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Roles of Supercooling and Cooling Rates in the Microstructural Evolution of Copper-Cobalt Alloys

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Roles of Supercooling and Cooling Rates in the Microstructural Evolution of Copper-Cobalt Alloys
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WANNAPARHUN, SURASAK ( Author, Primary )
Copyright Date:
2008

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Alloys ( jstor )
Cooling ( jstor )
Liquids ( jstor )
Liquidus ( jstor )
Simulations ( jstor )
Solidification ( jstor )
Solids ( jstor )
Spherulites ( jstor )
Supercooling ( jstor )
Velocity ( jstor )

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University of Florida
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University of Florida
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Copyright Surasak Wannaparhun. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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5/31/2006
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436098721 ( OCLC )

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ROLES OF SUPERCOOLING AND COOLING RATES IN THE MICROSTRUCTURAL EVOLUTION OF COPPER-COBALT ALLOYS By SURASAK WANNAPARHUN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Surasak Wannaparhun

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To my father, Narongsak Wannaparhun, who dedicated so much for my life and my education until the last day of his life. To my mother, Thipmanee; my brother, Surasen; and my wife, Yada, who support me with their en dless love. Last but not the least, to the Clark family in Greenville, SC , for their love and support.

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iv ACKNOWLEDGMENTS It is my honor to receive the Ph.D. degr ee under the supervision of Professor Reza Abbaschian. My accomplishment could not be achieved without his academic and financial support throughout my ti me at the University of Flor ida. He is a great example of a person who works hard and has a strong career determination. I also would like to thank Professor Michael Kaufma n for his casual and formal discussion. It is also my honor to have Professor DeHoff, Professor Fu chs, Professor Seifert, Professor Vu-Quoc, and Professor Chung as my committee members. They provided comments and suggestions whenever needed. I am very th ankful to Dr. Abraham Munitz (Nuclear Research Center, Negev, Beer Sheva, Is rael) for a great learning experience on the electromagnetic levitation system. I also w ould like to thank Dr. Andrew Deal and Dr. Ercan Balikci for their help and suggestions during the first 2 years of my study. Finally, I would like to thank my friends in the Department of Mate rials Science and Engineering for friendly conversation and discussion.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.....................................................................................................................xi ii CHAPTER 1 INTRODUCTION........................................................................................................1 2 LITERATURE REVIEW...........................................................................................10 2.1 Copper-Cobalt (Cu-Co) Phase Diagram...............................................................10 2.2 Driving Force for Solidification...........................................................................11 2.3 Homogeneous and Heterogeneous Nucleation in Solidification..........................12 2.4 Containerless Processing using th e Electromagnetic Levitation (EML) Technique...............................................................................................................14 2.5 Metastable Liquid Phase Separati on (MLPS) in Bulk Supercooled Cu-Co Alloys.........................................................................................................17 2.6 Coarsening, Impingement and Coalesce nce of Liquid Spherulites in the MLPS Cu-Co Liquid..............................................................................................21 2.7 Solidification of Alloys.........................................................................................23 2.7.1 Length Scale in Solidification....................................................................23 2.7.2 Effect of Solidification Veloci ty on the Partitioning Coefficient...............26 2.7.3 Partitionless Solidification and T0 Curve...................................................27 2.7.4 Mesoscale Solidification of Alloys............................................................29 2.7.5 Solidification Sequence of a MLPS Cu-Co Liquid....................................31 2.8 Heat Transport Phenomenon at the Mesoscale Solidification of Alloys..............32 2.9 Thermal Condition at the Mesoscale S/L Interface..............................................37 2.10 Numerical Methods for Solidification Problems................................................39 3 TECHNICAL APPROACHES...................................................................................64 3.1 Specimen Preparation...........................................................................................64 3.2 Experimental Procedures......................................................................................65

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vi 3.3 Specimen Characterization...................................................................................68 4 EXPERIMENTAL RESULTS AND DISCUSSIONS...............................................75 4.1 Results...................................................................................................................7 5 4.1.1 Thermal Information..................................................................................75 4.1.2 Microstructural Observation.......................................................................77 4.1.2.1 Specimens solidified during the levitation state...............................77 4.1.2.2 Specimens rapidly solidified in the cone-shape copper mold..........80 4.2 Discussions...........................................................................................................83 4.2.1 Specimens Solidified during the Levitation State without MLPS..............83 4.2.2 Relationship between Cooling rate s and Dendrite Arm Spacing (DAS)...85 4.2.3 Specimens Solidified during th e Levitation State with MLPS...................86 4.2.4 Specimens Rapidly Solidified in the Cone-Shaped Copper Mold without MLPS..................................................................................................88 4.2.5 Specimens Rapidly Solidified in the Cone-Shaped Copper Mold with MLPS...............................................................................................................88 4.2.6 Microstructure at region adjacen t to the mold/specimen interface............90 4.3 Conclusion............................................................................................................92 5 NUMERICAL APPROACHES................................................................................129 6 NUMERICAL RESULTS AND DISCUSSIONS....................................................140 6.1 Validation of Numerical Simulation...................................................................140 6.2 Results.................................................................................................................142 6.2.1 Effects of Heat Transfer Coefficient (h)...................................................142 6.2.2 Effects of Composition (X)......................................................................143 6.2.3 Effect of Bulk Supercooling ( T)............................................................143 6.3 Discussions.........................................................................................................145 6.3.1 Solidification of Bulk Supercooled Cu in the Cone-Shaped Copper Mold...............................................................................................................145 6.3.2 Comparison between Experiment al and Numerical Simulation..............145 6.3.3 Coarsening of MLPS Liquid Sphe rulites in the C12 Specimen during Rapid Solidification............................................................................146 6.3.4 Dynamic Supercooling.............................................................................148 6.4 Conclusions.........................................................................................................148 7 CONCLUSIONS......................................................................................................171 APPENDIX C++ CODE FOR NUMERICAL SIMULATION.....................................173 LIST OF REFERENCES.................................................................................................184 BIOGRAPHICAL SKETCH...........................................................................................192

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vii LIST OF TABLES Table page 1-1. Selected properties of elements that fo rm binary systems with copper, with large L+S regimes...............................................................................................................7 1-2. Selected properties of Co and Fe compared to those of Cu.......................................8 2-1. Techniques for obtaining bulk superc ooling in liquid metals and alloys.................42 2-2. Time line showing the study on metas liquid phase separation in the Cu-Co system.......................................................................................................................43 2-3. Time line showing rapid solidif ication works on the Cu-Co system.......................44 4-1. Levitated specimens with their thermal information................................................94 5-1. Boundary conditions for the numerical simulation in this work............................135 5-2. Selected properties of copper and cobalt................................................................136 6-1. Coarsening coefficient (k) and coarse ning exponent (n) under various heat transfer coefficients predicted using the numerical simulation in this work..........150

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viii LIST OF FIGURES Figure page 1-1. Mechanism of giant-magneto-resistance in Cu-Co alloys.........................................9 2-1. Equilibrium phase diagram of a Cu-Co system.......................................................45 2-2. Temperature-dependent equilibrium partitioning coefficient of the Cu-Co system in the range of 1113 to 1495 C....................................................................46 2-3. Wettability of a solid phase on a nucleation site.....................................................47 2-4. Plot between free energy and temperature (G-T) at a constant composition showing possible phase transfor mation of supercooled liquid.................................48 2-5. Coaxial levitation coil first used fo r containerless proces sing of metals. 49 2-6. Levitation of a specimen in the EML system...........................................................50 2-7. Thermodynamic functions indicating te ndency of liquid phase separation in Cu-Co alloys.............................................................................................................51 2-8. Cu-Co phase diagram with the miscibility boundary and extended T0, TS, and TL curves............................................................................................................52 2-9. Effects of electromagneti c filed on the MLPS microstruc ture in Cu-Fe alloys.......53 2-10. Solid-liquid interface................................................................................................54 2-11. Free energy profile across a S/L interface................................................................55 2-12. Velocity-dependent partitioning coefficient.............................................................56 2-13. Mechanism of solute trapping..................................................................................57 2-14. Morphology of the mesoscale S/L in terface with a positive temperature gradient in the liquid................................................................................................58 2-15. Morphology of the mesoscale S/L in terface with a negative temperature gradient in the liquid (a bulk supercooled liquid)....................................................59 2-16. Solidification microstructure s of the MLPS Cu-Co alloys......................................60

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ix 2-17. Enthalpy-temperature profiles..................................................................................61 2-18. Temperature profiles for solidifi cation of an alloy in a mold..................................62 2-19. Enthalpy-temperature diagrams for solidification under various conditions...........63 3-1. Minimum supercooling re quired for approaching T0 and TMLPS as a function of composition..............................................................................................................69 3-2. Arc-melting furnace for specimen preparation........................................................70 3-3. Electromagnetic levitation station............................................................................71 3-4. Electromagnetic splat qu enching apparatus (ESQA)...............................................72 3-5. Vacuum molds used for producing cone specimens................................................73 3-6. Metallographic imaging equipment.........................................................................74 4-1. Time-voltage profile of a levita ted specimen with bulk supercooling.....................96 4-2. Temperature profile of the levitated specimen.........................................................97 4-3. P6 specimen (6.26 at% Co and T = 0)...................................................................98 4-4. P15 specimen (11.54 at% Co and T = 0)...............................................................99 4-5. P4 specimen (28.07 at% Co and T = 0)...............................................................100 4-6. P8 specimens (35.76 at% Co and T = 0)..............................................................101 4-7. Optical micrographs at 100X of Cu-Co alloys with TR = T..............................102 4-8. Optical micrographs at 100X of Cu-Co alloys with TR < T..............................103 4-9. Optical micrographs at 100X of Cu-Co alloys with different thermal history.......104 4-10. P9 specimen (38.22 at% Co, T = 242, TR = 111, and TMLPS = 77).................105 4-11. P11 specimen (36.18 at% Co, T = 126, TR = 87, and TMLPS = 39).................106 4-12. P16 specimen (36.42 at% Co, T = 74, TR = 74, and TMLPS = 48)...................107 4-13. P18 specimen (22.93 at% Co, T = 87, TR = 35, and TMLPS = 74)...................108 4-14. C10 specimen (38.99 at% Co with 34 degrees superheated before rapid solidification).........................................................................................................109 4-15. Appearance of C10 specimen rapidl y solidified in a cone-shape mold.................110

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x 4-16. Detail microstructures along the center line of the C10 specimen.........................111 4-17. Dendrite arm spacing (DAS) (from B5 to C5) or the average particle diameter (from B-D5 to F5) versus distance along the center of the C10 specimen............112 4-18. C13 specimen (35.71 at% Co, T = 58)................................................................113 4-19. C7 specimen (37.09 at% Co, T = 193, TR = 121, and TMLPS = 68)................114 4-20. C15 specimen (36.94 at% Co, T = 77 and TMLPS = 63)....................................115 4-21. C16 specimen (37.89 at% Co, T = 77 and TMLPS = 68)....................................116 4-22. C12 specimen (36.94 at% Co, T = 60, TR = 0, and TMLPS = 63).....................117 4-23. Appearance of C12 specimen rapidl y solidified in a cone-shape mold.................118 4-24. Detail microstructures along th e center of the C12 specimen................................119 4-25. Average spherulite diameter versus distance along the cente r axis of the C12 specimen.................................................................................................................120 4-26. Microstructural evolutio n in specimens solidified without bulk supercooling in the levitation state..............................................................................................121 4-27. Schematic shows the microstructural e volution in specimens solidified in the levitation state after bulk supercooling with TR = T.........................................122 4-28. Schematic shows the microstructural e volution in specimens solidified in the levitation state after bulk supercooling with TR < T.........................................123 4-29. Relationships between experimentally obtained dendrite arm spacing with other parameters for Cu-Co alloys of 10 to 40at%Co............................................124 4-30. Schematic shows the formation of th e MLPS microstructure in Cu-Co alloys.....125 4-31. C8 specimen (35.95 at% Co with 135 degrees superheated before rapid solidification) shows the MLPS spheru lites formed by dynamic supercooling at the edge regime..................................................................................................126 4-32. C1 specimen (10.61 at% Co with 250 degrees superheated before rapid solidification shows a thin featureless layer was observed prior to the thin layer of MLPS microstructure................................................................................127 4-33 SX specimen (36.94 at% Co and spla t cooled at its equilibrium liquidus temperature)...........................................................................................................128

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xi 5-1. Schematic shows the setup for the finite difference simulation for 1D solidification of bulk s upercooled Cu-Co alloys....................................................137 5-2. Enthalpy-temperature-composition diagra m of Cu-Co alloys of 0 to 40 at% Co..138 5-3. Flow chart of C++ program us ed for the numerical simulation.............................139 6-1. Schematics show solidification of a pure liquid at its melting point.....................151 6-2. Comparison between the analytical and simulation results for the solidification of a pure liquid copper at the melting point in a copper mold...............................152 6-3. Plots between S/L interface position versus time for a pure Cu with various heat transfer coefficients........................................................................................153 6-4. Plots between S/L interface velocity ve rsus position for a pure cu with various heat transfer coefficients........................................................................................154 6-5. Plots between cooling rate versus pos ition for a pure cu with various heat transfer coefficients................................................................................................155 6-6. Plots between thermal gradients on the solid (GS,i) and liquid (GL,i) sides at the S/L interface versus position for a pure Cu with various heat transfer coefficients.............................................................................................................156 6-7. Plots between S/L interface temperatur e versus position for a pure cu with various heat transfer coefficients............................................................................157 6-8. Plots between S/L interface position versus time for various compositions..........158 6-9. Plots between S/L interface velocity versus position for various compositions....159 6-10. Plots between cooling rate vers us position for various compositions....................160 6-11. Plots between thermal gradients on the solid (GS,i) and liquid (GL,i) sides at the S/L interface versus position for various compositions.........................................161 6-12. Plots between S/L interface position versus time for a pure Cu with various bulk supercoolings..................................................................................................162 6-13. Plots between thermal gr adient on the solid side (GS,i) at the S/L interface versus position for a pure Cu w ith various bulk supercoolings.............................163 6-14. Plots between thermal gr adient on the liquid side (GL,i) at the S/L interface versus position for a pure Cu w ith various bulk supercooling...............................164 6-15. Plots between S/L interface velocity ve rsus position for a pure Cu with various bulk supercoolings..................................................................................................165

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xii 6-16. Plots between cooling rate versus pos ition for a pure Cu with various bulk supercoolings..........................................................................................................166 6-17. Plots between S/L interface temperatur e versus position for a pure Cu with various bulk supercoolings.....................................................................................167 6-18. Solidification velocity maps of a pure Cu..............................................................168 6-19. Microstructural maps of specimens solidified with and without bulk supercooling...........................................................................................................169 6-20. Average spherulite diameter along the center of C12 specimen versus solidification time predicted using the numerical simulation under various h values...................................................................................................................170

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xiii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ROLES OF SUPERCOOLING AND COOLING RATES IN THE MICROSTRUCTURAL EVOLUTION OF COPPER-COBALT ALLOYS By Surasak Wannaparhun May 2005 Chair: Reza Abbaschian Major Department: Materials Science and Engineering Copper-cobalt (Cu-Co) alloys (particularl y with small to intermediate cobalt content) have been widely studied because they exhibit several promising properties for magnetic, microelectronic, stru ctural, and catalytic applicat ions. In this work, Cu-Co alloys of 30 to 40 at% Co were of inte rest and were studie d under various bulk supercooling and cooling conditions using an electromagnetic levitation (EML) system equipped with rapid solidification devices . It was found that various types of microstructures can be obtained dependi ng on composition, and on bulk supercooling and cooling rates. Above the metastable liqui d phase separation (M LPS) temperature, depending on composition, the microstructure changed from dendr itic to nondendritic microstructure as the supercooling and coo ling rates increased. On the other hand, MLPS microstructures with Co-rich spherulites in Cu -rich matrix could be obtained if the liquid was bulk supercooled below the MLPS te mperature. It was also found that electromagnetic stirring and thermal recales cence during the levita tion stage could alter

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xiv or destroy the MLPS microstructure. However, rapid solidification immediately after the MLPS could yield a desirable microstructu re with homogeneous distribution of submicron-size spherulites in matrix. In addition to the EML experiment, numeri cal simulation was also used to explain and compare with the experimental results. It was numerically shown that an increase in cobalt content slightly suppresse d the solidification ve locity and cooling rate of the alloy. On the other hand, bulk supercooling and larg e mold/sample heat transfer coefficient significantly enhanced the so lidification velocity and c ooling rate of the alloy. Particularly, microstructural evolution predicted using the numerical simulation showed good agreement with experimental results. Nume rical simulation was also used to predict coarsening behavior during the liquid state of an MLPS Cu-Co alloy with 30 to 40 at% Co. The coarsening parameters in experime ntal results showed reasonable agreement with theoretical predictions.

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1 CHAPTER 1 INTRODUCTION Copper and copper alloys have a long hist ory in human civiliza tion. Early uses of copper and its alloys were found in China a nd the Middle East, and expanded to Europe from 4500-1500 B.C. (the copper and bronze ag e). Bronze was accidentally discovered, where the copper sites were rich with ti n, and it became a better choice for producing practical tools and weapons throughout Central Europe, Southern Spain, the British Isles, Northern Italy, and the South of France [1]. Around the 15th centur y, copper and bronze fabrication had become an important occupation and the foundation of human civilization. Currently, copper and its alloys have been widely used in several applications (architectural, c onstructional, transportation, st ructural, marine, electrical, telecommunication, and electronic) [2]. A great example is the Statue of Liberty: her beautiful greenish skin is made of oxidized copper [2]. Copper is also found in several advanced applications such as the computer chip. Copper interconnects improve the performance and efficiency of computers be cause it can provide much faster operating speeds and greater circuit inte gration. Up to 200 million tran sistors can be packed onto a single chip. According to a recent statistical report, global copper consumption has increased steadily every year. Most copper and copper alloys consumed in the United States are for electrical applications [2]. Fifty-four binary systems of copper (Cu) have been discovered and studied [3, 4]. Most of these systems have been thoroughly i nvestigated. Alloys of these systems have been used in various applications, while research and development are ongoing for some

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2 of these systems. Among the 54 binary system s, there are 15 binary systems of Cu with Boron (B), Bismuth (Bi), Carbon (C), Coba lt (Co), Chromium (Cr), Iron (Fe), Mercury (Hg), Iridium (Ir), Lithium (Li), Niobium (Nb) , Lead (Pb), Rhodium (Rh), Silicon (Si), Thallium (Tl), and Vanadium (V); indicati ng a dominating liquid/solid (S+L) regime covering a wide range of temperature a nd composition in their equilibrium phase diagrams. According to the physical propertie s of these 15 elements, the dominating S+L regimes in these binary systems may result from a significant difference between the melting temperatures of these elements and th at of Cu (Table 1-1). However, the most important reason for the dominating S+L regime s in these systems is the large positive enthalpy of mixing [5], which results in very small mutual solubility and hence immiscibility at low temperature. The 15 binary systems mentioned previously can be further categorized into two groups: Binary diagrams in which the liquidus cu rve monotonously decreases from one side to the other. Binary diagrams with a two-liquid mixture dome. For the first group, as temper ature decreases, the separa tion between the liquidus and solidus temperature increases. For the sec ond group, a unique phase diagram with a twoliquid mixture dome on the top of an L+S regime is known as a monotectic phase diagram [6] and the monotectic reaction is represented by the invariant reaction S L L 2 1. Below a monotectic temperature, the binary diagrams of the second group indicate a similar L+S regime to that of the first group. Among the above-mentioned binary system s, Cu-Fe and Cu-Co systems are of interest for several applications. Most of the physical properties of Fe and Co (Table 1-2)

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3 are compatible [7]; however, the ma gnetic transformation temperature (TC) of the Cu-Co system is approximately 300 C higher than that of the Cu-Fe system. Such a high TC can lead to various opportunities for Cu-Co a lloys in elevated-temperature magnetic applications. The Cu-Co system is the focu s of our study. The fundamental study of this system complements previous work on Cu-Fe [8]. Some experimental and computational studies show that Cu-Co alloys can be used for structural applications [9, 10]. It has b een suggested that the strengthening mechanism in Cu-Co alloys resulted from dislocation-particle interact ions, where the strain field around the coherent spherical Co precipitates (induced by the lattice mismatch between particles and matrix) interacted with dislocations. Neverthe less, such applications are limited to Cu-Co alloys with very fine Co-p recipitates (approximately 70 Angstrom) [11]. Besides the structural applic ation, Cu-Co alloys show prom ise for catalytic [12–14] and magneto-electronic [15] applications, where the performance of the alloys critically depends on the morphology of Co precipita tes. For catalytic applications, the electrochemical process between copper and cobalt on the surface of the alloys was found responsible for high selectivity to alcohol formation via a dual-site mechanism involving both Cu and Co of the alloy [14, 16–18], as shown in Equations 1-1 and 1-2. 2 2 02 ) 1 ( 2 ) ( nH nO Surface n C Surface nH nCO catalyst Con (1-1) O H n OH H C nH nO Surface n C Surfacen n n 2 1 2 2) 1 ( 2 ) 1 ( (1-2) A high volume fraction and homogeneous distribu tion of Co is also desirable for such catalytic reactions. Cu-Co alloys were also found to have a unique behavior ca lled Giant-MagnetoResistance (GMR), where the electrical resist ance of the alloys decreased under applied

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4 magnetic fields [19]. This GMR behavior has been observed in several materials composed of magnetic and nonmagnetic elemen ts, and the behavior is promising for sensing and data-storage app lications. The GMR behavior ev olves from the behavior of conducting electrons at the inte rfaces between magnetic and no nmagnetic layers [20]. In the absence of a magnetic field, electrons suffe r spin-dependent scatte ring at the interface (due to opposite electron-spin directions), resulting in lo w electrical con ductivity across the interface (Figure 1-1). In contrast, the a pplied magnetic field aligns the spins in the same direction and allows electrons to travel freely across the interface (Figure 1-1). The GMR ratio used to quantify such behavior [21] is calculated using Equation 1-3. ) , 0 ( ) , 0 ( ) , (T T T H ratio GMR (1-3) where (H,T) and (0,T) are the electrical resistance m easured at the temperature “T” at an applied magnetic field of “H” and zero, ac cordingly. Recent experiments showed that high performance Co-Cu alloys such as the GM R material could be obtained in granular Cu-Co alloys synthesized using rapi d solidification techniques [19, 22] . Magnetic properties of these alloys depended heavily on processing conditions, volume fraction of the constituent phases, and their microstructures [23]. Moreover, the GMR ratio was found to be proportional to the specifi c area of the Co precipitates [24] . However, for rapid solidification fo llowed by precipitation, the volum e fraction of the Co-phase was limited to around 15 at%, according to the maximum solubility of Co in Cu (which limited their GMR performance to about 11%) [25] . Therefore, one could achieve a high GMR ratio in a granular Cu-Co alloy, if a larger volume fraction of fine and homogeneously distributed Cophase could be obtained.

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5 The morphology of Co in Cu-Co alloys di ctating the properties and functionalities of the alloy depends on the processing techni que. Cu-Co alloys can be synthesized in several forms (such as a mu lti-layer, powders, and ribbons) through thin film deposition [26], pulse-plating [27], nebulized spray pyrolysis [28], atomization [29], ball milling [30], and melt spinning [31]. Although a conve ntional solidification process is more economical than other techniques for produci ng bulk-volume Cu-Co alloys, the challenge is to minimize and or eliminate chemical segregation. Rapid solidification processing (widely used to synthesize advanced alloys ) can minimize or eliminate such problems and can result in enhanced prope rties. As discussed later, it is possible to synthesize CuCo alloys with fine and homogeneous Co preci pitates in Cu-Co alloys of less than 15 at% Co (maximum solubility). However, chemical segregation becomes significant in alloys of more than 15 at% Co, where the difference between the liquidus and solidus temperatures is significant. Nevertheless, bul k supercooling before so lidification of liquid Cu-Fe and Cu-Co alloys could lead to meta stable liquid phase se paration (MLPS) [8] resulting in very fine and homogeneous dispersion of Fe-ri ch or Co-rich spherulites throughout a Cu-rich matrix, and vice versa. In addition, a large vol ume fraction of fine and homogeneously dispersed Co spherulite s could be obtained via bulk supercooling and liquid phase separation of a high Co-conten t liquid compared to that of conventional rapid solidification proc esses. To achieve such a fine-s cale microstructure in Cu-Co alloys with large Co contents, one must a void excessive coarsening, agglomeration, and coalescence by rapid solidification immediatel y after the MLPS. Therefore, we focused on finding the optimal condition for obtaining su ch large Co-content Cu-Co alloys with a large volume fraction of fine and homoge neous Co-rich dispersions; and also on

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6 fundamental understanding of the microstr uctural evolution in Cu-Co alloys under various bulk supercoolin g and cooling conditions.

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7 Table 1-1. Selected properties of elements that form binary systems with copper, with large L+S regimes Element Atomic number Atomic weight (g/mole) Melting temperature; Tm ( C) Tm-Tm ,Cu ( C) B 5 10.81 2092 1007 Bi 83 208.98 271 -813 C 6 12.01 3827 2742 Co 27 58.93 1495 410 Cr 24 52.00 1863 778 Fe 26 55.85 1538 453 Ir 77 192.22 2447 1362 Li 3 6.94 181 -904 Nb 41 92.91 2469 1384 Rh 45 102.91 1963 878 Si 14 28.09 1414 329 Hg 80 200.59 -39 -1124 Pb 82 207.20 328 -757 Tl 81 204.37 304 -781 V 23 50.94 1910 825 Cu 29 63.55 1085 0

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8 Table 1-2. Selected properties of Co and Fe compared to those of Cu Properties Fe Co Cu Atomic number 26 27 29 Atomic weight (g/mole) 55.847 58.933 63.55 Density (kg/m3) 7870 8832 8930 Melting temperature (ºC ) 1538 1495 1085 Crystal structure at room temperature BCC HCP FCC Goldschmidt metallic radius (Angstrom) 1.27 1.25 1.28 Electrical resistivity (nW-m)97.1 52.5 16.7 Thermal conductivity (W/m-K) 80.4 69.0 398.0 Specific heat capacity (kJ/kg-K) 0.447 0.414 0.385 Magnetic behavior Ferromagnetic Ferromagnetic Diamagnetic Saturation magnetic moment (mB) 2.216 1.715 — Curie temperature (ºC ) 771 1115 — Electronic configuration [Ar] 3d(6) 4s(2 ) [Ar] 3d(7) 4s(2) [Ar] 3d(10) 4s(1) Allotropic transformation L (1538ºC), (1394ºC), and (912ºC) L (1495ºC) and (422ºC) L S (1085ºC)

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9 Figure 1-1. Mechanism of giant-magneto-resis tance in Cu-Co alloys. A) Without applied magnetic field. B) With applied magnetic field

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10 CHAPTER 2 LITERATURE REVIEW 2.1 Copper-Cobalt (Cu-Co) Phase Diagram An equilibrium Cu-Co phase diagra m was first calculated in 1978 [32]. Retrogression of the solidus curve in the Cu-Co phase diagram wa s later reported [33]. The most accepted Cu-Co phase diagram [34] is shown in Figure 2-1. Details of the phase diagram are described next. The uniqueness of the Cu-Co system is the presence of a dominating L+S regime covering a wide range of te mperature and composition at above 1085ºC. On the cobalt side, two forms of cobalt, -Co (FCC) and -Co (HCP), exist accord ing to its allotropic transformations at 1495 and 422 C, respectively. Retrogression of the solidus curve takes place 1367 C, where the maximum solubility of Cu in Co is approximately 19.7 at%. As temperature decreases, the solubility of Cu in Co decreases, and the maximum solubility of Cu in Co are approximately 0.04 at% Cu at 442 C. The magnetic transformation temperature linearly increases from 1050 to 1120 C for 91 to 100 at% Co. On the other hand, the liquidus curve of the syst em nonlinearly decreases from 1495 to 1112 C and the separation between the liquidus and solidus curves increases significantly as temperature decreases. At 1112 C, a peritectic reaction takes place, where ) % 8 ( ) % 87 ( ) % 5 (2 1112 1 1Co at S Co at S Co at LC . At a constant temperature in the L+S region, the separation between the liquidus and solidus line s can be quantified using a parameter called an equilibrium partitioning coefficient (ke),

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11 * * L S eC C k (2-1) where CS* and CL* are the solid and liquid compositio ns, according to the solidus and liquidus curves. The equilibrium partitioning coefficient can be independent of temperature, if the slopes of liquidus and solidus curves are constant. On the other hand, the coefficient is temperature dependent, which is the case for the Cu-Co system. The equilibrium partitioning coefficient as a functi on of temperature is shown in Figure 2-2. Slightly above 1112 C, the ke value is approximately 0.0575. It should also be mentioned that on the copper side of the phase diagram, the ke value is constant at 1.6 from 1112 to 1085 C. The solubility of Co in Cu decrea ses significantly as temperature decreases toward 422 C. The maximum solubility of Co in Cu below this temperature is 0.04 at%. 2.2 Driving Force for Solidification Phase transformation from one to anothe r normally requires a driving force (dG), which can be in thermal (dT), mech anical (dP) and non-mechanical ( WÂ’) forms [35], as described by the Gibbs free-energy (G) equation. 'W VdP SdT dG (2-2) Solidification is one type of phase transforma tion, in which a liquid phase transforms into a solid phase, and the demarcation between the two phases is a solid/liquid (S/L) interface. With the emphasis on the thermal dr iving force, supercooling is a major driving force for a solidification process that can be obtained under several effects such as curvature (Tr), kinetics (Tk), pressure (Tp), composition (Tc), and temperature (Tt) [36]. The supercooling due to th e first three effects influen ces the solidification in the vicinity of the S/L interface (known as interf acial supercooling). The magnitude of these

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12 supercoolings is typically small (2K for r = 0.1 m for Tr, 0.01 to 0.05K for Tk, and 10-2 K/atm for Tp). On the other hand, constitutional or compositional supercooling resulting from solute build-up in the liquid ah ead of the S/L interface can result in several degrees of interfacial superc ooling, depending on the differe nce between the equilibrium liquidus profile and the temperature gradient ahead of the interface [6], which can be approximately calculated by using Equation 2-3. ) (0 *C C m TL c (2-3) where m is the slope of a liquidus line, CL* is the composition of liquid at the interface on the liquid side, and C0 is the composition of the bulk liquid. On the other hand, bulk supercooling or thermal supercooling (Tt) can be attributed to suppression of overall temperature of the liquid below its equilibrium melting or liquidus temperature; generally has a magnitude in the order of 10 or 100. If the liquid experiences large bulk or thermal supercooling, interfacial supe rcooling may be negligible. 2.3 Homogeneous and Heterogeneous Nucleation in Solidification Nucleation is the phenomenon of a new phase forming by the accumulation of atoms for the starting phase. A driving for ce is generally required to overcome the nucleation barrier (*S LG) of a new phase. The magnitude of the supercooling driving force required for nucleation of a solid phase fr om a liquid [37] is shown in Equation 2-4. 2 / 1 * 2 2 3 /) ( 3 16 S G H T V TS L f m S N S (2-4) where S/N is the surface energy between a solid phase and an active nucleation site, VS is the molar volume of a nucleating phase, Tm is the melting point of a solid, and Hf is the heat of solidification. The S() term is a geometric factor accounting for the wetting

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13 angle () between a solid phase and an active nuclea tion site; and it varies from 0 to 1 for = 0 to 180 (Figure 2-3). The wetting angle ca n be calculated using Young’s equation [35], where L S N S N L / / /cos (2-5) For copper and cobalt, the S/L surface energies (S/L) are approximately 0.186 and 0.289 J/m2 [38]. The wettability between a solid phase and the nucleation site resulting from the equilibrium among the surface energies dictat es the level of supercooling required for nucleation of a solid phase; the smaller the wetting angle, the better the wettability (and hence the smaller the geometric factor). As a result, a small amount of supercooling is required for nucleation when the liquid is in contact with a potent nucleant. Such a phenomenon is known as heterogeneous nuc leation. Heterogeneous nucleation in solidification generally takes place in the presence of a crucible wall or solid inclusions with similar chemistry to that of liquid. On the other hand, homogeneous nucleation (whereby a new solid phase nucleates within a liquid itself) can take place if the geometric factor is equal to one. As a resu lt, a large amount of supercooling is usually required for homogeneous nucleation. For exam ple, supercooling of about 410 degrees is required for homogeneous nucleation of a solid in Cu and Co liquid respectively [39]. A liquid can experience a considerable th ermal and bulk supercooling before the nucleation of a solid phase. The liquid may then experience metastable phase transformation if the formation of an equili brium phase is suppressed [40]. For example, the liquid (L) can transform into an “A” phase at below T* if it is supercooled for at least Tm-T* degrees and no preferential nucleation site for a solid (S) phase exists (Figure 2-4).

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14 However, difficulty obtaining large superc ooling in liquid metals and alloys under conventional processes is due to the presence of active nucleation site s such as container surface and impurities, which can result in a small value of the geometrical factor S(). In general, the following approach es can be used to achieve a large bulk supercooling in liquid. High purity materials (such as raw mate rials) are used, to minimize possible heterogeneous impurities. Since the probability of finding nucleants is proportional to the volume of liquid [39], dispersion of liquid into a large number of small droplets is needed. A nonreactive crucible material or containe rless processing may be required. Based on these requirements, several technique s such as emulsification [41], melt fluxing [42], atomization [43], drop tube [44], electromagnetic levita tion (EML) [45], and electrostatic levitation (ESL) [46] (Table 2-1) can be used to achieve large bulk supercooling in a liquid before solidification. Among these techniques, EML and ESL are of interest, because a metallic or nonmetallic (only for ESL) specimen can be cyclically melted and solidified without any physical cont act with a crucible material. The operating nature of these techniques allows controllab ility of the supercooling level [47, 48]. The EML technique can process a larger speci men (7-mm in diameter) than the ESL technique can (less than 1-mm in diameter) [ 48]. Therefore, we used the EML technique to study bulk supercooled Cu-Co alloys. 2.4 Containerless Processing using th e Electromagnetic Levitation (EML) Technique Electromagnetic field has been used in several metal processing techniques particularly induction melting [49]. In the EML technique, magnetic field is used for generating levitation forces on a specimen. The magnetic field also re sults in heating and

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15 melting of the specimen. To generate the levitation forces on the specimen, the AC current is supplied through an electrically conductive coil. The supplied current subsequently induces the magnetic field around the coil. The induced magnetic field then induces currents within the surface of the sp ecimen due to the skin effect [50] and the depth “” of the surface influenced by the magne tic field can be estimated using the following equation. 2 1 1 (2-6) where is the angular frequency of the applied field, and are the conductivity and the magnetic permeability of the specimen acco rdingly. The inductive currents due to the skin effect can result in the heating a nd melting of the specimen. In addition, the inductive currents produced with in the skin depth counteract with the applied magnetic field from the levitation coil and result in th e Lorentz forces acting toward the specimen as described by the following equation. B V q FLorentz (2-7) where V q is the analogous to the inductive curren t generated on the specimen’s surface, and B is the magnetic field generated by the levitation coil. The use of the EML technique to heating a nd melting metals without a crucible was first accomplished in 1952, wher e two sets of coils (Figure 25) were used to stabilize a specimen [51]. The design of a levitation coil in fluences the magnetic force, heating, and cooling rate on the specimen [52]. It has been demonstrated th at the coil with a cylindrical shape as shown in Figure 2-6 ha s several advantages for a containerless

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16 experiment [47]. For example, the cylindrical -shape coil can yield a good stability for the levitated specimen. In addition, the specimen can be processed in a reducing atmosphere by inserting a glass tube inside the coil and the reducing gase s such as argon or hydrogen can be delivered through the tube. In a ddition, the specimen can be cooled down by delivering the cooling gas such as he lium through the same glass tube. Besides the levitation forces, other aspects such as ther mal and fluid flow condition within the levitated sample are of interest. It was numerically demonstrated that temperature difference within the levitated sp ecimens of the diameter between 5 to 9 mm was less than 5 degrees [53–56]. However, fluid flow velocity within the specimens is quite severe. Therefore, the combination of such conditions is likely to induce the uniformity in temperature and composition of the levitated liq uid during the EML process. Due to a contactless nature of the tec hnique, the EML technique can provide bulk supercooling to the liquid by eliminating th e heterogeneous nucleation sites due to a container wall. In addition, the chance of he terogeneous nucleation within a liquid during the EML experiment can be minimized by supplying reducing gases such as hydrogen and/or argon. These gases prevent the form ation of inclusions that can result in heterogeneous nucleation, which decreases supercoolability of the liquid. The EML technique has been used for th e investigation of the effect of bulk supercooling in several metals and alloys. Particularly, the use of the EML technique for the study of the bulk supercooling effect in Cu-Fe and Cu-Co alloys was initially reporte d in 1990 [8] and the metastable liquid phase separation (MLPS) of bulk supercooled Cu-Fe and Cu-Co liquids

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17 was reported in these system. In the followi ng section, the scien tific background on the MLPS phenomenon particularly in the Cu-Co system will be discussed. 2.5 Metastable Liquid Phase Separation (MLP S) in Bulk Supercooled Cu-Co Alloys According to the equilibrium phase diag ram, the Cu-Co liquid is completely miscible at above liquidus temperature de pending on composition. However, the liquid exhibits a tendency toward liquid demixing in the bulk supercooled state as that of Cu-Fe system [57, 58]. Such tendency can be demons trated using the free energy of the Cu-Co liquid (L total Co CuG,)[32], where L mixing Co Cu L ideal Co Cu L total Co CuG G G, , , (2-8) ) 1 )( 623 . 9 12050 ( ) )( 16296 . 9 08 . 16192 (, Cu Cu L ideal Co CuX T X T G (2-9) ) 1 ln( ) 1 ( ) ln( (, , Cu Cu Cu Cu L mixing Co Cu L mixing Co CuX X X X T R H G (2-10) ) 1 ( ) )( 736 . 16 53555 ( ) 1 )( 368 . 8 40166 (, Cu Cu Cu Cu L mixing Co CuX X X T X T H (2-11) L ideal Co CuG, is the ideal free energy of mixing of Cu-Co liquid and L mixing Co CuG, is the excess free energy of mixing. XCu is the atomic fraction of Cu in Cu-Co liquid, R is 8.314 J/mole-K and T is temperature (K). Metast able liquid phase sepa ration in Cu-Co liquid can be attributed to a larg e positive enthalpy of mixing (L mixing Co CuH, ) (Figure 2-7). In order to demonstrate the MLPS in the Cu-Co liquid, the free energy of the liquid were plotted in the temperature range of the L+S regime; 1112 to 1495C (or 1385 to 1768 K) (Figure 2-7). As the temperature of the liq uid decreases during bulk supercooling, the free energy curve becomes undulated because of the influence of the enthalpy of mixing.

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18 If the liquid is bulk supercooled below a critical temperature, where the free energy of the liquid becomes undulating (for a given magnit ude of bulk supercooling and composition), the free energy of an initial bulk supercooled liq uid is larger than that of two liquids with compositions corresponding to two minima of the free energy curve. As a result, the initial liquid tends to separate into two ne w liquids to minimize the free energy of the system. By plotting the two compositions as described previously as a function of the critical temperature, the miscibility boundary can be obtained (Figure 2-8). For Cu-Co liquid alloys of less than 40 wt% Co bulk s upercooled into the mi scibility boundary, the liquid will separate into two new liquids, Co-ri ch spherulites as a minor phase (called L1) dispersed in Cu-rich liquid as a major phase ( called L2) [8]. On the other hand, the Cu-Co liquid alloys of more than 55 wt% Co bulke d supercooled into the miscibility boundary will separate and compose of Cu-rich liquid sp herulites as a minor phase (L2) dispersed in Co-rich liquid as a major phase (L1) [59] . For both cases, the fraction of both liquids follows the lever rule. The metastable liquid phase separation of the Cu-Co liquid mainly takes place by nucleation rather than spinodal decomposition. This is because the liquid/liquid interface energy is small; estimated to be less than 10 ergs/cm2 (as compared, for example, with 100-300 ergs/cm2 for solid/liquid interfaces) [8]. Therefore, an initial microstructure of the MLPS liquid should appear as many small spherulites of one liquid within another. The studies on the MLPS in Cu-Co system have been done since 1958 (Table 2-2). Around 1992, it was found that granular Cu-Co alloys could exhibit the giant-magnetoresistance (GMR) property and such finding ha s driven researchers to find methods to obtain a high GMR ratio [19]. Nakagawa was first to observe the MLPS in Cu-Co alloys

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19 of 50 and 76 at% Co [59]. In his study, the specimens of approximately 400 mg contained in a small half-fused pure alumina crucible were melted and quenched together. Magnetic susceptibility technique was used to dete rmine the MLPS boundary at which metastable liquid immiscibility occurred. It was also obs erved that if the specimens were quenched in water immediately after th e initial state of separation, spherical drops would form. After Nakagawa, Elder was the first to utiliz e the EML technique to bulk supercool CuCo alloys of various compositions [8, 58, 60]. The miscibility boundary of the system was determined from liquid phase separated specimens by plotting compositions of spherulites and matrices versus superc ooling temperatures. In addition, the experimentally measured MLPS boundary was in good agreement with that predicted by thermodynamic calculation [32, 33, 61]. Later on, the existence of the MLPS boundary was also confirmed by Li [62] and Robins on [63] through a melt fluxing technique. The later author applied a high temperature th ermodynamic method and showed a strong temperature dependence of the liquid speci fic heat, which was described in the framework of the self-association (clustering) of the binary liquid. Munitz had continued several investigations on th e system using the EML, drop tube, and electron beam surface melting techniques covering a wide range of composition from 10 to 80 at% Co [60, 64– 66]. Under free-fall containerl ess solidification of 3-mm diameter specimens using the drop tube technique, it was found that some specimens reveal ed the microstructure of fine spherulites in the matrix due to the MLPS. It was also found that the condition called dynamic supercooling due to ra pid solidification without a bulk supercooling caused by self-substrating using the electron beam su rface melting technique could result in the MLPS microstructure. More recently, Ya mauchi observed the MLPS in bulk Co-Cu

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20 alloys using a high-frequency induction furnace under an argon atmosphere [67]. In his study, small amounts of boron (B) were added to some alloys to achieve the MLPS. Since then, several investigations on the MLPS in Cu -Co system have been done repeatedly in order to obtain homogeneous distribution of fine Co-rich spherulites in Cu-rich matrix in high Co-content Cu-Co alloys [57, 59, 60, 62–79]. The MLPS was also observed in the ternar y Cu-Co-Fe system as well using the EML technique [80]. Bulk supercooling of th e ternary alloys containing more than 10 wt% Co and 10 wt% Fe could lead to the form ation of two separated liquid phases. In alloys containing more than 54 wt% Cu (dep ending on the Co and Fe content), the MLPS in this alloy generally appeared as dispersed (Fe, Co)-rich spherulite s in a Cu-rich matrix, whereas for alloys containing le ss copper, the separation resulted in Cu-rich spherulites in a (Fe, Co)-rich matrix. The compositions and phase separation temperatures were found to be consistent with the (Fe, Co)-Cu qua si-binary phase diagram. The MLPS in Cu-CoFe and Cu-Fe-Ni-Cr alloys were also observed by Munitz using the laser surface melting technique [66, 81, 82]. Such technique led to the formation of extremely fine particles of one phase in the other. The MLPS under such technique was believed to be due to dynamic supercooling of the laser-melted pool. Besides the formation of the MLPS micros tructure in a bulk supercooled Cu-Co liquid, the microstructural e volution of the MLPS liquid imme diately after the onset of the MLPS is also of interest. In the following section, the influence of physical conditions during the liquid state of MLPS will be discussed.

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21 2.6 Coarsening, Impingement and Coalescen ce of Liquid Spherulites in the MLPS Cu-Co Liquid When a Cu-Co liquid is bulk supercooled into the miscibility boundary depending on composition, it will separate into liquid sphe rulites dispersed in a liquid matrix with compositional difference corresponding to the miscibility boundary. Prior to solidification, these spherulite s can grow in order to reduce the free energy of the system in terms of the surface energy and compositional difference. If the liquid spherulites have no relative velocity respect to the liquid matr ix, the spherulites are expected to grow and coarsen by a pure diffusion process. This diffusive process lead s to the growth of larger spherulites at the expense of the smaller one s, which is known as Ostwald ripening. The relationship between average pa rticle radius and time duri ng the Ostwald ripening can be described using the Lipschitz-Slyozov-W agner (LSW) theory [83, 84], where t k r r 3 0 3 (2-12) ) ( ) (0 2 M D M D LLX X RT V DX V k (2-13) ro is original mean spherulite radius at the onse t of coarsening, r is mean spherulite radius at time “t”, VM, VD are the molar volume of the liquid matrix and spherulite, X0 is the concentration of the original liquid, XM and XD are the concentrations of the liquid matrix and spherulite, LL is the surface energy between the two liquids, R is the gas constant, D is the diffusion coefficient of the minor elemen t, T is the absolute temperature, and t is time. The purely diffusional growth coarsening th eory of LSW predicts the increase in the spherulite size with cubic root of time. On the other hand, if the relative velocity between the spherulite and the matrix is not zero, the deviation from the LSW theory; a

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22 pure diffusional growth coarsening theory is expected. There are ma ny factors that can induce the motion of the spherulites and among of those, Marangoni e ffect, Stokes effect, and physical stirring are of interest. First, Ma rangoni effect is the motion of liquid due to the surface tension induced by either the temperature gradient or compositional difference within the liquid. Another effect called Stokes e ffect is the motion of liquid spherulites due to the mass density differen ce between spherulites and matrix. The last effect of interest is the fl uid convection caused by physical stirring. In this case, the coarsening behavior is expected to deviate significantly from that predicted by the LSW theory. Moreover, it was suggested that the coarsening of liquid sphe rulites in the liquid matrix is faster than that of solid particles in the liquid matrix because the fluid inside the spherulites does not only occur by diffusion but also by convection, which is not the case for solid particles [85]. Severa l studies were done to inves tigate the Ostwald ripening in immiscible liquid systems [86–90]. Particular ly, Ratke [85] proposed a general equation for the coarsening of liquid/liquid systems fo r various coarsening conditions, where n nr Kt r r/ 1 0 01 (2-14) n is the coarsening exponent and K is the coarsening coefficient. When the relative velocity between the liquid spherulites a nd the liquid matrix is zero, the coarsening exponent is equal to 3 and the equation follows the LSW theory. If the spherulites travel with a constant velocity of U0 respect to the matrix, the co arsening exponent is predicted to be 5/2. If the coarsening takes pla ce under the Marangoni eff ect, the spherulites velocity is equal to r m/s, where r is the radius of liquid spheru lites and it can be demonstrated that the coarsening exponent is equal to 2. Similarly, under the Stokes

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23 effect, the spherulites velocity is approximately r2 m/s and the coarsening exponent is predicted to be 3/2. This situation can ta ke place in the MLPS Cu-Co liquid due to the difference in the composition of liquid spherul ites and matrix. In the EML technique, the physical stirring of the levitated liquid can be significant because of the electromagnetic field. As calculated by El-Kaddah [53, 54], flui d velocity in a levitated liquid can be as fast as 0.3 m/s at the surface and approximate ly 0.15 m/s at the center of the levitated specimen. Particularly for the MLPS Cu-Co liquid during the levitation state, severe swirling and impingement of the liquid spheru lites (Figure 2-19) can take place during the EML experiment as that of the Cu-Fe syst em [8]. Therefore, in the presence of both Marangoni and Stokes effects, it is likely that the coarsening coefficient should be less than 3/2. Moreover, it is e xpected that the coarsening e xponent of the MLPS spherulites in the presence of physical st irring such as the electroma gnetic stirring during the EML experiment should be significantly below th e coarsening exponents predicted by Ratke. The coarsening of liquid spherulites in the MLPS Cu-Co liquid due to all above effects prior to solidification can result in an undesirable destruction of the MLPS microstructure. Therefore, the coarsening beha vior especially the coarsening exponent in this particular case is of intere st and it is discussed later. Besides the MLPS phenomenon, solidifica tions of the Cu-Co liquid with and without the MLPS are also of in terest. In the following sectio ns, the fundamental of alloy solidification and the solidification of the MLPS Cu-Co liquid will be discussed. 2.7 Solidification of Alloys 2.7.1 Length Scale in Solidification Solidification is one type of phase transformations in which a liquid phase transforms into a solid phase and it requires a driving force. Consider at the S/L interface,

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24 solidification involves the move ment of atoms from liquid region toward the solid region and it can be mentioned that solidification is an atomic-s cale or nano-scale phenomenon. The demarcation between liquid and solid atom s can be termed as an atomic-scale or nanoscale solid/liquid (S/L) interf ace (Figure 2-10). On the other hand, at a larger length scale at the order of 10-4 m, the S/L interface can be term ed as a meso-scale S/L interface and it is composed of infinitesimal portions of the atomic or nano-scale S/L interface (Figure 2-10). For the later case, three regions covering the transition from liquid to solid can be identified as liquid, mushy (contai ning both liquid and solid) and solid [6]. At the atomic or nano-scale level, a transition from liquid to solid region continuously takes place over a distance and a continuous change in the free energy from the solid to liquid phase can be shown in Fi gure 2-11 [91]. The atomic scale S/L interface with a few atomic layers thick is mentione d to be an atomically-sharp interface and mentioned to be diffuse interface if the interface layer is relatively large compared to that of atomically-sharp one. It has been known th at transport phenomena at the atomic-scale S/L interface during solidification dictates solute distribution in solidifying alloys. For the case that limited diffusion in liquid and solid is assumed, solute atoms are rejected into the liquid ahead of the S/L interface acco rding to its corresponding equilibrium partitioning coefficient (ke). Solute rejection into the liquid region results in a solute boundary layer (o,i) [6]. The magnitude of the boundary layer can be calculated using the following equation. i i o i oV D, , (2-15) where Do,i is the interfacial diffusion coefficient of a liquid and Vi is the solidification velocity. For local-equilibrium solidification in which the interfacial composition can be

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25 approximated using an equilibrium phase diagram, the solidification velocity has to be small enough to allow for the compositio nal arrangement at the S/L interface corresponding to a ke value. In the other words, it can be mentioned that chemical diffusion is much higher in magnitude than that of thermal diffusion in the case of equilibrium solidification. For an equilibrium solidification, the Do,i and o,i are typically 2.5x10-9 m2/s and 0.5x10-9 m [6] and the solidification velocity is necessary to equal or less than the i o i oD, ,ratio or approximately 5 m/s in order to maintain an equilibrium at the S/L interface. On the other hand, an equilibrium condition at the S/L interfacial diffusion can no longer be assumed if the solidif ication velocity or the interdiffusion coefficient deviates significantly from the equilibrium condition. In this case, an interfacial Peclet number (Pi) (including a boundary layer thickness, the so lidification velocity, and the interfacial diffusion coefficient at the S/ L interface) is used to de scribe thermal and solutal conditions at the S/L interface and it can be represented by the following equation i i o i i i o iD V P , . (2-16) where Vi and Di are the velocity and diffusivity of a S/L interface for non-equilibrium condition. It can be seen that an increase in the solidification velocity or a decrease in the diffusion coefficient will result in a small value of solute boundary layer; i and hence a large Peclet number. Besides the solidificat ion velocity, diffusion coefficient can be affected by convection or flui d flow. Increase in convect ion in the liquid can also decrease the boundary layer thickness [92], whic h in turn results in an increase in the Peclet number. As will be discussed in th e following section, changes in the Peclet

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26 number, which is accounted for the interfacial diffusion coefficient and particularly the solidification velocity can alte r the partitioning coefficient at the S/L interface of alloys during solidification. 2.7.2 Effect of Solidification Velocity on the Partitioning Coefficient Solid/liquid interface velocity affects the partitioning coefficient of alloys [91, 93, 94]. According to the AzizÂ’s model, the velocity-dependent partitioning coefficient (k(Vi)) can be described by the following equation. i i i o i i i o e iD V D V k V k, ,1 ) ( (2-17) Another model proposed by Sobolev [94] can be described by the following equation. D i D i Di i D i Di i D i e iV V for and V V for V V V V V V V V k V k 1 1 1 ) (2 2 2 2 (2-18) where VD and VDi are the bulk and interfacial diffu sion speed. Another recent model accounting for the Peclet number proposed by Abbaschian and Kurz [91] can be described by Equation 2-19. i e i i iP k V k V k V k ) ( ln )) ( 1 ( 2 ) ( 1 (2-19) All models provide a common trend in which the coefficient approaches unity as the solidification velocity increases. In terms of the Peclet number, the partition coefficient also approaches unity as the Peclet number increases (Figure 2-12). As the partitioning coefficient approaches unity, the interface composition on the solid (CS*) and liquid

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27 (CL*) sides becomes equal and the partitionless solidification take place. In the following section, a brief discussion on the partitionless solidification will be provided. 2.7.3 Partitionless Solidification and T0 Curve For an equilibrium phase diagram, solidus (TS) and liquidus (TL) curves are constructed from a series of CS* and CL*compositions as a functi on of temperature in which the chemical potential () (the intercepts on both sides of the free energycomposition (G-X) curves) are equal (Figur e 2-13). Similarly, a series of Cm compositions in which the liquid and solid phases have the same free energy (the intersection between the two fr ee energy curves) can be constructed and the curve in this case is known as T0 curve. The T0 curve is located between the liquidus and solidus curves and it is normally not included in the phase diagram. However, the T0 curve has a technological importance for rapid solidifica tion processes [95]. Fo r the liquid of the composition between TS and T0 curves, there is a chance th at the liquid can transform into solid of the same composition correspond ing to the k value of 1. The theoretical study by Boettinger [96] showed that TS and TL curves converge to a single line below T0 curve at high solidification velocities indica ting that rapid solidi fication processes can enhance the homogeneity of solidified alloys by reducing chemical segregation. Solidification velocity is an important parameter in solidification processes dictating the final microstructural and pr operties of alloys [36]. A term rapid solidification is generally refe rred to rapid heat extraction fr om a liquid or particularly from a S/L interface. Rapid solidification of liquid alloys was first explored by Duwez [97]. Not only rapid solidification can enhance so lubility of alloys, it can also result in formation of metastable or amorphous phases [98]. Various types of rapid solidification

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28 apparatus [99, 100] have been invented and most common rapid solidification techniques are melt spinning [98], atomiza tion [43], spray forming [98] , laser surface melting, and laser forming techniques [101] . The fundamental of these techniques is basically to rapidly extract the heat of solidification from the liquid through solid. Rapid heat extraction in these techniques can be e nhanced by improving the contact condition between the mold or substrate and the liquid. On the other hand, disi ntegrating liquid into small portions can also improve the heat extr action rate from the liquid. However, rapid heat extraction from the S/L interface is the ultimate key to enhance the S/L interfacial velocity during solidification. Rapid solidification can enhan ce the solubility in several alloys that do not exhibit significant separation between liq uidus and solidus curves (the alloy system with a small k). However, as the difference between TL and T0 curves increases, it is more difficult to maintain the S/L interface temperature below the T0 temperature in which partitionless solidification can take place [102]. In addition, most rapid solidification techniques rely on rapid external heat extracti on and the thickness of the mate rial being processed [103]. As a result, the production of a large-dime nsion specimen with high solidification rate throughout is limited. Another important phenomenon involved in rapid solidification processes is known as dynamic supercooling. Dynamic supercoolin g takes place within a thin liquid region adjacent to the mold/liquid interface when the liq uid solidifies against a cold substrate. It is believed that a large difference in temp erature between the liquid and the substrate results in the suppression in the temperatur e of the S/L interface below the equilibrium liquidus temperature before so lidification leading to a metastable or partitionless

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29 solidification. Dynamic superc ooling is predominant in liqui d metal processes such as melt spinning, spray forming, and splat coo ling techniques. The phenomenon can also be observed in self-substrating techniques such as electron beam or laser surface melting in which the liquid region at the end of the meltpool can undergo metast able solidification. As mentioned earlier, solid solution of Cu-C o alloys with large cobalt content is desirable for several applications. Therefore, rapid solidification of Cu-Co alloys is the first choice to achieve such goal. There have been attempts to enhance the solubility of cobalt in copper through rapid solidification processes particularly melt spinning (Table 2-3) [25, 29, 31, 60, 64, 66, 97, 104–117]. However, it can be seen from the Cu-Co phase diagram that the difference between the liqui dus and solidus temper ature is significant and this is also true for the liquidus and the T0 temperature. Particularly, the T0 curve is significantly below TL for the Cu-Co alloys of 10 to 50 at% Co (Figure 2-8) and the enhanced solubility may not be attained. Th erefore, bulk supercooling followed by rapid solidification is requ ired in order to allow for the significant suppression of the S/L interface temperature below the T0 temperature before solidification. 2.7.4 Mesoscale Solidification of Alloys The mesoscale S/L interface during the solid ification of an alloy can be divided into 3 regions of solid, solid +liquid (mushy), and liquid. It has been known that the thermal and compositional profiles around the mesoscale S/L interface dictate the morphology of the interface [118]. The thermal pr ofile at the interface is dictated by the imposed temperature fields both sides of the interface. On the other hand, the compositional profile is dictated by solute dist ribution in the liquid ah ead of the interface. The liquidus temperature of the liquid ahead of the interface is varied depending on composition of liquid ahead of the interface. Fo r a large positive temperature gradient in

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30 the liquid, the thermal profiles can be demons trated using the diagram “a” in Figure 2-14. In this case, the temperature of the liqui d is larger than the equilibrium liquidus temperature profile correspondi ng to the solute concentr ation and the plane-front interface is stable. As the temperature grad ient in the liquid ahead of the interface decreases, there is a region that the temperatur e of the liquid is lower than the equilibrium liquidus temperature profile and therefore th e plane-front interface is no longer stable. Consequently, a cellular and dendritic morphol ogy is formed as the temperature gradient decreases as demonstrated using the diag ram“b and c” in Figure 2-14. As the temperature gradient in the liquid becomes sm all, equiaxed dendrites can form ahead of the interface as shown using the diagram “d”. For all cases above, the driving force and the morphological development during the soli dification is attributed to interfacial supercoolings such as kinetics, curvature, and particularly constitutional supercoolings [36]. On the other hand, if the liquid is signi ficantly supercooled due to thermal or bulk supercooling prior to solidification, the overa ll temperature of the liquid is significantly below its equilibrium liquidus temperature. When the nucleation of a solid takes place, the S/L interface is formed and the temperatur e gradient ahead of the interface is negative as shown using the diagram “a” in Figure 2-15. In this case, dendrites or equiaxed dendrites can form at the surface of within the bulk supercooled liquid. Another important aspect about the solidification of bulk supercooled alloys is that equixaed dendrites can form within the bulk supercooled liquid. Th e nucleation sites for the equiaxed dendrites in this case are not at the surface of the mold but potential nucleis within the liquid. As a result, isolated equiax ed dendrites can be observed at the onset of the solidification of a bulk supercooled liquid and their thermal profiles across the

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31 interface can be shown using the diagram “b” in Figure 2-15. For the Cu-Co alloys with out the MLPS, the dendritic microstructure is generally observed due to a non-facet nature of the system. However, in the alloys experienced a bulk supercooling below the MLPS temperature, the liquid spherulites inst ead of equiaxed dendrites are nucleated within a bulk supercooled liquid. In the follo wing section, the solidification of the MLPS Cu-Co liquid will be briefly discussed. 2.7.5 Solidification Sequence of a MLPS Cu-Co Liquid The solidification path of a MLPS Cu-Co li quid is considerably different and more complicated than that of a single phase supe rcooled liquid. This is because after the MLPS takes place, the initial liquid separates into two new liquids (Co-rich liquid (L1) and Cu-rich liquid (L2)) and each liquid phase does not only experience its own supercooling, which can be considerably diffe rent than the bulk supercooling, but may also follow a solidification path considerably different than the bulk. For example, when 80 wt% Cu-20 wt.% Co alloy is supercooled to 1425K (~200 degrees bulk supercooling), the L1 liquid will have a composition around 15 % Cu and 85% Co, whereas the L2 liquid will have a composition around 95% Cu and 5% Co. At this temperature, the L1 will experience 300 degrees superc ooling as compared to around 160 for L2. With such a large supercooling, L1 will most likely nuc leate and solidify first. Since the L1 composition is below the T0 curve for the cobalt-rich side of the diagram, it will have partitionless solidification at least at the be ginning. The L2 liquid, on the other hand, has smaller supercooling and gets nucleated by the L1 spherulites. Evidence for such nucleation hierarchy and the soli dification path for the Cu-Co alloys have been given in more detail in the references [60, 119]. An important aspect of the solidification of the MLPS liquid is the thermal conditions during recalescence of L1 and L2. If L1 is the

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32 minor phase, its heat of solidification can get absorbed by the larger L2 matrix. As a result, L1 spherulites will form a spherical solid shell before the temperature rises above the metastable immiscibility boundary, and th e L2 phase nucleates heterogeneously on the solid shells (Figure 2-16). On the other hand, if L1 is the major phase, it is first to solidify and L2 can heterogeneously nucle ates from the L1 surface (Figure 2-16). However, the temperature can increase a bove the metastable i mmiscibility region, causing the remaining liquids to remix [ 119]. When remixing happens, the distinct boundary between of solute rich spherulite s and solute poor matrix will disappear. Depending on the subsequent cooling rate, some compositionally solute rich regions may appear in the final microstructure. In the following chapters, some fundamen tal understanding of the heat transport phenomenon during mesoscale solidificati on will be discussed to explain the solidification behavior of Cu-Co alloys particularly with bulk supercooling. 2.8 Heat Transport Phenomenon at the Mesoscale Solidification of Alloys Thermal history during solidification processes may be used to predict the microstructural evolution in alloys. Several important parameters such as the S/L interface temperature, the S/ L interface position, the S/L interface velocity and the cooling rate are of interest in solidification problem because these parameters can be correlated to the final microstructure and pr operties of the casting [36]. These parameters are basically derived from temporal evoluti on of temperature within a solidifying alloy and therefore the understanding of heat tran sport phenomenon during solidification is necessary. At a mesoscale (the order of 10-4 m), a solidifying alloy ca n be divided into three regions; solid, solid+liquid and liquid. For a pur e metal, the transition from solid to liquid

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33 takes place at its melting point (Tm) and the demarcation between the solid and liquid region noted as IS in Figure 2-17 can be considered as a solid/liquid interface. In addition, the transition of an enthalpy; energy in th e form of heat contained in a substance according to its heat capacity (Cp) at temperature T;(H(T) co mpared to that of 298K (H298) T PdT C H T H298 298) ( (2-20) , abruptly occurs as demonstrated in Figur e 2-17. The heat of solidification for a pure metal is therefore the difference between the enthalpy of liquid (HL) and solid (HS) at its melting temperature, where ) ( ) (m S m L fT H T H H (2-21) For Cu and Co, the enthalpies of solidifi cation of both elements are 13017.6 and 15558.4 J/mole respectively. For an alloy, the tran sition from liquid to solid takes place over a distance known as a mushy zone and th e enthalpy changes gradually from TL to TS as demonstrated in Figure 2-17. In addition, the demarcation between liquid and solid may be defined as IM. The heat of solidification in this case ( Hf *) is the difference between the enthalpy of liquid at liquidus temperature (HL(TL)) and the enthalpy of solid at solidus temperature (HS(TS)). ) ( ) (* S S L L fT H T H H (2-22) For normal solidification of an alloy, the temperature pr ofile continuously decreases from liquid to solid region and the te mperatures at the begi nning and the end of the mushy zone are TL and TS respectively. In this case, heat of solidification is removed from the S/L interface through a mushy zone , a solid region and finally across the

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34 mold/metal interface into a mold as demonstr ated in Figure 2-18. For a bulk supercooled liquid, where its temperature is significan tly below an equilibrium melting or liquidus temperature, the heat of solidification can dissipate into both a supercooled liquid and into the mold through the solid region as s hown in Figure 2-18. The competition between the heat flow into both directions determines the temperature of th e S/L interface. If the magnitude of heat flow into the mold direc tion is lower than that of the supercooled liquid direction, the heat of solidification can increase the temperature of liquid, which is known as thermal recalescence. When the re calescence begins, the supercooled liquid absorbs the heat of solidification. After th e recalescence completes, the temperature of the remaining liquid will decrea se under the effect of exte rnal heat extraction and the remaining liquid no longer solidifies under the effect of supercooling. The enthalpy-temperature relationship was used to visualize the solidification of aluminum alloy powders during atomization processes [120, 121] and the examples of the enthalpy-temperature diagrams for a pur e metal and a binary alloy are shown in Figure 2-19. For normal solidif ication as mentioned earlier, the enthalpy paths during solidification follow the path “E” and the temperature profiles within a solidifying metal or alloy can be demonstrated us ing Figure 2-18. In this case, the solidification velocity is determined by the rate of heat flow through a solid part across the mold/metal interface and into the mold accordingly. When the s upercooled liquid can solidify without the aid of external heat extraction, the enthalpy of solidification can be totally absorbed by the supercooled liquid and the temp erature of the supercooled liq uids increases back to its equilibrium liquidus temper ature. Such phenomenon is known as an adiabatic solidification and the solidification paths in this case can be demonstrated as the path ”A”

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35 in Figure 2-19. In order to achieve the adia batic solidification, a minimum supercooling equal to the Hf/Cp,l ratio, where Hf is the enthalpy of solidification for normal solidification (J/mole) and Cp,l is the heat capacity of liquid (J/mole-K) is needed. For the case between the two mentioned previously, the enthalpy path during solidification can be demonstrated as the path “S” in Figure 2-19 and the fraction solid solidified due to thermal recalescence (fS,recalescence) can be estimated using the following equation. T T fR ce recalescen S , (2-23) where TR is the thermal recalescence and T is the maximum supercooling before recalescene. Besides the heat transport phenomenon w ithin a solidifying metal, the heat transport between a metal and a mold is also important. First, the heat transport between the mold and the metal related to external heat extraction can take place by either or all of three heat transfer mechanisms; conduction, convection, and radiation [122]. For the solidification of liquid metal against the mold, heat transfer coefficient (h) is used to measure the effectiveness of heat transfer between the metal and the mold and it is defined according to the following equation. ) (mold metal TT T J h (2-24) where JT is a heat flux across mo ld/material interface (W/m2), Tmetal is the temperature at the mold/metal interface on th e metal side (K), and Tmold is the temperature at the mold/metal interface on the mold side (K) (Fi gure 2-17). The heat tran sfer coefficient can be dependent of several factors such as su rface roughness, types of ma terials in contact, and so on. For a rough surface contact in which a mold and a solidifying material are not

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36 completely in contact, heat transfer acro ss mold/metal interface takes place by conduction through the gaseous medium, conduction thr ough actual contact sp ots and radiation across the gap at the interface [123]. Theref ore, the surface roughness is considered as one of several factors for the heat transfer coefficient. Another important aspect of the heat transfer coefficient is types of material s in contact [124]. In th is work, the reported heat transfer coefficient between Cu and Cu-Co alloys is not available. However, the heat transfer coefficient between Cu and Cu mold can be used to estimate the coefficient for that of Cu-Co/Cu contact. For a molten Cu droplet on a Cu mold, the heat transfer coefficient as a function of surface roughness (Ra); ( m) can be described using the following equation [125]. 13 . 0 410 52 . 6 aR h (2-25) In practice, most heat transf er analysis usually treated th e heat transfer coefficient as a factor. For example, Clyne selected a constant h of 2.2x103 W/m2-K throughout the numerical simulation for the so lidification of Al-4.5 wt% Cu in order to match the numerical result with the expe rimental one [126]. Kunjapur chose h values of 544 W/m2K for the numerical simulation for the solidification of integrated blade-disc castings against a copper chill [1 27]. Levi utilized a c onstant h value of 5x105 W/m2-K for the numerical analysis of atomization of severa l aluminum alloys [121]. Jonsson applied the h values between 1x104 and 1x106 W/m2-K for the numerical si mulation of melt spinning and splat quenching of Al-13 wt% Cu [128 ]. Similarly, Wang applied the h values between 1x105 and 1x108 W/m2-K for the numerical simulatio n of splat quenching of Al5 wt% Cu liquid on a cold substrate [129, 130]. It can be seen that the heat transfer coefficient is an important parameter dictati ng the effectiveness of heat flow out of a

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37 solidifying body and it is theref ore necessary to consider su ch coefficient in the heat transfer analysis of solidification. 2.9 Thermal Condition at th e Mesoscale S/L Interface Consider a small section of the mesoscal e S/L interface during solidification, an interface velocity can be calculated based on heat conservation described by the Stefans condition [131]. f S i L i L i S i S L S iH n T n T V , , , , / (2-26) where S,i and L,i are thermal conductivities on the so lid and liquid at the interface, i Sn T, and i Ln T, are temperature gradients in the nor mal direction (n) on the solid and liquid sides of the interface, S is the density of the solid, and Hf is the heat of solidification for either a pure metal or an alloy. Besides the thermal condition at the S/L interface, temperature gradients on both sides of the mesoscale S/L interface are al so important for the calculation of the solidification velocity. During so lidification, the temperature within a solidifying body is time and position dependent and a governi ng equation for the energy balance [124] within a solidifying body can be described as

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38 R z x y z x y z y x z y x T P T z q y q x q z T y T x T t T Cx z zx z y yz y x xy z zz y yy x xx z y x z y x z y x P (2-27) where is density, CP is heat capacity, T is temperature, t is time, is velocity, q is heat flux, P is pressure, is shear stress, and R* is the rate of energy or heat generation. If only heat conduction is considered and and are assumed to be constant, the energy balance can be reduced into the h eat conduction equation without heat generation, where 2 2 2 2 2 2z T y T x T k t T CP (2-28) or 2 2 2 2 2 2z T y T x T t T (2-29) PC k (2-30) where is the thermal diffusivity. Depending on boundary conditions and the geometry of the system, an analytical solution fo r heat conduction problem can be obtained by solving the above differential equation and th e temperature profile as a function of time. The examples of analytical solutions for heat conduction of simple geometries such as a plate, a cylinder, and a sphere etc. can be found in the reference [ 132]. However, the heat conduction with solidification is more complicat ed because the energy is generated at the

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39 solidification interface, wher e its position is time-dependent. Therefore, numerical methods become important for solving solidifi cation problem and they will be discussed briefly in the following section. 2.10 Numerical Methods for Solidification Problems Several important parameters such as the S/L interface temperature, the S/L interface position, the S/L inte rface velocity, and the cooling rate are of interest in solidification problem because these parame ters can be correlated to the final microstructure and properties of the casti ng. However, these parameters are basically derived from temperature information of a solidifying body. Unfortunately, it is inconvenient to predict temperature inform ation in a solidifying body using analytical solution because the boundary condition such as the temperature at the mold/metal interface for solidification probl em is normally time-dependent. Therefore, the use of numerical methods for the prediction of temp erature distribution dur ing solidification is necessary. There are two common classes of numerical methods, finite element (FEM) and finite difference (FDM) methods. Both numerical methods are based on the process called discretization, where the system of inte rest is divided into a number of small subregions, elements and nodes. On the other hand, the FEM method utilizes integral formulations to create a system of algebr aic equations. The complete solution obtained by this method is generated by connecting or assembling the individua l solutions, allowing for continuity at the inter-elemental boundari es. The formulation of FEM problem can be done in several ways and the formulation of the problem will lead to an equation in the form q T K (2-31)

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40 or [Conductance matrix]{Temperature matrix} = {heat flow matrix} where the final result is in the following form 1 K q T (2-32) For more details, the fundamental of the FEM method can be found in several textbooks particularly in the reference [133]. On the other hand, the FDM method, the di fferential equation is written for each node and the derivatives are re placed by difference equations, which results in a set of simultaneous linear equations [127]. There are se veral algorithms that can be used for the FDM analysis such as Euler methods, Leap -Frog method, Predictor-Corrector methods, Crank-Nicholson method, and Runge-Kutta methods [134, 135]. These methods are basically based on TaylorÂ’s series [134]. Th erefore, the advantag e of the FDM methods over the FEM method is that they do not requ ire the use of polynomial trial functions and a minimization procedure, which saves com putational time to obtain solutions. Among the previously mentioned FDM methods, th e explicit or forward Euler method is favorable in this work because it is most computationally efficien t and easy to program and the detail for the explicit Euler method wi ll be described in details in the next chapter. In addition, the one dimensional FDM method will be emphasized in order to basically understand the temporal and spatia l evolution of the S/L interface parameters during the solidification of bul k supercooled Cu-Co liquid. The final point to be mentioned here is that for conven tional solidification simulation, it is usually assumed that solid ification suddenly takes place at equilibrium melting or continuously occurs from the equi librium liquidus to solidus temperature. However, such situation is not applicable to rapid solidification or solidification of bulk

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41 supercooled liquid, where the equilibrium at S/L interface no longer exists. For example, the temperature of the S/L interface during the partitionless solidification has to be below the T0 temperature. Therefore, a special a ssumption at the interface based for the solidification of bulk supercooled liquid will be used for the numerical simulation and the detail will be describe d in the next chapter.

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42 Table 2-1. Techniques for obtaining bulk supercooling in liquid metals and alloys Technique Typical specim en Process description Atomization Powder Liquid stream is injected through the cooling medium (gas or liquid) Drop tube Droplets Free-fall in an atmospheric controlled tower Emulsification Droplets Specimen is injected into a denucleating agent (non-wetting liquid) Electromagnetic levitation (EML) 7-mm sphere Good for paramagnetic and diamagnetic materials with a good electrical conductivity. Levitation coil is critical. Magnetic force stabilizes as well as heats the specimen. Levitation-heating dependent Electrostatic levitation (ESL) <2-mm sphere Positive charge is generated on the specimen using high-energy UV light. Negative-charge plates stabilize the sample. Levitationheating independent Melt fluxing Droplets Specimen is encapsulated in a denucleating agent ( non-wetting solid)

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43 Table 2-2. Time line showing the study on me tastable liquid phase separation in the CuCo system Year Authors Composition Techniques 1958 Y. Nakagawa 50 and 76 at% Co Alumina-crucible fluxing 1989 S.P. Elder et al 30 and 40 wt% Co EML 1990 A. Munitz et al up to 80 wt% Co Electron beam surface melting, EML, and chill casting 1991 A. Munitz et al up to 50 wt% Co Drop tube 1992 A. Munitz et al 10 wt% Co Electron beam surface melting, EML, and chill casting 1998 D. Li et al 10 to 80 wt% Co Melt fluxing 1998 A .Munitz et al. up to 80 wt% Co Electron beam surface melting, EML 1998 C.D. Cao et al 30 at% Co , and melt fluxing 1998 B. Wei 7.8 at% Co Melt fluxing 1998 I. Yamauchi 20, 30, 50 and 70 at% Co Alumina-crucible fluxing 1999 C.D. Cao et al 7.77 at% Co Melt fluxing 1999 C.D. Cao et al 8.3 at% Co Drop tube 1999 M.B. Robinson et al 32 and 50 at% Co Melt fluxing 1999 M.B. Robinson et al 10 to 100 wt% Co Melt fluxing 2001 M. Kolbe et al 10.7 to 84 at% Co Melt fluxing, EML, and drop tube 2001 Z. Sun et al 15 and 25 at% Co Melt fluxing 2002 C.D. Cao et al 12.8 to 84 at% Co Melt fluxing 2003 X.Y. Lu et al 50 at% Co EML and drop tube 2003 C.D. Cao et al 16 at% Co Melt fluxing, EML, and drop tube 2004 M. Kolbe et al 41.8 to 95 at% Co EML 2004 X.Y. Lu et al 16 and 41.8 at% Co EML and drop tube

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44 Table 2-3. Time line showing rapid solidification works on the Cu-Co system Year Authors CompositionTechniques Specimen Objective 1963 P. Duwez — — — Fundamental 1990 A. Munitz up to 80 at% Co Electron beam, surface melting, and chill casting — Fundamental 1992 A. Munitz 10 wt% Co Electron beam, surface melting, and chill casting — Fundamental 1993 J. Wecker 15 at% Co Melt spinning Ribbon GMR 1995 P. Allia 10 at% Co Melt spinning 45-100 m ribbon GMR 1996 R. Busch 10 to 50 at% Co Melt spinning Ribbon Fundamental, GMR 1996 P. Allia 5 and 15 at% Co Melt spinning Ribbon GMR 1996 R.H. Yu 15 at% Co Melt spinning Ribbon GMR 1996 X. Song 30 at% Co Melt spinning 30 m ribbon GMR 1997 A. Hutten 0.5 to 25 at% Co Melt spinning Ribbon GMR 1997 X. Song 30 at% Co Melt spinning Ribbon GMR 1998 A .Munitz up to 80 wt% Co Electron beam surface melting Ribbon Fundamental, GMR 1998 E. Bonnetti 3,6 and 12 at% Co Melt spinning 50-m ribbon GMR 1998 M.G.M. Miranda 10 at% Co Melt spinning Ribbon GMR 1998 A. Lopez 10 at% Co Melt spinning 15-m ribbon GMR 1999 D. Fiorani 10 at% Co Melt spinning Ribbon GMR 1999 M. Kuzminski 10 at% Co Melt spinning Ribbon GMR 1999 T. Liu 15 at% Co Melt spinning 25-m ribbon GMR 2000 J.B. Corria 5 at% Co Melt spinning 45-m ribbon GMR 2002 M.G.M. Miranda 10 at% Co Melt spinning Ribbon GMR 2003 E. Bosco 3 to 25 at% Co Melt spinning and planar flow casting Ribbon GMR

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45 A B Figure 2-1. Equilibrium phase diagram of a Cu-Co system. A) Temperature range of 200 to 800C. B) Temperature range of 1000 to 1800C. [Reprinted from ASM International Staff, ASM handbook: Vol.3 Alloy Phase Diagram , ASM International, Materials Park, OH, USA, 1992]

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46 Figure 2-2. Temperature-de pendent equilibrium partitioning coefficient of the Cu-Co system in the range of 1113 to 1495C

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47 Figure 2-3. Wettability of a solid phase on a nucleation site. A) Poor wettability. B) Good wettability

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48 TLor TmFree energy (G)Temperature (T) GLGS GA T* ) (1T GS L T1At composition = X) (*T T GA L TLor TmFree energy (G)Temperature (T) GLGS GA T* ) (1T GS L T1At composition = X) (*T T GA L Figure 2-4. Plot between free energy and temperature (G-T) at a constant composition showing possible phase transfor mation of supercooled liquid

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49 Figure 2-5. Coaxial levitation coil first used for containerless pro cessing of metals. A) Solid state. B) Molten state. [Reprinted from Figure 10, p. 550 and Figure 11, p.551 in E.C. Okress, D.M. Wroughton, G. Comenxtz, P.H. Brace, and J.C.R. Kelly, J. Appl. Phys. 23(5) (1952) 545]

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50 Figure 2-6. Levitation of a specimen in the EML system

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51 Heat of Mixing (J/mole) XCu 1675 K 1300 K 1400 K 1500 K Heat of Mixing (J/mole) XCu 1675 K 1300 K 1400 K 1500 K A 1675 K 1500 K 1400 K 1300 K Gibbs free energy of mixing (J/mole) XCu 1675 K 1500 K 1400 K 1300 K Gibbs free energy of mixing (J/mole) XCu B Figure 2-7. Thermodynamic f unctions indicating tendency of liquid phase separation in Cu-Co alloys. A) Heat of mixing. B) Gibbs free energy of Cu-Co liquid between 1300 and 1675K

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52 Figure 2-8. Cu-Co phase diagram with the miscibility bound ary and extended T0, TS, and TL curves

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53 Figure 2-9. Effects of electromagnetic filed on the MLPS microstructure in Cu-Fe alloys. A) Severe swirling. B) Im pingement of liquid spherulites. [Reprinted from Figure 2.9, p. 40 and Figure 4.32, p. 143 in S.P. Elder, Metastable Liquid Immiscibility in Iron-Copper Alloys , Ph.D. Dissertation, University of Florida, Gainesville, 1990]

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54 Figure 2-10. Solid-liquid interf ace. A) Mesoscale. B) Nanoscale

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55 Figure 2-11. Free energy profile across a S/L interface. [Reprinted from Figure 4, p. 323 in R. Abbaschian and W. Kurz in Solidification Processes and Microstructures: A Symposium in Honor of Wilfried Kurz , M. Rappaz, C. Beckermann, and R. Trivedi eds., TMS, 2004, p. 319]

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56 Figure 2-12. Velocity-dependent partitioning coefficient. [Reprinted from Figure 6, p. 324 in R. Abbaschian and W. Kurz in Solidificati on Processes and Microstructures: A Symposium in Honor of Wilfried Kurz , M. Rappaz, C. Beckermann, and R. Trivedi eds., TMS, 2004, p. 319]

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57 CS *(T1)CL *(T1) GLGST = T1 Cm(T1)Gibbs free energy (G)AB CS *(T2)CL *(T2) GLGST = T2 < T1Cm(T2)Gibbs free energy (G)Composition (X) AB T1T2 CS *(T1) CS *(T2) CL *(T1) = Cm(T2) CL *(T2) TLTST0 Temperature (T)Composition (X) T=T1-T2 CS *(T1)CL *(T1) GLGST = T1 Cm(T1)Gibbs free energy (G)AB CS *(T2)CL *(T2) GLGST = T2 < T1Cm(T2)Gibbs free energy (G)Composition (X) AB T1T2 CS *(T1) CS *(T2) CL *(T1) = Cm(T2) CL *(T2) TLTST0 Temperature (T)Composition (X) T=T1-T2 Figure 2-13. Mechanism of solute trapping

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58 Figure 2-14. Morphology of the mesoscale S/L interface with a positive temperature gradient in the liquid. A) Plane-front. B) Cellular. C) Dendritic. D) Dendritic and equiaxed solidification from the mold surface

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59 Figure 2-15. Morphology of the mesoscale S/ L interface with a negative temperature gradient in the liquid (a bulk supercool ed liquid). A) Dendr itic and equiaxed solidification from the mold surface. B) Heterogeneous nucleation and growth of an equiaxed dendr ite within a liquid

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60 Figure 2-16. Solidification microstructures of the MLPS Cu-Co alloys. A) Co-rich (L1) is a major phase. B) Cu-rich (L2) is a major phase. [Reprinted from Figure 1a and 1d, p. 4051 in A. Munitz and R. A bbaschian, Metall. Trans. A27 (1996) 4049]

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61 Figure 2-17. Enthalpy-temperature profile s. A) Pure metal. B) Binary alloy

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62 Figure 2-18. Temperature profiles for solidif ication of an alloy in a mold. A) Normal solidification. B) Solidificat ion of a supercooled liquid

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63 A B Figure 2-19. Enthalpy-temperature diagrams for solidification under various conditions. A) Pure metal. B) Binary alloys

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64 CHAPTER 3 TECHNICAL APPROACHES As discussed earlier, the electromagnetic levitation (EML) technique is favorable for the investigation of the effect of bul k supercooling on Cu-Co alloys because the technique can physically isolat e the specimen from a contai ner using the electromagnetic field and hence heterogeneous nucleation of a solid phase due to the presence of a container can be prevented. As a result, a levitated specimen can be bulk supercooled below its equilibrium melting or liquidus te mperature. Besides bulk supercooling, rapid solidification of Cu-Co alloys from the liquid st ate is also of interest. In this chapter, specimen preparation, experimental pr ocedures including the overview on the electromagnetic levitation apparatus with a rapid solidification device and specimen characterization will be discussed. 3.1 Specimen Preparation The compositions of Cu-Co alloys in th is work were selected based on the metastable phase diagram of Cu-Co in Fi gure 2-8. The diagram was divided into 3 regimes based on the relative position be tween the MLPS boundary and the extended T0 curve. At less than 10.5 at% Co and more than 52 at% Co, the MLPS curve is below the T0 curve indicating that a bulk supercooled Cu-Co liquids of these compositions are likely to encounter partitionle ss solidification prior to the MLPS. On the other hand, CuCo alloys of the compositions between the two regimes are mostly susceptible to the MLPS. The plot indicating minimum supe rcoolings required for partitionless solidification and MLPS of various compositions is shown in Figure 3-1. The plot also

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65 indicates two cross-overs, wh ere partitionless solidificati on and MLPS require the same amount of supercooling. However, it should be noted that the minimum supercooling of less than 70 degrees for MLPS can be achieved in the alloys of approximately between 30 to 40 at% Co. In addition, the alloys of 30 to 40 at% Co are good candidates for applications as mentioned in the first chapte r. Therefore, the Cu-Co alloys of 30 to 40 at% Co were primarily investigated. A suitable geometry of the specimen for th e levitation was a 7mm diameter sphere with the weight between 1 to 1.5 grams. Se veral Cu-Co alloy specimens were prepared from high purity Cu (99.999%) wire of 1 mm-diameter and Co (99.99%) chunk by Alfa AESAR™ using a Centorr™ arc-melting furn ace (Figure 3-2). The raw materials were weighed using a Sartorius™ electron ic balance with a precision of 0.005 grams. The raw materials and titanium getter were placed in a bell-jar and flushed 4 to 5 times with high-purity argon to minimize oxidation during the arc-melting process and enhance the supercoolability. Prior to each arc-melting process, titanium getter was first melted to getter the residual oxygen. 3.2 Experimental Procedures To produce specimens with various coo ling conditions, the levitated specimens were solidified under 3 conditions; in the levitation state, in a conical copper mold, and splat cooled using the splat c ooling device. Such cooling cond itions resulted in specimens with different shapes; pear shape (P), cone-shape (C), and spat-cooled (S) specimens respectively. The P specimens were slowly solidified using the mixture of helium+4% hydrogen and argon gases under heat convecti on. The C specimens were dropped from

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66 the levitation state and rapi dly solidified agai nst a vacuum copper mold under heat conduction mode. The S specimens were sp lat cooled against copper platens. In order to achieve bulk supercooling followed by vari ous cooling conditions, an electromagnetic levitation sy stem equipped with a rapid solidification device named Electromagnetic Splat/Quenching Apparatus (ESQA) were customarily built for this study. The ESQA apparatus extended the capability of the existing Electromagnetic Levitation (EML) system at the Material s Science and Engineering Department, University of Florida. The ESQA appara tus was connected to power supply units, processing gas supplier, and a data acquisition system (Fi gure 3-3). The ESQA apparatus (Figure 3-4) was composed of a levitation co il, a processing gas inlet, a protective gas inlet, a splat chamber, a splat-cooling mech anism, a two-color pyrometer, and a specimen positioning mechanism. The levitation coil was fabricated from a dehydrated-soft copper refrigeration tube of 1/8-inch O.D. x 0. 030-inch wall thickness sl eeved with insulating fiberglass. The coil was shaped into a conf iguration of 2-ups and 4-downs around a 15mm glass tube (Figure 2-6) and the gap betw een each round and the gl ass tube was kept at minimum. The levitation coil was connected to a step-down transformer powered by a 10-kW high frequency (400 kHz) generator us ing brass couplings. A glass tube of 15-mm in diameter was inserted inside the coil, through whic h argon with 4%hydrogen and helium gases were delivered through the inle t B; the first gas wa s used to provide a reducing atmosphere, whereas the later pr ovided cooling when needed. Below the levitation coil, the splat chamber filled with argon gas delivered through the inlet C. The splat-cooling device, which was used to produce a thin foil specimen was located immediately below the levitation coil and encl osed in the splat chamber. In addition, a

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67 thin plastic membrane was inserted between the glass tube and the splat chamber to prevent the downward flow of the helium gas from the glass tube and to prevent oxygen contamination from the splat chamber. The splat cooling device was composed of two copper substrates; one of which was connect ed by a rod to another plate which was propelled by an electromagnetically activated coil. The electromagnetically activated coil was powered by a low inductance 6kJ, 180-F capacitor bank by Magneform™, which was used to store the electr ical energy for the activation [136]. The splat mechanism synchronized with the levitation system, was activated after the levitation power was turned off resulting in splat quenching of the liquid droplet be tween the two copper platens. During the levitation process, a tw o-color pyrometer was used to continuously monitor and record the temper ature of the levitated specime n. The voltage output from the pyrometer was recorded using a 10-Hz data acquisition system. The relationship between the voltage signal and the temper ature was determined using a calibration function of the pyrometer and the temperatur e-voltage profile of a pure copper and the following relationship was obtained. 25 0023 . 0 5044 . 1 V T (3-1) where T is temperature in degree Celsius and V is the pyrometer signal in volt. To produce a thin foil specimen, the capacito r tank was charged prior to the levitation power to be turned on and the splat mechan ism operated immediately after the levitation power was turned off. On the other hand, c one-shape specimens were produced using a vacuum mold with a conical cavity (Figure 35). The depth of the mold cavity was 1.6 cm and the diameter at the top of the cavity wa s 1 cm. In addition, a small hole of 1 mm in diameter was drilled through the bottom of the mold in order to allow for the generation

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68 of a vacuum suction during the processing. The vacuum mold was made of copper and designed to fit beneath the coupling between th e glass tube and the splat chamber (Figure 3-5). As a result, cone-shape specimens we re produced from the levitated liquid when the liquid was dropped from the levitation state. 3.3 Specimen Characterization The as-processed specimens were mount ed using a SAMPL-KWICK fast cure acrylic by Buehler™ and sectioned using a South Bay Technology™ diamond saw. The mounted specimens were roughly polishe d using 400, 600, 2400, and 4000-grinding papers followed by fine surface finishing on a polishing cloth using the water-based alumina ( -Al2O3) solutions of 5, 1, and 0.3 m, accordingly. The specimens were then etched using a 10% volume of a nitric acid (HNO3) solution for 12 to 15 minutes. The microstructures of the specimens were then examined using a Nikon™ stereo microscope and a Nikon™ Optiphot equipped with a digita l imaging system with a Nikon™ Coolpix 5000 digital camera (Figure 3-6).

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69 TMLPST0T0-TMLPS TMLPST0T0-TMLPS Figure 3-1. Minimum supercool ing required for approaching T0 and TMLPS as a function of composition

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70 Figure 3-2. Arc-melting furnace for specimen preparation

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71 Figure 3-3. Electromagnetic levitation station. A) Power supply units. B) Processing gas supplier. C) ESQA apparatus. D) Data acquisition system

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72 Figure 3-4. Electromagnetic splat quenching apparatus (ESQA). A) Levitation coil. B) Processing gas inlet. C) Protective gas inlet. D) Splat chamber. E) Splatcooling mechanism. F) Two-color pyrometer. G) Specimen positioning mechanism

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73 A B Figure 3-5. Vacuum molds used for produc ing cone specimens. A) Copper mold. B) Installation position

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74 Figure 3-6. Metallographic imaging equipment

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75 CHAPTER 4 EXPERIMENTAL RESULTS AND DISCUSSIONS In this chapter, the thermal and micros tructural information of the levitated specimens under various processing conditi ons will be presented and discussed. 4.1 Results 4.1.1 Thermal Information During the levitation stage, the time-voltage profiles of specimens were recorded and the examples of the profile are shown in Figure 4-1. For example, the time-voltage in Figure 4-1a represents the temperature hist ory of a specimen during several heating and cooling cycles in levitation stage. As the spec imen is heated up, its temperature increases indicating by the increase in the voltage signa l. On the other hand, the decrease in the voltage signal indicates that th e specimen is cooled down. During the heating cycle for the alloys of more than 5 at% Co, the melting point of a pure Cu (Tm, Cu) at 1085 C followed by the peritectic temperature (Tperitectic) at 1112 C was observed as the first and second inflection in the heating curve (Figure 4-1a). Above the first two inflections, an inflection point corresponding to liquidus temperature (TL) was also observed. During the cooling cycle of a levitated specim en solidified without bulk supercooling, the inflection point at the same voltage level as that of the liquidus temperature was observed. In contrast, th e specimens experiencing bulk supercooling during the cooling indicated no inflection point at the TL and the cooling curve continued until thermal recalescence occurred. In this case, the maximum bulk supercooled noted as T in Figure 4-1a was the difference between the voltage signals co rresponding to the TL

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76 and the inflection point immediately before the thermal recalescence. In addition, the specimens with metastable liquid phase sepa ration (MLPS) indicated an inflection point below the TL during the cooling cycle noted as TMLPS in Figure 4-1b and the difference between TL and TMLPS was the magnitude of bulk supe rcooling required for the MLPS ( TMLPS). For both the solidification of a bul k supercooled liquid with and without MLPS, the sharp increase in the voltage si gnal corresponding to th ermal recalescence noted as TR was also observed. The temperature profile during the cooling cycle of the levitated specimen can be represented by one of the diagrams shown in Figure 4-2. For specimens solidified without bulk supercooling ( T = 0), their temperature profil es can be represented by the diagram “a”. For specimens solidified af ter bulk supercooling but no MLPS, their temperature profiles can be represented by th e diagram “b or c”. If the magnitude of thermal recalescence is equal to the maximum supercooling ( TR = T), the temperature profile of the specimen can be represented us ing the diagram “b”. If the magnitude of thermal recalescence is less th an the maximum supercooling ( TR < T), the temperature profile of the specimen can be represented by the diagram “c”. On the other hand, the thermal history of the specimens with the MLPS can be represented by the diagram “d” or “e”. The specimens with their processing conditions and thermal information during the levitation state are summarized in Table 4-1.

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77 4.1.2 Microstructural Observation 4.1.2.1 Specimens solidified during the levitation state Specimens solidified with out bulk supercooling (T = 0). There were four specimens; P4, P6, P8, and P15 solidified wit hout bulk supercooling in the levitation state (Table 4-1) and their cooling rates were comparable in the range of 140 and 200 degree/sec. For a low cobalt -content; 6.26 at% Co (P6 sp ecimen) (Figure 4-3), the microstructure appeared to have small flowe r-like Co-rich dendrites distributed in a Curich matrix. As the cobalt content increas ed; 11.54, 28.07, and 35.76 at% Co (P15, P4, and P8 accordingly), small clusters of Co-rich dendrites began to form and the size and the thickness of the dendrite arm increased as shown in Figure 4-4, 4-5, and 4-6 accordingly. Specimens solidified aft er bulk supercooling with TR = T. There were five specimens (P7, P10, P13, P14, and P16) solidified after bul k supercooling with TR = T (Table 4-1). The compositions of these speci mens were between 30 and 40 at% Co and their average composition was 37.23 at% Co. The microstructures of these specimens were very similar indicating a common micr ostructural feature with well-connected secondary dendrites with long primary arms (Figure 4-7). Such microstructure was in contrast with that of a specimen with sim ilar composition (P8 in th is case) solidifying without bulk supercooling in which on ly short dendrites were observed. Specimens solidified aft er bulk supercooling with TR < T and without MLPS. There were five specimens (P1, P2, P3, P5, and P12) solidified with bulk supercooling with TR < T and no MLPS (Table 4-1). Th e microstructures of these specimens indicated the mixture of small dendr itic clusters and long dendrites (Figure 4-

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78 8). It was also observed that such microstruc tures were the mixture of the microstructures obtained under the so lidification without bulk supercooling ( T = 0) and the solidification with TR = T. It was also observed that the feature of microstructure changed with the magnitude of thermal recalescence respected to the maximum supercooling as demonstrated using three P specimens (P8, P12, and P13) with comparable compositions solidified under the different magnitude of thermal recalescence (Figure 4-9). The P8 speci men solidified without bulk supercooling ( T = 0) and its microstructure was primarily small dendritic clusters. The P12 specimen solidified after bulk supercooling with TR < T indicated the mixtur e of small dendritic clusters and well-connected long dendrites. Finally, the P13 specimen solidified after bulk supercooling with TR = T indicated long dendrites w ith well-connected secondary arms throughout. Specimens solidified after bul k supercooling with MLPS. As discussed earlier, the MLPS microstructure can be obtained if th e Cu-Co liquid is bulk supercooled into the miscibility boundary and the microstructure is composed of liquid spherulites dispersed in the matrix. There were four specimens; P9, P11, P16, and P18 with the average composition of 33.44 at% Co experienced the MLPS (Table 4-1). For the P9 specimen, it experienced the MLPS at 77 degree bulk s upercooling below its equilibrium liquidus temperature and it was further bulk supe rcooled for 165 degrees prior to thermal recalescence. However, the thermal history of the specimen indicated that its temperature remained below the MLPS temperature afte r the recalescence. As a result, the microstructure of the P9 specimen indicated the dispersion of large Co-rich spherulites with the diameters between 100 and 400 m within the Cu-rich matrix (Figure 4-10). At

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79 higher magnifications, the surfaces of these sphe rulites were composed of tiny spherulites of 2 to 5 m in diameter. For the P11 specimen, it experienced the MLPS at 39 degree bulk supercooling below its equilibrium liquidus temperature and further bulk supercooled for 87 degrees prior to thermal r ecalescence. Similar to the P9 specimen, the temperature of P11 specimen remained below the MLPS temperature after the recalescence. However, the microstructure wa s composed of large swirling and irregular Co-rich spherulites in the Cu-rich matrix (Figure 4-11). Another specimen indicating the MLPS in its thermal history was the P16 specimen. It was indicated that the specime n experienced the MLPS at 48 degrees bulk supercooling below its equilibrium liquidus temperature and further bulk supercooled for 26 degrees prior to thermal recalescence. However, the magnitude of thermal recalescence was equal to the maximum superc ooling, which resulted in the increase in the temperature of the specimen back to its equilibrium liquidus temperature. The microstructure of this specimen (Figur e 4-12) indicated no MLPS microstructural compared to that of P9, P11, and P18. I ndeed, the microstructure of this specimen resembled to that of the specimens solidified after bulk supercooling with TR = T as discussed previously. The last specimen that indicated the ML PS according to the thermal history was the P18 specimen. The P18 specimen experienced the MLPS at 74 degr ee bulk supercooling below its equilibrium liquidus temperature. However, the specimen was slightly bulk supercooled for 13 degrees after the MLPS a nd the thermal recalesence resulted in the increase in the temperature of the specimen to above the MLPS temperature. Contrary to that of the P9 and P11 specimens, the microstr ucture in this case was composed of small

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80 Co-rich spherulites of less than 30 m in diameter and small parts of Co-rich dendrites (Figure 4-13). 4.1.2.2 Specimens rapidly solidified in the cone-shape copper mold The specimens in this group were dropped from the temperatures above equilibrium liquidus temperatures (superheate d), below equilibrium liquidus temperatures but prior to the MLPS, and below the MLPS (T able 4-1). After the drop, the specimens were rapidly solidified against the cone-shape copper mold and their final shapes were conformed to the shape of the mold cavity . However, some specimens experienced thermal recalescence before they solidified against the mold and the shapes of these specimens were deviated from the cone shape as will be discussed later in this section. Specimens rapidly solidified from superheated state There were two specimens; C8 and C10 rapidly solidified from the superheat state. Howe ver, the microstructures of these two specimens were similar and only the microstructure of the C10 specimen will be discussed. The microstructure of the C10 specimen (F igure 4-14) was composed of a dendritic and non-dendritic structure depending on the position with respect to the mold/specimen interface. However, the transition from th e dendritic-to-non dendritic structure was obvious as indicated by a “y” shape at a low ma gnification. At the top of the “y” shape, the microstructure was dendritic and the scal e of the dendrite increased toward the center line the specimen. On the other hand, the outer regions of the “y” demarcation adjacent to the mold/specimen interface indicated no dendritic structure. The microstructures in these regions revealed small scale non -dendritic structure and the scale of the microstructure decreased toward the mold /specimen interface.

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81 Another way to look at the microstructure of the C10 specimen was to observe the microstructure along the cente r line of the specimen using a reference frame (Figure 415). It was observed that the transition in the microstructure took place along the center axis and the transition from dendritic-to-non dendritic was observed between the C5 and D5 position of the reference frame (Figure 4-16). The dendrite arm spacing (DAS) at various positions along the center of C10 speci men were measured (Figure 4-17) and the DAS at the C5 position, where the transi tion took place was measured to be 1.6 m. Specimens rapidly solidif ied from bulk supercooled state without MLPS. There were three specimens; C9, C11, and C13 ra pidly solidified from the bulk supercooled state without the MLPS. The co mpositions of these specimens were in between 30 and 40 at% Co. At a low magnification, the microstr uctures of these specimens were similar, where the microstructure was primarily com posed of non-dendritic microstructure of various scales. Along the center line of these specimens, a grainy feature was observed. Away from the center line toward the mold/s pecimen interface, the demarcation between the grainy and a smooth feature was obvious. However, the microstructures of these specimens no longer indicated a dendritic stru cture at the top sec tion as that of the specimens rapidly solidified from the superhea ted state. In order to demonstrate such microstructure, the C13 specimen was used as the representative of the specimens in this group. As mentioned earlier, the demarcati on between the grainy and the smooth feature resulted from the transition from a continuous to grain-like non-dendritic structure as shown in Figure 4-18. Specimens rapidly solidified from bulk supercooled state with MLPS. According to the thermal histories of the ra pidly solidified specimens, there were four

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82 specimens; C7, C12, C15, and C16 that experienced the MLPS prior to rapid solidification. The C7 specimen of 37.09 at% Co experienced the MLPS at 68 degree bulk supercooling below the equilibrium liquidus temperature. The specimen was further bulk supercooled for 125 degrees after the MLPS followed by thermal recalescence. As a result, the temperature of the specimen be fore the drop was at 72 degrees below the equilibrium liquidus temper ature or 3 degrees below the MLPS temperature. The microstructure of the as-processed specimen (Figure 4-19) was the MLPS microstructure composing of large Co-rich spherulites of 100 to 500 m in diameter dispersed in Cu-rich matrix. At a higher magnification, the surfaces of these spherulites were composed of tiny spherulites of less than 10 m in diameter. It was noticed that such microstructure was similar to that of the specimen solidif ied in the levitation state after the MLPS. The thermal history of the C15 and C16 sp ecimens indicated that these specimens experienced the MLPS. The compositions of these specimens were comparable (36.94 and 37.89 at% Co accordingly) in the range of 30 to 40 at% Co and they were both 77 degree bulk supercooled below their equili brium liquidus temperatures and the MLPS were detected at 63 and 68 degree bulk superc ooling. It also should be noted that these specimens were slightly bulk supercooled below the MLPS temperatures. It was also interesting that these specimens did not have the cone-shape as ot her specimens rapidly solidified in the cone-shape mold. In addi tion, the microstructures of both specimens (Figure 4-20 and 4-21) indicate some trace of MLPS structure. The last specimen that indicated the MLPS prior to rapid solidification was the C12 specimen. The C12 specimen of 36.04 at% Co experienced the MLPS at 53 degree bulk

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83 supercooled below its equilibrium liquidus temperature and further 7 degree bulk supercooled prior to rapid solidification. The specimen had a cone-shape and the microstructure indicated a smooth appearan ce, which could not be resolved at low magnifications (Figure 4-22). At a high magnification, the micr ostructure of the specimen revealed the homogeneous distribution of small Co-rich spherulites of less than 1 m in diameter throughout Cu-rich matrix. In additi on, the variation of the diameter of the spherulites along the center line was observe d and the diameters of spherulites were measured at various positions along the center line (Figure 4-23, 4-24, and 4-25). It was observed that the diameter of the spherul ite increased toward the thick section (A5 position) of the specimen. 4.2 Discussions 4.2.1 Specimens Solidified during the Le vitation State without MLPS Considering the Cu-Co alloy of 30 to 40 at% Co, it was observed that the microstructures of the specimens so lidified without bulk supercooling ( T = 0) were primarily small Co-rich dendritic clusters. In this case, it could be explained that solidification started at heterogeneous nucle ation sites on the surf ace of the specimens. The solidification front then propagated into the liquid a nd the specimens were then completely solidified (Figure 4-26). Since th e solidification took place slowly in this case, the effect of electromagnetic stirring wa s significant resulting in broken dendrites in the as-solidified microstructure. In contrast, the specimens solidified after bulk supercooling with TR = T indicated the networks of long dendrites. It could be explained that the equiaxed dendrites were first heterogeneously nucleated within the bulk supercooled liquid under the driving force equivalent to the maximum bulk

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84 supercooling ( T). These equiaxed dendrites then gr ew as long dendri tic networks and the heat of solidification was released into the bulk supercooled liquid during the growth process (Figure 4-27). As these dendritic ne tworks grew, the temp erature of the bulk supercooled liquid increased toward the equili brium liquidus temperature. However, such nucleation and growth of these dendrites took place rapidly and therefore the sharp increase in the temperature of the specimens ( TR) was observed. In this case, the effect of electromagnetic stirring was not significant compared to th e rapid growth of dendritic networks. Therefore, the dendritic networks instead of broken dendrites were observed in the as-solidified microstructure. The microstructures composed of the mixt ure between the dendritic networks and small dendritic clusters were also observed . Such microstructure was obtained when the specimens were solidified in the levita tion state after bulk supercooling with TR < T. It could be explained that the solidification si multaneously took place at the surface as well as within the bulk supercooled liquid. The solidification at the surface of the specimen resulted in the formation of equiaxed de ndrites, while the nucl eation and growth of dendrites within the liquid resulted in the formation of dendritic networks. The heat of solidification for the first case was primarily absorbed by the external heat extraction, while the heat of solidification for the late r case was absorbed by the bulk supercooled liquid. Therefore, the heat of solidification did not result in the complete increase in the temperature of the specimen to the equilibrium liquidus temperature. As a result, the magnitude of thermal recalescence in th is case was less than the maximum bulk supercooling. The mechanism for the microstruc tural formation in this case can be shown using Figure 4-28. It could also be suggested that the fracti on of dendritic networks in the

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85 microstructure was observed to be proportio nal to the magnitude of the recalescence TR, the larger the recalesc ence, the larger the fraction of the dendritic networks was. 4.2.2 Relationship between Cooling rates and Dendrite Arm Spacing (DAS) Among the above mentioned specimens solid ified in the levitation state, the specimens with known cooling rates were used as references for establishing the cooling rate ( *)-dendrite arm spacing ( 2) relationship. Optical micr ographs of the P specimens with know cooling rates were taken at 560X fr om 5 different areas adjacent to the surface with a dendritic microstructure and the DAS were measured and averaged. The relationships among alloy composition (X), cooling rate ( *), and supercooling ( T) were plotted (Figure 4-29). In general, the pl ots indicated that the DAS was inversely proportional to cooling rate and supercooli ng, while it showed the opposite trend for composition. General relationship between the experimentally obtaine d cooling rate and DAS can be represented by the following equation nA ) (* 2 (4-1) where A is a materials dependent and n is between 0.333 and 0.5 [92]. For Cu-Co alloys of 10 to 40 at% Co under various bulk supercooling without the MLPS, A and n were found to be 29.514 and 0.4207 using a curve fi tting method (Figure 4-29a). Even though, the 2* relationship is well quantified, however, the mathematical relationships between the DAS versus supercooling ( 2T) and the DAS versus composition ( 2-X) are unknown. Therefore, linear curve fitting method was ag ain used to predict both relationships (Figure 4-29b and 4-29c).

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86 4.2.3 Specimens Solidified during the Levitation State with MLPS For the specimens with the MLPS microstruc ture, it could be suggested that large spherulites were formed because the temper ature of the specimen was significantly below the MLPS temperature as shown by P9 a nd P11 specimens (Figure 4-10 and 4-11). However, the swirling and impingement of sp herulites in P11 specimen was due to the effect of electromagnetic stirri ng during the levitation state as described in the work on Cu-Fe system by Elder [8]. In contrast, sma ll spherulites as observed in P18 specimen were formed because the liquid was s lightly bulk supercooled below the MLPS temperature. Similar explanation for the effect of th ermal recalescence on the microstructure of the specimens solidified without the MLPS could also be used to explain the recalescence in the MLPS specimens. However, the differe nce between the two cases was that thermal recalescence for the specim ens without the MLPS was due to the formation of the dendritic networks within the liquid, while the thermal recalescence for the later case was due to the solidification of the liquids spheru lites. As discussed earlier, for the MLPS CuCo liquid, the liquid spherulites (Co-rich) were likely to solidify first because they experienced a larger magnitude of bulk supe rcooling compared to that of the liquid matrix (Cu-rich). As these liquid spherulites solidified, the heat of solidification was absorbed by the liquid matrix and resulted in the increase in the temperature of the liquid matrix as thermal recalescence (Figure 4-30). If there were no heterogeneous nucleation and solidification taking place at the surface of the specimen, thermal recalescence could lead to the complete increase in the temper ature of the liquid back to its equilibrium liquidus temperature ( TR = T ). As a result, the MLPS micr ostructure could be altered

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87 and the networks of dendrites could be formed as that of the specimens solidified after thermal recalescence. Such evidence was al ready demonstrated using the P16 specimen. On the other hand, if the heterogeneous nuc leation and solidificat ion at the surface as well as the solidification of the liquid spheru lites took place simulta neously, the heat of solidification released by the spherulites could be less absorbed by the liquid matrix and these could result in the magnitude of ther mal recalescence of less than the maximum bulk supercooling ( TR < T ). For the most extreme case, if the heterogeneous nucleation and solidification at the surf ace of the specimen took place before the solidification of the liquid spherulites, the heat of solidification released from these spherulites could be absorbed by the solidified solid inst ead of the bulk supercooled liquid. Such event therefore could result in TR << T and the destruction of the MLPS microstructure could be minimized. Such ev idence was also demonstrated using the P9, P11, and P18 specimens. It was demonstrated that thermal reca lescence had a significant influence on the final microstructure of the bulk supercooled liquid. Particularly for the MLPS specimens, thermal recalescence after the MLPS shoul d be prevented to preserve the MLPS microstructure after solidification. The MLPS microstructure with fine and homogeneous distribution of the liquid sphe rulites could be obtained if the specimen were rapidly solidified immediately after the MLPS and pr ior to thermal recalescence. In the next section, the microstructures of the Cu-C o alloys of 30 to 40 at% Co under rapid solidification immediately af ter various bulk supercooling particularly at below the MLPS temperature will be presented and discussed.

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88 4.2.4 Specimens Rapidly Solidified in the Cone-Shaped Copper Mold without MLPS Specimens dropped into the cone-shape coppe r mold were solidified faster than those solidified during the levitation state. Particularly, the rapidly solidified specimens indicated an observable microstructural di fference between the region close to the mold/metal interface and the central region of the specimen (Figure 4-14 and 4-18). For the C10 specimen (Figure 4-14) rapidly solid ified from the superheated state, the nondendritic microstructure was observed in the region close to the mold/specimen interface, while the dendritic microstructure started to develop as the distance from the mold/specimen interface increased. This is because the scale of microstructure is inversely proportional to the cooling rate [ 92] and the transition from the dendritic-tonon-dendritic microstructure ca n be observed as the cooling rate increased [45]. For the C13 specimen (Figure 4-18) rapi dly solidified from the bulk supercooled state, only the non-dendritic microstructure was observed. It could be suggested that bulk supercooling enhanced the cooling rate of this specimen as reflected by a predominant non-dendritic microstructure compared to that of the C10 specimen. 4.2.5 Specimens Rapidly Solidified in the Cone-Shaped Copper Mold with MLPS The specimens rapidly solidified into the cone-shape mold after the MLPS indicated similar microstructural feature to that of the specimens solidified during the levitation state. C7 specimen (Figure 4-19) was rapidly solidified from the liquid state after the MLPS and resulted in the MLPS micros tructure with large spherulites. However, the difference between the two t ypes of specimens was that the solidification rate of the specimens in the first group wa s higher than the later. The advantage of rapid solidification imme diately after the MLPS was that fine and homogeneous distribution of spherulites in another could be obtai ned. It could be

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89 suggested that rapid heat ex traction immediately after th e MLPS could minimize thermal recalescence and the growth of liquid spherulites. As di scussed earlier that thermal recalescence could also alte r the MLPS microstructure. Such evidence was also observed in the rapidly solidified specimens; the C15 and C16 specimens (Figure 4-20 and 4-21). First, the shape of these specimens deviated from the cone-shape compared to others. In addition, the microstructures of both specime ns indicated some trace of MLPS structure. Even though, there was no thermal recalescence observed in the temperature profiles of these specimens during the levitation stat e, it could be sugge sted that thermal recalescence took plac e during the drop. Thermal recales cence then resulted in partial solidification of the liquids and the mixture of solid and liquid subsequently solidified against the cone-shape mold. As a result, incomplete cone-shape specimens were obtained. In addition, thermal recalescence in these specimens could result in remelting and remixing of the MLPS structure as that of the specimen solidified in the levitation state after the MLPS and thermal recalescence. Besides, the swirling and disintegration of spherulites in the C15 specimen revealed the effect of thermal recalescence and electromagnetic stirring in this specimen. However, the MLPS microstructure was not observed in the C16 specimen. It could be suggested that the ma gnitude of thermal recalescene in the C16 specimen was larger than that of the C15 specimen, which resulted in more alteration of the MLPS microstructure. Such phenomenon was previously mentioned for the P16 specime n that experienced the MLPS but undergone thermal recalescence afterwards. From these examples, it was also necessary to rapidly solidify the MLPS liquid prior to thermal recal escence to prevent the destruction of the MLPS microstructure.

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90 The desirable MLPS microstructure with fine and homogeneous distribution of spherulites was obtained in the C12 specimen. It was observed that the diameter of the spherulite increased toward the thick secti on (A5 position) of the specimen (Figure 4-24 and 4-25), which was likely to solidify last. The increase in the diameter of the spherulites toward the thick section was due to the coarsening of the liquid spherulites before solidification. However, the major probl em to obtain such relationship was that the solidification times at various positions along th e center line were unknown experimentally. Therefore, as will be discu ssed in next chapters, the numerical simulation for the solidification of bulk supercoole d Cu-Co liquid was used to estimate the solidification times at vari ous positions along the center lin e of this specimen. 4.2.6 Microstructure at region adjacent to the mold/specimen interface Besides the microstructure in the bulk region of the rapidly solidified specimens, the thin regions adjacent to the mold/specimen interface of these specimens were also investigated. According to a general observati on, at a very thin region of C specimens adjacent to the mold/sample interface, different microstructures compared to that of the bulk region were observed. For example, it was observed that the MLPS microstructure of approximately 100 to 150 m thick was formed at a thin surface layer of the C8 specimen followed by the non-dendritic struct ure even though the specimen did not experience bulk supercooling (Figure 4-31). Th eoretically, in order to obtain the MLPS microstructure, the temperature of the liqui d had to be below the MLPS temperature. Therefore, the region experienced dynamic supercooling due to rapid heat extraction within the thin layer adjacent to the cold substrate. The contact condition between the

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91 mold and the specimen should also have a significant impact on the magnitude of dynamic supercooling. Another way to demonstrate the dynamic s upercooling was to rapidly solidify the alloy in which the bulk supercooling require d for the partitionless solidification is comparable to that of the MLPS. Accord ing to the diagram in Figure 2-8, at approximately below 15 at% Co, the crossover between the T0 and the TMLPS curves takes place and therefore partitionless solidification is likely to take place as well as the MLPS. However, large supercooling (more than 100 degree bulk supercooling) is required to obtain both the partitionless solidification a nd the MLPS in the Cu-Co alloys of less than 15 at% Co. This situation was demonstrated using the C1 specimen of 10.61 at% Co, where the specimen was rapidly solidified from 250 degrees a bove its equilibrium liquidus temperature. As a re sult, a thin featureless regi on of approximately 100 to 150 m thick adjacent to the mold /specimen interface was obtaine d. Immediately after the featureless region, the demarcation between such region and the MLPS microstructure was observed (Figure 4-32). It could be sugge sted that the featur eless microstructural obtained with partitionless solidification, where the S/L interface temperature was suppressed below the T0 curve. As the solidification proceeded, the S/L interface temperature increased into the MLPS temper ature regime, which resulted in the MLPS microstructure. Similar observations were previously re ported by Munitz [60, 64-66] that fine spherulites were obtained due to the ML PS mechanism at the end of the melt-pool without any initial bulk supercooling. W ith a good contact condition between the melt and the substrate such as in an e-beam or laser surface melting, large dynamic

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92 supercooling and hence the MLPS microstructure could be obta ined in the Cu-Co alloys of less than 10 at% Co. The specimens rapidly solidified using th e splat cooling device were also good examples to demonstrate the dynamic supercooli ng. For such characte ristic, the thin foil specimen is likely to experience the dynamic supercooling as that of the thin surface region of C specimens. In order to demonstrat e such assumption, a Cu-Co alloy of 36.94 at% Co was splat cooled from above the equilibrium liquidus te mperature. It was observed that the MLPS microstructure wa s obtained throughout the specimen without initial bulk supercool ing (Figure 4-33). It could be suggested that the dynamic supercooling obtained during the splat cooli ng process was large enough to suppress the S/L interface temperature below the MLPS temperature before solidification. 4.3 Conclusion According to the microstructural observati on of the Cu-Co alloys of 30 to 40 at% Co under various bulk supercoolings and cool ing conditions, the following remarks were made. For the alloys under nor mal solidification ( T = 0) in the levitation state, the microstructures were composed of small Co-rich dendritic clusters in Cu-rich matrix. In contrast, the alloys solidified in the levitation state after thermal recalescence with TR = T revealed the dendritic st ructure with long and wellconnected dendritic network. For the allo ys that experienced bulk supercooling and partially recalesced ( TR < T), the microstructures indicated the mixture between that obtained under T = 0 and TR = T conditions. As the magnitude of thermal recalescence increased, the fraction of long and well-connected dendritic networks increased. Dendritic to non-dendritic transition was observed as cooling rate increased. For the alloys bulk supercooled below the MLPS temperatures, the MLPS microstructures with Co-rich spherulites distributed in the Cu-rich matrix were obtained. The diameters of spherulites we re found to increase as the liquids were further bulk supercooled below the ML PS temperatures. In addition, the

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93 electromagnetic stirring duri ng the levitation state result ed in the impingement and swirling of the spherulites. Moreover, the MLPS microstructures were altered if the temperature of the MLPS liquids increased above the MLPS temperature prior to solidification due to thermal recalescence. Rapid solidification immediately after the MLPS led to the formation of small and homogeneous distribution of Co-rich s pherulites throughout Cu-rich matrix. The diameters of these spherulites increased towa rd the thick section of the specimen. It could be suggested that the increase in th e diameters of the spherulites was due to the coarsening of the liquid spherulites in the liquid matrix duri ng the solidification process. At the small region adjacent to the mold/s pecimen interface of th e rapidly solidified specimens, the MLPS or the partitionless mi crostructures could be obtained without an initial bulk supercooling. The phenomenon was known as the dynamic supercooling and it could be obtained using splat-cooling technique in this work.

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94 Table 4-1. Levitated specimens with their thermal information Characteristics of the thermal History* Specimen identification Composition T TR TMLPS P6 6.26 0 0 — P3 9.50 41 7 — P1 10.99 63 16 — P2 11.05 87 24 — P15 11.54 0 0 0 P5 16.00 52 35 — P18 22.93 87 35 74 P4 28.07 0 0 — P8 35.76 0 0 — P11 36.18 126 87 39 P13 36.36 41 41 — P12 36.42 39 19 — P16 36.42 74 74 48 P17 36.42 53 53 — P10 37.09 48 48 — P14 37.82 54 54 — P9 38.22 242 111 77 P7 39.24 41 41 — C11 34.67 63 0 — C6 35.57 48 0 — C13 35.71 58 0 — C8 35.95 (135) 0 — C12 36.94 60 0 53 C15 36.94 77 — 63 C7 37.09 193 121 68 C16 37.89 77 — 68 C10 38.99 (34) 0 — C9 39.13 39 0 — SX 36.94 0 0 —

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95 *The numbers in parentheses are superheated liquid.

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96 A B Figure 4-1. Time-voltage profile of a le vitated specimen with bulk supercooling. A) Without MLPS. B) With MLPS Pyrometer signal (volt) Time (sec) 8 12 16 20 4 TMLPS TL Pyrometer signal (volt) Time (sec) 8 12 16 20 4 TMLPS TL Time (sec) Pyrometer signal (volt) TL Recalescence Tm, Cu Tperitectic Tsupercooled 60 70 80 90 T TR Time (sec) Pyrometer signal (volt) TL Recalescence Tm, Cu Tperitectic Tsupercooled 60 70 80 90 T TR

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97 Figure 4-2. Temperature profile of the levi tated specimen. A) Without bulk supercooling ( T = 0). B) With bulk supercooling and TR = T. C) With bulk supercooling and TR < T. D) and E) With bulk supercooling followed by the MLPS and TR < T with MLPS

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98 Figure 4-3. P6 specimen (6.26 at% Co and T = 0)

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99 Figure 4-4. P15 specimen (11.54 at% Co and T = 0)

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100 Figure 4-5. P4 specimen (28.07 at% Co and T = 0)

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101 Figure 4-6. P8 specimens (35.76 at% Co and T = 0)

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102 Figure 4-7. Optical micrographs at 100X of Cu-Co alloys with TR = T. A) P7 (39.24 at% Co and T = 41). B) P10 (37.09 at% Co and T = 48). C) P13 (36.36 at% Co and T = 41). D) P14 (37.82 at% Co and T = 54). E) P16 (36.42 at% Co and T = 74). F) P17 (36.42 at% Co and T = 53)

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103 Figure 4-8. Optical micrographs at 100X of Cu-Co alloys with TR < T. A) P3 (9.5 at% Co, TR = 7, and T = 41). B) P1 (10.99 at% Co, TR = 16, and T = 63). C) P2 (11.05 at% Co, TR = 24, and T = 87). D) P5 (16 at% Co, TR = 35, and T = 52). E) P12 (36.42 at% Co, TR = 19, and T = 39)

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104 Figure 4-9. Optical micrographs at 100X of Cu-Co alloys with different thermal history. A) TR and T = 0 (P8 with 35.76 at% Co). B) TR < T (P12 with 36.42 at% Co). C) TR = T (P13 with 36.36 at% Co)

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105 Figure 4-10. P9 specimen (38.22 at% Co, T = 242, TR = 111, and TMLPS = 77)

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106 Figure 4-11. P11 specimen (36.18 at% Co, T = 126, TR = 87, and TMLPS = 39)

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107 Figure 4-12. P16 specimen (36.42 at% Co, T = 74, TR = 74, and TMLPS = 48)

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108 Figure 4-13. P18 specimen (22.93 at% Co, T = 87, TR = 35, and TMLPS = 74)

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109 Figure 4-14. C10 specimen (38.99 at% Co w ith 34 degrees superheated before rapid solidification)

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110 Figure 4-15. Appearance of C10 specimen rapidly solidified in a cone-shape mold

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111 Figure 4-16. Detail microstructures al ong the center line of the C10 specimen

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112 Figure 4-17. Dendrite arm spacing (DAS) (fro m B5 to C5) or the average particle diameter (from B-D5 to F5) versus distance along the center of the C10 specimen

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113 Figure 4-18. C13 specimen (35.71 at% Co, T = 58)

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114 Figure 4-19. C7 specimen (37.09 at% Co, T = 193, TR = 121, and TMLPS = 68)

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115 Figure 4-20. C15 specimen (36.94 at% Co, T = 77 and TMLPS = 63)

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116 Figure 4-21. C16 specimen (37.89 at% Co, T = 77 and TMLPS = 68)

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117 Figure 4-22. C12 specimen (36.94 at% Co, T = 60, TR = 0, and TMLPS = 63)

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118 Figure 4-23. Appearance of C12 specimen rapidly solidified in a cone-shape mold

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119 Figure 4-24. Detail microstructures along the center of the C12 specimen

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120 Figure 4-25. Average spherulite diameter versus distance along the center axis of the C12 specimen

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121 Figure 4-26. Microstructural evolution in specimens solidif ied without bulk supercooling in the levitation state

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122 Figure 4-27. Schematic shows the microstruc tural evolution in specimens solidified in the levitation state after bulk supercooling with TR = T

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123 Figure 4-28. Schematic shows the microstruc tural evolution in specimens solidified in the levitation state after bulk supercooling with TR < T

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124 Figure 4-29. Relationships between experi mentally obtained dendrite arm spacing with other parameters for Cu-Co alloys of 10 to 40at%Co. A) Cooling rate. B) Supercooling. C) Composition

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125 Figure 4-30. Schematic shows the formati on of the MLPS microstructure in Cu-Co alloys

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126 Figure 4-31. C8 specimen (35.95 at% Co w ith 135 degrees superheated before rapid solidification) shows the MLPS spheru lites formed by dynamic supercooling at the edge regime

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127 Figure 4-32. C1 specimen (10.61 at% Co w ith 250 degrees superheated before rapid solidification shows a thin featureless layer was observed prior to the thin layer of MLPS microstructure

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128 Figure 4-33 SX specimen (36.94 at% Co and splat cooled at its equilibrium liquidus temperature)

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129 CHAPTER 5 NUMERICAL APPROACHES The purpose of the numerical simulation in this work was to elucidate the effects of processing parameters on the solidification be havior of bulk supercooled Cu-Co alloys of less than 40 at% Co and to e xplain microstructural evoluti on in the alloys under various processing conditions described in the experimental chapters. To simulate the solidification of bulk s upercooled Cu-Co alloys, a one-dimensional finite difference method was used. The system for the simulation was composed of a mold and a sample region with the thickness of “wmold” and “wsample”, respectively (Figure 5-1). The system was equa lly divided into G intervals of x unit length using G+1 grids and the boundary conditions used fo r the simulation are shown in Table 5-1. Using an explicit Euler method, finite diffe rence discretization of the heat conduction equation without heat generation was used for the mold, the solid and the liquid parts of the system, where n i n i n i n i n iT T T x t T T1 1 2 12 ) ( (5-1) n is the time step and i is th e node number, where 0 < i < A is the mold part, i = A is the mold/sample interface and A < i < G +1 is the sample part. The 2) ( x t term is known as a Fourier number (F0) and the stability for numerical si mulation for 1D case is obtained if F0 0.5 [6, 131]. In addition, the numerical st ability applied at the mold/sample interface can be described as the following condition [6].

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130 1 / 01 2 1 s mk x h F (5-2) At the mold/sample (m/s) interface, the following equations are used to solve for temperatures on the mold and the sample sides. x T T k t h x T T x t T Tn A i mold n A i sample s m s m n A i mold n A i mold n A i mold n A i mold , , / / , 1 , 1 ,2 2 (5-3) and x T T k t h x T T x t T Tn A i sample n A i mold s m s m n A i sample n A i sample n A i sample n A i sample , , / / , 1 , 1 ,2 2 (5-4) where t is the time step (second) and x is the size of the grid (meter). The heat transfer coefficients between a Cu mold and Cu-Co alloys used in the simulation were estimated from the equation by Wang [125], where 13 . 0 410 52 . 6 aR h (5-5) For the surface roughness of 9 m (as polished by a 4000-grid paper), the heat transfer coefficient was calculated to be 4.9x104 W/m2-K. In addition, the heat transfer coefficient for the surface roughness of 0.05 m obtained using fine alum inum oxide solution was approximated to be 9.7x104 W/m2-K. It should be noted that the above equation is valid for surface contact between a free-fall liquid and the substrate. However, with the aid of vacuum used in this work, a good contact be tween the liquid and the copper mold were obtained and the further enhancement in the he at transfer coefficient could be obtained up

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131 to 1x105 W/m2-K or more. Therefore, the he at transfer coefficient of 1x105 W/m2-K was primarily used for the contact between the c opper mold and the Cu-Co alloys. In order to demonstrate the effect of the heat transfer coe fficient in the solidification behavior in this study, the coefficients of 1x104 and 1x106 W/m2-K were also used for comparison. To treat bulk supercooling situation, th e concept of the enthalpy-temperature diagram [121] was applied and it was assume d that the thermal recalescence tends to raise the interface temperature to th e equilibrium liquidus temperature (Tequil). Therefore, the following heat conduction condition was used as the boundary condition at the S/L interface instead of the heat conduction e quation with heat generation term as in conventional solidification [6]. n i n equil n i equil n i L ST T T x t T T1 1 2 , /2 ) ( (5-6) Depending on the temperatures around the S/L interface at the nodes “i-1” and “i+1”, the resulting S/L interface temperature (n i L ST, /) at the node location “i” for the time step “n” was solved numerically. In addition, other S/ L interface information such as temperature gradients on both sides of the S/L interface (n i L n i SandG G, ,), velocity (n i L SV, /) at the interface and cooling rate ( ’) were calculated using the following equations. x T T Gn i n i L S n i S 1 , / , (5-7) x T T Gn i L S n i L S n i L , / 1 , / , (5-8) S L n i S S n i L L n i L S effK K G K G K G , , , / , (5-9)

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132 ) , (, / * , , , , / n i L S f xCo Cu S n i L L n i S S n i L ST X H G K G K V (5-10) It should be noted that the enthalpy of solidification at the temperature n i L ST, /is required for the calculation of the S/ L interface velocity. For a Cu -Co alloy with the atomic fraction of cobalt equal to “X” (Cu-xCo) , a general equation for the enthalpy of solidification at the temperature n i L ST, /can be written as ) 1357 , ( ) , ( ) , (, / , / *X H T X H T X HS n i L S L n i L S f (5-11) Using the information in Table 5-2 [7, 35, 122], the enthalpy equations for solid copper (Cu SH), solid cobalt (Co SH), liquid copper (Cu LH) and liquid cobalt (Co LH) with units in J/mole were obtained. ) 298 ( 29 72 . 9875 T HCu S (5-12) ) 298 ( 193 . 40 8940 T HCo S (5-13) ) 1357 ( 40 . 31 40586 6 . 13017 T HCu L (5-14) ) 1768 ( 863 . 54 71 . 68083 4 . 15558 T HCo L (5-15) To calculate the enthalpies of solid and liquid Cu-Co alloy (xCo Cu L xCo Cu SH and H ) as a function of temperature, the rule of mi xing was used for the calculation and the enthalpies of mixing for solid and liquid Cu -Co alloys [32] were included in these equations. ) 31798 29288 ( )) 298 ( 193 . 40 8940 ( )) 298 ( 29 72 . 9875 (Cu Co Cu Co Co Cu xCo Cu SX X X X X T X T H (5-16)

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133 ) 53555 40166 ( )) 1768 ( 863 . 54 71 . 68083 4 . 15558 ( )) 1357 ( 40 . 31 40586 6 . 13017 (Cu Co Cu Co Co Cu xCo Cu LX X X X X T X T H (5-17) For a completion, the enthalpy of the mixtur e between solid and liquid Cu-Co alloy was also calculated using the following equation. ) 1 (f H f H HxCo Cu L xCo Cu S xCo Cu L S (5-18) and the fraction solid (f) was approximated to be proportional to temperature using the following equation 1357 1357 1xCo Cu tT T f (5-19) As a result, the enthalpy of Cu-Co alloys of less than 40 at% Co as a function of temperature and composition was obtained (Figure 5-2). Beside s the enthalpy of solidification, the last two parameters for th e calculation of the S/ L interface velocity are the thermal conductivity (xCo CuK) and the density (xCo Cu ) of the Cu-Co alloy of “x” at% Co. For the simplicity, it was assumed that these parameters for solid and liquid are comparable and the average thermal conductiv ity and density of a Cu-Co alloy of “x” at% Co could be estimated using the following equations. K m W x x KxCo Cu / 21 . 69 ) ( 6 . 165 ) 1 ( (5-20) kg mole x xxCo Cu/ 10 93 . 58 8 . 8 ) ( 10 55 . 63 94 . 8 ) 1 (3 3 (5-21) In addition, the cooling ra te at the S/L interface (' , / i L S) could be calculated using the following equation. n i L S n i L S eff i L SV G, / , / , ' , / (5-22)

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134 S L n i S S n i L L n i L S effK K G K G K G , , , / , (5-23) and the KL and KS were assumed to be equal as men tioned previously. According to all above information, the solidification simu lation was programmed using C++ language on Bloodshed Dev-C++ 4.0 version software® us ing Pentium-based processor. The flow chart of the program is shown in Figure 5-3 and the detail of the program can be found in the Appendix.

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135 Table 5-1. Boundary conditions for the numerical simulation in this work Grid position Description Prescribed condition i = 0 Mold/environment interface env iT T0 i = A Mold/sample interface A i mold SampleT T Q h ) ( i = G+1 End of the sample 01 G ix T

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136 Table 5-2. Selected prop erties of copper and cobalt Thermo-physical Properties Symbol Cu Co Atomic weight (g/mole) Aw 63.55 58.93 FCC density(kg/m3) 8.94 8.80 FCC Tm (K) Tm 1357 1768 HL/fcc (J/mole) Hm 13017.6 15558.4 SL/fcc (J/mole-K) Sm 9.62 8.80 Liquid heat capacity (J/mole-K) CL 31.40 54.86 Solid heat capacity (J/mole-K) CS 29.00 40.19 Entropy at 298 K (J/mole-K) S298 33.14 30.00 Enthalpy at 298 K (J/mole) H298 9875.72 8940.00 Enthalpy at Tm (J/mole) HM 40586.00 68083.71 Thermal conductivity at 1357 K (W/m-K) K 165.6 69.2

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137 Figure 5-1. Schematic shows the setup fo r the finite difference simulation for 1D solidification of bulk s upercooled Cu-Co alloys

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138 A t o m i c f r a c t i o n o f c o b a l tT e m p e r a t u r e ( K )Enthalpy (J/mole) Liquidus Solidus Liquidus Solidus A t o m i c f r a c t io n o f c o b a l tT e m p e r a t u r e ( K )Enthalpy (J/mole) A t o m i c f r a c t i o n o f c o b a l tT e m p e r a t u r e ( K )Enthalpy (J/mole) Liquidus Solidus Liquidus Solidus A t o m i c f r a c t io n o f c o b a l tT e m p e r a t u r e ( K )Enthalpy (J/mole) Figure 5-2. Enthalpy-temperat ure-composition diagram of Cu -Co alloys of 0 to 40 at% Co

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139 Figure 5-3. Flow chart of C++ progr am used for the numerical simulation

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140 CHAPTER 6 NUMERICAL RESULTS AND DISCUSSIONS 6.1 Validation of Numerical Simulation First of all, the relationship between the distance solidified (M; meter) versus time (t; sec) for a pure liquid copper solidified at its melting temperature (1357K) against a copper mold at 298K was simulated in compar ison with the most suitable analytical solution for solidification of pure liquid meta l against a metal mold with the solution given by the following equation [124]. t c k Ms s s 2 (6-1) f s M m m m s s sH c T T erf c k c k e ) (02 (6-2) where k, and c are the thermal conductivity, th e density, and the heat capacity accordingly. S and m are the notation for solid and mold. TM is the melting temperature of a pure metal. T0 is the temperature of the mold. Hf is the enthalpy of solidification of a pure metal. is a constant. First, it should be mentioned that the analytical solution assumes that both mold and metal are semi-i nfinite. Second, the analytical solution assumes that there is no resist ance between mold and metal and therefore the heat transfer coefficient is said to be infinite. The so lidification of a pure metal according to the analytical and numerical simulation are schematically shown in Figure 6-1. By substituting physical properties of mold and metal for the solidification of a pure copper against a copper mold, the final form of the analytical solution was

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141 t M ) 10 1075 . 0 ( ) 80995 . 0 ( 23 (6-3) The analytical results were then plotted in comparison with numerical results of different heat transfer coefficients an d mold thicknesses (Figure 6-2). It was demonstrated that the analytical result yiel ded shorter solidification times compared to that of numerical results. First, the reason for the discrepancy between the two results was because the analytical solution was not acco unted for the mold/sample interface heat transfer resistance. Therefore, for the same distance solidified, the numerical simulation always provided a longer solidification time. By increasing the heat transfer coefficients (from 1x105 to 1x106 W/m2-K in this case) for the numerical simulation, it was demonstrated that a larger h resulted in a shorter solidification time. It was understandable because a good contact at th e mold/sample interface enhanced the heat flow across the mold/sample interface and henc e resulted in better heat extraction from the sample. It should also be mentioned that the temperature at the mold/sample interface was not constant according to our simulatio n and the M-t plot i ndicated non-linearity with t at the early stage of solidification and became linear afterward. This was also another reason for obtaining a longer solidification time using the numerical simulation. Another possible reason for the discrepa ncy was that the analytical solution was valid for an infinite mold thickness, while the numerical simulation was assumed to have a finite mold thickness. Therefore, for the same distance solidified, it was reasonable that the analytical solution yielded a shorter so lidification time compared to the numerical one. However, by increasing the mold thickness (wmold) in the numerical simulation, it was demonstrated that the numerical result approached the analytical solution. Such result was reasonable because one assumptio n for the analytical solution was that the

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142 thickness of the mold was infinite. However, for an increasing h value and the mold thickness, the numerical result approached the analytical solu tion with no interface resistance and an infinite mold thickness. 6.2 Results In this section, the numerical simulation for a 1D solidification of Cu-Co alloys was done in order to demonstrate the effects of heat transfer coefficient (h), composition (X) and bulk supercooling ( T) on the solidification parameters such as the S/L interface temperature, the S/L interface velocity, the te mperature gradients on both sides of the S/L interface and the cooling rate at the S/L interface. For the following simulations, the mold (wmold) and sample (wsample) thickness were set constant at 0.01 and 0.005 meter corresponding to the mold thickness and the maximum radius of the cone-shape mold in this study and the heat transfer coefficien t between the liquid copper and the copper mold was designated to be primarily at 1x106 W/m2-K according to the surface condition mentioned previously. 6.2.1 Effects of Heat Transfer Coefficient (h) Solidification of a pure Cu at the me lting point (1357K) with three different h values; 1x104, 1x105, and 1x106 W/m2-K were compared. It was found that the increase in the h value was found to increase solidific ation time (Figure 6-3). In addition, the increase in the h value enhanced the S/L interface velocity and the cooling rate of solidified sample (Figure 6-4 and 6-5). In all three cases, thermal gradients on the solid and liquid sides of the S/L interface were al ways positive for the entire solidification (Figure 6-6). It was also observed that the increase in the h value significantly suppressed the S/L interface temperature at a th in region close to the mold /sample interface (Figure 6-7).

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143 For the h value of 1x104 W/m2-K, the temperature suppression ( Tdy) at the thin region adjacent to the mold/specimen interface was only 1 degree below the melting point. As the h value increased to 1x105 W/m2-K, the Tdy value increased to 14 degrees below the melting point. Ultimately, the h value of 1x106 W/m2-K suppressed the temperature up to 120 degrees below the melting point. The simulation also showed that the thickness of the thin regions were relatively cons tant at approximately less than 150 m. However, the S/L interface temperature during solidificati on within the zone depended on h value; the larger the h value, the lower the interface temp erature was. On the other hand, the larger the h value, the larger th e temperature suppression ( Tdy) was (Figure 6-7). 6.2.2 Effects of Composition (X) Solidification Cu-Co alloys of 0, 10 , 20, 30, and 40 at% Co with no bulk supercooling were simulated to check the compositional effect on the solidification behavior of Cu-Co alloys. It was demonstr ated that an increa se in cobalt content increased the solidification time (Figure 6-8) and tended to suppress S/L interface velocity (Figure 6-9) during solidification. Nevertheless, composition had small effect on the cooling rate (Figure 6-10). It was also obs erved that the thermal gradients in the solid and liquid sides of the interface were always positive in all cases (Figure 6-11) because the solidification of three alloys were simulated without bulk supercooling. 6.2.3 Effect of Bulk Supercooling (T) The effect of bulk supercooling on the solid ification behavior was also simulated in a pure copper for 0, 100, and 200 degree bulk su percooling. The heat tr ansfer coefficients for all cases were set at 1x106 W/m2-K. It was found that an increase in bulk supercooling decreased solidification time (Figure 6-12). In terms of thermal condition at the S/L

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144 interface, the thermal gradient s on the solid side of the S/L interface were comparable and always positive (Figure 6-13). However, with bulk supercooling, the thermal gradient on the liquid side of the S/L interface was no longer positive (Figure 6-14). As the solidification proceeded, the thermal gradie nt at the interface on the liquid side (GL,i) increased from negative toward zero. It wa s observed that an end point where the GL,i rapidly approached zero was dependent of bu lk supercooling level. On the other hand, it could be mentioned that the effect of bulk supercooling started to fade out and the specimen solidified under the effect of pure external cooling afte r this end point. In addition, the larger the bulk supercooling, the larger the fraction solidified under the effect of supercooling was. Similar end poi nts were also observed in the S/L interface velocity-position (Figure 6-15) and coo ling rate-position (Figure 6-16) plots. Similar to that of the heat transfer coeffi cient, bulk supercooling also enhanced the magnitude of the temperature suppression ( Tdy) at the thin region adjacent to the mold/specimen interface (Figure 6-17). It was shown that without the bulk supercooling, the temperature of the thin region was suppres sed 20 degrees below the melting point. As the initial bulk supercooling incr eased to 100 and 200 degrees, the Tdy were 160 and 182 degrees below the melting point accordingly. Therefore, it was shown that the initial bulk supercooling could enhance the temper ature suppression of the thin region. However, the thickness of the thin region was again constant at approximately less than 150 m for all bulk supercooling level.

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145 6.3 Discussions 6.3.1 Solidification of Bulk Supercooled Cu in the Cone-Shaped Copper Mold The numerical simulations for solidificatio n of a pure copper without and with 357 degree bulk supercooling in the cone-shape copper mold were done. In order to map out the numerical results, a reference frame of 8x10 mm grid corresponding to the geometry of the mold cavity as shown in Figure 4-15 was used. By combining numerical results of the section A to I, solidification velocity contours were construc ted for two different cases (Figure 6-18). It was shown that bulk supercooling altered the solidification pattern as indicated by the change in the solidi fication velocity profile of the specimen. 6.3.2 Comparison between Experiment al and Numerical Simulation It was previously numerically shown that bulk supercooling prior to solidification could result in the enhancements in solidific ation velocity and cooling rate. Using the experimental results from the previous ch apter, the example of the alteration of solidification pattern was show n using the C10 and C13 of comparable compositions as mentioned previously. It should be noted that the C10 specimen was rapidly solidified from the superheated state, while the C1 3 was rapidly solidified from the bulk supercooled state. Two different simulation s for the alloy composition of 37.5 at% Co (the average composition of C10 and C13) were performed, with no supercooling and h = 1x105W/m2-K and with 100 degree bulk supercooling and h = 1x106 W/m2-K and the simulation results for velocity and cooling rate were shown in Figure 6-19. In this case, the cooling rate contours were used for microstructural representative. By superimposition of the microstructures of both specimens with the cooling rate maps for both conditions, it was found that the numerical simulation yields r easonable results for

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146 both cases. However, small discrepancy be tween the experimental and numerical simulation could be due to The mapping results were obtained from a 1D simulation The mold/sample contact condition during the experiment might not be the same and this could result in the microstructure different from those predicted numerically. However, it was shown that the numerical simulation yielded a reasonable outcome compared to the experimental results and it was successfully used to visualize the solidification of Cu-Co alloys with bulk supercooling. 6.3.3 Coarsening of MLPS Liquid Spherulites in the C12 Specimen during Rapid Solidification The microstructure of the C12 specimen indicated an interesting and desirable microstructure, where spherulites were uniform ly distributed within the matrix. The C12 specimen was bulk supercooled a few degr ees below the MLPS temperature prior to rapid solidification against the conical copper mold. However, the diameter of spherulites varied with position. According to the microstructural mapping respected to the 8x10 mm2 reference frame, it was found that the diam eter of spherulites at different positions along the sample axis (5-axis) had a relations hip with the distance as shown previously in Figure 4-25. In order to predict the coarsening ra te of MLPS liquid spherulite during solidification, the solidification times at various positions along the center of the C12 specimen were estimated using the numeri cal simulation with the heat transfer coefficients between 5x104 and 1x106 W/m2-K. The spherulites diameter (d) was then plotted against t1/3 for each heat transfer coefficient an d data points were fit using a power

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147 function (Figure 6-20). It was found that th e relationships betw een the spherulite diameters versus t1/3 were in the following form. at K d ) (3 / 1 ' (6-1) On the other hand, the above equation could be written in a general coarsening equation [85], where ) / 1 (nt K d (6-2) a n 3 (6-3) nK K ) (' (6-4) and K and a for each numerical simulation are li sted in Table 6-1. It was found that the coarsening coefficients (k) for the simulation were between 3.271 and 7.868 and the coarsening exponents (n) were approximat ely between 0.9805 and 1.3503 for the heat transfer coefficient between 5x104 and 1x106 W/m2-K respectively. According to the LSW theory, where the coarsening of either li quid or solid spherulites takes place due to a pure diffusion effect with no relative motion, the n value is equal to 3. On the other hand, the coarsening of liqui d spherulites due to Stokes flow is reflected by the coarsening exponent of 1.5. However, th e coarsening exponents obtained using the numerical simulation was alwa ys below 1.5 depending on the heat transfer coefficient used for simulation. It was quite reasonable because the liquid flow during the levitation state was relatively severe due to the electromagnetic stir ring and could result in random impingement of liquid spherulites prior to rapid solidification.

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148 6.3.4 Dynamic Supercooling The simulation result on the effect of th e heat transfer coe fficient supported the assumption and the experimental results for the C1 and C8 specimen on the dynamic supercooling phenomenon. It was demonstrat ed that a good heat transfer condition between the mold and the specimen indicating by a large heat transfer coefficient was favorable for the dynamic supercooling. It wa s also confirmed that the thickness of the dynamically supercooled region was rela tively constant at less than 150 m from the mold/specimen interface. This result also confirmed that dynamic supercooling was limited only to a thin region of rapidly solidified specimen. The example for this phenomenon was also experimentally found in splat cooled specimens. In addition, it was found that the ini tial bulk supercooling could enhance the magnitude of the dynamic supercooling. Howe ver, the thickness of the dynamically supercooled region was insensitive to bulk supercooling. Nevertheless, such finding signifies that the initial bulk supercooling may be required if a large dynamics supercooling is needed. 6.4 Conclusions In summary, numerical simulati ons provided several understanding of solidification behavior of rapid solidifi cation of bulk supercooled liquid and the following conclusion remarks were made. Increase in cobalt content suppressed the S/ L interface velocity and the cooling rate of the alloy. Large h value was favorable for temperatur e suppression at the thin surface region of rapidly solidified specimen. However, the simulation showed that the thickness of the layer was apparently constant at less than 150 m regardless the magnitude of the h value. Bulk supercooling enhanced th e solidification velocity a nd hence the cooling rate.

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149 Bulk supercooling also enhanced temperat ure suppression at the thin surface region of rapidly solidified spec imen. However, the thickne ss of the thin region was relatively constant regardless the magnitude of bulk supercooling

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150 Table 6-1. Coarsening coeffi cient (k) and coarsening expon ent (n) under various heat transfer coefficients predicted using the numerical simulation in this work Heat transfer coefficient (W/m2-K) used for the simulation Coefficient 5 x 104 1 x 105 5 x 105 1 x 106 KÂ’ 3.349 4.2093 4.6322 4.9074 a 3.0597 2.7828 2.2786 2.2218 K 3.271 4.709 7.526 7.868 n 0.9805 1.0781 1.3166 1.3503

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151 Figure 6-1. Schematics show solidificati on of a pure liquid at its melting point. A) Analytical solution without mold/sample resistance. B) Numerical simulation in this work with mold/sample resistance

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152 Figure 6-2. Comparison between the anal ytical and simulation results for the solidification of a pure li quid copper at the melting point in a copper mold

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153 Figure 6-3. Plots between S/L interface positi on versus time for a pure Cu with various heat transfer coefficients

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154 Figure 6-4. Plots between S/L interface ve locity versus position for a pure cu with various heat transfer coefficients

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155 Figure 6-5. Plots between coo ling rate versus position for a pure cu with various heat transfer coefficients

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156 Figure 6-6. Plots between th ermal gradients on the solid (GS,i) and liquid (GL,i) sides at the S/L interface versus position for a pur e Cu with various heat transfer coefficients

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157 Figure 6-7. Plots between S/L interface temp erature versus position for a pure cu with various heat transfer coefficients. A) General plots. B) Same plots indicate various levels of dynamic supercooli ng obtained from various h values

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158 Figure 6-8. Plots between S/L interface posi tion versus time for various compositions

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159 Figure 6-9. Plots between S/L interface velocity versus position for various compositions

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160 Figure 6-10. Plots between cooling rate versus position for various compositions

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161 Figure 6-11. Plots between thermal gradients on the solid (GS,i) and liquid (GL,i) sides at the S/L interface versus position for various compositions

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162 Figure 6-12. Plots between S/L interface positio n versus time for a pure Cu with various bulk supercoolings

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163 Figure 6-13. Plots between thermal gradient on the solid side (GS,i) at the S/L interface versus position for a pure Cu w ith various bulk supercoolings

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164 Figure 6-14. Plots between thermal gradient on the liquid side (GL,i) at the S/L interface versus position for a pure Cu with vari ous bulk supercooling. Dotted circle indicates a position, where the gradients for different T are merged

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165 Figure 6-15. Plots between S/L interface velocity versus position for a pure Cu with various bulk supercoolings . Dotted circle indicates a position, where S/L interface velocities for different T are merged

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166 Figure 6-16. Plots between cooling rate vers us position for a pure Cu with various bulk supercoolings. Dotted circle indicates a position, where cooling rates for different T are merged

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167 Figure 6-17. Plots between S/L interface temp erature versus position for a pure Cu with various bulk supercoolings. A) General plots. B) Same pl ots indicate various levels of dynamic supercooling obtained from various T values

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168 Figure 6-18. Solidification velo city maps of a pure Cu. A) Without bulk supercooling. B) With 357 degree bulk supercooling

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169 Figure 6-19. Microstructura l maps of specimens solidified with and without bulk supercooling. A) C10. B) C13 specimens

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170 Figure 6-20. Average spherulite diameter along the center of C12 specimen versus solidification time predicted using the numerical simulation under various h values

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171 CHAPTER 7 CONCLUSIONS Cu-Co alloys of less than 40 at% Co w ith various bulk supercooling and cooling conditions were successfully produced usi ng an electromagnetic levitation system equipped with rapid solidification devices. It was experimentally and numerically found that alloy composition, supercool ing, and cooling rate influen ced the final microstructure of the solidified alloys. For the alloys with small cobalt content, the microstructures were primarily small Co-rich dendritic clusters distributed in Cu-ri ch matrix. As the cobalt content increased toward 40 at% Co, small clusters of dendrites formed and the thickness of dendrite increased significantly. Bulk supercooling refined the microstructure due to the enhancement in solidification velocity. In addition, the dendr itic to nondendritic transition took place at the cooling rate approximately 1000 degree/sec for the Cu-Co alloy with 30 to 40 at% Co. The connectiv ity and the length of dendrites could be influenced by the magnitude of thermal recalescence respected to the initial bulk supercooling. For the specimens in which ther mal recalescence resulted in the increase in the liquid temperature back to its equilibrium melting temperature ( TR = T), the dendritic structure with well connectivity a nd long dendrite arms was observed in this case. As the magnitude of thermal recalescen ce respected to the in itial bulk supercooling decreased ( TR < T), the connectivity of the de ndritic structure decreased. For the alloys bulk supercooled be low the MLPS temperature depending on composition, the metastable liquid phase separation microstructures with Co-rich

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172 spherulites dispersed in Cu-rich matrix were obtained. However, thermal recalescence and electromagnetic stirring could alter the MLPS microstructure. Thermal recalescence of the MLPS Cu-Co liquid could also result in a dendritic structure due to remelting and remixing of phase separated liquid. On the other hand, rapid solidification of the MLPS Cu-Co liquid of 30 to 40 at% Co immediatel y after the MLPS could yield a desirable homogeneous distribution of fine Co-rich spherulites in Cu-rich matrix. It was numerically predicted using h = 1x106 W/m2-K that the coarseni ng exponents (n) for the MLPS spherulites in Cu-Co liquid of 30 to 40 at% Co was 1.35, which was below n = 2 and 1.5 for the coarsening exponent under Marangoni and Stokes conditions, accordingly. Such prediction was reasonable because the co arsening of the MLPS spherulites in this work was significantly affected by the electromagnetic stirring. Numerical simulation in this work was al so useful for explaining the effects of alloy composition, bulk supercooling, and heat transfer coefficient on the solidification behavior of the alloy. It was numerically demonstrated that an increase in cobalt content slightly suppressed the solidification velocity and cooling rate of th e alloy. On the other hand, increases in bulk supercool ing and heat transfer coeffi cient significantly enhanced the solidification velocity and cooling rate. The numerical simulation also confirmed that dynamic supercooling was predominant only at a thin region approximately less than 150 m adjacent to the mold/sample interface. However, the magnitude of dynamics supercooling depended on both initial bulk su percooling level and the heat transfer coefficient. The higher the value of these two factors, the larg er the magnitude of dynamic supercooling was.

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173 APPENDIX C++ CODE FOR NUMERICAL SI MULATION #include #include #include //////////////// //////////////// //////////////// //////////////// //////////////// //Solidification of Bulk Supercooled Cu-Co Alloys //C++ Code written by Surasak Wannaparhun 2004 //////////////// //////////////// //////////////// //////////////// //////////////// int main() { ////////////////// ///////////////V ariable Assignment///// //////////// /////////// int n,j,G,I,A,msgrid, P, p, i; int COUNTER; float GS, GL, Geff, V, E, fs; float a, PL, PR, step; float wmold, wsample, hms, Tmold, Tsampl e, Tnucl, Tenv, Tequil, dt, dy, endtime; float kmold, cpmold, dmold; float kint, cpint, dint; float alphamold, alphassample, alphalsample, alphaint; float T[500000], Tnew[500000]; float Time[500000], Position[500000], Te mperature[500000], Velocity[500000]; float Coolingrate[500000] , Gradsolid[500000], Gradliq uid[500000], Gradeff[500000]; double Tmoldint, Tmoldintnew, Tsam pleint, Tsampleintnew, Tint; float fourier; float K[500000]; float Cp[500000]; float D[500000]; float Alpha[500000]; float t = 0; float sigma, Tintnew, yi, Y, Ynew, grid, difference; float X; //Atomic fraction of cobalt ( between 0 to 1)// ////////////////// /////////End of Variable Assi gnment///////////// ////////////// //////////////// ////////////////Output file////////// ///////////// ////////////// ofstream fout ("Solidification of Bu lk Supercooled Cu_Co_Alloys.txt"); ////////////////// ///////////////Out put file/////////////// /////////// ////////// std::cout<<"================ ==================== =============="; std::cout<<"\nPlease provide the following simulation Parameters";

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174 std::cout<<"\n============== ==================== =============="; /////////////Thermophysical pr operties of Cu, Co and Cu -xCo alloy/////////////// float awCu = 63.55e-3; //Atomic weight Cu (kg/mole)// float awCo = 58.93e-3; //Atomic weight Co (kg/mole)// float dlCu = 8933; //Density of liquid Cu (kg/m3)// float dsCu = 8933; //Density of solid Cu (kg/m3)// float dlCo = 8862; //Density of liquid Co (kg/m3)// float dsCo = 8862; //Density of solid Cu (kg/m3)// float cpsCu = 401; //H eat capacity of solid Cu (J/kg-K)// float cplCu = 401; //H eat capacity of liquid Cu (J/kg-K)// float cpsCo = 733; //H eat capacity of solid Co (J/kg-K)// float cplCo = 733; //H eat capacity of liquid Co (J/kg-K)// float ksCu = 385; //Thermal conductivity of solid Cu (W/m-K)// float klCu = 385; //Th ermal conductivity of liquid Cu (W/m-K)// float ksCo = 49.3; //Thermal conductivity of solid Co (W/m-K)// float klCo = 49.3; //Th ermal conductivity of liquid Co (W/m-K)// ////////////End of Thermophysical properti es of Cu, Co and Cu-xCo alloy///////// ////////////Calculations of Thermophysical properties of Cu-xCo alloy/////////// float klsample = (1-X)*klCu + X*klCo; //(W/m-K)// float kssample = (1-X)*ksCu + X*ksCo; //(W/m-K)// float cpssample = (1-X)*cpsCu + X*cpsCo; //(J/kg-K)// float cplsample = (1-X)*cplCu + X*cplCo; //(J/kg-K)// float dssample = (1-X)*dsCu + X*dsCo; //(kg/m3)// float dlsample = (1-X)*dlCu + X*dlCo; //(kg/m3)// float AW = (1-X)*awCu + X*awCo ; //Atomic weight of Cu-xCo alloy (kg/mole)// ////////End of Calculations of Thermophysic al properties of Cu-xCo alloy//////// ////////////////// //////////////Parameter input// /////////////// //////////////// std::cout<<"\nPlease type the atomic fr action of Cobalt in Cu-xCo alloy ? "; std::cin>>X; std::cout<<"\nLiquid temperature (K) ? "; std::cin>>Tsample; std::cout<<"\nEquilibrium li quidus temperature (K) ? "; std::cin>>Tequil; std::cout<<"\nMold width (meter) ? "; std::cin>>wmold; std::cout<<"\nSample width (meter) ? "; std::cin>>wsample; std::cout<<"\nNumber of interval (i nteger) (should be at l east 200) ? "; std::cin>>I; std::cout<<"\nMold/Sample Heat tr ansfer coefficient (W/m2-K) ? "; std::cin>>hms; std::cout<<"\nMold temperature (K) ? "; std::cin>>Tmold;

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175 std::cout<<"\nEnvironment temperature (K) ? "; std::cin>>Tenv; std::cout<<"\nThermal conduc tivity of mold (W/m-K) ? "; std::cin>>kmold; std::cout<<"\nHeat capacity of mold (J/kg-K) ? "; std::cin>>cpmold; std::cout<<"\nDensity of mold (kg/m3) ? "; std::cin>>dmold; ////////////////// /////////////End of parameter input//////////// /////////////// ////////////////// //////////////Thermal diffusivity///////// //////////////////// alphamold = kmold/(cpmold*dmold); alphassample = kssample/(cpssample*dssample); alphalsample = klsample/(cplsample*dlsample); ////////////////// //////////End of thermal diffusi vity////////// //////////////// ////////////////// ///////////////// M/S Interface///////// //////////// /////////// kint = (kssample+kmold)/2; cpint = (cpssample+cpmold)/2; dint = (dssample+dint)/2; alphaint = (alphamold+alphalsample)/2; ////////////////// //////////////////M/S Interface//////////// //////////// /////// ////////////////// ///////Grid interval calculati on/////////////// /////////////// G = I+1; dy = (wmold+wsample)/I; a = (wmold/dy)+1; A = a*1; std::cout<<"\nThe grid number for the mold/sample interface is "<>msgrid; ////////////////// /////////Grid interval calculat ion///////////// /////////////// ////////////////// ///////Numerical stability crit erion/////////// /////////////// float fouriermold = 0.5; float fouriersample = 0.5; float dtmold = fouriermold*(dy*dy)/alphamold; float dtssample = fouriersample*(dy*dy)/alphassample; float dtlsample = fo uriersample*(dy*dy)/alphalsample; float factor = ((hms*dy/kint)+1); float fourierint = 0.5/factor; float dtint = fourierint*(dy*dy)/alphaint; { if (dtmold <= dtssample) dt = dtmold;

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176 else dt = dtssample; } { if (dtssample <= dtlsample) dt = dtssample; else dt = dtlsample; } { if (dt >= dtint) dt = dtint; else dt = dt; } dt = dt/10.0; std::cout<<"\nA proper time step is "<>step; ////////////////// //////End of Numerical stability criterion/// ///////////////// ////////////////// /////////////Nucleation Temperat ure///////////// ////////////// Tnucl = Tsample; ////////////////// /////////////Nucleation Temperat ure///////////// ////////////// ////////////////// //////////////// ////Print out/////////// ////////// //////////// fout<<"\n========= ================== ================== =========== ======="; fout<<"\nSolidification of Bulk Supercool ed Cu-Co alloys "; fout<<"\nProgram written by Surasak Wannaparhun, 2004 "; fout<<"\n========= ================== ================== =========== ======="; fout<<"\n Simulation Parameters "; fout<<"\n========= ================== ================== =========== ======="; fout<<"\nSolidification of a bulk supercooled Cu-"<
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177 fout<<"\nMold/Sample Heat transf er coefficient (W/m2-K): "<
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178 } //End of Mold/Sample Interface// //Sample Part// for (j = 1; j < G+1; ++j) { if (j > msgrid) { T[j] = Tsample; K[j] = klsample; Cp[j] = cplsample; D[j] = dlsample; Alpha[j] = alphalsample; // fout<<"\n"<
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179 float GS0 = (Tsampleint-Tmoldint)/dy; //Initial temp. gradient in the solid// float GL0 = (T[msgrid+1]-Tsampleint)/dy; //Initial temp. gradient in the liquid// float Geff0 = GS0-GL0; float V0 = ((kssample*GS0)-(kls ample*GL0))/(dssample*Heff); //Initial interface velocity in the solid// float Y0 = (msgrid-1)*dy; //Initial interface position// float E0 = Geff0 *V0; //Initial cooling rate// float fs0 = 0; //Fraction solidified// Y = Y0; V = V0; COUNTER = 0; ///////////////End of Calculate the initial interf ace parameters//////////////// // To display temperature history at various positions in the sample// // fout<<"\nTime(sec) "<<(msgrid)*dy<<"(m) "< PL) { if (Y < PR) {

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180 // yi = ((PR+PL)/2); // fout<<"\n\n Interface detected"; // fout<<"\n counter is "<
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181 T[msgrid] = Tsampleintnew; { for (n = 1; n < G+1; ++n) if (n > msgrid) { Tnew[n] = T[n] + (dt/dy)*(alphassa mple*((T[n-1]-T[n])/dy) + alphassample*((T[n+1]-T[n])/dy)); } } //End of sample part// //////To display temperature profile of the system as a function of time//////// //Print out new temperatures// // { // for (n = 1; n < msgrid; ++n) // { // fout<<"\n"< msgrid) // { // if (n < P) // fout<<"\n"<msgrid) T[n] = Tnew[n]; }

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182 } T[0] = Tenv; T[G+1] = T[G]; Tint = T[P]; Tmoldint = Tmoldintnew; Tsampleint = Tsampleintnew; //End of Replacing old temperatures with new ones ///////////////////End of r ecalculating the temperature profile///////////////// ////////////////// ////Calculating new interface in formation////// /////////////// //The effective enthal py at the interface of temperature T// solidcopper = (98 75.72 + 29*(1357-298))*(1-X); //J/mole// solidcobalt = (8940 + 40.193*(1357-298))* X; //J/mole// solidexcess = X*(1-X)*(( 29288*X)+(31798*(1-X))); //J/mole// Hsolid = solidcopper + solidcobalt + solidexcess; //J/mole// liquidcopper = (53603.6 + 31.40*(Tint-1357))*(1-X); //J/mole// liquidcobalt = (83642. 11 + 54.863*(Tint-1768))*X; //J/mole// liquidexcess = X*(1-X)* ((40166*X)+(53555*(1-X))); //J/mole// Hliquid = liquidcoppe r + liquidcobalt + solidexcess; //J/mole// Heff = (Hliquid-Hsolid)/AW; //(J/kg)// //End of The effective enth alpy at the interface of temperature T// GS = (Tint-T[P-1])/dy; GL = (T[P+1]-Tint)/dy; Geff = GS-GL; V = ((kssample*GS)-(klsample*GL))/(dssample*Heff); E = Geff*V; t = t + dt; fs = (Y-wmold)/wsample; //Store data// Time[COUNTER] = t; Position[COUNTER] = Y; Temperature[COUNTER] = Tint; Velocity[COUNTER] = V; Coolingrate[COUNTER] = E; Gradsolid[COUNTER] = GS; Gradliquid[COUNTER] = GL; Gradeff[COUNTER] = Geff; //Store data// //screen and prin t out the interface information//

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183 grid = Position[COUNTER]/dy; difference = P grid; if (difference < 0.05) fout<<"\n"<
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192 BIOGRAPHICAL SKETCH Surasak Wannaparhun was born on October 19, 1974, in Bangkok, Thailand. He is the first son of Narongsak and Thipma nee Wannaparhun, who own an automotive maintenance business. He attended Panthasuks a School for the secondary school level. At the age of 11, he passed the entrance exam ination to study at Su ankularb Vidhayalai. Thailand and received his high school diploma in 1992. During his high school education, he had a 3-year experience in military training and ranked as a commander. In May 1992, he passed the national entrance examin ation to study in the engineering school at Chulalongkorn University, Thailand. A ccording to his childhood experience and family background, he decided to choose meta llurgical engineering as his major, and received his Bachelor of Engineering degr ee in metallurgical e ngineering in May 1996. At the same time of his graduation, he wa s one of 15 runners-up for commercial pilot positions at Thai Airways International, Co., Ltd., after several physical and psychological examinations. In September 1996, he was employed by the Siam Cement Group Co., Ltd., and worked as a metallurgi st and production engineer for almost 2 years. In 1998, he ordained and meditated as a monk in the northern part of Thailand to learn about Buddhist philosophy. After that, he decided to pu rsue a graduate degree in Materials Science and Engineering in the U.S. A. In summer 2001, he received his Master of Science in Materials Science and Engineerin g from the University of Central Florida, Orlando, under the guidance of Dr. Sudipta Seal. In the same year, he was admitted to the Department of Materials Science and Engineerin g at the University of Florida. He studied

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193 under the guidance of Professor Reza Abbaschi an, and received his Ph.D. in Materials Science and Engineering in May 2005.