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Liquid metal flow in horizontal rods 1972

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LIQUID METAL FLOW IN HORIZONTAL RODS by LYLE CAMPBELL MACAULAY B.A.Sc. (Met. Eng.), Uni v e r s i t y of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1972 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f M e t a l l u r g y The U n i v e r s i t y o f B r i t i s h C olumbia V a n c o u v e r 8, Canada Date J u l Y 1 7 ' 1972 ABSTRACT Radioactive tr a c e r techniques have been developed which allow d i r e c t i n s i t u observation of the nature of f l u i d flow i n l i q u i d t i n contained i n a long shallow covered h o r i z o n t a l boat. Extensive s e r i e s of experiments have been conducted i n order to confirm the a c c e p t a b i l i t y and accuracy of the techniques employed. The findings of the i n v e s t i g a t i o n e s t a b l i s h the dependence of flow v e l o c i t y on temperature difference across the melt, average melt temperature and t o t a l melt length. The flow v e l o c i t y was observed to increase l i n e a r l y with the average temperature gradient between the hot and cold ends of the melt. An increase i n flow v e l o c i t y with increasing average melt temperature was also observed. Flow was observed to occur at very small temperature gradients. When the temperature gradient was zero at any point between the hot and cold ends of the melt, two flow c e l l s developed. Convective mass transf e r did not occur between these two c e l l s . Autoradiography of quenched specimens showed the flow pattern to be a laminar u n i c e l l u l a r l o n g i t u d i n a l flow upon which a traverse double c e l l flow i s superimposed. The r e s u l t s of the flow pattern and flow v e l o c i t y experiments are compared to a modification of Batchelor's s o l u t i o n of thermal convection i n a rectangular enclosure. In general, the agreement between the experimental r e s u l t s and the modified s o l u t i o n i s good. i i A separate i n v e s t i g a t i o n of the macrosegregation associated with casting structure c o n t r o l l e d by forced convection i s also pre- sented. ACKNOWLEDGEMENT The author g r a t e f u l l y acknowledges the advice and encourage- ment given by his research d i r e c t o r , Dr. Fred Weinberg. Thanks are also due to fellow graduate students and members of the Faculty f o r many help- f u l discussions. The assistance of the t e c h n i c a l s t a f f , throughout the experimental program, has been greatly appreciated. The f i n a n c i a l assistance provided by the National Reseach Council and an Alcan Fellowship are g r a t e f u l l y acknowledged. i v TABLE OF CONTENTS Page PART I - THERMAL CONVECTION IN HORIZONTAL RODS OF MOLTEN TIN 1 1 - INTRODUCTION 1 2 - DETERMINATION OF FLOW VELOCITIES IN HORIZONTAL RODS OF MOLTEN TIN 17 2.1. Flow Velocity Determination by Manually Monitoring the Movement of Radioactive Tracer 17 2.1.1. General Experimental Apparatus and Procedure .. .. 17 2.1.2. Tracer Introduction by Melting Back Through a Region Containing Radioactive Material 22 2.1.2.1. Experimental Apparatus and Procedure 22 2.1.2.2. Results and Discussion 25 2.1.2.3. Evaluation of Technique .. 33 2.1.3. Tracer Introduction by Rotating a Vertical Cylinder Located at the End of the Graphite Boat .. 35 2.1.3.1. Experimental Apparatus and Procedure 35 2.1.3.2. Results and Discussion 35 2.1.3.3. Evaluation of Technique 40 2.1.4. Tracer Introduction by Rotating a Vertical Cylinder Situated in the Covered Section of the Graphite Boat 42 2.1.4.1. Experimental Apparatus and Procedure 42 2.1.4.2. Results and Discuss 44 2.1.4.3. Evaluation of Technique 44 2.1.5. Tracer Introduction by Rotating a Horizontal Cylinder Located i n the Cover of the Graphite Boat 46 2.1.5.1. Experimental Apparatus and Procedure 46 2.1.5.2. Results and Discussion 46 V Page 2.1.5.3. Evaluation of Technique . 5 0 2.1.6. Tracer Introduction by Rotating a Horizontal Cylinder Located i n the Cover of the boat and then Gently Pushing Tracer i n t o the Melt 52 2.1.6.1. Experimental Apparatus and Procedure 52 2.1.6.2. Results and Discussion 56 2.1.6.2.1. Flow V e l o c i t y Measurements 56 2.1.6.2.2. Autoradiography 56 2.1.6.3. Evaluation of Technique 62 2.1.7. Return to Introduction by Rotating a V e r t i c a l Cylinder Located i n the Covered Section of the Channel 63 2.1.7.1. Experimental Apparatus and Procedure 63 2.1.7.2. Results and Discussion .. . * 68 2.1.7.2.1. V a r i a t i o n of Flow V e l o c i t y with Temperature Difference Across the Melt 68 2.1.7.2.2. E f f e c t of Varying Average Melt Temperature .. .. 68 2.1.7.2.3. E f f e c t of Varying Trace A l l o y and Melt Density .. 72 2.1.7.2.4. Evaluation of Technique 74 2.1.8. Single Aluminum Channel Supported by Graphite Reservoirs 76 2.1.8.1. Experimental Apparatus and Procedure 76 2.1.8.2. Results and Discussions 79 2.1.8.3. Evaluation of Technique 82 2.2. Flow V e l o c i t y Determination by Dual Monitoring 83 2.2.1. Experimental Apparatus and Procedure 83 2.2.2. Analysis of A c t i v i t y Versus Time Data 83 2.2.3. Results and Discussion 94 2.2.3.1. V a r i a t i o n of Flow V e l o c i t y with Temperature Difference between the Hot and Cold Ends 94 v i Page 2.2.3.2. Variation of Flow Velocity with Average Melt Temperature . 94 2.2.3.3. Variation of Flow Velocity with Total Melt Length 97 2.2.3.4. Evaluation of Technique 104 2.2.3.4.1. Effect on Flow Velocity of Varying the Nature of the Temperature Distribution 106 2.2.3.4.2. Effect of Flow Velocity of Varying the Position of the Monitoring Interval 108 2.2.3.4.3. Effect of Flow Velocity of Varying the Height of Metal in the Reservoirs I l l 2.2.3.4.4. Effect on Flow Velocity of Introducing Tracer in the Cold End of the Melt 117 2.2.3.4.5. Extent of Inductive Mixing .. 117 2.2.3.4.6. Reproducibility of Results 119 2.2.3.4.7. Summary of Technique Evaluation 120 2.3. Summary of Flow Velocity Determination Results i. .. 120 3 - FLOW PATTERNS IN HORIZONTAL RODS OF MOLTEN TIN .. .. 122 3.1. Introduction 122 3.2. Experimental Apparatus and Procedure 122 3.3. Results from Quenching Wired Top U-Channel 123 3.4. Autoradiography of Quenched Specimens Using a Completely Closed Square Aluminum Channel 124 3.4.1. Experimental Apparatus and Procedure 3.4.2. Results from Square Aluminum Channel With No Water Shield . . . . 124 v i i Page 3.4.3. Results and Discussion of Experiments Using Aluminum Channel with a Water Shield 125 3.4.4. Results and Discussion of Attempts to Confirm the V a l i d i t y of Observed Flow Patterns 144 3.4.4.1. E f f e c t of Quench Cylinder on Observed Flow "Velocity 144 3.4.4.2. Quench Time Determination 145 3.4.4.3. Quenching i n a Prearranged Tracer D i s t r i b u t i o n .. 147 3.4.4.4. Extent of Inductive Mixing 150 3.4.4.5. Determination of Transverse Temperature Gradients 154 3.5. Interaction of U n i c e l l a r Flow with a Moving S o l i d L i q u i d Interface 161 3.6. Summary .. 165 4 - ANALYSIS OF RESULTS 167 4.1. Introduction 167 4.2. Previous Investigations 175 (9) 4.2.1. Solution of Utech v J 176 4.2.2. Solution of C o l e ( 5 ) 180 (23) 4.2.3. Solution of Batchelor v 1 185 (2k) 4.2.4. Solution of Poots v 1 186 4.2.5. Solution of Stewart^ 1 7^ 186 4.3. M o d i f i c a t i o n of the Batchelor Solution 188 4.4. Comparison of The o r e t i c a l Predictions and Experimental Results 193 4.4.1. V a r i a t i o n of Flow V e l o c i t y with Average Temperature Gradient Across the Melt 193 v i i i Page 4.4.2. Variation of Flow Velocity with Total Melt Length .. 194 4.4.3. Variation of Flow Velocity with Average Melt Temperature , 194 4,5. Summary 195 5 - CONCLUSIONS 196 6 - SUGGESTIONS FOR FUTURE WORK 198 PART II - FLUID FLOW DURING SOLIDIFICATION - ITS EFFECT ON GRAIN STRUCTURE AND MACROSEGREGATION .. .. 199 1 - INTRODUCTION 199 1.1. Grain Structure 199 1.2. Macrosegregation 200 2 - MACROSEGREGATION IN CASTINGS ROTATED AND OSCILLATED DURING SOLIDIFICATION 202 2.1. Introduction 202 2.2. Experiment .. 203 2.3. Results 206 2.4. Discussion , 214 2.5. Conclusion .. 217 2.6. Appendix to Section 2 219 ix LIST OF FIGURES Figure No. Page 1 Segregation resulting from (a) complete mixing (b) no mixing and (p) partial mixing in the liquid 2 2 Convective flow pattern arising from horizontal temperature gradient .. . . . . , 5 3 Representation of the flow pattern in the hori- zontal boat.. .. . . 12 4 The apparatus employed for i n i t i a l series of ex- periments , . 18 5 The graphite boat used for i n i t i a l studies of convective flow in horizontal rods of molten tin 23 6 Results of the test to evaluate the accuracy of the collimated counting procedure ,. 26 7 (a) The temperature profiles at the inidicative times after the tracer had melted, (b) The dis- , tribution of tracer at the indicated times after melting . . .. 28 8 (a) The temperature profiles at the indicated times, (b) The distribution of tracer before and after moving the furnace 29 9 The change in activity with time at various positions along the melt 30 10. (a) The temperature profile 1/2 hour after the tracer melted. (b) The distribution of tracer before and after melting 32 11. The expected flow pattern when a zero gradient is present . . 34 12. (a) Top view of graphite boat with tracer intro- duction cylinder in place. (b) Introduction cy- linder, (c) Tracer loading block 36 (a) The temperature p r o f i l e along the melt at the time of tracer introduction, (b) The d i s - t r i b u t i o n of tracer before and 15 minutes a f t e r i n t r o d u c t i o n (a) The temperature gradients along the melt. (b) The d i s t r i b u t i o n of tracer before and a f t e r passing argon (a) The temperature p r o f i l e s before and a f t e r passing argon. (b) The d i s t r i b u t i o n of tracer at the times indicated (a) D e t a i l s of the graphite boat employed for ex- periments i n which the tracer was introduced i n the covered section of the melt, (b) Tracer i n - troduction cylinder 113 The d i s t r i b u t i o n of Sn ( i n a pure Sn melt having zero h o r i z o n t a l temperature gradient) be- fore and a f t e r (a) tracer introduction and (b) melting with the introduction c y l i n d e r i n the open p o s i t i o n s . D e t a i l s of tracer introduction from the boat covers (a) The temperature p r o f i l e along the melt, (b) The d i s t r i b u t i o n of Tl204 before and a f t e r tracer introduction (a) The temperature p r o f i l e along the melt, (b) The d i s t r i b u t i o n of AgH^ before and a f t e r tracer i n - troduction D e t a i l s of mechanism used to f a c i l i t a t e tracer i n - troduction from the boat cover. (a) Top view-(b) Side section view. T y p i c a l a c t i v i t y versus time data for experiments employing forced tracer i n t r o d u c t i o n from the boat cover. The dependence of flow v e l o c i t y on the temperature differ e n c e between the hot and the cold ends of the melt. Longitudinal section autoradiographs of specimens quenched (a) 0.5 minutes (b) 1 minute and (c) 10 minutes a f t e r tracer i n t r o d u c t i o n i n t o a melt having zero h o r i z o n t a l temperature gradient (a) P o s i t i o n from which autoradiographs were ob- tained, (b) Transverse section autoradiographs (from p o s i t i o n s indicated i n (a)) of a specimen quenched 1 minute a f t e r tracer introduction i n t o a melt having zero h o r i z o n t a l temperature grad- ient Transverse section autoradiographs (from the p o s i - tions indicated) of a specimen quenched 1 minute a f t e r introduction of tracer into a melt having a 70 °C temperature diffe r e n c e between the hot and cold ends. . (a) Tube furnace wiring diagram (b) D e t a i l s of furnace temperature c o n t r o l l e r . T y p i c a l a c t i v i t y versus time data for experi- ments employing tracer i n t r o d u c t i o n by r o t a t i n g a v e r t i c a l c y l i n d e r located i n the covered section of the melts. The dependence of flow v e l o c i t y on the temperature differ e n c e between the hot and the cold ends of the melt. The e f f e c t on the flow v e l o c i t y of varying the average melt temperature The e f f e c t on the flow v e l o c i t y of having i d e n t i c a l tracer a l l o y and melt d e n s i t i e s . The e f f e c t on the flow v e l o c i t y of varying the density d i f f e r e n c e between the trace a l l o y and the melt. Comparison of the flow v e l o c i t y measurements obtained employing the rotated v e r t i c a l c y l i n d e r and p i s t o n mechanism introduction techniques. D e t a i l s of the graphite and supported s i n g l e aluminum channel boat Comparison of the flow v e l o c i t y measurements obtained employing the two channel graphite boat (Figure 29) and the s i n g l e aluminum channel boat Sectional view of the double s l i t collimator with two s c i n t i l l a t i o n counters F i e l d of view of 35 mm camera employed to c o l l e c t a c t i v i t y versus time data, (b) A section of the 35 mm f i l m showing some t y p i c a l data x i i Figure No. Page 38 The counting characteristics of the double s l i t collimator-scintillation counter arrangement. .. 87 39 F u l l size schematic diagram showing the length of melt subtended by the s c i n t i l l a t i o n detector. .. 88 40 The response of the dual simultaneous counting to a constant activity source travelling at a known velocity. 91 •41 Typical activity versus time data obtained by the simultaneous dual monitoring. 93 42 The dependence of flow velocity on the temperature difference between the hot and the cold ends of the melt. 95 43 The effect on flow velocity of varying the average melt temperature (with a constant temperature difference across the melt of 214°C). 98 44 The dependence of flow velocity for three d i f f e r - ent melt lengths , on temperature difference across the melt 100 45 The dependence of flow velocity for three different melt lengths, on the temperature gradient between the hot and cold ends of the melt 102 46 The dependence of flow velocity on the temperature gradient across the melt with an average melt tempera- tur of 400 °C 103 47 Comparison of the velocity versus temperature gradi- ent results obtained using the two channel graphite boat and the single aluminum channel boat. Average melt temperature was approximately 310 °C 105 48 Temperature profiles from two experiments designed to show that the temperature gradient across the melt, and not the gradient across the monitoring interval, is the driving force for the observed velocity. .. 107 49 Temperature profile from an experiment undertaken to determine the effect on flow velocity of changing the position of the monitoring interval 109 50 Comparison of the results of Figures 48 and 49 with results of Figure 46. HO 51 The effect on flow velocity of varying the liquid metal height in the reservoirs and of introducing the tracer near the cold end. H2 x l i i Figure No. Page 52(a) A c t i v i t y versus time r e s u l t s when there was a 3 mm head of l i q u i d t i n i n the hot r e s e r v o i r .. .. 114 52(b) A c t i v i t y versus time r e s u l t s when there was no differen c e i n the l i q u i d t i n l e v e l i n the hot and cold r e s e r v o i r s 115 52(c) A c t i v i t y v e r s i s time r e s u l t s when there was a 3 mm head of l i q u i d t i n i n the cold r e s e r v o i r .. 116 53 Results of the i n v e s t i g a t i o n of the extent of induct- t i v e mixing 118 54 Schematic representation showing the p o s i t i o n at which the specimen was sectioned to obtained trans- verse section autoradiographs .. 126 55 Longitudinal section autoradiographs of specimens quenched (a) 40 sec and (b) 1 minute a f t e r i n t r o - duction of trace a l l o y (0.85% Sb i n pure Sn contain- ing 3.5% Sn-'--'-3). Surface autoradiograph was 0.04 inches below outside surface (X2) 127 56 Transverse section autoradiographs of a specimen quenched 40 seconds a f t e r introduction of Snll3_ Sb-Sn tracer. Sections are at 1 cm i n t e r v a l s with the s t a r t (top l e f t hand corner) 4 cm from point of introduction near the hot end (X4) 129 57 Comparison of transverse section autoradiographs from specimens quenched 40 seconds ( f i r s t , t h i r d and f i f t h rows) and 1 minute (second, fourth and s i x t h rows) a f t e r introduction 131-132 58 Comparison of transverse s e c t i o n autoradiographs from specimens quenched 1 minute ( f i r s t , t h i r d and f i f t h rows) and 2 minutes (second, fourth and s i x t h rows) a f t e r introduction 133-134 59 Transverse section autoradiographs of a specimen quenched 1 minute a f t e r introduction of a trace a l l o y containing 0.85% Sb i n S n 1 1 3 3.5% (0.994 pSn). .. 136 60 Transverse section autoradiographs of a specimen quenched 1 minute a f t e r i n t r o d u c t i o n of a trace a l l o y containing 3.5% S n 1 1 3 i n Sn (1.0000 pSn) .. 137 61 Transverse section autoradiographs of a specimen quenched 1 minute a f t e r introduction of a trace a l l o y containing 0.5% T I 2 0 4 i n Sn (1.0020 pSn). •• •• 138 xiv Figure No. Page 62 The expected appearance of a transverse section autoradiograph i f only unicellular longitudinal flow were present (X12) 140 63 Transverse section autoradiographs of a specimen quenched 1 minute after introduction of a trace alloy containing 0.5% T I 2 0 4 in Sn. The f i r s t section (top l e f t hand corner) is 4 cm from the point of introduction near the cold end. 142 64 Transverse section autoradiographs of a specimen quench 1 minute after introduction of a trace alloy composed of 60% Pb in Sn contained 0.5% T I 2 0 4 . Intro- duction took place near the cold end 143 65 Typical results of quench time determination experiments 146 66 Schematic representation of the prearranged tracer distribution (a) transverse section and (b) longi- tudinal section 148 67 Transverse section autoradiographs of the specimen which had the prearranged tracer distribution fhown in Figure 66. 151 68 Comparison of transverse section autoradiographs of specimens quenched 1 minute after introduction of 3.5% SnJ-L-) in Sn tracer into the melt, while the furnace power was on ( f i r s t , third and f i f t h rows) and 2 minutes after the furnace power had been turned off (second, fourth and sixth rows) 152-153 69 Schematic representation of apparatus used to measure transverse temperature gradients (X2) 155 70 The numbering systems for locating positions on the temperature tranverse 157 71 The relation between the horizontal and v e r t i c a l temper- ature gradients for an uncovered tin melt of depth 0.94 cm (after Utech). .. 159 72 Transverse section autoradiograph of a directionally s o l i d i f i e d tin melt containing 500 ppm T I 2 0 4 (X20). 162 73 Transverse section autoradiographs of a directionally s o l i d i f i e d tin melt contain 100 ppm T I 2 0 4 (X6).. 163 XV Figure No. Page 74 (a) Schematic representation of the double s p i r a l flow observed during forced convection through a tube.(b) Expected appearance of transverse s e c t i o n autoradiographs i f double s p i r a l flow were present 168 75 The s i m p l i f i e d flow system i n the long shallow rectangular enclosure . . . . 174 76 Comparison of the r e s u l t s of the present i n v e s t i g a - t i o n with the p r e d i c t i o n of the s o l u t i o n of Utech .. 179 77 The v a r i a t i o n of l o n g i t u d i n a l flow v e l o c i t y with v e r t i c a l p o s i t i o n i n the melt 191 78 The experimental apparatus used f o r producing the stationary, rotated, and o s c i l l a t e d castings .. .. 204 79 Representative ingots cast i n (a) stationary, (b) r o t a t i n g , and (c) o s c i l l a t i n g moulds .. .. 207 80 Equiaxed grains i n the cen t r a l region of the o s c i l l a t e d casting 208 81 . Representative ingots cast i n (a) sta t i o n a r y , (b) r o t a t i n g , and (c) o s c i l l a t i n g moulds. .. .. 208-209 82 The r a d i a l s i l v e r d i s t r i b u t i o n i n a stationary casting: (a) 1/4 inch d r i l l holes i n 1/4 inch steps, (b) 1/4 inch d r i l l holes i n 1/8 inch steps, (c) 0.030 inch lathe turnings, and (d) 0.050 inch lathe turnings dissolved i n acid 211 83 The r a d i a l s i l v e r d i s t r i b u t i o n i n (a) stationary (b) rotated, and (c) o s c i l l a t e d ingots using method (b) of Figure 82. 213 84 An autoradiograph of the cross s e c t i o n of the o s c i l l a t e d ingot showing the s i l v e r d i s t r i b u t i o n i n the casting 215 85 The development of the r a d i a l macrosegregation in an o s c i l l a t e d ingot, (a) p r i o r to the time of the CET, (b) at the time of the CET, and (c) the f i n a l s i l v e r d i s t r i b u t i o n i n the casting. .. .. 218 xv i LIST OF TABLES Table No. Page 1 Properties of Radioisotopes 21 2 Flow V e l o c i t y Results 69 3 Flow V e l o c i t y Results 80 4 Results of Dual Collimator S e n s i t i v i t y Test .. 90 5 Flow V e l o c i t y Results 96 6 Properties of Molten T i n 99 7 Flow V e l o c i t y Results f o r Three Melt Lengths .. 101 PART I - THERMAL CONVECTION IN HORIZONTAL RODS OF MOLTEN TIN 1 - INTRODUCTION During the s o l i d i f i c a t i o n of metals, solute r e d i s t r i b u t i o n can lead to macro and micro segregation which i n turn can markedly i n - fluence the mechanical properties of the r e s u l t i n g s o l i d metal. In s o l i d i f i c a t i o n of binary a l l o y s the extent of mixing i n the l i q u i d metal greatly influences the solute r e d i s t r i b u t i o n . The two l i m i t i n g cases are: (1) Complete mixing i n the l i q u i d during s o l i d i f i c a t i o n which r e s u l t s i n a solute d i s t r i b u t i o n given by^"^: C s = k o C o ( 1 - f ) k ° 1 (2) No mixing i n the l i q u i d , that i s , solute transport i n the l i q u i d i s by d i f f u s i o n only. The r e s u l t i n g solute d i s t r i - bution i n the i n i t i a l l y s o l i d i f i e d p ortion of the melt i s . (2) given by k Rx C = C {(1 - k )[1 - exp (- — )] + k } (1.2) s o O p o where: C q i s the average composition of the s t a r t i n g l i q u i d C g i s the composition of the r e s u l t i n g s o l i d CT i s the composition of the l i q u i d i n equilibrium J_i with s o l i d of composition C g k^ - C g / C L = equilibrium d i s t r i b u t i o n c o e f f i c i e n t . 2 f i s the f r a c t i o n s o l i d i f i e d R i s the freezing rate D i s the d i f f u s i o n c o e f f i c i e n t f o r solute i n the l i q u i d ' x i s the distance from the s t a r t of u n i d i r e c t i o n a l s o l i d i - f i c a t i o n . In a r r i v i n g at Equations (1.1) and (1.2) i t was assumed that the s o l i d - l i q u i d i n t e r f a c e remained planar, that no solute d i f f u s i o n occurred i n the s o l i d and that equilibrium conditions existed at the i n t e r f a c e during s o l i d i f i c a t i o n . Figure 1 i l l u s t r a t e s the solute r e d i s t r i - bution that a r i s e s as a r e s u l t of varying the extent of mixing i n the l i q u i d . Figure 1. Segregation r e s u l t i n g from (a) complete mixing, (b) no mixing and (c) p a r t i a l mixing i n the l i q u i d . From Figure 1 i t i s apparent that complete mixing i n the l i q u i d , curve (a), causes long range compositional v a r i a t i o n s (macrosegregation) whereas no mixing, (b), y i e l d s a uniform solute d i s t r i b u t i o n (except for the i n i t i a l and terminal t r a n s i e n t s ) . The intermediate case of (2) p a r t i a l mixing, ( c ) , can be represented by : k -1 C S = k e C q (1 - f ) ° (1.3) where k , the e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t , i s defined to be e (2) C /C and i s given by s o J k o 4- (1 - k Q ) exp (- f ) where 6 i s the thickness of the d i f f u s i o n boundary layer which e x i s t s at the i n t e r f a c e . The magnitude of k £ (assuming k Q < 1) ranges from a minimum of k Q for complete mixing to a maximum of 1 for no mixing i n the l i q u i d . I t i s apparent from Equation (1.4) that an increase i n 6 r e s u l t s i n an increase i n k g. The boundary la y e r thickness i s l a r g e l y dependent on the extent of l i q u i d mixing. Maximum values of 6 occur when no mix- ing i s present and minimum values a r i s e under conditions of extensive mixing. Thus, control of mixing i n a s o l i d i f y i n g l i q u i d can a f f o r d control over the solute r e d i s t r i b u t i o n i n the s o l i d i f i e d product. Mixing i n the l i q u i d may a r i s e from one or more of several sources. F l u i d flow may r e s u l t from natural convection. This i s examined i n Part I of t h i s t h e s i s . Flow may also r e s u l t from forced convection. Part II considers the solute segregation which occurs as a r e s u l t of c o n t r o l l i n g ingot grain structure by forced convection. 4 Natural convection occurring during s o l i d i f i c a t i o n can be divided into two main categories, solute convection and thermal convection. Solute convection may occur when concentration d i f f e r e n c e s , a r i s i n g from solute r e j e c t i o n at a s o l i d - l i q u i d i n t e r f a c e , cause the appearance of (3) density gradients i n the l i q u i d metal. Wagner has studied the i n t e r a c t i o n of solute convection with the d i f f u s i o n boundary layer and has developed equations to describe the r e s u l t i n g solute r e d i s t r i b u t i o n . An evaluation of the e f f e c t of mixing i n the l i q u i d on solute d i s t r i b u t i o n along u n i d i r e c t i o n a l l y s o l i d i f i e d h o r i z o n t a l rods of d i l u t e (4) s i l v e r i n t i n a l l o y s has been made by Weinberg • . He varied the f l u i d flow i n a q u a l i t a t i v e way by varying the diameter of the rods being s o l i d i f i e d . Weinberg found that, based on the d i s t r i b u t i o n of s i l v e r i n the s o l i d i f i e d rods, extensive mixing occurred i n the l i q u i d during s o l i d i f i c a t i o n of a l l rods of diameter greater than 2mm. Suggested causes for t h i s mixing were (a) thermal convection (b) convective currents set up by volume changes during f r e e z i n g , and (c) solute con- vection. Evidence was presented that causes (b) and (c) were not p r i - marily responsible for solute mixing. This conclusion led to several extensive studies on thermal convection i n h o r i z o n t a l melts. Thermal convection w i l l occur when the melt i s subjected to a h o r i z o n t a l temperature gradient. The explanation of t h i s phenomenon i s quite simple. Because the density of most l i q u i d metals decreases with increasing temperature, the h o r i z o n t a l temperature gradient re- s u l t s i n a h o r i z o n t a l density gradient. .The system i s unstable and the l i q u i d can be expected to flow i n a fashion s i m i l a r to that shown i n Figure 2. 5 O o o X Liquid Solid Figure 2. Convective flow pattern a r i s i n g from h o r i z o n t a l temperature gradient. During in v e s t i g a t i o n s to determine s o l i d i f i c a t i o n conditions necessary to eliminate macrosegregation and i n t e r c e l l u l a r segregation, these features was the temperature gradient i n the l i q u i d G^. Con- sequently, i n early experiments, s e n s i t i v e thermocouples were placed i n d i r e c t contact with the l i q u i d i n order to measure G^. I t was found that the temperature i n the l i q u i d fluctuated i n a random manner. Kramer , Cole found that the presence of the s o l i d - l i q u i d i n t e r f a c e had no bearing on the appearance of the f l u c t u a t i o n s . Thus, experiments were designed to study the character of temperature f l u c t u a t i o n s i n a completely l i q u i d system. From these experiments Cole concluded that temperature flu c t u a t i o n s occurred when the l o n g i t u d i n a l temperature gradient G L exceeded a c r i t i c a l value G . The amplitude and frequency of temperature Cole (5) found that one of the most important parameters i n c o n t r o l l i n g 6 flu c t u a t i o n s were found to decrease (a) as decreased, (b) as the angle of heating was decreased from the h o r i z o n t a l (with the cold end of the l i q u i d being the lowest point of the system) and (c) as the height of the l i q u i d i n the system decreased. I t was also found that 3 c the r e l a t i o n s h i p - (Height of Melt) G^ = constant described the con- d i t i o n s necessary f o r the onset of temperature f l u c t u a t i o n s . The greater the melt height, the greater the i n s t a b i l i t y of the systems with respect to thermal convection. Cole further concluded that the presence of temperature fl u c t u a t i o n s r e s u l t e d from the existence of na t u r a l thermal convection i n the l i q u i d metal and therefore n a t u r a l thermal convection could be detected by s e n s i t i v e thermocouples placed i n the l i q u i d . I t was suggested that convection could be eliminated by s u i t a b l y c o n t r o l l i n g the temperature d i s t r i b u t i o n i n the l i q u i d . Subsequent experiments by Cole investigated f l u i d flow during s o l i d i f i c a t i o n . As a r e s u l t of the i n t e r a c t i o n of thermal con- vective flow with the s o l i d - l i q u i d i n t e r f a c e a "thermal boundary l a y e r " was found to e x i s t . This was described by the parameter 6 ^ . Pro- ceeding away from the i n t e r f a c e , the flow i s f i r s t laminar, a buffer or t r a n s i t i o n region follows and for distances away from the i n t e r f a c e greater than 6 ^ the flow i s e s s e n t i a l l y turbulent. The thickness of the thermal boundary lay e r , as a function of the f l u i d properties of the l i q u i d metal and the growth v a r i a b l e s , was found to be given by the . (5) expression : 7 6, - H 1' 5 203a 2 R 6 T • ^ a - (1 + 1.58 Pr ) . 203R 2L 2 . 406RLa , , R 6 T . ' 1 / 5 T ~ ~ + 77 ( 1 " ) c J g g ( G ° ) 3 C p g B ( G ° ) 2 2 a where: L i s l a t e n t heat of fusion g i s the ac c e l e r a t i o n due to g r a v i t y g i s the c o e f f i c i e n t of volume expansion a i s the thermal d i f f u s i v i t y Pr i s the Prandtl number H i s the height of the s o l i d - l i q u i d i n t e r f a c e G° i s the temperature gradient at the i n t e r f a c e C i s the s p e c i f i c heat P (1.5) R i s the growth rate Using t h i s experession 6^, was ca l c u l a t e d f o r the experimental conditions employed (0.001 < R cm/sec. < 0.005, 10 < G° °C/cm < 20) giving values of the order of 1 cm. These values were i n good agreement with the experimentally observed boundary layer thicknesses. In order to estimate the e f f e c t of thermal convection on macrosegregation a theory was developed which accounted f o r the i n t e r - action of convection with the solute boundary layer 6 g which e x i s t s at the s o l i d - l i q u i d i n t e r f a c e of a s o l i d i f y i n g a l l o y . The r e l a t i o n s h i p formulated to determine the magnitude of <5g was: 806^ (R5 - 2D) 6 5 - 4 6 T 6 4 + 56;<SJ + ± § -r- (1.6) T S T S 53.3 H [a + R (_L_ _ «1 )] C GT° 2 p L 8 where 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 solute i n l i q u i d solvent. To obtain the solute d i s t r i b u t i o n s during h o r i z o n t a l s o l i d i - f i c a t i o n the following procedure was u t i l i z e d : (1) Substitute appropriate values of f l u i d flow para- meters and G° and R into Equation (1.5) and thus c a l c u l a t e 6^,. (2) Substitute t h i s value of 6^ into Equation (1.6) and solve for 6 . s (3) Substitute this value of 6 into the equation: s k e = (1 - k ) 6 R ( 1 * 7 ) ^ _ o s 2D and obtain the value of k . When the growth parameters are such that the value of k e = l , a s o l i d i f i e d product which has uniform composition over most of i t s length (Figure 1,, curve b) should be obtained (providing c o n s t i t u t i o n a l super- cooling does not occur and cause the planar to c e l l u l a r i n t e r f a c e trans- i t i o n ) . Cole also obtained an expression f o r c a l c u l a t i n g the maximum v e l o c i t y of f l u i d flow p a r a l l e l to the i n t e r f a c e : u 53.3 H m .2 6 T L 6T a + R ( -±- - -1 ) C GT° 2 p L (1.8) from (1.8) and (1.5) I t would be expected that U increases as the m height of the melt increases and as the temperature gradient G° increases, Equation (1.8) shows that u should increase with increasing H. This i s m consistent with the f i n d i n g that the c r i t i c a l h o r i z o n t a l gradient G° necessary for the onset of temperature f l u c t u a t i o n s decreases as H i n - creases. That i s , increasing the melt height decreases the s t a b i l i t y of the melt with respect to convective flow. For a stationary system (R = 0) the expression for u m be- comes : 3/5 u = 53.3 a H ' m 1 2 / 5 203a 2 (1 + 1.58 Pr) (1.9) or, f o r a given melt height and average melt temperature: u a (G ) m L C l e a r l y then, for any non-zero h o r i z o n t a l temperature gradient one would expect convective flow, that i s , u^ ^ 0. This indicates that the de- t e c t i o n of temperature fl u c t u a t i o n s at some c r i t i c a l gradient G^ > 0 does not i n d i c a t e the onset of f l u i d flow. The Cole technique then i s c not s u f f i c i e n t l y s e n s i t i v e to detect f l u i d flow at G^ < G^. No attempt was made to measure flow v e l o c i t i e s and thus v a l i d a t e the expression f o r m ( 8) Muller and Wiehelm have also demonstrated the existence of temperature f l u c t u a t i o n s i n the melt during the growth of metal and semi- conductor c r y s t a l s by the h o r i z o n t a l normal freeze, and zone melting techniques. C o r r e l a t i o n of the p e r i o d i c v a r i a t i o n i n temperature with the spacing of concentration s t r i a e i n c r y s t a l s of InSb was established. Experiments showed that f or melts between 10 and 30 cm long the amplitude and frequency of the observed temperature f l u c t u a t i o n s were independent of the melt length provided that the temperature and temper- ature gradient were kept constant at the measuring point. The f i r s t d i r e c t measurements of flow v e l o c i t i e s i n l i q u i d (9) metals contained i n h o r i z o n t a l boats were c a r r i e d out by Utech . In studies of thermal convection i n molten t i n the observation was made that a sequence of temperature f l u c t u a t i o n s recorded by a thermocouple inserted into the melt was repeated a short time l a t e r by a second thermocouple located down stream. By measuring the time required f o r the temperature f l u c t u a t i o n to t r a v e l a known distance downstream, an i n d i c a t i o n of mean flow v e l o c i t y could be obtained. Utech found ( i n agreement with Cole) that a c r i t i c a l h o r i z o n t a l temperature gradient was necessary to produce temperature f l u c t u a t i o n s . Evidence that flow Q occurred at gradients below G was obtained by observing that as the hor i z o n t a l temperature gradient increased from zero a corresponding increase i n v e r t i c a l temperature gradient (hot l i q u i d above cold) appeared. Suppression of convective flow by a magnetic f i e l d and the resultant disappearance of the v e r t i c a l gradient showed conclusively that the v e r t i c a l temperature gradient was a d i r e c t consequence of con- v e c t i v e flow. The r e s u l t s of the i n v e s t i g a t i o n of Utech f o r convective flow i n a h o r i z o n t a l boat with an open top can be summarized as follows. At small h o r i z o n t a l temperature gradients c i r c u l a t i o n of l i q u i d begins, causing a v e r t i c a l temperature gradient to appear. This convective flow may be considered laminar i n as much as the temperature at any point i n 11 the system remains constant, once steady state conditions have been attained. The flow pattern under these conditions could not be deter- mined d i r e c t l y . Utech i n f e r r e d the pattern would be s i m i l a r to that observed i n low v i s c o s i t y o i l , that i s , a narrow stream along the bottom flowing from the cold end to the hot end of the boat, a r i s i n g column of l i q u i d at the hot end of the boat with the hot l i q u i d which had been ca r r i e d to the top f a l l i n g more or less uniformly along the e n t i r e length, Figure 2. As the h o r i z o n t a l gradient i s increased, t h i s uniform flow breaks down and a number of c e l l s of c i r c u l a t i n g l i q u i d appear along the length of the boat. Their presence i s manifested by the f l u c t u a t i o n s i n temperature as measured by a thermocouple located at any point i n the system. The r e s u l t i n g "turbulence" becomes in c r e a s i n g l y severe as the temperature gradient i s increased. When the l i q u i d t i n i s approximately 1 cm deep and the gradient i n the l i q u i d i s about 12°C/cm, mean ve l o - c i t i e s i n the l i q u i d of the order of 1 cm/second are observed. The flow v e l o c i t i e s measured by Utech are approximately an order of magni- tude l e s s than would be predicted by the Cole a n a l y s i s . Utech employed the boundary layer analysis of Eckert and Drake f or flow past a v e r t i c a l p l ate with surface temperature T , immersed i n a f l u i d at uniform temperature T , to obtain the expression for maximum flow v e l o c i t y : u = 0.766V (0.952 + Pr) ( ̂  ^ < 1- 1 1> m 2 12 where: v i s the kinematic v i s c o s i t y x i s the v e r t i c a l distance from the leading end of the v e r t i c a l w a l l T i s the temperature d i f f e r e n c e across the boundary layer. According to Utech (although i t i s not evident from an (9) examination of h i s r e s u l t s ) Equation (1.11) agrees reasonably w e l l with h i s v e l o c i t y measurements. A NaCl melt (transparent) was used i n order to v e r i f y t h i s v e l o c i t y determination technique and to d i r e c t l y observe the flow pattern associated with a h o r i z o n t a l temperature gradient across a melt The flow pattern observed i n NaCl appears i n Figure 3. Superimposed on the generally steady flow along the bottom and top of the boat i s a pattern of c e l l s that r e s u l t i n upward and downward v e r t i c a l currents along the e n t i r e length of the boat. Figure 3. Representation of the flow pattern i n the h o r i z o n t a l boat. 13 This pattern of c e l l s changed with time. Only at the cold and hot ends was the v e r t i c a l flow always i n the same d i r e c t i o n . Since the Prandtl number (a dimensionless parameter c l a s s i f y i n g the convective behaviour of f l u i d s ) of molten NaCl (Pr = 0.13) approaches those of l i q u i d metals ( t y p i c a l l y 0.1 - 0.01) i t was assumed that flow patterns i n l i q u i d metals would resemble those observed i n molten NaCl. The fa c t that l i q u i d NaCl i s transparent suggests that heat transf e r by r a d i a t i o n i s appreciable and therefore the convective heat transf e r for NaCl and a l i q u i d metal, constrained by the same thermal en- vironment, would be appreciably d i f f e r e n t . If the heat t r a n s f e r modes were d i s s i m i l a r the flow patterns would also be d i s s i m i l a r . (12) Observations by Hurle that the mode of temperature flu c t u a t i o n s could be changed by quite small movements of the thermo- couple or by i n s e r t i n g a 50 u diameter wire v e r t i c a l l y into the melt c l e a r l y indicated that the presence of any obstruction i n the melt, including the thermocouple, had a profound e f f e c t on the temperature o s c i l l a t i o n s . This observation suggested that the temperature f l u c t u - ations reported e a r l i e r (5,6,7,8,9) were probably not c h a r a c t e r i s t i c of the melts themselves. I t was subsequently found that, provided the thermocouples were inserted to a depth of. less than 0.04 cm, o s c i l l a t i o n s could s t i l l be recorded and these o s c i l l a t i o n s were not aff e c t e d by moving the thermocouples. Hurle also observed that above a c r i t i c a l h o r i - zontal temperature gradient temperature o s c i l l a t i o n s appeared. This c r i t i c a l gradient was found to increase with decreasing melt length. (At a boat length of 4 cm i t was 5.0 °C/cm and at 2.6 cm i t was 7.5 °C/cm). 14 Davis and Fryzuk studied thermal convective mixing i n h o r i z o n t a l melts with known i n i t i a l solute d i s t r i b u t i o n s . Results showed that observable convective mixing ( i n rods 2 mm i n diameter) occurs at h o r i z o n t a l temperature gradients greater than 5°C/cm and that extensive solute r e d i s t r i b u t i o n occurs for temperature gradients 15°C/cm or (5) 3 c greater. Cole and Winegard's formulation , H G = 3.1, predicts that temperature f l u c t u a t i o n s ( i n d i c a t i v e of the onset of turbulent thermal convection) would not appear u n t i l a temperature gradient of approximately 400°C/cm was attained. Obviously then, the occurrence of temperature f l u c t u a t i o n s i n the melt i s not s u f f i c i e n t l y s e n s i t i v e to detect the presence of extensive thermal convection. (14) Carruthers and Winegard employed yet another technique for determining the extent of convectivemixing i n h o r i z o n t a l melts. In the i r experiments a s o l i d h o r i z o n t a l rod of pure lead was melted by moving a tube furnace along the rod. The l i q u i d i n contact with the s o l i d lead contained approximately 10% thallium. A f t e r steady state melting had been achieved over 5 to 10 cm, the l i q u i d was s o l i d i f i e d by removing the furnace. Since the d i s t r i b u t i o n c o e f f i c i e n t of thallium i n lead i s close to unity, very l i t t l e solute r e d i s t r i b u t i o n occurred during freezing. Concentration p r o f i l e s r e s u l t i n g from boundary layer flow at the i n t e r f a c e were revealed by a s u i t a b l e etching technique. The v a r i - ation of boundary la y e r thickness and shape was then taken as a measure of the extent of convective flow. The following conclusions were ob- tained: (1) Convective mixing increases with increasing h o r i z o n t a l temperature gradient and also with increasing r a d i a l heat transfer. 15 (2) Increasing the length of the melt promotes more v i g o r - ous thermal convection. (3) The l i q u i d height exerts very l i t t l e e f f e c t on e i t h e r the extent or the configuration of mixing due to thermal convection. (4) The e f f e c t of introducing thermocouples i n t o the melt i s to cause increased convective mixing. Another important conclusion of the work of Carruthers i s that the onset of temperature o s c i l l a t i o n s seen by Cole corresponds to a flow t r a n s i t i o n from laminar boundary la y e r to turbulent boundary layer flow. Thus, i t i s again apparent that appreciable f l u i d flow may be present at gradients w e l l below those necessary f o r the onset of temperature f l u c t u a t i o n s . Of the techniques described above not one i s capable of measuring flow v e l o c i t i e s i n melts subjected to h o r i z o n t a l temperature gradients below GT , the gradient associated with the onset of temperature f l u c t u a t i o n . Nor i s i t possible to accept the flow patterns observed i n nonmetallic m e l t s ^ a s being t y p i c a l of the convective flow patterns which occur i n l i q u i d metals. However, any theory attempting to p r e d i c t the solute d i s t r i b u t i o n i n a s o l i d i f i e d metal requires i n - formation concerning the extent of f l u i d flow i n the l i q u i d metal during s o l i d i f i c a t i o n . In the absence of such information i t becomes necessary to make assumptions about the f l u i d flow present i n the melt. Accordingly, the present i n v e s t i g a t i o n was undertaken to obtain d i r e c t i n s i t u measurements of f l u i d flow v e l o c i t i e s and to ob- serve f l u i d flow patterns i n l i q u i d metals. This was accomplished by (16) the use of radioactive t r a c e r s . Stewart and Weinberg have em- ployed radioactive tracer techniques to observe flow v e l o c i t i e s and flow patterns i n t h i n c e l l s with length to height r a t i o of approximately 1. However, f o r the purpose of the present i n v e s t i g a t i o n a h o r i z o n t a l rod configuration (length to height r a t i o s between 40 and 70) was selected since t h i s i s the geometry adopted i n most fundamental examinations of solute segregation during s o l i d i f i c a t i o n . Also the boat used to con- t a i n the melt was provided with a cover to reduce asymmetric heat losses from the system and to simulate conditions required f o r growth of cry- s t a l s of a s p e c i f i e d s i z e . Although t h i s geometry provides a simple configuration for s o l i d i f i c a t i o n studies i t presents a complex and as yet unsolved problem from the thermal convection and f l u i d dynamics points of view. 2 - DETERMINATION OF FLOW VELOCITIES IN HORIZONTAL RODS OF MOLTEN TIN 2.1. Flow V e l o c i t y Determination by Manually Monitoring the Movement of Radioactive Tracer As outlined i n the intr o d u c t i o n , one of the purposes of the present i n v e s t i g a t i o n was to develop a technique that would permit d i r e c t measurement of flow v e l o c i t i e s i n h o r i z o n t a l rods of molten metal. I t was considered e s s e n t i a l that the measurement technique employed should not perturb the l i q u i d metal system. S p e c i f i c a l l y , the v e l o c i t y ob- served should be due only to the f l u i d properties of the system and the experimentally imposed conditions. I t was decided that a method i n - volving the external monitoring of radi o a c t i v e tracer as i t flowed along with the melt would best s a t i s f y the condition of not i n t e r f e r i n g with the f l u i d flow that would normally occur. The development of such a technique i s presented below. 2.1.1. General Experimental Apparatus and Procedure The apparatus employed for the f i r s t s e r i e s of experiments i s shown i n Figure 4. The molten metal (pure t i n ) was contained i n a graphite boat which was equipped with a device f o r introducing the radi o - active tracer. The boat was inserted into a 45 mm O.D. Vycor tube surrounded by an 18 inch long tube furnace. The furnace was constructed i n the following way. An 18 inch length of 2 inch diameter copper tube was Tube Furnace =1 , — -n=f 1 Graphite Boat I F=r— ^-Thermocouple to o leads ^ inch L e a d Collimator Scintillation Counter Figure 4 . The apparatus employed for i n i t i a l s e r i e s of experiments. wrapped with a layer of 1/16 inch t h i c k asbestos c l o t h . Four re- sistance windings (26 gauge nichrome) each 4 inches long, separated by 1/2 inch, and having separate power terminals were wound on to the asbestos. The resistance of each winding was approximately 120 ohms. Each winding was coated with S a i r s e t r e f r a c t o r y cement. The wound tube was surrounded by glass wool and placed i n an aluminum container. The container was mounted on a set of wheels so that the e n t i r e furnace assembly could be moved. This f a c i l i t a t e d changing the thermal en- vironment of the melt without p h y s i c a l l y disturbing the melt i t s e l f . The inner two windings were connected i n s e r i e s to a 0 to 130 v o l t , 10 ampere, v a r i a c . The outer windings were s i m i l a r l y connected to a second v a r i a c . The Vycor tube and tube furnace were supported by a Handy Angle framework. A s c i n t i l a t i o n counter surrounded by a lead c o l l i m a t o r (constructed from lead b r i c k s ) and mounted on a moveable carriage was located below the graphite boat, Vycor tube and furnace assembly. A loc a t i n g device was attached to the side of the carriage r a i l to allow f i x i n g the p o s i t i o n of the s c i n t i l a t i o n counter-lead co l l i m a t o r assembly at any desired p o s i t i o n . The a r r i v a l of r a d i o a c t i v e trace isotope above a given collimator s l i t p o s i t i o n would be detected by a rapid increase i n the a c t i v i t y reaching the s c i n t i l l a t i o n counter through the collimator s l i t . The v e l o c i t y of f l u i d flow i n the melt above could then be measured by determining the time d i f f e r e n c e for the movement of r a d i o a c t i v e tracer from one p o s i t i o n to a p o s i t i o n a known distance away. The a c t i v i t y passing through the collimator was measured with a Quantum E l e c t r o n i c s Q-6A, video s c a l a r using a sodium iodide s c i n t i l l a t i o n counter. To e s t a b l i s h the optimum operating voltage for the counter, a r a d i o a c t i v e source was placed above the counter and the a c t i v i t y was measured as a function of applied voltage, i n 25 v o l t steps. The optimum operating voltage was taken as the voltage i n the center of the plateau obtained on the a c t i v i t y versus applied voltage curve. Radioactive trace isotopes used during the course of t h i s i n v e s t i g a t i o n were Aĝ "*"̂ , Sn^^ and T l 2 ^ 4 . Table 1 l i s t s the pertinent properties of these isotopes. Non-radioactive Ag, Sn, Sb and TI of 59's or better q u a l i t y was sent to e i t h e r A.E.C.L. at Chalk River, Canada,or to Radioactive Materials Corporation, B u f f a l o , New York, for i r r a d i a t i o n . Trace a l l o y s of varying composition were prepared from the r e s u l t i n g isotopes. The a l l o y was melted i n a resistance wound v e r t i c a l tube furnace and mixed frequently (by vigorous shaking) for at l e a s t 15 minutes to insure homogeneous d i s p e r s a l of the r a d i o a c t i v e isotope throughout the trace a l l o y . The a l l o y was then cast i n t o a graphite mold and the r e s u l t i n g casting was cut into conveniently siz e d pieces (2-4 gms i n weight), packaged, l a b e l l e d and then stored i n a lead c a s t l e u n t i l needed. Throughout the following presentation the density of trace a l l o y s w i l l be given r e l a t i v e to the density of pure molten t i n at a s i m i l a r temperature. The r e l a t i v e d e n s i t i e s of the trace a l l o y s , calculated on the assumption of independent behaviour of the species alloyed, were determined by the r e l a t i o n : TABLE 1 Properties of Radioisotopes Isotope Half L i f e Type of Radiation and Energy (Mev) A g 1 1 0 270d 6 (.53), y (.66 - 2.0) 113 Sn 112d X-ray, y (.26) S b 1 2 4 60d f3~ (2.31), y (.60-2.11) T I 2 0 4 4.1y B~ (.76) 22 / 100 P l p a l l o y % ( w t %Sn) p + (100 - wt %Sn) pSn where p^ i s the density of the trace isotope. The major problem associated with the measurement of flow v e l o c i t y by a r a d i o a c t i v e tracer technique l i e s i n discovering a way to introduce the tracer without disturbing the melts. The observations and r e s u l t s obtained from an extensive s e r i e s of experiments undertaken to develop a s u i t a b l e tracer introduction technique are presented se- q u e n t i a l l y i n Sections 2.1.2. to 2.1.8. 2.1.2. Tracer Introduction by Melting Back Through a Region Containing Radioactive M a t e r i a l 2.1.2.1. Experimental Apparatus and Procedure The graphite boat used f o r the i n i t i a l attempt to study the extent of convective flow i n h o r i z o n t a l rods of molten t i n i s shown i n Figure 5. The boat had two channels which were covered f o r approxi- mately 90% of the channel length with a short uncovered s e c t i o n at each end. In the covered section the melt cross section was 0.64 cm wide and 0.64 cm high. The height of metal i n the uncovered r e s e r v o i r s was approximately 1 cm. Thermocouples (30 gauge iron-constantan, insulated by 2 hole-1/16 inch O.D. m u l l i t e tubing) were positioned at 3 cm i n t e r - vals along one of the channels with the thermocouple beads situated i n the centre of the channel. Thus, the temperature d i s t r i b u t i o n could be measured i n one channel while study of the f l u i d flow, unimpeded by temperature measuring devices, could be c a r r i e d out i n the other channel. It was assumed that the two channels had i d e n t i c a l temperature d i s t r i b u t i o n s . (a) 27 cm h— 3 cm —*- Sectional View Figure 5 . The graphite boat used for i n i t i a l studies of convective flow i n h o r i z o n t a l rods of molten t i n . The boat was f i l l e d with 59's t i n (supplied by Vulcan Metals) and allowed to sol i d i f y . Approximately 3 gms of tin was removed from one end of the "clear" channel and in i t s place was cast radio- active tracer, a Sn-0.2wt % A g 1 1 0 alloy. A g 1 1 0 was chosen as the trace isotope since i t is a strong gamma emitter capable of penetrating the Vycor tube and furnace assembly and thus i t s presence over the collimator s l i t i s easily detected. The loaded boat was then placed in the Vycor tube and the thermocouple leads were connected through a Leeds and Northrup multi-point switch to a Honeywell Electronik 194 recorder. An ice water bath was employed as the cold junction and the.thermo- couples were periodically calibrated against the freezing point of pure t i n . Temperatures measured were believed to be correct within ± 0.1 °C. The distribution of activity along the length of the channel was determined prior to melting with the moveable collimator- s c i n t i l l a t i o n counter described earlier. The furnace was switched on and the tin melted. When the thermocouple adjacent to the radioactive tracer indicated the tracer was molten, monitoring of tracer movement began. This Was accomplished by equal time interval counting at various positions along the length of the channel. Any movement of tracer would be accompanied by a change in the observed distribution of activity along the boat. In order to evaluate the capability of the collimator to accurately determine the distribution of activity along the boat the following test was devised. Following the procedure outlined above, the d i s t r i b u t i o n of tracer was determined some time a f t e r melting had occured. The melt was then quenched (by f i l l i n g the Vycor tube with water) and, with the boat s t i l l i n the same p o s i t i o n , the d i s t r i b u t i o n of t r a c e r was again monitored. The boat was taken from the furnace and the s o l i d i f i e d t i n was removed from the clear channel of the boat. The d i s t r i b u t i o n of tracer along the t i n was determined by sectioning i t i n t o 1/4 inch pieces, weighing each piece, and measuring i t s a c t i v i t y by f i x e d geometry counting with a Tracerlab Inc. s c i n t i l l a t i o n counter and ampliscalar. 2.1.2.2. Results and Discussion Results of the test to evaluate the accuracy of the collimated counting procedure appear i n Figure 6. The open squares are from the i n s i t u monitoring a f t e r quenching and the f i l l e d c i r c l e s from the sectioning and counting procedure. The a c t i v i t i e s have been normalized .to f a c i l i t a t e comparison of the r e s u l t s . Both sets of data can be represented by one curve. Accordingly, the a c t i v i t y versus p o s i t i o n p r o f i l e determined by the c o l l i m a t o r - s c i n t i l l a t i o n counter arrangement can be taken as an accurate representation of the h o r i - zontal d i s t r i b u t i o n of radioactive tracer along the melt length. Figures 7, 8, and 9 show res u l t s t y p i c a l of those obtained from preliminary experiments to determine the amount of f l u i d flow associated with small h o r i z o n t a l temperature gradients along the l i q u i d t i n . Figure 7(a) shows the temperature d i s t r i b u t i o n along the t i n melt 1/2 hour, 1 hour and 4 hours a f t e r melting had occured. Although the average temperature of the melt changes, the temperature d i s t r i - 0 1 2 3 4 5 6 7 8 9 10 POSITION ALONG BOAT (SN) Figure 6. Results of the test to evaluate the accuracy of the collimated counting procedure. ho bution across the melt remains essentially the same for the 4 hour period. Figure 7(b) shows the distribution of tracer before melting and at approximately 1/2 hour, 1 hour and 4 hours after melting. The tracer has moved approximately half the length of the melt in the f i r s t 1/2 hour but very l i t t l e movement occurs over the subsequent 3h hours. A gradual leveling of the tracer distribution in the f i r s t half of the melt was observed over the 4 hours. Comparison of Figures 7(a) and 7(b) indicates that the position of furthest advance of tracer and the position of zero temperature gradient are approxi- mately coincident. To establish whether the stoppage of flow was uniquely determined by the position of the zero temperature gradient the tube furnace was moved, thus changing the temperature distribution in the melt. Figure 8(a) shows the temperature distribution 5, 10 and 20 minutes after moving the tube furnace. Figure 8(b) shows the effect of the temperature changes on the distribution of tracer along the melt. The coincidence of tracer redistribution with movement along the boat of the zero gradient i s made more obvious by comparing Figures 8(a) and 9. Figure 9 is a plot of activity at a particular position along the boat at various times after melting. As can be seen from Figure 8, positions at 8.5, 11 and 13.5 cm are on one side of the zero gradient whereas those at 18.5 and 21 cm are on the other side. Very l i t t l e change in the activity observed at each position occurred between 1 hour after melting and 4 hours after melting. Significant changes occur shortly after the furnace is moved. Figure 8(a) indicates that at between 5 minutes after and 10 minutes after 28 280 o 270 260 [ U J 250 h 1000 h - 800 h Heoo t 400 > o < 200 0 0 3 6 9 12 15 18 21 24 27 POSITION ALONG BOAT (CM) Figure 7. (a) The temperature p r o f i l e s at the indicated times a f t e r the tracer had melted. (b) The d i s t r i b u t i o n of tracer at the indicated times a f t e r melting. 29 ? 280 o: H 270 T 1 1 1 1 1 r (a) 20 min after- Before moving furnace 1000 h ~. 8 0 0 o - 6 0 0 t 4 0 0 > r- o < 2 0 0 0 ( b ) O Before moving furnace J L 20 min after 0 3 6 9 12 15 18 21 24 27 POSITION ALONG BOAT (CM) Figure 8. (a) The temperature p r o f i l e s at the indicated times. (b) The d i s t r i b u t i o n of tracer before and a f t e r moving the furnace. 1400 1200 - 1 0 0 0 3 8 0 0 t 6 0 0 o < 4 0 0 2 0 0 Furnace moved — i 1 A 8-5 cm from tracer end O 110 cm " " " a 13-5 cm " " " ©18-5 cm " » " A 210 cm from tracer end J A . 120 180 240 3 0 0 3 6 0 TIME A F T E R TRACER MELTED (MIN) 4 2 0 Figure 9. The change i n a c t i v i t y with time at various positions along the melt, Co O moving the furnace the zero gradient has moved past the 18.5 cm p o s i t i o n . Correspondingly the 18.5 cm p l o t on Figure 9 shows that tracer s t a r t s moving past t h i s p o s i t i o n approximately 6 minutes a f t e r moving the furnace. S i m i l a r l y the zero gradient moves past the 21 cm p o s i t i o n about 10 minutes a f t e r furnace movement and Figure 9 i n d i c a t e s tracer movement past t h i s p o s i t i o n at approximately the same time. These r e s u l t s c l e a r l y show that: (1) The region of zero h o r i z o n t a l temperature gradient i s not permeable to thermal convective flow. (2) An extremely small h o r i z o n t a l temperature d i f f e r e n c e , apparently any gradient greater than zero, provides s u f f i c i e n t d r i v i n g force for thermal convective flow. The conclusion that thermal convective mixing w i l l not pass through a region of zero h o r i z o n t a l temperature gradient i s i n agreement with (13) the findings of Davis and Fryzuk who studied the r e d i s t r i b u t i o n of a r a d i o a c t i v e solute along 2 mm diameter h o r i z o n t a l melts. How- ever, they were unable to detect convective mixing at temperature gradients below 5 °C/cm. Evidence that convective mixing occurs on both sides of the region of zero gradient i s presented i n Figure 10. The i n i t i a l d i s t r i b u t i o n was achieved, by allowing tracer to move down the boat to a region of zero gradient (at approximately 21 cm), waiting u n t i l the tracer d i s t r i b u t i o n i n the f i r s t 21 cm became homogeneous and then quenching. The boat was removed from the furnace and a new piece of Sn-0.2 % Ag"*""̂  was cast into the end of the boat. Figure 10(a) shows 32 265 o o QJ LU 260 h 255 h i - i — 1 1 1 1 1 r (a) i hr after m e l t i n g 1200 h 1000 h o : 8 0 0 d 6 0 0 >- > P 4 0 0 o < 2 0 0 ( b ) 0 ~ hr af ter melting • 0 3 6 9 12 15 18 21 24 27 POSITION ALONG BOAT (CM) Figure 10. (a) The temperature p r o f i l e 1/2 hour a f t e r the tracer melted. (b) The d i s t r i b u t i o n of tracer before and a f t e r melting. that a zero gradient occurred approximately 15 cm along the boat. Correspondingly there was movement of tracer up to, but not past the 15 cm mark. Also, the d i s t r i b u t i o n of tracer to the r i g h t of the 15 cm mark had evened out. Thus, thermal convective mixing was taking place on both sides of the zero gradient, but the presence of the zero gradient prevented mixing along the e n t i r e length of the boat. This r e s u l t suggests the existence of a quiescent zone i n the region of zero gradient. Figure 11 i l l u s t r a t e s the type of flow pattern which would be expected under the experimental condition employed here. The zero gradient functions as a valve i n that convection occurs on both sides of the zero gradient but there i s no mass transport between the two c e l l s . Stewart's a u t o r a d i o g r a p h y ^ ^ of double c e l l flow has now provided v i s u a l confirmation of the existence of a quiescent zone i n a zero gradient region. 2.1.2.3. Evaluation of Technique Although the tracer introduction technique j u s t described was rather unsophisticated, i t did show that detectable thermal con- vective flow occurs at any h o r i z o n t a l gradient greater than zero. This flow could not have been detected by temperature o s c i l l a t i o n techniques. Unfortunately i t was not possible to determine the cont r i b u t i o n of volume changes on melting to the observed flow. The major short- coming of t h i s tracer introduction technique i s the lack of con t r o l over the time at which the tracer was introduced into the melt. A much more desirable technique would allow introduction of tracer at any s p e c i f i e d time, for example, a f t e r achieving a stable temperature Zero Gradient Figure 1 1 . The expected flow pattern when a zero gradient i s present. d i s t r i b u t i o n i n the melt. 2.1.3. Tracer Introduction by Rotating a V e r t i c a l Cylinder Located at the End of the Graphite Boat 2.1.3.1. Experimental Apparatus and Procedure The graphite boat used for t h i s s ection of the i n v e s t i - gation i s shown i n Figure 12. I t i s the same boat as was used i n the previous section but with one modification; one end of the clear channel has been f i t t e d with a hollow cy l i n d e r which i s opened on one side, Figure 12(b). The cylinder was loaded with tracer i n the tracer loading block shown i n Figure 12(c). The block was heated with a Bunsen Burner u n t i l the tracer melted and flowed into the introducing c y l i n d e r . The cy l i n d e r was then rotated such that the cylinder opening was not i n l i n e with the channel to the tracer r e s e r v o i r . Following s o l i d i f i c a t i o n of the t r a c e r , the introducing cylinder was removed from the loading block and placed i n the graphite boat such that the cylinder opening was not aligned with the channel. Introduction of tracer into the melt was achieved, at any desired time a f t e r melting, by r o t a t i n g the c y l i n d e r u n t i l the channel and cy l i n d e r opening were coincident. The movement of tracer along the melt was monitored by the method described e a r l i e r . 2.1.3.2. Results and Discussion In order to determine the extent of mixing associated with tracer i n t r o d u c t i o n , experiments were c a r r i e d out i n which there was a zero h o r i z o n t a l temperature gradient i n the melt j u s t ahead of the ( b ) (c) Tracer Introduction Cylinder Tracer Loading Block Figure 12. (a) Top view of graphite boat with tracer introduction cylinder i n place. (b) Intro- duction c y l i n d e r . (c) Tracer loading block. ON tracer introducer. Figure 13 shows r e s u l t s of such an experiment. From Figure 13(a) i t can be seen that there i s a region of zero grad- ient approximately 3 cm ahead of the tracer introducer. Movement of tracer past the region of zero gradient i s c l e a r l y shown i n Figure 13(b). It i s evident that there i s some a d d i t i o n a l d r i v i n g force f o r the move- ment of tracer along the melt. This flow may a r i s e from solute convec- t i o n , since the Sn-0.2 wt % Ag"*""*"̂  a l l o y i s more dense than pure t i n , (1.0005 pSn) or from some mechanical disturbance associated with t r a c e r i n t r o d u c t i o n , or from a combination of both. To eliminate the e f f e c t of mixing associated with i n t r o - duction, experiments were conducted i n which tracer was introduced i n t o a melt which had a zero gradient approximately 6 to 10 cm ahead of the tracer introducer. With the zero gradient further down the melt than was the case i n the experiment shown i n Figure 13 mixing associated with introduction was not s u f f i c i e n t to carry the tracer past the re- gion of zero gradient. A f t e r i n i t i a l flow along the melt had stopped the temperature d i s t r i b u t i o n i n the melt was changed by passing argon through the Vycor tube. The temperature gradients at various p o s i t i o n s along the boat appear i n Figure 14(a) and the tracer d i s t r i b u t i o n i n Figure 14(b). The " i n i t i a l " gradient d i s t r i b u t i o n represents the con- di t i o n s under which tracer was introduced and flow along the melt stopped. One and one h a l f hours a f t e r i ntroduction the stable tracer d i s t r i b u t i o n marked " i n i t i a l " was observed. The times shown on Figure 14 are times a f t e r turning on the argon. Comparison of Figures 14(a) and 14(b) show that increasing the gradient above zero r e s u l t s i n flow along the boat. Figure 13. (a) The temperature profile along the melt at the time of tracer introduction. (b) The distribution of tracer before and 15 minutes after introduction. 3 9 0 - 6 o ? 0 - 4 1 0 -2 h a: 0 0 UJ - 0 - 2 h o < 2 0 0 Initial (90 min after intro.) 3 min 3 6 9 12 15 POSITION ALONG 18 21 24 BOAT (CM) Figure 14. (a) The temperature gradients along the melt. (b) The d i s - t r i b u t i o n of tracer before and a f t e r passing argon. 40 In the experiments described i n the previous section the temperature d i s t r i b u t i o n was changed by moving the furnace whereas during t h i s s e r i e s of tests argon flow was employed to a l t e r the temperature along the melt. Since the furnace i s i n d u c t i v e l y wound i t could be speculated that electromagnetic s t i r r i n g e f f e c t s were responsible for the flow which occurred a f t e r moving the furnace. The r e s u l t s of the experiments using argon to a l t e r the temperature gradient along the melt agree with those obtained i n the previous section. Thus, i t can be concluded that i t i s the thermal d r i v i n g force that causes the f l u i d flow. The average flow v e l o c i t y estimated from the rate of advance of the points of i n t e r s e c t i o n with the abscissa of a tangent drawn along the leading edge of the a c t i v i t y versus p o s i t i o n _3 curve (Figure 14(b))was 5 x 10 cm/sec. During the course of experimentation to evaluate the ex- tent and cause of mixing associated with tracer introduction occasional anomalous r e s u l t s of the type shown i n Figure 15 occurred. The temper- ature p r o f i l e 25 minutes a f t e r turning on the argon (Figure 15(a))would, from previous r e s u l t s , be considered extremely favourable for f l u i d flow. However, Figure 15(b) shows that no flow occurred. Apparently under some conditions there i s no mixing between the uncovered r e s e r v o i r where tracer i s introduced and the covered section of the boat. 2.1.3.3. Evaluation of Technique The estimate of flow v e l o c i t y obtained above i s of l i m i t e d value since the temperature gradient along the melt was continually changing during the v e l o c i t y measurement. In order to determine the 41 T 1 1 1 1 1 1 r POSITION ALONG BOAT (CM) Figure 15. (a) The temperature p r o f i l e s before and a f t e r passing argon, (b) The d i s t r i b u t i o n of tracer at the times indicated. r e l a t i o n s h i p between temperature gradient and flow v e l o c i t y i t i s necessary to introduce the tracer i n t o the melt a f t e r a steady state temperature d i s t r i b u t i o n has been attained. Although the amount of mixing associated with tracer introduction may be small compared to flow v e l o c i t i e s which would occur at higher temperature gradients, the anomalous phenomenon displayed i n Figure 15 necessitated that sub- sequents attempts at tracer introduction be c a r r i e d out i n the covered section of the boat. 2.1.4. Tracer Introduction by Rotating a V e r t i c a l Cylinder Situated i n the Covered Section of the Graphite Boat 2.1.4.1. Experimental Apparatus and Procedure Introduction of tracer into the covered s e c t i o n of the boat was accomplished using the apparatus shown i n Figure 16. The graphite boat was e s s e n t i a l l y the same as that used previously, that i s , two channels and an o v e r a l l melt length of 27 cm. Modifications included the addition of a graphite heating block and a copper cooling block, (coated with a graphite suspension, Aquadag). The heat source for the heating block was a resistance winding powered by a Variac. Argon flow through the cooling block was measured and c o n t r o l l e d by a V i c t r o - meter model 0158 flowmeter. The tracer was loaded into the i n t r o d u c t i o n cylinder i n the same way as described i n Section 2.1.3.1. Introduction of tracer into the melt was accomplished by r o t a t i n g the i n t r o d u c t i o n c y l i n d e r , Figure 16(b), u n t i l the square hole i n the c y l i n d e r and the clear channel were aligned. Stainless s t e e l guides and stops (not shown i n the diagram) were employed to insure that the cylinder could be mani- pulated to the f u l l y opened or f u l l y closed p o s i t i o n s remotely. O v e r a l l ( a ) Copper cooling block Graphite heating block Argon j Tracer Introducer (closed) Push to open Variac (b) Figure 16. (a) Details of the graphite boat employed for experiments in which the tracer was introduced in the covered section of the melt. (b) Tracer introduction cylinder. experimental set-up and monitoring techniques were the same as described e a r l i e r . 2.1.4.2. Results and Discussion To determine the amount of flow associated with t h i s i n t r o - duction technique tracer was introduced when the melt had a stable zero 113 temperature gradient along i t s e n t i r e length. Sn was used as the trace isotope to remove the p o s s i b i l i t y of solute convection. Figure 113 17(a) shows the r e s u l t s of introducing Sn tra c e r i n t o a melt having zero gradient. Appreciable flow has accompanied tracer i n t r o d u c t i o n as the tracer has moved approximately 10 cm i n 40 minutes. To a s c e r t a i n whether or not the mixing on introduction was due s o l e l y to r o t a t i n g the cylinder (and possibly disturbing the boat) an experiment was under- taken i n which the tracer introducer was placed i n the f u l l y opened p o s i t i o n p r i o r to melting and the temperature was gradually r a i s e d (maintaining a f l a t temperature d i s t r i b u t i o n ) u n t i l melting occurred. The r e s u l t s of t h i s experiment are shown i n Figure 17(b). The movement of tracer along the boat was almost as far as occurred i n Figure 17(a). This indicated that the r o t a t i o n of the cyl i n d e r to e f f e c t tracer i n t r o - duction was not the major cause of the f l u i d flow associated with the introduction of trac e r . 2.1.4.3. Evaluation of Technique The r e s u l t s shown i n Figure 17 indi c a t e d that r o t a t i o n of the cylinder was not a major cause of flow associated with i n t r o d u c t i o n ; they also c l e a r l y showed that flow did occur under thermal conditions which 45 1200 a: 9 0 0 h d 6 0 0 - a < 3 0 0 - 0 0 T 1 — i 1 1 1 1 r (a ) Initial 24 min after intro. 4 0 min 12 15 18 21 24 27 1200 a: 9 0 0 h d >- > H O < 6 0 0 - 3 0 0 - 0 ( b ) — Initial 15 min after melting 4 0 min 0 3 6 9 12 15 18 21 24 27 POSITION ALONG BOAT (CM) 113 Figure 17. The d i s t r i b u t i o n of Sn (in a pure Sn melt having zero h o r i z o n t a l temperature gradient) before and af t e r (a) tracer introduction and (b) melting with the int r o d u c t i o n cylinder i n the open po s i t i o n s . have heretofore been shown to be unfavourable. Therefore, t h i s technique was temporarily abandoned i n hopes of developing a method of i n t r o d u c t i o n which would i n no way a l t e r the f l u i d flow that was occurring p r i o r to tracer i n t r o d u c t i o n . 2.1.5. Tracer Introduction by Rotating a Horizontal Cylinder Located i n the Cover of the Graphite Boat. 2.1.5.1. Experimental Apparatus and Procedure The only d i f f e r e n c e between the graphite boat used for t h i s section of the i n v e s t i g a t i o n and the one shown i n Figure 16 i s the method of tracer introduction. D e t a i l s of the i n t r o d u c t i o n technique are shown i n Figure 18. In order to prevent any i n t e r a c t i o n between the tracer introducer and the melt the introduction c y l i n d e r was placed i n the boat cover. To introduce tracer the cylinder opening was ro- tated i n t o alignment with the hole i n the cover. Flow past the hole should then draw tracer out i n t o the melt. The movement of t r a c e r , due to the f l u i d flow present, could then be monitored by the procedure des- cribed e a r l i e r . i 2.1.5.2. Results and Discussion Three d i f f e r e n t trace isotopes, S n ^ 3 , Ag"'"''"̂  and T l 2 ^ 4 were used to evaluate the effectiveness of the tracer introduction technique 113 shown i n Figure 18. I n i t i a l experiments were conducted using Sn as the trace isotope, therefore, there would be no solute convection to i n t e r f e r e with the thermal convection. When the tracer introducer or "gate" was opened to the melt under conditions of zero h o r i z o n t a l 47 1 ) - - - ir - l ~ " - ) push to introduce tracer Tracer V///////////////////////////A sectional view Figure 18. D e t a i l s of tracer introduction from the boat cover. temperature gradient no detectable change i n the tracer d i s t r i b u t i o n occurred over a h a l f hour period. The gate was then closed and the gradient i n the melt was changed such that thermal convection would be expected. The gate was then reopened. Even under conditions favourable for flow no change i n the tracer d i s t r i b u t i o n along the boat was ob- served. The tracer had not entered the melt. To a s s i s t introduction of tracer into the melt a 30 wt % ,̂̂ 204 a l l o y was used i n a subsequent experiment. Since T l ^ ^ ̂ g a 204 s o f t 3-emmitter, the r e l a t i v e l y high weight per cent of TI i n the trace a l l o y was necessary to f a c i l i t a t e monitoring. This a l l o y was then appreciably more dense than the pure t i n melt (1.133 pSn) and would be expected to enter the melt by solute convection a f t e r opening the gate. This was confirmed experimentally as the tracer p r o f i l e became uniform approximately 4 minutes a f t e r opening the gate, Figure 19(b). With the temperature d i s t r i b u t i o n shown i n Figure 19(a) one would expect tracer movement to be predominantly to the l e f t of i t s o r i g i n a l p o s i t i o n as t h i s would follow the thermal convective flow pattern expected. That i s , the more dense f l u i d moving from the cold end to the hot end along the bottom of the channel. Autoradiography of the quenched melt c l e a r l y showed that the trace a l l o y had f a l l e n to the bottom of the channel and spread i n both d i r e c t i o n s . Solute convection must then have overcome the therma convective flow. To reduce the density of the trace a l l o y but s t i l l maintain a high enough s p e c i f i c a c t i v i t y an a l l o y of 0.5 wt % Ag"*""*"̂  i n Sn was pre- pared. This a l l o y had a s p e c i f i c a c t i v i t y high enough to f a c i l i t a t e moni toring and i t was s l i g h t l y more dense than the pure t i n (1.0013 pSn) thus 49 295 ? 290 | 285 |- UJ I— 280 1000 - 8 0 0 H 6 0 0 h t 4 0 0 h > o < 200 ( b ) Initial 4 min after intro. J 0 3 6 9 POSITION 12 15 18 21 24 27 ALONG BOAT (CM) Figure 19. (a) The temperature p r o f i l e along the melt. (b) The d i s t r i b u t i o n of T l 2 ^ 4 before and a f t e r tracer introduction. aiding introduction into the melt. Opening the gate with a zero gradient along the melt produced n e g l i g i b l e flow along the channel over a 20 minute i n t e r v a l . The gate was closed and the temperature d i s t r i b u t i o n adjusted to that shown i n Figure 20(a). Figure 20(b) shows the re- s u l t i n g movement of tracer. As expected the more dense trace a l l o y moved to the l e f t of the place of introduction. 2.1.5.3. Evaluation of Technique 113 Experiments using Sn showed that .this t r a c e r introduction technique depends on solute convection f o r entry of trace a l l o y into the melt. That i s , the tracer must be more dense than the melt. I f the 204 tracer i s too dense, as was the case with the 30 wt % TI i n Sn a l l o y , i t i n t e r f e r e d with or overcame the thermal convective flow present. Even the reasonably successful experiment with the 0.5 wt % Ag"^^ i n Sn trace a l l o y requires that the s l i g h t l y more dense tracer drop from the top to the bottom of the melt i n order to follow the thermal convective flow. How t h i s i n t e r f e r e s with the thermal convection i s not known. AI90, t h i s method of tracer introduction leads to continuous d i l u t i o n of the tracer even as the tracer i s being introduced thus making detection of the passage of tr a c e r over a given collimator p o s i t i o n more d i f f i c u l t . A f a r more desirable technique would allow introduction of a concentrated amount of tracer i n t o a small area w i t h i n a short period of time. Such a technique i s described i n the following section. i 51 3 0 0 F o o C L UJ 290 280 5 0 0 0 QL :4000 3 0 0 0 p 2 0 0 0 o < 1000 0 L 0 (b) Initial 5 min after intra _L_ I 1 L 3 6 9 12 15 18 21 24 27 POSITION ALONG BOAT (CM) Figure 20. (a) The temperature p r o f i l e along the melt, (b) The d i s - t r i b u t i o n of Az^® before and a f t e r tracer introduction. 52 2.1.6. Tracer Introduction by Rotating a Horizontal Cylinder Located i n the Cover of the Boat and then Gently Pushing Tracer i n t o the Melt. 2.1.6.1. Experimental Apparatus and Procedure Figure 21 shows the modifications that were made to the introduction technique i l l u s t r a t e d i n Figure 18. A piston arrangement has been added to f a c i l i t a t e rapid i n t r o d u c t i o n of tracer i n t o the melt and thus avoid the tracer d i l u t i o n problem discussed i n the previous section. Tracer introduction was accomplished by r o t a t i n g the gate to the open p o s i t i o n and then gently forcing the tracer i n t o the melt with the piston mechanism shown i n Figure 21(b). Detection of tracer movement was c a r r i e d out as described previously. Data t y p i c a l of that obtained employing the new i n t r o d u c t i o n technique appears i n Figure 22. The two curves represent the change i n a c t i v i t y observed above two collimator positions "downstream" from the place of introduction. The monitoring posi t i o n s were 6.3 cm apart. The f i r s t p o s i t i o n was approximately 3 cm away from the gate to reduce the e f f e c t s on the observed flow v e l o c i t y , of transients associated with introduction. A c t i v i t i e s p l o t t e d are average count rates over a 30 second time i n t e r v a l . The time required for movement of tracer between the two collimator p o s i t i o n s was determined by measuring the time d i f f e r e n c e be- tween the i n t e r s e c t i o n s of the extrapolations of the a c t i v i t y - t i m e curve and the abscissa. J u s t i f i c a t i o n of t h i s method of analysis i s presented l a t e r i n the t h e s i s . Observed flow v e l o c i t y was then calculated by d i v i d i n g the known separation of 6.3 cm by the measured time d i f f e r e n c e . The v a r i a t i o n i n observed flow v e l o c i t y with temperature 53 Figure 21. D e t a i l s of mechanism used to f a c i l i t a t e tracer introduction from the boat cover. (a) Top view (b) Side s e c t i o n a l view. 5 0 0 I 1 1 1 1 1 1 1 r TIME AFTER INTRO. (MIN) Figure 22. T y p i c a l a c t i v i t y versus time data for experiments employing forced tracer i n t r o d u c t i o n from the boat cover. 55 124 differe n c e between the hot and cold ends was studied using a 1% Sb 124 i n pure Sn trace a l l o y . Sb was chosen as the trace isotope, as i t i s a strong y - emmitter of high s p e c i f i c a c t i v i t y and because i t i s s l i g h t l y less dense than pure Sn (0.9993 pSn). Since the tracer i s l e s s dense than the t i n , i t should tend to remain near the top of the melt i n moving from the hot end to the cold end. Thus, motion of tracer from the top to the bottom of the melt by solute convection w i l l not occur as i t did with the more dense Ag"*""̂  and T l " ^ ^ a l l o y s . Sn'"^ i s not a s u i t a b l e isotope for v e l o c i t y measurements since flow along the boat causes d i l u t i o n of the isotope, which has a low's p e c i f i c a c t i v i t y re- 124 l a t i v e to Sb , and makes detection of i t s presence above a given collimator p o s i t i o n d i f f i c u l t . 113 Although Sn i s not a good trace isotope f o r the collimated monitoring system used to determine flow v e l o c i t i e s , i t s low energy r a d i a t i o n makes i t an acceptable tracer for autoradiography experiments. 113 For t h i s reason Sn trace a l l o y s were used to determine flow patterns i n the melt and to evaluate the tracer introduction technique. A series of specimens to be autoradiographed was prepared by quenching the melt (by f i l l i n g the Vycor tube with water) at various times a f t e r tracer introduction and with d i f f e r e n t temperature d i s t r i b u t i o n s . Auto- radiographs were obtained by placing the quenched specimens on double emulsion X-ray f i l m i n l i g h t t i g h t boxes. Areas of the f i l m adjacent to regions of tracer appear darkened on developing. A l l autoradiographs which appear i n the thesis have been printed such that dark regions i n - dicate the presence of tracer. 56 2.1.6.2. Results and Discussion 2.1.6.2.1. Flow V e l o c i t y Measurements The v a r i a t i o n of flow v e l o c i t y with temperature d i f f e r e n c e between the hot and cold ends of the boat i s shown i n Figure 23. The increase i n flow v e l o c i t y with increasing temperature d i f f e r e n c e across the melt was expected, however, the large degree of s c a t t e r made i t im- possible to determine the form of the r e l a t i o n s h i p between these two v a r i a b l e s . 2.1.6.2.2. Autoradiography The extent of flow associated with tracer i n t r o d u c t i o n was evaluated by introducing t r a c e r i n t o a melt having zero h o r i z o n t a l temperature gradient and then quenching the r e s u l t i n g tracer d i s t r i b u t i o n . 113 The p o s s i b i l i t y of solute convection was avoided by employing Sn as the trace isotope. Autoradiographs of specimens quenched 0.5, 1 and 10 minutes a f t e r introduction of the tracer are shown i n Figure 24. It i s evident that appreciable mixing accompanies introduction of t r a c e r . What i s more s i g n i f i c a n t i s that the tracer has not only spread through the melt, under conditions where convective flow would not be expected, but has also spread i n a nonreproducible and unexpected manner. One might expect a s l i g h t amount of tracer dispersion to be associated with the forcing of the tracer i n t o the melt v i a the piston mechanism. This i s shown to be so i n the specimen which was quenched 0.5 minutes a f t e r introduction, Figure 24(a). Since the h o r i z o n t a l gradient i n the melt was zero and the trace a l l o y the same density as the melt, specimens . TEMP. DIFF. ACROSS MELT (°C) Figure 23. The dependence of flow v e l o c i t y on the temperature difference between the hot and the cold ends of the melt. Cn Cold end Hot end Figure 24. Longitudinal section autoradiographs of specimens quenched (a) 0.5 minutes (b) 1 minute and (c) 10 minutes a f t e r tracer introduction into a melt having zero h o r i z o n t a l temperature gradient. quenched at times greater than 0.5 minutes a f t e r i n t r o d u c t i o n should show no further r e d i s t r i b u t i o n of tra c e r . However, Figure 24(b) shows movement of tracer towards the cold r e s e r v o i r and to the bottom of the channel. The specimen quenced 10 minutes a f t e r i n t r o d u c t i o n of tr a c e r again shows movement of tracer to the bottom of the channel but i n t h i s case the r e d i s t r i b u t i o n about the point of introduction i s quite uniform. Figure 25 contains transverse section autoradiographs of a specimen quenched one minute a f t e r introduction of tracer i n t o a melt having zero h o r i z o n t a l temperature gradient. These autoradiographs show a double c e l l flow pattern i n the transverse d i r e c t i o n . This suggests that the tracer must be more dense than the melt. Even with a 70 °C temperature diffe r e n c e between the hot and cold ends the trans- verse flow pattern maintains i t s double c e l l appearance, Figure 26. Since the average time required to quench the melt was of the order of 15 seconds i t was questioned whether flow patterns observed r e f l e c t e d the flow patterns that existed p r i o r to quenching, or, whether the double c e l l appearance was a quench e f f e c t . In order to study the e f f e c t of the quench on the observed flow pattern a s e r i e s of experiments was c a r r i e d out i n which the quench was i n i t i a t e d from the top side of the melt. (Re c a l l , that to t h i s time quenching was accomplished by f i l l i n g the Vycor tube with water, therefore, the quench was i n i t i a t e d at the bottom of the melt). Any major change i n the observed flow pattern f o r a given set of experimental conditions would then i l l u s t r a t e the presence of a quench e f f e c t . A spray tube over the covered section of the boat was employed to f a c i l i t a t e quenching. Both opened res e r v o i r s were covered with s t a i n l e s s s t e e l caps and sealed with Sairset cement to pre- (a) Cold end 1 0 8 Hot end Top 2 ^ > Outside Top (b) I -w W 9 10 II (a) Position from which autoradiographs were obtained . (b) Transverse section autoradiographs (from positions indicated in (a)) of a specimen quenched 1 minute aft e r tracer introduction into a melt having zero horizontal temperature gradient. Figure 26. Transverse section autoradiographs (from the positions indicated) of a specimen quenched 1 minute a f t e r introduction of tracer into a melt having a 70 °C tempera- ture difference between the hot and cold ends. vent quench water contacting the molten t i n . The top quench tests proved to be unsuccessful as i t was impossible to prevent water from seeping into the melt. This resulted i n radioactive t i n being sprayed throughout the Vycor tube y i e l d i n g an obviously unrepresentative flow pattern. In order to reduce the quench time a d i f f e r e n t type of boat was developed and the r e s u l t s of autoradiography studies using t h i s boat w i l l be discussed i n Section 3. 2.1.6.3. Evaluation of Technique Although i t was not possible to confirm the accuracy of the autoradiographs obtained, i t was apparent that the tr a c e r was more dense than the melt. Quenching from the bottom f i r s t (normal procedure) should create an i n i t i a l condition of cooler l i q u i d below warmer l i q u i d and therefore one would not expect the double c e l l pattern observed to be a r e s u l t of such quenching. Since the melt and trace a l l o y were of i d e n t i c a l chemical composition, that i s , pure t i n and pure t i n con- taining radioactive t i n , the p o s s i b i l i t y of solute convection must be ruled out. The higher density of the tracer must r e f l e c t the fa c t that the tracer i s at a lower temperature than the melt into which i t i s introduced. Since the tracer i s o r i g i n a l l y located i n the cover of the boat and the tracer introduction mechanism extends approximately 5/16 inch above the cover (and could thus be effected more by a i r convection i n the Vycor tube), i t i s not unreasonable that the tracer could be s l i g h t l y cooler than the melt below i t . This would account for the double c e l l flow pattern observed i n the transverse section autoradio- graphs. From Figure 24(b) i t was apparent that t h i s tracer i n t r o d u c t i o n technique can cause a net flow of tracer i n one d i r e c t i o n rather than a uniform spread about the point of introduction. Flow due to f o r c i n g the tracer into the melt was probably the main cause of the s c a t t e r observed i n Figure 23 and therefore t h i s i ntroduction technique was aban- doned. 2.1.7. Return to Introduction by Rotating a V e r t i c a l Cylinder Located i n the Covered Section of the Channel 2.1.7.1. Experimental Apparatus and Procedure Research to this point i n the i n v e s t i g a t i o n has shown that: (1) Tracer must be introduced i n the covered s e c t i o n of the boat to avoid the anomalous r e s u l t s caused by the convective currents i n the uncovered r e s e r v o i r s at the end of the graphite boat (Section 2.1.3.). (2) Tracer cannot be held i n the boat cover as t h i s causes the tracer to be cooler than the melt (Section 2.1.6.2.2.). This r e s u l t s i n the formation of a double c e l l flow pattern i n transverse section and thus i n t e r f e r e s with the convective flow that would normally occur under s i m i l a r experimental conditions. Of the f i v e introduction techniques studied i n t r o d u c t i o n of tracer by r o t a t i n g a v e r t i c a l c ylinder located i n the covered section of the boat appears most s a t i s f a c t o r y . Therefore, the i n t r o d u c t i o n technique discussed i n Section 2.1.4.1. and i l l u s t r a t e d i n Figure 16 was readopted. In order to f a c i l i t a t e greater f l e x i b i l i t y i n the e s t a b l i s h - 64 merit and control of experimental temperature d i s t r i b u t i o n s the follow- ing modifications were made to the furnace and furnace power supply. A 0 to 92 ohms rheostat was placed i n s e r i e s with one of the end furnace windings to enable establishment of steeper temperature gradients along the furnace, Figure 27(a). The Variac power supplies were replaced by the dual zone power supply and temperature c o n t r o l l e r shown i n Figure 27(b). The control thermocouple was located between the two cen- t r a l furnace windings. The temperature gradient along the furnace could then be adjusted by manipulation of the c e n t r a l and end windings power discriminators and the 0 to 92 ohm rheostat. Average furnace temperature was adjusted and maintained with the thermocouple bucking p o t e n t i a l s and Honeywell c o n t r o l l e r . As before, the temperature diff e r e n c e across the melt could be further adjusted by the heating c o i l and cooling block shown i n Figure 16. Flow v e l o c i t y measurements were.carried out i n the following way. The furnace power, heating c o i l power and argon flow rate through the cooling block were adjusted to give a desired temperature d i s t r i b u t i o n along the melt. This temperature p r o f i l e , as monitored by the Honeywell E l e c t r o n i c 194 recorder, was maintained f o r approximately one hour to insure steady state heat tran s f e r through the boat and melt. The tra c e r was then introduced i n t o the melt and the movement of tracer r e s u l t i n g from the convective flow present was monitored by the moveable co l l i m a t o r - s c i n t i l l a t i o n counter assembly described e a r l i e r . As i n Section 2.1.6., the f i r s t collimator p o s i t i o n was approximately 3 cm away (towards the cold end) from the place of introduction. Once i t was apparent that the tracer had passed t h i s p o s i t i o n the collimator was moved 6.3 cm "down- (a) 0 - 9 2 X 2 Rheostat i/> 8 a n to £ o o c C O (D C O _J Figure 27. Tube furnace wiring diagram.(b) Det a i l s of furnace temperature c o n t r o l l e r . A 0-5 mv Honeywell Controller B Ammeter for center windings C&D Power discriminators for center windings E Ammeter for end windings F&G Power discriminator for end windings H Control thermocouple input I 0-50 mv (10 mv steps) backing p o t e n t i a l J 0-10 mv (1 mv steps) backing p o t e n t i a l stream" and counting was continued u n t i l the tracer was observed to pass. Figure 28 shows a t y p i c a l a c t i v i t y - t i m e curve; the a c t i v i t i e s p l o t t e d are average count rates over a 15 second time i n t e r v a l . As before, the time required f or flow of tracer from one collimator p o s i t i o n to another was determined by measuring the time diffe r e n c e between the i n t e r s e c t i o n of the extrapolation of the a c t i v i t y - t i m e curves and the abscissa. Experi- ments were conducted to determine:- (1) The v a r i a t i o n of flow v e l o c i t y with temperature diffe r e n c e 124 between the hot and cold ends of the melt. Sb was used as the trace isotope f o r reasons s i m i l a r to those presented i n 124 Section 2.1.6. The trace a l l o y was 0.46 wt % Sb i n pure t i n . Average temperature across the melt was maintained at approximately 312 °C, with 309 °C minimum and 320 °C maximum. (2) The e f f e c t on the observed flow v e l o c i t y of allowing the aver- age temperature to be outside the l i m i t s set above. This was accomplished by conducting v e l o c i t y determination experiments at 300 °C and 325 °C and then comparing these values with the r e s u l t s obtained i n (1). (3) The e f f e c t on observed flow v e l o c i t y of varying the density difference between trace a l l o y and melt. To evaluate t h i s e f f e c t f i v e experiments were undertaken i n which the trace a l l o y and melt were of the same density. This was accomplished by making the melt composition the same as that of the trace a l l o y , name- l y 0.46 wt % Sb i n Sn (Sb used i n the melt was nonradioactive). The melt was prepared under an argon atmosphere and was s t i r r e d p e r i o d i c a l l y f o r appoximately one h a l f hour to insure homogeniety. Further comparison of flow v e l o c i t y with trace a l l o y density was provided by increasing the amount of Sb i n the trace a l l o y to 1 6 0 0 Q: 1 2 0 0 - o v- 8 0 0 - JT 4 0 0 < * 1 I 3 TIME AFTER INTRO. (MIN) Figure 28. T y p i c a l a c t i v i t y versus time data for experiments employing tracer introduction by rot a t i n g a v e r t i c a l cylinder located i n the covered section of the melt. ON 68 3.0 wt % (by adding nonradioactive Sb), thus making the trace 124 a l l o y appreciably less dense than the 0.46 wt % Sb used above. 2.1.7.2. Results and Discussion 2.1.7.2.1. V a r i a t i o n of Flow V e l o c i t y with Temperature Difference Across the Melt The r e s u l t s of experiments to determine the v a r i a t i o n of flow v e l o c i t y with temperature diffe r e n c e between the hot and cold ends of the 27 cm long melt are tabulated i n Table 2 and p l o t t e d i n Figure 29. As ex- pected flow v e l o c i t y increases with increasing temperature d i f f e r e n c e along the melt. Furthermore, the r e s u l t s show flow v e l o c i t y increases l i n e a r l y with temperature difference over the range of experimental con- d i t i o n s investigated. 2.1.7.2.2. E f f e c t of Varying Average Melt Temperature To evaluate the e f f e c t (on observed flow v e l o c i t y ) of varying the average melt temperature, the r e s u l t s of experiments c a r r i e d out with average melt temperature of 300 °C and 325 °C have been p l o t t e d , Figure 30, for comparison to the r e s u l t s shown i n Figure 29. The l i n e which appears i n Figure 30 i s that which was determined from the data p l o t t e d i n Figure 29. The minimum and maximum average melt temperatures of the r e s u l t s which determined the r e l a t i o n s h i p obtained i n Figure 29 were 309 °C and 320 °C. I f average melt temperature had any major e f f e c t on the flow v e l o c i t y one might expect, due to the temperature dependence of v i s - c o s i t y (Table 6), to see the r e s u l t s of the experiment conducted with T = 300 °C to l i e below the l i n e and those from the t e s t at T = 325 °C to l i e above the l i n e . Since both points are above the l i n e , i t must be concluded that v a r i a t i o n i n average melt temperature, over the range des- TABLE 2 Flow V e l o c i t y Results A Temperature V e l o c i t y °C cm/sec. 5.5 7.1 14.5 17.6 20.2 22.7 24.2 27.2 33.2 41.8 55.5 60.8 61.6 0.014 0.018 0.042 0.047 0.052 0.060 0.083 0.075 0.080 0.111 0.140 0.167 0.162 Experiment Number Average Temp. °C. 1 2 3 4 5 6 7 8 9 10 11 12 13 312 309 309 312 311 311 312 310 314 320 313 310 311 0 * 2 0 i 1 1 1 1 1 1 1 1 1 T Figure 29. The dependence of flow v e l o c i t y on the temperature diffe r e n c e between the hot and the cold ends of the melt. o TEMP. DIFF. ACROSS MELT (°C) Figure 30. The e f f e c t on the flow v e l o c i t y of varying the average melt temperature. cribed for these experiments, has no e f f e c t on the flow v e l o c i t y measured by the presently employed monitoring technique. Points which do not f a l l on the l i n e must then do so because of normal experimental s c a t t e r inherent i n the tracer introduction and v e l o c i t y determination techniques. 2.1.7.2.3. E f f e c t of Varying Trace A l l o y and Melt Density 124 Since the trace a l l o y , 0.46 % Sb i n Sn, used to obtain the r e s u l t s p l o t t e d i n Figure 29 i s less dense than the melt (0.9997 pSn) i t was necessary to determine what e f f e c t t h i s density d i f f e r e n c e might have on the observed flow v e l o c i t y . Figure 31 shows the r e s u l t s of ex- periments i n which the melt and tracer were of the same composition, namely 0.46 % Sb i n pure Sn. As i n Figure 30, the r e s u l t s are p l o t t e d along with the l i n e a r r e l a t i o n s h i p obtained,in Figure 29. There i s excellent agree- ment between four of the f i v e experimental points and the l i n e . There was no apparent reason for the large deviation displayed by the one point. The r e s u l t s of Figure 31 c l e a r l y show that no discrepancy i n observed flow v e l o c i t y occurs as a r e s u l t of the trace a l l o y being s l i g h t l y l e s s dense than the melt. Further evidence of theabsenceof any major tracer density e f f e c t on observed flow v e l o c i t y i s presented i n Figure 32. A c t i v i t y - time curves for three d i f f e r e n t tracer-melt, combinations are p l o t t e d : 1) Tracer and melt same density (both 0.46 wt % Sb i n Sn) 2) Tracer s l i g h t l y less dense (0.9997 pSn ) than the melt (tracer 0.46 wt % Sb i n Sn, melt pure Sn). TEMP. DIFF. ACROSS MELT (°C) Figure 31. The e f f e c t on the flow v e l o c i t y of having i d e n t i c a l trace a l l o y and melt d e n s i t i e s . 74 3) Tracer appreciably less dense (0.9978 pSn ) than the melt (tracer 3.0 wt % Sb i n Sn, melt pure Sn). The temperature diffe r e n c e for a l l three experiments was approximately 30 °C and the separation between monitoring p o s i t i o n s was 10 cm. To s i m p l i f y comparison of the curves the time scale of each test has been adjusted so that the time of a r r i v a l of tracer at the f i r s t monitoring p o s i t i o n i s coincident. Examination of the points represent- ing the increase i n a c t i v i t y at the second monitoring p o s i t i o n shows that the time f o r movement of tracer between the two monitoring p o s i t i o n s i s e s s e n t i a l l y the same. The flow v e l o c i t i e s i n the three cases are there- fore the same, from which i t may be concluded that trace a l l o y s con- taining up to 3.0 wt % Sb can be introduced into pure t i n melts without solute density differences a f f e c t i n g the flow v e l o c i t y . 2.1.7.2.4. Evaluation of Technique The small s c a t t e r of the r e s u l t s p l o t t e d i n Figure 29 i n - dicates that t h i s technique for introducing tracer i s acceptably repro- ducible. Although previous investigations of t h i s technique (Section 2.1.4.) had shown that some f l u i d flow was associated with t r a c e r i n t r o - duction the magnitude of the flow must be n e g l i g i b l y small when compared with the v e l o c i t i e s which r e s u l t from thermal convection. This conclusion arises from the fact that the data p l o t t e d i n Figure 29 l i e s on a l i n e which passes through zero v e l o c i t y when zero thermal d r i v i n g force i s pre- sent. When the v e l o c i t i e s obtained i n Section 2.1.6.2.1. are p l o t t e d along with those of Figure 29 i t becomes apparent that introduction of 6 0 0 0 TIME (MIN) Figure 32. The e f f e c t on the flow v e l o c i t y of varying the density diff e r e n c e between the trace a l l o y and the melt. tracer by a piston mechanism has more mechanical mixing associated with i t than does the technique j u s t employed. This comparison appears i n Figure 33, the f i l l e d i n c i r c l e s are from Figure 29 and the open c i r c l e s which display s l i g h t l y l a rger s c a t t e r are the r e s u l t s obtained when tracer was introduced by the piston mechanism. The tracer i n t r o d u c t i o n technique of revolving a v e r t i c a l c y l i n d e r located i n the covered section of the boat was therefore permanently readopted and employed f o r a l l subsequent v e l o c i t y measurement and autoradiography experiments. 2.1.8. Single Aluminum Channel Supported by Graphite Reservoirs Although a s a t i s f a c t o r y tracer introduction technique has been developed the preliminary autoradiography r e s u l t s presented i n Section 2.1.6.2.2. indicated that melts contained i n the two channel graphite boat could not be quenched r a p i d l y enough. To decrease the quench time the graphite boat was replaced by a boat constructed of a sing l e aluminum channel with both ends held i n graphite r e s e r v o i r s . The s i n g l e channel boat was designed p r i m a r i l y to f a c i l i t a t e rapid quenching but was also used for v e l o c i t y measurement experiments since i t was anticipated that the l a t e r a l temperature gradients i n the aluminum boat might d i f f e r s i g n i f i c a n t l y from the larger cross-section graphite boat. 2.1.8.1. Experimental Apparatus and Procedure The new boat i s shown schematically i n Figure 34. The a l u - minum channel was 0.64 cm square (inside dimensions) and the o v e r a l l melt length was 37.5 cm, approximately 10 cm longer than that used i n previous 0 0 6 0 0 5 $ 0 - 0 4 H o - 0 0 3 o Q 0 0 2 > 0 0 1 0 0 0 0 from Figure 29 ©Rotating vertical cylinder O Piston mechanism 4 6 8 10 12 14 16 TEMP. DIFF. ACROSS MELT (°C) 18 2 0 Figure 33. Comparison of the flow v e l o c i t y measurements obtained employing the rotated v e r t i c a l cylinder and piston mechanism introduction techniques. iron-constantan thermocouples Figure 3 4 . D e t a i l s of the graphite end supported s i n g l e aluminum channel boat. 00 experiments. The channel was constructed by wiring a 0.05 inch t h i c k s t r i p of aluminum over the top of a length of 3 sided aluminum U-channel having a w a l l thickness of 0.06 inches. Thermocouples (30 gauge iron-constantan insulated by 2 hole, 1/16 inch O.D. m u l l i t e tubing) were inserted i n the graphite r e s e r v o i r s at the positions shown i n Figure 34. Four a d d i t i o n a l thermocouples were fix e d along the aluminum channel. These thermocouples were attached to the aluminum channel by d r i l l i n g 1/8 inch long, 0.02 inch diameter holes up the sidewalls of the channel, i n s e r t i n g the thermocouple wire, and then hammering the hole shut around the wire. S e l e c t i o n and con- t r o l of the temperature difference along the melt and introduction of tracer were c a r r i e d out i n the same way as described i n Section 2.1.7.1. The f i r s t c ollimator p o s i t i o n was approximately 5 cm downstream (towards the cold end) from the place of introduction and the second positon was 20 cm beyond the f i r s t . 2.1.8.2. Results and Discussions The r e s u l t s of v e l o c i t y determination experiments are tabu- lated i n Table 3 and pl o t t e d i n Figure 35. I t i s c l e a r l y evident from Figure 35 that the experimental r e s u l t s f i t a l i n e a r r e l a t i o n s h i p between observed flow v e l o c i t y and temperature difference between the hot and cold ends of the melt. The slope of the l i n e obtained f o r the 37.5 cm sing l e alumium channel boat i s less than that obtained f o r the 27 cm long two channel graphite boat used e a r l i e r . Possible causes f or t h i s difference i n slope are: TABLE 3 Flow V e l o c i t y Results Experiment Average A Temperature V e l o c i t y Number Temp. °C. °C cm/sec. 1 306 20 0.04 2 310 43 0.07 3 310 56 0.12 4 300 85 0.16 5 303 135 0.21 6 322 177 0.32 7 325 182 0.33 0 - 5 TEMP. DIFF. ACROSS MELT (°C) Figure 35. Comparison.of the flow v e l o c i t y measurements obtained employing the two channel graphite boat (Figure 29) and the sing l e aluminum channel boat. 00 (1) A difference i n the l a t e r a l temperature gradients i n the two boats. (2) A v a r i a t i o n of flow v e l o c i t y with t o t a l melt length. The e f f e c t of melt length on flow v e l o c i t y w i l l be discussed below when more experimental r e s u l t s are a v a i l a b l e . 2.1.8.3. Evaluation of Technique The a c c e p t a b i l i t y of the tracer introduction technique has been established. However, measurement of flow v e l o c i t i e s by the manual c o l l e c t i o n of a c t i v i t y versus time data i s extremely d i f f i c u l t when the flow v e l o c i t y exceeds 0.5 cm/second. Even with the larger monitoring i n t e r v a l used i n t h i s l a s t s e r i e s of experiments (20 cm as opposed to the 6.3 cm and 10 cm i n t e r v a l s used e a r l i e r ) there i s not s u f f i c i e n t time (less than 40 seconds) to c o l l e c t data that w i l l accurately determine the time of a r r i v a l of tracer above a given collimator p o s i t i o n . Furthermore, f o r flow v e l o c i t i e s exceeding 0.5 cm/sec a counting i n t e r v a l of 15 seconds i s far too long to y i e l d s u f f i c i e n t l y s e n s i t i v e data f o r accurate determina- ti o n of tracer a r r i v a l . I t i s , however, extremely d i f f i c u l t to manually c o l l e c t data with count time i n t e r v a l s appreciably less than 15 seconds. The necessity to move the collimator from one p o s i t i o n to the next further decreased the time a v a i l a b l e for monitoring the increase i n a c t i v i t y over the second collimator p o s i t i o n . Improvement i n the s e n s i t i v i t y of the tracer monitoring system was necessary before i n v e s t i g a t i o n of the v a r i - ation of flow v e l o c i t y with thermal d r i v i n g force could continue,to flow v e l o c i t i e s above 0.5 cm/second. These improvements and the r e s u l t s from them are discussed i n the next section. 2.2. Flow V e l o c i t y Determination by Dual Monitoring 2.2.1. Experimental Apparatus and Procedure To f a c i l i t a t e measurement of higher flow v e l o c i t i e s two collimator s l i t s were used and the a c t i v i t y of r a d i a t i o n passing through the s l i t s was monitored continuously with two separate Quantum E l e c t r o n i c Q6-A s c i n t i l l a t i o n counters. This arrangement i s shown schematically i n Figure 36. The collimator separation was 20 cm. In a t y p i c a l ex- periment the s i n g l e channel aluminum boat shown i n Figure 34 was placed i n the tube furnace and a desired temperature p r o f i l e along the melt was established and maintained for about one hour. When the tempera- 124 ture p r o f i l e had s t a b i l i s e d , the trace a l l o y (0.85 wt % Sb i n Sn) was introduced into the t i n melt. The v i s u a l display on the two sca l e r s plus the v i s u a l display from a Hamner NT-15F-1 timer was photographed on 35 mm f i l m at 5 second i n t e r v a l s . The f i e l d of view of the camera i s shown i n Figure 37(a) and some t y p i c a l data i n Figure 37(b). Analysis of the data c o l l e c t e d i s discussed below. 2.2.2. Analysis of A c t i v i t y Versus Time Data As active material approaches and passes through the section of l i q u i d subtended by the collimator s l i t the a c t i v i t y detected by the counter i n i t i a l l y increases slowly and then r a p i d l y . To e s t a b l i s h whether the shape of the a c t i v i t y - t i m e curves i s e n t i r e l y due to a corresponding increase i n a c t i v i t y i n the l i q u i d above the collimator s l i p or p a r t l y due to the collimating procedure used the following ex-  m i M i Fuacrtoi raiMR 8 5 Figure 3 7 . (a) Field of view of 3 5 mm camera employed to collect activity versus time data. (b) A section of the 3 5 mm film showing some typical data. 86 periment was c a r r i e d out. A 0.6 cm square b y 16 cm long rod of t i n 124 containing 100 ppm of Sb was positioned along the Vycor tube at various distances away from the region int e r s e c t e d by the collimator s l i t and the a c t i v i t y reaching the s c i n t i l l a t i o n counter was monitored f o r a 1 5 second i n t e r v a l . The r e s u l t s of t h i s test are shown i n Figure 38. The most important c h a r a c t e r i s t i c s of t h i s p l o t are: (1) There i s a marked increase i n the a c t i v i t y seen by the s c i n - t i l l a t i o n counters as the radioactive source approaches the collimator s l o t s . (2) The rapid increase i n a c t i v i t y as the radioactive source moves over the collimator s l o t i s spread over an i n t e r v a l of approximately 1 cm. (3) The count rate observed through collimator n o . l i s less than that observed through no.2. The collimators c l e a r l y do not exhibit a step function response to the movement of a radioactive source past them. The fact that the rapid i n - crease i n a c t i v i t y occurs over a 1 cm i n t e r v a l can be r e a d i l y understood by examining Figure 39. The collimator s l i t i s 1/8 inch wide by 4 inches long and the distance b e t w e e n the top of the collimator s l o t and the plane along which the radioactive source passes i s 3 inches. From Figure.39 i t can be seen that under these circumstances t h e . s c i n t i l l a t i o n counter sees an i n t e r v a l approximately 1 cm long at the plane of the radioactive source. Therefore, the rapid increase i n a c t i v i t y w i l l begin before the source i s d i r e c t l y over the collimator s l i t . The gradual increase i n a c t i v i t y reach- ing the s c i n t i l l a t i o n counter which occurs as the source approaches the  Source Level Figure 3 9 . Full size schematic diagram showing the length of melt subtended by the s c i n t i l l a t i o n detector. 89 the collimator s l i t i s a r e s u l t of ; (1) A decrease i n distance between the source and detector. (2) A decrease i n the thickness of lead s h i e l d through which the r a d i a t i o n must pass. The reason for the increased count rate observed through collimator no.2 i s that the a c t i v i t y versus counter voltage plateau for detector no.2 occurred at a higher voltage than f o r n o . l . This re s u l t e d i n a higher count rate being recorded by scaler no.2. To test the response of the collimator to a moving source, the 0.6 cm square by 16 cm long radioactive source was p u l l e d through the Vycor tube at a constant v e l o c i t y of 0.32 cm/second. The r e s u l t s of t h i s test appear i n Table 4 and are p l o t t e d i n Figure 40. The timer and sc a l e r readings appearing i n Table 4 were read o f f the 35 mm f i l m . Back- ground r a d i a t i o n was determined by f i x e d count timing p r i o r to movement of tracer. In Figure 40 the average net count rate during the time i n t e r - v a l has been p l o t t e d against the time at the end of the i n t e r v a l . It would be more correct to p l o t count rate versus the time at the middle of the i n t e r v a l , but, since a l l time i n t e r v a l s are f i v e seconds and the d i f f e r - ence i n time between the increase i n the a c t i v i t y at each collimator was the only measurement of i n t e r e s t this was not necessary. The most s i g n i f i - cant features of Figure 40 are: (1) As expected there i s a gradual increase i n a c t i v i t y before the tracer appears over the collimator. TABLE 4 Results of Dual Collimator S e n s i t i v i t y Test Collimator No .1 Collimator No .2 Background 58 cps Background 30 cps Time sec. Scalar Reading Net CR. cps Scalar Reading Net c; 5.0 440 10.0 695 0 14.9 965 0 19.9 1285 5 25.0 1760 35 29.8 2270 50 865 34.9 3500 180 1025 0 39.9 6000 440 1200 5 45.0 8640 460 1410 10 50.1 11300 465 1600 5 55.0 1815 15 60.0 2070 20 65.0 2365 30 70.1 2690 35 75.1 3100 50 80.0 3600 75 85.0 4190 90 90.0 4830 100 95.0 5510 105 100.0 6670 200 104.9 8930 430 110.0 11880 550 115.0 14870 570 120.1 17930 570 TIME (SEC) Figure 40. The response of the dual simultaneous counting to a constant a c t i v i t y source t r a v e l l i n g at a known v e l o c i t y . (2) In the ra p i d l y increasing portion of the curves the slopes are almost i d e n t i c a l . Since the tracer was of constant composition and t r a v e l l i n g at constant speed, the time rate of change of a c t i v i t y as the tracer moved over each collimator should be the same, that i s , the slopes i n the r a p i d l y i n - creasing portion of the curves should be i d e n t i c a l . For the case of constant composition tracer moving at constant speed, v e l o c i t y determination i s s i m p l i f i e d by the fac t that the time difference between appearance of tracer over the two collimator s l o t s may be obtained by taking the time difference at any average count r a t e , see Figure 40. The experimentally measured v e l o c i t y of 0.31 cm/second agrees w e l l with the "true" v e l o c i t y of 0.32 cm/second. During an actual experiment the tracer w i l l be d i l u t e d as i t moves through the melt. Even more important i s the fac t that the lead- ing edge of the tracer i s more d i l u t e than the regions behind the lead- ing edge. This i s shown i n the l o n g i t u d i n a l section autoradiographs appearing i n Figure 55 (Section 3.4.3.). I t i s apparent from Figure 55 that i n moving from the cold end towards the hot end (place of tracer introduction) the average cross s e c t i o n a l composition of tracer increases. The net r e s u l t o f . t h i s w i l l be that the slope of the l i n e a r portion of the collimator response curve w i l l be lower f o r collimator no.2 than f o r collimator n o . l . This e f f e c t i s shown i n Figure 41. I f the collimators were capable of sh i e l d i n g the s c i n t i l l a t i o n counters from a l l r a d i a t i o n other than that which reached them through the collimator s l i t i t s e l f , the a c t i v i t y versus time curves would probably be approximately l i n e a r 6 0 0 j 1 1 1 1 1 1 1 1 r TIME (SEC) Figure 41. T y p i c a l a c t i v i t y versus time data obtained by the simultaneous dual monitoring. vo starting from zero activity. Therefore, the intersection of the extra- polation of the rapidly increasing linear portion of the curve and the abscissa was taken to be the time at vihich the tracer f i r s t appeared over the collimator s l i t . The time difference at zero activity was used for a l l flow velocity measurements reported in this investigation. 2.2.3. Results and Discussion 2.2.3.1. Variation of Flow Velocity with Temperature Difference between the Hot and Cold Ends Figure 42 shows the increase i n flow Velocity which occurs as a result of increasing the temperature difference between the hot and cold ends of the melt. Data plotted in Figure 42 appears in Table 5. As observed previously (Figures 23, 29 and 35), the relationship between flow velocity and temperature difference is linear. The line represent- ing the data plotted in Figure 35 also appears in Figure 42. The same single aluminum channel boat was used for both series of experiments. Flow velocity measurements plotted in Figure 42 were obtained when the average melt temperature was approximately 400 °C (Table 4) whereas the average melt temperature for Figure 35 was 310 °C (Table 2). In Section 2.1.7.2.2. increasing the average melt temperature from 300 °C to 325 °C had no , apparent effect on the observed flow velocity. As can be seen from Figure 42 an increase in average melt temperature from 310 °C to 400 °C leads to a 25% increase in flow velocity. This apparent disparity is discussed in the next section. 2.2.3.2. Variation of Flow Velocity with Average Melt Temperature The dependence of flow velocity on average melt temperature is 0 4 0 8 0 120 160 2 0 0 240 280 320 3 6 0 4 0 0 TEMR DIFF. ACROSS M E L T (°C) Figure 42. The dependence of flow v e l o c i t y on the temperature difference between the hot and the cold ends of the melt. vo TABLE 5 Flow V e l o c i t y Results Experiment Average A Temperature V e l o c i t y Number Temp. °C. °C . cm/sec. 1 401 161 0.33 2 400 190 0.46 3 398 196 0.44 4 402 214 0.48 5 400 259 0.57 6 403 306 0.67 7 425 384 0.88 shown in Figure 43. The temperature difference across the melt was 214 °C for a l l three points. The increase in flow velocity with increas- ing average melt temperature might be anticipated since increasing the average melt temperature decreases the viscosity of the molten tin (Table 6). From Figure 43, one would expect about a 7% increase in flow veloc- ity as a result of increasing the average melt temperature from 300 °C to 325 °C. Since this increase was not observed in Section 2.1.7.2.2., i t must be concluded that manual collection of data from a single move- able collimator i s less sensitive than simultaneous dual monitoring of the flow velocity. 2.2.3.3. Variation of Flow Velocity with Total Melt Length The results of flow velocity measurements in melts of d i f f e r - ing lengths appear in Figure 44 and Table 7. The average melt temperatures were approximately 400 °C. Decreasing the total melt length from 48.5 cm to 37.5 cm and then to 28.8 cm leads to an increase in the flow velocity observed for a given temperature difference between the hot and cold ends. If flow velocity is plotted against the average temperature gradient across the melt, Figure 45, i t becomes apparent that velocity increases linearly-with increasing average temperature gradient. In Figure 46 data from Table 5 ( f i l l e d circles) has been.plotted along with the data in Table 7. From Figure 46 i t can be concluded that for covered liquid tin melts 0.64 cm high, ranging in length from approximately 25 to 50 cm and at an average temperature of 400 °C, the flow velocity i s linearly dependent on the average temperature gradient across the melt such that Velocity (cm/sec) = 0.082 x Temperature gradient (°C/cm). This relation- Figure 43. The e f f e c t on flow v e l o c i t y of varying the average melt, temperature (with a constant temperature diffe r e n c e across the melt of 214 °;C). TABLE 6 Properties of Molten T i n Temperature V i s c o s i t y S p e c i f i c Thermal. Coef. of Density (51) Heat Conductivity V ol. Exp. (53) (52) (52) (17) centip o i s e cal/gm°C cal/cm sec °C 1/°C x .10 gm/cm Kinematic V i s c o s i t y 2, cm /sec x 10 Thermal D i f f . 2 / cm /sec 250 300 400 500 1.70 1.53 1.29 1.15 0.0565 0.080 1.0229 1.0284 1.0393 1.0502 6.961 6.925 6.854 6.783 2.44 2.21 1.88 1.70 0.203 0.204 0.206 0.207 vo TEMR DIFF. ACROSS MELT (°C) Figure 44. The dependence of flow v e l o c i t y for three d i f f e r e n t melt lengths on temperature difference across the melt. TABLE 7 Flow V e l o c i t y Results f o r Three Melt Lengths 101 Experiment Melt A Temperature Temperature V e l o c i t y Number Length °C Grad. °C/cm cm/sec. 1 2 3 4 48.5cm 156 189 189 229 3.22 3.90 3 .90 4 .72 .27 .28 ,28 - .35 .39 5 6 7 8 9 37.5cm 92 156 158 196 231 2.46 4.16 4 .22 5 .22 6.17 .18 .36 .35 .43 .51 10 11 12 13 14 28.8cm 105 153 167 198 218 3.65 5.31 5.80 6.88 7.58 .29 .34 .52 .52 .54 AVERAGE TEMR GRAD. (°C/CM) Figure 45. The dependence of flow v e l o c i t y for three d i f f e r e n t melt lengths on the temperature gradient between the hot and cold ends of the melt. 0 - 9 0 - 8 o co 0 - 6 from Table 5 O from Table 7 2 3 4 5 6 7 8 A V E R A G E TEMP. GRAD. (°C/CM) 9 10 Figure 46. The dependence of flow v e l o c i t y on the temperature gradient across the melt with an average melt temperature of 400 °C. t— 1 o 104 ship holds true up to average h o r i z o n t a l temperature gradients of at l e a s t 10 °C/cm. In Section 2.1.8.2., Figure 35, i t was observed that the slope of the l i n e obtained for the 37.5 cm long s i n g l e aluminum channel boat was less than that obtained f o r the 27 cm long two channel graphite boat. Two possible causes for t h i s d i f f e r e n c e i n slope were offe r e d , namely, a difference i n l a t e r a l gradients and/or a dependence of flow v e l o c i t y on t o t a l melt length. When the flow v e l o c i t i e s appearing i n Figure 29 and 35 are p l o t t e d against average temperature gradient (as opposed to t o t a l temperature difference) across the melt, Figure 47, i t becomes apparent that the slope difference observed i n Figure 35 was a r e s u l t of flow v e l o c i t y dependence on t o t a l melt length. I f there were d i f f e r e n t l a t e r a l gradients i n the two channel graphite and s i n g l e aluminum channel boats they did not s i g n i f i c a n t l y effect the l o n g i t u d i n a l . flow v e l o c i t y observed. Figure 47 shows, i n agreement with Figure 45, that flow v e l o c i t y i s .linearly dependent on the average h o r i z o n t a l temper- ature gradient across the melt. The slope of the l i n e i n Figure 47 i s less than that i n Figure 45 since the average melt temperature was lower. 2.2.3.4. Evaluation of Technique In order to evaluate the s e n s i t i v i t y of t h i s flow v e l o c i t y measurement technique a series of experiments was performed i n which experimental procedures and parameters were var i e d from the norm. This was done to determine what e f f e c t inadvertent v a r i a t i o n s from normal ex- perimental procedure would have on the observed flow v e l o c i t y . Results 0 - 4 i 1 — r A V E R A G E T E M R GRAD. (°C/CM) Figure 47. Comparison of the v e l o c i t y versus temperature gradient r e s u l t s obtained using the two channel graphite boat and the sin g l e aluminum channel boat. Average melt temperature was approximately 310 °C. of these tests appear below. 2.2.3.4.1. E f f e c t on Flow V e l o c i t y of Varying the Nature of the Temperature D i s t r i b u t i o n Figure 48 compares the temperature d i s t r i b u t i o n imposed during two separate experiments designed to show that i t i s the average temperature gradient between the hot and cold ends of the melts, and not the average temperature gradient between the two collimator s l o t s (monitoring i n t e r v a l ) that determines the resultant flow v e l o c i t y . As can be seen i n Figure 48, the average temperature, gradient across the monitoring i n t e r v a l i s the same for both experiments. The average grad- ients between the hot and cold ends are however quite d i f f e r e n t . The flow v e l o c i t i e s observed for the two tests were 0.39 cm/sec f o r the ex- periment with the lower gradient, 5.0 °C/cm, and 0.47 cm/sec when the average gradient between the ends of the melt was 5.8 °C/cm. When these r e s u l t s are compared, Figure 50, to the r e s u l t s of Figure 46 excellent agreement i s found. C l e a r l y then,the average gradient across the t o t a l melt length and not that i n the monitoring i n t e r v a l i s responsible f o r the flow v e l o c i t y observed. Also, from Figures 48 and 50 i t can be concluded that the flow v e l o c i t y i s independent of the shape of the temperature p r o f i l e , that i s , whether the temperature d i s t r i b u t i o n between the hot and cold ends i s non-linear or nearly l i n e a r (as was generally the case) the same flow v e l o c i t y w i l l be observed when the average gradients are the same. The l i m i t i n g case occurs when there i s a maximum (or minimum) i n the temperature p r o f i l e between the hot and cold ends which stops f l u i d flow 2 5 0 1 1 * 1 1 1 1 0 5 10 15 2 0 25 30 35 POSITION ALONG BOAT (CM) Figure 48. Temperature p r o f i l e s from two experiments, designed to show that the temper- ature gradient across the melt, and not the gradient across the monitoring i n t e r v a l , i s the driving force for the observed v e l o c i t y . 108 at that point (Section 2.1.3.). 2.2.3.4.2. Effect on Flow Velocity of Varying the Position of the Monitoring Interval Although the position of the monitoring interval remained reasonably constant during a given series of experiments, experiments were conducted to determine whether changing the position of the monitor- ing interval would change the measured flow velocity. For these experi- ments a shorter interval of 13.8 cm was employed. The temperature pro- f i l e shown in Figure 49 was established and for the f i r s t test the monitoring interval was between thermocouples A and C. The graphite . boat was emptied and reloaded, the temperature profile of Figure 49 re- established, and the second experiment carried out with the monitoring interval between B and D. The average gradient across the melt was 5.1 °C/cm. The gradient between A and C was 4.3 °C/cm and that between B and D 6.0 °C/cm. Flow velocities determined from both intervals were approximately the same, 0.42 and 0.43 cm/sec respectively. If these velocities are plotted against the average temperature gradient between the hot and cold end, Figure 50, i t is found that they are in excellent agreement with the results of Figure 46. Thus, i t can be concluded that the position of the monitoring interval does not affect the flow velocity observed. However, i t was necessary to keep the f i r s t collimator s l i t approximately 5 cm downstream of the place of tracer introduction and thus avoid any spurious effects which may be associated with introduction of tracer. Figure 49. Temperature p r o f i l e from an experiment undertaken to determine the e f f e c t on flow v e l o c i t y of changing the p o s i t i o n of the monitoring i n t e r v a l . 0 '9 I 1 1 1 —r 1 1 1 1 — r 0 1 2 3 4 5 6 7 8 9 10 A V E R A G E TEMP. GRAD. (°C/CM) Figure 50. Comparison of the results of Figures 48 and 49 with results of Figure 46. 2.2.3.4.3. E f f e c t on Flow V e l o c i t y of Varying the Height of Metal i n the Reservoirs E a r l i e r i n the thesis i t was stated that the melt was covered for approximately 90% of i t s length with each end having an uncovered r e s e r v o i r . The height of l i q u i d metal i n the oovered portion was 0.64 cm while the melt was about 1 cm deep i n both r e s e r v o i r s . Since the height of l i q u i d metal i s a major parameter i n any f l u i d dynamics a n a l y s i s , ex- periments were conducted to determine the e f f e c t on flow v e l o c i t y of varying the height of metal i n the r e s e r v o i r s . I t was found that reducing the melt height i n the reservoirs from. 1 cm to 0.7 cm had no e f f e c t on the flow v e l o c i t y . This i s shown i n Figure 51 were the v e l o c i t y of 0.50 cm/second measured for the 0.7 cm height i s p l o t t e d on the l i n e from Figure 46, where the height of melt i n the r e s e r v o i r was 1.0 cm. Thus, i t can be concluded that the height of melt i n the reservoirs does not effect the observed flow v e l o c i t y and, therefore, i t i s appropriate to use the height i n the covered sec t i o n , namely 0.64 cm, for the purpose of analyzing the h o r i z o n t a l melt system studied here. Another v a r i a t i o n i n experimental procedure which may a f f e c t the observed flow v e l o c i t y i s a diffe r e n c e i n height of metal in;the two r e s e r v o i r s . The tracer introducer i s i n the closed position (blocking the channel) when the boat i s loaded with pure t i n . I t i s quite possible then that the height of metal i n one r e s e r v o i r was d i f f e r e n t than i n the other. Thus, when the tracer was introduced i n t o the boat by r o t a t i n g the c ylinder there would be a head of l i q u i d metal i n one r e s e r v o i r and th i s would most assuredly cause f l u i d motion through the channel. An experiment was conducted i n which a 0.3 cm difference i n l i q u i d l e v e l i n the hot and cold reservoirs was established p r i o r to r o t a t i o n of the 0*9 i i 1 1 — i 1 — i 1 1 r 0 f 2 3 4 5 6 7 8 9 10 AVERAGE T E M P GRAD. (°C/CM) Figure 51. The effect on flow velocity of varying the liquid metal height in the reserviors and of introducing the tracer near the cold end. tracer introducer. V i s u a l observation of the melt following r o t a t i o n of the cylinder to the open p o s i t i o n showed a rapid r i s e i n the l i q u i d l e v e l i n what had been the low l e v e l end. This was followed by o s c i l l a t o r y f l u c t u a t i o n s i n the r e s e r v o i r l e v e l s . The o s c i l l a t i o n s disappeared with- i n 10 to 15 seconds. To determine the e f f e c t of l i q u i d head i n the r e s e r v o i r s on the flow v e l o c i t y a s e r i e s of experiments was conducted i n which there was: (1) A 0.3 cm head i n the hot r e s e r v o i r , -G = 5.5 °C/cm. (2) Levels i n hot and cold reservoirs equal, G = 6.1 °C/cm. (3) A 0.3 cm head i n the cold r e s e r v o i r , G = 5.6 °C/cm. The a c t i v i t y versus time curves for these three experiments are shown i n Figures 52(a), 52(b) and 52(c) r e s p e c t i v e l y . In going from Figure 52(a) to ( c ) , there i s an increase i n the time required for tracer to reach the f i r s t collimator s l i t . (Recall that the tracer i s introduced at the hot end). However, when the flow v e l o c i t y i s p l o t t e d versus average gradient (opened c i r c l e s i n Figure 51), the points coincide with the l i n e taken from Figure 46. The i n i t i a l l e v e l i n g of the reservoirs causes a surge of tracer i n the l e v e l i n g d i r e c t i o n , but apparently, the subsequent os- c i l l a t o r y motion has no net e f f e c t on the flow v e l o c i t y . Since the 0.3 cm difference i n r e s e r v o i r l e v e l was much larger than that which could have normally occurred during a series of experiments i t was concluded that differences i n melt l e v e l i n the r e s e r v o i r s could not have eff e c t e d the flow v e l o c i t i e s observed. 114 Figure 52 (a). A c t i v i t y versus time r e s u l t s when there was a 3 mm head of l i q u i d t i n i n the hot r e s e r v o i r . 115 Figure 52(b),, A c t i v i t y versus time r e s u l t s when there was no diffe r e n c e i n the l i q u i d t i n l e v e l i n the hot and cold r e s e r v o i r s . 116 Figure 52(c). A c t i v i t y versus time r e s u l t s when there was a 3 mm head of l i q u i d t i n i n the cold r e s e r v o i r . 117 2.2.3.4.4. E f f e c t on Flow V e l o c i t y of Introducing Tracer i n the Cold End of the Melt In almost a l l the v e l o c i t y measurement experiments tracer was introduced near the hot end of the melt. To determine whether addi- tion near the hot end, as opposed to near the cold end, was s i g n i f i c a n t an experiment was conducted i n which tracer was introduced near the cold end. The r e s u l t s are p l o t t e d i n Figure 51 (open t r i a n g l e ) . The ex-1 c e l l e n t agreement with the l i n e taken from Figure 46 leads to the con- clusio n that the s i t e of introduction, e i t h e r near the hot end or cold end, has no bearing on the flow v e l o c i t y measured by the present tracer monitoring technique. 2.2.3.4.5. Extent of Inductive Mixing The fa c t that the tube furnace which surrounded the melt was ind u c t i v e l y wound necessitated i n v e s t i g a t i o n of the extent of e l e c t r o - magnetic s t i r r i n g . This was p a r t i a l l y accomplished by conducting a ser i e s of"power off"experiments. In these experiments a desired temper- ature gradient was established, the furnace power was then turned o f f and introduction of tracer took place some time l a t e r . The s o l i d c i r c l e s appearing i n Figure 53 are the r e s u l t s of four experiments i n which the furnace power was turned o f f at 1, 3, 3 and 5% minutes p r i o r to tracer introduction. The sc a t t e r about the re s u l t s of Figure 46 indicates that there i s no s i g n i f i c a n t inductive s t i r r i n g i n the l o n g i t u d i n a l d i r e c t i o n . Further evidence of the absence of inductive mixing was ob- tained from the following experiments. The furnace power, heating block Q . 9 1 — i j 1 1 1 1 1 1 r 0 I 2 3 4 5 6 7 8 9 10 AVERAGE TEMR GRAD. (°C/CM) Figure 53. Results of the i n v e s t i g a t i o n of the extent of inductive.mixing. power and argon flow rate were adjusted to give a temperature gradient of approximately 6 °C/cm and the resulting flow velocity determined. Employing the same furnace power settings; the heating block power and argon flow rate were adjusted to give a gradient of approximately 4 °C/cm and the resulting velocity measured. The tube furnace windings are the only possible cause of electromagnetic stirring in the liquid metal. If induced flow due to the furnace windings contributes i n a major way to the driving force of the observed flow, then, since the furnace power settings were identical for the two experiments just described, one would expect to observe similar flow velocities. The results 'of these experiments are the open circles plotted in Figure 53. The agreement between these results and the results of Figure 46 is very good. Clearly then, i t i s the average temperature gradient across the melt, that i s , the thermal driving force, and not an electromagnetic driving force, which determines the velocity dependence obtained in Figure 46. 2.2.3.4.6. Reproducibility of Results Most of the experiments presented in this "Evaluation of Technique" Section were conducted during different phases of the project The f i r s t stage of any series of experiments was to correlate the i n i t i a l results to the results of Figure 46. It was found that as long as the average melt temperature was approximately 400 °C agreement between experi ments to reconfirm the velocity versus average temperature gradient depend ence and the results shown in Figure 46 was good. This occurred even when the appearance,that i s , the slope of the rapidly increasing portion and maximum activity of the activity versus time curves changed. Changes 120 i n the appearance of the a c t i v i t y versus time curves occcurred as a r e s u l t of weakening of the t r a c e r , due to radioactive decay, and as a r e s u l t of s l i g h t i r r e g u l a r i t i e s accompanying tracer i n t r o d u c t i o n . 2.2.3.4.7. Summary of Technique Evaluation The dual collimator system with photography of the video s c a l e r and timer outputs allows accurate and reproducible measurement of flow v e l o c i t i e s up to approximately 1 cm/second. I t has been established previously that the introduction technique of ro t a t i n g a v e r t i c a l c y l i n d e r located i n the covered section of the melt causes le s s interference with normally occurring f l u i d flow than any of the other techniques i n v e s t i - gated. Furthermore, the i n s e n s i t i v i t y of observed flow v e l o c i t y with respect to s l i g h t v a r i a t i o n s i n experimental procedure confirms the a c c e p t a b i l i t y of the data analysis employed. R e p r o d u c i b i l i t y of data has been excellent and the accuracy of the r e s u l t s , from Figure 46,appears to be of the order of ± 10% or better. The s c a t t e r of r e s u l t s about the l i n e drawn i n Figure 46 would probably have decreased had more care been taken i n holding average melt temperature constant. 2.3. Summary of ELow V e l o c i t y Determination Results A summary of a l l r e s u l t s obtained throughout the course of t h i s i n v e s t i g a t i o n leads to the following important conclusions: (1) F l u i d flow a r i s i n g from thermal convection w i l l not cause mass transfer through a region of zero h o r i z o n t a l temperature gradient. (2) An extremely small h o r i z o n t a l temperature gradient, apparently any non-zero gradient, provides s u f f i c i e n t thermal d r i v i n g force for f l u i d flow. (3) The flow v e l o c i t i e s observed are the r e s u l t of the presence of buoyancy forces created by the h o r i z o n t a l temperature difference across the melt. These v e l o c i t i e s are not de- pendent on electro-magnetic s t i r r i n g e f f e c t s . (4) The v e l o c i t y of f l u i d flow increases with; increasing average melt temperature, increasing temperature diff e r e n c e across the melt, and decreasing t o t a l melt length (for a given temperature d i f f e r e n c e ) . (5) For the covered h o r i z o n t a l rod configuration i n v e s t i g a t e d herein the flow v e l o c i t y i s l i n e a r l y dependent on the average temperature gradient between the hot and cold ends of the melt. 122 3 - FLOW PATTERNS IN HORIZONTAL RODS OF MOLTEN TIN 3.1. Introduction To completely define f l u i d flow i n l i q u i d metals the flow pattern i n the melt, as w e l l as the flow v e l o c i t i e s , must be s p e c i f i e d . Preliminary autoradiography r e s u l t s presented i n Section 2.1.6.2.2. i n - dicated the presence of a transverse double c e l l flow pattern. There was no evidence of the l o n g i t u d i n a l m u l t i - c e l l flow patterns suggested by Utech et a l ^ " ^ and Stewart However, i t could not be established unambiguously that the flow patterns shown i n Figure 25 and 26 were d i - r e c t l y associated with the f l u i d flow and not p a r t i a l l y due to quenching e f f e c t s . The r e l a t i v e l y long time (greater than 15 seconds) required f o r quenching plus the fact the tracer introduction was from the cover of the boat suggested that the flow patterns observed were not representative of the f l u i d flow i n the melt. In order to appreciably reduce the quench- ing time the si n g l e channel thin walled aluminum boat was adopted f o r sub- sequent flow pattern observation experiments. 3.2. Experimental Apparatus and Procedure The aluminum boat used to contain the melt i s that shown pre- vi o u s l y i n Figure 34. The square channel portion of the boat was sur- rounded by a 3/4 inch I.D. open ended copper quenching jacket. Quench- ing water was directed from the cold end towards the hot end. The water 123 supply to the quenching jacket was co n t r o l l e d by a pressure reducer and valve. In a t y p i c a l experiment a desired temperature d i f f e r e n c e across the melt was established and maintained f o r approximately one hour, the tracer was then introduced into the melt and quenching took place at some s p e c i f i e d time a f t e r introduction. The water pressure at the be- ginning of the quench was 5 psig and was quickly increased to about 15 psig once quenching had been i n i t i a t e d . Water pressure was kept low at the beginning of the quench to prevent any water surges from p h y s i c a l l y disturbing the boat. A f t e r quenching, the t i n f i l l e d aluminum channel was cut from the graphite ends with a jewellers saw. The sample was then sectioned, mechanically polished, and placed on double emulsion X-ray f i l m f o r a period of time s u f f i c i e n t to y i e l d a s a t i s f a c t o r y auto- radiograph. The autoradiograph r e s u l t s from the r a d i a t i o n received from a f i n i t e thickness of material adjacent to the photographic f i l m . The thickness of th i s contributing layer increases with increasing energy of r a d i a t i o n , thus reducing the r e s o l u t i o n obtained i n the autoradiograph. 113 Since the r a d i a t i o n from Sn (X-ray and gamma less than 0.4 Mev) i s 12 ̂  1X3 much less energetic than that from Sb (gamma up to 2 Mev), Sn was used f o r the flow pattern experiments. The trace a l l o y commonly used for the flow pattern experiments was 0.85% non-radioactive Sb i n pure 113 Sn with approximately 3.5% Sn . This a l l o y has the same density as the trace a l l o y used for the v e l o c i t y determination measurements c a r r i e d out i n the previous section. 3.3. Results from Quenching Wired Top U-Channel In i n i t i a l experiments the square aluminum channel had been 124 constructed by wiring an aluminum cover over aluminum U-channel. A l l attempts to obtain s u i t a b l e quenched specimens for autoradiography f a i l e d since quench water was able to seep under the cover and react v i o l e n t l y with the l i q u i d metal. 3.4. Autoradiography of Quenched Specimens Using a Completely Closed Square Aluminum Channel 3.4.1. Experimental Apparatus and Procedure In order to avoid the disasterous r e s u l t s brought on by contact of quench water with the melt i t became necessary to obtain t o t a l l y enclosed square channel. I t was not possible to obtain 1/4 inch square aluminum channel from commercial sources and therefore an approxi- mately square channel was manufactured from 3/8 inch O.D., 0.038 inch w a l l thickness aluminum tubing. This was accomplished by f o r c i n g the tubing over a 1/4 inch square mandrel (with s l i g h t l y rounded corners) followed by r o l l i n g i n a h o r i z o n t a l r o l l i n g m i l l . The r e s u l t i n g channel was approximately 0.26 inches square with the corners having a radius of curvature of about 0.03 inches. The channel was cut to length such that the o v e r a l l melt length was the same, as that used i n Section 2.1.8. and most of Section 2.2., namely 37.5 cm. The channel, surrounded by the quenching jacket, was inserted into the graphite r e s e r v o i r s and the j o i n t s were sealed with Sairset cement. General experimental procedure for obtaining autoradiographs has already been described i n Section 3.2. 3.4.2. Results from Square Aluminum Channel With No Water Shield Even with the t o t a l l y enclosed square aluminum channel quench- 125 ing of melts to provide specimens f o r subsequent autoradiography usually r e s u l t e d i n the spraying of melt out of the hot r e s e r v o i r . This caused a decrease i n the l i q u i d metal l e v e l i n the hot end of the channel and again re s u l t e d i n specimens which were unacceptable f o r autoradiography. It appeared that quench water, which was dir e c t e d from the cold and to- wards the hot end of the channel, was able to leak through the S a i r s e t cemented aluminum channel-graphite r e s e r v o i r j o i n t and cause v i o l e n t d i s - ruption of the melt at the hot end. Another possible cause could be that quench water h i t the hot graphite r e s e r v o i r creating a spray of water i n the v i c i n i t y of the r e s e r v o i r with some of the spray f i n d i n g i t s way into the uncovered section of the r e s e r v o i r . 3.4.3. Results and Discussion of Experiments Using Aluminum Channel with a Water Shield To prevent water from leaking through the aluminum channel- graphite r e s e r v o i r j o i n t and to remove the p o s s i b i l i t y of water f i n d i n g i t s way i n t o the uncovered section of the r e s e r v o i r a 3/32 inch t h i c k , 3/4 inch O.D. aluminum water s h i e l d was welded around the aluminum channel at approximately 1/8 inch from the hot end support. As before, the channel, equipped with water s h i e l d and surrounded by the quench jacket, was cemented into the r e s e r v o i r s . A l l autoradiographs which appear i n t h i s subsection were obtained from quenched melts which had an average temperature gradient of approximately 6 °C/cm. Figure 54 shows how most of the specimens were sectioned for autoradiography. Sections were taken perpendicular to the l o n g i t u d i n a l axis of the rod at 0.5 cm i n t e r v a l s s t a r t i n g at 4 cm from the point of introduction. Several other specimens were sectioned p a r a l l e d to the "outside" w a l l i n order to Water shield End of—1 sectioning Outside Start (~4cm from introduction point) Figure 54. Schematic representation showing the positions at which the specimen was sectioned to obtain the transverse section autoradiographs. (a) Hot Cold (b) Hot Cold Figure 55. Longitudinal section autoradiographs of specimens quenched (a) AO sec. and (b) 1 minute a f t e r introduction of trace a l l o y (0.85% Sb i n pure Sn containing 3.5% Surface autoradiograph was 0.04 inches below outside surface (X2). Sn ) S3 128 determine the flow pattern i n the l o n g i t u d i n a l d i r e c t i o n . Figure 55 shows autoradiographs of l o n g i t u d i n a l sections of specimens which have been quenched 40 seconds (Figure 55(a)) and 1 minute (Figure 55(b)) a f t e r tracer introduction. The surface autoradiographed was approximately 0.04 inches below the outside surface of the t i n . The d i s t r i b u t i o n of tracer i n both specimens i s e s s e n t i a l l y i d e n t i c a l and, as expected, the tracer has moved farther along the melt i n the specimen that was quenched one minute a f t e r i n t r o d u c t i o n , Figure 55(b), than i n the specimen quenched 40 seconds a f t e r tracer i n t r o d u c t i o n . There i s no evidence of m u l t i - c e l l flow. I t appears that the l o n g i t u d i n a l flow i s u n i c e l l u l a r with l i q u i d moving from the hot end to the cold end along the top of the melt and returning from the cold end to the hot end along the bottom. This statement i s not confirmed by the autoradiographs of Figure 55 since i t i s apparent that tracer has not reached the cold end of the melt and therefore the tracer which appears at the bottom of the melt did not a r r i v e there as a r e s u l t of u n i c e l l u l a r l o n g i t u d i n a l flow. The transverse section autoradiographs, Figure 56, of another specimen which was quenched 40 seconds a f t e r tracer introduction show that the tracer has been c a r r i e d towards the bottom of the melt by a transverse flow which i s superimposed on the u n i c e l l u l a r l o n g i t u d i n a l flow. The sections i n Figure 56 are at 1 cm i n t e r v a l s along the rod s t a r t i n g at 4 cm from the point of introduction i n the hot r e s e r v o i r . Going from the hot end to the cold end of the melt the flow pattern becomes less com- plex but t h i s i s most probably due to the fac t that as the tracer approaches the cold end i t has spent less time at a given p o s i t i o n and therefore the transverse flow has had less time to sweep the tracer with i t i n order to Top Figure 56. Transverse section autoradiographs of a specimen quenched 40 sec. a f t e r introduction of 113 Sn -Sb-Sn tracer. Sections are at 1 cm i n t e r v a l s with the s t a r t (top l e f t hand corner 4 cm from point of introduction near the hot end (x 4). 130 outline the complete flow pattern. In order to study the development of the transverse flow pattern, Figures 57 and 58 have been prepared so that a comparison can be made between the transverse flow observed AO seconds, 1 minute, and 2 minutes a f t e r tracer i n t r o d u c tio n . The f i r s t , t h i r d and f i f t h rows of Figure 57 are transverse sections from the 40 second specimen and the second, fourth and s i x t h rows are from equivalent po s i t i o n s along the specimen quenched 1 minute a f t e r introduction of tracer. As expected, and i n agreement with Figure 55, tracer has moved further along the specimen quenched 1 minute a f t e r introduction. Comparison of rows three and four shows that increased time before quenching has also allowed more extensive transverse flow of the tracer. Figure 58 compares the specimens quenched 1 minute (rows one, three and f i v e ) and 2 minutes (rows two, four and s i x ) a f t e r t r a c e r introduction. There i s no obvious diffe r e n c e i n the transverse flow patterns observed at each point along the melt. The extra minute before quenching has no doubt allowed more extensive d i l u t i o n of the trac e r by the melt. This i s r e f l e c t e d i n the f a c t that the time required to obtained a s u i t a b l e autoradiograph of the 2 minute specimen was 240 hours whereas only 24 hours was required for the 1 minute specimen. Since 1 minute was s u f f i c i e n t time f o r the tracer to t r a v e l from the place of i n troduction to the cold end of the aluminum channel, i t would be ex- pected that 2 minutes would be enough time for the tracer to pass through the cold r e s e r v i o r and, at the cold w a l l , move to the bottom of the boat and proceed along the bottom of the melt back towards the hot end. Thus, one would expect to observe tracer along the bottom of the transverse Figure 57. Comparison of transverse section autoradiographs from specimens quenched 40 seconds ( f i r s t , t h i r d and f i f t h rows) and 1 minute (second, fourth and s i x t h rows) a f t e r introduction. r f * r k ^ r m n o p < > — — i Figure 57 - Continued. Figure 58. Comparison of transverse section autoradiographs from specimens quenched 1 minute ( f i r s t , t h i r d and f i f t h rows) and 2 minutes (second, fourth and s i x t h rows) a f t e r introduction. Figure 58 - Continued. 135 section autoradiographs of the melt which was quenched 2 minutes a f t e r tracer i n t r o d u c t i o n . The f a c t that tracer i s not observed along the bottom of these sections can be explained by r e c a l l i n g that extensive d i l u t i o n of the tracer has occurred over the two minutes and therefore i t i s conceivable that by the time the tracer has moved to the bottom of the melt v i a the u n i c e l l u l a r l o n g i t u d i n a l flow i t has become s u f f i c i - ently d i l u t e d to be undetectable by autoradiographing f o r a reasonable length of time. The e f f e c t of small v a r i a t i o n s i n trace a l l o y density on the transverse flow pattern was also studied during, t h i s phase of the pro- j e c t . As outlined previously, the trace a l l o y used to obtain the auto- radiographs shown i n Figures 55-58 contained 0.85% Sb and was therefore s l i g h t l y less dense (0.9994 pSn) than the melt. Figures 59-61 show the transverse flow patterns observed one minute a f t e r introducing trace a l l o y whioh i s of lower density (Figure 59), equal density (Figure 60) and greater density (Figure 61) than the melt. The trace a l l o y used to 113 obtain Figure 59 was 0.85% Sb i n pure Sn (with 3.5% Sn ) and was 113 0.9994 times the density of the pure t i n melt. A 3.5% Sn i n pure t i n 204 was the equal density trace a l l o y and a 0.5% TI i n Sn trace a l l o y was prepared to observe the e f f e c t on the flow pattern of having the tra c e r more dense than the melt (1.0020 pSn). Although these density d i f f e r - ences due to a l l o y i n g are small, they must be considered s i g n i f i c a n t i n comparison to the density changes a r i s i n g from temperature d i f f e r e n c e s . For a l i q u i d the r e l a t i v e change i n density due to a temperature d i f f e r - ence i s given by: pT„ - ~ = 1 - B (T - T ) pT 2 1 •••nnnnn Figure 59. Transverse section autoradiographs of a specimen quenched 1 minute af t e r introduction of a trace a l l o y containing 0.85% Sb in S n 1 1 3 with 3.5% Sn (0.9994 p S n ) . Figure 60. Transverse section autoradiographs of a specimen quenched 1 minute a f t e r introduction 113 of a trace al l o y containing 3.5% Sn i n Sn (1.0000 pSn).  where $ is the volume coefficient of thermal expansion. Since g for -4 /o molten t i n is of the order of 10 / C the change in density arising from small local temperature differences w i l l be of the same order of magnitude as those caused by the addition of a small amount of alloying element- The flow pattern illustrated in Figures 59-61 are essentially identical and therefore i t can be concluded that the thermal convective flow i s sufficiently strong to overcome the solute convection which might be expected i n view of the density difference between the trace alloys and the melt. In going from the less dense to the more dense trace alloy i t might be expected that there would be an increased tendency for tracer to move via solute convection from the top to the bottom of melt. This was not observed. To this point in the autoradiography studies, trace alloy has been introduced near the hot end of the melt and i f i t followed a unicellular longitudinal flow i t would be expected to move along the top of the melt from the hot to cold end and then return along the bottom of the melt. A transverse autoradiograph of the unicellular flow would then look like Figure 62 (providing there had been sufficient time for tracer to make a complete circuit with the flow). Under the experimental condition of an average temperature gradient along the melt of approximately 6 °C/cm, 2 minutes should be sufficient time for tracer to outline the return flow (from cold to hot) along the bottom of the melt. Figure 58 (rows two, four and six) showed the 1 cm interval transverse sections from a specimen which had been quenched 2 minutes after tracer introduction and there was no evidence of a tracer rich region along the bottom of the melt. The fact that tracer did not appear along the bottom of melt has been ex- ure 62. The expected appearance of a trans- verse section autoradiographs i f on u n i c e l l u l a r l o n g i t u d i n a l flow were present (X12). 141 plained by assuming that the tracer became diluted to the extent that i t was not detectable by autoradiographing (for a reasonable length of time). To f a c i l i t a t e observation of flow along the bottom of the melt two experiments were conducted in which tracer was introduced in the cooler section of the melt. (This was accomplished by interchanging the heating and cooling blocks so that the graphite end support in which the introduction took place became the cold end). As before the average temperature gradient along the melt was 6 °C/cm. Quenching was initiated one minute after tracer introduction in both cases. Figure 63 shows the trans- verse section autoradiographs (the f i r s t being 4 cm from the place of introduction in the cold reservoir and subsequent sections at 1 cm inter- 204 vals towards the hot end) obtained after introducing a 0.5% TI in Sn tracer into the melt. As expected the tracer moves from the cold end to the hot end along the bottom of the melt. Approximately one-third of the way along the channel transverse flow i s observed. Although the trace alloy is slightly more dense than the melt (1.0020 pSn) the trans^ verse flow is sufficiently strong to cause mixing of tracer throughout the cross section . The nature of the transverse flow is similar to that observed in Figures 56-61. The flow travels down the sides of the section and as i t returns to the top, through the middle of the section, the radioactive tracer is drawn upwards by i t . The transverse flow is greatly suppressed by using a dense (1.257 pSn) trace alloy composed of 60% Pb in Sn containing 0.5% TI , Figure 64. In Figures 56-61 the apparent extent of transverse flow de- creases with increasing distance from the point of introduction near the Fig ure 63. Transverse sect ion autoradiographs of a specimen quenched 1 minute af t e r introduct ion 2 0 A of a trace a l l o y containing 0.5% TI in Sn. The f i r s t section (top l e f t hand corner) i s 4 cm from the point of introduction near the cold end. •p- lo T r a n s v e r s e s e c t i o n a u t o r a d i o g r a p h s of a s p e c i m e n quenched 1 m i n u t e a f t e r i n t r o d u c t i o n O A / o f a t r a c e a l l o y composed of 60% Pb i n Sn contained 0.5% TI . I n t r o d u c t i o n t o o k p l a c e n e a r t h e c o l d end. 144 hot end. This has been explained by noting that as the distance from the introduction s i t e increases the tracer has had continuously de- creasing time i n which to f u l l y o u t l i n e the transverse flow present. The net r e s u l t i s that one would observe move extensive transverse flow near the hot end (place of introduction)than near the cold end. In Figures 63 and 64 i t i s observed that the extent of transverse flow increases with increasing distance from the place of introduction. This observation i s not consistent with the explanation j u s t offered. Recalling that Figures 56-61 were obtained by introducing tracer i n the hot end whereas for Figures 63 and 64 intr o d u c t i o n took place i n the cold end (and the f i r s t section in. each fi g u r e i s approxi- mately 4 cm from the place of in t r o d u c t i o n ) , i t i s apparent that trans- verse flow i s more extensive near the hot end than the cold end. Since more heat must be removed from the hot end than the cold end of the melt during quenching i t i s pos s i b l e that more time i s required f o r s o l i d i f i c a t i o n i n the hot end and that during t h i s a d d i t i o n a l time more extensive transverse flow may occur. Also, l a t e r a l temperature gradients which a r i s e during quenching may cause transverse flow that i s more ex- tensive than was occurring p r i o r to quench i n i t i a t i o n . The r e s u l t s of quench time determination experiments and several other tests to attempt to confirm the v a l i d i t y of the observed flow patterns as we l l as the driv i n g force for the transverse flow are discussed i n the next se c t i o n . 3.4.4. Results and Discussion of Attempts to Confirm the V a l i d i t y of Observed Flow Patterns 3.4.4.1. E f f e c t of Quench Cylinder on Observed Flow V e l o c i t y In order to determine what, i f any, e f f e c t the presence of 145 the quenching cylinder had on the flow taking place in the melt a velocity determination experiment was carried out in which the quench cylinder was in place. The results of this experiment were velocity equals 0.36 cm/sec for an average temperature gradient across the melt of 4.16 °C/cm. Figure 46 shows that for a gradient of 4.16 °C/cm one would expect to observe a flow velocity of 0.35 cm/sec. From this i t can be assumed that the quench cylinder does not affect the longitudinal flow. 3.4.4.2. Quench Time Determination The time required for complete s o l i d i f i c a t i o n was determined at both the hot and cold ends of the square aluminum channel. The thermocouples (30 gauge iron-constantan insulated by 1/16" O.D. mullite tubing) were inserted through the top of the channel such that the beads were located in the cross sectional centre of the melt. The hot end thermocouple was positioned 5 mm downstream from the water shield and the cold end thermocouple was 5 mm ahead of the cold end support. The thermocouples were connected through a multipoint switch to the Honey- well recorder. Results of typical quench time determination tests are shown in Figure 65. On the basis of six tests the average time for total s o l i d i f i c a t i o n at the hot end was 2\ seconds and at the cold end was h\ seconds. At f i r s t glance a somewhat surprising result. The latent heat of fusion of t i n is 14.5 cal/gm and the heat capacity of liquid tin at 350 °C is approximately 0.06 cal/gm °C. If the hot end of the melt was 200 °C higher than the cold end the amount of heat that would have to be removed from the hot end would be roughly 1.2 cal/gm more than that removed from the cold end. Since this i s less 146 Figure 65. T y p i c a l r e s u l t s of quench time determination experiments. 147 than 10% of the heat of fusion i t would not be unreasonable for the hot and cold ends to s o l i d i f y i n approximately the same length of time. Also, since the quench water enters the chamber 3 cm ahead of the cold r e s e r v o i r and the stream i s dir e c t e d towards the water s h i e l d at the hot end, the observation that the hot end of the channel s o l i d i f i e s 2 seconds before the cold end i s understandable. In any case, the quench time tests conclusively show that the hot end does not take longer to s o l i d i f y than the cold end. The p o s s i b i l i t y that the more extensive transverse flow i n the hot end r e s u l t s from delayed quenching i n t h i s region must be ruled out. 3.4.4.3. Quenching i n a Prearranged Tracer D i s t r i b u t i o n The p o s s i b i l i t y that the quenching operation was the prime driving force for the development of the observed transverse flow pattern was further investigated by conduction experiments which involved quenching a melt which had a prearranged and thus known tracer d i s t r i - bution. The prearranged tracer d i s t r i b u t i o n i s shown i n Figure 66. This d i s t r i b u t i o n was achieved by the following technique. A 0.04 inch t h i c k , 113 0.24 inch wide by 11 inch long layer of 0.5% Sn i n Sn was placed along the bottom of a square aluminum channel which was an inch longer than the usual channel length. The graphite ends were attached and the boat placed i n the furnace. A furnace temperature of 200 °C(30 °C below the melting point of pure t i n ) was established and maintained. When the temperature along the boat was 200 °C l e a d - t i n e u t e c t i c (m.p. 183 °C) at approximately 210 °C was poured into the boat. Upon s o l i d i f i c a t i o n of the e u t e c t i c the boat was removed from the furnace and the channel (a) Figure 66. Schematic representation of the prearranged tracer d i s t r i b u t i o n (a) transverse section and (b) l o n g i - tudinal section. i—1 00 149 which now had l e a d - t i n e u t e c t i c over the 3.5% Sn i n Sn layer was removed with a jewellers saw. The r e s e r v o i r s were reheated to remove the eu t e c t i c and the ends of the aluminum channel which were l e f t a f t e r 113 sawing. The channel was then inverted so that the Sn layer was above the e u t e c t i c , the boat was reassembled and the re s e r v o i r s r e f i l l e d . The aluminum blanks were placed across each end of the channel to insure that, once molten, no movement of the melt (due to differences i n head between the hot and cold r e s e r v o i r s or due to p h y s i c a l disturbance) could occur through the channel and thus change the tracer d i s t r i b u t i o n . In the f i r s t test the boat, with the tracer d i s t r i b u t i o n j u s t described, was gradually heated to approximately 285 °C to give a super- heat of about 100 °C. This superheat was chosen so as to reproduce the conditions of e a r l i e r quenching experiments where the average superheat was of the order of 100 °C. During the melting and superheating a l l possible care was taken to maintain a zero h o r i z o n t a l temperature gradient along the melt and thus avoid the p o s s i b i l i t y of thermal con- vection. Solute convection should not occur since the configuration of the less dense t i n layer over the more dense e u t e c t i c (1.257 pSn) should be stable. Since neither solute nor thermal convection i s expected,the quenched specimen should y i e l d transverse section autoradiographs which are s i m i l a r to Figure 66(a). Results of t h i s f i r s t test showed a com- p l e t e l y uniform d i s t r i b u t i o n of tra c e r . This showed that mixing had e i t h e r occurred during the superheating period (approximately 3/4 hour) or as a r e s u l t of the quench. The idea that the quench (which from pre- vious tests i s known to take le s s than 5 seconds) was s o l e l y responsible for t h i s complete mixing i s t o t a l l y unacceptable. I t was not possible 150 to maintain a perfectly f l a t temperature profile during the superheat- ing and therefore some thermal convection must have occurred. The second test was conducted i n a similar manner but this time quenching was started shortly after the melting point of t i n (232 °C) was passed. The total time from the melting of the eutectic to the time of quenching was 12 minutes. The results of this test are shown i n Figure 67. The sections are at 1 cm intervals. Although some mixing 113 of Sn into the eutectic has occurred, there i s no evidence of the transverse flow observed in previous autoradiographs. The conclusion that the quench technique is not responsible for the transverse flow ob- served would now appear valid. 3.4.4.4. Extent of Inductive Mixing In Section 2.2.2.5. evidence was presented to show that i n - ductive mixing is not the driving force for the longitudinal flow of the liquid t i n . The extent to which inductive mixing effects the trans- 113 verse flow pattern was determined by introducing tracer (3.5 % Sn ) into the melt two minutes after the furnace power had been turned off. The gradient across the melt was 6 °C/cm and quenching took place one minute after tracer introduction. Rows two, four and six of Figure 68 show the results of the power off test. The results of a test with the same temperature gradient and tracer but with the furnace power on (normal procedure) are shown in rows one, three and five. Comparison of rows one and two, and three and four shows the transverse flow patterns in the power on and power off experiments to be virtually identical. The only apparent difference between the two being that the power off Figure 67. Transverse section autoradiographs of the specimen which had the prearranged tracer d i s t r i b u t i o n shown i n Figure 66. Figure 6 8 . Comparison of transverse section autoradiographs of specimens quenched 1 minute af t e r 113 introduction of 3 . 5 % Sn in Sn tracer into the melt; while the furnace power was on ( f i r s t , t h i r d and f i f t h rows) and 2 minutes a f t e r the furnace power had been turned off (second, fourth and s i x t h rows). ^> Figure 68 - Continued. flow seems to be somewhat more d i f f u s e . There i s considerably more transverse mixing towards the cold end i n the power o f f t e s t (comparing rows f i v e and six) and t h i s coupled with the f a c t that the flow i n t h i s test i s generally more d i f f u s e suggests a s l i g h t increase i n the d r i v i n g force f or transverse flow when the power i s o f f . The probable source of th i s d r i v i n g force would be an increase i n transverse temperature gradients which a r i s e a f t e r turning o f f the furnace power. 3.4.4.5. Determination of Transverse Temperature Gradients Measurements were made of the temperature d i s t r i b u t i o n on planes transverse to the boat axis using the apparatus i l l u s t r a t e d i n Figure 69. This apparatus allowed complete freedom of two dimensional movement of the thermocouple bead i n a given transverse plane. One moveable thermocouple was chosen over a s e r i e s of f i x e d thermocouples so that accurate r e l a t i v e temperature diffences could be measured without having to be concerned about thermocouple c a l i b r a t i o n corrections. The boat i n which the transverse gradients were measured was the two. channel graphite boat used i n Section 2.1.6.. This boat was chosen since i t was much easier to adapt the moveable thermocouple i n t h i s case than i t would have been f o r the s i n g l e channel aluminum boat. Since the transverse flow patterns observed i n the two channel graphite boat (Figures 25 and 26) are s i m i l a r to ones observed i n the s i n g l e channel aluminum boat i t was assumed that transverse temperature gradients would also be s i m i l a r ( e s p e c i a l l y so i n the graphite end supports used on the s i n g l e channel aluminum boat). Figure 69(a) i s a top view of the boat showing the wedging mechanism used to move the thermocouple from one side of the channel . Figure 69. Schematic representation of apparatus used to measure trans- verse temperature gradients (x2). Ul to the other. The s t a i n l e s s s t e e l rod was fastened on to the boat at the cold end and had s u f f i c i e n t e l a s t i c i t y to cause i t to return to i t s o r i g i n a l p o s i t i o n (1) when the wedge was withdrawn. A cam mechanism, which could be operated remotely by a lever system, was employed to r a i s e and lower the thermocouple, Figure 69(b). The s t a i n l e s s s t e e l rod would return to the low p o s i t i o n due to i t s own e l a s t i c i t y . The thermo- couple was connected to the end of the s t a i n l e s s s t e e l rod such that i t was s e l f a l i g n i n g ( i n the plane of Figure 69(b)) with the s l o t i n the boat cover. The thermocouple was 38 gauge chromel-alumel wire and was insulated by two hole 1/32 inch O.D. m u l l i t e tubing. To strengthen the thermocouple probe the m u l l i t e was surrounded f o r approximately 90% of i t s length (2 cm) by s t a i n l e s s s t e e l tubing which had been produced by d r i l l i n g out a 0.050 inch O.D. hypepdermic needle on a jewe l l e r s lathe. The temperature traverse of the cross section was done while the average temperature gradient across the melt was A °C/cm. Figure 70 shows the numbering system which w i l l be used to describe the res u l t s of the traoverse. During the traverse the Honeywell recorder was on the 0.1 mv f u l l scale span ( for the chromel-alumel thermocouple employed t h i s represents a f u l l scale span of less than 2.5 °C). I t was not p o s s i b l e to determine the absolute temperature at each point shown on Figure 70 since temperature v a r i a t i o n s associated with c y c l i c furnace temperature c o n t r o l l i n g were present i n the melt. The technique adopted was to move the thermocouple bead to a bottom p o s i t i o n (1,4, or 7) and then move the bead up and down between t h i s bottom and the corres- ponding top p o s i t i o n at 2 second i n t e r v a l s . A f t e r about 3 cycles the temperature diffe r e n c e between the upper and lower p o s i t i o n s decreased i n d i c a t i n g the probe was causing some mixing. The temperature 157 Figure 70. The numbering systems for lo c a t i n g positions on the temperature traverse. 158 differences stated below are the average values a f t e r 3 cycles between the top and bottom p o s i t i o n s . The r e s u l t s of the traverse were: (a) P o s i t i o n 3 i s colder than p o s i t i o n 1 by approximately 0.25 °C. (b) P o s i t i o n 6 i s colder than p o s i t i o n 4 by approximately 0.25 °C. (c) P o s i t i o n 9 i s colder than p o s i t i o n 7 by approximately 0.1 °C. No differences i n temperature were detected i n the h o r i z o n t a l d i r e c t i o n . The r e s u l t s show that the top of the melt i s s l i g h t l y cooler than the (9) bottom. This i s a d i r e c t c o n t r a d i c t i o n of the findings of Utech The r e s u l t s Utech obtained for the increase i n v e r t i c a l temperature gradient (hot l i q u i d above cold) with increasing h o r i z o n t a l ( l o n g i t u d i n a l ) temperature gradient are shown i n Figure 71. According to Figure 71 the v e r t i c a l and h o r i z o n t a l temperature gradients are nearly equal. Utech demonstrated that the v e r t i c a l temperature arose as a d i r e c t con- Sequence of convection. This was accomplished by suppressing convection with a magnetic f i e l d and observing that the v e r t i c a l gradient went to zero. I t must be pointed out that the experiments of Utech were conducted i n an open top boat with a melt depth of 0.94 cm whereas the experi- ments presented i n t h i s thesis were ca r r i e d out i n closed top boat with a melt depth of 0.64 cm. A d i f f e r e n c e i n the nature of the flow i s understandable. F i r s t , the melt whose depth i s 0.64 cm would be more stable with respect to f l u i d flow than a melt 0.94 cm deep. Secondly, the closed top graphite boat, a good thermal conductor, might prevent the establishment of a v e r t i c a l gradient i n the melt. 159 HORIZONTAL GRAD. (°C/CM) Figure 71. The r e l a t i o n between the h o r i z o n t a l and v e r t i c a l temperature gradients for an un- covered t i n melt of depth 0.94 cm (after Utech). Cole, i n a l i t e r a t u r e review of convection , stated that recent i n v e s t i g a t i o n s i n a rectangular cavity bounded by v e r t i c a l plates i n d i c a t e that a weak u n i c e l l u l a r motion i s generated for a l l non- zero temperature di f f e r e n c e s . Furthermore, the heat transported by t h i s flow i s n e g l i g i b l e , except f o r small contributions near the corners of the walls. The numerical analysis of thermal convection i n l i q u i d by Stewart showed that large flow rates may be developed i n a melt while the thermal p r o f i l e i s s t i l l unaltered from the pure conduction form. This i s i n t o t a l agreement with the r e s u l t s of the present work. At a h o r i z o n t a l temperature gradient of 4 °C/cm Figure 46 shows that a flow v e l o c i t y of greater than 0.3 cm/sec would be observed. At t h i s h o r i z o n t a l gradient the temperature traverse has shown that heat trans- port i n the melt must be almost completely conductive. In f a c t , the v e r t i c a l gradient measured here i s opposite to that which would be expected, that i s , the temperature traverse has shown a very small v e r t i c a l gradient (less than 0.3 °C/cm) i n which the cold l i q u i d i s above the hot l i q u i d . This gradient may r e s u l t from the f a c t that the bottom of the graphite boat i s i n contact with the Vycor tube whereas the top surface of the boat may be cooled by the convective a i r currents within the Vycor tube. The transverse flow observed i s the type of flow one would expect i n a c e l l which i s heated from below and cooled from above, namely, a double c e l l flow pattern with cooler l i q u i d from the top moving down the c e l l w a l l s , being heated at the bottom and then r i s i n g i n the middle of the c e l l . For the case of the square aluminum channel supported by the graphite ends i t would be expected that the most extensive flow would occur i n the v i c i n i t y of the graphite ends. This i s e s p e c i a l l y apparent i n the autoradiographs shown i n rows one and f i v e of Figure 58. It i s also observable i n rows two and s i x of Figure 58, but to a l e s s e r degree, probably due to the f a c t that t h i s specimen was quenched 2 minutes a f t e r i ntroduction (specimen i n rows one, three and f i v e was quenched at 1 minute) and therefore the tracer becomes much more d i l u t e . The observation that transverse flow i n the v i c i n i t y of the hot r e s e r v o i r i s more extensive than the transverse flow near the cold r e s e r v o i r must r e f l e c t the fact that the adverse v e r t i c a l gradient i n the hot r e s e r v o i r i s greater than that present i n the cold r e s e r v o i r . 3.5. Interaction of U n i c e l l a r Flow with a Moving So l i d L i q u i d Interface F l u i d flow across a s o l i d - l i q u i d i n t e r f a c e at which solute segregation i s taking place i s prime of importance i n determining the solute d i s t r i b u t i o n that appears i n the r e s u l t a n t s o l i d . During s o l i d i f i c a t i o n of an a l l o y , solute build-up (assuming k Q i s le s s than 1) w i l l occur at the i n t e r f a c e and t h i s i n turn can lead to c o n s t i t u t i o n a l supercooling. Following the onset of c o n s t i t u t i o n a l supercooling the morphology of the i n t e r f a c e w i l l change from planar to c e l l u l a r and then p o s s i b l y to d e n d r i t i c (provided the growth rate and temperature gradient are favourable for such a t r a n s i t i o n ) . A general observation i n experiments used to determine the growth c r i t e r i a f o r the planar to c e l l u l a r t r a n s i t i o n i s that breakdown occurs f i r s t at the melt-container i n t e r f a c e . Examples of t h i s are shown i n Figures 72 and 73. Both figures are from unpublished work by F. Weinberg. Figure 72 i s an autoradiograph of a transverse (to the growth d i r e c t i o n ) s e c t i o n of a 1/4 inch square rod. The rod was produced by d i r e c t i o n a l l y s o l i d i f y i n g 204 a melt of pure t i n containing 500 ppm of TI . The autoradiographs of Figure 72. Transverse section autoradiograpy of a d i r e c t i o n a l l y s o l i d i f i e d t i n melt containing 500 ppm TI ( X 2 0 ) . 163 Figure 73. Transverse section autoradiographs of a d i r e c t i o n a l l y 204 s o l i d i f i e d t i n melt containing 100 pom TI (X6) . 164 Figure 73 are from 3 d i f f e r e n t transverse sections of a d i r e c t i o n a l l y 204 s o l i d i f i e d pure t i n plus 100 ppm TI melt. The c r o s s - s e c t i o n a l dimensions of th i s rod are 1/2 inch wide by 1/4 inch high. The growth rate i n both cases was approximately 2 x 10 cm/sec and the temperature gradient i n the melt was of the order of 0.5 °C/cm. The most widely accepted mechanism for p r e f e r e n t i a l break- down of the planar i n t e r f a c e near the container walls invokes the concept of an enlarged solute r i c h boundary layer ( 6 - layer) i n t h i s region. s That i s , thermal convection i s reasonably e f f e c t i v e i n removing re- 2 OA jected solute (in t h i s case TI ) from the c e n t r a l region of the s o l i d - l i q u i d i n t e r f a c e , but i s much less e f f e c t i v e i n removing rejected solute from regions where the i n t e r f a c e and container meet. The reason f o r thi s i s that l i q u i d s metals with t h e i r low Prandtl numbers ( t y p i c a l l y of ar tl (17) _2 the order of 10 ) tend to maintain c i r c u l a r flow paths rather than con- form to the shape of the container i n which they are flowing Therefore, the extent of convective mixing i n the interface-container region w i l l be small i n comparison to the mixing which occurs at the cen t r a l region of the i n t e r f a c e . This w i l l r e s u l t i n the build-up of a much larger solute r i c h layer ahead of the periphery of the i n t e r f a c e . The net r e s u l t i s that conditions s u i t a b l e for c o n s t i t u t i o n a l supercooling and thus planar to c e l l u l a r breakdown w i l l occur f i r s t i n regions where the i n t e r f a c e and container meet. The main objection to t h i s mechanism i s that the s i z e of the 6 - layer required to produce as pronounced an e f f e c t as i s shown i n Figures 72 and 73 i s much larger than i s normally observed i n l i q u i d metal systems. (& s~ layer sizes are generally considered to range from a low lOu for complete mixing to lOOOu when no mixing i s present ). The type of convective flow described i n the previous sections, that i s , u n i c e l l u l a r l o n g i t u d i n a l flow with a superimposed transverse double c e l l flow would c e r t a i n l y encourage the onset of i n t e r f a c e breakdown to occur near the i n t e r f a c e container junction. The transverse flow would tend to d i s t r i b u t e solute, which had been picked up by the uni- c e l l u l a r l o n g i t u d i n a l flow, around the outside edges of the melt. Although the transverse double c e l l flow would bring solute into c e n t r a l region of the melt, t h i s solute would not be seen by the i n t e r - face since the l o n g i t u d i n a l flow i s constantly sweeping the ce n t r a l region of the i n t e r f a c e . The r e s u l t i s that the i n t e r f a c e would be growing into a melt which had greater portion of the rejected solute d i s t r i b u t e d around the outer edges, that i s , adjacent to the melt con- tainer w alls. As before,the net r e s u l t would be p r e f e r e n t i a l break- down of the planar i n t e r f a c e i n th i s region. The c l a s s i c a l mechanism requires the establishment of an u n r e a l i s t i c a l l y large solute layer at the container w a l l s . The fact that the 5 - layer around the periphery i s larger than that which e x i s t s at the ce n t r a l portion of the i n t e r f a c e cannot be denied. I t would appear that the most acceptable mechanism for the p r e f e r e n t i a l onset of the planar to c e l l u l a r t r a n s i t i o n near the melt container walls must be a combination of the c l a s s i c a l mechanism and the mechanism j u s t proposed. 3.6. Summary The flow which occurs i n the h o r i z o n t a l melt system studied here i s an u n i c e l l u l a r l o n g i t u d i n a l flow i n which the l i q u i d moves from the hot end to the cold end along the top of the melt and returns from the cold end to the hot end along the bottom. This mode of flow has been suggested but not observed by C a r r u t h e r s . However, Carruthers made no mention of the p o s s i b i l i t y of transverse flow. A d d i t i o n a l movement of f l u i d from the top to the bottom of the c e l l has been herein observed to occur by a double c e l l transverse flow which i s superimposed on the l o n g i t u d i n a l motion. The dri v i n g force f o r the transverse flow i s an adverse v e r t i c a l temperature gradient (cold l i q u i d above hot). The d r i v i n g force for the l o n g i t u d i n a l u n i c e l l u l a r flow i s the imposed h o r i z o n t a l temperature gradient. The heat transferred by t h i s flow i s n e g l i g i b l e . Although the heat transferred by the flow i s n e g l i g i b l e , the flow v e l o c i t i e s and the r e s u l t i n g convective mixing must be considered important i n the s o l i d i f i c a t i o n process. 167 4 - ANALYSIS OF RESULTS 4.1. Introduction In order to analyse the flow v e l o c i t y r e s u l t s obtained dur- ing t h i s i n v e s t i g a t i o n i t i s f i r s t necessary to determine the exact physi- c a l nature of the v e l o c i t y measured. In p a r t i c u l a r , i s the flow which gives r i s e to the observed v e l o c i t y simply a superposition of a trans- verse double c e l l flow on a longi t u n d i n a l u n i c e l l u l a r flow or could i t be more accurately defined as a double s p i r a l flow of the type observed (19) during forced convection through a c y l i n d r i c a l tube , Figure 74. The broken l i n e s i n Figure 74(a) show the path that would be followed by a p a r t i c l e as i t moved along with the s p i r a l flow. I f tracer was i n j e c t e d into t h i s system, the r o t a t i o n a l flow would cause transverse s e c t i o n auto- radiographs to have the appearance of Figure 74(b). Since the autoradio- graphs appearing i n Figures 56-64 do not, for the most part, display f u l l y outlined transverse double c e l l flow, i t may be concluded that the concept of s p i r a l flow does not accurately describe the flow system investigated herein. I t i s p o s s i b l e , however, that the flow could be described as a slow s p i r a l flow (rather than a s t r i c t l y transverse flow) superimposed on the more dominant u n i c e l l u l a r l o n g i t u d i n a l motion. In any case, the major contribution to the observed v e l o c i t y comes from the l o n g i t u d i n a l flow. The l o n g i t u d i n a l flow v e l o c i t y close to the top and bottom of the enclosed melt must be much greater than the v e l o c i t i e s i n the cen- 168 Figure 74, ( a) Schematic representation of the double s p i r a l flow observed during forced convection through a tube .(b) Expected appearance of trans- verse section autoradiographs i f double s p i r a l flow were present. t r a l region. This conclusion r e s u l t s from a consideration of the tracer introduction technique employed. E s s e n t i a l l y , tracer i n t r o d u c t i o n i n - volves placing a 0.64 cm cube of trace a l l o y i n the covered channel. I f the l o n g i t u d i n a l v e l o c i t y did not vary s i g n i f i c a n t l y with v e r t i c a l p o s i - t i o n i n the melt one would not expect to observe (as i s shown by the autoradiographs) the tracer to be concentrated i n the top and bottom layers of the melt. The observed predominance of flow close to the top and bottom surfaces of the melt suggests that i t may be appropriate to apply boundary layer theory to analyse the flow v e l o c i t y r e s u l t s obtained i n Section 2. . • The r a t i o of the buoyancy forces generated as a r e s u l t of temperature differences i n the f l u i d to the viscous force i n the f l u i d , i s given q u a l i t a t i v e l y by the dimensionless Grashof number. For a rectangular enclosure with heated and cooled v e r t i c a l walls the Grashof number i s generally written as: G r = ^ (4.1) v where: Gr i s the Grashof number g i s the acc e l e r a t i o n of gravity 8 i s the c o e f f i c i e n t of volume expansion AT i s the temperature diff e r e n c e between the hot and cold walls L i s the distance between the hot and cold walls v i s the kinematic v i s c o s i t y a i s the thermal d i f f u s i v i t y In order that the buoyancy force be consistent with the re- su l t s of the present i n v e s t i g a t i o n , i t i s necessary to redefine the 170 Grashof number. I t has been established above that the d r i v i n g force for the observed flow i s the average temperature gradient between the hot and cold ends of the melt. I f the Grashof number as presently defined i s s l i g h t l y modified to allow incorporation of the average h o r i z o n t a l temperature gradient across the melt, G , i t becomes: i-j G r " — — L (4.2) v . Thus the buoyancy force, which i s the d r i v i n g force for the observed flow, would appear to be strongly dependent on the melt length for a given average gradient. This grossly contradicts the experimental re- s u l t s which c l e a r l y show (for two d i f f e r e n t boat designs and 4 melt lengths ranging from 27 to 48.8 cm) that flow v e l o c i t y i s independent of t o t a l melt length, provided the average gradient across the melt re- mains constant. When the Grashof number i s further modified to remove the melt length dependence i t becomes: g3H 4 G Gr = j-± (4.3) v where the melt height H has replaced the length L. This Grashof number now has the experimentally determined properties of l i n e a r dependence on average gradient and i s independent of t o t a l melt length. This modification i s s i m i l a r to that employed by C o l e ^ 2 ^ to describe the dependence of the c r i t i c a l h o r i z o n t a l temperature gradient c required for the onset of thermocouple o s c i l l a t i o n , G , on the melt height. Cole redefined the Rayleigh number (Grashof x Prandtl) for a l i q u i d heated 171 from below, namely: g3H4 G t_. . R a = 1 Yertrcal ( 4 > 4 ) av by assuming that H x G (vertical) could be replaced by L x G (horizontal) The new Rayleigh number then became: g3H3LG Ra = (4.5) av from which can be obtained the expression: H 3 GT = ^ (4.6) SSL 3 c c Cole established experimentally that H G = 3.1 (cgs units) where G is Lj Li the c r i t i c a l horizontal gradient required for the onset of thermocouple fluctuations which in turn were taken to be indicative of the onset of turbulent convection. Using this result, an expression for the c r i t i c a l Rayleigh number Ra necessary for the onset of turbulent convection was obtained: R a c = (3-D g3L ( 4 > ? ) av Thus i t would appear that Ra i s a function of the melt length L. Cole did not determine whether in fact Ra varied with melt length. However, since Ra i s a dimensionless parameter of dynamic similarity i t i s reasonable to assume that i t should not vary with melt length. Therefore, since g is a constant and a , 3 and v remain essentially constant, provided the average melt temperature does not vary g r e a t l y , the product H L G must also remain constant. For a melt of height H i t follows that thermo- couple f l u c t u a t i o n s should be observed once the appropriate value (that c c which makes Ra > Ra ) of the product G L exceeds a constant G L. (12) Hurle's r e s u l t s noted i n Section 1.1. showed that f o r a melt length of 4.0 cm, G£ = 5.0 °C/cm and for L = 2.6 cm, G^ = 7.5 °C/cm. The values of G L for these two experiments are 20°C and 19.5°C r e s p e c t i v e l y . Thus i t becomes apparent that whereas flow v e l o c i t i e s are dependent on the average temperature gradient(independent of melt length) across the melt, the onset of turbulent convection i s determined by a c r i t i c a l temperature diffe r e n c e (again independent of melt length ) between the hot and cold ends of the melt. ( 8) The r e s u l t s of Miiller and Wiehelm i n d i r e c t l y support the fi n d i n g that flow v e l o c i t i e s are independent of melt length for a given h o r i z o n t a l temperature gradient. They found that f or melts between 10 and 30 cm long the observed temperature f l u c t u a t i o n s were independent of melt length provided the temperature and temperature gradient remain constant at the measuring point. I f the amplitude and frequency of the temperature f l u c t u a t i o n s can be taken as being representative of the ex- tent of convective flow and thus an i n d i r e c t measure of flow v e l o c i t i e s , then the r e s u l t s of Miiller and Wiehelm are i n agreement with those of the present i n v e s t i g a t i o n . Therefore, for t h i s i n v e s t i g a t i o n the buoyancy d r i v i n g force, as represented by a Grashof number, w i l l be given by Equation (4.3). In Section 2.2.3.4.3. i t was shown that varying the height of l i q u i d metal i n the open reservoirs had n e g l i g i b l e e f f e c t on the flow v e l o c i t y . I t should, therefqre, be possible to consider the system as being covered for the e n t i r e melt length. In summary one obtains the following p i c t u r e of f l u i d flow i n a covered h o r i z o n t a l rod of l i q u i d metal: (1) The flow which gives r i s e to the observed v e l o c i t y i s laminar l o n g i t u d i n a l u n i c e l l u l a r flow confined to the outer ex- tremeties of the melt, Figure 75. The transverse flow w i l l be neglected thus reducing the mathematical analysis to a 2- dimensional problem. The assumption that the transverse flow can be neglected i s based on autoradiography experiments which show that the transverse flow does not make a s i g n i - f i c a n t contribution to the l o n g i t u d i n a l flow. (2) The buoyancy forces which generate the l o n g i t u d i n a l flow can be represented by a modified Grashof number of the form: g3H 4 GT Gr = v . (3) The covered h o r i z o n t a l rod with the two small open res e r v o i r s can be considered to be a t o t a l l y enclosed rectangular system as shown i n Figure 75. Successful mathematical analysis of the s i m p l i f i e d two d i - mensional problem must p r e d i c t : (1) A l i n e a r r e l a t i o n s h i p between flow v e l o c i t y and average temperature gradient across the melt. Figure 75. The s i m p l i f i e d flow system i n the long shallow retangular enclosure 175 (2) A lack of v e l o c i t y dependence on t o t a l length. (3) A dependence of flow v e l o c i t y on average melt temperature. 4.2. Previous Investigations Hydrodynamic analysis of natural thermal convective flow i n l i q u i d metals having the h o r i z o n t a l rod configuration investigated here has received l i t t l e attention i n the l i t e r a t u r e . The vast majority of e x i s t i n g solutions have been p r i m a r i l y concerned with the heat transferred v i a convection, rather than the magnitude of the flow v e l o c i t i e s . A l - though heat transfer i s a i n t e g r a l part of the s o l i d i f i c a t i o n process, the purpose of the present i n v e s t i g a t i o n was to study flow patterns and flow v e l o c i t i e s . Attempts that have been made to analyse f l u i d flow i n a l i q u i d (5 9) metal contained i n a h o r i z o n t a l boat ' and thus predict flow v e l o c i t i e s have suffered from a lack of accurate reproducible r e s u l t s with which to (9) confirm or dispute the mathematical s o l u t i o n . The analyses of Utech and C o l e ^ which were outlined b r i e f l y i n Section 1.1. w i l l now be re- viewed and discussed with respect 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 . (9) 4.2.1. Solution of Utech^ ' The s o l u t i o n used by Utech was developed by Eckert and D r a k e f o r laminar flow along a v e r t i c a l p l a t e at a temperature T w immersed i n a f l u i d at temperature T q. The momentum equation f o r the boundary layer adjacent to the w a l l i s : 6 d f d x j U 2dy = gS J 0dy - v ( ̂ u ) w a i i ( 4 ' 8 ) The heat flow equation i s : 4" ) uGdy = - a ( ) i n (4.9) ax y dy w a l l where: x i s the distance along the w a l l y i s the distance perpendicular to the w a l l * 6 i s the boundary layer thickness u i s the v e l o c i t y i n the x d i r e c t i o n •3 = T - T o T i s the temperature at some y p o s i t i o n i n s i d e the boundary layer (21) * Merks . has shown that the thermal and hydrodynamic boundary layers are equal for free convection i n l i q u i d s metals, so that ^ t n e r m a ^ = hydro By assuming a temperature d i s t r i b u t i o n i n the boundary layer of: s - w w - V <!-i> ( 4.1 0) and a v e l o c i t y p r o f i l e of the form: u = u i J ^ " A > 2 (4 .1D 1 6 v 6 where u^ i s an a r b i t r a r y function with the dimension of v e l o c i t y , Equations (4.8)and (4.9) assume the form: ±- ^ (u 2 6) =igB ( T w - T o ) 6 - v i 105 dx 3 3o (Tw " T o ) k ( u i 5 ) = 2 a ( ~ ^ T ~ £ ) Solving these equations simultaneously employing the substitutions u^ = x and 6 = x gives: u r - 5,17V (0.952 + P r ) - 1 / 2 ^iJ^lIsf^2 ^ (4.12) From Equation (4.11) i t can be seen that the maximum v e l o c i t y i n the boundary layer, u^, i s 0.148 u^. Introducing t h i s into Equation (4.12) gives: u = 0.766v (0.952 + P r ) ~ 1 / 2 ( g B (TW " V) ^ x 1 / 2 . m ^ (.4.13) v 178 For molten t i n at an average melt temperature of 400 °C intr o d u c t i o n of the appropriate f l u i d parameters (Table 6) y i e l d s the following expression for the maximum flow v e l o c i t y i n the boundary layer: <V400 - ° ' 2 5 (TW " V 1 / 2 * 1 / 2 ( 4 ' 1 4 ) The average v e l o c i t y along a w a l l of height H would be: <V400 = ° - 2 5 < T W - V 1 / 2 l J H x l / 2 d x (4.15) = 0.166 (T T T - T ) 1 / 2 H 1 / 2 W o The melt height for the system studied i n Sections 2 and 3 was 0.64 cm. The temperature difference which created the bouyancy forces i n the melt i s obtained from Equation (4.3) and i s H G . Thus the average maximum J-i v e l o c i t y r e s u l t i n g from a h o r i z o n t a l temperature gradient between the v e r t i c a l walls at the ends of the melt would be: <»m>400 - 0 ' 1 0 6 G L 1 / 2 ( 4 ' 1 6 ) In Figure 76, the l i n e from Figure 46 i s p l o t t e d along with the modified Eckert and Drake s o l u t i o n given i n Equation (4.16). A l - though the calculated v e l o c i t i e s are of the same order of magnitude as the experimentally determined values, the l i n e a r dependence of flow v e l o c i t y on temperature gradient i s not s a t i s f i e d by t h i s s o l u t i o n . Furthermore, when the value of (u )„__ i s ca l c u l a t e d , the predicted r a t i o m 300 ^Um̂  300^ um^400 * S whereas experimentally, Figure 43, t h i s r a t i o i s 0.78. 0 9 I 1 1— 1 1 1— s — i — r — r AVERAGE TEMR GRAD. (°C/CM) Figure 76. Comparison of the r e s u l t s of the present i n v e s t i g a t i o n with the p r e d i c t i o n of the s o l u t i o n of Utech. 180 4.2.2. Solution of C o l e ^ The s o l u t i o n used by Cole to ca l c u l a t e was the Eckett and Drake analysis modified to include the latent heat of s o l i d i f i c a t i o n X and the growth rate R i n the heat flow Equation (4.9). Assuming the v e l o c i t y and temperature d i s t r i b u t i o n s were those given by Equations (4.10) and (4.11) (except Cole made u^ = u m ) , the d i f f e r e n t i a l equations which have to be solved simultaneously are then: 1 'd , 2 1 „ / m m . „ Um — - - ( u 5) - 3g3 ( T w - T o ) 6 - v - ( 4 a ? ) 105 dx o T - T T - T W o d ,: x S , W o \ , R / X . — — — (u 5) = a ( fi • _ ) + -j < — " <Tw " T o » (4-18) 40 dx p Employing the substitutions = x 1 7 2 , 6 = A.^ x"^ 4 Cole obtained a r e l a t i o n for u , which for the case of R = 0 (no s o l i d present or a m' r (22) stationary s o l i d - l i q u i d i n t e r f a c e ) becomes : u = 4.2 ( _ M ) ! / 2 ( R A T ) 1 7 2 (4.19) m .63 + Pr I f the appropriate f l u i d parameters from Table 6 are in s e r t e d , and as be- fore AT i s taken to be H G , then Equation (4.19) becomes: •Li ( % } 4 0 0 = ° ' 7 1 5 ^ L (4.20) The Cole analysis has the same parabolic dependence of u on temperature gradient G^ as the Eckert and Drake r e l a t i o n of Equation (4.16) but the calculated value of from Equation (4.20) i s approximately an order of magnitude larger than that calculated from Equation (4.16). Since Cole's s o l u t i o n i s e s s e n t i a l l y the Eckert and Drake s o l u t i o n with the addition of terms accounting for the latent heat of s o l i d i f i c a t i o n and the growth rate R, Equation (4.2.0) should be i d e n t i c a l to Equation (4.16) when no s o l i d i f i c a t i o n or melting (R = 0) i s occurring. Examin- ation of Cole's analysis reveals the following erro r . Cole assumed the v e l o c i t y p r o f i l e was: u = u £ (1 - £ ) 2 (4.21) m o o and eventually obtained a s o l u t i o n for u^, the maximum v e l o c i t y p a r a l l e l to the i n t e r f a c e . By d i f f e r e n t i a t i n g Equation (4.21) and s e t t i n g du/dy = 0, one can obtain the value of y for which u = u . This value m i s 1/36 and s u b s t i t u t i n g t h i s into Equation (4.21) y i e l d s : u = 0.148 u m m C l e a r l y then, Cole's calculated values of x j i l l be too large by a factor of 6.85. When th i s c orrection i s applied to Equation (4.20) the r e s u l t i s : ( V 4 0 0 = °- 1 0 6V / 2 which agrees with the Eckert and Drake r e l a t i o n . In view of the lack of agreement between the Eckert and Drake type of s o l u t i o n and the r e s u l t s obtained during t h i s i n v e s t i g a t i o n , i t becomes necessary to examine more c a r e f u l l y the assumptions involved i n 182 deriving the v e l o c i t y r e l a t i o n s h i p predicted by Equation (4.16). One of the major assumptions of t h i s analysis i s that f u l l y developed boundary layer flow e x i s t s along the v e r t i c a l w a l l . Thus, corner e f f e c t s can be neglected and the integrated boundary layer Equations(4.8) and (4.9) re s u l t s as a s i m p l i f i c a t i o n of the governing equations of thermal con- vection, namely: Momentum equation i n the x - d i r e c t i o n |H + u |H + v-|u = _ G 3 A T , I |£l + v ( v 2 u ) ( 4 > 2 2 ) d t 3x dy • p O X v Momentum equation i n the y - d i r e c t i o n 3v 3v • 3v 1 V_ , ,„2 (4.23) u — + v — = - — Tf— + v (V v) 3t 3x 3y p 3y Energy equation Continuity equation - ^ + ̂ = 0 (4.25) 3x 3y where: x i s the distance i n the v e r t i c a l d i r e c t i o n u i s the v e l o c i t y i n the v e r t i c a l d i r e c t i o n y i s the distance i n the h o r i z o n t a l d i r e c t i o n v i s the v e l o c i t y i n the h o r i z o n t a l d i r e c t i o n p' i s the pressure deviation from the i n i t i a l s t a t i c pressure. 183 The assumptions used i n obtaining the above equations are: (1) A l l f l u i d p roperties, with the exception of the density changes which give r i s e to the buoyancy forces, are con- stant for a given average melt temperature. (2) The temperature diff e r e n c e across the melt i s small compared with 1/3. (3) The viscous d i s s i p a t i o n i s neglected. (4) Compressibility e f f e c t s are neglected. Purely a n a l y t i c a l attempts to solve the flow and heat trans- fer c h a r a c t e r i s t i c s of convection are severely. handicapped by the com- p l e x i t y of the governing equations. The i n t e g r a l boundary layer s o l u t i o n j u s t discussed i s l i m i t e d by a minimum height to length r a t i o of the c e l l . Since t h i s s o l u t i o n and the r e s u l t s of the present i n v e s t i g a t i o n are not i n agreement i t must be concluded that the height to length r a t i o s employed herein were outside the range of a p p l i c a b i l i t y of the i n t e g r a l boundary layer s o l u t i o n . Approximate solutions of the governing equations have been (23) (24) developed by Batchelor and Poots . Both solutions use non-dimen- s i o n a l forms of the governing equations. These non-dimensional forms are obtained by using the following dimensionless parameters: 1 8 4 X = - Y = * L' L u = i i H v = _ i * 9 ¥ L 8Y L 8X ( 4 . 2 6 ) T - T o _ „ 2 „ 0 = ii jr = _ T, - T 1 o where and T q are the temperature of the v e r t i c a l w a l l s , Y i s defined as the dimensionless stream function and z; i s defined as the dimension- less v o r t i c i t y . Substituting the r e l a t i o n s h i p s i n ( 4 . 2 6 ) i n t o Equations ( 4 . 2 2 ) to ( 4 . 2 5 ) and eliminating the pressure terms by d i f f e r e n t i a t i n g ( 4 . 2 2 ) with respect to Y and ( 4 . 2 3 ) with respect to X r e s u l t s i n : 1 _ Pr c I S . ^ 3X 3Y 5V 8g ax BY Ra W + v2C ( 4 . 2 7 ) !§. II i®. = v20 ( 4 . 2 8 ) 9X 3Y ~ 8Y S X In obtaining Equations ( 4 . 2 7 ) and ( 4 . 2 8 ) a l l the time d e r i - vatives (3/3t) have been equated to zero since only the steady state solu- t i o n i s of i n t e r e s t . The boundary conditions i n dimensionless form are: 0 = Y (4.29) Y = 1 <j/ = | X = Q 0 = 1 4.2.3. Solution of Batchelor Batchelor developed seri e s s o l u t i o n for 0 and ¥ by expanding them i n power se r i e s of the Rayleigh number, namely: These s e r i e s can be substituted i n t o Equations (4.27) and (4,28) and upon equating c o e f f i c i e n t s of l i k e powers of the Rayleigh number equations describing 0^, 0^, ^ and ^ c a n be obtained. For values of Rayleigh 3 less than 10 and for H/L r a t i o s close to unity the value of 4^ can be approximated by: Thus, under these conditions, and assuming that series (4.31) converges s u f f i e n t l y r a p i d l y , the s o l u t i o n for the stream function can be written as: (4.30) (4.31) (4.32) .¥ = RaH'1(X,Y) (4.33) 186 The flow v e l o c i t i e s can be obtained d i r e c t l y from Equation (4.33) with the use of the v e l o c i t y r e l a t i o n s h i p s i n Equation (4.26). Before continuing with the development of the Batchelor (24) s o l u t i o n , i t i s convenient to b r i e f l y discuss the solutions of Poots and Stewart . (24) 4.2.4. Solution of Poots Employing the dimensionless forms of the two-dimensional governing equations, Poots obtained approximate solutions for 0 and ¥ by expanding them as series of orthogonal polynomials. The general con- clusions of t h i s i n v e s t i g a t i o n were that: (1) The s o l u t i o n of Poots was i n agreement with the Batchelor 3 s o l u t i o n up to Rayleigh equals 10 . (2) The labour involved i n obtaining Poots' solutions for 4 Rayleigh greater than 10 and H/L greater than 4 was made p r o h i b i t i v e by the slow convergence of the ser i e s s o l u t i o n s . 4.2.5. Solution of Stewart Stewart, employing a radioactive tracer technique, measured flow v e l o c i t i e s associated with n a t u r a l convection of l i q u i d metal con- tained i n a c e l l with a height to length r a t i o of unity. During t h i s i n - v e s t i g a t i o n the Rayleigh number ranged from 10 1 to 10^. These values of Rayleigh are w e l l outside the range i n which the solutions of Batchelor and Poots may be applied. In order to analyse h i s experimental r e s u l t s , Stewart developed a f i n i t e d i f f e r e n c e s o l u t i o n of the governing equations. (25) The s o l u t i o n was based on the work of Wilkes and Samuels and (26) C h u r c h i l l . I t was necessary to modify these solutions since the Wilkes analysis became unstable at large values of Rayleigh, and the r e - su l t s of Samuels and C h u r c h i l l did not apply as t h e i r s o l u t i o n was for a system with a v e r t i c a l l y applied temperature gradient whereas Stewart worked with a h o r i z o n t a l d i f f e r e n c e i n temperature. The f i n i t e d i f f e r e n c e numerical technique used by Stewart for the s o l u t i o n of a dimensionless form of the governing equations ( s l i g h t l y d i f f e r e n t form than that used by Batchelor) was the i m p l i c i t a l t e r n a t i n g d i r e c t i o n technique. Stewart found that the s o l u t i o n ob- tained for the flow v e l o c i t y was i n excellent agreement with the solu- 5 3 ti o n of Batchelor up to Grashof equals 10 (Rayleigh approximately 10 ). For Grashof greater than 10^ Stewarts s o l u t i o n deviated from the Batchelor s o l u t i o n and then approached the Eckert and Drake boundary layer s o l u t i o n 9 for values of Grashof of the order of 10 . During the course of the present i n v e s t i g a t i o n the values of Grashof (for an average melt temperature of 400 °C), as defined by Equation 4.3, was: ( G r ) 4 Q 0 = 4800 G L (4.34) and ( R a ) 4 0 0 ^ 4 3 . 7 G L (4.35) The maximum value of G for which v e l o c i t y measurements were made was less than 10 °C/cm. Therefore, from Equations (4.34) and (4.35) i t becomes apparent that the conditions studied during t h i s i n v e s t i g a t i o n f a l l w e l l within the range i n which there i s good agreement between the solutions of Batchelor, Poots and Stewart. Since the s o l u t i o n of Batchelor i s by f a r the simplest of the three i t i s appropriate to i n v e s t i g a t e i t further i n the hopes of finding a s u i t a b l e analysis for the experimental re- s u l t of t h i s i n v e s t i g a t i o n . 4.3. M o d i f i c a t i o n of the Batchelor Solution It w i l l be shown below that the s o l u t i o n of Batchelor can be modified and extended so as to adequately describe the r e s u l t s of t h i s i n v e s t i g a t i o n . As stated i n Section 4.2.3. an approximate s o l u t i o n for the stream function i s given by: ¥ - | R a A (X) Y 2 (1-Y) 2 ( ^ 3 ( > ) where A(X) = (1 + (fA 1 X 2 ( ~ - X ) 2 Although the experimental values of Rayleigh l i e within the range for which t h i s approximation i s u s e f u l , the experimental values of H/L are much less than unity. However, Batchelor states that i t i s un- l i k e l y that the convergence of the s e r i e s would vary appreciably with the (27) value of H/L. Furthermore, Carruthers has suggested that Equation (4.36) i s v a l i d for flows i n the neighbourhood of a v e r t i c a l i n t e r f a c e even for low values of the aspect r a t i o n H/L. Accordingly, the follow- ing the expression for the v e l o c i t y p a r a l l e l to the v e r t i c a l w a l l i s obtained: a 8¥ U = L W (4.26) | ~ A ( x ) ( 4 Y 3 _ 6 y2 + 2 y ) ( 4 3 ? ) If i t i s further assumed that Equation (4.36) i s also v a l i d for flow p a r a l l e l to the much longer horizonal boundaries, then the l o n g i t u d i n a l flow v e l o c i t y as defined by; i s given by the expression: v = - £ | Ra Y 2 ( l - Y ) 2 ( l + (|)4) Vx3 - 6 ^ + 2 (f)2 X) (4.38) The Rayleigh number, as obtained by nondimensionlizing the governing equations, i s : Ra= fiSlAl av The aspect r a t i o s employed during t h i s i n v e s t i g a t i o n were: 0.013 < - < 0.024 XJ Therefore, (H/L) 4 << 1 and the (1 + ( H / L ) 4 ) - 1 term i n Equation (4.38) reduces to unity where upon one obtains the following expression des- cr i b i n g the dependence of l o n g i t u d i n a l flow v e l o c i t y on l i q u i d metal properties, melt geometry, temperature gradient between the hot and cold ends of the melt and p o s i t i o n i n the melt: 3 2 v = 2 SBL g y 2 ( 1 _ Y ) 2 ( 4 x 3 _ 6 I x 2 + 2 A X) (4.39) 3v At f i r s t appearance, Equation (4.39) predicts a strong de- pendence of flow v e l o c i t y on melt length L. However, when the l a s t group of terms i n Equation (4.39) i s alte r e d such that the v a r i a t i o n of flow v e l o c i t y with v e r t i c a l p o s i t i o n i n the melt i s described by a new var i a b l e XL/H , the following appears: 2 3 3 2 4X3 - 6 f X 2 + 2 ) X = ( f ) ( 4 ( ^ ) - 6 (|̂ ) + 2(f^)) (4.40) Substitution of the r i g h t hand side of Equation (4.40) in t o Equation (4.39) y i e l d s the following expression: 3 3 2 v o M j f - ^ Y 2 ( l - Y ) 2 ( 4,(1̂) - 6 (f^) + 2 f - ) (4.41) The expression 4(XL/H) 3 - 6(XL/H) 2 + 2XL/H describes the v a r i a t i o n of l o n g i t u d i n a l flow v e l o c i t y with v e r t i c a l p o s i t i o n i n the melt. This v e l o c i t y dependence on p o s i t i o n i s shown i n Figure 77, and i s consistent with the r e s u l t s of the autoradiography experiments which * Since X = x/L (by Equations (4.26)) the new v a r i a b l e XL/H i s x/H, that i s , XL/H i s the dimensionless distance i n the v e r t i c a l d i r e c t i o n whose magnitude ranges from 0 to 1. -0 -3 -0-2 -0-1 0 0 +0-1 +0-2 +0-3 ^relative Figure 77. The v a r i a t i o n of l o n g i t u d i n a l flow v e l o c i t y with v e r t i c a l p o s i t i o n i n the melt. VO show that the regions of more predominant' flow e x i s t close to the top and bottom of the melt. The v e l o c i t y measured by the tracer monitoring technique em- ployed during t h i s i n v e s t i g a t i o n would be expected to be very close to the maximum v e l o c i t y i n the boundary laye r s . The maximum v e l o c i t y occurs at XL/H = 0.212 (and 0.788). Thus the expected maximum l o n g i t u d i n a l flow v e l o c i t y w i l l be given by: 3 v = 0.128 ̂  G Y 2 ( l - Y ) 2 (4.42) V .Li Equation (4.42) s t i l l contains the flow v e l o c i t y dependence on p o s i t i o n along the melt with v being 0 at the v e r t i c a l walls and reaching a maxi- mum at Y = 0.5 (half way along the melt). This maximum value of v i s given by: 3 v = 0.008 GT (4.43) The integrated average value of v between Y = 0 and Y - 1 i s given by: 3 _ v = 0.0043 GT ( l ,,\ v L (4.44) Comparison of the experimental r e s u l t s with the predictions of Equations (4.43) and (4.44) appear below. 193 4.4. Comparison of Theoretical Predictions and Experimental Results 4.4.1. V a r i a t i o n of Flow V e l o c i t y with Average Temperature Gradient Across the Melt When the appropriate f l u i d parameters from Table 6 are i n - serted into Equations (4.43) and (4.44), the t h e o r e t i c a l l y expected average and maximum flow v e l o c i t i e s (at an average melt temperature of 400°C and melt height of 0.64 cm) are given by: <vm>400 = ° - 1 1 3 G L (4.43(b)) (V400 - 0 ' 0 6 1 G L The experimentally determined r e l a t i o n (from Figure 46); V400 = ° ' 0 8 2 G L f a l l s midway between the predicted average and maximum v e l o c i t i e s of Equations (4.43(b)) and (4.44(b)). 4.4.2. V a r i a t i o n of Flow V e l o c i t y with T o t a l Melt Length Experimentally i t has been determined that the flow v e l o c i t y i s independent of t o t a l melt length provided the average h o r i z o n t a l temperature gradient remains constant. As can be seen by inspection of Equations (4.43) and (4.44), t h i s experimental observation i s i n agree- ment with the predictions of the modified Batchelor s o l u t i o n . , 4.4.3. V a r i a t i o n of Flow V e l o c i t y with Average Melt Temperature From Figure 43 the experimentally measured r a t i o of the 194 v e l o c i t y at an average melt temperature of 300°C and 400°C i s : ^ - 0.78 V400 Equations (4.43) and (4.44) pr e d i c t that t h i s r a t i o should be 0.84. Since Figure 43 was constructed with only three data points, and the o v e r a l l experimental accuracy i s believed to be ± 10% (or b e t t e r ) , i t i s the opinion of t h i s author that the t h e o r e t i c a l and experimental values of flow v e l o c i t y dependence on average melt temperature are i n good agreement. 4.5. Summary Although Batchelor's s o l u t i o n of free thermal convection i n rectangular enclosures of high aspect r a t i o i s not generally applied to low aspect r a t i o enclosures, the modified Batchelor s o l u t i o n appearing above does adequately describe the experimental r e s u l t s obtained i n t h i s i n v e s t i g a t i o n . There i s very good agreement between t h i s s o l u t i o n and the observed dependence of flow on t o t a l melt length and average melt temperature. Equations (4.43) and (4.44) both p r e d i c t the observed l i n e a r dependence between flow v e l o c i t y and the average h o r i z o n t a l temperature gradient across the melt. Furthermore, the magnitude of the predicted average and maximum v e l o c i t y of l o n g i t u d i n a l flow i s i n reasonably good agreement with the r e s u l t s of the present i n v e s t i g a t i o n . Since the solutions of Batchelor and Stewart are i n good agreement (over the range of Grashof and Rayleigh numbers employed here), i t i s reasonable to expect that Stewart's more elaborate f i n i t e d ifference s o l u t i o n could have been used to analyse the r e s u l t s of t h i s i n v e s t i g a t i o n . However, the solutions used by Cole and Utech c l e a r l y do not describe the flow i n a long h o r i z o n t a l rod of l i q u i d metal for the experimental conditions employed herein. 196 5 - CONCLUSIONS A ra d i o a c t i v e tracer technique has been developed to examine the nature of f l u i d flow i n l i q u i d t i n contained i n a lpng h o r i z o n t a l covered boat. Extensive tests have shown that the tracer i n t r o d u c t i o n and monitoring techniques employed allow accurate and reproducible measurement of the flow v e l o c i t i e s . Further experimentation has r e - vealed the appearance of the flow patterns which occur i n the melt. The most s i g n i f i c a n t findings of th i s i n v e s t i g a t i o n are summarized below: (1) An extremely small h o r i z o n t a l gradient, apparently any non- zero gradient, provides s u f f i c i e n t d r i v i n g force f o r thermal convective flow. (2) Laminar flow a r i s i n g from thermal convection w i l l not cause mass transfer through a region of zero h o r i z o n t a l temperature gradient. (3) The flow v e l o c i t i e s observed are the r e s u l t of the presence of buoyancy forces created by a temperature gradient between the hot and cold ends of the melt. These v e l o c i t i e s are not dependent on electromagnetic s t i r r i n g e f f e c t s . (4) For the covered h o r i z o n t a l rod configuration investigated herein the flow v e l o c i t y i s l i n e a r l y dependent on the average temperature gradient across the melt (and not on l o c a l h o r i - zontal temperature gradients). (5) The flow v e l o c i t y increases with increasing average melt temperature. (6) Although the flow v e l o c i t i e s measured were less than 1 cm/ second, they are large r e l a t i v e to the slow grow rates commonly employed i n u n i d i r e c t i o n a l s o l i d i f i c a t i o n experi- ments and, therefore, must be considered s i g n i f i c a n t . (7) The flow pattern occurring i n the molten t i n i s a laminar u n i c e l l u l a r l o n g i t u d i n a l flow upon which i s superimposed a transverse double c e l l flow. The transverse flow does not contribute s i g n i f i c a n t l y to the l o n g i t u d i n a l flow v e l o c i t y . (8) The transverse flow observed would be expected to be a con- t r i b u t i n g factor to the p r e f e r e n t i a l breakdown of s o l i d - l i q u i d i n t e r f a c e morphology near the melt container. (9) When the s o l u t i o n of Batchelor i s extended and modified, there i s good agreement between t h i s s o l u t i o n and the r e - s u l t s of the present i n v e s t i g a t i o n . 198 6 - SUGGESTIONS FOR FUTURE WORK Employing the tracer i n t r o d u c t i o n and monitoring techniques developed i n t h i s i n v e s t i g a t i o n , the experiments l i s t e d below could be performed i n order to provide a d d i t i o n a l information on the nature of f l u i d flow i n h o r i z o n t a l rods of l i q u i d metal: (1) Examination of the dependence of flow v e l o c i t y on tempera- ture gradient i n uncovered melts. (2) Examination of the dependence of flow v e l o c i t y on melt depth. (3) Examination of the v a r i a t i o n of flow v e l o c i t y with d i f f e r e n t cross s e c t i o n a l geometries. (4) Examination of the e f f e c t on flow v e l o c i t y of introducing a moving s o l i d - l i q u i d i n t e r f a c e i n both pure metal and a l l o y systems. (5) A quantitative evaluation of the dependence of the e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t on flow v e l o c i t y . 199 PART II - FLUID FLOW DURING SOLIDIFICATION - ITS EFFECT _ _ _ , _ „ . , . , , . , ,—"T"-— ' • . , - ,- . , - - ON GRAIN STRUCTURE AND MACROSEGREGATION 1 - INTRODUCTION 1.1. Grain Structure F l u i d flow of r e s i d u a l l i q u i d metal during ingot s o l i d i f i c a - t i o n i s necessary (under normal conditions) i f the columnar to equiaxed t r a n s i t i o n (CET) i s to occur. The reduction of temperature gradients i n the l i q u i d ahead of the s o l i d - l i q u i d i n t e r f a c e i s hastened by increasing the convective mixing (free or forced). Since lowering of temperatures i n the melt w i l l allow n u c l e i (whatever t h e i r source be )to sur- vive and grow, increased f l u i d flow w i l l promote an e a r l i e r CET. Grain structure manipulation can, therefore, be accomplished by c o n t r o l l i n g the l i q u i d flow during s o l i d i f i c a t i o n . Flow control may be accomplished i n the following ways: . ( 1 ) Magnetic f i e l d s can be used to enhance or reduce f l u i d motion. Since metals are e l e c t r i c a l conductors they are forced to ( 3 5 ) move i n the presence of a rot a t i n g magnetic f i e l d , or i n a constant magnetic f i e l d i f a d.c. current i s passed through the l i q u i d metal . Reduction of convection occurs i n a fi x e d magnetic f i e l d since there w i l l be a retarding force u u *• , , ( 1 1 , 3 7 , 3 8 ) to the motxon of a conductor through the f i e l d 200 (2) Motion of the mold during s o l i d i f i c a t i o n can be used to control casting grain structure. The effect of steady- state mold rotation has been studied extensively by Cole and Boiling »^0) ̂  Wo j ciechowski and Chalmers f as well as Cole and Boiling, have examined the effect on grain structure of oscillating the mold during s o l i d i f i c a t i o n . Vertical reciprocation of semi-continuous D.C. cast aluminum ingots has also proved effective in producing finer grained , (42) ingots (3) The use of ultra-sonic energy to effect grain nucleation i s another mode of grain structure control. whether i t should be classed as a form of mechanical mixing i s s t i l l contro- , ,(43,44) versial 1.2. Macrosegregation Various forms of macrosegregation occur as a result of con- vection. Normal segregation has been discussed in Part I, Section 1. Back-flow along interdendritic channels (caused by volume changes on freezing), of normally segregated residual liquid, i s generally accepted (45) as the mechanism for inverse segregation Solute convection cutting across dendrites is believed to be responsible for 'A' type segregates in ingots and for the formation of 'freckles' in unidirectionally s o l i d i f i e d castings. Support of this theory is provided^ by observation of so l i d i f i c a t i o n in ammonium chloride- (46.47) water systems 201 Suppression of convection (by magnetic f i e l d s ) eliminates (37) temperature f l u c t u a t i o n s which would otherwise cause banding , and also changes the macrosegregation^ 1"^. U n t i l recently, differences i n macrosegregation a r i s i n g from the ro t a t i n g and o s c i l l a t i n g modes of ingot s o l i d i f i c a t i o n had not been studied. The remainder of Part II w i l l discuss the i n v e s t i g a t i o n by the author and fellow graduate student M.J. Stewart on macros- segregation a r i s i n g from these various s o l i d i f i c a t i o n techniques. The study w i l l be presented here i n the same form as i t appeared i n M e t a l l u r g i c a l T r a n s a c t i o n s ^ 4 8 ^ . The thesis of M.J. S t e w a r t c o n - tains a s i m i l a r section. 2 - MACROSEGREGATION IN CASTINGS ROTATED AND OSCILLATED DURING SOLIDIFICATION •2.1. Introduction Castings which have a small equiaxed grain structure are considered to be more homogeneous and to have better mechanical pro- p e r t i e s than equivalent castings with a p a r t i a l l y columnar structure. One way of c o n t r o l l i n g the grain structure i s by mechanically mixing the r e s i d u a l l i q u i d . d u r i n g s o l i d i f i c a t i o n . This can be done by moving the mould. Constant r o t a t i o n of a c y l i n d r i c a l mould, r a d i a l l y cooled, w i l l suppress the columnar to equiaxed t r a n s i t i o n (CET); o s c i l l a t i o n of the mould w i l l promote an e a r l i e r CET; and a stationary (39 mould w i l l have a structure between the r o t a t i o n and o s c i l l a t i o n cases The control of grain structure by mechanical mixing of the l i q u i d during casting may cause macrosegregation - - (a function of the kind and ex- tent of l i q u i d mixing). In addition, r o t a t i o n a l forces might influence solute transport i n the l i q u i d i f there i s a large density d i f f e r e n c e between solute and solvent. I f macrosegregation i s enhanced by l i q u i d mixing t h i s could be detrimental to casting q u a l i t y . The purpose of the present i n v e s t i g a t i o n i s to determine the extent of macrosegregation i n stationary, rotated, and o s c i l l a t e d castings, and r e l a t e the r e s u l t s to the cast structure. 203 2.2. Experiment The macrosegregation i n the castings was determined by a radioactive tracer technique. The a l l o y used was Al-3 wt.% Ag made up of 99.99% A l and 99.8% Ag. The ingots were c y l i n d r i c a l , 3h inches i n diameter and approximately 6 inches high. The casting apparatus used, Figure 78, enabled the casting of Al-Ag a l l o y s to be made i n stationary, r o t a t i n g , or o s c i l l a t i n g moulds. Melting was done i n a graphite c r u c i b l e i n a resistance furnace. The a l l o y was superheated to approximately 800 °C and immediately p r i o r to casting, a small 110 amount of radioactive Ag was added into the melt. The castings were a l l poured at 750 °C (90 °C superheat) into s t a i n l e s s s t e e l moulds, water cooled before and during casting. A graphite hot top was used to keep the heat transfer from the upper surface to a minimum. Three casting conditions were used: stationary mould, rotated mould at 126 rpm, and an o s c i l l a t e d mould. The o s c i l l a t i o n was a r o t a t i o n of 126 rmp with the d i r e c t i o n of ro t a t i o n being reversed every f i v e seconds. The casting microstructure was determined by sectioning and etching of the castings p a r a l l e l and perpendicular to the c y l i n d r i c a l axis. Etching was done i n a Modified Tucker etch (HCL, HNO^, HF, and Ĥ O i n a 2:2:1:15 r a t i o ) and the etching products were washed o f f immediately with concentrated n i t r i c a cid. To measure the macrosegregation i n the ingot, the most ex- pedient procedure, as commonly used, i s to measure the solute concentra- ti o n of cuttings taken at various points i n the ingot by d r i l l i n g . This i s s a t i s f a c t o r y i f there i s no microsegregation and no short range v a r i a t i o n s i n the macrosegregation, which i s r a r e l y the case. To improve 204 IOT TOP STEEL MOULD WATER COOLING A l - A g CASTING MOTOR Figure 78. The experimental apparatus used for producing the stationary, rotated, and o s c i l l a t e d castings of A l - 3wt. % Ag. the averaging process, more d r i l l i n g s and analyses could be made, or a l t e r n a t i v e l y a layer of the casting can be machined o f f and samples taken from t h i s . F i n a l l y , the e n t i r e casting can be machined and the concentration of a l l the casting by sections can be measured. The time and e f f o r t involved increases very greatly from the f i r s t to f i n a l process l i s t e d above. Accordingly, a l l four procedures were used i n i t i a l l y to determine t h e i r accuracy and r e p r o d u c i b i l i t y for the pre- sent castings. Four methods of sampling were employed to determine thi degree of r a d i a l macrosegregation. (a) Holes of 1/4 inch diameter were d r i l l e d through the casting i n 1/4 inch steps i n the r a d i a l d i r e c t i o n . A f i x e d weight of s o l i d turnings was packed into a standard container. The a c t i v i t y of the radioactive s i l v e r present i n each sample was then measured with a s c i n t i l l a t i o n w e ll counter. (b) Holes of 1/4 inch diameter were d r i l l e d as i n method (a) except 1/8 inch steps were used. The analysis was the same as method (a). (c) The castings were mounted i n a lathe and 0.030 inch t h i c k concentric cylinders one inch long were progressively r e - moved. From each cut a random f i v e gram sample was taken and the a c t i v i t y of the sample measured i n a s c i n t i l l a t i o n w e l l counter under conditions of fixed geometry. (d) The castings were machined as i n (c) except the cut was 0.050 inches thick. A l l the material removed i n each cut was dissolved i n a concentrated s o l u t i o n of n i t r i c acid containing a small amount of mercury i n s o l u t i o n . The solutions were then made up to e i t h e r 250 or 500 ml. by adding water. A 10 ml. sample was taken from each s o l u t i o n and the a c t i v i t y of each sample measured. In evaluating the r e s u l t s the concentration of s i l v e r i s taken to be proportional to the measured a c t i v i t y . A g 1 1 ^ i s a strong gamma emitter and aluminum a weak absorber. As a r e s u l t , small geometri- c a l differences i n samples counted i n (a), (b) and (c) techniques should be n e g l i g i b l e . Autoradiography was used to show q u a l i t a t i v e l y the macro- segregation i n the ingots. Since the energy of the r a d i a t i o n i s high and the sample absorption i s low the autoradiograph w i l l represent the a c t i v i t y of a large distance i n t o the ingot. Therefore to obtain reasonable r e s o l u t i o n t h i n sections are required. Thin discs per- pendicular to the c y l i n d r i c a l axis were prepared by machining and p o l i s h - ing the discs to a thickness of 0.020 inches. 2.3. Results V e r t i c a l sections of castings which were stationary, r o t a t i n g , and o s c i l l a t i n g during s o l i d i f i c a t i o n are shown i n Figures 79(a), 79(b) and 79(c) r e s p e c t i v e l y . The stationary casting has a small equiaxed region i n the centre, the rotated casting has a columnar zone to the centre of the casting, and the o s c i l l a t e d casting has a large region, i n agreement with previous observations. The equiaxed grains i n the o s c i l l a t e d ingot are c l e a r l y shown to have grown d e n d r i t i c a l l y i n Figure 80, taken at higher magnification. I Figure 80. Equiaxed grains in the central region of the o s c i l l a t e d casting, magnification AO times. 209 The structures obtained on etched cross sections of the ingots (Figures 81(a), 81(b), and 81(c)) show the e f f e c t of the applied f l u i d motion on the columnar zone. In Figure 81(a) of the stationary cast ingot the columnar region i s i n a r a d i a l d i r e c t i o n with a l l the grains growing perpendicular to the mould w a l l . The columnar region for the rotated ingot (Figure 81(b))shows a s p i r a l shape with the i n - i t i a l columnar grains growing non-perpendicular to the mould walls. These grains are growing tov/ards the oncoming f l u i d i n the l i q u i d pool. In the o s c i l l a t e d ingot (Figure 81(c))the d i r e c t i o n of the columnar zone changes when the mould r o t a t i o n . i s reversed so that they always grow into the flow. A s i m i l a r observation has been made by Roth and (49) Schippen . In both the rotated and o s c i l l a t e d ingot there i s a renucleation of the columnar grains to achieve the curved e f f e c t s . There were no grains observed which curved or had a kink, i n d i c a t i n g that the c r y s t a l l o g r a p h i c growth o r i e n t a t i o n was always maintained. The solute concentration of Ag in.a stationary casting using the four sampling techniques described i s shown i n Figure 82. Comparing the four sets of points i t i s evident that the d i f f e r e n t techniques have various degrees of s c a t t e r associated with them. For the d r i l l e d holes with 1/4 inch steps (Figure 82(a)) the macro- segregation appears c y c l i c from the outer mould w a l l to the c e n t r e l i n e . The experimental accuracy of the points p l o t t e d i s such that they are a true representation of the concentration of the sample measured i n the s c i n t i l l a t i o n counter. Thus the s c a t t e r must be due to a change i n the concentration along the d r i l l hole. To test i f t h i s c y c l i c behaviour i s genuine the 1/8 inch step hole method i s shown i n Figure 82 211 cc U l > CO z o a: u a x a UJ 3.2 r 3.0 2.8 3.2 3.0 (a) 2.8 - 5.2 - 3.0 » 2.8 2.6 3.2 3.0 2.8 - po o o ° o ° o/ooo°oo °° (b) •o—tr— CP o ° OO ° O o o o o f a 0 0 - 0 o n . o ° n 0 o 0 (O O o — a6 - o " o (d) J L 0 0.5 1.0 1.5 DISTANCE FROM MOULD WALL (INCHES) Figure 82. The r a d i a l s i l v e r d i s t r i b u t i o n i n a stationary casting; (a) 1/4 inch d r i l l holes i n 1/4 inch steps, (b) 1/4 inch d r i l l holes i n 1/8 inch steps, (c) 0.030 inch lathe turnings, (d) 0.050 inch lathe turnings dissolved i n ac i d . 212 Again the points show a , c y c l i c behaviour, but the cycle period i s d i f f e r - ent for the two cases. Thus microsegregation along the d r i l l hole must be the cause of the c y c l i n g . The p l o t f o r the s o l i d lathe turnings (Figure 82(c))shows an extensive s c a t t e r between points. This large scatter could be caused by the microsegregation, by the s e l e c t i o n of the material taken from the whole sample, or by not having a s u f f i c i e n t l y con- stant sample geometry due to the nature of the lathe turnings. The f i n a l method of d i s s o l v i n g the turnings of the e n t i r e sample gave the r e s u l t s of Figure 82(d), which shows much less scatter than the other methods. In t h i s case the counting geometry i s not a problem as the l i q u i d i s con- tained i n standard tube and the l i q u i d counted i s a true average of the sample composition. This method gave reproducible r e s u l t s and was used for a l l the subsequent macrosegregation measurements. The r a d i a l macrosegregation i n the three types of ingots i s shown i n Figure 83. Three sets of data were obtained for the r a d i a l macrosegregation, one from the c e n t r a l region of one group of castings, and the other two from near the top and bottom of a second s i m i l a r group of castings. A l l the r e s u l t s for a p a r t i c u l a r type of casting were very s i m i l a r . The s i l v e r concentration i n the stationary and rotated ingots, shown i n Figures 83(a) and 83(b), i s e s s e n t i a l l y constant i n - d i c a t i n g l i t t l e macrosegregation, except for a small drop i n concen- t r a t i o n at the c e n t r e l i n e of the casting. There i s no e f f e c t on the macrosegregation due to the d i f f e r e n c e i n density of the s i l v e r and aluminum i n the rotated casting. In the o s c i l l a t e d case macrosegregation i s present, with an i n i t i a l r i s e i n the s i l v e r concentration up to a peak. The concentration then decreases to the c e n t r e l i n e of the casting 213 UJ o UJ I UJ 5 3.1 3.0 2.9 3.1 3.0 2.9 3.2 3.1 3.0 ° OO o o o o o o 0 (a) j — ° - » o ° o°° o ° o 1 o o o - (b) I ° o ° ° o „ o ^ n G o o c 0 0 O " 6 o o ° o o o - o u " ! O 1 O O o o / X / 1 °x i. o^- (c) j i 0.5 1.0 1.5 DISTANCE FROM MOULD WALL ( INCHES ) Figure 83.The r a d i a l s i l v e r d i s t r i b u t i o n i n (a) stationary, (b) rotated, and (c) o s c i l l a t e d ingots using method (d) of Figure 82. 214 to a value over 0.25% Ag below the C q value. The p o s i t i o n of the CET i s shown on the curve; t h i s p o s i t i o n corresponds to the CET i n Figure 83(c). The r e s u l t s show that the CET corresponds to the maximum s i l v e r concentration. An autoradiograph of the o s c i l l a t e d ingot (Figure 84) shows the macrosegregation q u a l i t a t i v e l y . The l i g h t e r areas towards the centre of the ingot represent s i l v e r depleted areas which correspond to the quantitative measurements (Figure 83(c)). Due to t h i s mottled e f f e c t i n the s i l v e r d i s t r i b u t i o n i t can e a s i l y be seen that the d r i l l hole methods of analysis could give spurious r e s u l t s , as can any analysis that does not include the t o t a l r a d i a l sample. 2.4. Discussion The cast structure associated with stationary, rotated, and (39) o s c i l l a t e d castings are s i m i l a r to those reported by Cole and B o i l i n g and others and w i l l not be discussed here. Two points w i l l be con- sidered. (1) The r e l a t i o n of the observed macrosegregation with the cast structure. (2) The shape of the solute curves. Conditions for the CET are met much e a r l i e r i n the o s c i l l a t e d casting than i n e i t h e r the rotated or stationary casting. This i s be- l i e v e d due to the lowering of the temperature gradient i n the molten region ( o s c i l l a t i o n causes extensive mixing) thus allowing " n u c l e i " , produced by large, shear forces at the i n t e r f a c e , to survive and grow. 215 84. A" autoradiograph of tha cross-section of the oscillated ingot showing tha s i l v e r d i s t r i b u t i o n i n the casting. Actual s i z e * 216 During r o t a t i o n r e v e r s a l these large shear forces w i l l cause remelting (34 41) and/or breaking o f f of dendrite fragments ' which can act as " n u c l e i " . These can e a s i l y be swept i n t o the c e n t r a l region of the l i q u i d pool by the v i o l e n t turbulent flow occurring as a r e s u l t of o s c i l l a t i o n . Observation of t h i s flow i n a rheoscopic l i q u i d shows the existence of a turbulent wave generated at the i n t e r f a c e and r a p i d l y moving to the centre. I f the mould i s rotated at a constant speed (39) the temperature gradient w i l l remain high and no shear forces w i l l be present at the i n t e r f a c e . Therefore, no n u c l e i w i l l be produced and the CET w i l l be suppressed, as observed. For the stationary ingot natural convection w i l l y i e l d low shear forces at the i n t e r f a c e and the temperature gradient w i l l be of some intermediate value. The lack of macrosegregation i n the rotated and stationary ingots can be a t t r i b u t e d to the lack of s i g n i f i c a n t f l u i d flow i n the i n t e r d e n d r i t i c region. Without f l u i d flow there w i l l be no net solute flux from the i n t e r f a c e region, and therefore, no macrosegregation. For the o s c i l l a t e d casting high shear forces i n the v i c i n i t y of the s o l i d - l i q u i d i n t e r f a c e w i l l produce more extensive i n t e r d e n d r i t i c flow. This flow w i l l sweep solute r i c h l i q u i d out of the mushy zone. The solute d i s t r i b u t i o n near the mould w a l l w i l l then tend to conform to the equation f o r complete mixing: c s = k C ^ l - g ) ^ 1 where C G i s the s o l i d solute composition, k the d i s t r i b u t i o n c o e f f i c i e n t , C q the average i n i t i a l solute composition and g the f r a c t i o n s o l i d i f i e d . When the r o t a t i o n i s reversed a turbulent wave i s produced which w i l l 217 transport this solute towards the centre of the solidifying ingot. During columnar growth the solute distribution w i l l therefore be as shown in Figure 85(a). When the CET is imminent the distribution w i l l be that shown in Figure 85(b). The i n i t i a l part of the curve corresponds to a complete mixing situation up to the peak. Beyond the peak the composition gradually decreases towards the centre due to the incomplete mixing of the solute rich liquid generated at the interface. Concurrent with this solute movement is the reduction of the temperature gradient which, unt i l the CET occurs, does not allow survival of nuclei. (At every rotation reversal high shear forces and temperature fluctuations, due to turbulence, w i l l produce a large number of dendrite fragments). When the temperature gradient is sufficiently low these fragments w i l l be able to survive and grow and be swept by the turbulent wave throughout the remaining liquid. Since these fragments are of composition less than C Q the overall composition in this region w i l l be reduced as shown in Figure 85(c). Also, due to the lowering of the temperature gradient the mushy zone w i l l be i n - creased in length. The mass and composition of dendrite fragments necessary to cause this reduction in composition (Figure 85(b) - Figure 85(c)) is calculated in the Appendix, Section 2.6. The solute distribution profile of Figure 85(c) w i l l be that of an ingot oscillated during so l i d i f i c a t i o n . The macrosegregation predicted above was ob- served in the oscillated ingot, Figure 83(c). 2.5. Conclusion The present investigation has shown that no significant 218 DISTANCE FROM MOULD WALL Figure 85. The development of the r a d i a l macrosegregation i n an o s c i l l a t e d ingot, (a) p r i o r to the time of the CET, (b) at the time of the CET, and (c) the f i n a l s i l v e r d i s t r i b u t i o n i n the casting. 219 macrosegregation accompanies s o l i d i f i c a t i o n i n stationary or rotated moulds for the system examined. This implies that the large density difference between the solvent (Al) and solute (Ag) has no e f f e c t on the r a d i a l solute d i s t r i b u t i o n . However, appreciable macrosegregation i s associated with the o s c i l l a t i o n mode of s o l i d i f i c a t i o n . The i n i t i a l r i s e i s at t r i b u t e d to solute mixing i n the l i q u i d i n t e r f a c i a l region due tothe turbulent flow. The maximum concentration i s associated with the columnar to equiaxed t r a n s i t i o n . The solute depletion i n the centre of the casting i s caused by small grains of low solute con- centration being swept, by the turbulent waves, from the mushy zone to the ingot centre. 2.6. Appendix to Section 2 The model proposed for macrosegregation i n the o s c i l l a t e d ingot assumes s u f f i c i e n t dendrite fragments are swept into the ce n t r a l l i q u i d zone, to give the change i n the d i s t r i b u t i o n between Figure 85(b) and 85(c). The following analysis i s an approximate c a l c u l a t i o n for the mass of fragments which i s required. Assume V i s the volume of the ce n t r a l l i q u i d region j u s t p r i o r to the CET. The average composition i n t h i s volume a f t e r t o t a l s o l i d i f i c a t i o n assuming a l i n e a r d i s t r i b u t i o n p r o f i l e i n t h i s region and C^ = 3.0 wt % Ag, i s given by: ) 2TT r C(r)dr 75 = V° Jo 2TT rdr where C(r) i s composition as a function of radius and R i s radius of CET. From Figure 83(c), C(r) = r + 2.70, therefore~C = 3.02 wt % Ag. Comparing Figures 85(b) and 85(c) an estimate of the average composition i n V j u s t p r i o r to the CET can be made (C(r) = r + 3.00) and i s equal to 3.10 wt % Ag. Assuming the composition of dendrite fragments swept into the c e n t r a l region i s ctk C , where a i s a fac t o r to account f o r the i n - o o crease i n solute concentration i n the dendrite branches as s o l i d i f i c a t i o n progresses, assumed to be 1.5, k i s 0.25 for the a l l o y under consider- ation. Therefore: a k C = (1.5)(0.25) (3.0) o o = 1.12 wt % Ag Let v be the volume of dendrite fragments swept in t o the c e n t r a l molten region (V„) at the time of the CET. The r e s u l t i n g change i n the average concentration i n V can then be used to solve for v. Therefore: 3.10 V + 1.12 v =• 3.02 (V + v) Therefore: v = 0.04 V„ This c a l c u l a t i o n shows that a small amount of s o l i d f r a g - ments i s required r e l a t i v e to the t o t a l l i q u i d volume to cause the de- crease i n concentration observed. 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