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Interdendritic fluid flow Kaempffer, Fred L. 1970

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- 1 -INTERDENDRITIC FLUID FLOW by FRED L. KAEMPFFER A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of METALLURGY We accept t h i s t h e s i s as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE THE UNIVERSITY OF BRITISH COLUMBIA August, 1970 In p r e s e n t i n g t h i s t h e s i s in 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 d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , 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 a g r e e t h a 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 t h e Head o f my Depar tment 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 . Depar tment 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 o l u m b i a V a n c o u v e r 8, Canada Date September 24. 1970 - i i -ABSTRACT A q u a l i t a t i v e i n v e s t i g a t i o n of i n t e r d e n d r i t i c l i q u i d flow was car r i e d out on pre-cast Pb-20Sn ingots at temperatures where the casting was p a r t i a l l y l i q u i d . The l i q u i d flow was found to be p r e f e r e n t i a l i n nature, and strongly dependent on surface tension e f f e c t s . Castings of Cu-8Ag and Al-30Ag were made i n which the c h i l l was removed during s o l i d i f i c a t i o n to cause exudation of solute r i c h l i q u i d . Hacrosegregation was detected using radioactive tracer elements. The castings were characterized by a solute enriched exuded zone and a solute depleted region adjacent to the c h i l l . Models based on the simple back-flow of residual l i q u i d to feed exudation were developed to explain the composition p r o f i l e s adjacent to the c h i l l . - i i i -TABLE OF CONTENTS Page ABSTRACT 1 1 TABLE OF CONTENTS 1 1 1 LIST OF FIGURES . v i LIST OF TABLES i x ACKNOWLEDGEMENT x INTRODUCTION • 1 PART I - INTERDENDRITIC FLOW IN LEAD-TIN 5 1. I n t r o d u c t i o n 5 1-1. O r i g i n a l Intent 5 1- 2. Choice of M a t e r i a l s 6 2. Experimental 8 2- 1. A l l o y P r e p a r a t i o n 8 2-2. Tracer P r e p a r a t i o n 10 2-3. Apparatus 10 2-4. Metallography and Autoradiography 14 2- 5. E l e c t r o n Microprobe A n a l y s i s 15 3. Results 15 3- 1. Temperature D i s t r i b u t i o n w i t h i n the Pb-20Sn Ingot 15 3-2. Experiments on Type E Ingots 16 3-3. Experiments on Type SC Ingots 17 3-4. Determination of I n t e r d e n d r i t i c Flow-rate 21 3-5. The E f f e c t of D i f f u s i o n and Convection... 24 3-6. Experiments on Type LC Ingots 26 3-7. E l e c t r o n Microprobe Results 28 - i v -Page 4. Discussion 34 PART I I - BACK-FLOW IN COPPER-SILVER AND ALUMINUM-SILVER 37 1. Introduction 37 1-1. Objective 37 1- 2. Choice of Materials 37 2. Experimental 40 2- 1. Apparatus and Casting Technique 40 2-2. Alloy Preparation 42 2-3. Composition Analysis 43 2-4. Metallography and Autoradiography of Cu-8Ag 44 2- 5. Electron Microprobe Analysis 45 3. Results 45 3- 1. General 45 3-2. The Cu-8Ag System 46 3-2-a. Composition P r o f i l e s 46 3-2-b. Op t i c a l Examination 49 3-2-c. Autoradiography 51 3-2-d. Electron Microprobe Results 51 3-3. The Al-30Ag System 56 3-3-a. Composition P r o f i l e s 56 3-3-b. Discussion 59 3- 4. The Length of the Semi-Solid Zone 60 4. Discusssion 60 4- 1. General 60 4-2. Model I 64 - v -Page 4-2-a. F i r s t Approximations 64 4-2-b. S e l e c t i o n of the D i s t r i b u t i o n C o e f f i c i e n t 68 4-2-c. M o d i f i c a t i o n s 70 4-2-d. The E f f e c t of Remelting 76 4-3. Model I I 78 4-4. Comparison of Models w i t h Experiment .... 80 4-4-a. General ... 80 4-4-b. Casting A 81 4-4-c. Casting B 82 4-4-d. Casting C 82 4-5. A P a r a b o l i c S o l i d - L i q u i d D i s t r i b u t i o n ... 83 GENERAL DISCUSSION AND CONCLUSIONS 87 SUGGESTED FUTURE WORK 88 REFERENCES 89 APPENDICES 90 A. E l e c t r o n Microprobe C o r r e c t i o n s f o r Pb-Sn 90 B. E l e c t r o n Microprobe Co r r e c t i o n s f o r Cu-Ag 95 C. The Extension Factor 97 - v i -LIST OF FIGURES Figure Page 1 T y p i c a l inverse segregation p r o f i l e f or d i r e c t i o n a l l y s o l i d i f i e d castings 2 2 Apparatus for measuring the flow-rate of i n t e r d e n d r i -t i c l i q u i d using tracers 5 3 Phase diagram of the Pb-Sn system 7 4 Apparatus for making columnar Pb-20Sn ingots 9 5 Furnace for heating Pb-20Sn ingots 11 6 The temperature control c i r c u i t f o r heating Pb-20Sn ingots 13 7 Locations of thermocouples to determine the tempera-ture d i s t r i b u t i o n i n s i d e a Pb-20Sn ingot 15 8 Section of a type E ingot i n which i n t e r d e n d r i t i c flow has occurred 18 9 Autoradiographs of type SC ingots showing l i q u i d flow patterns 20 10 The e f f e c t of bubble s i z e on l i q u i d flow 21 11 The l i q u i d flow-rate i n type SC ingots 23 12 Autoradiograph of a type LC ingot to show d i f f u s i o n e f f e c t s 25 13 A type LC ingot a f t e r the f i r s t droplet has f a l l e n . . . 27 14 Section of a type LC ingot quenched at 196°C 27 15 Section of a type LC ingot quenched at 209°C 29 16 Cross-section of a type LC ingot quenched at 209°C .. 30 17 E.egions analyzed for composition and an electron back-scatter image of a type LC ingot 32 18 The e f f e c t of d i s s o l u t i o n on the composition i n s i d e a flow-pipe 33 19 I n t e r d e n d r i t i c f l u i d flow model for Pb-20Sn 35 - v i i -Figure Page 20 Phase diagrams of Cu-Ag and Al-Ag 38 21 Apparatus for casting Cu-Ag and Al-Ag ingots 41 22 A t y p i c a l Cu-8Ag casting 45 23 Composition p r o f i l e s of Cu-8Ag ingots 47 24 Cooling curves for Cu-8Ag castings 48 25 Longitudinal section of a Cu-8Ag casting 50 26 Micrograph of the i n t e r f a c e between the depleted zone and the rest of the ingot 52 27 Longitudinal section through the c h i l l - f a c e 53 28 Cross-section at the c h i l l - f a c e of casting A 54 29 Microsegregation 0.21" above the c h i l l - f a c e 55 30 Plot of C vs distance from the c h i l l 56 s 31 Composition p r o f i l e s of Al-30Ag ingots 57 32 Cooling curves for Al-30Ag castings 58 33 Cooling curves to determine the length of the mushy zone i n Cu-8Ag 61 34 Cooling curves to determine the length of the mushy zone i n Al-30Ag 62 35 Schematic representation of model I 65 36 A l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n 66 37 Plot of Equation 6 for various k values 68 38 Solute d i s t r i b u t i o n across primary dendrites 69 39 I n t e r d e n d r i t i c l i q u i d displacement 71 40 Displacement of l i q u i d for a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n 72 41 The increase i n width of downward moving l i q u i d elements 73 42 Plot of Equation 14a and 14b 74 - v i i i -Figure Page 43 The remelting of dendrites 76 44 Plot of Equation 17 77 45 Schematic representation of model II 78 46 Si m p l i f i e d solute d i s t r i b u t i o n and i t s r e l a t i o n to a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n 79 47 Comparison of models with experimental Cu-8Ag solute d i s t r i b u t i o n p r o f i l e s 83 48 A comparison of models 84 49 The s h i f t i n minima caused by a parabolic s o l i d - l i q u i d d i s t r i b u t i o n 86 50 Microprobe corrections f o r Pb-Sn 93 51 The summation of %Pb and %Sn for spot counts 94 52 Microprobe corrections for Cu-Ag 96 - i x -LIST OF TABLES Table Page 1 Thermal Conditions for Experiments on Type SC Ingots. 17 2 Comparison of Flow-Rates with Darcy's Law 24 3 Theoretical and Experimental Penetration Distances of Master Alloy 26 4 Compositions of a Type LC Ingot 31 5 De t a i l s of Cu-8Ag Castings 46 6 Details of Al-30Ag Castings 59 7 Estimated Lengths of the Semi-Solid Zone 60 8 The V a r i a t i o n of C with Respect to g 75 9 Additional D e t a i l s of Cu-8Ag Castings 81 ACKNOWLEDGEMENT I am greatly indebted to my research d i r e c t o r , Dr. F. Weinberg, for h i s excellent guidance and encouragement throughout t h i s work. Assistance from other f a c u l t y members and fellow graduate students i s also g r a t e f u l l y acknowledged. I extend s p e c i a l thanks f o r generous assistance given by many members of the departmental te c h n i c a l s t a f f ; i n p a r t i c u l a r Mr. J. Brezden for h i s u n f a i l i n g a id during much of the experimental work. I g r a t e f u l l y acknowledge f i n a n c i a l assistance from the Defence Research Board [grant number 9535-51]. INTRODUCTION Extensive t h e o r e t i c a l c a l c u l a t i o n s that q u a n t i t a t i v e l y predict inverse segregation behaviour have been formulated by Scheil,"^ 2 3 Kirkaldy and Youdelis, and Flemings et a l . The models used i n these c a l c u l a t i o n s are based on the assumption that inverse segregation i s caused s o l e l y by the back-flow of i n t e r d e n d r i t i c l i q u i d to compensate for the volume shrinkage of dendrites on freezing and coo l -ing. As a r e s u l t , nearly a l l the experimental work i n t h i s f i e l d has been done on aluminum a l l o y s because of t h e i r high volume changes on freezing and thermal expansion c o e f f i c i e n t s . A t y p i c a l inverse segregation experiment consists of d i r e c t i o n a l l y s o l i d i f y i n g a melt from bottom to top and chemically determining the composition of thin s l i c e s cut from the ingot perpendicular to the s o l i d i f i c a t i o n d i r e c t i o n . T y p i c a l r e s u l t s f o r r a p i d l y cooled castings 3 4 i n the Al-Cu system a f t e r Flemings and Adams are shown i n F i g . 1. The inverse segregation curve i s generally explained i n the following manner: As s o l i d i f i c a t i o n begins, a semi-solid (mushy) zone i s formed, and r e s i d u a l enriched l i q u i d ( r e s u l t i n g from normal segregation during freezing) feeds downwards to compensate for freezing shrinkage causing an enrichment i n solute near the c h i l l . As a r e s u l t , the enriched l i q u i d at the upper part of the mushy zone i s - 2 -I.l c_ i.o Co 0.9 o Flemings AI-4.6%Cu A Adams AI-7%Cu S > AO O © \ £ \ \ CHILL 0.2 0.4 0.6 0.8 FRACTIONAL DISTANCE ALONG INGOT 1.0 Figure 1. T y p i c a l inverse segregation p r o f i l e f o r d i r e c t i o n a l l y s o l i d i f i e d castings. replaced by l i q u i d of nominal composition, Co, causing a solute impoverishment i n th i s region. As s o l i d i f i c a t i o n progresses, this impoverished region i s also fed by solute enriched l i q u i d causing another impoverished zone to form above i t . This process continues u n t i l the impoverished zone reaches the top of the ingot at which point feeding i s no longer possible and the composition drops. - 3 -3 Flemings et a l , who present the most comprehensive a n a l y s i s of macrosegregation i n bin a r y a l l o y s , consider a volume element i n the s e m i - s o l i d zone c o n t a i n i n g both s o l i d and l i q u i d m a t e r i a l , and examine the flow of f l u i d through t h i s element. To p r e d i c t microsegregation i n the element, they use the c l a s s i c a l n o n - e q uilibrium f r e e z i n g eauation: C g = k C o ( l - g ) k 1 where C g = s o l i d composition at the s o l i d - l i q u i d i n t e r f a c e g = f r a c t i o n of s o l i d m a t e r i a l Co = i n i t i a l average composition w i t h i n the volume element considered, k = p a r t i t i o n r a t i o This equation, which assumes no d i f f u s i o n i n the s o l i d and no macro-segregation, was derived f o r one-dimensional s o l i d i f i c a t i o n . The other important assumptions made i n the Flemings a n a l y s i s are: (a) N e g l i g i b l e undercooling before n u c l e a t i o n . Cb) No net flow of s o l u t e from the volume element by d i f f u s i o n . (c) D i f f u s i o n i n the l i q u i d w i t h i n the volume element i s complete. (d) The p a r t i t i o n r a t i o , k, a p p l i e s at the i n t e r f a c e and i s constant throughout s o l i d i f i c a t i o n . In s h o r t , a number of assumptions are made concerning the flow of i n t e r d e n d r i t i c l i q u i d to derive t h e o r e t i c a l s o l u t e d i s t r i b u t i o n p r o f i l e s which are subsequently compared to experimental p r o f i l e s . The i n i t i a l aim of t h i s p r o j e c t was to d i r e c t l y study the f l o w - r a t e of i n t e r d e n d r i t i c - 4 -l i q u i d i n Pb-Sn a l l o y s u s i n g r a d i o a c t i v e t r a c e r s . The p a r t i c u l a r e x p e r i m e n t d e s i g n e d f o r t h i s i n v e s t i g a t i o n was u n s u c c e s s f u l , however, but y i e l d e d q u a l i t a t i v e r e s u l t s w h i c h l e d t o t h e s t u d y of e x u d a t i o n s i n t h e Cu-Ag and A l - A g systems. T h i s t h e s i s , c o n s e q u e n t l y , i s d i v i d e d i n t o two p a r t s . I n P a r t I , Pb-Sn i n g o t s a r e h e a t e d i n t o the s e m i - s o l i d range and i n t e r d e n d r i t i c l i q u i d i s d i s p l a c e d by e u t e c t i c l i q u i d u s i n g g r a v i t y as the d r i v i n g f o r c e . The o n l y s i m i l a r work known t o the a u t h o r was done by Piwonka and Flemings"' who used m o l t e n l e a d t o d i s p l a c e the i n t e r d e n d r i t i c f l u i d o f Cu a l l o y . The f l o w o b s e r v e d was homogeneously d i s t r i b u t e d between d e n d r i t e s and was compared to f l o w t h r o u g h porous beds. T h i s can be e x p e c t e d when one r e a l i z e s the e x t r e m e l y low s o l u b i l i t y o f aluminum i n m o l t e n l e a d (0.1 wt. p e t . A l at 600°C). The purpose o f t h e p r e s e n t work, t h e r e f o r e , was t o s t u d y a more r e a l i s t i c s i t u a t i o n , where one might e x p e c t t h e p a r t i a l d i s s o l u t i o n of d e n d r i t e s and subsequent w i d e n i n g o f i n t e r d e n d r i t i c c h a n n e l s . I n P a r t I I , m e l t s of Cu-Ag a l l o y and A l - A g a l l o y a r e p a r t i a l l y s o l i d i f i e d from one end, and the c h i l l i s moved a s h o r t d i s t a n c e away from the c a s t i n g c a u s i n g r e h e a t i n g and e x u d a t i o n a t t h e c h i l l - f a c e o f the i n g o t . To t h e a u t h o r ' s knowledge, t h i s t y p e of e x p e r i m e n t has not been p r e v i o u s l y s t u d i e d i n any d e t a i l . - 5 -PART I - INTERDENDRITIC FLOW IN LEAD-TIN 1. I n t r o d u c t i o n 1-1. O r i g i n a l I n t e n t The o r i g i n a l o b j e c t i v e was t o measure the r a t e o f f l o w o f i n t e r d e n d r i t i c l i q u i d u s i n g r a d i o a c t i v e t r a c e r e l e m e n t s and t r a c e r d e t e c t i o n d e v i c e s . The m a t e r i a l chosen f o r t h i s s t u d y was t o have a broa d s e m i - s o l i d r e g i o n w i t h r e s p e c t t o b o t h c o m p o s i t i o n and tempera-t u r e . The i n i t i a l i d e a i s shown p i c t o r i a l l y i n F i g . 2. The i n g o t CONSTANT TEMP. ENCLOSURE EUTECTIC + TRACER CASTING •MOVABLE AL FOIL SCREEN GEIGER COUNTER F i g u r e 2. A p p a r a t u s f o r m e a s u r i n g the f l o w - r a t e o f i n t e r d e n d r i t i c l i q u i d u s i n g t r a c e r s . - 6 -was to be held at constant temperature i n the s e m i - s o l i d region and the t r a c e r c o n t a i n i n g e u t e c t i c would flow downwards through i n t e r -d e n d r i t i c channels. L i q u i d f a l l i n g through the i n g o t would be caught on an aluminum screen and immediately removed. A geiger counter would monitor the a c t i v i t y of the descending m a t e r i a l and the count rat e would be adjusted to give the f l o w - r a t e of i n t e r d e n d r i t i c l i q u i d . This s p e c i f i c experiment, u n f o r t u n a t e l y , was not s u c c e s s f u l , as w i l l be seen l a t e r , and s t u d i e s of i n t e r d e n d r i t i c flow were confined to autoradiography, metallography, and drop experiments. 1-2. Choice of M a t e r i a l s A Pb-20 wt.pct. Sn a l l o y was chosen f o r the f o l l o w i n g reasons: (a) The low melting p o i n t of the system (327°C f o r pure lead) made furnace c o n s t r u c t i o n and handling r e l a t i v e l y easy. (b) At the composition s e l e c t e d , a broad s e m i - s o l i d zone e x i s t s w i t h respect to both t i n concentration and temperature. The phase diagram^ i s shown i n F i g . 3. 204 * (c) Radioactive T l ( T l ) was a v a i l a b l e as a t r a c e r element. Large concentrations of T l are completely s o l u b l e i n lead and the p h y s i c a l p r o p e r t i e s of T l are v i r t u a l l y i d e n t i c a l to those f o r pure lead. Being a beta e m i t t e r , T l i s i d e a l f o r autoradiography because photographic f i l m i s much more s e n s i t i v e to low energy r a d i a t i o n as opposed t o , f o r example, higher energy gamma r a d i a t i o n . Good contrast and r e s o l u t i o n are a l s o p o s s i b l e s i n c e lead has a l a r g e capture c r o s s -s e c t i o n f o r beta r a d i a t i o n . Figure 3 . Phase diagram of the Pb-Sn system. - 8 -During the experimental work, other advantages of Pb-20 Sn were discovered: (d) The softness of the a l l o y made machining and p o l i s h i n g of specimens r e l a t i v e l y simple, (e) Eutectic formations made dendrites e a s i l y d i s t i n g u i s h a b l e for metallographic studies. (f) The high c o e f f i c i e n t of absorption of lead with respect to t i n for electrons and X-rays made high r e s o l u t i o n electron backscatter images possible on the electron microprobe. 2. Experimental 2-1. Alloy Preparation The a l l o y was prepared using high p u r i t y Cominco Pb (99.999%) and high purity Vulcan Sn (99.999%). Starting ingots were made by melting the constituents i n a graphite c r u c i b l e , s t i r r i n g , and casting into graphite moulds. F i n a l c y l i n d r i c a l ingots having various d e n d r i t i c structures were prepared by the following techniques: (a) The ingot was made by furnace cooling the melt from 350°C i n a graphite c r u c i b l e , producing an equiaxed d e n d r i t i c structure (E). (b) A s t a r t i n g ingot was placed inside the graphite mould of the apparatus shown i n F i g . 4. The mould was heated and the melt was held at 310.0 i 0.2°C for 35 minutes to insure homogeniety. The bottom end of the ingot was c h i l l e d by spraying cold tap water from a constant head (18") against the copper plug. Ingots 2.2" long and 0.88" i n diameter were made using t h i s technique under an argon atmo-sphere to prevent oxidation. This produced a de n d r i t i c columnar - 9 -£ Ar IN ure 4. Apparatus'for making columnar Pb-20Sn ingots. - 10 -structure with a small primary dendrite arm spacing (SC). (c) This process i s the same as (b) except that the c h i l l i s done using a i r at a constant flow-rate, producing a d e n d r i t i c columnar structure of larger spacing (LC). After casting the SC and LC ingots, 0.4" was machined o f f both ends to remove macrosegregation e f f e c t s ( i . e . the solute enriched zone near the c h i l l and the depleted zone at the top of the ingot). Desired lengths were cut from the remaining casting, and the ends were machined smooth.. 2-2. Tracer Prepartion To investigate the e f f e c t of adding T l to the Pb-20Sn a l l o y , ingots were cast containing 1000 ppm. of T l as received from Chalk River. One ingot was quenched from the melt i n water and the other was furnace cooled. The ingots were sectioned l o n g i t u d i n a l l y and auto-radiographed using Kodak Contrast Process Ortho Film. In both cases the f i l m was blackened evenly, i n d i c a t i n g that any segregation of T l could not be resolved using t h i s technique. A eutectic Pb-Sn a l l o y containing 1700 ppm. of T l was made for use i n subsequent experiments and w i l l be referred to as "Master A l l o y " . Being of eutectic composition, t h i s a l l o y melts a l l at once at the lowest temperature at which l i q u i d can e x i s t i n the Pb-Sn system. The importance of t h i s w i l l become obvious l a t e r . 2-3. Apparatus Prepared specimens were placed i n the furnace shown i n Fig. 5. - 11 -SUPPORTING TUBE TC TO TEMP. CON. TC TO TEMP. REC. VYCOR TUBE FURNACE SHELL VERMICULITE SAIRSET CU CYLINDER MAIN ELEMENT PB-SN EUTECTIC PB-SN ALLOY ASBESTOS LAYER SEC. ELEMENT ASBESTOS GASKETS CU RING CU GASKET AL GASKETS gure 5. Furnace for heating Pb-20Sn ingots. - 12 -The most important part of the furnace was a copper cylinder to provide temperature homogeniety. The ins i d e of the cylinder had a diameter of 0.88" and was tapered such that the diameter of the bottom end was 0.020" greater than that of the top end. Specimens were pushed into the cy l i n d e r using a 0.75" diameter brass rod with a f l a t polished end. The r e s u l t was a snug f i t between the outside of the ingot and the ins i d e of the copper cyl i n d e r , preventing any molten material from flowing down along t h i s i n t e r f a c e . Both inside and outside surfaces of the cylinder were coated with an adherent graphite layer using a c o l l o i d a l graphite wash. This prevented any d i s s o l u t i o n of copper by the lead or the t i n . The graphite layer could be thickened somewhat to provide a snug f i t for s l i g h t l y under-sized ingots. In some cases a thin wafer of Master A l l o y was placed on top of the ingot. To accommodate th i s wafer a small depression 0.1" deep and 0.73" i n diameter was machined into the top,of the ingot. Two iron-constantan thermocouples were inserted i n the copper block, as shown i n Fig. 5; one for a Honeywell temperature c o n t r o l l e r , and the other for a Honeywell E l e c t r o n i k 194 temperature recorder. An i c e bath was used as a cold junction f or both thermocouples. The temperature control system using two heating elements i s shown schematically i n F i g . 6. The control c i r c u i t prevented a temperature drop at the open end of the furnace, while the main c i r c u i t c o n t r o l l e d the o v e r a l l temperature. The complete copper cylinder assembly was supported by a brass tube and could be lowered into a water bath below the furnace for Figure 6. The temperature control c i r c u i t for heating Pb-20Sn ingots. - 1 4 -quenching. A long pyrex tube was inserted down the supporting tube to introduce an argon atmosphere and prevent oxidation of the upper surface of the ingot. A long copper tray l i n e d with a wire mesh and f i l l e d with water was used to catch drops of molten metal below the furnace. After a drop f e l l into the tray, the tray was s h i f t e d so that the next drop f e l l on a separate area and could subsequently be weighed separately. The time of f a l l i n g was recorded on the temperature chart by b r i e f l y shorting the thermocouple. 2-4. Metallography and Autoradiography Specimens were mi l l e d to the desired surface i n the ingot with a 0.50" diameter m i l l i n g t o o l at high speed. The m i l l e d surface was s u f f i c i e n t l y smooth to proceed d i r e c t l y to a 5 micron alumina p o l i s h -ing lap, followed by a 0.05 micron alumina lap. The etching action of the water used i n p o l i s h i n g was s u f f i c i e n t to obtain good r e s o l u t i o n of d e n d r i t i c structures. A diamond lap was found unsatisfactory for po l i s h i n g Pb-20Sn specimens. Mounted specimens were also d i f f i c u l t to p o l i s h because the a l l o y was cut away fa s t e r than the epoxy mounting material. Metallographs were made with u n f i l t e r e d l i g h t i n g using a Reichert microscope and Polaroid Type 55 Positive/Negative f i l m . Radioactive specimens were prepared and polished as above. To autoradiograph, the polished surface was placed against a sheet of Kodak Contrast Process Ortho f i l m for periods of time varying from 24 to 93 hours u n t i l the best r e s o l u t i o n was obtained. In a l l the autoradiographs shown, tracer i s present i n the dark regions. - 15 -2- 5. Electron Microprobe Analysis Composition analysis of metallographic specimens was done using a JEOL Model JXA-3A Electron Probe X-ray Microanalyzer. D e t a i l s of electron backscatter and absorption corrections are given i n Appendix A. 3. R.esults 3- 1. Temperature D i s t r i b u t i o n within the Pb-20Sn Ingot A Pb-20Sn ingot 0.75" i n length was cast with thermocouples i n the locations shown i n F i g . 7. Thermocouple #8 was placed up through the bottom Cu CYLINDER Pb-Sn INGOT Figure 7. Locations of thermocouples to determine the temperature d i s t r i b u t i o n inside a Pb-20Sn ingot. - 16 -of the furnace and j u s t touched the surface of the ingot. The system was held at 200°C and the con t r o l c i r c u i t was adjusted to give the most homogeneous temperature d i s t r i b u t i o n . This s e t t i n g was used f o r a l l subsequent experiments. The temperature difference between thermocouples / / l and #2 was not detectable to within 0.1°C. The temperature recorded by the thermocouple inside the copper cyl i n d e r , therefore, was considered representative of the temperature of the ingot. The maximum temperature difference between any two thermo-couples (#1 and #8) was 0.2°C. 3-2. Experiments on Type E Ingots Type E ingots of Pb-20Sn a l l o y , 0.7" i n length, were held at the eute c t i c temperature (183°C) for 5 minutes and then heated slowly at a rate of 0.5°C per minute. The undersurface of the ingot was observed using a mirror. Small bubbles of molten metal were v i s i b l e at 209°C and these increased i n size as heating continued. F i n a l l y these bubbles coalesced into one large bubble which hung from the bottom of the ingot. This bubble continued increasing i n size and f i n a l l y dropped into the water quench at 248°C. A s i m i l a r experiment was conducted with a thi n wafer (0.1" thick) of Master Alloy covering the top of the specimen. The furnace was held at 248°C for 40 minutes. The f i r s t drop of molten metal f e l l when 248°C was f i r s t reached and a l l subsequent drops f e l l within the f i r s t 13 minutes. Nine droplets, each having approximately the same volume and weight, f e l l i n a l l . The l a s t droplet was quite radioactive i n d i c a t i n g that some l i q u i d from the top of the ingot had flowed through I - 17 -to the bottom. The t o t a l weight of the d r o p l e t s was 9.7% of the t o t a l weight of the o r i g i n a l i n g o t . According to the phase diagram ( F i g . 3), the ingot was about 30% l i q u i d . The system was quenched and the remaining i n g o t , which had shrunken s l i g h t l y i n both length and diameter, was sectioned l o n g i t u d i n a l l y . (The time f o r the ingot to become completely s o l i d during quenching was 10 seconds.) The micrographs and autoradiographs are shown i n F i g . 8. The Master A l l o y was the f i r s t m a t e r i a l to melt and i t flowed downward r e p l a c i n g the i n t e r d e n d r i t i c l i q u i d i n the c a s t i n g . From F i g . 8, one observes that the flow was concentrated towards the center of the i n g o t , but was i n t e r d e n d r i t i c i n nature. The same phenomena was observed i n repeated experiments using the same equiaxed s t r u c t u r e . 3-3. Experiments on Type SC Ingots A s e r i e s of experiments were conducted on type SC ingots 0.4" i n length. The ingots had a re g u l a r columnar s t r u c t u r e and an average primary dendrite spacing of about 400 microns. The thermal c o n d i t i o n s of the experiment are l i s t e d i n Table 1. In a l l cases i d e n t i c a l heating Table 1. Thermal Conditions f o r Experiments on Type SC Ingots Experiment Holding Holding Time at Other Conditions No. Temperature Temperature before Quenching A 220°C 0 B 235°C 0 C 245°C 2.3 min. D 245°C 2.3 min. Wire mesh p o s i -tioned at the bottom face of the ingot. Figure 8 . Micrographs (a) and autoradiographs (b) of a l o n g i t u d i n a l section of a type E ingot i n which i n t e r d e n d r i t i c flow has occurred. - 19 -rates of 6°C per minute were used i n heating to temperature. For experiment D, a 24 mesh brass screen having a hole diameter of 0.03" was placed against the bottom face of the ingot. The mesh was coated with c o l l o i d a l graphite to prevent wetting by molten Pb-Sn a l l o y . After quenching, the ingots were sectioned and autoradiographed as shown i n F i g . 9. The fineness of the dendrite structure, unfortunately, prevented good r e s o l u t i o n . One observes, however, that the flow of i n t e r d e n d r i t i c l i q u i d was not homogeneously d i s t r i b u t e d over the e n t i r e cross-section of the ingot, but was p r e f e r e n t i a l i n nature. Comparing the autoradiographs of tests C and D (Fig. 9), one sees that the presence of the wire screen greatly i n h i b i t e d the flow of l i q u i d . The g r i d , i n e f f e c t , broke the large bubble, which normally hangs below the ingot as i n F i g . 13, up into smaller bubbles. This indicates that surface tension e f f e c t s at the surface of the ingot play an important r o l e i n r e s t r i c t i n g l i q u i d flow. The pressure, P, due to surface tension, T, on a droplet of radius r i s given by: Referring to F i g . 10, as r decreases (due to the presence of a screen), the pressure r e s t r i c t i n g the flow of l i q u i d increases. - 20 -Figure 9. Autoradiographs of l o n g i t u d i n a l sections of type S C ingots showing l i q u i d flow patterns. - 21 -Pb-Sn INGOT P > P \ 2 Figure 10. Schematic r e p r e s e n t a t i o n showing the e f f e c t of bubble s i z e on l i q u i d flow. 3-4. Determination of the L i q u i d Flow-rate A type SC ingot 0.4" i n length w i t h a 0.1" t h i c k wafer of Master A l l o y on top was heated at 6°C per minute to 245°C and hel d there u n t i l l i q u i d d r o p l e t s of metal stopped f a l l i n g . Droplets Xv-ere c o l l e c t e d i n the movable t r a y underneath the furnace and the time of f a l l i n g was recorded. By weighing each d r o p l e t , the f l o w - r a t e was determined as f o l l o w s . In the i n t e r v a l of time during which a drop s t a r t s to form u n t i l i t f a l l s , a l i n e a r build-up r a t e of m a t e r i a l i n grams per minute i s assumed. The f i r s t d r o p l e t i s assumed to s t a r t forming at the f i r s t l i q u i d temperature (183°C) and stop forming when i t f a l l s . The weight of the f i r s t droplet i s divided by t h i s time i n t e r v a l to give the average rate of formation. The rate of build-up of subsequent droplets i s determined by using the time i n t e r v a l between the f a l l i n g of the droplet i n question and the preceding one. The r e s u l t s for 3 such experiments are shown i n F i g . 11. The important feature to notice i s that most of the flow occurred c a t a s t r o p h i c a l l y during a short i n t e r v a l of time. In work done by Piwonka and Flemings,^ the flow-rate of molten lead through a semi-solid Al-4.5Cu a l l o y was compared to f l u i d flow through porous beds using Darcy's Law: Q _ K A P yL where 0 = flow rate per unit area. AP = pressure drop across an ingot of length L. u = v i s c o s i t y of the l i q u i d . K = permeability of the bed. The permeability was found to vary with the square of the f r a c t i o n of l i q u i d , f , present i n the ingot. Using t h e i r permeability versus f r a c t i o n l i q u i d data, assuming the l i q u i d i s of e u t e c t i c composition, and estimating the l i q u i d f r a c t i o n from the Pb-Sn phase diagram, the flow-rates obtained i n t h i s work (Fig. 11) were compared to Darcy's Law. The pessure drop, AP, was calculated from: AP = pgL - 23 -Figure 11. The l i q u i d flow-rate i n type SC ingots heated to 245°C. - 24 -where p = den s i t y of the e u t e c t i c g = g r a v i t a t i o n a l f i e l d s t r e n g t h L = ingot length Two flo w - r a t e s were considered: the i n i t i a l r a t e at low temperature (0.3 gm/min.) and that during c a t a s t r o p h i c flow (2.5 gm/min.). The r e s u l t s are l i s t e d i n Table 2. During c a t a s t r o p h i c flow one observes that the flow was at l e a s t one order of magnitude gre a t e r than what i s pr e d i c t e d by flow through porous beds. Table 2 Comparison of Flow-rates w i t h Darcy's Law Temperature (°C) 203 223 L i q u i d f r a c t i o n , f 0.03 0. ,14 L P e r m e a b i l i t y , K (cnr) 3 x 10" 1 1 10" -10 L i q u i d v i s c o s i t y , ^ u (poise) 0.025 0. 023 8 3 L i q u i d d e n s i t y , p (gm/cm ) 8.41 8. 42 Ingot l e n g t h , L (cm) 1.0 1. ,0 2 Pressure drop, AP (dynes/cm ) 8. ,25 x 103 8.25 x i o 3 C a l c u l a t e d f l o w - r a t e (cm/sec) 1. .0 x 10 - 5 3.6 x i o " 5 Experimental f l o w - r a t e (cm/sec) 1. -4 .5 x 10 1.3 x i o "3 3-5. The E f f e c t of D i f f u s i o n and Convection The experiment co n s i s t e d of determining the rate of p e n e t r a t i o n of Master A l l o y i n t o a p a r t i a l l y melted c a s t i n g w i t h no flow out of the bottom of the ingot. As shown i n F i g . 9 , the d e n d r i t i c s t r u c t u r e of type SC ingots was too f i n e f o r good r e s o l u t i o n i n the autoradiographs. - 25 -For further study, therefore, type LC ingots with larger dendrite spacings were used. The average primary dendrite arm spacing was 1400 microns. The bottoms of the ingots were blocked o ff with a graphite plug. A wafer of Master A l l o y was placed on top of the ingot and the system was held at 250°C f or various periods of time. Heating between the f i r s t l i q u i d temperature (183°C) and 250°C required 11 minutes. The penetration of tracer material was measured from autoradiographs as -5 2 i n F i g . 12. Using a value of D = 10 cm /sec i n the approximate TOP OF INGOT TRACER PENETRATION LEVEL X 8 Figure 12. Autoradiograph of a l o n g i t u d i n a l section of a type LC ingot to show d i f f u s i o n e f f e c t s . Holding time: 20 minutes at 250°C. 2 expression: x = 2Dt, where x i s the d i f f u s i o n distance and t i s the time, penetration distances were calculated and compared with measure-ments as l i s t e d i n Table 3. - 26 -Table 3 Theoretical and Experimental Penetration Distances of Master A l l o y Temperature conditions Penetration of tracer observed x calculated x 5 min. at 250°C 0.1 cm 0.14 cm 20 min. at 250°C 0.2 cm 0.19 cm The observed and calculated values of the penetration are e s s e n t i a l l y the same. This demonstrates that n e g l i g i b l e f l u i d flow existed i n the i n t e r d e n d r i t i c l i q u i d for the thermal conditions used i n the experiments. 3-6. Experiments on Type LC Ingots Experiments were done with two equally sized ingots, each 0.4" long, placed one on top of the other. The upper ingot was Master Alloy and the lower one was a type LC ingot. The furnace was heated at 6°C per minute and the system was quenched at various temperatures. The following observations were made: (a) The f i r s t small bubbles of l i q u i d metal became v i s i b l e at the undersurface of the ingot at 190°C. (b) At 198°C, molten droplets began f a l l i n g at a rate too fast to count using the s l i d i n g tray. A view of the bottom of the ingot a f t e r the f i r s t droplet has f a l l e n i s shown i n F i g . 13. Cc) A l l the e u t e c t i c , which o r i g i n a l l y sat above the lower - 27 -EUTECTIC Pb-Sn INGOT X 3 Figure 13. Bottom view of a type LC ingot a f t e r the f i r s t droplet has f a l l e n . Figure 14. Longitudinal section of a type LC ingot quenched at 196°C. - 28 -ingot, passed through the ingot leaving i t s t r u c t u r a l l y i n t a c t . Figures 14 and 15(a) show l o n g i t u d i n a l sections of ingots quenched at 196°C and 209°C. In the f i r s t case, flow of i n t e r d e n d r i t i c l i q u i d has barely begun, but one can see t h i n continuous i n t e r d e n d r i t i c pipes which extend the f u l l length of the Pb-20Sn ingot. In the second case, flow has been completed and one observes widening of a few channels. Inside these channels are what could be interpreted as dendrite sections broken or melted o f f the side of the channel. If * this was, i n f a c t , true, these dendrite sections would not contain T l and would appear white i n an autoradiograph. The autoradiograph of the channels, F i g . 15(b), shows an enrichment of tracer i n the d e n d r i t i c sections, i n d i c a t i n g that the dendrites inside the pipes did not come from the casting, but were associated with freezing during the quenching process. The p r e f e r e n t i a l "flow-pipes" are c l e a r l y shown i n a section of the ingot perpendicular to the columnar axis i n F i g . 16. The plane shown i s 0.1" from the o r i g i n a l bottom end. The autoradiograph i n Fig. 16(b) shows several large pipes and the outline of a d e n d r i t i c structure i n two large regions. This indicates that some of the flow was i n t e r d e n d r i t i c i n nature without s u b s t a n t i a l widening of pipes. 3-7. Electron Microprobe Results. The purpose of t h i s study was to determine compositional changes inside a flow-pipe. The microprobe was used to analyze composition at cross-sections taken from the top and bottom of an LC ingot through which complete flow of eutectic had occurred. Random counts were taken - 29 -Figure 15. Longitudinal section of a type LC ingot quenched at 209°C: micrograph (a) and autoradiograph (b). - 30 -Figure 16. Cross-section of a type LC ingot quenched at 209°C: micrograph (a) and autoradiograph (b). - 31 -i n v a r i o u s regions of the ingot as depicted i n F i g . 17(a), and averaged to give the r e s u l t s shown i n Table 4. 20 random counts were taken f o r each region. An e l e c t r o n b a c k s c a t t e r photograph of the ingot showing the two-phase d e n d r i t i c s t r u c t u r e and the two-phase e u t e c t i c s t r u c t u r e i s shown i n F i g . 17(b). Table 4 Compositions of a Type LC Ingot Region of ingot Composition (wt.%)  Top of ingot Bottom of ingot Pb r i c h phase i n a flow-pipe (a^) Sn r i c h phase i n a flow-pipe (3^) Pb r i c h phase of a dendrite (a^) Sn r i c h phase of the i n t e r d e n t r i t i c e u t e c t i c ( 3 2 ) 83.5% Pb 84.8% Sn 90.0% Pb 80.5% Sn 91.9% Pb 93.2% Sn 89.7% Pb 80.9% Sn The measured t i n compositions are not b e l i e v e d to be very accurate because of the high a b s o r b i t i v i t y of lead. Consider, t h e r e f o r e , the composition of the phase i n a flow-pipe. On quenching, n u c l e a t i o n of dendrites i n the channel occurred f i r s t , followed by the sudden f r e e z i n g of e u t e c t i c . Homogeneous f r e e z i n g i s assumed to occur since the dendrites have an equal s i z e and d i s t r i b u t i o n throughout the channel. R e f e r r i n g to F i g . 18, one s t a r t s w i t h e u t e c t i c composition above the ingot. At the top of the i n g o t , enrichment of the e u t e c t i c - 32 -Figure 17. Regions analyzed for composition (a) and an electron backscatter image (b) of a cross-section of a type LC ingot. Figure 18. Phase diagram showing the e f f e c t of d i s s o l u t i o n on the composition inside a flow-pipe. - 34 -i n lead by d i s s o l u t i o n at the walls of the pipe produces an o f f eutectic composition, A. The f i r s t s o l i d of t h i s material forms at B. With continued cooling, s o l i d B approaches F, and l i q u i d A approaches C u n t i l e utectic nucleates and the remaining l i q u i d freezes. At the bottom of the pipe, increased d i s s o l u t i o n causes a greater enrichment of the eutectic D. As before, D approaches C and E approaches G. The lead concentration, G, at the bottom of the pipe i s , therefore, greater than the lead concentration, F, at the top of the pipe. This enrichment of eutectic was observed experimentally as shown i n Table 4 ( phase ). 4. Discussion (a) The rate of i n t e r d e n d r i t i c l i q u i d flow i n a sing l e pipe could not be measured with the experimental apparatus used because of the preferred nature of the f l u i d flow. Had the flow been homogeneously d i s t r i b u t e d , one could have calculated the i n t e r d e n d r i t i c flow-rate by d i v i d i n g the t o t a l flow-rate by the number of i n t e r d e n d r i t i c channels. Cb) The use of a geiger counter to measure the flow-rate was impractical because of the formation of large l i q u i d droplets at the underside of the ingots. Determining a flow-rate by counting the a c t i v i t y of T l i n these droplets would introduce complicated geometrical factors concerning the size and shape of these droplets since lead i s a good beta r a d i a t i o n absorber. Cc) Flow on a more expensive scale, producing massive exudation of l i q u i d metal, was, therefore, studied. The model for such flow i s shown schematically i n F i g . 19. With eutectic l i q u i d above the ingot, - 35 -Figure 19. I n t e r d e n d r i t i c f l u i d flow model f o r Pb-20Sn. flow occurs as f o l l o w s : As flow s t a r t s , i t i s more or l e s s evenly d i s t r i b u t e d between dendrites over the e n t i r e c r o s s - s e c t i o n of the ingot. Because no two i n t e r d e n d r i t i c channels are e x a c t l y a l i k e , flow i s more r a p i d i n some channels than i n others. The more r a p i d flow i n these channels causes f a s t e r d i s s o l u t i o n of the channel w a l l s and hence more r a p i d widening. These p i p e s , as a r e s u l t , pass more f l u i d causing f u r t h e r widening. Given a c e r t a i n c r o s s - s e c t i o n of i n g o t , t h e r e f o r e , flow becomes more and more l o c a l i z e d w i t h time. L o c a l i z a t i o n of exudations i s observed i n continuous cast aluminum i n g o t s , and i s b e l i e v e d to occur when the ingot breaks away from the mould w a l l due to shrinkage. - 36 -(d) Surface tension e f f e c t s at the surface of the ingot can a f f e c t the flow of i n t e r d e n d r i t i c l i q u i d . (e) No c o r r e l a t i o n was found between l i q u i d flow-rates i n Pb-20Sn and those predicted by porous bed theory. The experimental flow-rates were considerably higher than those predicted by Darcy's Law, presumably because of the d i s s o l u t i o n and widening of i n t e r d e n d r i t i c channels causing increased flow. PART II - BACK-FLOW IN COPPER-SILVER AND ALUMINUM-SILVER 1. Introduction 1-1. Objective The r e s u l t s of Part I demonstrated that flow through i n t e r d e n d r i t i c channels i n the model system examined was not homogeneous. As a r e s u l t , further attempts to analyze the rate of back-flow using c l a s s i c a l inverse segregation concepts were abandoned. A new type of experiment was developed instead, to study the more massive back-flow phenomenon responsible for exudation at the c h i l l - f a c e of a casting. Forced exudation was produced i n melts of binary a l l o y systems by p a r t i a l l y s o l i d i f y i n g a melt from one end, and removing the c h i l l . Tracer elements were used for composition analysis. 1-2. Choice of Materials Binary systems having a broad semi-solid range as i n the Pb-Sn system were chosen. Most of the experimental work was done on Cu-8 wt. pet. Ag a l l o y and l a t e r experiments on Al-30 wt. pet. Ag. The phase diagrams are shown i n F i g . 20. S i l v e r was chosen as a solute 110 * constituent so that radioactive Ag (Ag ) could be used as a tracer element. This tracer was used to c a l c u l a t e solute concentrations and was chosen for the following reasons: Figure 20(a). Phase diagram of Cu-Ag - 3 9 -Figure 20(b). Phase diagram of Al-Ag. - 40 -(a) The properties of Ag are v i r t u a l l y i d e n t i c a l to those of pure s i l v e r . The tracer, therefore, i s assumed to segregate i n exactly the same manner as the s i l v e r . * (b) Ag i s a strong Y emitter. High energy r a d i a t i o n i s required to minimize geometry e f f e c t s when counting the a c t i v i t y of radioactive specimens. (c) Ag has a reasonably long h a l f - l i f e (249 days) which eliminates the necessity.of correcting for decay e f f e c t s during the counting operation. * 9 (d) In the Pb-Ag system, Weinberg found a l i n e a r dependence between the a c t i v i t y of the a l l o y and the composition. 2. Experimental 2-1. Apparatus and Casting Procedure The equipment, as shown i n F i g . 21, consisted of an upper graphite c r u c i b l e for holding a molten charge, and a lower graphite mould with a water-cooled copper c h i l l at the bottom end. The c h i l l consisted of a movable copper pedestal. A Lepel induction furnace provided power. Molten charges were held i n the upper c r u c i b l e f o r 1 hour with occasional s t i r r i n g by an alumina paddle to insure homogeniety of the melt. The temperature of the melt was monitored by a chromel-alumel thermocouple. Temperature corrections were made by manually adjusting the power s e t t i n g on the induction furnace. During t h i s operation, the copper pedestal was i n a lowered p o s i t i o n , removed from the graphite mould. - 41 -TO VAC. PUMP PORCELAIN WOOL PORCELAIN CAP GRAPHITE CRUCIBLE MELT PLUG WITH PADDLE CARBON FELT INDUCTION COIL TC'S GRAPHITE MOULD VYCOR SLEEVE COPPER PEDESTAL VYCOR TUBES VAC. SEAL RETAINING RING WATER OUT< ]< WATER IN Figure 21. Apparatus for casting Cu-Ag and Al-Ag ingots. - 42 -Immediately before casting, the induction furnace was switched off and the pedestal was raised into p o s i t i o n . This l a s t minute r a i s i n g of the pedestal prevented the graphite mould, whose temperature was comparable to that of the melt, from cooling s u b s t a n t i a l l y before casting. A vycor sleeve around the top of the c h i l l helped to hinder such cooling. To cast, the alumina plug was pulled causing the molten charge to pour into the lower mould against the c h i l l A fter pouring, the c h i l l could be pulled away at any desired time. A chromel-alumel thermocouple contained i n a 0.13" diameter s i l i c a tube was located on the l o n g i t u d i n a l axis of the casting 0.3" from the c h i l l . Using room temperature as a cold junction, t h i s thermocouple monitored the cooling rate on a Honeywell chart recorder. The ingots made using t h i s method were c y l i n d r i c a l i n shape: 1.0" i n diameter and 3.2'' long. In a l l cases, the casting temperature for Cu-8Ag was 1250°C and for Al-30Ag was 800°c. 2-2. A l l o y Preparation Cu-8Ag a l l o y was prepared by adding the constituents to the upper c r u c i b l e and holding at 1250°C. High purity Koch-Light Cu (99.99%) and Johnson-Matthe-Mallory Ag (99.95%) were used to make a 370 gm molten charge. In some cases, 50 ppm. of Ag , as received from Chalk River, were added to the melt. The a l l o y was prepared at a pressure of about 10 microns of mercury; the vacuum being supplied by a Welch Duo-Seal vacuum pump. This prevented oxidation of the a l l o y and the graphite - 43 -components of the apparatus. Al-30Ag a l l o y was prepared from high p u r i t y Alcan A l (99.99%) and the same s i l v e r as above, to make a 140 gm molten charge. For composition a n a l y s i s , 35 ppm. of Ag were added. This a l l o y was prepared under an argon atmosphere at 800°C. 2-3. Composition Analysis To analyze for composition, t h i n c r o s s - s e c t i o n a l s l i c e s 0.005" * thick were removed from ingots containing Ag perpendicular to the s o l i d i f i c a t i o n d i r e c t i o n ( i . e . p a r a l l e l to the c h i l l - f a c e ) on a lathe. The a c t i v i t i e s of the turnings from these sections were measured with a Hamner s c i n t i l l a t i o n counter. Counts were taken over a 20 sec. time i n t e r v a l . Ten such counts were made on each batch of turnings. These were averaged and normalized to the weight of the sample, giving counts/ 20 sec./gm. Loose batches of turnings gave the same counts as compacted batches. Geometry e f f e c t s were, therefore, neglected. From s t a t i s t i c s , the counting error involved i s approximately equal to the square root of the counts. Since most of the counts obtained were i n the 12,000 counts/20 sec. range, the counting error i s about 1%. The measured a c t i v i t y was assumed to be d i r e c t l y proportional 9 to the s i l v e r concentration. Experimental r e s u l t s by Weinberg show a d i r e c t l i n e a r correspondence between the a c t i v i t y and the s i l v e r concentration i n Pb-Ag a l l o y s . The above assumption i s reasonable, therefore, because aluminum and copper both have much lower capture cross-sections for y r a d i a t i o n than lead. - 44 -A c t i v i t i e s were plotted versus distance along the ingot. A mean a c t i v i t y l i n e was then drawn to equalize areas under the curve, above and below th i s l i n e . This a c t i v i t y corresponded to the average composition, Co, of the ingot. The actual composition p r o f i l e was established by multip l y i n g the a c t i v i t y r a t i o s , taken with respect to the mean a c t i v i t y , by Co. 2-4. Metallography and Autoradiography of Cu-8Ag. The f i n a l stages of p o l i s h i n g were done on 6 micron and 1 micron diamond laps. Polished specimens were etched with a d i l u t e s o l u t i o n of HC1 and FeCl^. Best result's were obtained with unounted specimens and metallographic photographs were taken as i n Part I. Autoradiography was done as i n Part I. 2- 5. Electron Microprobe Analysis Electron microprobe analysis was done on polished etched specimens using the same apparatus as i n Part I the correction factors for Cu-Ag are given i n Appendix 3. Results 3- 1. General A number of castings were done i n which the c h i l l was rmeoved at various times during s o l i d i f i c a t i o n , causing l i q u i d metal to flow down through the o r i g i n a l c h i l l face. Removing the c h i l l did not arrest the o v e r a l l cooling of the system. Cooling continued at a slower rate u n t i l the back-flow of l i q u i d eventually stopped. A t y p i c a l Cu-8Ag casting i s shown i n F i g . 22. and s l i g h t l y D e t a i l s of B. - 45 -CHILL X 2 Figure 22. A t y p i c a l Cu-8Ag casting i n which the c h i l l has been removed during s o l i f i c a t i o n . - 46 -Most of the experimental work was directed towards Cu-8Ag a l l o y since d i f f i c u l t i e s were encountered i n obtaining consistent and reproductable r e s u l t s with Al-30Ag. 3-2. The Cu-8Ag System 3-2-a. Composition P r o f i l e s The composition p r o f i l e s and the accompanying cooling curves are shown i n Figures 23 and 24 r e s p e c t i v e l y . The p r o f i l e l a b e l l e d N represents a "normal casting" i n which the c h i l l was not removed. This p r o f i l e shows c l a s s i c a l inverse segregation with a s l i g h t increase i n solute concentration near the c h i l l and a depletion i n solute at the top of the ingot. In the cases where the c h i l l has been pulled away (A, B, and C), one observes a solute r i c h region below the c h i l l (the flow-through zone) and a solute depleted region j u s t above the c h i l l . A l l ingots exhibited a depletion i n solute at the top of the ingot. Det a i l s of the castings are l i s t e d i n Table 5. Table 5 Details of Cu-8Ag Castings Casting N A B C Time between pouring and removing the c h i l l (sec.) 0 12 14 16 Estimated volume of the flow-through zone (in.3) - 0. 23 0. 094 0. 023 Average composition of the flow-through zone (%Ag) - 10. 3 12. 3 12. 6 Minimum composition of the depleted zone adjacent to the c h i l l (%Ag) - 5. 25 6. 05 7. 25 - i l 1 r CHILL-FACE i r o o N 0 0 A - - - 0 8 — * C •0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 24 2 6 2 8 DISTANCE FROM CHILL (in.) J L 3.0 3.2 Figure 23. Composition p r o f i l e s of Cu-8Ag ingots. - 48 -l 1 1 1 1 r i - i 1 8 t a i I 0 5 0 100 150 2 0 0 2 5 0 3 0 0 TIME (sec.) Figure 24. Cooling curves for Cu-8Ag castings. - 49 -The important features to notice are: (a) As the time i n t e r v a l between pouring and the removal of the c h i l l increases, the maximum reheat temperature at the thermocouple l o c a t i o n decreases and l e s s back-flow of l i q u i d metal occurs. (b) As the flow-through region increases i n volume, the average solute concentration i n t h i s region decreases, while the maximum dip i n concentration adjacent to the c h i l l increases. (c) In castings A and C, the bottom of the flow-through zone came i n contact with the c h i l l causing rapid freezing of the zone and the d i s t r i b u t i o n of solute within t h i s zone as shown i n F i g . 23. The l i q u i d to flow through the c h i l l - f a c e f i r s t was presumably the r i c h e s t i n solute and froze f i r s t . (d) Back-flow i n casting B occurred without a second c h i l l contact being made. The flow-through zone cooled slower, producing the reverse segregation e f f e c t to that i n (c). (e) The r i s e i n composition above Co, past the depleted zone adjacent to the c h i l l , i s believed to be a r e s u l t of normal inverse segregation a f t e r back-flow has stopped. 3-2-b. O p t i c a l Examination A l o n g i t u d i n a l section of a casting where the c h i l l has been pulled causing considerable back-flow, as i n casting A, i s shown i n F i g . 25. Notice the columnar structure which was c h a r a c t e r i s t i c of a l l the Cu-8Ag castings. Above the o r i g i n a l c h i l l - f a c e a region can be observed which etches l i g h t e r than the rest of the ingot. This region i s solute - 50 -Figure 25. Longitudinal section of a Cu-8Ag casting i n which the c h i l l has been removed during s o l i d i f i c a t i o n . - 51 -d i l u t e since the etchant used darkens solute r i c h regions which are not e u t e c t i c . There e x i s t s , however, no d i s c o n t i n u i t y of grain structure at the i n t e r f a c e between t h i s region and the rest of the ingot. A higher magnification photograph of the i n t e r f a c e i s shown i n F ig. 26. Notice also the increase i n e u t e c t i c above the boundary. Coalescence of porosity i s observed at the c h i l l - f a c e as shown i n Fig. 27. 3-2-c. Autoradiography Cross-sections taken at the c h i l l - f a c e and 0.05." above the c h i l l -face of casting A were autoradiographed. The films showed a uniform darkening, and, therefore, gave no i n d i c a t i o n of p r e f e r e n t i a l flow of i n t e r d e n d r i t i c l i q u i d . One must note, however, that the y r a d i a t i o n from Ag can penetrate copper to a considerable depth allowing only l i m i t e d r e s o l u t i o n using the autoradiograph technique. Micrographs of the same cross-sections, as i n F i g . 28, also show no signs of preferred flow. One assumes, therefore, that back-flow occurred i n a homogeneous i n t e r d e n d r i t i c fashion without the formation of large pipes as seen i n Part I. 3-2-d. Electron Microprobe Results A normal casting was sectioned p a r a l l e l to the c h i l l - f a c e , 0.21" from the face, and examined by microprobe a n a l y s i s . Line counts were taken through dendrite centers and eutectic regions at 1.25 micron steps, as shown i n F i g . 29. Random l i n e counts using 5 micron steps were also taken at other distances above the c h i l l of a normal.casting. - 52 -X 100 Figure 26. Longitudinal section through the in t e r f a c e between the depleted zone and the rest of the ingot. - 53 -X 7 Figure 27. Longitudinal section through the c h i l l - f a c e . - 54 -X 160 Figure 28. Cross-section at the c h i l l - f a c e of casting A. Figure 29. Microsegregation 0.21" above the c h i l l - f a c e . - 56 -A l l the counts corresponding to a s i l v e r concentration less than Co were averaged. For each cross-section about 100 such counts were averaged to give a s i l v e r concentration, C g, for use i n a model to be discussed l a t e r . See F i g . 30. % A g 0 0.2 0.4 0.6 0.8 DISTANCE FROM CHILL (in.) 1.0 Figure 30. Plot of C vs. distance from the c h i l l . ° s 3-3. The Al-30Ag System 3-3-a. Composition P r o f i l e s As with Cu-8Ag, a number of castings were made i n which the c h i l l was removed at various times a f t e r pouring. The composition p r o f i l e s and the cooling curves are shown i n Figures 31 and 32 respectively. P r o f i l e s and represent a normal casting, and D and E are castings where the c h i l l has been removed. 50 46 42 38 %Ag 34 30 26 22 CHILL-FACE X C 0 , 0 — 0 — o I8H o N, 0 Nj o n * E 1 1— COLUMNAR EQUIAXED 9 -A ©--'.<>•'- .-0-A-.A' --^.oV'^VO V v I 2.4 -0 .2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 DISTANCE FROM CHILL (in.) 1.8 2.0 2.2 2.6 2.8 3.0 3.2 Figure 31. Composition p r o f i l e s of Al-30Ag ingots. - 58 -100 200 300 TIME (sec.) 400 Figure 32. Cooling curves for Al-30Ag castings. - 59 -In the cases where the c h i l l has been removed, one observes a solute r i c h flow-through region below the c h i l l , and a solute depleted region j u s t above the c h i l l . D e t a i l s are given i n Table 6. Table 6 D e t a i l s of Al-30Ag Castings Casting N N D E Temp, at which the c h i l l was removed (°C) 569 580 Estimated volume of flow-through zone (in.3) 0.047 0.078 Minimum solute concentration of depleted zone adjacent to 22.3 22.0 the c h i l l (%Ag) Average composition of flow-through zone (%Ag) 30.8 32.5 Distance from c h i l l of columnar to equiaxed t r a n s i - 2.8 0.6 1.0 0.7 tion (in.) 3-3-b. Discussion The composition p r o f i l e s , unfortunately, were not reproducible, on the casting apparatus used. Normal castings(N^ and N^), for example were i n some :cases completely columnar and i n others almost completely equiaxed. Aluminum has a considerably higher s p e c i f i c heat and latent heat of fusibn than copper. This property, combined with the lower pouring temperature, produced a d r a s t i c a l l y lower cooling rate for Al-30Ag than for Cu-8Ag. As a r e s u l t , nucleation occurred ahead of the columnar d e n d r i t i c i n t e r f a c e at unpredictable distances from the c h i l l , producing an equiaxed structure. Small amounts of impurities - 60 -may have acted as nucleants to a s s i s t t h i s t r a n s i t i o n from a columnar to an equiaxed structure. 3-4. The Length of the Semi-solid Zone Normal castings were made with two chromel-alumel thermocouples i n place; 0.4" and 2.0" from the c h i l l . Each thermocouple was connected to a separate temperature recorder. The cooling curves are shown i n Figures 33 and 34. Defining the mushy zone as l y i n g between the liquidus and solidus temperature of the phase diagram f o r the p a r t i c u l a r composition of the ingot, and assuming a l i n e a r temperature gradient between the two thermocouples, the length of the mushy zone at various times from the beginning of s o l i d i f i c a t i o n was estimated. These estimates at the instant the c h i l l i s pul l e d are given i n Table 7. Table 7 Estimated Lengths of the Semi-solid Zone Casting A , B C D E Lengtn of the semi-solid zone (in.) 0.45 0.56 0.66 0.85 0.85 4. Discussion 4-1. General The back-flow phenomena observed i s necessary. .Measurements were made are complex and a s i m p l i f i e d model of the average solute concentrations - 61 -1300 1200-1100 1000 900 0 TC SEPARATION =1.6" A B 10 20 TIME (sec.) TC-2 Ist SOLID TEMR TC-I 30 LENGTH OF MUSHY ZONE BETWEEN TC'S X 1.6" LENGTH OF MUSHY ZONE BETWEEN TC-I a CHILL ASSUMED = 3.2" 40 Figure 33. Cooling curves to determine the length of the mushy zone i n Cu-8Ag. - 62 -TC SEPARATION = 1.6" i 1 1 i i | 0 20 40 60 80 100 TIME (sec.) LENGTH OF MUSHY ZONE Figure 34. Cooling curves to determine the length of the mushy zone in. :Al-30Ag. - 63 -of t h i n s e c t i o n s cut p a r a l l e l to the c h i l l face. Before the c h i l l was removed, the s e c t i o n was made up of s o l i d and l i q u i d of d i f f e r e n t and non-homogeneous compositions defined by the c o n d i t i o n s f o r s o l i d i f i c a t i o n i n that s e c t i o n . In a d d i t i o n , l i q u i d flow perpendicular to the s e c t i o n plane occurred due to volume changes on c o o l i n g and f r e e z i n g which changed the average s o l u t e concentration of the l i q u i d i n the plane s e c t i o n . When the c h i l l was removed followed by reheating of the p a r t i a l l y s o l i d i n g o t , s e v e r a l things occurred: (a) L i q u i d pipes were present or opened up, a l l o w i n g v e r t i c a l flow of l i q u i d below the i n i t i a l c h i l l - f a c e . This markedly changed the composition of the r e s i d u a l l i q u i d i n the s e c t i o n . (b) The composition change of the plane s e c t i o n was a f u n c t i o n of the composition of the l i q u i d e n t e r i n g as w e l l as that l e a v i n g . (c) The remelting of dendrite arms changed the l i q u i d composition. Two models (I and I I ) are proposed to e x p l a i n the dip i n concentra-t i o n adjacent to the c h i l l face; one f o r minor back-flow (I) and one fo r extensive back-flow ( I I ) . In both cases the inverse segregation e f f e c t i s neglected. As seen from the experiments, compositional changes due to inv e r s e segregation are small compared to the concentra-t i o n d i f f e r e n c e s caused by exudations. The simplest model i s chosen f i r s t and then expanded to reach the best approximation to experimental data. - 64 -4-2. Model I 4-2-a. F i r s t Approximations Assume an ingot i s cast, as i n the experiments, and a f t e r a given i n t e r v a l of time a semi-solid (mushy) zone of length, L, i s formed. (The mushy zone i s defined as the zone l y i n g between the liquidus and solidus of the a l l o y . ) At t h i s point, the c h i l l i s suddenly removed. Because of the hydrostatic pressure of the l i q u i d above the semi-solid zone, the l i q u i d i n s i d e the zone i s pushed out and replaced by l i q u i d of composition C , the average composition of the o r i g i n a l melt. This back-flow occurs concurrently with the continued cooling of the ingot at a slower rate, and, hence, the flow stops a f t e r a period of time. During t h i s period, remelting of dendrites at t h e i r t i p s and i n i n t e r d e n d r i t i c regions can occur. In this model i t w i l l be assumed that L remains constant while back-flow i s occurring. This may not be unreasonable since the o v e r a l l system i s s t i l l cooling with the c h i l l removed causing dendrites to grow; but at the same time heat transfer from the superheated l i q u i d causes dendrites to melt. It i s also, assumed, therefore, that the p o s i t i o n of the region of length L remains f i x e d with respect to the o r i g i n a l c h i l l - f a c e during back-flow. Consider a s l i c e of thickness dy i n the mushy zone perpendicular to the s o l i d i f i c a t i o n d i r e c t i o n . The d i s t r i b u t i o n of solute i n the s o l i d portions of t h i s s l i c e i s assumed to follow the Pfann equation: c = c o k(i - g ) k ' (1) - 65 -where, g, the f r a c t i o n s o l i d i f i e d , i s measured i n the plane of the s l i c e . This equation which was derived for one-dimensional s o l i d i f i c a t i o n , i s , therefore, being applied d i r e c t l y to a two-dimensional s i t u a t i o n . The equation assumes 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 and 3 1 no d i f f u s i o n i n the s o l i d . For rapid cooling rates, other researchers ' have found t h i s equation to agree reasonably well with experimental microsegregation data for g values up to about 0.8. For higher values of g, the composition, C, goes to i n f i n i t y and the equation becomes meaningless. The model proposed here, however, compensates for t h i s e f f e c t , because as the composition approaches i n f i n i t y , the amount of material having t h i s composition approaches zero. This w i l l become apparent i n the mathematics to follow. Some s o l i d - l i q u i d d i s t r i b u t i o n i s assumed i n the region L, making the volume of s o l i d per unit thickness of the casting some function of distance from the c h i l l . For convenience, reference points and axes are denoted as i n F i g . 35. CHILL Figure 35. Schematic representation of Model I. - 66 -Consider the f r a c t i o n s o l i d i f i e d at some point i n an element of width dy. Assuming a Pfann d i s t r i b u t i o n of solute i n the s o l i d , the t o t a l solute, S, i n th i s f r a c t i o n i s given by: S = kC Q/ 1 (1-g) dg o (2) Co " V 1 " ^ Therefore, the average composition, C , i n the s o l i d at point y. i s o /V -1-given by: ^SA Co - V 1 ^ g l k (3) For s i m p l i c i t y , a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n during s o l i d i f i c a t i o n i s now assumed. This model, shown i n F i g . 36, makes the f r a c t i o n s o l i d g = Figure 36. A l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n . - 67 -a l i n e a r function of distance along the ingot. The average composition of the s o l i d i n a cro s s - s e c t i o n a l s l i c e at some point y now becomes: C - C (1 - f ) k and the average composition of the e n t i r e s l i c e , C , i s : CA = C S A ( y / L ) + C L ( 1 " y / L ) ( 5 ) where C = average composition of the l i q u i d i n the cros s - s e c t i o n a l element. Using t h i s a n a l y s i s , i t i s not necessary to know the structure of the ingot. One now assumes that a l l the re s i d u a l l i q u i d i s displaced by l i q u i d of composition C^. Assuming no segregation i n the y d i r e c t i o n when th i s l i q u i d eventually freezes, the composition of th i s new l i q u i d when averaged i n cross-section w i l l be C . The average composi-t i o n , C , at some point y i s given by: CA = C S A ( y / L ) + C o ( 1 _ y / L ) ( 6 ) A family of these curves are plotted i n F i g . 37 for various k values. Notice that these curves are independent of the absolute value of L. - 68 -1.0 0.9 0.8 C Co 0.7 0.6 I'.O 0 8 0.6 0 4 02. 0 Figure 37. Plot of Equation 6 for various k values. 4-2-b. Selection of the D i s t r i b u t i o n C o e f f i c i e n t . In determining a reasonable value for the d i s t r i b u t i o n c o e f f i c i e n t k, two sets of data are a v a i l a b l e : (i) According to experiments done by Weinberg"*"^ on Cu-8Ag using the same apparatus as i n t h i s work, the average k value 0.2" to 1.0" from the c h i l l l i e s somewhere between 0.55 and 0.69 (see F i g . 38). - 69 -COPPER - 8% SILVER I -0 4 8 12 J6 20 24 28~ DISTANCE FROM DENDRITE CENTRE (MICRONS) F i g u r e 38. S o l u t e d i s t r i b u t i o n a c r o s s p r i m a r y d e n d r i t e s a t v a r i o u s d i s t a n c e s , d, from t h e c h i l l . The concave upwards c u r v e s were c a l c u l a t e d u s i n g the P f a n n e q u a t i o n and t h e k v a l u e shown. ( i i ) I f k ;= 0.6, the minimum c o m p o s i t i o n a t t h e d e n d r i t e c e n t e r s , g i v e n by k C o , i s 4.8% Ag f o r Cu-8Ag a l l o y . T h i s i s c l o s e t o what i s o b s e r v e d i n the m i c r o p r o b e d a t a , F i g . 29. A l t h o u g h k d e c r e a s e s con-s i d e r a b l y w i t h i n c r e a s i n g d i s t a n c e from t h e c i l l ( F i g . 3 8 ) , t h e r e g i o n of i n t e r e s t i n Cu-8Ag ex t e n d s o n l y 0.7" p a s t t h e c h i l l . I n subsequent c a l c u l a t i o n s , t h e r e f o r e , k i s assumed c o n s t a n t a t 0.6. - 70 -4-2-c. M o d i f i c a t i o n s A more d e t a i l e d a n a l y s i s of back-flow i s considered by c a l c u l a t i n g the composition of the i n t e r d e n d r i t i c l i q u i d j u s t before the c h i l l i s p u l l e d away. Let part of t h i s l i q u i d be d i s p l a c e d by l i q u i d of composi-t i o n C . Assume that no mixing occurs between the C l i q u i d and the o o o r i g i n a l i n t e r d e n r i t i c l i q u i d during back-flow. This i s a reasonable assumption f o r two r e a s o n s : ^ ( i ) The l i q u i d of composition C q which i s probably the l e s s dense of the two s o l u t e enriched l i q u i d s , r e s t s above the i n t e r d e n d r i t i c l i q u i d . ( i i ) The temperature gradient i s such that hot l i q u i d i s above cooler l i q u i d . Both these e f f e c t s would hinder any f r e e convection from o c c u r r i n g . To determine the composition of the i n i t i a l i n t e r d e n d r i t i c l i q u i d , l e t C = C i n Equation 5. (Neglecting inverse segregation A O e f f e c t s , the average composition of a c r o s s - s e c t i o n a l s l i c e before the c h i l l i s removed must be C . ) o Therefore: C. = C = C - C (1 o o o y/L)"" + C L(1 - y/L) (7) C (1 - y/L)' o ( l - y/L) The author could f i n d no informa t i o n regarding the density vs. composition of Cu-Ag a l l o y s . - 71 -This gives the i n i t i a l average composition, C , of the l i q u i d i n any given cross-sectional element of the mushy zone. Let a given volume of i n t e r d e n d r i t i c l i q u i d be displaced by an equal volume of l i q u i d having composition C q . Schematically this occurs as i n F i g . 39. Figure 39. In t e r d e n d r i t i c l i q u i d displacement. For a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n , the volumes of l i q u i d displaced are shown i n F i g . 40. Pipes at the bottom of the mushy zone are assumed small and neglected i n the following c a l c u l a t i o n s . - 72 -V v2 Figure 40. Displacement of l i q u i d for a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n . When V 0 i s removed, (V^ + V^) f i l l up the volume (V 0 + V Q) Therefore: 2 y 1 . 1 ( l - - l i ) 2 2 2 k L ; (8) • 1 ^2 2 V =. - (1 ) z 2 2 ^ L ' (9) Equating (8) and (9) since = V t and g = y/L: S 2 = 1 - / l - ( l - g x) (10) The l i q u i d which was once d i s t r i b u t e d between 0 and -— i s now J_j d i s t r i b u t e d between — and 1. Li - 73 -Every ci-oss-sectional l i q u i d element of constant width, a, when moved down a given distance, b, increases i n width by a constant amount, c, as shown i n F i g . 41. This indicates that one can simply replot the Figure 41. The increase i n width of downward moving l i q u i d elements. l i q u i d composition function, f (y/L), formerly between 0 and — , on an expanded scale between -— and 1. One does- t h i s mathematically using J-j an extension f a c t o r , y. For d e t a i l s see Appendix C. 1 " Si (ID The average l i q u i d composition, C , as defined by Equation 7 becomes: LJ C o ( l - Mg) \ = (1 - yg) (12) i f -— i s used as a zero reference point for LJ - 74 -Equating back to the o r i g i n a l zero reference: C between 0 and — o L c o [ i - M(g - g x ) ] y1 CT = — ; r between -— and 1 L 1 - M(g - g 1) L (13) Using Equation 5, the t o t a l average composition, therefore, i s given by: k yl C = C - C (1 - g) + C (1 - g) between 0 and — (14a) A o o o L A o [ i - y(g - g j ] c o d - g ) + c o ( i - g ) L ^ g . ^ between T— and 1 (14b) where g = y/L Equations 14a and 14b are plotted i n F i g . 42 for k = 0.6 and various values of g . |_Q Figure 42. 1.0 0.8 0.6 0.4 0.2 9 Plot of Equations 14a and 14b. - 75 -y2 Integrating Equation 7 between -— and 1, and d i v i d i n g by the J_j l i q u i d volume i n t h i s region, gives the average composition of the l i q u i d , C , which has flowed through the c h i l l - f a c e . is C L = ^ 2 ~ f (1 - g)kdg 1/2(1 - g2)Z Jg2 - 2 C o ( 1 " S 2 ) k _ 1 C L = k + l ( 1 5 ) In the s p e c i a l case where a l l the o r i g i n a l i n t e r d e n d r i t i c l i q u i d has been completely displaced, g 2 = 0. 2C Therefore: C T = . (16) Solving Equation 15 for various values of g^ and for C Q = 8% Ag, one obtained Table 8. Table 8 The V a r i a t i o n of C with respect to g JLI (k = 0.6; C Q = 8) 0.05 15.96 0.10 13.94 0.20 12.27 1.00 10.00 - 76 -The important point to note here i s that the less material that has flowed back, the higher the average composition of the flow-through zone. This e f f e c t was observed experimentally. 4-2-d. E f f e c t of Remelting In considering the remelting of dendrites, one assumes that a substantial amount of i n t e r d e n d r i t i c l i q u i d has been displaced. Solute d i l u t e material i s dissolved from the surface of the dendrites and swept downwards as shown schematically i n Fig. 43. (a) (b) Figure 43. The remelting of dendrites. The length of the mushy zone, L, i s assumed constant during d i s s o l u t i o n and the s o l i d - l i q u i d d i s t r i b u t i o n i s assumed to remain l i n e a r a f t e r d i s s o l u t i o n (Fig. 43b). The e f f e c t of pipes forming at the base of the mushy zone i s neglected. The d i s s o l u t i o n of dendrite material causes the solute concentra-ti o n of the d i s p l a c i n g l i q u i d to drop. As a f i r s t approximation, t h i s d i l u t i o n i s assumed to be l i n e a r with respect to y/L. Referring to Fig . 43a, therefore, the composition of the l i q u i d at the base of the semi-solid zone, C , i s less than C q . Incorporating t h i s e f f e c t into Equation 6, the average composition, C , i s given by: C A = C o - C o ( 1 - s ) k + [C o+ (C a - C o ) g ] ( l - g ) (17) An i n t e r e s t i n g feature of t h i s equation i s i t s use as a f i r s t approxi-mation to Equation 14 i f > C . Equation 17 i s plotted i n Fig. 44 for various values of ( C - C ) . Notice the s h i f t i n minima from l e f t a o I I I I I 1 1.0 0.8 0.6 0.4 0.2 0 • 9 Figure 44. Plot of Equation 17. - 78 -to r i g h t as the remelting s i t u a t i o n i s approached. Such a s h i f t was observed experimentally for Cu-8Ag. 4-3. Model II This model considers the case where considerable back-flow has occurred a f t e r a l l the i n i t i a l i n t e r d e n d r i t i c l i q u i d has been washed away. Considerable widening of i n t e r d e n d r i t i c channels i s believed to occur i n the region which i s almost completely s o l i d at the base of the mushy zone. Schematically t h i s i s shown i n Figure 45. Figure 45. Schematic representation of Model I I . One must remember that the Pfann equation for solute d i s t r i b u t i o n i s not v a l i d i n the lower region of the semi-solid zine. A s i m p l i f i e d d i s t r i b u t i o n i s , therefore, adopted and re l a t e d to a l i n e a r s o l i d -l i q u i d d i s t r i b u t i o n as i n F i g . 46. - 79 -Figure 46. S i m p l i f i e d solute d i s t r i b u t i o n (a) and i t s r e l a t i o n to a l i n e a r s o l i d - l i q u i d d i s t r i b u t i o n (b). C G represents the average of a l l compositions below C q , and i s the eutectic composition. The f r a c t i o n of eutectic i n a normal casting i s given by n. Assume a l l the o r i g i n a l i n t e r d e n d r i t i c l i q u i d and a l l the eutectic i n the region n has been displaced by l i q u i d of composition C . The average composition, C , taken i n cross-section at some point y/L becomes: C . = C g + C (1 - g) for 0 < y/L < (1 - n) (is') i\ s o C = C for (1 - n) < y/L < 1 A o - 80 -To evaluate n, an estimate of C g i s required. By equating areas under the solute d i s t r i b u t i o n curve (Fig. 46a) : (C - C )n = (C - C ) (1 - n) (19) e o o s 4-4. Comparison of Models with Experiment. 4-4-a. General A d i r e c t quantitative comparison i s made between the two models proposed and castings A, B, and C. Castings D and E were not con-sidered because of the u n r e p r o d u c i b i l i t y of the r e s u l t s . In these castings other more complex s o l i d i f i c a t i o n variables must have existed which were not considered i n the models. The l o c a t i o n of the base of the mushy zone at the instant the c h i l l i s removed i s not accurately known. From the micrograph i n Fig . 27, i t i s assumed to be at the termination of the i n i t i a l f i n e -grained c h i l l structure: 0.075" from the c h i l l . This corresponds approximately to the point where the composition p r o f i l e s (Fig. 23) f i r s t cross the C l i n e . The distance between t h i s point and the o point where the second i n t e r s e c t i o n occurs i s assumed to be the length of the mushy zone, L. The i n i t i a l volume of i n t e r d e n d r i t i c l i q u i d i s assumed to be 1/2 the volume of the semi-solid zone. Det a i l s are given i n Table 9. - 81 -Table 9 Additional D e t a i l s of Cu-8Ag Castings A 0.25 0.45 0.10 0.23 B 0.55 0.56 0.22 0.094 C 0.50 0.66 0.20 0.023 4-4-b. Casting A The volume of l i q u i d which has flowed back i s about twice the volume of l i q u i d i n the mushy zone. This indicates that a l l the o r i g i n a l i n t e r d e n d r i t i c l i q u i d has been washed out causing remelting of dendrites and the widening of i n t e r d e n d r i t i c channels. Because the v e l o c i t y o f , l i q u i d i s highest at the base of the dendrites, most widening and remelting i s assumed to occur at t h i s l o c a t i o n . In t h i s region the Pfann equation i s not v a l i d and Model II i s considered. As a f i r s t approximation, one assumes that a l l the solute r i c h material has been displaced by l i q u i d of composition C q and no remelting of solute d i l u t e material has occurred. From the microprobe data (Figure 29 and 30), C s = 5.4% Ag and C g = 70% Ag. Substituting into Equation 19, n = 0.04. This value of n i s used i n p l o t t i n g Equation 18 as i n F i g . 47. In t h i s case, the equation describes only 1 half of the composition p r o f i l e . The remaining p r o f i l e i s not described by the model, and i s merely considered as a transient between the minimum composition and the solute-enriched flow-through region. The important information given by the model i s - 82 -the minimum composition of the solute depleted zone. 4-4-c. Casting B In t h i s case, 0.4 volume f r a c t i o n of the o r i g i n a l i n t e r d e n d r i t i c l i q u i d has been displaced. This means that a l l the greatly solute enriched l i q u i d has been washed away. From equation 15, the average composition of the flow-through zone i s 12.0% Ag; comparing favourably with the experimental value of 12.3% Ag. One cannot attach too much si g n i f i c a n c e to t h i s since the Pfann equation i s not v a l i d for l i q u i d highly enriched i n solute. Note, however, that the e f f e c t of the Pfann d i s t r i b u t i o n approaching i n f i n i t y i s compensated for as the volume of material having such a d i s t r i b u t i o n approaches zero i n Model I. It i s a r b i t r a r i l y assumed that the composition of the new l i q u i d i n the mushy zone has been altered by the remelting of dendrites such that a l i n e a r composition gradient of (C - C ) = -2% Ag exists i n SL o the l i q u i d . (Refer to F i g . 43). This assumption must be made since no data i s a v a i l a b l e on the nature and magnitude of remelting. Using Equation 17, the t h e o r e t i c a l curve i s compared with experiment i n F i g . 47. 4-4-d. Casting C Comparing the volume of l i q u i d i n the mushy zone with that i n the flow-through region, only a small amount of displacement of the o r i g i n a l i n t e r d e n d r i t i c l i q u i d has occurred. Assume, therefore, that no remelting of dendrites occurred. Using the volume data i n Table 9 - 83 -and Equation 8, = 0.05. The t h e o r e t i c a l solute d i s t r i b u t i o n i s calculated using Equation 14 and compared with experiment i n F i g , 47. 0 A O B A C THEORETICAL - - - EXPERIMENTAL TRANSIENT 0.1 0.2 0.3 0.4 0.5 0.6 0. DISTANCE FROM CHILL (in.) Figure 47. Comparison of models with experimental Cu-8Ag solute d i s t r i b u t i o n p r o f i l e s adjacent to the c h i l l - f a c e . 4-5. A Parabolic S o l i d - L i q u i d D i s t r i b u t i o n The comparison of the models with experiment show that a l l the t h e o r e t i c a l composition curves are s h i f t e d to the l e f t of the experimental ones. The e f f e c t s of a parabolic d i s t r i b u t i o n of s o l i d i n the mushy.zone are, therefore, b r i e f l y considered. A comparison of l i n e a r and parabolic d i s t r i b u t i o n s i s depicted i n F i g . 48. Consider Equation 6 of Model I i n a general case: - 84 -Figure 48. A comparison of models: Model I (a), Model II (b), and a parabolic s o l i d - l i q u i d d i s t r i b u t i o n (c). - 85 -C A = C Q - C Q [ 1 - f ( y / L ) ] K + C Q [ 1 - f ( y / L ) ] ( 1 9 ) where f(y/L) i s a function of the s o l i d - l i q u i d d i s t r i b u t i o n For a parabolic d i s t r i b u t i o n : g = f(y/L) = 1 - (1 - y / L ) 2 (20) and Equation 19 becomes: 2Y 2 C. = C - C (1 - y/Lr K + C (1 - y/L)* (21) A o o o S i m i l a r l y for Equation 17 of Model I I : C A = C s [ l - (1 - y / L ) 2 ] + C o ( l - y / L ) 2 ( 2 2 ) for 0 < y/L < (1 - i^ n) C A = C Q for (1 - JfT) < y/L < 1 P l o t t i n g (21) and (22), as i n F i g . 49, one observes that the minima are sh i f t e d to the r i g h t . - 86 -1.0 0.8 0.6 0.4 0.2 0 9 Figure 49. The s h i f t i n minima caused by a parabolic s o l i d - l i q u i d d i s t r i b u t i o n . From simple phase diagram considerations, a parabolic d i s t r i b u t i o n may not be unreasonable. Considering the curvature of the solidus l i n e of the phase diagram (Fig. 20a), a plot of the f r a c t i o n l i q u i d versus the temperature would have a "parabolic type" shape which could be correlated to the proposed parabolic s o l i d - l i q u i d d i s t r i b u t i o n i f one assumes the temperature gradient i n the casting i s l i n e a r with respect to distance from the c h i l l . - 87 -GENERAL DISCUSSION AND CONCLUSIONS In Part I i t was discovered that the flow of i n t e r d e n d r i t i c l i q u i d need not n e c e s s a r i l y be d i s t r i b u t e d homogeneously between dendrites. A major force determining the movement of r e s i d u a l l i q u i d a r ises from the surface energy of that l i q u i d . 4 12 In experiments done by Adams and Fricke on r a p i d l y c h i l l e d d i r e c t i o n a l Al-Cu castings, a solute depleted zone was observed about 0.1" from the c h i l l . In such castings, Adams noticed a t h i n exuded layer at the c h i l l - f a c e , but made no c o r r e l a t i o n between t h i s and the depleted zone. Fricke, on the other hand, observed small protuberances on the c h i l l - f a c e which he claims were associated with i n t e r d e n d r i t i c voids within the casting. These voids would, therefore, cause the depleted zone. In t h i s work, a large coalescence of voids was observed r i g h t at the c h i l l - f a c e , with a reasonably homogeneous d i s t r i b u t i o n of voids throughout the rest of the ingot. The depleted zone adjacent to the c h i l l , therefore, was not a t t r i b u t e d to the formation of voids, but was explained by the simple back-flow of r e s i d u a l l i q u i d to feed exudations at the c h i l l - f a c e . The formation of large flow-pipes as i n the Pb-20Sn experiments was not observed i n the Cu-8Ag castings. The back-flow was presumably reasonably homogeneous, therefore, and confined to the i n i t i a l stage of the flow-rate curve (Fig. 11). In other words, back-flow did not have s u f f i c i e n t time to reach the catastrophic stage. - 88 -SUGGESTED FUTURE WORK For a given composition and s t r u c t u r a l make-up of a binary a l l o y , and given s o l i d i f i c a t i o n conditions, i t should be possible to cal c u l a t e the d i s t r i b u t i o n and s i z e of flow-pipes per unit area of the casting taken perpendicular to the flow d i r e c t i o n . Flemings 13 et a l have already attempted t h i s i n a recent paper. In the type of experiment done i n Part I I , other variables to investigate are the casting temperature (the temperature gradient) and the head of l i q u i d above the mushy zone when the c h i l l i s removed. It would be useful to f i n d a more s p e c i f i c c o r r e l a t i o n between the models proposed here and exudation phenomena observed i n the continuous casting processes. - 89 -REFERENCES 1. E. S c h e i l : Metallforschung 20 (1942) p. 69. 2. J.S. Klrkaldy and W.V. Youdelis: Trans, of Met. Soc. of AIME 212 (1958) p. 833. 3. M.C. Flemings et a l : "Macrosegregation" - parts I, I I , and I I I ; Trans, of Met. Soc. of AIME 239 (1967) p. 1449 and 242 (1968) p. 41. 4. D.E. Adams: J. Inst. Metals. 75 (1948), p. 809. 5. T..S. Pinwonka and M.C. Flemings: Trans, of Met. Soc. of AIME 236 (1966) p. 1157. 6. M. Hanson: "Constitution of Binary A l l o y s " , McGraw-Hill Book Co. New York (1958). 7. H.R. Thresh and A.F. Crawley: M e t a l l u r g i c a l Transactions JL (1970) p. 1531. 8. H.R. Thresh et a l : Physical Metallurgy D i v i s i o n of the Department of Energy, Mines, and Resources (Ottawa); Internal P.eport PM-R-67-16. 9. F. Weinberg: Trans, of Met. Soc. of AIME 221 (1961) p. 844. 10. F. Weinberg and E. Teghtsoonian: "Dendritic S o l i d i f i c a t i o n i n A l l o y s " , University of B r i t i s h Columbia, F i n a l Report to the Welding Research Council (1969). 11. M.J. Stewart: University of B r i t i s h Columbia, pr i v a t e communication (1970). 12. W.G. Fricke, J r . : Trans, of Met. Soc. of AIME 245 (1969) p. 1126. 13. R. Mehrabin, M. Keane, and M.C. Flemings: M e t a l l u r g i c a l Transactions 1 (1970) p. 1209. 14. L.C. Brown and H. Thresh: "Tools and Techniques i n Physical Metallurgy", edited by F. Weinberg, Marcel Dekker Inc. (1970) p. 600. 15. A. Pasparakis: University of B r i t i s h Columbia, pr i v a t e communication (1969). , 16. J. P h i l i b e r t : "X-ray Optics and X-ray Microanalysis", Academic Press, New York (1963) p. 379. 17. K.F.J. Heinrich: "The Electron Microprobe", John Wiley and Sons, Inc. (1966) p. 351. - 90 -APPENDIX A Electron Microprobe Corrections for Pb-Sn X-ray analysis was done at 35 KV on Pb-La^ and Sn-La^ radiations. Because of the large d i f f e r e n c e i n atomic numbers, 82 for Pb and 50 14 for Sn, fluorescence corrections are not necessary. To correct for electron backscattering e f f e c t s , Belk's atomic number correction"'""' was used: CA KAb - ; Z- (23) ZA " Z  A ^100 ' where K„, = apparent concentration of element A due to electron back-Ab scatter. C. = actual concentration of element A A Z, = atomic number of element A A Z = average atomic number for a given concentration, C . For a binary system with 2 elements, A and B: 1 = fA CA + ( 1 " f A ) C B where f, = weight f r a c t i o n of element A. A An absorption c o r r e c t i o n was then applied using P h i l i b e r t ' s 16 absorption f a c t o r , F ( x ) : ~ y = ( i + J ) [ i + h ( i + £)] (24) - 91 -where h = 1.2 Z a 2f 1 8 2 0 ( f ) 2 X A = y ' A esc a V ' A = f A V A A + fB UBA a = Lenard C o e f f i c i e n t a = take-off angle V = accelerating voltage of the electron beam A = average atomic weight = s e l f absorption c o e f f i c i e n t of element A for i t s own c h a r a c t e r i s t i c r a d i a t i o n u.,. = mass absorption c o e f f i c i e n t of element B for c h a r a c t e r i s t i c r a d i a t i o n from element A. The apparent concentration, K , for element A i s given by: h F A ( X ) h00A A b F 1 0 0 A ( X ) where I = X-ray i n t e n s i t y from some concentration of element A i n B. ''"lOOA = ^ - r a y i n t e n s i t y from pure element A F (x) = absorption correction factor of some concentration of element A i n B. F^QQ A(X) = absorption correction f o r pure element A. Actual c o e f f i c i e n t s are: h(Pb) = 0.037 h(Sn) = 0.057 - 92 -a = 20° a = 1,340 ^ P b S n = 1 5 2 8 - 9  USnPb = 1 2 3 - 2  VSnSn = 4 3 7 * 4 ^PbPb = 1 1 6 - 6 The c a l i b r a t i o n curve (Equation 25) i s plo t t e d i n Figure 50. Some experimental microprobe data i s plotted i n F i g . 51 such that the corrected Pb and Sn compositions of a spot count are summed The actual sum, therefore, must be 100%. The scatter shows the quantity ative inaccuracy for the Pb-Sn system. - 93 -Figure 50. Microprobe corrections for Pb-Sn. 110 i i i T" 1 - 1 1 1 1 105 %Sn + %Pb 100 95 o 0 o o o o o ° _ o o o o o° 8. o o o u o ° o o ° o 90 o, 1 1 1 1 1 1 I I ! r_j I I ! I I ! 1 0 10 20 30 40 50 60 70 80 90 100 % Sn Figure 51. The summation of %Pb and %Sn for spot counts. - 95 -APPENDIX B Electron Microprobe Corrections for Cu-Ag X-ray analysis was done at 25 KV on Ag-La^ and Cu-Ka^. ra d i a t i o n s . Fluorescence c a l c u l a t i o n s were neglected because of the large difference 14 in atomic numbers. 29 for Cu and 47 for Ag. The cor r e c t i o n formulas used, therefore, were the same as those i n A.ppendix A. Actual c o e f f i c i e n t s are : h(Ag) = 0.058 h(Cu) = 0.091 a = 20° a = 2,620 uf, . = 802.7 CuAg % C u = 2 1 7 - 6 ^CuCu= 5 3 • 7 The c a l i b r a t i o n curve i s plotted i n F i g . 52. In t h i s case the re s u l t s were much more accurate than for Pb-Sn. Summations of Cu and Ag concentrations f o r spot counts were within 100 i 0.7%. For C < 8% Ag the c a l i b r a t i o n i s l i n e a r and the cor r e c t i o n factor i s simply 1.40. - 96 -- 97 -APPENDIX C The Extension Factor Consider a function, f ( g ) , between 0 and g •. This function i s replotted between g^ and 1 to form a new function, F(g), such that f(g 2> = F ( l ) and f(0) = FCg^). Considering an a r b i t r a r y point, g^: F(g n) = f l C g ^ C ^ ) ] g2 where := y, the extension factor. 1 " g1 '•• 

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