°C for 4 hours under a stress of 1000 ps i to give a wide band of Ag^Sb after which the stress was released and d i f f u s i o n was allowed to take place at zero stress for various times. The results are plotted i n f i g . 18 and 19 . I t can be seen i n f i g . 18 that the width of the d i f f u s i o n zone increased with increasing time, following the same curve as the test at 1000 p s i for about 20 hours, after which the growth rate decreased and the curve began to approach the zero p s i curve. Fig. 19 shows that parabolic growth i s obeyed i n two different regions. After the stress was released, the Ag^Sb phase continued to grow at the rate characteristic of a. 1000 p s i stress. After a long time of anneal, however, the growth rate decreased to the 0-psi value. Hence when stress i s altered i n the di f f u s i n g system there i s a transient effect before the growth rate characteristic of the new stress i s established. 3.2.5 HYDROSTATIC TEST Hydrostatic tests were carried out to see whether there was any difference i n growth rate between uniaxial compressive stress and t r i a x i a l hydrostatic pressure. Specimens were prebonded at 350°C for 1 hour under a compressive stress of 1000 ps i and then diffused under a hydrostatic pressure of 400 psi at 350°C for different times. The results are plotted i n f i g . 20 . I t can be seen that the growth rate under hydrostatic pressure i s much less than the growth rate.under a compressive load of the same magnitude. Indeed, the growth rate under hydrostatic pressure very closely resembles that for a compressive test at 0 p s i . Hence application of a hydrostatic pressure to the Ag-Sb system 1000 psi compressive i n i t i a l stress O released Normal growth Diffusion at zero stress after i n i t i a l high stress anneal 10 Fig. 18 20 30 40 50 60 70 80 90 100 Time i n hr. Growth of Ag-Sb at 350 C. Growth took place i n i t i a l l y at 1000 p s i for 4 hrs. after which stress was released and d i f f u s i o n allowed at zero stress, Growth tests at 1000 p s i and zero p s i are included for comparison — — — — Normal growth F i g . 19 P a r a b o l i c p l o t of the r e s u l t s shown i n f i g . 18 Normal growth Time i n hr. Fig. 20 Growth of Ag^Sb at 350°C under a hydrostatic pressure of 400 p s i . Specimens prebonded for 1 hr, at 1000 p s i . Normal growth tests at zero p s i and 400 p s i . are included for comparison purpose s. 54 d i d not produce any e f f e c t on the growth r a t e and only a compressive load i s of any s i g n i f i c a n c e . 3.2.6 KIRKENDALL EXPERIMENTS K i r k e n d a l l t e s t s were c a r r i e d out using 0.001" d i a . tungsten w i r e markers. The r e s u l t s are shown i n f i g . 21 . I t was observed that the markers stayed at the Ag/Ag-Sb i n t e r f a c e i n d i c a t i n g that s i l v e r i s the d i f f u s i n g s p e c ies. F i g . 21 (a) - (d) show K i r k e n d a l l marker experiments c a r r i e d out at 350 C under 1000 p s i f o r d i f f e r e n t lengths of time. I t can be seen that the markers i n i t i a l l y act as b a r r i e r s to d i f f u s i o n and that the d i f f u s i o n zone has zero width at the marker p o s i t i o n s . As d i f f u s i o n proceeds l a t e r a l d i f f u s i o n takes place to give a band of Ag^Sb at the marker l o c a t i o n s ( f i g . 21 (c))»and w i t h i n c r e a s i n g time ( f i g . 21 (d)) the thickness of the d i f f u s i o n zone at these p o s i t i o n s becomes comparable w i t h the width of the d i f f u s i o n zone away from the markers. Ledges of s i l v e r and antimony formed at the markers i n the i n i t i a l stages of d i f f u s i o n g r a d u a l l y decay u n t i l both the Ag/Ag-Sb and the Ag^Sb/Sb boundaries become f a i r l y p l anar. However, small sharp wedges at the Ag^Sb/Sb i n t e r f a c e are r e t a i n e d f o r a long time. F i g . 22 shows that the height of the s i l v e r and antimony ledges depends on the s i z e of the markers, and so on the amount of l a t e r a l d i f f u s i o n r e q u i r e d . I n order to o b t a i n a q u a l i t a t i v e idea of the K i r k e n d a l l e f f e c t i n a system not s e n s i t i v e to s t r e s s , experiments were c a r r i e d out on a Cu/a-Brass couple using d i f f e r e n t s i z e markers. F i g . 23 shows a micrograph of the d i f f u s i o n zone. Observing the s t r u c t u r a l changes i n the d i f f u s i o n zone,and taking them to correspond to composition c o n t o u r s ^ i t 55 F i g . 21 Photomicrographs of K i r k e n d a l l marker experiments i n Ag-Sb, f o r specimens annealed f o r d i f f e r e n t times at 350°C under 1000 p s i . 22 x ,01" ,005" .0035" ,0025" ,001" marker d i a . F 1 g - . . 2 2 Photomicrographs of the K i r k e n d a l l experiment i n Ag-Sb with d i f f e r e n t marker w i r e diameters, specimen annealed f o r 50 h r . at 350°C under 1000 p s i s t r e s s . 30 x F i g . 23 Photomicrograph of K i r k e n d a l l experiment i n Cu/ct-Brass w i t h d i f f e r e n t s i z e markers. Experiment c a r r i e d out at 900°C f o r 60 hrs. 23 x 58 can be seen that there i s no ledge formation,except adjacent to the largest marker. This would suggest that formation of ledges at the Kirkendall marker positions i s c h a r a c t e r i s t i c of a stress sensitive system. 3.2.7 DISCUSSION The stress effect i n d i f f u s i o n i n Ag-Sb i s a true growth effect and does not depend on pressure influenced nucleation. As discussed i n the Introduction there are three possible effects which can account for a pressure influenced growth - v a r i a t i o n of the d i f f u s i o n c o e f f i c i e n t , v a r i a t i o n of the phase boundary composition and modification of the Kirkendall porosity. A very large Kirkendall s h i f t i s observed i n this system indicating s i l v e r to be the d i f f u s i n g species and so there would be a large vacancy f l u x towards the s i l v e r , these vacancies condensing mainly at the Ag/Ag-Sb interface. Hence conditions are i d e a l for the development of the Kirkendall porosity. The growth rate reached a maximum at 800 p s i and then became constant, independent of applied pressure. This would be very d i f f i c u l t to explain from the viewpoint of changes i n the d i f f u s i o n c o e f f i c i e n t and phase boundary composition since these would be expected to increase continuously with applied stress. However, once the stress applied i s s u f f i c i e n t l y great to give an unrestricted f l u x across the Ag/Ag^Sb interface with no r e s t r i c t i o n from the i n c i p i e n t Kirkendall porosity, pressure would have no effect on the growth rate. Application of a hydrostatic pressure did not have any effect on the growth rate, unlike compressive stress. This would again be impossible to explain from changes i n the phase boundary composition and d i f f u s i o n 59 c o e f f i c i e n t s i n c e h y d r o s t a t i c pressure should be j u s t as e f f i c i e n t i n a l t e r i n g the d i f f u s i o n c o e f f i c i e n t and phase boundary compositions as compressive s t r e s s . The r e s u l t s can be explained, however, from the viewpoint of the K i r k e n d a l l p o r o s i t y . Because of the d e f e c t i v e nature of the Ag/Ag^Sb i n t e r f a c e r e s u l t i n g from the K i r k e n d a l l p o r o s i t y the outside h y d r o s t a t i c pressure may introduce a pressure at the boundary, which may be equivalent to the e x t e r n a l pressure and t h i s w i l l e l i m i n a t e the e f f e c t i v e pressure across the i n t e r f a c e . Hence, although compressive s t r e s s e s are developed across c e r t a i n p o r t i o n s of the d i f f u s i o n zone there i s no compressive f o r c e at the c r i t i c a l Ag/Ag^Sb boundary and so no improvement i n the bonding. With compressive loading,however, the s i t u a t i o n i s completely d i f f e r e n t s i n c e the f u l l load i s developed across the complete d i f f u s i o n zone i n c l u d i n g the Ag/Ag^Sb i n t e r f a c e . The bonding at t h i s i n t e r f a c e i s ,therefore,improved and the f l u x of atoms increased. Experiments i n which pressure was suddenly reduced i n the course of a d i f f u s i o n anneal show that once a good bond i s developed at an i n t e r f a c e i t tends to be r e t a i n e d f o r a short period before development of a poorer bond c h a r a c t e r i s t i c of lower pressure. This i s reasonable,since as discussed i n the I n t r o d u c t i o n (p. 11) the tendency f o r development of the K i r k e n d a l l p o r o s i t y i s greatest at the beginning of d i f f u s i o n . I f a good bond i s e s t a b l i s h e d at t h i s t i m e , i t w i l l tend to be maintained f o r a short time a f t e r the pressure i s removed before the growth r a t e c h a r a c t e r i s t i c of the lower pressure i s developed. The development of ledges at the K i r k e n d a l l markers i s much more evident i n Ag-Sb than i n Cu-a brass, and i s considered to be due to the s t r e s s s e n s i t i v i t y i n Ag-Sb. The maximum height of ledges increases with 60 i n c r e a s i n g marker s i z e and r e f l e c t s the amount of l a t e r a l d i f f u s i o n r e q uired w i t h i n c r e a s i n g wire diameter. Ledges at the s i l v e r i n t e r f a c e l a s t much longer than those at the antimony i n t e r f a c e and are caused by r e s t r i c t e d f l u x of s i l v e r atoms i n t o the Ag^Sb at the i n t e r f a c e normal to the d i r e c t i o n of d i f f u s i o n . The reason f o r t h i s i s that there i s no a p p l i e d compressive s t r e s s i n t h i s d i r e c t i o n and so f l u x of s i l v e r atoms w i l l be q u i t e r e s t r i c t e d i n comparison w i t h the normal d i f f u s i o n d i r e c t i o n . These r e s u l t s are again i n agreement w i t h the mechanism of r e s t r i c t e d f l u x due to the i n c i p i e n t K i r k e n d a l l p o r o s i t y . 3.3 SILVER-SELENIUM SYSTEM The r e s u l t s i n the Ag-Se system were very s i m i l a r to those i n Ag-Sb and f o r t h i s reason a l e s s d e t a i l e d i n v e s t i g a t i o n was c a r r i e d out. 3.3.1 THE PHASE DIAGRAM The phase diagram of the Ag-Se system i s shown i n f i g . 24 . Only one i n t e r m e t a l l i c phase, Ag^Se (26.8 wt pet Se), i s s t a b l e . This phase undergoes an order-disorder transformation at 128°C s i m i l a r to that i n 41 Ag„S . The high temperature 3- m o d i f i c a t i o n has a CaF„ type s t r u c t u r e o 7 1 (cubic) w i t h a =4.993A , and the low temperature a - phase i s e i t h e r 72 orthorhombic, monoclinic or t e t r a g o n a l . The l a r g e Se ions l i e i n f i x e d l a t t i c e p o s i t i o n s and the smaller Ag ions d i f f u s e through i n t e r s t i t i a l s i t e s between the Se i o n s . At low temperatures the Ag ions are d i s t r i b u t e d at random among the i n t e r s t i t i a l s i t e s and have a very high m o b i l i t y . S p e c i f i c volume c a l c u l a t i o n s i n d i c a t e that there i s a 3.2 pet expansion 61 10 15 20 25 30 WEIGHT PER CENT SELEN IUM 40 50 60 80 90 960.5° ; i * / TWO MELTS / 1 ,J °,90° i i 897" i 1 , • 12 19) M \ 1 1 \ \ e » o ° \ 1 TWO rfELTS \ \ \ 1 V 616 ° I 1 1 115 t 137] \ 1 I \ I 1 217° 12815° 0 6, 20 30 40 50 60 70 ATOMIC PER CENT SELEN IUM 90 100 S» F i g . 24 Phase diagram of Ag-Se (Hansen ) 62 i n forming Ag-Se from s i l v e r and selenium. 3.3.2 IDENTIFICATION OF THE PHASE D i f f u s i o n experiments were c a r r i e d out at 130°C j u s t above the polymorphic t r a n s i t i o n temperature of Ag-Se. As expected only one phase appeared i n the d i f f u s i o n zone and the e l e c t r o n probe t r a v e r s e confirmed that the composition corresponded to Ag-Se ( f i g . 25 ). The X-ray d i f f r a c t i o n a n a l y s i s (Appendix 1 ) i n d i c a t e d that the phase was the high temperature 6 - phase as expected from the temperature of the experiment. 3.3.3 EFFECT OF STRESS ON DIFFUSION The width of Ag-Se i n the d i f f u s i o n zone showed a s i g n i f i c a n t s e n s i t i v i t y to s t r e s s . F i g . 25 shows the v a r i a t i o n of the thickness of the d i f f u s i o n zone w i t h s t r e s s f o l l o w i n g d i f f u s i o n f o r 25 hours at 130°C. I t was observed that the width of Ag-Se increased w i t h i n c r e a s i n g s t r e s s from 137y at zero s t r e s s to 392p at 800 p s i , beyond which there was no e f f e c t . Hence the e f f e c t observed i n t h i s system i s s i m i l a r to that i n Ag-Sb , except that the increase i n width i s somewhat grea t e r . 3.3.4 KINETICS Curves showing the growth of Ag-Se at various s t r e s s e s are shown i n f i g . 27 . In every case the growth was parabolic, i n d i c a t i n g a mechanism c o n t r o l l e d by a d i f f u s i o n process. 3.3.5 KIRKENDALL TEST A photomicrograph of a t y p i c a l marker experiment i s shown i n f i g . 28 . The markers were at the Ag/Ag-Se i n t e r f a c e i n d i c a t i n g that s i l v e r i s 100 90 80 70 60 f 50 wt % Se 40 -30 -20 -10 —a O Se 26.6% Se <^ cb~Q~o~o~Q Q O Ag 2Se Ag o <b Q 6 6 i 50 100 150 200 250 300 350 400 450 500 550 600 650 700 dis t a n c e i n \i F i g . 25 E l e c t r o n microprobe t r a v e r s e f o r a Ag-Se d i f f u s i o n couple annealed at 130°C f o r 25 hrs. at 200 p s i . Composition measured using S e - K a r a d i a t i o n ON 500 0 200 400 600 800 1000 1200 1400 1600 Stress i n p s i F i g . 26 Thickness of Ag-Se as a f u n c t i o n of s t r e s s f o l l o w i n g d i f f u s i o n f o r 25 h r s . at 130°C 65 66 F i g . 28 Micrograph showing K i r k e n d a l l markers. Couple diffused for 25 hrs. at 130°C and 400 p s i , 30 x 67 the d i f f u s i n g species as expected from the structure of Ag 2Se (see p. 60). The figure also shows ledges of s i l v e r at the Ag/Ag^Se boundary similar to those i n Ag-Sb. These can be explained by differences i n the flu x across the Ag2Se/Ag interface perpendicular and p a r a l l e l to the applied stress. 3.3.6 DISCUSSION I t was unfortunate that the temperature used i n studying d i f f u s i o n i n this system was 130°C, just at the transformation temperature of 128 ± 5°C. However, i n view of the consistency of the data i t would appear that a l l measurements were carried out above the t r a n s i t i o n temperature and the proximity of the transformation temperature did not s i g n i f i c a n t l y affect the r e s u l t s . The effect of stress i n the Ag-Se system i s very similar to that observed i n Ag-Sb except that the v a r i a t i o n i s rather greater. The growth rate reaches a maximum at 800 p s i and then remains constant independent of stress just as i n Ag-Sb. The explanation for stress s e n s i t i v i t y i n Ag-Se must be the same as i n Ag-Sb i n view of the s i m i l a r i t y of the re s u l t s . Applying a stress to the Ag2Se/Ag interface increases the Ag flu x across the boundary by improving the interface. At 800 p s i , the Ag flu x i s unrestricted and no further stress effect i s observed. Specific volume calculations show a 3.2 pet increase i n forming Ag 2Se and a 6.1 pet decrease i n forming Ag^Sb. Since both systems show very similar effects of stress i t can be concluded that this has no effect on the stress s e n s i t i v i t y . 68 3.4 NICKEL-ANTIMONY SYSTEM D i f f u s i o n c o u p l e s of N i - S b showed t h a t t h e r e were t h r e e i n t e r m e t a l l i c compounds i n t h e d i f f u s i o n zone, r a t h e r t h a n j u s t the one phase o b s e r v e d i n Ag-Sb and Ag-Se. Hence t h e r e s u l t s w i l l be c o n s i d e r e d i n a l i t t l e more d e t a i l t h a n i n Ag-Se. 3.4.1 THE PHASE DIAGRAM The most r e c e n t phase d i a g r a m f o r the N i - S b system i s shown i n f i g . 29 . The low t e m p e r a t u r e p o r t i o n o f t h e d i a g r a m i s u n c e r t a i n , e x p e c i a l l y i n the c o m p o s i t i o n range o f 24 - 31 a t . p e t Sb. H a n s e n ^ s u g g e s t s t h a t f i v e i n t e r m e t a l l i c s a r e s t a b l e a t 400°C, the t e m p e r a t u r e o f t h e e x p e r i m e n t s . These phases a r e l i s t e d i n T a b l e 3, t o g e t h e r w i t h t h e r e p o r t e d c r y s t a l s t r u c t u r e s and s p e c i f i c volumes. The B-phase ( N i _ S b - ) i s r e p o r t e d t o 73 o undergo a m a r t e n s i t i c r e a c t i o n (B') below 580 C. However, a l l o y s o f 33.3 a t - p e t Sb, a n n e a l e d above and below t h e t r a n s f o r m a t i o n t e m p e r a t u r e and quenched have t h e same s t r u c t u r e , thus t h r o w i n g some doubt on t h e B 6' 74 t r a n s f o r m a t i o n . The s t r u c t u r e o f Ni-Sb i s u n c e r t a i n and d i f f e r e n t r e s e a r c h e r s 73 * 7 A 75 have t a k e n i t t o be e i t h e r h e x a g o n a l , c u b i c , or o r t h o r h o m b i c 3.4.2 IDENTIFICATION OF THE PHASES Three out of t h e f i v e s t a b l e phases were o b s e r v e d i n t h e d i f f u s i o n zone a f t e r a 400°C d i f f u s i o n a n n e a l . A t t e m p t s were made t o i d e n t i f y t h e s e phases by e l e c t r o n p r o b e a n a l y s i s and by X - r ay d i f f r a c t i o n . The N i - r i c h and S b - r i c h phases i n t h e d i f f u s i o n zone were v e r y narrow (10 - 20y) and X - r a y d i f f r a c t o m e t r i c a n a l y s i s of t h e s e phases was n o t p o s s i b l e , d - s p a c i n g v a l u e s and X-ray i n t e n s i t i e s o b t a i n e d f o r t h e phase i n t h e m i d d l e 10 20 16001 L 30 J _ 40 _L WEIGHT PER CENT ANTIMONY 50 60 70 75 60 85 90 _ L : i . i i_ 630.5° 29 The phase diagram of Ni-Sb (Hansen ) 70 TABLE 3 CHARACTERISTICS OF INTERMEDIATE PHASES IN Ni-Sb AT 400°C Phase Composition at 400°C wt pet Sb Crystal Structure Specific Volume c.c./gm. N i 1 5 S b 12.4 76 Superstructure of cubic l a t t i c e with 32 atoms/cell 0.1072 76 Ni 3Sb N i 5 S b 2 NiSb 38.3 41.1 - 44.2 65.5 - 70.0 Tetragonal 7 3 0.1238 with 2 atoms/cell 73 Hexagonal 0.1325 with 52 atoms/cell 73 77 NiSb, 83.2 Orthorhombic 73 0.1274 78 71 are shown i n Table 4. There was no agreement w i t h any of the suggested c r y s t a l s t r u c t u r e s f o r Ni^Sb and NiSb. However, as may be seen i n Table 4, there was good agreement between the intense l i n e s i n the d i f f r a c t o m e t e r t r a c e and the high temperature s t r u c t u r e of Ni^Sb^. The e x t r a low i n t e n s i t y l i n e s i n the d i f f r a c t o m e t e r t r a c e may conceivably be r e l a t e d to a s u p e r l a t t i c e s t r u c t u r e c h a r a c t e r i s t i c of the low temperature. An e l e c t r o n probe t r a v e r s e f o r the d i f f u s i o n couple i s shown i n f i g . 29 . The phases adjacent to n i c k e l and antimony were l e s s than 20y t h i c k and q u a n t i t a t i v e a n a l y s i s was not p o s s i b l e w i t h the e x i s t i n g U.B.C. e l e c t r o n probe which had a spot diameter of ~ lOy. The probe t r a c e shown i n f i g . 30 was c a r r i e d out on a J.E.O.L. Co. JXA -3A e l e c t r o n probe w i t h an e l e c t r o n beam diameter of l e s s than l y . The phase i n the middle of the d i f f u s i o n zone gives a composition of 43.1 wt pet Sb and corresponds to the composition of N i ^ S b 2 i n agreement w i t h X-ray a n a l y s i s . The N i - r i c h phase has a composition of 36.8 wt. pet Sb, which i s l e s s than, but f a i r l y c l o s e t o , the composition of Ni^Sb (40.0 wt pet Sb). The composition of the phase on the antimony s i d e of the d i f f u s i o n couple,as given by the probe a n a l y s i s (60 wt pet Sb),does not agree w e l l w i t h any of the compounds given i n the phase diagram. This i s probably due to the phase being too t h i n f o r accurate a n a l y s i s . The phase c l o s e s t i n composition to i t i s NiSb and occurs at 66.0 — 70 wt pet Sb. Thus the phases i n the d i f f u s i o n zone are, most probably, NiSb, N i Sb and N i Sb. * The author would l i k e to express h i s a p p r e c i a t i o n to Mr. J . Roussos of J.E.O.L. Co L t d . f o r h i s help i n c a r r y i n g out t h i s a n a l y s i s . 72 TABLE 4 X-RAY DATA FOR N i Sb 2 Experimental ASTM Standard card f o r g.Ni^Sb 2 d I / I 0 d I / I Q 3.12 10 3.03 12 3.97 8 2.85 60 2.86 70 2.68 50 2.68 50 2.41 15 2.42 70 2.33 12 2.24 30 2.03 100 2.04 100 1.99 15 1.96 20 1.96 100 1.87 8 1.65 8 1.65 50 1.61 8 1.52 10 1.49 10 1.43 20 1.35 60 1.36 70 1.22 15 100 90 80 -w t % Sb ' 70 h 60 50 40 30 20 h 10 0 >NiSb ( ? ) 4 3 . 1 % Sb ( N i 5 S b 2 ) 0 - Q J_ _L 3 6 . 8 % Sb ( N i 3 S b ) N i I l 0 - 4 ) - O - , <D O - d ) L 10 20 30 40 50 60 70 80 90 100 110 120 130 D i s t a n c e i n p F i g . 30 E l e c t r o n p r o b e t r a v e r s e f o r N i - S b d i f f u s i o n c o u p l e a g e d f o r 49 h r s . a t 400°C a t 400 p s i . P r o f i l e m e a s u r e d u s i n g S b - L r a d i a t i o n a 74 3.4.3 THE EFFECT OF STRESS ON DIFFUSION A p p l i c a t i o n of s t r e s s was found to have a l a r g e e f f e c t on the width of the d i f f u s i o n zone. F i g . 31 shows photomicrographs of the d i f f u s i o n zones obtained by annealing specimens at d i f f e r e n t s t r e s s e s f o r 25 hours at 400°C. F i g . 32 shows the width of the d i f f u s i o n zone as a f u n c t i o n of s t r e s s . The maximum s t r e s s was l i m i t e d to 1500 p s i s i n c e above t h i s antimony began to creep. F i g . 31 shows that Ni^Sb and NiSb e x i b i t a very s m a l l increase i n thickness w i t h i n c r e a s i n g s t r e s s . The Ni^Sb2 phase i s however very s e n s i t i v e to a p p l i e d s t r e s s w i t h i t s thickness i n c r e a s i n g l i n e a r l y w i t h s t r e s s - from 26.Oy at zero s t r e s s to 68.Oy at 1500 p s i . The s t r e s s c h a r a c t e r i s t i c s i n t h i s system are d i f f e r e n t from those i n Ag-Sb and Ag-Se,since i n t h i s system there i s no apparent tendency f o r the thickness of the phase to reach a l i m i t i n g value w i t h i n c r e a s i n g s t r e s s . 3.4.4 KINETICS T y p i c a l growth curves are shown i n f i g . 33 and f i g . 34 . The growth of a l l three phases at a l l pressures i s p a r a b o l i c w i t h time, i n d i c a t i n g a mechanism c o n t r o l l e d by d i f f u s i o n . A l l the curves pass through the o r i g i n suggesting that there i s no delayed n u c l e a t i o n and that the e f f e c t of the s t r e s s i s a genuine growth e f f e c t . F i g . 35 shows the growth r a t e (a) of N i ^ S b 2 as a f u n c t i o n of s t r e s s . The growth r a t e increases apparently l i n e a r l y w i t h s t r e s s - from 0.88 x 10 cm//sec. at zero s t r e s s to 2.2 x 10 cm ec. at 1500 p s i . A s e r i e s of t e s t s were c a r r i e d out i n which d i f f u s i o n took place at a low s t r e s s f o l l o w i n g a high pressure anneal. Specimens were i n i t i a l l y 1 0 0 P s l 200 p s i 400 p s i 800 p s i 1000 p s i F 1 g * 3 1 Photomicrographs of the d i f f u s i o n zone i n Ni-Sb annealed at 400°C f o r 25 h r s . a t d i f f e r e n t s t r e s s e s . 600 x Total „ - ,_, • N i o S b • • , Q • • • • ~ A — - 3 " A A £ £ Z Z A — — — S A A N i S b 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Stress i n p s i Thickness of the intermediate phases i n d i f f u s i o n couples of Ni-Sb, annealed at 400°C for 25 hrs, as a function of stress. 80 d i f f u s e d at 400 C f o r 4 hours under a s t r e s s of 1000 p s i to give a wide band of Ni^Sb2> a f t e r which the s t r e s s was r e l e a s e d and d i f f u s i o n experiments were c a r r i e d out f o r various lengths of time at zero s t r e s s . The r e s u l t s are shown i n f i g . 36 and f i g . 37 . I t can be seen from f i g . 36 that the width of Ni^Sb^ increases w i t h i n c r e a s i n g time, approaching the curvature of the 0-psi curve a f t e r long d i f f u s i o n times. F i g . 37 shows that a p a r a b o l i c growth law i s obeyed at longer times of d i f f u s i o n , the growth r a t e being the same as that at zero p s i . There i s a short t r a n s i e n t period before the growth r a t e c h a r a c t e r i s t i c of zero s t r e s s i s e s t a b l i s h e d . The growth ra t e s of Ni^Sb and NiSb f o l l o w the same r a t e as that of the 1000 p s i experiment. Growth of these phases i s not s i g n i f i c a n t l y a f f e c t e d by s t r e s s , hence no e f f e c t should be expected on removal of the s t r e s s . 3.4.5 KIRKENDALL TESTS A t y p i c a l micrograph of a K i r k e n d a l l marker experiment i s shown i n f i g . 38 . The markers l i e on the Ni/Ni^Sb^ boundary suggesting that n i c k e l i s the d i f f u s i n g species i n the Ni^Sb^ phase. Ledges of n i c k e l are observed at the marker p o s i t i o n as i n Ag-Sb and Ag-Se. 3.4.6 DISCUSSION An a p p l i e d compressive s t r e s s has a l a r g e e f f e c t on d i f f u s i o n i n Ni-Sb w i t h the thickness of the Ni,.Sb2 phase i n c r e a s i n g by a f a c t o r of 2.6 from zero p s i to 1500 p s i . U n l i k e Ag-Sb and Ag-Se, the thickness of the Ni^Sb2 phase does not appear to approach a l i m i t i n g value w i t h i n c r e a s i n g s t r e s s . In t h i s regard the r e s u l t s are s i m i l a r to those 6 3 observed i n Cu-Te and Al-U (see page 4,6). 81 Time i n hr. F i g . 36 Growth of Ni^Sb„ when an i n i t i a l s t r e s s of 1000 p s i i s released a f t e r 5 hrs. of anneal at 400°C. Normal growth curves at,zero p s i and 1000 p s i are included f o r comparison 82 F i g . 37 P a r a b o l i c p l o t s of the r e s u l t s of the same experiment as i n F i g . 36 F i g . 38 Micrograph of K i r k e n d a l l experiment. Specimen aged at 400°C at 1000 p s i f o r 237 h r s . 84 In view of the l a r g e s t r e s s s e n s i t i v i t y i n Ni-Sb, i t seems most reasonable that i n t h i s system,just as i n Ag-Sb and Ag-Se, the e f f e c t of s t r e s s i s to l i m i t the amount of the K i r k e n d a l l p o r o s i t y . This explanation has a l s o been used i n the Al-U and Cu-Te systems. The K i r k e n d a l l marker experiment suggests that n i c k e l i s the d i f f u s i n g species i n Ni^Sb2 and NiSb. In Ni^Sb, however, the s i t u a t i o n i s r a t h e r i n d e f i n i t e s i n c e the markers l i e at the Ni/Ni,-Sb2 boundary and i t i s not p o s s i b l e to say whether n i c k e l o r antimony i s the d i f f u s i n g s p e c ies. Growth of Ni^Sb,which i s the phase adjacent to the n i c k e l , i s not s i g n i f i c a n t l y a f f e c t e d by the a p p l i e d s t r e s s and the main e f f e c t of s t r e s s i s seen i n the adjacent Ni,.Sb2 phase. These observations are somewhat d i f f e r e n t from Al-U and Cu-Te, where the s t r e s s s e n s i t i v e phase i s adjacent to the metal w i t h the l a r g e r d i f f u s i o n c o e f f i c i e n t . Thus, i t seems that i n Ni-Sb the c r i t i c a l i n t e r f a c e i s between Ni^Sb and Ni^Sb2- Two suggestions may be made to account f o r t h i s . The f i r s t i s that d i f f u s i o n i n Ni^Sb i s due to the motion 'of antimony atoms. The K i r k e n d a l l marker experiments are not i n disagreement w i t h t h i s . Hence there i s a vacancy f l u x through Ni,-Sb2 to the Ni^Sb2/Ni 3Sb i n t e r f a c e caused by the f l u x of n i c k e l atoms and there i s a l s o a vacancy f l u x from Ni^Sb to the same i n t e r f a c e caused by the f l u x of antimony atoms. Both vacancy f l u x e s condense at the same i n t e r f a c e , thus weakening the Ni^Sb2/Ni 3Sb i n t e r f a c e . The other p o s s i b l e explanation i s that the Ni/Ni^Sb boundary may be b e t t e r than the N i ^ Sb/Ni,-Sb2 i n t e r f a c e . N i c k e l atoms w i l l be considered to d i f f u s e i n both Ni^Sb and Ni^Sb2- Growth of Ni^Sb i s very slow i n comparison w i t h Ni^Sb2« Hence the vacancy f l u x condensing at the Ni^Sb2/Ni 3Sb i n t e r f a c e i s almost as great as that at the Ni/Ni^Sb i n t e r f a c e . The i n t e r f a c e between Ni^Sb and Ni^Sb2 i s d e f e c t i v e , however, and so the i n c i p i e n t K i r k e n d a l l p o r o s i t y w i l l develop at t h i s i n t e r f a c e rather 85 than at the Ni/Ni^Sb boundary. Whichever of these two suggestions i s c o r r e c t , there i s no doubt that the s t r e s s e f f e c t a r i s e s because of the atom t r a n s f e r across the Ni^Sb/Nij.Sb2 i n t e r f a c e . A p p l i c a t i o n of a compressive load improves t h i s bond and so increases the atom t r a n s f e r i n t o Ni^ .Sb2» thus causing the growth r a t e of t h i s phase to in c r e a s e . I f the f i r s t mechanism i s op e r a t i v e , improvement of the Ni.jSb/Ni^Sb2 boundary would increase the antimony f l u x i n t o the Ni^Sb phase w i t h i n c r e a s i n g s t r e s s . However, the d i f f u s i o n c o e f f i c i e n t i n t h i s phase i s very s m a l l as seen from i t s small growth r a t e s , even at high s t r e s s e s , and hence the change i n f l u x would not make a s i g n i f i c a n t change i n the growth r a t e . The n i c k e l f l u x across the Ni^Sb^/ Ni2Sb i n t e r f a c e i s q u i t e s m a l l and so there i s only a s l i g h t tendency f o r the t r a n s f e r of atoms across t h i s i n t e r f a c e to be r e s t r i c t e d . Hence NiSb would be expected to grow e s s e n t i a l l y independent of a p p l i e d s t r e s s , and t h i s i s observed experimentally. The K i r k e n d a l l experiment ( f i g . 36 (b)) provides proof that t r a n s f e r of n i c k e l atoms i n t o Ni^Sb i s e a s i e r than i n t o Ni<.Sb2 at low s t r e s s e s . This can be seen by examining the n i c k e l ledge under the tungsten marker, which i s thinner when surrounded by Ni^Sb than by Ni^Sb2» This i s shown i n the schematic r e p r e s e n t a t i o n i n f i g . 39. NiSb K i r k e n d a l l marker F i g . 39 Schematic r e p r e s e n t a t i o n of d i f f u s i o n around markers i n Ni-Sb 86 There i s no compressive s t r e s s across the Ni/Ni^Sb^ or Ni/Ni.jSb2 i n t e r f a c e s i n the l a t e r a l d i r e c t i o n , w h i l e the f u l l a p p l i e d s t r e s s i s developed across the Ni^Sb/Ni^Sb^ i n t e r f a c e . Hence there i s no r e s t r i c t i o n to atom t r a n s f e r across the Ni 3Sb/Ni^Sb2 boundary. Ni^Sb grows i n the l a t e r a l d i r e c t i o n i n t o the n i c k e l ledge whereas growth of Ni^Sb2 i n t h i s d i r e c t i o n i s r e s t r i c t e d and hence the r e l a t i v e width of the n i c k e l ledge i n the two regions i s a true measure of the ease of t r a n s f e r of atoms i n t o Ni^Sb and Ni^Sb2» The growth r a t e of Ni^Sb2 appears to i n c r e a s e continuously w i t h the a p p l i e d s t r e s s up to 1500 p s i . I t might be thought that t h i s dependence over such a wide range of s t r e s s was c h a r a c t e r i s t i c of a d i f f u s i o n couple with more than one i n t e r m e t a l l i c compound, sin c e systems l i k e Cu-Te and Al-U which a l s o have 2-3 phases i n the d i f f u s i o n zone show a s i m i l a r s t r e s s e f f e c t . I t i s , however, very d i f f i c u l t to suggest any ex p l a n a t i o n as to why the e f f e c t of s t r e s s i n a system w i t h one i n t e r m e t a l l i c phase should be d i f f e r e n t from that i n a system w i t h 2-3 i n t e r m e t a l l i c compounds,since an equivalent vacancy f l u x should be condensing i n both cases. I t seems more l i k e l y that i n systems l i k e Ni-Sb, Cu-Te and U-Al, one of the phases has a very high growth r a t e but because of the corresponding very l a r g e vacancy f l u x a high pressure i s necessary to e s t a b l i s h a good i n t e r f a c e . The maximum s t r e s s of 1500 p s i used i n the experiments with Ni-Sb couples was presumably not s u f f i c i e n t f o r a good i n t e r f a c e to develop. Experiments i n which the s t r e s s was suddenly released i n the course of a d i f f u s i o n anneal showed a short t r a n s i e n t period before the growth r a t e c h a r a c t e r i s t i c of the new s t r e s s was a t t a i n e d . This observation i s s i m i l a r to that i n Ag-Sb, and i n d i c a t e s that a bond across the i n t e r f a c e 87 c h a r a c t e r i s t i c of a high a p p l i e d s t r e s s w i l l be r e t a i n e d f o r a short, time a f t e r the s t r e s s i s removed u n t i l the bond c h a r a c t e r i s t i c of the new s t r e s s develops. The Ni-Sb system showed a wide v a r i a t i o n i n the growth rates of the v a r i o us s t a b l e phases. Two of the f i v e s t a b l e phases d i d not appear i n the d i f f u s i o n zone at a l l , two other phases have very narrow widths, w h i l s t the f i f t h phase (Ni^Sb2) i s very much t h i c k e r than any other, even though i t s growth i s r e s t r i c t e d by t r a n s f e r of atoms across i t s i n t e r f a c e . This suggests that the d i f f u s i o n c o e f f i c i e n t i n Ni^Sb^ i s much higher than i n any other phase i n t h i s a l l o y system. This i s r e l a t e d , presumably, to a defect s t r u c t u r e i n t h i s phase. However, because of u n c e r t a i n t i e s i n the c r y s t a l s t r u c t u r e t h i s f a s t growth r a t e cannot be discussed i n a q u a n t i t a t i v e manner. 88 3.5 COPPER-SELENIUM SYSTEM D i f f u s i o n couples of Cu-Se annealed at 170°C showed two phases i n the d i f f u s i o n zone. The s t r e s s e f f e c t i n t h i s system was d i f f e r e n t from that observed i n Ni-Sb and the r e s u l t s w i l l , t h e r e f o r e , be presented i n some d e t a i l . 3.5.1 THE PHASE DIAGRAM The complete phase diagram of the Cu-Se system i s not a v a i l a b l e i n the l i t e r a t u r e . Hansen^ reports the existence of three i n t e r m e t a l l i c phases^Cu^Se, Cu^Se,, and CuSe,with h i g h l y r e s t r i c t e d composition ranges. 79 Cu 2Se (38.22 wt pet Se) i s f . c . c . w i t h 12 atoms per u n i t c e l l . This compound i s h i g h l y d e f e c t i v e and should be w r i t t e n Cu 2_ xSe w i t h a maximum 80 value of x = 0.14 . At the S e - r i c h end of the composition range of Cu 2_ xSe, the f . c . c . s t r u c t u r e i s r e t a i n e d to room temperature, w h i l e , at the Cu-rich end ,a s e r i e s of low temperature phase transformations occur and i t has been reported that no l e s s than seven d i f f e r e n t c r y s t a l s t r u c t u r e s e x i s t ^ . 81 Cu.jSe 2 (45.4 wt pet Se) i s orthorhombic w i t h 20 atoms per u n i t c e l l . This compound i s a l s o very d e f e c t i v e w i t h the excess cations occupying i n t e r s t i t i a l p o s i t i o n s . CuSe (55.4 wt pet Se) i s hexagonal,most l i k e l y i s o t y p i c w i t h the 82 CuS s t r u c t u r e 3.5.2 IDENTIFICATION OF THE PHASES Only two phases were observed i n the d i f f u s i o n zone. They were i d e n t i f i e d by e l e c t r o n microprobe a n a l y s i s and by X-ray d i f f r a c t i o n technique. The probe t r a v e r s e i s shown i n f i g . 40. Compositions of 36.2 wt pet Se found f o r the Cu - r i c h phase and 46.5 wt pet Se f o r the S e - r i c h phase agreed w e l l w i t h the composition of Cu 2Se (38.2 pet Se) and Cu 3Se 2 (45.4 wt pet Se), wt % Se 100 90 80 70 60 50 40 30 20 10 L_ 0 Se C u 3 S e 2 46.5% l^rry^<y-^^-^^^ Se Cu„ Se 2-x 36.2% Se cx^ >yr0-<>x9\ Cu CD O O O cD 100 200 300 400 500 600 700 Distance i n y F i g - 40 E l e c t r o n probe t r a v e r s e of the d i f f u s i o n zone i n a Cu-Se couole annealed at 170°C f o r 25 h r s . at 200 p s i oo 90 r e s p e c t i v e l y . The probe t r a v e r s e d i d not show any s o l i d s o l u b i l i t y of the elements i n one another nor any concentration gradient w i t h i n the phases. X-ray d i f f r a c t i o n confirmed that the S e - r i c h phase was Cu,jSe2 (Appendix 1) . The d-spacings obtained f o r the Cu-rich phase did not correspond to those of the high temperature form of (X^Se. However, as discussed i n page 88 there are s e v e r a l complex low temperature t r a n s i t i o n s i n t h i s phase and the observed s t r u c t u r e may w e l l be one of these. 3.4.3 THE EFFECT OF STRESS ON DIFFUSION A p p l i c a t i o n of s t r e s s has a l a r g e e f f e c t on the width of the d i f f u s i o n zone i n t h i s system, s i g n i f i c a n t l y greater than i n any of the other systems i n v e s t i g a t e d i n t h i s work. F i g . 41 shows the thickness of the d i f f u s i o n zone obtained by annealing specimens f o r 25 hours at 170°C, as a f u n c t i o n of s t r e s s . I t was seen that the width of C^Se increased l i n e a r l y w i t h i n c r e a s i n g s t r e s s - from 30p at zero s t r e s s to 660y at 1500 p s i . The thickness of Ci^Se comprised 76.0 pet of the t o t a l d i f f u s i o n zone width at 1500 p s i compared to 9.0 pet at zero s t r e s s . The only other system i n which t h i s magnitude of s t r e s s s e n s i t i v i t y has been observed i s Cu-Te . The width of Cu^Se2 decreased w i t h i n c r e a s i n g s t r e s s - from 310y at zero s t r e s s to 215y at 1500 p s i . The e f f e c t on Cu 3Se2, however, was small compared to that i n Cu2Se. 3.4.4 KINETICS T y p i c a l growth curves at 50,400 and 1000 p s i are shown i n f i g . 42 and 43 and others are given i n Appendix 2. At high pressures (1000 p s i ) growth of both phases was p a r a b o l i c i n d i c a t i n g d i f f u s i o n was r a t e determining. At low s t r e s s e s (50 and 400psi) there was an i n c u b a t i o n period before Cu„Se 400 p s i 5 10 15 20 25 30 35 40 Time i n hr. F i g . 43 Growth of Cu Se, at 170°C and.50, 400 and 1000 p s i 94 forms and during which growth of Cu^Se^ was very slow. This i n c u b a t i o n time decreased l i n e a r l y w i t h i n c r e a s i n g s t r e s s as shown i n f i g . 44 and above 560 p s i no i n c u b a t i o n period was observed. In c o n s i d e r i n g x vs / t p l o t s i t seemed most reasonable that the time o r i g i n f o r the Cu 2Se phase be taken as the time necessary f o r i t s n u c l e a t i o n . Before the Cu.jSe2 phase s t a r t e d to grow q u i c k l y i t achieved a c e r t a i n thickness and the time o r i g i n f o r t h i s phase could be found by e x t r a p o l a t i n g the true growth curve of Cu 3Se2 to zero t h i c k n e s s . As seen i n f i g . 45 , t h i s method gives p l o t s which are p a r a b o l i c , i n d i c a t i n g that the procedures f o r determining the time o r i g i n are reasonable and that the growth i s d i f f u s i o n c o n t r o l l e d at low s t r e s s e s . Even when the time o r i g i n i s taken as the beginning of d i f f u s i o n , t h e x vs / t p l o t s give s t r a i g h t l i n e s , but such p l o t s do not have t h e o r e t i c a l v a l i d i t y and hence are not used f o r a n a l y s i s of the r e s u l t s . F i g . 46 shows the p a r a b o l i c growth at 1000 p s i where there i s no i n c u b a t i o n p e r i o d . Growth r a t e s of Cu2Se and Cu^Se are p l o t t e d as a f u n c t i o n of s t r e s s i n f i g . 47 . I t was observed that the growth r a t e of Cu 2Se increased apparently l i n e a r l y w i t h the s t r e s s , and that the growth r a t e of Cu 3Se2 decreased apparently l i n e a r l y w i t h the s t r e s s . A s e r i e s of t e s t s were c a r r i e d out i n which d i f f u s i o n was allowed to take place at low pressure f o l l o w i n g an i n i t i a l high s t r e s s d i f f u s i o n anneal. Specimens were annealed at 170°C f o r 4 hours under a s t r e s s of 1000 p s i to give a wide band of Cu2Se a f t e r which the pressure was r e l e a s e d and d i f f u s i o n was allowed to proceed at zero p s i . The r e s u l t s are given i n f i g . 48 . I t was seen that the thickness of C^Se decreased continuously w i t h i n c r e a s i n g d i f f u s i o n time and a f t e r 45 hours i t had disappeared completely. The Cu,.Se9 grew at the expense of the Cu„Se, 600 99 0 p s i normal t e s t Time i n hr r F i g . 48 Graph i l l u s t r a t i n g the s h r i n k i n g of Cu 2Se at 170°C when an i n i t i a l s t r e s s of 1000 p s i i s released a f t e r 4 hr. anneal and d i f f u s i o n allowed at zero s t r e s s 100 although i t s growth r a t e was very much l e s s than would be expected from normal growth measurements at zero s t r e s s . I t should be noted that there was s t i l l some growth of Cu.jSe2 even a f t e r the Cu2Se had disappeared, i n d i c a t i n g that some t r a n s f e r of atoms i n t o the d i f f u s i o n zone was taking p lace. The above r e s u l t s are s i g n i f i c a n t l y d i f f e r e n t from s i m i l a r t e s t s i n the other systems i n v e s t i g a t e d . For example, other systems have shown the development of growth rates c h a r a c t e r i s t i c of the new s t r e s s a p p l i e d . In Cu-Se, the growth of Cu.jSe2 i s much slower than i s c h a r a c t e r i s t i c of the zero s t r e s s w h i l s t C^Se would be expected to sh r i n k but not.disappear completely. For t h i s reason a second s et of experiments was c a r r i e d out i n which d i f f u s i o n was allowed to take place i n i t i a l l y f o r 4 hours at 1000 p s i and then the pressure was reduced to 120 p s i r a t h e r than to the zero p s i . The r e s u l t s i n f i g . 49 show that the Cv^Se phase s t i l l disappeared although at 120 p s i i t should have a f a i r l y high growth r a t e . However, the Cu^Se2 now grew at a r a t e which was cl o s e to the expected 120 p s i growth r a t e . 3.4.5 HYDROSTATIC TEST Hy d r o s t a t i c t e s t s were c a r r i e d out i n order to study the d i f f e r e n c e between the e f f e c t of u n i a x i a l s t r e s s and h y d r o s t a t i c pressure i n t h i s rather complicated system. Specimens were prebonded at 170°C f o r one hour under a compressive s t r e s s of 1000 p s i and then d i f f u s i o n continued under a h y d r o s t a t i c pressure of 400 p s i at 170°C f o r d i f f e r e n t lengths of time. The r e s u l t s are shown i n f i g . 50 . I t was observed that the Cu2Se continued to grow f o r about 6 hours a f t e r which the width of t h i s phase began 101 120 p s i compressive Regression t e s t at 120 p s i 10 20 30 40 50 60 70 80 90 100 Time i n hr, F i g . 49 Graph showing the s h r i n k i n g of Ci^Se a t 170°C when i n i t i a l s t r e s s of 1000 p s i i s released a f t e r 4 h r s . and d i f f u s i o n allowed under a new s t r e s s of 120 p s i 102 10 20 30 40 50 60 70 80 90 100 Time i n hr. 0 ^ 1 I 1 I i i i i l L 10 20 30 40 50 60 70 80 90 100 Time i n hr. (b) F i g . 50 Graph showing the growth of Cu 2Se and Cu„Se 2 under a h y d r o s t a t i c pressure of 400 p s i at 170OC 103 to decrease and i t disappeared a f t e r about 100 hours. The Cu^Se^ phase i n i t i a l l y continued to grow at the r a t e c h a r a c t e r i s t i c of 1000 p s i s t r e s s . However, a f t e r the Cu 2Se s t a r t e d r e g r e s s i n g the growth r a t e of Cu^Se,, increased by a f a c t o r of 2.2. The disappearance of Cu 2Se at a h y d r o s t a t i c pressure of 400 p s i i s very s i m i l a r to the disappearance of Cu 2Se under a compressive s t r e s s of zero and 120 p s i f o l l o w i n g an i n i t i a l high pressure anneal ( f i g . 48 and 49 ). This suggests that i n t h i s system h y d r o s t a t i c pressure has no s i g n i f i c a n t e f f e c t on growth r a t e s and only compressive loading i s of any importance. S i m i l a r r e s u l t s were a l s o found i n the Ag-Sb system. 3.4.6 KIRKENDALL TEST A photomicrograph of the d i f f u s i o n zone i n a K i r k e n d a l l marker experiment i s shown i n f i g . 51 . I t can be seen that the tungsten markers stayed a t the Cu/Cu 2Se i n t e r f a c e suggesting that copper was the d i f f u s i n g s p e cies. Ledges of copper were observed a t the marker p o s i t i o n as i n the systems reported p r e v i o u s l y . 3.4.7 DISCUSSION I t has been shown that d i f f u s i o n i n Cu-Se i s very s e n s i t i v e to compressive s t r e s s e s w i t h the width of Cu 2Se at 1500 p s i being 22 times that at zero s t r e s s . There seems l i t t l e doubt that t h i s s t r e s s e f f e c t i n Cu-Se i s due to the e l i m i n a t i o n of p o r o s i t y at the Cu/Cu 2Se i n t e r f a c e by the a p p l i e d pressure, j u s t as i n the other systems i n v e s t i g a t e d i n t h i s s tudy. F i g . 51 Photomicrograph of K i r k e n d a l l experiment i n Cu-Se at 170°C f o r 25 h r s . under 1000 p s i . 22 x 105 At low s t r e s s e s the Cu^Se^ phase grows much f a s t e r than (X^Se. This would be expected s i n c e w i t h a s m a l l copper f l u x i n t o the d i f f u s i o n zone there would be a tendency f o r the formation of the S e - r i c h phase. With i n c r e a s i n g s t r e s s the copper f l u x increases and growth of the Cu-rich Ci^Se phase i s f a c i l i t a t e d and i t s thickness increases l i n e a r l y w i t h the a p p l i e d s t r e s s . The s t r e s s dependence i n t h i s phase i s thus s i m i l a r to that i n Ni-Sb and as discussed i n page 86 i s c h a r a c t e r i s t i c of a phase w i t h a high i n t r i n s i c d i f f u s i o n c o e f f i c i e n t . The thickness of Cu 3Se2 decreases w i t h i n c r e a s i n g s t r e s s . Growth of t h i s phase depends on the f l u x of copper atoms from C^Se i n t o Cu^Se^. This f l u x depends p r i m a r i l y on the c o n c e n t r a t i o n gradient i n the Cu2Se and as can be seen i n f i g . 52 , t h i s i s greatest when Cu~Se i s t h i n i . e . at Cu Cu^e Cu„Se i Se 3 2 Cu Cu 2Se Cu 3Se 2 Se F i g . 52 Schematic r e p r e s e n t a t i o n of the dependence of c o n c e n t r a t i o n gradient on the thickness of Ci^Se low s t r e s s e s . S i m i l a r reductions i n thickness w i t h i n c r e a s i n g pressure occur 6 i n the Cu.Te. and CuTe phases i n Cu-Te 4 3 106 Cu-Se i s d i f f e r e n t from other systems examined so f a r i n that there i s a n u c l e a t i o n period before the Cu^Se forms and during which growth of Cu^Se^ i s slow. This n u c l e a t i o n time appears to decrease l i n e a r l y w i t h pressure and v a r i e s from 6.2 hr. at zero s t r e s s to zero time above 560 p s i . This n u c l e a t i o n time appears to be i n d i c a t i v e of poor bonding across the i n t e r f a c e of the d i f f u s i o n couple. Tests i n which the pressure was suddenly reduced i n the course of a d i f f u s i o n anneal a l s o gave r e s u l t s i n Cu-Se which were d i f f e r e n t from the systems discussed before. I n other systems, the growth r a t e which developed on removal of the a p p l i e d s t r e s s was c h a r a c t e r i s t i c of the new pressure. I n Cu-Se at zero s t r e s s ,the growth r a t e was s i g n i f i c a n t l y l e s s f o r both the Cu 2Se and Cu^Se,, phases. Some copper atoms entered the d i f f u s i o n zone from the pure metal s i n c e the Cu.jSe2 phase continued to grow a f t e r the Cu 2Se phase had disappeared. However, t h i s growth r a t e was very s m a l l i n d i c a t i n g that the Cu/Cu^Se,^ i n t e r f a c e was very d e f e c t i v e . At 120 p s i , Cu.jSe2 grew at the r a t e c h a r a c t e r i s t i c of the a p p l i e d pressure. However, the Cu 2Se phase s t i l l d i d not grow, suggesting that t r a n s f e r of atoms from copper i n t o the d i f f u s i o n zone i s s t i l l r e s t r i c t e d . The i n c u b a t i o n period at the beginning of d i f f u s i o n and the slow d i f f u s i o n which occurs on removal of the s t r e s s a f t e r an i n i t i a l high pressure anneal, i n d i c a t e a tendency to form poor i n t e r f a c e s i n t h i s sys tern. As w i l l be shown i n the next s e c t i o n s i m i l a r r e s u l t s were obtained i n the Cu-Sb system and p o s s i b l e suggestion as to why these systems should be d i f f e r e n t w i l l be taken up i n the f i n a l chapter of t h i s t h e s i s . 107 3.6 COPPER - ANTIMONY SYSTEM 4 5 Heumann ' has reported that d i f f u s i o n i n the copper-antimony system was s i g n i f i c a n t l y a f f e c t e d by a p p l i e d s t r e s s and the present i n v e s t i g a t i o n was c a r r i e d out i n order to extend the previous r e s u l t s . However, as w i l l be seen l a t e r ,the observations proved to be s i g n i f i c a n t l y d i f f e r e n t from those reported p r e v i o u s l y . 3.6.1 THE PHASE DIAGRAM ' The phase diagram of Cu-Sb i s w e l l e s t a b l i s h e d and i s shown i n f i g . 53 . The temperature of i n v e s t i g a t i o n was 390°C, the same as that 4 5 used by Heumann et. a l . ' . At t h i s temperature three phases,Cu^ ,-Sb (complex hexagonal), Cu^Sb (orthorhombic) and Cu 2Sb ( t e t r a g o n a l ) , a r e s t a b l e . S p e c i f i c volume c a l c u l a t i o n s show that there are c o n t r a c t i o n s of 12.2 and 9.5 pet when copper and antimony react to form Cu^Sb and C^Sb r e s p e c t i v e l y anc there i s an increase of 7.1 pet when the phase Cu^ ^Sb i s formed. These volume changes are l a r g e compared to the other systems i n v e s t i g a t e d . 3.6.2 IDENTIFICATION OF THE PHASES The two phases present i n the d i f f u s i o n zone were i d e n t i f i e d by microprobe a n a l y s i s and by X-ray d i f f r a c t i o n (Appendix 2). The probe traverse i s shown i n f i g . 54 ; the compositioniof the phases agree w e l l w i t h Cu 2Sb(Y) and Cu3Sb(,<). j 3.6.3 THE EFFECT QF STRESS ON DIFFUSION The e f f e c t of s t r e s s on d i f f u s i o n i n Cu-Sb i s q u i t e s m a l l , F i g . 55 shows the photomicrographs of the d i f f u s i o n zone obtained by F i g . 53 Phase diagram of Cu-Sb (Hansen ') 60 h 40 f-10 h Sb Cu„Sb 5070 wt % Sb 100 200 300 400 Distance i n y Cu 3Sb 33.0 wt % Sb Cu Q Q (0 Q Q O 500 600 700 F i g . 54 E l e c t r o n probe t r a v e r s e of the d i f f u s i o n zone i n Cu-Sb. Specimen annealed f o r 9 h r s . at 350°C and 50 p s i . Probe a n a l y s i s c a r r i e d out using Cu-K r a d i a t i o n 0 p s i 100 p s i 300 p s i 400 p s i 500 p s i F i g . 55 Photomicrographs of the d i f f u s i o n zone obtained by annealing specimens f o r 9 hrs, a t 390°C at d i f f e r e n t s t r e s s e s . 58 x I l l annealing specimens at 390 C f o r 9 hours under d i f f e r e n t s t r e s s e s . F i g . 56 shows the width of the d i f f u s i o n zone as a f u n c t i o n of s t r e s s . The thickness of Cu^Sb increased w i t h i n c r e a s i n g s t r e s s up to 400 p s i - from 220p at zero s t r e s s to 360y at 400 p s i - w h i l s t the width of Cu 2Sb d i d not change. The degree of s t r e s s s e n s i t i v i t y i n Cu-Sb i s s i m i l a r to that observed i n Ag-Sb and Ag-Se, although i n Cu-Sb two phases are observed i n the d i f f u s i o n zone. 3.6.4 KINETICS Growth curves at d i f f e r e n t s t r e s s e s are shown i n f i g . 57 and 58 . F i g . 57 shows that there i s an i n c u b a t i o n period f o r the formation of Cu^Sb at low s t r e s s e s ; t h i s p eriod decreased l i n e a r l y w i t h s t r e s s , as shown i n f i g . 59 , w i t h no i n c u b a t i o n period being observed above 80 p s i . I t w i l l be r e c a l l e d that a s i m i l a r e f f e c t has been observed i n Cu-Se. At lower s t r e s s e s , the C^Sb phase grew i n i t i a l l y at a f a s t rate,which slowed down a f t e r the appearance of Cu^Sb, and followed the same curve as the high pressure r e s u l t s . I n c o n s i d e r i n g x vs /t~ p l o t s the time o r i g i n f o r Cu^Sb i s taken as the time at which the phase nucleated, j u s t as i n Cu-Se. When the data are p l o t t e d i n t h i s way the r e s u l t s i n d i c a t e p a r a b o l i c growth behaviour f o r both the phases ( f i g . 60 and 61 )• F i g . 62 shows the r e s u l t a n t growth ra t e s of Cu^Sb and Cu 2Sb as a f u n c t i o n of s t r e s s . I t i s observed that the growth r a t e of Cu^Sb increases p r o g r e s s i v e l y w i t h i n c r e a s i n g s t r e s s upto 400 p s i and above t h i s s t r e s s no v a r i a t i o n i n the growth r a t e i s observed. The growth r a t e of C^Sb i s apparently unaffected by the a p p l i e d s t r e s s . Tests i n which d i f f u s i o n was allowed to take place at zero s t r e s s a f t e r an i n i t i a l high pressure d i f f u s i o n anneal gave r e s u l t s s i m i l a r 600 500 400 -300 -200 100 200 400 600 800 Stress i n p s i "LT -o-1000 1200 T o t a l Cu 3Sb Cu 2Sb 1400 F i g . 56 Graph showing the width of d i f f u s i o n zone obtained by a 9 hr. anneal at 390°C as a f u n c t i o n of s t r e s s -Q-- A -5 10 15 20 25 30 35 40 F i g . 57 Time i n hr. Growth of Cu 0Sb at 390°C at d i f f e r e n t s t r e s s e s 400 4 119 to those i n Cu-Se ( f i g . 63 ). I t was observed that the width of Cu^Sb was reduced and that t h i s phase disappeared a f t e r 34 hours w h i l s t the antimony-rich phase, Cu^Sb, grew at the expense of the Cu^Sb, but nevertheless continued to grow even a f t e r the disappearance of the Cu^Sb phase. 3.6.5 HYDROSTATIC TESTS For studying the d i f f u s i o n under h y d r o s t a t i c pressure, specimens were prebonded at 390°C f o r 1 hour under a compressive s t r e s s of 400 p s i and then d i f f u s e d under a h y d r o s t a t i c pressure of 315 p s i . The r e s u l t s are shown i n f i g . 64 . I t can be seen that the r e s u l t s are very s i m i l a r to those i n Cu-Se. The Cu^Sb phase grew i n i t i a l l y f o r a short length of time (10 hours) a f t e r which i t s thickness decreased. The Cu 2Sb phase, however, grew w i t h i n c r e a s i n g heating time, i n i t i a l l y at a slower r a t e , but the growth r a t e increased when Cu^Sb s t a r t e d to regress. The r e s u l t s are s i m i l a r to the experiments c a r r i e d out at zero s t r e s s a f t e r an i n i t i a l high pressure anneal i n d i c a t i n g that h y d r o s t a t i c pressure i s of no s i g n i f i c a n c e i n the d i f f u s i o n c h a r a c t e r i s t i c s of t h i s system. 3.6.6 KIRKENDALL TESTS A photomicrograph of a t y p i c a l K i r k e n d a l l marker experiment i s shown i n f i g . 65 . The markers stayed on the Cu^Sb/Cu i n t e r f a c e i n d i c a t i n g that copper i s the d i f f u s i n g species. Ledges of copper are observed under the tungsten markers, c h a r a c t e r i s t i c of a pressure s e n s i t i v e d i f f u s i o n process. A f a i r l y d e t a i l e d examination of the K i r k e n d a l l e f f e c t was 120 400 300 200 c •rl CO CO <1J c ^4 o •H .c H Cu.Sb s t r e s s released here / 400 p s i / 100 / zero psx Normal growth Growth at 0 p s i a f t e r i n i t i a l high pressure anneal -G- - 0 -20 40 60 80 100 120 Time i n hr. / . / . L J , 1 1 I _ i 20 40 60 80 100 120 Time i n hr» (b) F i g . 63 Graph showing the shrinkage of Cu^Sb and growth,of Cu2Sb when i n i t i a l s t r e s s of 400 p s i i s released a f t e r 16 h r s . and d i f f u s i o n proceeds at zero s t r e s s . Re-s u l t s f o r growth of Cu^Sb and Cu^Sb at 400 p s i and zero p s i are provided f o r comparison 121 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Time i n hr. (b) F i g . 64 Growth of Cu Sb and Cu 2Sb, annealed at 390°C . under h y d r o s t a t i c pressure of 315 p s i . Normal growth curves a t 400 p s i and zero p s i are shown f o r comparison 122 F i g . 65 Micrograph of K i r k e n d a l l experiment. Specimen annealed f o r 50 h r s . at 390 C and 1000 p s i . 30 x 123 c a r r i e d out i n t h i s system s i m i l a r to the t e s t s made i n Ag-Sb (page .54 ) . F i g . 66 shows K i r k e n d a l l marker experiments c a r r i e d out f o r 0,1 and 2\ hours. I n i t i a l l y the markers act as b a r r i e r s to d i f f u s i o n and the width of the d i f f u s i o n zone i s zero at the marker p o s i t i o n w i t h ledges of both s i l v e r and antimony on e i t h e r s i d e of the markers. As d i f f u s i o n proceeds., l a t e r a l d i f f u s i o n takes place and the Cu^Sb/Sb boundary i s smoothed out q u i c k l y . The copper ledge at the Cu/Cu^Sb boundary i s maintained f o r a long time s i n c e d i f f u s i o n of copper i n t o Cu^Sb i n the l a t e r a l d i r e c t i o n i s r e s t r i c t e d due to the absence of ap p l i e d pressure. F i g . 67 shows a marker experiment using d i f f e r e n t s i z e markers. The height of the copper ledge increased w i t h i n c r e a s i n g marker s i z e due to the i n c r e a s i n g amount of l a t e r a l d i f f u s i o n r e q u i r e d . The r e s u l t s i n Cu-Sb are, t h e r e f o r e , very s i m i l a r to those i n Ag-Sb i n d i c a t i n g that the presence of two phases i n the d i f f u s i o n zone i s of no s i g n i f i c a n c e to the mode of development of the ledges. 3.6.7 DISCUSSION The s t r e s s e f f e c t i n Cu^Sb i s s i m i l a r to that i n Ag-Sb and Ag-Se and has i t s o r i g i n i n the e l i m i n a t i o n of the K i r k e n d a l l p o r o s i t y at the Cu/Cu^Sb i n t e r f a c e . The growth of Cu^Sb i s unaffected by pressure as might be expected s i n c e the growth of t h i s phase depends on the copper f l u x across and out of the Cu^Sb phase, i . e . on the con c e n t r a t i o n gradient i n Cu^Sb, and t h i s d i d not change very much with pressure. At low stresses, a n u c l e a t i o n e f f e c t i s observed i n Cu-Sb which i s f a i r l y s i m i l a r to but smaller than that observed i n Cu-Se. There i s a n u c l e a t i o n time required f o r the formation of Cu^Sb and t h i s time decreased as the a p p l i e d pressure increased. The Cu-Sb had a s l i g h t l y f a s t e r growth 124 21 x (c) 2h hrs. F i g . 66 Photomicrographs of K i r k e n d a l l experiments i n Cu-Sb annealed at 390°C f o r various times at 1000 p s i 126 r a t e before Cu^Sb nucleated than when both phases were present. However, the f l u x of copper atoms i n t o the d i f f u s i o n zone increases markedly when Cu^Sb nucleates, i n d i c a t i n g that the i n i t i a l i n t e r f a c e formed i s d e f e c t i v e , although not as poor as i n the Cu-Se system. The Cu-Sb system shows a tendency f o r the formation of a poor i n t e r f a c e between copper and the d i f f u s i o n zone j u s t as i n Cu-Se. This i s evidenced by the n u c l e a t i o n time at the beginning of d i f f u s i o n discussed above,and by t e s t s i n which the pressure was suddenly released i n the middle of the d i f f u s i o n anneal and the Cu^Sb phase s t a r t e d to s h r i n k . This e f f e c t was observed i n two of the f i v e systems i n v e s t i g a t e d and p o s s i b l e explanations are discussed i n the next chapter. The s t r e s s e f f e c t i n Cu-Sb observed i n the present i n v e s t i g a t i o n 4 5 i s s i g n i f i c a n t l y d i f f e r e n t from that reported by Heumann et. a l . ' (see page 4 ). They found that even at high s t r e s s e s there was s t i l l a s i g n i f i c a n t n u c l e a t i o n time f o r the formation of Cu^Sb (e.g. 1 hour at 850 p s i , see F i g . 68 ). 1 2 3 4 5 6 /Time i n /hr. F i g . 68 Growth of Cu 2Sb and Cu 3Sb at 390 C and 850 p s i (Heumann e t . a l . ) 127 In the present work Cu^Sb was found to be present a f t e r 4 hours anneal at zero s t r e s s and above 80 p s i i t appeared from the beginning of d i f f u s i o n . I t i s d i f f i c u l t to account f o r such a l a r g e discrepancy between the two sets of data which were apparently obtained under s i m i l a r experimental c o n d i t i o n s . Heumann has a l s o reported that the growth of Cu^Sb occurred i n three stages, w i t h a f a s t growth stage apparently superimposed between two slower r a t e s . I t i s very d i f f i c u l t indeed to give any explanation f o r such a growth curve, and i t may w e l l be that Heumann i s p u t t i n g too much weight on the accuracy of two experimental points . However, the growth r a t e at longer time (11.5 x 10 ^ cm//sec.) i s i n good agreement w i t h the growth r a t e at zero s t r e s s (11.3 x 10 ^ cm//sec.) i n the present i n v e s t i g a t i o n . Heumann a l s o c a r r i e d out a set of experiments i n which the pressure was suddenly changed during the course of a d i f f u s i o n anneal. From these experiments i t was concluded that below a c r i t i c a l pressure of 570 p s i , Cu^Sb d i d not appear i n the d i f f u s i o n zone. These r e s u l t s are s i m i l a r to the r e s u l t s obtained i n the present i n v e s t i g a t i o n , although the magnitude of s t r e s s i n v o l v e d was v e r y much greater i n Heumann's work. 4' 5 The d i s c r e p a n c i e s between the r e s u l t s of Heumann e t . a l . * and the present i n v e s t i g a t i o n are p o s s i b l y due to the f r i c t i o n between the specimen and the d i e w a l l s i n Heumann's apparatus, whereas the s t r e s s i s purely compressive i n the present i n v e s t i g a t i o n w i t h no p o s s i b i l i t y of f r i c t i o n a f f e c t i n g the r e s u l t s i n any way. I f such f r i c t i o n i s in v o l v e d the a p p l i e d s t r e s s would not be a true measure of the pressure a p p l i e d to the d i f f u s i o n couple. CHAPTER IV 128 SUMMARY AND CONCLUSIONS In previous chapters, i t has been suggested that the effect of stress on d i f f u s i o n i s due to the elimination of the Kirkendall porosity thereby increasing the surface area for d i f f u s i o n and thus the atomic f l u x . I t has also been stated that variations i n the d i f f u s i o n c o e f f i c i e n t and phase boundary compositions are not,significant i n the stress range used i n the experiments. In the following section attempts w i l l be made to obtain a quantitative measure of these effects and their r e l a t i v e significance. 4.1. RELATIVE VARIATIONS OF DIFFUSION COEFFICIENT AND PHASE  BOUNDARY COMPOSITION 59 Castleman has shown that the r e l a t i v e effect of variations of the d i f f u s i o n c o e f f i c i e n t and phase boundary compositions with pressure depend on the factor u, given i n eq. (1.21) (see page 29). He suggested that a pressure induced change i n the interface concentration would not be important unless the factor 'u' has a value , say, greater than f i f t y . This factor has been calculated for the Ag-Sb and Ag-Se system and i s given i n Table 5. Eq. (1.21) has been derived on the assumption that the growth rates of the two interfaces of the d i f f u s i o n zone are equal and opposite, and i t i s not completely accurate when applied to Ag^Sb and Ag 2Se. The 'u' factors calculated w i l l therefore be approximate. However, the values are very small, being less than two for both Ag^Sb and Ag 2Se, suggesting that the change i n phase boundary composition i s i n s i g n i f i c a n t i n comparison with apparent changes i n the d i f f u s i o n c o e f f i c i e n t . These calculations could not be extended to the Cu-Se, Cu-Sb and Ni-Sb systems since more than one phase was present i n the d i f f u s i o n zone and so Castleman's theory cannot be used. However, i t seems reasonable that i n these systems 129 as w e l l , the v a r i a t i o n i n phase boundary c o m p o s i t i o n i s n e g l i g i b l e compared w i t h t h e v a r i a t i o n i n the d i f f u s i o n c o e f f i c i e n t . 4.2 EFFECT OF PRESSURE ON DIFFUSION COEFFICIENT I t has been shown i n page 2 2 t h a t d i f f u s i o n c o e f f i c i e n t s g e n e r a l l y d e c r e a s e w i t h p r e s s u r e as r e p r e s e n t e d by eq. ( 1 . 1 6 ) . There i s i n s u f f i c i e n t d a t a on a c t i v a t i o n volumes to c a l c u l a t e a c c u r a t e l y t h e e f f e c t o f p r e s s u r e on d i f f u s i o n c o e f f i c i e n t s i n the systems i n v e s t i g a t e d i n t h i s work. However, e s t i m a t e s c a n be made by assuming t h a t t h e a c t i v a t i o n volumes f o r f o r m a t i o n and f o r m i g r a t i o n of v a c a n c i e s a r e e q u a l and t h a t b o t h a r e e q u i v a l e n t t o the a t o m i c volume o f the d i f f u s i n g s p e c i e s . These as s u m p t i o n s w i l l y i e l d a n upper l i m i t f o r the v a r i a t i o n i n d i f f u s i o n c o e f f i c i e n t s w i t h p r e s s u r e s i n c e the r e l a x a t i o n o f atoms around 83 a v a c a n c y have been i g n o r e d I n A g 2 S e and C u 2 S e , t h e sum o f the c o v a l e n t r a d i i o f the s p e c i e s (2.69A° f o r A g 2 S e and 2.54A° f o r Cu 2Se) a r e i n r e a s o n a b l y good agreement w i t h t h e n e a r e s t n e i g h b o u r d i s t a n c e (2.16A° f o r A g 2 S e and 2.54A° f o r Cu 2Se) c a l c u l a t e d from a knowledge o f the C a F 2 t y p e . s t r u c t u r e and the l a t t i c e p a r a m e t e r . Hence A g 2 S e and C u 2 S e a r e c o n s i d e r e d t o have e s s e n t i a l l y c o v a l e n t b o n d i n g and t h e a t o m i c volumes o f Ag and Cu were c a l c u l a t e d from t h e i r r e s p e c t i v e c o v a l e n t r a d i i . I n Ag^Sb and Cu^Sb, t h e b o n d i n g i s e s s e n t i a l l y m e t a l l i c and t h e a t o m i c d i a m e t e r s o f Cu and Ag were t a k e n t o 84 be r e p r e s e n t a t i v e o f the d i f f u s i n g s p e c i e s . U s i n g t h e s e v a l u e s t h e r a t i o of the d i f f u s i o n c o e f f i c i e n t a t 1000 p s i t o t h a t a t z e r o p r e s s u r e was c a l c u l a t e d a t the t e m p e r a t u r e o f t h e e x p e r i m e n t and t h e r e s u l t s p r e s e n t e d i n T a b l e 5. I t i s s e e n t h a t the d i f f u s i o n c o e f f i c i e n t s d e c r e a s e by l e s s t h a n 130 TABLE 5 V FACTORS AND D(P)/D(o) FOR INTERMEDIATE PHASES Phase Growth r a t e Temp, y A c t i v a t i o n n/^s a t i n cm//sec, volume f o r d i f f u s i o n D(o) 1000 p s i , 3 Ag 3Sb 13.7 x 10 350°C 1.47 11.9 A° 97,7% _ s 3 Ag 2Se 14.8 x 10 130°C 2.02 30.0 A° 91.6% _ s 3 Cu 2Se 22.4 x 10 170°C - 22.0 A° 96.5% 3 Cu 3Sb 18.3 x 10 390°C - 17.12 A° 97.0% 131 10 pet f o r a l l the phases at 1000 p s i whereas the experimentally observed i n c r e a s e i n growth ra t e s of a l l these phases with s t r e s s suggests a l a r g e i n c r e a s e i n the d i f f u s i o n c o e f f i c i e n t s . The s i g n i f i c a n t decrease i n the d i f f u s i o n c o e f f i c i e n t i n Ag^Se at 1000 p s i i s due to the l a r g e value of the 85 86 a c t i v a t i o n volume assumed i n the c a l c u l a t i o n . In known cases (Cu , Au , ) , the a c t i v a t i o n volumes are of the order of h a l f the atomic volume and t h i s would make the e f f e c t much l e s s . However, i t can be concluded that the s t r e s s s e n s i t i v i t y observed i n t h i s work i s not due to changes i n the phase boundary composition or i n the d i f f u s i o n c o e f f i c i e n t . Other experimental evidence supports t h i s c o n c l u s i o n . In Ag-Sb, Ag-Se and Cu-Sb there i s a maximum growth r a t e above a c e r t a i n l i m i t i n g s t r e s s r a t h e r than the continuously v a r y i n g r a t e which would be expected from v a r i a t i o n s i n phase boundary composition and d i f f u s i o n c o e f f i c i e n t . Furthermore, t e s t s i n Ag-Sb show that h y d r o s t a t i c pressure does not have any i n f l u e n c e on growth rate s , whereas f o r v a r i a t i o n s i n the e q u i l i b r i u m composition and d i f f u s i o n c o e f f i c i e n t h y d r o s t a t i c pressure should have an e f f e c t " v e r y s i m i l a r to that of compressive s t r e s s . 4.3 EFFECT OF STRESS ON THE KIRKENDALL POROSITY As discussed i n the previous chapter the r e s u l t s of the experiments can be explained very s a t i s f a c t o r i l y i n terms of the K i r k e n d a l l p o r o s i t y . In multiphase systems showing a l a r g e K i r k e n d a l l e f f e c t , there w i l l be a l a r g e vacancy f l u x equal and opposite to the atomic f l u x . These vacancies can condense on one s i d e of the d i f f u s i o n zone, at the i n t e r f a c e between the d i f f u s i n g species and the d i f f u s i o n zone, to form vo i d s . This would decrease the e f f e c t i v e surface area f o r d i f f u s i o n , thus reducing the f l u x of atoms i n t o the d i f f u s i o n zone. A p p l i c a t i o n of s t r e s s 132 w i l l improve the i n t e r f a c e by reducing the K i r k e n d a l l p o r o s i t y , thus i n c r e a s i n g the atomic f l u x i n t o the d i f f u s i o n zone and so i n c r e a s i n g the growth r a t e . However, once the a p p l i e d s t r e s s i s s u f f i c i e n t l y great to give u n r e s t r i c t e d f l u x , no e f f e c t of s t r e s s w i l l be observed as seen i n Ag-Sb, Ag-Se and Cu-Sb. The thicknesses of Cu^Se and Ni^Sb^ (and Cu^Te i n the work of Brown e t . a l , ) appeared to increase l i n e a r l y w i t h the a p p l i e d s t r e s s and no l i m i t i n g s t r e s s was observed above which the growth rat e s were constant. This i s probably because the d i f f u s i o n c o e f f i c i e n t s i n these phases are very l a r g e , much higher than i n any of the other thermally s t a b l e phases. In Cu2Se, f o r example, the chemical i n t e r -89 -4 2 d i f f u s i o n c o e f f i c i e n t of copper has been reported to be 2.45 x 10 cm /sec. at 170°C, which i s about three orders of magnitude l a r g e r than other systems i n v e s t i g a t e d . These systems ther e f o r e tend to have a l a r g e vacancy f l u x and a high pressure w i l l be necessary to e s t a b l i s h a good i n t e r f a c e . The maximum s t r e s s of 1500 p s i a p p l i e d i n these systems i s presumably i n s u f f i c i e n t to a t t a i n these l i m i t i n g c o n d i t i o n s . In multiphase systems the K i r k e n d a l l p o r o s i t y develops at a s i n g l e i n t e r f a c e of the d i f f u s i o n zone and i t i s d i f f i c u l t to determine the pore d e n s i t y by d i r e c t observation. However, an estimate of the p o r o s i t y i n Ag-Sb and Ag-Se can be made, assuming that the width of the intermediate phase i s p r o p o r t i o n a l to the e f f e c t i v e i n t e r f a c e area. Beyond the l i m i t i n g s t r e s s , the t o t a l i n t e r f a c e area of the expecimen i s e f f e c t i v e and hence: T - - (1-24) A c x c where A = e f f e c t i v e i n t e r f a c e area at pressure P. A c = c r o s s - s e c t i o n a l area of the specimen, x = width of the d i f f u s i o n zone at s t r e s s P. x c = width of the d i f f u s i o n zone above the l i m i t i n g s t r e s s . 133 Eq. (1.24) gives an e f f e c t i v e area of 61.0 pet and 31.0 pet f o r 36 Ag-Sb and Ag-Se r e s p e c t i v e l y , at the zero s t r e s s . . Barnes and Mazey have -4 found that the average v o i d radius at the zero s t r e s s i s 5 x 10 cm i n 5 2 Cu-Ni and that there are 6.4 x 10 voids/cm i n the r e g i o n of maximum p o r o s i t y . I f the v o i d radius i s assumed to be the same i n the present 5 2 5 2 work Ag-Sb gives 4.9 x 10 voids/cm and Ag-Se 8.1 x 10 voids/cm at zero s t r e s s , these values being of the same order of magnitude as i n the Cu-Ni system. As discussed i n page 40 , no s t r e s s e f f e c t was observed i n the Cu-Zn, Cu-Sn, and A l - Z r systems (at s t r e s s e s up to 1500 p s i ) . These systems show a small K i r k e n d a l l e f f e c t compared w i t h the systems i n v e s t i g a t e d i n d e t a i l i n t h i s t h e s i s . The vacancy f l u x i s thus smaller and p o r o s i t y would be developed over a s i g n i f i c a n t volume of the d i f f u s i o n zone r a t h e r than j u s t at an i n t e r f a c e , Hence, the e f f e c t i v e surface area of d i f f u s i o n i s not a f f e c t e d s i g n i f i c a n t l y by the K i r k e n d a l l p o r o s i t y . I t t h e r e f o r e appears that the s t r e s s e f f e c t i s s i g n i f i c a n t only i n systems w i t h a l a r g e K i r k e n d a l l e f f e c t . There seems l i t t l e doubt that the e f f e c t of s t r e s s i s to reduce the amount of p o r o s i t y so that the vacancies are now removed e x c l u s i v e l y by d i s l o c a t i o n movement. The d e t a i l s of the mechanism by which t h i s occurs .are somewhat u n c e r t a i n , however, and i t i s not p o s s i b l e to say whether the e f f e c t i s thermodynamic or-mechanical i n o r i g i n . I t has been shown that growth rates are not a f f e c t e d by h y d r o s t a t i c pressure and that only compressive loading i s e f f e c t i v e i n preventing K i r k e n d a l l p o r o s i t y . This would tend to i n d i c a t e that the 134 r e d u c t i o n i n p o r o s i t y i s mechanical i n o r i g i n w i t h any pores tending to form being compressed i n the d i r e c t i o n of d i f f u s i o n and so prevented from developing. The compression could take place by a micro-creep process around the i n c i p i e n t pore, although i t should be emphasised that no de t e c t a b l e creep was observed i n any of the systems examined and the temperatures and pressures used i n t h i s work were very low f o r any creep. 36 Barnes and Mazey found that when pressure i s a p p l i e d to a s i n g l e phase d i f f u s i o n couple c o n t a i n i n g pores, the pores s h r i n k but maintain t h e i r s p h e r i c a l shape. This would i n d i c a t e that the e f f e c t of pressure i s to render the pores thermodynamically unstable. I n the present system, i t may w e l l be that the s t r e s s prevents n u c l e a t i o n of the pores s i n c e an e x t r a energy term i s now involved i n t h e i r formation (see page 31 ). However, i t i s d i f f i c u l t to see how pressures as low as 50 p s i should be s u f f i c i e n t f o r t h i s . 4.4 ' GROWTH KINETICS A l l systems i n v e s t i g a t e d i n t h i s work showed a p a r a b o l i c growth f o r a l l phases over the complete s t r e s s range i n v e s t i g a t e d . In Cu-Sb and Cu-Se there was an i n c u b a t i o n period at low s t r e s s l e v e l s before normal growth took place. However, once t h i s e f f e c t was accounted f o r , these systems, l i k e w i s e , showed a p a r a b o l i c growth. The f a c t that p a r a b o l i c growth i s always observed i n d i c a t e s that the r e s t r i c t i o n to growth at low pressures has i t s o r i g i n i n a d i f f u s i o n process. This r e s t r i c t i o n to growth appears to occur at a phase boundary. However, i t i s not a normal example of an i n t e r f a c e c o n t r o l l e d process which would o r d i n a r i l y give a l i n e a r growth r a t e . Rather, the development of 135 the K i r k e n d a l l p o r o s i t y causes a p h y s i c a l r e d u c t i o n i n the i n t e r f a c e area and so a decrease i n the growth r a t e . Experiments i n which d i f f u s i o n was allowed to take place at low s t r e s s a f t e r an i n i t i a l high s t r e s s d i f f u s i o n anneal showed two d i f f e r e n t c h a r a c t e r i s t i c s depending on the system i n v e s t i g a t e d . I n Ag-Sb and Ni-Sb, growth continued f o r a short time at a r a t e c h a r a c t e r i s t i c of the i n i t i a l high pressure. E v e n t u a l l y , however, the growth r a t e s decreased and assumed the rates c h a r a c t e r i s t i c of the new s t r e s s . This t r a n s i e n t e f f e c t i s expected s i n c e a f i n i t e time i s necessary f o r the development of the degree of the K i r k e n d a l l p o r o s i t y c h a r a c t e r i s t i c of the new pressure. During t h i s time the good bond developed at high pressure w i l l be r e t a i n e d . Results of s i m i l a r experiments i n Cu-Se and Cu-Sb produced growth r a t e s much slower than expected, and these w i l l be discussed i n a l a t e r s e c t i o n . A l l the s t r e s s s e n s i t i v e systems were found to have a l a r g e K i r k e n d a l l e f f e c t . Ledges were i n v a r i a b l y found adjacent to the tungsten markers. This e f f e c t was much greater than i n non-pressure-s e n s i t i v e systems and was a t t r i b u t e d to the absence of s t r e s s i n the l a t e r a l d i r e c t i o n of d i f f u s i o n , thus g i v i n g r e s t r i c t e d atomic f l u x i n t h i s d i r e c t i o n . The nature of r e s u l t s obtained here allows the r e s u l t s of Brown et. a l . ^ on d i f f u s i o n i n Cu-Te to be i n t e r p r e t e d somewhat b e t t e r . There seems l i t t l e doubt now that growth of Cu^Te at high pressure i s s t r i c t l y p a r a b o l i c and the apparent d e v i a t i o n from the p a r a b o l i c growth found by Brown et. a l . ^ i s due to the s i g n i f i c a n t s c a t t e r i n t h e i r experimental r e s u l t s . In the experiments at zero s t r e s s f o l l o w i n g a high pressure anneal ( f i g . 3 (b) page 7 ), the experimental data at short times was neglected. I f t h i s data i s incorporated i n the p l o t , a 136 t r a n s i e n t period can be seen to precede the r e g r e s s i o n of Cu^Te j u s t as have been found i n Ag-Sb and Ni-Sb. Although experiments at d i f f e r e n t temperatures were not c a r r i e d out i n a l l the systems, the r e s u l t s of Ag-Sb and Cu-Te^ show that pressure s e n s i t i v i t y i s not c h a r a c t e r i s t i c of a p a r t i c u l a r temperature and that the nature of the v a r i a t i o n of the growth r a t e w i t h pressure remains e s s e n t i a l l y the same. However, the degree of v a r i a t i o n may change w i t h temperature. 4.5 RESTRICTED DIFFUSION IN Cu-Sb AND Cu-Se The Cu-Sb and Cu-Se systems showed a tendency f o r a r e s t r i c t e d atom t r a n s f e r from the copper i n t o the d i f f u s i o n zone under c e r t a i n circumstances. This occurred at the beginning of d i f f u s i o n under low st r e s s e s when there was a n u c l e a t i o n time f o r the Cu^Sb and Cu 2Se phases. In t e s t s i n which d i f f u s i o n was allowed to take place at a low s t r e s s a f t e r an i n i t i a l high s t r e s s anneal, there was again a very small copper f l u x i n t o the d i f f u s i o n zone and t h i s l e d to the gradual disappearance of the C u-rich phases i n both systems. I n t h i s s e c t i o n various p o s s i b i l i t i e s are explored to e x p l a i n the r e s u l t s . Table 6 l i s t s values of energy of formation (where a v a i l a b l e ) 39 f o r the s t a b l e compounds i n the various a l l o y systems s t u d i e d . B a i r d has suggested that i n Cu-Sb, the d i f f u s i o n temperature (390°C) i s only 15° above the temperature at which Cu^Sb decomposes by a e u t e c t o i d r e a c t i o n , so that the f r e e energy r e d u c t i o n on forming Cu^Sb from the a d j o i n i n g phases at 390°C must be small and therefore a f i n i t e n u c l e a t i o n time would be expected, s i n c e the d r i v i n g f o r c e to form the nucleus w i l l be s m a l l . 137 TABLE 6 ENERGY OF FORMATION, CRYSTAL STRUCTURE AND SPECIFIC VOLUME CHANGES FOR INTERMETALLIC PHASES Phase C r y s t a l Heat of g^ gg Entropy of Change i n St r u c t u r e Formation ' Formation^?,88 S p e c i f i c at 298°K, at 298°K, Volume % kcal/mol. cal/mol/deg. Ag 3Sb C (Ag-Sb) Orthorhomic ( C u 3 T i type) h. c. p. -5.5 ± 1.5 41. 0 ± 3.0 -6.11 10.35 Ag 2Se F.C.C. (CaF 2 type) -10.3 ± 0.2 35. 9 ± 0.1 +3.23 N i 1 5 S b Superstructure of cubic - - -8.4 Ni 3 S b ? - - ? N i 5 S b 9 Tetragonal -36.4 ± 2.5 - -0.03 NiSb Hexagonal -15.5 ± 1.0 - -3.64 N i S b 2 Othorhombic -17.7 ± 1.0 - -11.2 Cu 2Se F.C.C. (CaF 2 type) -14.2 ± 0.2 - +0.4 Cu 3Se 2 Orthorhombic -23.65 ± 1.0 - -5.2 CuSe Hexagonal -9.45 ± 0.5 22. 5 ± 1.5 +0.99 Cu. cSb 4. 5 Cu 3Sb h.c.p. Orthorhombic ( C u 3 T i type) - -+7.07 -12.4 Cu 2Sb Tetragonal -3.0 ± 0.4 24. 25 ± 0.8 -9.5 * Pressure s e n s i t i v e phases 138 However, the small range of s t r e s s i n which delayed n u c l e a t i o n i s observed would not a l t e r the f r e e energy of the system s i g n i f i c a n t l y and i t would appear that t h i s suggestion i s not c o r r e c t . A c t u a l values of energy of formation are not a v a i l a b l e i n Cu-Sb. However, heats of formation are a v a i l a b l e f o r the pressure s e n s i t i v e phases i n Cu-Se, and i t can be seen that these values are q u i t e l a r g e , being higher than f o r pressure s e n s i t i v e phases i n Ag-Sb and Ag-Se but l e s s than f o r Ni^Sb2« Hence the r e s t r i c t e d d i f f u s i o n i n Cu-Sb and Cu-Se i s not r e l a t e d to the energy of formation of the phases. 39 B a i r d has a l s o suggested that delayed n u c l e a t i o n may be caused by a poor contact between the mating surfaces of'the d i f f u s i o n couple or by the presence of an oxide l a y e r at the i n t e r f a c e . A p p l i c a t i o n of s t r e s s would improve the i n t e r f a c e by producing b e t t e r contact between the surfaces or by f r a c t u r i n g the oxide l a y e r , thus decreasing the time f o r the s t a r t of normal d i f f u s i o n . These suggestions may be a p p l i c a b l e , t o some extent,to n u c l e a t i o n e f f e c t s at the beginning of d i f f u s i o n . However, they f a i l to e x p l a i n the r e s t r i c t e d d i f f u s i o n which occurs when the s t r e s s i s suddenly removed from a couple which was allowed to d i f f u s e at a higher s t r e s s pre-v i o u s l y . Here,good contact has already been e s t a b l i s h e d and there i s no pos-s i b i l i t y of an oxide l a y e r i n t e r f e r i n g w i t h d i f f u s i o n . In any case, these suggestions do not e x p l a i n why there i s poor mating or an oxide f i l m i n Cu-Sb and Cu-Se but not i n the other systems i n v e s t i g a t e d . Table 6 shows that there i s a l a r g e c o n t r a c t i o n i n volume involved i n forming Cu^Sb (-12.2 p e t ) . This would c e r t a i n l y make i t d i f f i c u l t to nucleate the phase at a low pressure. Furthermore, i n the course of a d i f f u s i o n anneal, a high s t r e s s w i l l be generated at the Cu/Cu„Sb i n t e r f a c e . 139 This stress would make the interface very f r a g i l e and any shock or change i n the d i f f u s i o n conditions would cause i t to crack. Varying the stress i n the middle of a d i f f u s i o n anneal could cause such a crack to develop and so would give very r e s t r i c t e d atom transfer across the interface. This suggestion has many att r a c t i v e features as i t would explain why the effect was not observed i n the Ag-Sb, Ag-Se and Ni-Sb systems, since i n these systems the phases formed with much smaller changes i n s p e c i f i c volume than i n Cu-Sb. However, i t has the major drawback that i t cannot possibly explain the results i n Cu-Se since Cu2Se apparently forms with 0.4 pet increase i n volume. Hence, i t has not been possible to find any explanation which can adequately account for a l l aspects of the r e s t r i c t e d d i f f u s i o n i n Cu-Sb and Cu-Se. There seems some merit i n the suggestion that the effect i s caused by a decrease i n the s p e c i f i c volume i n the pressure sensitive phase although i t cannot adequately explain a l l the experimental r e s u l t s . I t would be very interesting to find other systems which show this r e s t r i c t e d d i f f u s i o n effect as this might help to find the underlying cause. 4.6 DIFFUSION COEFFICIENTS AND NON-APPEARANCE OF THE STABLE PHASES Diffusion coefficients for the intermetallic phases were estimated from the growth rate data, assuming a lin e a r composition p r o f i l e using the method discussed i n the Introduction (page 19 ). Values are l i s t e d i n Table 7. I t i s observed that the d i f f u s i o n coefficients are generally about.two orders of magnitude greater than the growth constants. The d i f f u s i o n coefficients for Cu^Sb and C^Sb calculated from, the present 4 5 data are i n good agreement with those reported by Heumann et. a l . ' . 140 TABLE 7 DIFFUSION COEFFICIENTS OF INTERMETALLIC PHASES System I n t e r m e t a l l i c Temp. Composition Rate 'D' c a l c u l a t e d phases range Cons tant cm 2/sec. a i n cm//sec. Ag-Sb A 8 3 s b 3 5 0 ° c 7 3 - 6 - 7 8 - 6 1 3 - 7 x 10 5 2.98 x 10 8 Cu-Sb at % Ag Ag-Se Ag 2Se 170°C 66.7 - 67.3 14.8 x 10 5 1.34 x 10 7 at % Ag Cu-Sb 390°C 77.7 - 79.2 18.3 x 10 5 1.1 x 10" 7 * at % Cu (1.3 x IO" 7) Cu Sb 390°C 65 . 4 - 6 7 . 7 7.2 x 10~ 5 7.8 x 10" 7 A at % Cu (6.9 x I O - 7 ) * 4 Heumann's r e s u l t s 141 The d i f f u s i o n c o e f f i c i e n t s f o r Ni^-Sb 2 and Cu^Se cannot be c a l c u l a t e d s i n c e there i s no l i m i t i n g s t r e s s above which the growth r a t e i s constant. However, as discussed i n s e c t i o n (4.3) the d i f f u s i o n c o e f f i c i e n t i n o -4 2 Cu 2Se at 170 C i s 2.45 x 10 cm /sec. which i s much higher than the d i f f u s i o n c o e f f i c i e n t s c a l c u l a t e d f o r other systems. In the systems s t u d i e d , some of the s t a b l e phases p r e d i c t e d from the phase diagram were not observed i n the d i f f u s i o n zone, f o r example £ i n Ag-Sb; N ^ 5 s b » N i S b 2 i n Ni-Sb; CuSe i n Cu-Se; and Cu^ 5Sb 8 3 i n Cu-Sb. S i m i l a r observations have a l s o been made i n N i - A l and U-Al . Non-appearance of these phases even a f t e r the a p p l i c a t i o n of a high s t r e s s suggests that they are not s e n s i t i v e to a p p l i e d s t r e s s and that t h e i r 90 non-appearance i s a true growth e f f e c t . Castleman and Froot , i n v e s t i g a t i n g Ni-Al,suggested that the absence of N i A l and N i ^ A l i n the d i f f u s i o n zone was due to t h e i r s m aller growth ra t e s compared to the other phases. I n the Cu-Sb system, Cu^ ,-Sb has a d i f f u s i o n c o e f f i c i e n t of -9 2, 4 ~ 10 cm /sec. which i s about two orders of magnitude l e s s than that of -7 2 -7 2 Cu^Sb (~10 cm /sec.) and C^Sb (-10 cm /sec.) Hence i t s growth r a t e w i l l be very s m a l l and i t would not be observed i n the d i f f u s i o n zone. The d i f f u s i o n c o e f f i c i e n t s f o r phases i n other systems are not a v a i l a b l e f o r a q u a n t i t a t i v e comparison; however, the same exp l a n a t i o n probably w i l l a l s o hold true f o r them . 142 4.7 CONCLUSIONS 1. The growth of the i n t e r m e t a l l i c phases i n a l l systems i n v e s t i g a t e d i s p a r a b o l i c and hence c o n t r o l l e d by d i f f u s i o n . 2. The e f f e c t of s t r e s s i s to increase the growth rates of the s t r e s s s e n s i t i v e phases by decreasing the amount of the K i r k e n d a l l p o r o s i t y developed during d i f f u s i o n and thus i n c r e a s i n g the c r o s s - s e c t i o n of d i f f u s i o n . The s t r e s s s e n s i t i v e phase i s g e n e r a l l y the one adjacent to the pure metal p r o v i d i n g the d i f f u s i n g atoms. 3. In those systems i n which the pressure s e n s i t i v e phase has a very l a r g e i n t r i n s i c growth r a t e , t h i s r a t e increases l i n e a r l y w i t h s t r e s s , whereas i n other systems there i s a l i m i t i n g s t r e s s above which there i s no v a r i a t i o n i n growth r a t e s , the l i m i t i n g s t r e s s corresponding to the absence of the K i r k e n d a l l p o r o s i t y . 4. The s t r e s s e f f e c t i s observed a t d i f f e r e n t temperatures and i s not c h a r a c t e r i s t i c of any p a r t i c u l a r temperature. 5. In systems showing delayed n u c l e a t i o n the n u c l e a t i o n time decreases l i n e a r l y w i t h s t r e s s . 6. H y d r o s t a t i c pressure has no s i g n i f i c a n t e f f e c t on the growth r a t e s of the i n t e r m e t a l l i c phases and the r e s u l t s do not correspond to the e f f e c t observed under compressive s t r e s s of the same magnitude. 7. I t i s a necessary c o n d i t i o n f o r s t r e s s s e n s i t i v e systems to have a la r g e K i r k e n d a l l e f f e c t and the presence of ledges under the markers i s character-i s t i c of these systems. APPENDIX I X-RAY DIFFRACTION ANALYSIS OF INTERMEDIATE PHASES 144 Table A l X-Ray A n a l y s i s of Ag 3Sb Phase Experimental From ASTM Standard Card Ag 3Sb d i n A 0 \ d i n A 2.611 25 2.61 30 2.415 90 2.42 40 2.287 100 2.29 100 1.769 35 1.771 30 1.508 20 1.506 30 1.370 40 1.370 40 1.275 20 1.278 30 1.256 15 1.258 20 1.208 15 1.207 10 1.096 15 1.096 10 1.012 , 15 1.012 20 145 Table A2 X-Ray D i f f r a c t i o n A n a l y s i s of Ag 2Se (f3) Experimental From ASTM Standard Card Ag 2Se (6) o o d i n A 1/ d i n A I , I 'l o Lo - - 4.15 20 3.77 8 3.77 5 3.31 10 3.30 10 3.89 15 2.89 10 2.73 15 2.72 10 2.67 100 2.67 100 2.57 90 2.57 100 2.42 30 2.42 20 2.23 40 2.23 60 2.117 15 2.11 20 2.078 15 2.07 20 2.004 20 2.00 40 1.939 5 1.94 5 1.872 10 1.872 20 1.817 8 1.820 10 - - 1.717 10 - - 1.668 10 _ 1.609 20 146 Table A3. X-Ray A n a l y s i s of Cu Se Experimental From ASTM f o r Cu^Se2 Standard Card Phase o d i n A \ o o d i n A o 3.56 90 3.56 100 3.199 60 3.20 60 3.11 60 3.11 70 2.97 5 2.97 2 2.86 40 2.86 20 2.56 15 2.56 20 2.379 10 2.38 10 2.26 60 2.26 70 2.137 35 2.14 40 2.024 40 2.02 40 2.00 30 2.00 30 1.933 20 1.933 20 1.908 50 1.908 50 1.829 100 1.829 90 1.778 75 1.778 80 1.638 20 1.639 20 1.360 20 1.359 20 1.204 40 1.204 40 1.187 20 1.188 30 1.165 15 1.166 20 147 Table A4. X-Ray A n a l y s i s of Cu-Sb Phase Experimental ASTM Standard Card f o r Cu 3Sb o o d i n A % d i n A \ o o 4.808 5 4.78 5 3.616 40 3.60 60 3.423 40 3.41 65 2.763 25 2.776 40 2.383 55 2.383 80 2.178 20 2.185 30 2.092 100 2.090 100 1.860 15 1.860 40 1.609 40 1.607 70 1.378 40 1.375 70 1.235 40 1.238 70 1.205 10 1.207 25 1.190 12 1.191 35 1.163 30 1.162 70 148 Table A5 X-Ray A n a l y s i s of Cu„Sb Phase Experimental ASTM Standard f o r Cu 3Sb Card d i n A X / I o J • A 0 d i n A 3.348 30 3.34 50 3.065 25 3.07 50 2.849 50 2.84 75 2.588 58 2.59 75 2.432 35 2.43 50 2.075 100 2.07 100 2.036 25 2.03 50 2.000 85 2.00 100 1.822 15 1.82 25 1.719 45 1.72 75 1.673 40 1.67 75 1.549 25 1.55 50 1.529 29 1.53 75 1.425 35 1.43 100 1.413 20 1.42 75 1.302 10 1.30 50 A P P E N D I X I I Growth K i n e t i c s i n Cu-Se and Cu-Sb 150 1 2 3 4 5 6 (t - to)* 5 i n A r . F i g . I I - 2 Growth of Cu~Se and Cu-Se. at 170°C and 200 p s i 151 152 153 154 155 BIBLIOGRAPHY 1. S. Storchheim, J.L. 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