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MAGNESIUM BASED METAL MATRIX NANOCOMPOSITES BY MAGNETO ACOUSTIC MIXING TECHNOLOGY By HUNTER HENDERSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014
Â© 2014 Hunter Henderson
To my parents
4 ACKNOWLEDGMENTS I would first like to thank my advisor Prof. Michele Manuel, for her advice, gu idance, and patience. I thank all members of the Materials Design and Prototyping Laboratory , especially Zachary Bryan, Ryan Hooper, Billy Valderrama and Glenn Bean, with whom I have worked closely and had many thoughtful discussions. I would like to thank collaborators from Oak Ridge National Laboratory who made the experiments possible, including Dr. Gerard Ludtka, Dr. Gail Mackiewicz Ludtka and Dr. Alexander Melin. Most of all, I would like to thank Dr . Orlando Rios for his excellent suggestions and for always being generous with his time. Finally, I would like to thank my mother and father, on whom I can rely unconditionally.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 15 ABSTRACT ................................ ................................ ................................ ................... 16 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 17 2 BACKGROUND ................................ ................................ ................................ ...... 23 2.1 Effect of Magnetic Fields on MMC Processing ................................ .............. 23 2.1.1 Magnetic Alignment of Individual Particles ................................ .......... 25 2.1.2 Particle Particle Interactions ................................ ............................... 28 2.1.3 Magnetohydro dynamic Effects ................................ ............................ 29 2.1.4 Magnetohydrodynamic Particle Interactions ................................ ....... 30 2.1.5 Magnetic Effects During Solidification ................................ ................. 32 2.2 Effect of Acoustic Fields on MMC Processing ................................ ............... 33 2.2.1 Principles of Sound Waves ................................ ................................ . 33 2.2.2 Cavitation ................................ ................................ ............................ 36 2.3 Electromagnetic Vibration ................................ ................................ ............. 37 2.4 Induction Heating of Materials ................................ ................................ ....... 38 2.5 Metal Matrix Nanocomposites ................................ ................................ ....... 39 2.5.1 Strengthening Mechanisms in MMNCs ................................ ............... 39 2.5.2 Particle Incorp oration Methods ................................ ........................... 43 3 FUNDAMENTALS OF MAMT PROCESSING ................................ ........................ 46 3.1 Basic Principles of EMAT ................................ ................................ .............. 46 3.2 Calculation of Acoustic Pressure ................................ ................................ ... 51 3.3 Propagation Effects ................................ ................................ ....................... 52 3.4 Frequency Dependence ................................ ................................ ................ 55 3.4.1 Static Loading ................................ ................................ ..................... 55 3.4.2 Inertial Loading ................................ ................................ ................... 58 3.4.3 Application to the Curren t System ................................ ....................... 59 3.5 Solidification Velocity ................................ ................................ .................... 60 3.5.1 Infinite Thermal Conductivity ................................ ............................... 60 3.5.2 Stefan Problem ................................ ................................ ................... 62
6 4 MATERIALS SELECTION AND DESIGN ................................ ............................... 65 4.1 Particle Thermodynamic Stability ................................ ................................ .. 65 4.2 Mechanical Effects of Particles ................................ ................................ ..... 67 4.3 Particle Availability and Reliability ................................ ................................ . 70 4.4 Current Methodology ................................ ................................ ..................... 70 5 EXPERIMENTAL METHODS AND PROCEDURES ................................ .............. 73 5.1 Pre Processing ................................ ................................ .............................. 73 5.2 MAMT Processing ................................ ................................ ......................... 75 5.3 Variable Processing Routes ................................ ................................ .......... 76 5.4 Experimental Design ................................ ................................ ..................... 78 5.5 Analytical Techniques ................................ ................................ ................... 80 5.5.1 As Received Particle Evaluation ................................ ......................... 80 5.5.2 X ray Radio graphy ................................ ................................ .............. 81 5.5.3 Metallographic Preparation ................................ ................................ . 81 5.5.4 Microstructural Analysis ................................ ................................ ...... 82 6 EFFECT OF MAMT ON PARTICLE DISPERSION ................................ ................ 84 6.1 As Received Particle Analysis ................................ ................................ ....... 84 6.1.1 Rare Earth Oxide Particles ................................ ................................ .. 84 6.1.2 Diamond Particles ................................ ................................ ............... 88 6.2 Non Destructive Dispersion Quantification ................................ .................... 89 6.3 Structure of Rare Earth Oxide Reinforced Composites ................................ . 91 6.4 Particle Containment Interaction ................................ ................................ ... 98 6.5 Summary ................................ ................................ ................................ ..... 104 7 EFFECT OF MAMT ON MICROSTRUCTURE ................................ ..................... 106 7.1 Non MAMT Microstructure ................................ ................................ .......... 106 7.2 Grain Refinement By EMAT ................................ ................................ ........ 107 7.2.1 Non EMAT Control ................................ ................................ ............ 108 7.2.2 MAMT at High Power During Solidification ................................ ....... 109 7.2.3 Low Induction Power During Solidification ................................ ........ 112 7.2.4 No Induction During Solidification ................................ ..................... 113 7.3 Effects of Magnetic Anisotropy ................................ ................................ .... 115 7.4 Alloying Additions ................................ ................................ ........................ 118 7.4.1 Microstructural Analysis ................................ ................................ .... 119 7.4.2 Compositional Analysis ................................ ................................ ..... 123 7.5 Summary ................................ ................................ ................................ ..... 124 8 CONCLUSIONS ................................ ................................ ................................ ... 125 9 FUTURE WORK ................................ ................................ ................................ ... 128
7 9.1 MAMT Processing Investigations ................................ ................................ 128 9.1.1 Fundamental Physical Mech anisms ................................ .................. 128 9.1.2 MAMT Specific Investigations ................................ ........................... 129 9.2 Potential Applications ................................ ................................ .................. 131 9.2.1 Other Systems of Interest ................................ ................................ . 131 9.2.2 Sonochemistry ................................ ................................ .................. 131 9.3 Sonofusion ................................ ................................ ................................ .. 133 APPEND IX A CALCULATION OF ACOUSTIC PRESSURE AND INTENSITY IN MAMT CRUCIBLE VIBRATION MODE ................................ ................................ ............ 134 B CALCULATION OF ACOUSTIC INTENSITY DISTRIBUTION FOR HORN AND EMAT BASED SONICATION ................................ ................................ ............... 140 B.1 MAMT Acoustic Intensity Distribution ................................ .......................... 140 B.2 Sonotrode Acoustic Intensity Distribution ................................ .................... 141 C INDIRECT COMPOSITIONAL MEASUREMENTS IN MG LI ALLOYS ................. 144 C.1 Microstructure Based Compositional Measurement ................................ .... 144 C.2 Hardness Based Compositional Measurement ................................ ........... 150 D ADDITIONAL DATA ................................ ................................ .............................. 151 D.1 Mechanical Testing Data ................................ ................................ ............. 151 D.2 Thermal Profiles ................................ ................................ .......................... 155 D.3 Radiography Data ................................ ................................ ....................... 159 LIST OF REFERENCES ................................ ................................ ............................. 165 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 185
8 LIST OF TABLES Table page 1 1 Comparison of properties o f light metals to steel. ................................ ............... 17 5 1 Complete list of samples. P ac corresponds to the maximum acoustic pressure. ................................ ................................ ................................ ............ 78 6 1 Mass attenuatio n coefficient (Âµ m coefficient (Âµ l =Âµ m 5 at 8keV (Cu K ). ............ 89 6 2 Free energies of formation for possible reaction products of Mg , C, (Fe, Cr, Ni) at 1000K .. ................................ ................................ ................................ ... 102 7 1 Processing conditions for the samples analyzed in Section 7.2. ...................... 108 7 2 Relevant processing conditions for the sa mples analyzed in Section 7.4. .. ...... 119 A 1 Summary of input variables for calculating acoustic pressure and intensity in the EMAT system by Equations A 20 and A 21. ................................ ............... 139 C 1 Percentage of BCC in the microstructure under Sheil and Equilibrium conditions as a function of Li at.%. ................................ ................................ ... 145
9 LIST OF FIGURES Figure page 1 1 Comparison of EMAT technologies . ................................ ................................ ... 20 1 2 Diagram of the relative applicability of high power EMAT relative to other sonic technologies. ................................ ................................ ............................. 21 2 1 Influence of magnetic field on the solidification texture of AZ91D. ...................... 27 2 2 Field lines and eddy currents generated by a particle mo ving in conductive fluid while in a magnetic field. ................................ ................................ ............. 32 2 3 Two principle modes of wave propagation. ................................ ........................ 35 2 4 Overview of Electromagn etic Vibration (EMV). ................................ ................... 38 3 1 Overview of the Electrom agnetic Acoustic Transduction . ................................ ... 47 3 2 Skin depth as a function of alternating current frequency in 304 and 316 stainless steel at 1000K . ................................ ................................ ..................... 49 3 3 Schematic of the effect of skin depth on vibration mode of EMAT. ..................... 50 3 4 Distribution of e ddy currents for two situations . ................................ .................. 50 3 5 Intensity distribution based on aco ustic propogation. ................................ ......... 53 3 6 Estimated pressure distribution for melt vibration in EMAT ................................ 54 3 7 Maximum radial displacement for static and ine rtia limited cases of vibration as a func tion of frequency.. ................................ ................................ ................ 59 3 8 Solidification velocity as a function of inverse radius in the EMAT system by two models. ................................ ................................ ................................ ........ 63 4 1 Elling ham diagram of MgO and oxides more stabl e than MgO . ......................... 67 4 2 Modeled yield strength of Mg reinforced with varying sizes and volume fractions of Al 2 O 3 particles ................................ ................................ .................. 68 4 3 common Mg reinforcement particle chemistries ................................ ................. 71 5 1 Experimental flowchart showing the pro cessing route of MMNCs by MAMT. ..... 73 5 2 EMAT sample overview ................................ ................................ ...................... 74
10 5 3 Representative temperature profile for EMAT processing. ................................ . 76 5 4 Process types in the MAMT system. ................................ ................................ .. 77 5 5 Naming convention f or the samples in this document . ................................ ....... 78 5 6 Pressure distribution as a function of distance from the crucible for all samples. ................................ ................................ ................................ ............. 79 5 7 Sectioning methodology. ................................ ................................ .................... 82 6 1 Particle distribution of Er 2 O 3 nanoparticles.. ................................ ....................... 85 6 2 Particle size distribution of Dy 2 O 3 nanorods measured by DLS. ......................... 87 6 3 Settling velocity of Er 2 O 3 and Dy 2 O 3 spheres in water at 20Â°C. .......................... 87 6 4 Diamond nanoparticle properties . ................................ ................................ ....... 88 6 5 X Ray radiography of samples of interest. ................................ .......................... 90 6 6 Elemental analysis of large particles in Sample 7. ................................ .............. 92 6 7 Backscatter electron micrograph of Sample 7 showing large particles aligned with the vertical magnetic field. ................................ ................................ ........... 92 6 8 Elemental analysis of Sample 1 Mg Dy(r) 18T (4,4)MPa. ................................ .. 94 6 9 Microstructure of Sample 1. ................................ ................................ ................ 94 6 10 TEM HAADF micrograph of Sample 1 showing dispersed Dy 2 O 3 nanorods. ...... 95 6 11 Orientation of Dy 2 O 3 rods . ................................ ................................ .................. 96 6 12 Surfaces of the boundary between regions of alignment vs. non alignment for Dy 2 O 3 prolate ellipso ids as a function of volume, aspect ratio, and magnetic field at 300 K and 1000 K. ................................ ................................ .................. 97 6 13 Microstructur e of diamond reinforced samples . ................................ .................. 98 6 14 Aligned group of particles in Sample 5 Mg Dia(s) 18T (1.5,0)MPa. ................... 99 6 15 Crucible morphology of Samples.. ................................ ................................ .... 100 6 16 Crucible Mg interfaces.. ................................ ................................ .................... 100 6 17 XRD spectrum of Sample 5, post EMAT procesing. ................................ ......... 101 6 18 T EM HAADF micrograph of Sample 5 . ................................ ............................. 103
11 6 19 TEM HAADF of Sample 6. ................................ ................................ ................ 103 6 20 TEM HAADF micrograph of a string of particles in Sample 5. .......................... 104 7 1 Sample 0 Mg NA 0T (0,0)MPa, a no n MAMT control of air cooled Mg . ........... 107 7 2 Microstructure of a cross section of Sample 0 Mg NA 0T (0,0)MPa, unreinforced Mg cont rol. ................................ ................................ ................... 108 7 3 Microstructure of a cross section of Sample 1 Mg Dy(r) 18T (4,4)MPa. .......... 109 7 4 Acoustic pressure and grain size (G.S) a s a function of distance from the crucible wall for Sample 1 Mg Dy(r) 18T (4,4)MPa. ................................ ......... 110 7 5 Top down schematic of inward solidifying mat erial in the MAMT system . ........ 111 7 6 Microstructure of a cross section of Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa. .... 113 7 7 Microstructure of a cross section of Sample 3 Mg Dy(r) 0T (0,0)MPa. ............ 113 7 8 Microstructure of a cross section of Sample 4 Mg NA 18T (1.5,0)MPa. .......... 114 7 9 Microstructure of a cross section of Sample 5 Mg D ia(s) 18T (1.5,0)MPa. ...... 115 7 10 Microstructure of a cross section of Sample 6 Mg Dia(s) 0T (0,0)MPa. ........... 115 7 11 Electron Backscatter Diffraction (EBSD) of the Sample 1 Mg Dy(r) 18T (4,4)MPa. ................................ ................................ ................................ .......... 116 7 12 Magnetocrystalline energy of different sized Mg crystals in a 20T magnetic field as a function of c axis to magnetic field mis alignment. ............................. 117 7 13 Schematic of the tendency of a particle to align in the presence of m agnetic and acoustic fields . ................................ ................................ ........................... 118 7 14 Mg Li phase diagram showing the nominal matrix compositions of Samples 9 through 13.. ................................ ................................ ................................ ...... 119 7 15 Grain size of Samples 9 13 as a function of distance from the crucible. .......... 120 7 16 Microstructure of Sample 9 Mg7Li NA 18T (1.5,1.5)MPa. ............................... 121 7 17 Microstructure of a cross section of Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa. ................................ ................................ ................................ .... 121 7 18 Microstructure of a cross section of Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa. ................................ ................................ ................................ .... 122
12 7 19 Microstructure of a cross section of Sample 12 Mg15Li NA 18T (1.5,1.5)MPa. ................................ ................................ ................................ .... 122 7 2 0 Microstructure of a cross section of Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa. ................................ ................................ ................................ .... 123 7 21 IC P AES locations and atomic % compositions for Samples 9 13.. ................. 124 9 1 Schematic of a potential MAMT apparatus for continuous sonochemical applications. ................................ ................................ ................................ ...... 132 C 1 Equilibrium BCC volume fraction in Mg Li as a function of Li at.%. The linear fit to the variable model is displayed in black. ................................ ................... 146 C 2 Li at.% as a function of BCC Fraction for the case of Sheil solidification and a power law model. ................................ ................................ .............................. 147 C 3 Difference between Sheil data and the power model in Figure C 2: as a function of BCC Fraction, along with a linear fit. ................................ ............... 147 C 4 Li at.% as a function of BCC Fraction for the case of Sheil solidification, along with the corrected model found in Equation C 2. ................................ .... 148 C 5 Boundaries of potential Li at.% in MgLi alloys as a function of BCC phase fraction. ................................ ................................ ................................ ............. 148 C 6 Range of possible Li at.% as a function of fraction BCC in MgLi binary alloys. 149 C 7 Vickers hardness as a fun ction of Li at.% and wt.%. ................................ ........ 150 C 8 L i at.% and wt.% as a function of Vickers hardness. ................................ ........ 151 D 1 Tension Curves for Samples 4, 5, and 6 . ................................ ......................... 151 D 2 Etched tension specimen of sample 4 Mg NA 18T (1.5,0)MPa . ....................... 152 D 3 Etched tension specimen of sample 5 Mg Dia(s) 18T (1.5,0)MPa. .................. 152 D 4 Etched tension specimen of sample 6 Mg Dia(s) 0T (0,0)MPa . ....................... 153 D 5 C ompression Curves for Samples 4, 5, and 6. ................................ ................. 154 D 6 Structure of a compression specim en from 6 Mg Dia(s) 0T (0,0)MPa . ............ 154 D 7 Temperature and magnetic field profile for Sample 1 Mg Dy(r) 18T (4,4)MPa . 155 D 8 Temperature and mag netic field profile for Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa ................................ ................................ ................................ ..... 155
13 D 9 Temperature and magnetic field profile for Sample 3 Mg Dy(r) 0T (0,0)MPa ... 156 D 10 Temperature and magnetic field profile for Sample 4 Mg NA 18T (1.5,0)MPa . 156 D 11 Temperature and magnetic field profile for Sample 5 Mg Dia(s) 18T (1.5,0)MPa ................................ ................................ ................................ ........ 156 D 12 Temperature and magnetic field profile for Sample 6 Mg Dia(s) 0T (0,0)MPa . 157 D 13 Temperature and magnetic field profile for Sample 7 M g Er(s) 18T (1.5,0)MPa ................................ ................................ ................................ ........ 157 D 14 Temperature and magnetic field profile for Sample 8 Mg Er(s) 0T (0,0)MPa ... 157 D 15 Temperature and magnetic field profile for Sample 9 Mg7Li NA 18T (1.5,1.5)MPa ................................ ................................ ................................ ..... 158 D 16 Temperature and magnetic field profile for Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa ................................ ................................ ................................ ..... 158 D 17 Temperature and magnetic field profile for Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa ................................ ................................ ................................ ..... 158 D 18 Temperature and magnetic field profile for Sample 12 Mg15Li NA 18T (1 .5,1.5)MPa ................................ ................................ ................................ ..... 159 D 19 Temperature and magnetic field profile for Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa ................................ ................................ ................................ ..... 159 D 20 Orthogonal perspe ctives for X ray radiography. ................................ ............... 160 D 21 Radiography for Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa ................................ ... 160 D 22 Radiography for Sample 3 Mg Dy( r) 0T (0,0)MPa ................................ ........... 160 D 23 Radiography for Sample 4 Mg NA 18T (1.5,0)MPa ................................ ......... 161 D 24 Radiography for Sample 5 Mg Dia(s) 18T (1.5,0)MPa ................................ ..... 161 D 25 Radiography for Sample 6 Mg Dia(s) 0T (0,0)MPa ................................ .......... 161 D 26 Radiography for Sample 7 Mg Er(s) 18T (1.5,0)MPa ................................ ....... 162 D 27 Radiography for Sample 8 Mg Er(s) 0T (0,0)MPa ................................ ............ 162 D 28 Radiography for Sample 9 Mg7Li NA 18T (1.5,1.5)MPa ................................ .. 162 D 29 Radiography for Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa ........................... 163
14 D 30 Radiography for Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa ............................. 163 D 31 Radiography for Sample 12 Mg15Li NA 18T (1.5,1.5)MPa .............................. 163 D 32 Radiography for Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa ......................... 164
15 LIST OF ABBREVIATIONS BTU British Thermal Unit DLS Dynamic Light Scattering EMAT Electromagnetic Acoustic Transduction, a mechanism that transforms electromagnetic energy into acoustic energy HP EMAT High Power Electromagnetic Acoustic Transduction MAM T Magneto Acoustic Mixing Technology, a technology that combines a high magnetic field and EMAT sonication for materials processing MHD Magnetohydrodynamics, the study of interactions of conductive fluids with magnetic fields NDE Non Destructive Evaluati on PALS Phase Analysis Light Scattering PSD Particle Size Distribution RMS Root mean square, the quadratic mean of a varying quantity, such as a waveform. SEM Scanning Electron Microscopy TEM Transmission Electron Microscopy XRD X Ray Diffraction
16 Abstr act of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MAGNESIUM BASED METAL MATRIX NANOCOMPOSITES BY MAGNETO ACOUSTIC MIXING TECH NOLOGY By Hunter Henderson May 2014 Chair: Michele V. Manuel Major: Materials Science and Engineering Sonication of metallic melts is a well established method of modifying cast microstructure s and aiding nanoparticle incorporation. Here we investigate a novel fabrication method: Magneto Acoustic Mixing Technology (MAMT), which uses Electromagnetic Acoustic Transduction (EMAT) as a method to produce acoustic waves in molten meta l, inducing cavitation and breaking up nanoparticle agglomerates . This method uses a combination of static and alternating magnetic fields to induce sonication. MAMT is used in this study to produce metal matrix nanocomposites. The cast microstructures were analyzed with a number of techniques to quantify the grain structure and t he multi modal particle distribution. Additionally, analytical models of acoustic pressure were developed and compared to the resuting microstructure to provide insight into the physics active in the system. Both magnetic and acoustic effects were observe d in the materials resulting from MAMT treatment. The theoretical and experimental basis for MAMT may be expanded upon and adapted to a large number of applications in the future.
17 CHAPTER 1 INTRODUCTION Transportation activities accounted for 27.08 quad rillion BTUs (British Thermal Units), 28% of energy use in the United States in 2011, almost all of which derived from fossil fuels [ 1 ] . This vast consumption of oil is concerning both from the perspective of energy independence and CO 2 pollution. Thus, improving the energy efficiency of cars and trucks has been identified as an important method of improving nationwide energy efficiency [ 2 ] . Light metals (Mg, Al, and Ti) are attractive materials for transportation applications because of their low densities and high specific strength and modulus [ 3 5 ] (seen in Table 1 1), and r eplacing steel components with light metals can reduce vehicle weight , improving fuel economy [ 2 ] . Mg has specifically been targeted for integration into cast structural transportation components because of its high castability, low densit y, and high component rigidity [ 3 , 6 8 ] . Table 1 1 . Comparison of properties of light metals to steel. Alloy Base Density [g/cm 2 ] [ 9 ] UTS [MPa] Specific Strength [kNÂ·m/(kg)] Elastic Modulus [GPa] [ 9 ] Specific Modulus [kNÂ·m/(kg)] Titanium 4.5 700 1300 [ 9 ] 155 290 110 24.4 Aluminum 2.7 200 [ 9 ] 800 [ 10 ] 75 295 70 25.9 Magnesium 1.7 200 500 [ 11 ] 120 295 45 26.5 Steels 7.8 300 1500 [ 9 ] 40 190 210 26.9 While the specific strength and modulus of Mg alloys compare well to steel, further improvements in stiffness, strength, and creep resistance are needed for Mg to be competitive in more specific a pplications [ 3 ] . Reinforcing Mg with ceramic particles to create metal matrix composites (MMCs) is a promising route to achieve these property improvements [ 12 15 ] . P articularly in applications such as engine mounts and
18 material parameters, respectively, Mg MMCs can reduce component weight considerably [ 14 ] . Additionally, composite reinforcement has been shown to improve wear resistance, thermal stability, and fracture toughness [ 12 , 16 20 ] . Unfortunately, reinforcement with large ceramic particles (>1 Âµm) typically has a detrimental effect o n ductility, since the particles can act as void nucleation sites [ 17 , 21 ] . This lack of ductility limits the implementation of composites, especially in transportation applications [ 15 ] . A solution to this problem is to reduce the particle size to below 100 nm to produce metal matrix nanocomposites (MMNCs), in which both high strength and ductility can be maintained [ 22 30 ] . Furthermore, nanoparticle additions have de monstrated dramatic improvements in creep resistance [ 31 ] , one of the main limitations of Mg alloys [ 6 ] . With respect to creep, ceramic nanoparticles have an advantage over precipitation strengthening because they are coarsening resistant [ 32 ] . Because their interparticle spacing is small, MMNCs can strengthen b y Orowan looping, in which mobile dislocations generate dislocation loops around small particles [ 33 ] . Orowan looping is additionally beneficial to strengthening b ecause the creation of dislocation loops increases the overall dislocation density, further increasing strength [ 34 , 35 ] . MMNCs are also frequently associated with a reduction in grain size due to grain boundary pinning, improving both strength and ductility by the Hall Petch mechanism [ 36 , 37 ] . Efficient and effective fabrication of MMNCs remains an unresolved challenge, since nanoparticles have a strong tendency to agglomerate during fabrication [ 23 ] . At nanoscale particle sizes, capillary forces become increasingly dominant, making separation more difficult than for micron sized particles [ 38 ] . If nanoparticles are
19 gathered into agglomerations in the final microstructure, the overall strengthening potency will be reduced and the clusters will act as crack initiation sites, reducing both strength and ductility [ 39 ] . The success of MMNCs is therefore dependent on achieving a homogeneous dispersion of nanoparticles in the matrix [ 40 ] . Several m ethods have been explored with the objective of overcoming this challenge, including powder metallurgy [ 17 ] , spray forming [ 41 ] , friction stir processing [ 42 ] , in situ techniques [ 43 ] , and melt sonication [ 44 ] . Of these methods, sonic melt treatment has been isolat ed as a promising method of producing complex castings necessary for implementation of MMNCs into transportation components [ 26 , 28 , 45 51 ] . Historically, s onic m elt treatment has primarily been used to reduce as cast grain size [ 52 54 ] . This is achieved by inducing cavitation (the rapid expansion and collapse of bubbles in a liquid) and acoustic flow during solidification , locally remelting dendrite side arms and increasing the density of nuclei in the melt [ 55 ] . Cavitation is also able to disperse particles by heterogeneously nucleating at gas bubbles in particle ag glomerations, breaking up clusters and improving particle/melt wettability [ 44 ] . The most common method of acoustic melt treatment has been immersion of a sonicating horn into a melt, but this approach has limited industrial flexibility due to temperature limitations and sonotrode degradation [ 51 ] . Another metho d that has been proposed by Manuel and Rios is the use of coupled magnetic and induction fields to produce high intensity sonication in a process known as Magneto Acoustic Mixing Technology (MAMT) [ 56 ] . This technique uses a high powered version of the electromagnetic acoustic transduction (EMAT) method as the sonication mechanism [ 57 ] .
20 Electroma gentic Acoustic Transduction is the transformation of electromagnetic energy directly into acoustic energy. Traditional ly, EMAT has been used as a non contact source of sonication for non destructive evaluation (NDE), an application that has been studied extensively [ 58 63 ] . In EMAT, an alternating Lorentz force is generated by the interaction of alternating currents and a static magnetic field. A schematic of EMAT for NDE applic a tions can be seen in Figure 1 1 A . A permanent magnet produces a magnetic field normal to the material surface, while an EMAT circuit induces small eddy currents perpendicular to the surface. The magnetic field and eddy currents interact to produce an alt ernating Lorentz force that displaces the surface , creating surface and bulk shear waves that may be detected with the original or an additional EMAT circuit [ 61 , 64 , 65 ] . Changes in the wave properties may be correlated to defects with which it interacted during propagation , forming the basis for crack det ection and thickness measurements in NDE. Figure 1 1 . Comparison of EMAT technologies. A ) conventional EMAT for non destructive evaluation (NDE) purposes and B ) high power EMAT for materials processing.
21 Recently, magnetic fields of high strength (>5 T) have become r outinely available [ 66 ] , increasing the potential sonic intensity for materials processing. High power EMAT is distinct from established applications of EMAT for NDE in both geometry and the l evel of power supplied. Whereas NDE EMAT produces bulk shear waves at low intensities, high power EMAT induces bulk longitudinal waves (seen in Figure 1 1 B ) with amplitudes high enough to induce cavitation in molten metals [ 55 ] . This difference in wave mode is due to the relative orientations of the static magnetic field and eddy currents, seen i n Figure 1 1. The fact that high power EMAT produces longitudinal waves is of key importance because shear waves require a rigid body through which to propagate [ 67 ] , making them ineffective for liquid processing. High power EMAT combines the benefits of conv entional EMAT (a non contact mechanism ) with the high power of ultrasonic horns (Figure 1 2 ). This combin ation opens a number of avenues t hat were previously unavailable, including processing of high temperature and reactive materials. Figure 1 2 . Diagram of the relative app licability of high power EMAT relative to other sonic technologies. Piezoelect ric sonic transducers are a mature technology for non destructive evaluation (NDE) and materials processing, while EMAT is only currently used as an NDE technology. High power EMAT, discussed in this document, combines the non contact benefits of conventio nal EMAT with the processing ability of ultrasonic horns.
22 MMNC fabrication is a promising application for MAMT and forms the basis of the current studies. In Chapter 2, relevant information on acoustic and magnetic materials processing, MMNC strengthening mechanisms, and MMNC fabrication technologies is presented. Chapter 3 establishes a theoretical framework for acoustic production by MAMT and Chapter 4 offers important considerations when choosing MMNC reinforcement. Chapter 5 contains the methods used i n the current research. Chapters 6 and 7 present experimental results on the effect of MAMT processing on MMNC structure, in terms of particles and microstructure. Finally, Chapters 8 and 9 conclude and discuss future directions for the research. It is fou nd that EMAT is a viable candidate for MMNC fabrication, but special considerations (like crucible choice and particle stability) are required for successful implementation of the technology.
23 CHAPTER 2 BACKGROUND This chapter covers fundamental information on magnetic and acoustic effects as they relate to MMC fabrication, as well as details on specific MMC processing routes and strengthening mechanisms. 2.1 Effect of Magnetic Fields on MMC Processing The presence of a magnetic field during mater ials processing operations can have a dramatic impact on the resulting structure. Materials can interact with a magnetic field in a variety of ways , from magnetic pinning of a conductive liquid to dipole dipole interactions between particles . Of critical i mportance is the type of magnetism exhibited by a material: ferromagnetism, ferrimagnetism, antiferromagnetism, paramagnetism, or diamagnetism [ 68 ] . Ferromagnetic and ferrimagnetic materials exhibit perma nent magnetization below their C urie temperature , and show the strongest interaction wit h magnetic fields. Above their C urie tempe rature , these materials are paramagnetic [ 69 ] . Antiferromagnetic materials have equally opposing magnetic moments with zero total magnetic moment , resu lting in behavior similar to paramagnets. P aramagnetic material s exhibit magnetization proportional to the applied field, while the magnetization of a diamagnetic material is inversely proportional to the applied field. While paramagnetic and diamagnetic m they can exhibit significant magnetic effects at high fields ( usually considered greater than 5 T) [ 70 , 71 ] . There is an additional type of magnetism known as superparamagnetism, in which a n isolated ferromagnetic particle of sufficiently small size and high temperature continuously and spontaneously reverses magnetic . This spo ntaneous polarization
24 leads to observed urement is taken over a sufficiently long time period [ 72 ] . The nomenclatur e of magnetic fields can easily cause confusion . There are two in matter, they are related by the magnetic susceptibility of the material [ 73 ] . The B field is referred to is SI units for B and H field are tesla (T) and amperes per meter (A/m), respectively. For simplicity, the B field will be primarily referenced in this document. Both magnetic fields may be static or alternating with time. The relative intensities of magnetic fields available for materials research and processing vary widely surface magnetic flux density is 25 65 ÂµT and has relatively little imp act on materials processing outside of sensitive electronics [ 69 ] . The strongest permanent magnets, Nd 2 Fe 14 B, saturate to a local magnetic flux density of 1.4 T [ 74 ] , enough to magnetize most ferromagnetic materials and change the behavior of conductive liquids. For higher strength fields, specialized electromagnets consisting of current loops are required. These are split into two types: res istive and superconducting. Resistive electro magnets simply consist of loops of metallic wire through which direct or alternating current is discharged [ 73 ] . High strength resistive magnets require active cooling and reinforced coils. The highest strength steady magnetic fields achieva ble (>50 T) are in Bitter magnets that use conducting plates instead of wire, but require very large continuous currents (>1 MW) for operation [ 75 ] . Superconducting magnets take advantage of zero resistivity materials, consisting of loops of NbTi or Nb 3 Sn cooled to below 10 K by liquid helium [ 66 ] . With zero resistance,
25 these materials can carry large currents without Joule heating, a main limitation of resistive electromagnets. These materials remain superconducting up to 9 T for NbTi and 25 30 T for Nb 3 Sn [ 76 ] . A useful feature of superconducting magnets is they can be persistent mode Once the magnet is energized, it is short circuited with a segment of superconductor, creating a continuous current loop with no resistive losses. Subsequently, no energy in put is required to maintain magnet operation, other than refrigeration for the helium coolant. In this document, all magnetic fields are assumed to be homogeneous. While unexplored here, magnetic field gradients have important additional effects on solute segregation [ 77 , 78 ] , convection [ 79 ] , and particle segregation [ 71 , 80 ] . 2.1.1 Magnetic Alignment of Individual Particles In a field of sufficient strength, a particle may orient by magnetocrystalline and/or the particle with magnetic fie ld lines . This configuration results in a minimization of magnetic energy of the system [ 81 ] . Magnetocrystalline anisotropy arises when a crystal exhibits differing magnetic many hexagonal materials, where the perpendicular c and a axes typically exhi bit different susceptibilities [ 70 ] . In the presence of a magnetic field and assuming a spherical particle, this anisotropy results in a magnetization energy that is dependent on orientation of the particle. This energy can be described by Equation 2 1 , where V is the v ( c a,b ), B 0 0 is the permittivity of vacuum [ 70 ] . This angle dependent energy
26 produces a torque that rotates the crystallite such that the easy axis (the c axis in the case of Mg [ 82 ] ) aligns with the magnetic field. (2 1) Studies have shown anisotropic crystals to align in the presence of a magnetic field under a variety of circumstances. This effect is pronounce d in solidificatio n processing where primary cr y stallites are free to rotate in the melt. A study of the solidification of Mg 9Al 1Zn in varying static field by Li [ 82 ] showed this ef fe ct clearly, and results are reported in Figure 2 1. T w o regions are shown in each micrograph, separated by the white line. Above the white line are grains that were heterogeneously nucleated from a solid/liquid interface, in which texture is not depende nt on magnetic field. Below the white line are equiaxed grains that were free to rotate in the melt prior to being engulfed by the solidifying interface; texture in these grains is highly dependent on magnetic field. This mechanism is also active in non liqui d systems. For instance, cold rolled Ti has been shown to orient to the field direction when recrystallized under a magnetic field [ 83 ] . In this case, individual recrystalliztion nuclei are not reorienting, but rather nuclei of the critical nucleus size more readily than nuclei of other orientations. Another mechanism by which individual particle s may align is magnetic shape [ 84 ] . In an external magnetic field, a set of free poles is created on the surface of the particle, which in turn, induce the internal demagnetizing field. Because the distribution of the free poles is dependent on shape of the particle, the internal demagnetizing field and its energy are shape and orientation dependent. The demagnetizing field is
27 proportional to a quantity called the demagnetizing factor by Equation 2 2 , where H d is the demagne tizing field, N is the demagnetization factor (a tensor quantity), and M is the magnetization of the particle [ 84 ] . Figure 2 1 . Influence of magnetic field on the solidification texture of AZ91D [ 82 ] (Reprinted with permis sion from Springer) . (2 2) The demagnetization factor of a general shape is n on trivial to calculate, but is relatively simple for the case of ellipsoids. The solution for these shapes was presented by Maxwell in A Treatise on Electricity a nd Magnetism [ 85 ] , but appears in a more convenient form elsewhere [ 69 ] . The magnetostatic energy density of the demagnetizing field in a prolate spheroid is described by Equations 2 3 [ 84 ] and 2 4 [ 69 ] , in which V is the volume, Âµ 0 is the permeability of free space, N x,y is the between the long axis and the field, M is the magnetization of the particle, and m is the
28 ratio of the long axis of the prolate spheroid to the short axis. While most particles are not in the shape of ellipsoids, the prolate spheroid case is a good approximation for particles with rod morphology [ 86 ] . (2 3) (2 4) For small particles, these forces can be similar to the thermal disordering energy, of the same order of magnitude as k b T/2, where k b is the Boltzmann constant, and T is the absolute temperature [ 82 ] . If the thermal disor dering energy is orders of magni tude higher than the magnetizat ion energy, one would expect the orientation to be mostly independent of field direction. 2.1.2 Particle Particle Interactions In addition to effects on individual particles, a magnetic field can influence how particles interact with each other. Mobile mag netized particles exhibit dipole dipole interactions, and can reorder themselves much like macro scale magnets [ 87 ] . The energy of the magnetic dipole interaction is described by Equation 2 5 , where Âµ 0 is the permeability of vacuum, m a and m b are the magnet ic dipoles, and r and r are the vector and distance between the two dipoles, respectively [ 88 ] . This force is usually only significant for particles greater than 1Âµm. These magnetized particles frequently align in strings, but can also form more co mplex arrang e ments [ 88 ] . It should be noted that superparamagnetic particles will not spontaneously reverse polarization when in the vacinity of other superparamagnetic particles, and will therefore behave as standard ferromagnets [ 72 ] .
29 (2 5) 2.1.3 Magnetohydrodynamic Effects Magnetic fields can change the behavior of conductive fluids dramatically . The study of this phenomenon is called magnetohydrodynamics (MHD) [ 89 91 ] . When f ree electrons in the conductive melt cross field lines , they induce local eddy currents that in turn restrict further movement [ 90 ] . This phenomenon results in c onductive fluids being may travel along a field line unhindered, but is restricted from crossing field lines [ 89 ] . This effect is most dramatically seen in astrophysical phenomena such as coronal loops, in which conductive plasma travels along protruding fi eld lines on the sun, but is also important for metallic melts in a magnetic field. The most prevalent effect for metallic melts in a magnetic field is an increase in apparent melt viscosity [ 92 ] . This results in reduced bulk motion of the conductive fluid, advection, often changing the solidification behavior of metals significantly [ 93 ] . While b ulk fluid motion is commonly thought of as convection, convection is the combination of advection (bulk transport of material) and diffusion (transport by individual units). When conside ring MHD effects, advection is more relevant . In determining the effect of a magnetic field on a conductive fluid, the Hartmann number is an important quantity. Similar to Reynolds number, Hartmann number is a dimensionless quantity that describes the relative importance of one mechanism vs. another [ 94 ] . Whereas Reynolds number des cribes the ratio between inertial forces and viscous forces, the Hartmann number describes the ratio between electromagnetic and viscous forces. Functio nally, it indicates whether MHD effects must be considered in a
30 given situation. The Hartmann number is calculated by Equation 2 6 , where Ha is the Hartmann number, B is the magnetic flux density, r i [ 95 ] . Relative dimens ion refers to the distance over whi ch fluid motion takes place, e.g . the radius of a casting for the case of melt advection during solidification . If the Hartmann number is much lower than unity, the system may be described accurately by standard fluid mec hanics without considering MHD . Conversely, if the Hartmann number is greater than unity, the T) are sufficient to suppress bulk melt advection [ 96 ] . (2 6) While macro scale bulk convection is highly damped in conductive melts under a magnetic field, momentum transport on smaller length scales is still present (due to the relative dimension being smaller) , but can be affected by the magnetic field. For instance, in the presence of a magnetic field, vortices will elongate substantially in the direction of magnetic field lines [ 97 ] . Since the eddy is much longer in the direction parallel to the field than perpendicular to it, most of the local bulk motion occurs in the field direction. 2.1.4 Magnetohydro dynamic Particle Interactions Before considering the effect of magnetic fields on particles in a conductive melt, it is important to understand how particles interact with a fluid under normal conditions. The primary forces acting on a particle in a fluid are buoyancy and drag. The force due to buoyancy , F g , is shown in Equation 2 7 p ,
31 f , gravitational acceleration g, and particle radius R [ 98 ] . When moving conditions. The magnitude of this force is given by Equation 2 8 , where F d is the he dynamic viscosity, R is the particle radius, and s is the settling velocity [ 98 ] . When F g and F d are equal, the particle is at terminal velocity s . Because F g scales by R 3 and F d scales by R, the settling velocity scales quickly with particle size as a function of R 2 . Functionally, this means that for a given time frame, there is a critical size above which particles will settle and below which pa rticles will remain suspended in the fluid. These considerations are for particles m oving through a fluid, so they do not apply to bulk transport of a particle containing fluid. (2 7) (2 8) Th e situation is altered when the fluid is conductive and a magnetic field is present. When a particle moves through a metallic melt, it displaces the melt, a situation subject to MHD effects when in the presence of a magnetic field [ 99 ] . The current loops formed by a moving particle are shown schematically in Figure 2 2 . For the case of a particle moving vertically in a vertical field, the horizontal component of fluid motion at the top and bottom of the particle induce the currents. Once generated, th ese currents produce a Lorentz [ 100 ] . As opposed greater than ~10 Âµm [ 99 ] . Once again, the Hartmann number, introduced in the previous section, is useful for discerning whether fluid dynamics or MHD is more descriptive of the particle motion. In
32 this case, the relative dimension is the particle radius. If the fi eld is parallel to particle motion, the drag force can be amended to Equation 2 9 , where F d force (Equation 2 8 ) and Ha is the Hartmann number (Equation 2 6 ) [ 100 ] . O(Ha) magnetic field were perpendicular to the flow direction, the drag force will be lower than that predicted in Equation 2 9 , as only a fraction o f the particle surface would force liquid to cross field lines. (2 9) Figure 2 2 . Field lines and e ddy currents generated by a particle moving in conductive fluid while in a magnetic field . Adapted from [ 100 ] . 2.1.5 Magnetic Effects During Solidification Magnetic fields influence cast microstructures in a number of ways. As described in Section 2.1.3 , magnetohydrodynamic effects suppress melt advection. T his can reduce macrosegregation in systems with sufficiently low diffusion [ 93 ] . Magnetic fields also tend to increase the rate of homogeneous nucleation by lowering th e free energy of
33 crystallites and increasing the effective supercooling of the liquid [ 101 ] . Additionally, particle engulfment by a solid/liquid interface can be enhanced by magnetic fields, depe nding on whether MHD effects are present (determin ed by Hartmann number ) [ 102 ] . 2.2 Effect of Acoustic Fields on MMC Processing Sonic treatment is used in num erous scientific applications and m ost basically involves the production a nd propagation of mechanical waves through a material. A common use is in non destructive evaluation of mechanical components, in which scattering of sonic waves from defects is measured [ 103 , 104 ] . In materials processing applications, high intensity fields (usually above 100 W /cm 2 ) are used [ 55 ] . For sound waves, frequency is usually split into three regimes based on the range of human perception: infrasound (<20 Hz), audible sound (20 Hz 20 kHz), and ultrasound (>20 kHz) [ 55 ] . In sonic processing of materials, frequency usually ranges from 1 kHz to 100 kHz [ 55 ] , so the distinction between sound and ultrasound is largely for any sound wave s propagating through a medium and do not specify a frequency range. 2.2.1 Pri nciples of Sound Waves Sound waves are the result of propagating disturbances in the equilibrium positio n of atoms in a material. If an atom is displaced from its equilibrium position , electrostatic interactions displace atoms further along the propagation direction, transferring energy. There are two basic types of sound waves, longitudinal (also known as compression or P waves) and transverse waves (also known as shear or S waves) [ 67 ] . The difference between these modes is in which direction the material is disturbed
34 relative to the propagation direction of the wave. In longitudinal waves, atoms are displaced in the direction of wave propagation, while in transverse waves, atoms are displaced perpendicularly to the propagation direction. The difference is shown schematically in Figure 2 3 . Sound waves in liquids and gases are primarily longitudinal, consisting of alternating regions of compression and rarefaction (lower density of components) [ 105 ] . Solids have rigidity, and thus can support both lon gitudinal and transverse waves [ 105 ] . A wave may be described by three quantities: frequency ( f ), amplitude (A), and from its equilibrium position. For longitudinal waves, amplitude can also be the pressure variation between compression and rarefaction regions of t he wave. Speed and wavelength are also important, and depend on material properties. The speed of sound (c) can be calculated based on eq u ations 2 10, 2 11, or 2 12 , depending on whether the medium is a solid, liquid, or gas, respectively. In these express modulus, ad is the adiabatic compressibility, P 0 is p /c v , the ratio of specific heats at constant pressure and volume) [ 55 ] . The wavelength is a function of s peed and frequency in Equation 2 13 . Two more variables are especially important in acoustic processing, the maximum acoustic pressure [Pa], and the acoustic intensity [W/cm 2 ], given by Equations 2 14 and 2 15 [ 55 ] , where A 0 is the maximum particle displacement. Acoustic pressure and i ntensity are necessary to understand whether the cavitation threshold has been reached in a fluid [ 106 ] , a topic discussed in the next section .
35 Figure 2 3 . Two princip le modes of wave propagation, A ) lo ngitudinal and B ) transverse. A dapted from [ 107 ] . (2 10) (2 11) (2 12) (2 13) (2 14) (2 15)
36 2.2.2 Cavitation In liquids, above a material dependent critical acou stic pressure, rarefaction in longitudinal sound waves becomes strong enough to overcome the binding energy of the fluid. This manifests by the rapid growth and collapse of vacuum bubbles in the liquid, known as cavitation [ 108 ] . The presence of cavitation bubbles can dramatically affect physical processes in the liquid and during solidification [ 109 ] . As cavitation bubbles collapse, the local area experiences extreme pressure and temperature (low estimates are 5000 K and 100 atm [ 110 ] or rea ction sites for numerous mechanisms, forming the basis for sonochemistry [ 111 , 112 ] . The spontaneous for mation of cavitation can occur homogeneously, but in practice, most cavitation occurs heterogeneously a t small gas pockets or interfaces [ 113 ] . In the preparation of MMCs , cavitation is employed as a method of dispersing nanoparticle agglomerates [ 28 ] . H igh intensity acoustic waves are most commonly produced by an ultrasonic transducer [ 55 ] , which consists of two parts: an electromechanical transducer that transforms electrical power to mechanical vibrations, and a waveguide horn that increases the vibration amplitude [ 114 ] . In treating molten metals, the horn is placed directly into a melt to transfer sonic power. Before nanoparticles are added to an alloy melt, they exist as complex agglomerations with regions of a ir between the particles. Metallic melts often poorly wet ceramic particles [ 20 ] , so this air in the particle agglomerations persists in the melt. As high power sonic energy is applied to the melt, the air pockets between particles act as heterogeneous nuclei for cavitation , which in turn provides energy for particles to separate . This
37 targeted cavitation is thought to be the primary mechanism by which sonication disperses nano particles [ 44 , 46 ] . Another factor in cavitation is microjet formation, in which a cavitation bubble collapses asymmetrically near an interface, causing a jet of liquid to be driven at high speed into the surface [ 108 , 115 ] . This jet can reach hundreds of meters per second and can contribute significantly to damage of the solid material [ 116 ] . This mechanism may be responsible for observed improvements in wettability of metallic liquids on ceramics , another beneficial acoustic effect for particle dispersion [ 47 ] . 2.3 Electromagnetic Vibration The comb ined effects of acoustic and magn etic processing of liquid melts occurs in a technology called Electromagnetic Vibration (EMV) [ 117 , 118 ] . The geometry of Electromagneti c Vibration is shown in Figure 2 4 . This technique relies on similar physics to high power EMAT, but differs in important respects. In EMV, m olten metal is contained within an elongated insulating c ontainter with graphite electrodes at either end. The entire structure is in a transverse static magnetic field. When an alternating current is driven through the melt, it interacts with the static field to produce time dependent displacement and acoustic waves. The acoustic pressure P(t) in EMV can be predicted as Equation 2 16, where B 0 is the static field, I is the current, L and a are the [ 119 ] . (2 16) EMV is similar to the melt vibration mode in EMAT (discussed in Section 3. 2 ), but unlike EM AT, which is dependent on skin depth, the acoustic pressure in EMV is relatively constant throughout the melt. Skin depth effects are avoided in EMV by
38 utilizing relatively low alternating current frequencies, usually below 100 Hz [ 119 ] (Skin depth is discu ssed in more detail in Section 3.2 ). While EMAT operates with a relatively small curren t and large static field (30 70 A induction current, 20 T), EMV can operate with large currents and a small field (3500 A and 0.7 T) [ 119 ] . However, EMV may also be conducted at high fields in superconducting magnets [ 120 ] . A disadvantage of EMV is that, unlike EMAT, electrodes must be in contact with the melt. With respect to microstructural effects in Mg, EMV has been demonstrated to reduce grain size [ 121 ] and alter solidification texture [ 122 ] . Thus far, EMV has not been evaluated as a nanoparticle dispersion technique. Figure 2 4. Overview of Electromagnetic Vibrati on (EMV) adapted from [ 118 ] . Contained in an insulating ceramic, graphite electrodes transmit alternating current (J(t)) to a melt. An external magnetic field (B o ) interacts with this current by the Lorentz force (F(t)) to cause a time dependent displacement (U(t)) and pressure (P(t )) in the liquid. 2.4 Induction Heating of Materials Induction heating is the application of an alternating magnetic field to a material with the goal of adding heat to the part. This may be accomplished by three principle mechanisms, eddy current (otherwi se known as Joule, ohmic, or resistive) heating, hysteresis losses, and residual losses. Joule heating is the release of heat by the passage of electric current through a resistor. The energy dissipated by a direct current through a conductor follows Equat ion 2 17 , where P is heat evolved per time [W], I is [ 73 ] . For alternating
39 current, th e average power can be calculated with the root mean square (RMS) value for current. (2 17) Hysteresis losses are caused by continued irreversible magnetization of a ferro or ferrimagnetic material in an alternating magnetic field [ 123 , 124 ] . In an applied field, magnetic domains can reorient to a minimum energy configuration and domain walls can move, both of which dissipate energy as heat. Residual losses constitute heating that cannot be accounted for by Joule or hysteresis losses. The mechanics of both hysteresis and residual loss are quite involved and not important for this document, as no fe rromagnetic materials are investigated. More information on both mechanisms may be found in [ 125 128 ] 2.5 Metal Matrix Nanocomposites MMNCs are similar to more traditional MMC materials, but have particle sizes smaller than 100 nm, compared to >1 Âµm for MMCs [ 23 ] . This reduction in particle size has been shown to broadly improve mechanical propertie s like strength and ductility, compared to MMCs [ 31 , 129 , 13 0 ] . To effectively produce MMNCs, strengthening mechanisms and fabrication processes must be understood, both of which will be discussed. 2.5.1 Strengthening Mechanisms in MMN Cs MMNCs are promising materials for structural applications because of their c ombination of strength and ductility [ 23 ] . Nanoparticle reinforcement can contribute to the strength of a material in a variety of ways. The mechanisms discussed here are Orowan strengthening , load transfer, thermal misfit, and Hall Petch strengthening.
40 Orowan strengthening occurs when a small impenetrable particle impedes dislocation motion . This dislocation m ust bow around the particle, leaving a dislocation loop around the particle once it has passed [ 131 133 ] . The strength contribution by Orowa n l ooping is given in Equation 2 18 , where M is the Taylor factor, G is the shear modulus, b is the Burg interparticle distance. For Mg, M=6.5 [ 134 ] , G=17.3 GPa [ 9 ] , b =0.321 nm [ 34 ] , and [ 9 ] . The interparticle distance may be ca lculated according to Equation 2 19 , where r is the av erage particle size and V f is the volume fraction [ 135 ] . This mechanism is commonly cited as a primary contributor to strength in MMNCs [ 130 , 136 , 137 ] . (2 18 ) (2 19) Load transfer to particles can be caused by both differences in elastic modulus between particle and matrix and the shape of the particle [ 138 , 139 ] . In MMCs, the particle is stiffer than the matrix, so it carries more of the applied stress, leading to less stress in the matrix and greater global strength. Th is phenomenon has been modeled by a modified shear lag mecha nism, described by Equation 2 20 y is the ym is the unmodified yield strength, L is the length of the particle perpendicular to the applied stress, t is the length of the particle parallel to the applied stress, A is the particle aspect ratio, and V f is the particle volume fraction [ 140 , 141 ] . For equiaxed particles, Equati on 2 20 reduces to Equation 2 21 , which is only a
41 function of volume fraction [ 142 ] . It can be seen that for equiaxed particles, the strength improvement by this mechanism is relatively insignificant. (2 20) (2 21) Relative differences in coefficient of thermal expansion (CTE) are another source of strengthening in composites [ 139 , 143 ] . As a composite cools from the processing temperature, ceramic particles contract less than the hole they occupy in the metallic matr ix, leading to misfit strain [ 144 , 145 ] . This misfit strain can produce an increase in dislocation de nsity [ 143 , 146 ] according to Equation 2 22 T is the induced dislocation density, B is a constant (12 for f is the volume fraction, [ 135 ] . Dislocation generation by this mechanism shows a dominant size effect, meaning that below a certain particle size (usually ~1Âµm) these stresses do not produce dislocations as expected [ 144 ] . This is due to low dislocation density and source availability at short length scales. The strength change associated with an increase in dislocation density can be estimated with Equation 2 23 where Âµ is the Taylor factor (6.5 for Mg), and G is the shear modulus [ 135 ] . S ince this mechanism increases the dislocation density of the material , overall elongation will be reduced . (2 22) (2 23)
42 Hall Petch strengthening, while not due to a direct interaction of particles and matrix, is a result of many nanoparticle incorporation methods. Hall Petch strengthening is in increase in yield strength due to a reduction of grain size [ 134 , 147 ] . The primarily cited reason for the increase in st rength is that dislocations pile up less in smaller grains, increasing the stress necessary for transgranular motion [ 148 ] . The Ha ll Pet ch relationship in Equation 2 24 gives the increase in strength associated with grain size reduction, where k is the Hall Petch slope (0.28 MNm 3/2 for Mg [ 35 ] ) and d g is the average grain diameter. Grain size reduction commonly accompanies nanoparticle reinforcement, depending on the fabrication method, and has been cited as a primary strengthening component [ 36 ] . The equilibrium grain size at a given dispersion of particles was described by Smith in 1948 [ 149 ] and the proportio nality is given by Equation 2 25 , where d g is the grain size, d p is the particle size, and f is the volume fraction of particles. It can be seen that either reducing particle size or increasing volume fraction will reduce the equilibrium grain size. This relationship assumes a homogeneous dispersion of particles. (2 24) (2 25) While strengthening mechanisms are established, the effect of nanoparticle reinforcement on other properties is not well understood, especially ductility. For example, one study [ 146 ] found elongation decrease d slightly in Mg reinforced with the addition of 100 nm Al 2 O 3 while another study [ 150 ] found that elongation increased by nearly 100 % with similar reinforcement under different processing conditions. The
43 fabrication method an d specific processing route appear to correlate strongly to the duct ility , since the resulting dispersion and grain structure are all highly variable. This is complicated by difficulties in quantifying nanoparticle spatial distribution. Consequently, established structure property relationships for MMCs with large reinforc eme nt are not necessarily applicable to nanoparticle reinforced material. 2.5.2 Particle Incorporation Methods The primary difficulty in producing MMNCs is dispersing particles evenly in the matrix, since particles tend to agglomerate because of poor wetta bility and high specific surface areas [ 23 ] . Several fabrication methods have been used prevent this from occuring and will be summarized, along with their relative strengths and weaknesses. Powder Metallurgy (PM) was one of the first method s investigated to disperse ceramic particles in a metal [ 17 ] . PM begins by mechanical allo ying, in which two powders (metal and particulate reinforcement) and media (usually steel or carbide bearings) are mixed in a ball mill [ 151 ] . This refine s the powder and integrates the two species together by repeated cold welding [ 17 , 152 ] . Once mechanical allo ying is complete, the powder is either separately pressed and sintered or compressed in a hot isostatic press (HIP) to form a monolithic material [ 13 ] . PM is a successful technique largely because many materials can be mixed with little reg ard to interfacial interactions between the matrix and particle. Since it is a solid state and relatively low temperature process, many chemical reactions that are thermodynamically favorable do not proceed because of limited kinetics [ 13 ] . P ressing is required, so the shape of the formed part is a limited . Another drawback is the potential for residual porosity [ 153 ] . Spray forming is a modificat ion of powder metallurgy that warrants separate consideration [ 41 , 143 , 154 , 155 ] . A typical spray forming process for composite
44 production involve mixing a metallic melt with a reinforcing particle just prior to being forced through a nozzle at high velocity. The molten metal droplets solidify around the particles upon impact with the piece being formed. Spray forming has many of the same advantages of typical PM processes, including limited interfacial interactions (the melt and particles are only in contact for a short time) and very high cooling rates that result in small grain sizes [ 41 ] . Unfortunately, this process exhibits inherently limited scalability. Also, a seco ndary forming operation is necessary to reduce residual porosity, making spray forming unsuitable for complex shapes . Mechanical stirring consists of simply inserting a stirring instrument into a melt containing particles prior to solidification [ 156 ] . While straightforward and industrially scalable, this technology is only useful in the fabrication of composites with reinforcements larger than 10Âµm . Below this size, particle pushing at the solid/liquid interface causes macro scale particle segregation and shear forces are not strong enough to separate agglomerates , making this process unsuitabl e for nanocomposite fabrication [ 18 ] . Friction stir processing (FSP) is primarily used as an alternative to welding to intimately join two pieces of metal (usually called friction stir welding) [ 42 ] . In application to composite processing, FSP is not a forming process, but a dispersion process. In a material in which particles are agglomerated in the microstructure, FSP induces a significant amount of high temperature deformation that breaks up agglomerations [ 157 159 ] . This technique has the ability to produce material with excellent properties by incorporating high volume fractions of particles (>20 v ol.%) evenly in a resulting nano -
45 grained material [ 27 , 160 ] . FSP has an extremely low yield of material and is only operable on material with low thickness. In situ particle reinforcement can be thought of as a mix of standard ex situ particle reinforcement and precipitation. In in situ reinforcement processes, the reinforcing particle is formed in the liquid pri or to solidification [ 43 , 161 163 ] . This process can produce extremely fine particles (<20 nm) that do not requir e a dispersion method, since they do not begin as an agglomerated powder, though they are subject to gathering in the melt. Because this technique is reaction based, careful consideration of chemistry and kinetics is required [ 43 , 164 ] . Sonic m elt treatment is primarily used for microstructural refinement [ 52 54 ] . This technique requires the insertion of an ultrasonic probe into the melt [ 51 ] . Sonication is also promising for nanoparti cle dispersion [ 46 , 48 , 49 , 165 ] . In this case, particle agglomerations are broken up by ultrasonic cavitation and their wettability with the melt is improved [ 44 ] . This technology is discussed more in Section 2.2 . The next chapter (Chapter 3) discusses another sonic dispersion technology, MAMT, which utilizes high power EMAT to produce MMNCs.
46 CHAPTER 3 FUNDAMENTALS OF MAMT PROCESSING The high power E MAT system at the foundation of MAMT used in the current studies differs significantly from conventional EMAT for non destructive evaluation. In the interest of brevity, High p ower EMAT will be referred to simply as EMAT , unless otherwise specified. EMAT is used to prod uce high intensity acoustic waves in the molten material as part of MAMT to induce structural changes and disperse nanoparticles. Before the experimental investigation can proceed, a theoretical framework should be established on which to draw conclusions. The acoustic production mechanism, geometry, distribution of acoustic pressure, frequency dependence, and calculations of solidification front velocity will be presented. 3.1 Basic Principles of EMAT The EMAT mechanism transforms electromagnetic energy in to vibration s that are used to induce structural changes in a material . This is achieved by coupling alternating induction eddy currents with a perpendicular static magnetic field to produce an alternating displacement . There are two mechanisms by which th is coupling may proceed, magnetostriction and the Lorentz force [ 128 ] . Only ferromagnetic and ferrimagnetic materials experience magnetostriction. The current studies include no ferromagnetic or ferrimagnetic materials , so only generation by the Lore ntz force will be explored here. D etailed descriptions of the magnetostriction me chanism may be found elsewhere [ 166 , 167 ] . Figure 3 1 displays the relative orientations of fields, cur rent, and force in EMAT. A n alternating induction field (produced by an induction coil ) induces horizontal eddy currents at the same frequency in the sample. These currents impart heat to the crucible and the material inside of the crucible by Joule heatin g [ 125 ] . I n the
47 presence of a perpendicular static magnetic field, the eddy currents couple to produce a Lorentz force. The Loren tz force, F, is given in Equation 3 1, where q is the charge, E is the electric field, v is the charge velocity, and B is the magnetic flux density [ 73 ] . There is no electric field active in the system, so Equation 3 1 simplifies to Equation 3 2. Charge velocity is analogous to current, so the Lorentz force is always perpendicular to the magnetic field and current. The geometry of the system is cylindrical (Figure 3 1b) so the vibrations are radial in direction. The current in the sample oscillates at the induction frequency , as does the Lorentz force and corresponding acoustic waves. Figure 3 1 . Over view of the Electrom agnetic Acoustic Transduction A ) mechanism and B ) sample orientation compared to the static magnetic field and induction coil [ 56 ] . (3 1) (3 2)
48 In the current geometry of a liqu id in a cylindrical container, EMAT may proceed by two mechanisms (or vibration modes): (1) using the crucible as a sound source (crucible vibration) or (2) directly vibrating the melt (melt vibration). Which mechanism is most active depends on the depth o f the induction current, which in turn is determined by a phenomenon called the skin effect [ 168 ] . When alternating cur rent travels in a conductor, the current density is highest on the surface because of internally induced current loops that in turn oppose bulk current flow. The current density drops exponentially away from the surface, by the r elation in Equation 3 3 , in which J is the current density [A/m 2 ] at depth d , J s is the surface current density [A/m 2 skin depth [ 125 ] . The s kin depth, the depth from the surface at which the current density has dropped to 1/ e (or ~37%) of the surface val ue, is described in Equation 3 4 , where f 0 is the permeability of free space, r is the relative permeability [ 125 ] . 63% of the current is within the skin depth. Figure 3 2 shows skin depth as a function of fr equency for 304 and 316 stainless steel at 1000 K , the crucible material s in the current studies. (3 3) (3 4) (3 5)
49 Figure 3 2 . Skin depth as a function of alternating current frequ ency in 304 and 316 x10 6 [ 169 ] , Âµ r =1.03 [ 9 ] ). The factor that determines whether the active mode is melt or cruc ible sonication (shown schematically in Figure 3 3) is whether a majority of the induced current is in the crucible or in the melt. This can be determined by calculating the cumulative distribution function of Equation 3 3, given in Equation 3 5, which giv es the fraction of total current within a certain depth. At 10k Hz, the skin depth for 1000 K stainless steel is 5.4 mm. Substituting the crucible thickness (0.5 mm) for d and 5.4 mm into the skin depth in equation 4 5, 8.7% of the current is in the crucibl e. This means that for the current studies, a majority of the induction current vibrates the melt directly. This profile is shown in Figur e 3 4, along with a profile at 5 00 kHz and For the purposes of calculation, it is assumed hereafter that the crucible is infinitesimally thin and all of the current is in the melt.
50 Figure 3 3. Schematic of the effect of skin dep th on vibration mode of EMAT; A) melt vibration and B ) crucible vibration. Figure 3 4. Distribution of eddy currents for two situations, melt vibration seen in the current studies, and a hypothetical crucible vibration mode, obtained by varying frequency and resistivity.
51 3.2 Calculation of Acoustic Pressure To understand how MAMT affects a material, the acoustic pressure must be calculated. Howe ver, before this can be done, the distribution of induced current density in the melt must be determined. First, the total induced current is calculated, based on the relationship between induction coil current I c , number of turns in the coil N c and induct ion current I w in Equation 3 6 [ 125 ] . Next, the surface current density, J s from Equation 3 3, must be determined. Taking the int egral of Equation 3 multiplying by the height of the workpiece (h w ) gives the total current in Equation 3 7. Rearranging in Equation 3 8 gives the surface current density in terms of induction and material parameters. At this point, the s kin depth used is that for the metallic melt, not the crucible. (3 6) (3 7) ( 3 8) The local particle acceleration a due to the Lorentz force is given in Equation 3 9, melt [ 118 ] . Particle acceleration may be related to acoustic pressure p ac by Equation 3 ad 1/2 ad is the melt adiabatic compressibility, and f is the frequency [ 55 ] . Because pressure is directly dependent on the current density, it will decrease away from the edge as a consequence of the skin effect.
52 (3 9) (3 10) The final expression for acoustic pressure, assuming melt sonication, is Equation 3 11, a combination of Equations 3 3, 3 8, 3 9 and 3 10. It can be seen that the pressure is proportional to both the induction current and the static field. The influence of relative permeability is minimal for liquid metals, since they are non ferromagnetic, with Âµ r very close to 1 [ 170 ] . This will change for liquids containing ferromagnetic particles, however. The pressure is inversely proportional to the square root of frequency, so as frequency decreases, pressure increases. Lowering the frequency will not increase the pressure without limit, however. A lower frequency will increase the skin depth, and if the skin depth approaches the radius of the workpiece, induction (and therefore EMAT) becomes much less effective [ 125 ] . The effect of frequency on EMAT is discussed more in depth in the Section 3.4. (3 11) The previous derivation of acoustic pressure assumes melt vibration mode with no crucible. For the other extreme of behavior, in which all induction current is con tained in the crucible, an altern ate derivation of acoustic pressure is presented in Appendix A. 3.3 Propagation Effects The previous model predicts acoustic production but does not account for propagation of sound waves. Since the system is cylindrically symmetric, the intensity profile is distinct from that for traditionally used ultrasonicati ng probes . A model was
53 created to describe this difference based on geometric spreading and is derived in Appendix B . The results are displayed in Figure 3 5. In MA MT, the waves propagate inward from the source of the sound, whereas with horn based sonication, the waves emanate outward, lowering in intensity away from the source. The MAMT profile bears resemblance to convergent cylindrical shock waves in thermonuclea r devices, and in both cases, the intensity increases by 1/r away from the source [ 171 ] . In thi s framework, limited both by the mean free path [ 171 ] and the threshold or homogeneously nucleated cavitation. This analysis of intensity for MAMT assumes a discrete source at the surface, so is most applicable to the crucible vibration mode. Figure 3 5. In tensity distribution based on acoustic propogation. A) MAMT and B ) horn based sonication . The application of propagation to the melt vibration mode, and the resultant delocalized sound production, is to this point uncertain. An estimate of the pressure distribution was made by combining th e two models in Figure 3 6. 3 6 A is the pressure
54 distribution from sound production for Sample 1 (specific details are given in Table 5 1 ), based on Equation 3 11. The effect of propagation is accounted for by assumin g the emitter pressure (at the crucible) is equivalent to the pressure at t Figure 3 6 B ). These models are combined by selecting the largest value of pressure from either production or propagation in Fig ure 3 6 C . It can be seen that the total pressure is lowest mid radius, and high both at the edges and cent er of the sample. To facilitate a more accurate description of pressure distribution, more sophisticated finite element approaches that account for acoustic reflection, absorption, and scattering are needed. Figure 3 6. Estimated pressure distribution f or melt vibration in EMAT, regarding A) acoustic production, B) acoustic propagation, and C ) a combined maximum from both sources.
55 3.4 Frequency Dependence Based on Equation 3 11, frequency has a dominant effect on the acoustic pressure. The previous model did not account for inertia limited displacement that occurs at high frequency, however. At low harmonic loading frequencies , an elastic material deforms proportionally to the applied load. Conversely, at higher frequencies, a phase lag between the load a nd displacement reduces the magnitude of oscillation as inertial forces become more dominant. Both conditions will be calculated and combined in the succeeding sections. 3.4.1 Static Loading First, the static loading limit for the MAMT system will be calc ulated based on the maximum load exerted by the Lorentz force on the liquid in a cylindrical geometry. Because of the skin effect, the maximum force occurs in a thin shell at the surface of the liquid. For simplicity, this shell of liquid with thickness t will be treated as unbounded with displacement dependent on the adiabatic compressibility of the liquid. The volume of this shell can be expressed as: (3 12) h is the height of the shell, and t is the shell thickness. The element is assumed to deform uniformly along the expressed as: (3 13)
56 where changes in circumference, radius, and thickness, respectively. Since height is unaffected by the loading, the strain dependent vol ume of the shell is: (3 14) Subtracting the Equation 3 12 from Equation 3 14, the change in volume is (3 15) The adiabatic compressibility is defined as the volume normalized ratio between change in volume and change in pressure in: (3 16) Rearranging Equation 3 16 and substituting in Equations 3 12 and 3 15 gives: (3 17) Since strains are usually close to zero (i.e. below 10 3 ), the 2 term will be dominated by the 2 term, and can be eliminated. Als o, P will be referred to as , since it represents the internal stress in the liquid. Eliminating 2 from Equation 3 17 and substituting in part of Equation 3 13 gives:
57 (3 18) which can be arranged to give the radial displacement as a function of pressure change, radius, and compressibility in: (3 19) Next, the pressure exerted by the Lorentz force is calculated. Because the current, force, and magnetic field are orthogonal, the Lorentz force density , f , (in N/m 3 ) is given by [ 73 ] : (3 20) where J is the current density (A/m 2 ) in the shell and B is th e static magnetic field strength. Force density can be changed to force by multiplying by the outer circumference C (where the maximum current density exists), the height h, and the shell thickness t. The total force exerted on the shell is thus: (3 21) Additionally, the pressure exerted radially on the shell is: (3 22) Combining Equations 3 21 and 3 22 gives: (3 23) To convert this radial pressure to an internal stress, t he hoop stress equation for thin walled pressure vessels [ 172 ] is used and combined with Equation 3 23:
58 (3 24) Finally, substituting Equation 3 24 into Equation 3 19 gives the static radial displacement as: (3 25) 3.4.2 Inertial Loading At higher frequencies, an estimate of the displacement can be made by assuming that the conduct ing melt has mass, but no stiffness (compressibility of zero). This is the inertial mass limited strain, in which the mass of the material provides the dominant force restraining motion, as opposed to mechanical strength [ 173 ] . The peak acceleration caused by the Lorentz force is: (3 26) where F is force, m is mass, f is force density [N/m 3 Integrating the time dependent acceleration, a(t) = a o (3 27) Integrating the time dependent velocity, v(t) = v o displacement, d(t), (3 28) Therefore the maximum (peak) displacement is given by: (3 29)
59 3.4.3 Application to the Current System Both the static and inertia limited displacement are plotted in Figure 3 7 for the specific case of EM AT in this document: static field = 20 T, resistivity of molten Mg = 2.5e [ 174 ] , density of molten Mg = 1575 kg/m 3 [ 175 ] , adiabatic compressibility of liquid Mg = 4.1e 11 Pa 1 [ 176 ] , height of sample = 80 mm, radius of sample = 18 mm and coil current = 700 A with 10 coil turns. It should be noted that the actual displacement would be lower than predicted for two reasons. First, the model ignores induction current that is absorbed by the crucible, making the current available to displace the liquid smaller. Second and more importantly, the real liquid is bounded, both by the crucible and itself. The trend i n frequency response will be similar to Figure 3 7, however. Figure 3 7. Maximum radial displacement for static and inertia limited cases of vibration, as a function of frequency. An approximate transition between the two is also shown.
60 3.5 Solidificat ion Velocity The velocity of a solid/liquid interface can have an effect on microstructure and how particles are distributed in a metallic matrix [ 177 , 178 ] . To calculate how the velocity may change as a function of radial position, two model s were employed, which assume either infinite or finite thermal conductivity. Before models are chosen, however , the theoretical framework must be described. Solidification may be understood in terms of heat transfer. During solidification of a pure metal in a crucible, heat is removed from the exterior crucible wall, lowering the temperature of the crucible/liquid meta l system until the metal is at its melting point. If more heat is removed, solid metal will nucleate on the crucible wall, transferring its heat of fusion to the crucible. Further removal of heat will move the solid/liquid boundary inward, until the materi al is completely solid. It should be noted that this process is more complicated for alloys with melting ranges. First the problem will be solved assuming infinite thermal conductivity, and then taking finite thermal conductivity it into account. The simp lified geometry most similar to EMAT is constant heat flux at the exterior wall of an inward solidifying cylinder. Constant heat flux is appropriate because the gas mixture with which the crucible is quenched is at a much lower temperature and a high flow rate, meaning heat conduction out of the crucible will be relatively constant. The system is modeled as an infinite cylinder due to symmetry. This approximation will make the calculations less accurate for material near the top or bottom of the final sampl e. 3.5.1 Infinite Thermal Conductivity The geometry of the system plays an important role in determining solidification rate. In a cylinder, as the solidification progresses toward the center, the solidification front becomes geometrically smaller, which w ould tend to accelerate the front velocity. If
61 one assumes infinite thermal conductivity in the material already solidified, then the solidification velocity is only dependen t on the volume heat of fusion H [J/m 3 ], the heat flux at the surface of the cruci ble Q [W/m 2 ], and the radius of the cylinder a . The volume of a shell material from radius r i to r i 1 is: (3 30) The energy to solidify each shell is: (3 31) Dividing Equation 3 31 by time t gives: (3 32) The quenching power (P) and heat flux at the surface are related by: (3 33) Because the material is solidifying inward, the distance solidified d is equivalent to r i r i 1 . The solidification velocity is thus: (3 34) Substituting in a rearranged Equation 3 32 and Equation 3 30, Equation 3 34 becomes: (3 35) Finally, substituting Equation 3 33 into Equa tion 3 35 gives the final expression:
62 (3 36) This equation describes how the solidification velocity changes as a function of radial placement. The variables in the current experimental se tup are Q=13 W/cm 2 (estimated by the total solidification time of 40 seconds, total latent heat of 23.5 kJ, and crucible area of 45.2 cm 2 ), C=577.6 J/cm 3 for Mg [ 179 ] , and a =1.8 cm. The results of the model are plotted in Figure 3 8. Based only on this model, the so lidification velocity 3.5.2 Stefan Problem As solidification progresses the front becomes further removed from the heat sink, which tends to slow solidification. This is a complex situation to model, sin ce the heat equation must be solved in a framework in which one of the boundaries is moving with time. The mathematical formulation is called a moving boundary problem or Stefan problem [ 180 ] . Th e S tefan problem has been so lved for a number of geometries including inward solidification of an infinite cylinder with constant heat flux , the situation most similar to MAMT . A solution to this condition was presented by Gammon in 1996 [ 181 ] . An important quantity in these problems is the dimensionless Stefan number, which gives the ratio between heat conduction and latent heat in the system. In the current mo del, this is given in Equation 3 37 H is the latent heat of fusion, K is the thermal conductivity of the solid, C is the molar heat capacity, and a is the cylinder radius [ 181 ] . For Mg in a crucible 36 mm in diameter (L=8480 J/mol [ 182 ] , K=124 W/m*K [ 183 ] , C=32.5 J/mol*K [ 183 ] , Q=13 W/cm 2 ) the Stefan number is 14, meaning the solution by Gammon may be utilized (it is applicable at Stefan number >10 [ 181 ] ). Next, the time -
63 [ 181 ] fraction s of the solid liquid boundary (s=(1 r)/a, or the fraction of radiu s away from the heat sink) in Equation 3 39. Combining Equations 3 38 and 3 39, the position of the solid liquid boundary as a function of time and the position can be calculated. The results are shown in Figure 3 8. It can be seen that the Gammon model an d the previous model are similar near the heat sink, but diverge as the solid liquid boundary progresses toward the center. (3 37) (3 38) (3 39) Figure 3 8. Solidification velocity as a function of inverse radi us in the EMAT system (radius=18 mm) by two models. The models are identical at the heat sink (the exterior of the cylinder), as expected, as latent heat is quickly removed from the solid liquid interface. As the
64 solidification front progresses inward, the Stefan model by Gammon predicts a slowing of the solidification front, since heat must travel through previously solidified material to 410 Âµm/s at the crucible wall and appr oaching the center of the crucible, respectively. The reduction in front velocity near the center is an unphysical property of the solution caused by the converging interface and is a limitation of the model [ 181 ] ; the true velocit y would continue to increase toward the center. The front velocities predicted by these models are relatively high, compared to many castings [ 178 ] , and most p articles would be engulfed by the front [ 184 ] .
65 CHAPTER 4 MATERIALS SELECTION AND DESIGN This chapter highlights the design consideratio ns for producing Mg MMnCs by melt processes. Here, these principles are applied to fabrication by EMAT, but they are also applicable other sonic dispersion processes. The first consideration is particle stability in molten Mg, as reactions and reaction pro ducts can dramatically change the resulting composite structure. The second consideration is of how particle reinforcement will change the properties of the final composite. For this, particle size, volume fraction, thermal expansion, modulus, and dispers ion homogeneity are considered. A common aim is to increase strength, but composite reinforcement has been found to improve other properties like toughness, ductility, and thermal conductivity [ 17 , 23 , 30 ] . Besides these theoretical matters, the realities of particle availability and quality are a third conside ration. Finally, particle chemistries for the current studies are chosen. 4.1 Particle Thermodynamic Stability One of the primary concerns for ex situ reinforcement is the thermodynamic stability of the particle in the matrix, since reactions can result in unintended products in final structure [ 17 , 38 ] . Particle matrix reactivity has been found to benefit inter facial bonding in some circumstances [ 185 , 186 ] , but is difficult to control and system dependent [ 187 , 188 ] , thus making it disadvantageous for studying particle dispersion in a general system. Because of their ve ry high interfacial density, nanoparticles are especially subject to reactivity effects. Additionally, the high reactivity of Mg makes particle degradation more likely [ 185 ] . For the current studies, the particle must be thermodynamically stable in molten Mg at 700Â°C .
66 The relative stability of one compound over another can be p redicted by comparing their free energies of formation, shown in Equation 4 [ 182 ] . Evaluating the stability of TiO 2 in Mg is a convenient example, since there exist no Mg Ti reactions [ 189 ] . Thus, the potential for reaction is only dependent on the relative stabilities of TiO 2 and MgO per mol of the ion being exchanged. The free energies of formation of TiO 2 and MgO are 427 [ 190 ] and 496 [ 191 ] kJ/(mol oxygen ) at 700Â°C, respectively. MgO has a lower free energy of formation, meaning Mg(l) will react with TiO 2 to form MgO. Thus, TiO 2 is an unsuitable particle composition for Mg composites from the standpoint of stability. (4 1) A convenient way to evaluate the relative thermodynamic stability of several materials concurrently is the Ellingham diagram, which gives the relative thermodynamic stability of compounds with respect to a mutual anion [ 192 ] . Commonly, this is in terms of oxides, as the relative reduction energies of metal oxides are well known a nd easily compared. An Ellingham diagram (Figure 4 1 ) shows the relative free energy of formation of MgO and all oxides more stable than MgO [ 190 , 191 ] . Upon inspect ion, only rare earth oxides (and calcium oxide) have lower free energies of formation than MgO, meaning they will be thermodynamically stable as reinforcement.
67 Figure 4 1 . Ellingham diagram of MgO and oxides more stable than MgO [ 190 , 191 ] . 4.2 Mechanical Effects of Particles Melt fabrication of ex situ part icle reinforced metals is useful from a materials selection perspective, because it allows for direct selection of the mechanical interaction between the particle and the matrix. From a mechanical perspective, the most important parameters are relative coeffic modulus [ 135 , 143 , 146 ] . The ceramic particle s commonly have a smaller CTE and higher modulus than the matrix. Upon cooling from the melt, the relative CTE creates a hydrostatic stress in the particle and a symm etric triaxial stress state that lessens in intensity away from the particle [ 144 ] . This stress can nucleate dislocations, effectively work harden ing the material [ 143 , 146 ] , as discussed minus room temperature). The elastic modulus is an indication of how stiff the particle is matrix deforms. This causes high stresses locall y and increases the overall composite
68 modulus [ 193 ] . All of the strengthening mechanisms discussed in Section 2.5.1 are dependent on the volume fraction of reinforcement, since a higher density of particles will enhance the density and overall scale of composite effects. Particle size affects composite properties mostly as a consequence of num ber density (number of particles/volume). For instance, if material A is reinforced with 1 vol.% 1 Âµm particles and material B is reinforced with 1 vol.% 100 nm particles, material B has a number density 1000 times that of material A. The combined effects volume fraction and particle size are demonstrated by a model of yield strength (an analytical combination of Orowan strengthening, residual dislocations, and load transfer) of Al 2 O 3 reinforced Mg by Zhang [ 33 ] in Figure 4 2. Figure 4 2. Modeled yield strength of Mg reinforced with varying sizes and volume fractions of Al 2 O 3 particles [ 33 ] (Reprinted with permission from Pergamon) . To maximize strength, the largest volume fraction of the smallest nanoparticles possible should be used. Besides number density, small particle sizes can change
69 by which small volumes have higher apparent yield strengths than larger volumes. This is primarily due to decreased dislocation availability at smaller volumes [ 144 , 194 ] . These induced higher localized stresses may activate deformation modes that are normally unavailable in the bulk material, such as slip in Mg [ 195 , 196 ] . For sonic processing of MMC , particle chemistry is limited by the thermodynamic stability, as discussed in the previous section. For this reason, rare e arth oxides are the primary choice for reinforcement. The rare earth oxides occupy a relatively narrow span of properties. Elastic modulus ranges from 140 200 GPa [ 197 ] and linear CTE ranges from 6Ã—10 6 10Ã—10 6 [ 198 ] (CTE Mg CTE RE oxide nly 21% across the range of RE oxides. Consequently, the properties of the composites formed of Mg and rare earth oxides will be primarily determined by the size and volume fraction of particles. Particles are most commonly fabricated as spheres, but a ch ange in particle morphology can produce additional effects. Rods of varying chemistry may be available (Dy 2 O 3 rods and Er 2 O 3 spheres were utilized in the current study). The most extreme particles, in terms of aspect ratio, are carbon nanotubes, which may have aspect ratios of greater than 1000 [ 199 , 200 ] . In the case of non spherical particles, averag e particle orientation becomes an important factor in material properties. For instance, in textured Mg, rods aligned with the c axis of the HCP crystal would create a much stronger material than rods aligned with the a axis, because they would block basal dislocation motion more effectively. This reasoning is similar to the relationship of strength to prismatic vs. basal precipitates in Mg alloys [ 11 ] .
70 The effect of p articles on ductility is not as well understood as their effect on strength. However, it is generally understood that the additi on of nanoparticles can reduce the grain size and consequently improve ductility [ 36 ] . Of course, all of these considerations are predicated on the ability to fabricate composites with a homogeneous dispersion of particles. If particles are agglomerated in the matrix, they will act as cr ack initiation sites, increasing the likelihood of brittle fracture [ 39 ] . 4.3 Particle Availability and Reliability Successful application of the considerations in t he Sections 4.1 and 4.2 is dependent on the availability of particles with which to reinforce a metal. Additionally, particle quality is especially important for nanoparticles. Rare earth oxide nanoparticles are commonly produced by flame spray pyrolysis [ 201 , 202 ] , and may not be of high quality (i.e. not monodisperse spheres). The calculation of average parti cle size is typically same specific surface area of a 100nm sphere. Thus, it is prudent to evaluat e the particle size distribution and morphology of particles prior to incorporation. This effect is seen in the current studies and explored more in Section 6.1 . 4.4 Current Methodology Dy 2 O 3 and Er 2 O 3 were used as reinforcement in the current research. Th ese were chosen primarily for their thermodynamic stability and size availability . Dy 2 O 3 was also chosen because it was available in rod morphology, which was of interest to investigate magnetic alignment. A nother particle was investigated to provide dispa rate values of elastic modulus and CTE , with the goal of investigating the effect of these variables on mechanical properties . To facilitate this se lection, an Ashby plot (Figure 4 -
71 3 ) of populated with several candidate material s . Based values, Dy 2 O 3 and Er 2 O 3 would be expected to induce similar changes in the deformation behavior as many typical Mg reinforcements (such as SiC and Al 2 O 3 [ 130 ] ). Figure 4 3 . common Mg reinforcement particle chemistries [ 198 , 203 ] . Diamond was identified as the additional reinforcement material . Diamond has the high est modulus of elasticity and smallest C TE of any bulk material [ 203 ] , so a ny strain effects caused by the rare earth oxide rei nforcement would be intensified for d iamond. The residual strain field from CTE mismatch will be stronger and the load transfer to the particles will increase [ 144 ] , potentially changing the deformation mechanics. Reactivity is a conce rn, but there is no solubility in or known rea ctions of
72 carbon with Mg. Although diamond is thermodynamically metastable under standard conditions , does not decompose until ~1700Â°C, [ 204 ] so Mg melt processing (700 Â°C ) was not expected to react or decompose in an Mg environment. In the current studies, the diamond particles graphitized and reacted with the stainless steel containment, a reaction that was catalyzed to lower temperature by the presence of iron. This effect, discussed in Section 6.4 , highlights the importance of considering all of the components in a processing system.
73 CHAPTER 5 EXPERIMENTAL METHODS AND PROCEDURES This chapter details the experimental methods used to study the effect of MAMT on MMN C fabrication. An experimental flowchart is shown in Figure 5 1 . The experiments bega n with the choice of nano particle addition (discussed in Chapter 4 ), followed by pre processing for MAMT . MAMT processing was then used to disperse particles and induce structural changes, which were quantified with various analytical characterization techniques . Figure 5 1. Experimental flowchart showing the processing route of MMNCs by MAMT. 5.1 Pre Processing Prior to EMAT processing, samples were pre p rocessed, which consists of three steps: nanoparticle refinement, casting of the matrix , and particle insertion. First, the nanoparticles (discussed later) were refined with a mortar and pestle for 5 minutes. For the pre casting step, 100 mL of 99.8% Mg ro d (Sigma Aldrich) was melted at 750Â°C in cylindrical 100 mL stainless steel crucibles under an Ar atmosphere in a glove box with a contained furnace . For Mg Li samples, 99% Li shot (Alfa Aesar) was manually mixed with the Mg in this step. While the Mg was molten, the samples were allowed to air cool and a stainless steel thermocouple sleeve was held in the melt during solidification. The thermocouple sleeve was necessary to p rotect the thermocouple used for temperature
74 acquisition during MAMT processing. Th e MAMT process minimally affected the thermocouple sleeve , since it was along the centerline of the crucible , where eddy currents are the lowest . In the second step ( particle insertion ) 0.25 inch diameter holes were d rilled in the pre cast materials and th e requisite amount of particles was placed in the holes. The diamond particles (Advanced Abrasives) were initially suspended in water , so the particles were dried in a beaker on a hot plate at 90Â°C prior to incorporation into the samples. After particle in sertion, separate 0.25 inch diameter Mg cylinders (99.9%, Alfa Aesar) were used to contain the particles in the drilled holes. A schematic and photograph of the pre cast sample can be seen in Figure 5 2. A stainless steel lid was placed on the crucible to contain and cap the melt during MAMT processing. Figure 5 2. EMAT sample overview with A ) a schematic of p article insertion and B ) a sample prior EMAT processing (Photo courtesy of Orlando Rios) . Additionally, mechanical stirring was attempted as a meth od of particle pre insertion . The metallic matrix was melted and the requisite amount of particles was
75 poured into the crucible, whereupon the melt was stirred with a graphite rod. The operation was performed in an inert atmosphere in a glove box. This met hod was unsuccessful in incorporating particles, as they wetted poorly and gathered in the slag of the melt. For this reason, mechanical stirring was discarded as an option and the pre insertion m ethod described above was the preferred method of incorporat ion in this document. 5.2 MAMT Processing To achieve high acoustic amplitudes (discussed in Chapter 3), MAMT requires both a high strength static magnetic field and a powerful induction system. To meet these requirements, a customized induction system was designed to operate housed in a large bore, high strength magnet. The specific magnet used was the Cell 4, a resistive Bitter magnet at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, Florida. This magnet bore was 195 mm and it had maxi mum field of 20 T. Collaborators from the Materials Processing & Manufacturing Group in the Materials Science & Technology Division of Oak Ridge National Laboratory designed this system [ 57 , 205 ] , which integrated Ar and He gas , induction power, and temperature acquisition to control the temperature and acousti c power in the sample . The gas system uses a mixture of Ar and He (which has a higher thermal conductivity) to avoid oxidation of the sample and control temperature. Ar and He have thermal conductivities of 43.5 and 361 mW/(m*K) at 1000K, respectively [ 206 ] . Changing the ratio of gases, as well as the flow, controlled the quenching power independently of induction power. In this way the temperature is controlled by both the induction coil and gas system. The specific details of the experimental setup and induction coil are currently held as proprietary by ORNL.
76 A represent ative thermal profile for the current MAMT studies is shown in Figure 5 3. First, samples were heated under Ar with the induction coil to the melting temperature (650Â°C for Mg), at which point a thermal arrest for melting occurred. The samples were heated to the processing temperature of 730Â°C (1000 K) and held for 5 minutes. The temperature was held constant by increasing the He:Ar ratio, compensating for Joule heating by induction. Subsequently, the sample was cooled by increasing the He:Ar ratio further in the gas and in some cases reducing or eliminating the power to the induction coil. The thermal profile only accounts for the temperature of the sample, not the acoustic power delivered. EMAT only occurs when both the static magnet and induction power ar e active, so EMAT power is independent of temperature. Thermal profiles for all samples under investigation can be found in Appendix D.2. Figure 5 3 . Representative temperature profile for EMAT processing . 5.3 Variable Processing Routes The MAMT process is highly customizable, depending on the desired effect in the material. One of the most important processing variables is whether or not EMAT is pres ent during solidification, controlled by whether or not the induction coil is powered
77 while the material solidifies. This divides EMAT into the first two processing types seen in Figure 5 4. Type 1 imparts sonic energy by EMAT to the sample both while molten and during solidification. In type 2, the sample is sonicated while molten, but the induction coil is deactivated prior to solidification . Thus, no sonication is present during solidification during type 2. Since the static field required for EMAT has a significant ramping time (>5 min), the field is still active during solidification and magnetic alignmen t will occur in type 2. Grain refinement should only occur in type 1, since sonic power needs to be active during solidification for grain refinement to be active [ 53 , 54 ] . Figure 5 4 . Process types in the MAMT system.
78 I t was expected that grain and particle alignment would be more active in type 2, since ultrasonication can disorder the magnetic alignment [ 207 ] . Type 3 is a control with no static magnetic fiel d, and thus, no sonication at any point during processing. Processing scenarios that were not explored include sample size, melt treatment time, and solidification velocity. 5.4 Experimental Design A list of experimental runs and corresp onding names is gi ven in Table 5 1, along with a sample naming legend in Figure 5 5 . The samples chosen give a range of conditions. Samples 1 3 were intended to evaluate microstructural refinement and particle dispersion under varying EMAT power. Samples 4 8 were designed t o study the effect of melt treatment on the dispersion of diamond and Er 2 O 3 nanoparticles. Samples 9 13 contained Li alloying additions to study the resulting effect on microstructure and particle dispersion. Controls were found throughout each experimenta l group. Sample 0 was used as a non EMAT control and was air cooled in a glove box (solidified in ~30 seconds) to observe the typical cast microstructure for Mg in cylindrical geometry. Figure 5 5. Naming convention for the samples in this document, wit h Sample 1 as an example. Details for each sample can be found in Table 5 1.
79 Table 5 1. Complete list of samples. P ac corresponds to the maximum acoustic pressure. Sample Name Matrix Particle Particle Size (nm) Volum e % Field (T) Pac to Liquid (MPa) Pac During Solidification (MPa) 0 Mg NA 0T (0,0)MPa Mg None N/A N/A 0 0 0 1 Mg Dy(r) 18T (4,4)MPa Mg Dy2O3 25x225 1 18 4 4 2 Mg Dy(r) 18T (1.5,1.5)MPa Mg Dy2O3 25x225 1 18 1.5 1.5 3 Mg Dy(r) 0T (0,0)MPa Mg Dy2O3 25x225 1 0 0 0 4 Mg NA 18T (1.5,0)MPa Mg N one N/A N/A 18 1.5 0 5 Mg Dia(s) 18T (1.5,0)MPa Mg Diamond 50 1 18 1.5 0 6 Mg Dia(s) 0T (0,0)MPa Mg Diamond 50 1 0 0 0 7 Mg Er(s) 18T (1.5,0)MPa Mg Er2O3 50 1 18 1.5 0 8 Mg Er(s) 0T (0,0)MPa Mg Er2O3 50 1 0 0 0 9 Mg7Li NA 18T (1.5,1.5)MPa Mg 7.5at%Li None N/A N/A 18 1.5 1.5 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa Mg 7.5at%Li Diamond 50 1 18 1.5 1.5 11 Mg7Li Er(s) 18T (1.5,1.5)MPa Mg 7.5at%Li Er2O3 50 1 18 1.5 1.5 12 Mg15Li NA 18T (1.5,1.5)MPa Mg 15at%Li None N/A N/A 18 1.5 1.5 13 Mg15Li Dia(s) 18T (1.5,1. 5)MPa Mg 15at%Li Diamond 50 1 18 1.5 1.5 Figure 5 6. Pressure distribution as a function of distance from the crucible for all samples.
80 The distribution of acoustic pressure in the sample while liquid, based on Equation 3 11, is shown in Figure 5 6. W ithout accounting for propagation effects, a larger portion of Sample 1 should be subject to cavitation from acoustic production than in Samples 2, 4, 5, 7, and 9 14. Samples 0, 3, and 6 have no static magnetic field applied and thus have no acoustic produ ction associated with their processing. 5.5 Analytical Techniques The particles used in the study were studied both before and after incorporation by EMAT with the following techniques. In addition, the microstructure was quantified in a systematic manner. 5.5.1 As Received Particle Evaluation A combination of TEM for morphology , and Dynamic Light Scattering ( DLS ) for Particle Size Distribution ( PSD ), was used to evaluate the as received particles prior to incorporation . TEM imaging provides nanometer scal e resolution to characterize the shape of particles. DLS, on the other hand, measures many particles suspended in solution simultaneously, providing a statistical measure of PSD. Three particle types were investigated, 25x225 nm Dy 2 O 3 rods, 50nm Er 2 O 3 sph eres, and 50nm diamond particles. All sizes are nominal values. Nanostructured and Amorphous Materials, Inc. supplied the rare earth oxide particles and Advanced Abrasives Corporation supplied the diamond nanoparticles. TEM analysis began by dipping a copp er/carbon film TEM grid in an aqueous suspension of 0.1 1% particles and allowing it to dry. Subsequently, grids were analyzed primarily using a JEOL 200cx TEM operating at 200keV. Bright field imaging was used to determine particle shape and size. The PSD of the RE oxides was quantified by first treating a suspension of nanoparticles in deionized water with a sonicating horn. Though the sonication power
81 was uncalibrated due to the experimental setup, it was high enough to induce visible cavitation, acousti c streaming, and significant heating in water (from room temperature to near boiling in 5 minutes). After sonicating for 5 minutes, samples were extracted from the liquid with a pipette and analyzed by DLS with a Brookhaven ZetaPlus operating by Phase Anal ysis Light Scattering (PALS). The diamond samples were received in an aqueous condition , so sonic dispersion was not required. 5.5.2 X ray Radiography After MAMT dispersion and before sectioning, selected samples were imaged via X ray radiography. This wa s performed using a Cu X ray source at 250 kV and 120 ÂµA at a resolution of 50 Âµm and a digital flat panel detector. The samples were imaged in three orthogonal directions. 5.5.3 Metallographic Preparation From the overall cylindrical shape, microstructur al samples were sectioned for analysis acco rding to the steps illustrated in Figure 5 7 . The resulti ng microstructural area provided a perspective of solidification from crucible to center of sample, in the radial/longitudinal plane . Microstructure samples were vertically positioned near the c enter of the sample (Figure 5 7 B ), and so minimized any vertical solidification effects from the bottom or top of the sample. After sectioning, the samples were mounted in cylindrical molds in quick set epoxy. Metall ography specimens were grou nd on a Struers RotoPol with a series of grinding steps (320, 800, 1200 grit SiC paper) at 300 rpm. They were then polished with 3 and 1 Âµm alumina powder mixed with water on a low nap polishing pad at 150 rpm . The final step was 0.05 Âµm silica on a Struers MD Chem pad. Samples were etched
82 with an acetal picral etchant (100 mL ethanol, 10 mL water, 5 mL acetic acid, 5 g picric acid [ 208 ] ) to reveal the grain structure. Figure 5 7. Sectioning methodology A ) a vertical section was removed from the overall sample, then B ) a cutaway view of t he section outlined in red in A . 5.5.4 Microstructural Analysis Microstr uctural analysis was predominantly carried out with optical microscopy using a Leica DM2500M. For the composite images, micrographs were taken primarily with a polarizing filter on etched samples, which provided the best grain contrast. To produce the comp osite images in Chapter 7, micrographs were taken in an overlapping raster pattern across the sample and then stitched to form a complete image using Photoshop software. The samples were not etched when imaging particles, as the etchant could preferentiall y attack the particle matrix boundary, making particles appear larger. Grain size measurements were conducted using the linear intercept method (ASTM E112). Particle size quantification was conducted using ImageJ software, with
83 which optical bright field m icrographs were thresholded, and particle size and area fractions were calculated. Scanning Electron Microscopy (SEM) was performed on a JEOL 6400 SEM and an FEI XL 40 FEG SEM. Energy Dispersive X Ray Spectroscopy (EDS) was used on both instruments for qua litative elemental analysis. Electron Backscatter Diffraction (EBSD) took place at 20 kV in 900 Âµm x 600 Âµm windows on a Zeiss Auriga CrossBeam Workstation with a NordlysF detector with a 4Âµm step size at the Electron Microscope Unit at the University of N ew South Wales. Transmission Electron Microscopy (TEM) was performed on a combination of an FEI Technai F 20 at the University of Alabama, a JEOL 200cx and a JEOL 2010F. Both Bright Field (BF) and Scanning Transmission Electron Microscopy High Angle Annula r Dark Field (STEM HAADF) imaging modes were used during particle analysis. Sample preparation for TEM followed standard Focused Ion Beam (FIB) liftout techniques [ 209 ] on an FEI Dual Beam Strata DB235. The compositions of Samples 9 13 (Mg Li) were analyzed with Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP AES). 100 mg cubes sectioned from specific areas of the samples were dissolved in 10 mL wat er, 5 mL nitric acid, and 5 mL hydrochloric acid, and subsequently diluted with N anopure (Thermo Scientific) water to an estimated 50 ppm. ICP AES was performed on a Perkin Elmer Optima 3200 RL and samples were compared to 1, 10, and 100 ppm Mg and Li stan dards to determine the concentration
84 CHAPTER 6 EFFECT OF MAMT ON PARTICLE DISPERSION A central objective of this work was to understand resultant processing microstructure relationships of the MAMT process . Reinforcement with three types of nanoparticles was investigated: Dy 2 O 3 , Er 2 O 3 , and diamond. These particles were analyzed both prior to and after dispersion in Mg (and Mg Li) with MAMT. The rare earth oxide reinforcement was determined to be stable during the process while the diamond reinforcement was accompanied by interactions with the crucible to produce secondary particles. Samples 1 8 (refer to Table 5 1) were specifically investigated in this chapter . A description of the sample naming convention can be found in Figure 5 5. 6.1 As Received Partic le Analysis Particle size plays a key role in its eventual distribution in the sample, thus as received particles were fully characterized in order to compare to particles in the dispersed state . The particle shape and size distribution are mea sured with T EM and DLS , respectively. 6.1.1 Rare Earth Oxide Particles The analysis of Er 2 O 3 particles ( nomina lly 50 nm) can be seen in Figure 6 1. T he Er 2 O 3 n a noparticles appear to include a number of sintered agglomerates . The particle size distribution ( PSD ) of t he Er 2 O 3 p articles by number and by volume are shown in Figure 6 1 B and Figure 6 1 C , respectively. A bimodal distribution with peaks at 100 and 500 nm is evident. In the context of MMnCs, both number and volume PSDs are important for a bimodal distributi on, since either alone can be misleading when predicting composite behavior. In Figure 6 1 B , the cluster at 100nm is 15.7 times larger than the cluster at 500nm, indicating that there are many more particles near 100nm.
85 Figure 6 1 . Particle distributi on of Er 2 O 3 nanoparticles . A ) Bright fi eld TEM micrograph of particles. P a rticle size distribution by B) number and C ) volume, as measured by DLS . Relative cluster frequency refers the ratio of peak magnitudes, given the different normalization techniques (Photo courtesy of Author) . For a material mechanism that was purely dependent on the number of particles at a given size, the 100nm clu ster would dominate the behavior. Conversely , quantification of the particle size distribution by volume gives an indica tion of the effective level of reinforcement at each size. For instance, if a material were reinforced with 7.5 vol.% of th e Er 2 O 3 shown in Figure 6 1 , the material would only be reinforced
86 with 1 vol.% of particles 100nm in size. In addition, the resultan t interparticle spacing of an ex situ composite is dependent on volume fraction at a given size. The effectiveness of Orowan looping and Zener pinning (discussed in Section 2.5.1), scales with particle size and interparticle spacing, and given equal volume fractions, larger clusters reduced the efficacy of these mechanisms. The PSD of Dy 2 O 3 rods is quantified in Figure 6 2, and a bimodal distribution similar to the Er 2 O 3 particles is evident, with a larger peak near 500 nm. After ultrasonic dispersion for size quantification (by inserting an ultrasonic transducer in the water particle mixture), many of the Er 2 O 3 and Dy 2 O 3 particles settled quickly, thus they could not be analyzed by techniques that required particles to be suspended, such as TEM dipping an s , based on buoyancy of the particle, is given in Equation 6 1 [ 98 ] p f are the densities of particle and fluid (~8.5 g/cm 3 [ 210 ] and 1 g/cm 3 is the dynamic viscosity of water (0.55 mPa*s at 50 Â° C [ 21 1 ] ), g is gravitational acceleration, and r is the particle radius. The settling velocity of rare earth oxide spheres in water as a function of particle radius is given in Figure 6 3. A significant fraction of particles settled a distance greater than 10 mm in ~30 seconds, so it was deduced that many particle agglomerations larger than 10 Âµm were present in the powder. An attempt was made to refine the powder by using a mortar and pestle, but this method was ineffective at refining the particle size. Give n the wide range of particle size seen in the powder, care should be taken in future studies to incorporate particles with a more controlled size distribution.
87 Figure 6 2. Particle size distribution of Dy 2 O 3 nanorods by A) number and B ) volume as measur ed by DLS. Figure 6 3. Settling velocity of Er 2 O 3 and Dy 2 O 3 spheres in water at 20Â°C. (6 1)
88 6.1.2 Diamond Particles The diamond nanoparticles were monodisperse (Figure 6 4), unlike Er 2 O 3 and Dy 2 O 3 . Thus, the re is minimal difference in quantifying b y number or volume (Figures 6 4 B and 6 4 C ). The particles are faceted and near 50 nm in size, larger than the 20 nm measured by DLS. Differences in measured size are commonly seen with irregularly shaped particles and can be attributed non ideal (i.e. non spherical) scattering [ 212 , 213 ] . The particles are determined t o be monodisperse by DLS, but the size is quantified more reliably by TEM. Figure 6 4 . Diamond nanoparticle properties. A ) M orphology determined by TEM and B, C ) p article size distribution and DLS (Photo courtesy of Author) .
89 6.2 Non Destructive Dispe rsion Quantification Before sectioning the composites, non destructive testing was conducted with X ray radiography to detect any macrosegregation of particles. The results for Samples 2 through 8 are found in Figure 6 5. Radiography data was unavailable f or Sample 1. The central void visible in each of the samples is a shrinkage pipe that will discussed in Section 7.1. The tran sparent horizontal region in A contained particles prior to the crucible being removed. A list of the narrow beam attenuation coeff icients for the relevant species is given in Table 6 1 . Based on the attenuation coefficients, both Dy 2 O 3 and Er 2 O 3 attenuate the X rays more strongly than Mg, while diamond attenuates less. Therefore, clustered Dy 2 O 3 or Er 2 O 3 will appear darker than the M g matrix, while diamond will appear lighter. Table 6 1. Mass attenuation coefficient (Âµ m coefficient (Âµ l =Âµ m 5 at 8keV (Cu K ). Species Âµm [cm2/g] 1] Mg 40.59 [ 214 ] 1.78 [ 9 ] 72.2 Dy2O3 286.3 [ 214 ] 7.81 [ 174 ] 2236 Er2O3 117.8 [ 214 ] 8.64 [ 174 ] 1017 C 4.576 [ 214 ] 3.5 [ 215 ] 16.0 Figure 6 5 shows that in the oxide reinforced samples (top row, 2, 3, 7, and 8), particles did not disperse fully. Upon inspection of the radiographs, the diamond reinforced samples (4, 5 , and 6) showed no evidence of macrosegregation, indicating particles are evenly dispersed in the microstructure within 50 Âµm the resolution of the instrument. In Samples 2 and 3 (Figure 6 5 A and B )) the particles did not break up from their original tub ular form.
90 Figure 6 5. X Ray radiography of samples of intere st. Top Row (Dy 2 O 3 particles) A and B) samples 2 and 3. Middle Row (Er 2 O 3 particles) C and D) samples 7, and 8. Bot tom row (diamond particles) E G) s amples 4,5, and 6. Samples 3, 8 and 6 (b, d, g) were not processed with MAMT.
91 The level of macrosegregation inherent in the Dy 2 O 3 and Er 2 O 3 containing samples can be attributed in part to particle interlocking. It has been found that particles with complex surface morphologies (such as sintered agg lomerates) are more difficult to separate from each other than spherical particles [ 216 ] . This is due to a large number of contact points between particles, increasing the effective bonding energy. The Er 2 O 3 particles seen in Figure 6 1 are susceptible to t his effect, meaning that cavitation may not be fully separate and disperse them. Besides this chemical interlocking effect, the more complex shape of the of Dy 2 O 3 rods may have lead to physical interlocking. This could explain why the Er 2 O 3 in Figure 6 5 C was partially dispersed while the Dy 2 O 3 particles in Figure 6 5 A were not dispersed. 6.3 Structure of Rare Earth Oxide Reinforced Composites Upon metallographic examination of Mg reinforced with Er 2 O 3 nanospheres (Sample 7 Mg Er(s) 18T (1.5,0)MPa ), mutu ally aligned particles larger than 25 Âµm were observed. An example is shown in Figure 6 6 A . EDS maps (Figure 6 6(b f)) of the area were collected and large clusters were found to be Er and O based. Oxygen generally produces a weak signal via EDS and was m inimally visible. Along with the large Er 2 O 3 particles, several iron rich regions can be seen. Fe based inclusions were found to be systemic in the microstructures of EMAT produced composites. These inclusions have several potential origins. These include abrasion of the melt against the oscillating crucible due to a phase lag between the two, impact of the thermocouple sleeve against the interior wall, and spalling of the crucible during mechanical oscillations from stress. Further studies are needed to id entify and eliminate the specific cause of contamination.
92 Figure 6 6 . Elemental analysis of large particles in Sample 7 A ) Seco ndary electron i mage and B F ) corresponding e lemental analysis by EDS mapping (Photos courtesy of Author) . Figure 6 7. Backs catter electron micrograph of Sample 7 showing large particles aligned with the vertical magnetic field. Inset is a secondary electron image (Photos courtesy of Author) .
93 A higher magnification BSE micrograph of the large Er 2 O 3 particles is found in Figure 6 7. They are complex agglomerations with features less than 100 nm in size. This is consistent with the earlier discussion of particle settling and interlocking. In Figure 6 7, the static magnetic field is in the vertical direction, meaning that particles are aligned with each other in the field direction. This is caused by dipole dipole interactions between magnetized particles. These interactions are usually only present for particles larger than 5 Âµm [ 77 , 99 ] , which is consistent with the observed aligned strings of particles in the microstructure. Sample 1 Mg Dy(r) 18T (4,4)MPa , Mg reinforced with Dy 2 O 3 rods, also contained large particles in the matrix. A SEM micrograph and corresponding EDS elemental analysis as shown in Figure 6 8. Unlike Sample 7, the large particles in the microstructure were not primarily rare earth oxide based, but rather contained Fe . Sampl e 1 Mg Dy(r) 18T (4,4)MPa received greater acoustic power than Sample 7 Mg Er(s) 18T (1.5,0)MPa , and consequently the interaction with the crucible may have caused a greater number of Fe based impurities to be introduced into the microstructure. This highe r power was also apparently more effective at breaking up large agglomerations. The particles in Sample 1 Mg Dy(r) 18T (4,4)MPa were predominantly found at grain boundaries, unlike Sample 7 Mg Er(s) 18T (1.5,0)MPa , in which they were aligned with the magne tic field. This is caused by the sonication during solidification in Sample 1 Mg Dy(r) 18T (4,4)MPa , which tends to inhibit alignment with the field. Sample 7 Mg Er(s) 18T (1.5,0)MPa did not receive sonic power during solidification, so large particles wer e free to align in the melt prior to being engulfed by the solidification front.
94 Figure 6 8 . Elemental analysis of Sample 1 Mg Dy(r) 18T (4,4)MPa A ) s eco ndary electron image and B F ) e lemental analysis by EDS mapping of a n apparent grain boundary (Photo s courtesy of Author) . Figure 6 9. Microstructure of Sample 1 A) near the crucible, B) mid radius, C ) near the center of the sample, and C ) particle volume fractions at A , B , and C (Photos courtesy of Zachary Bryan) .
95 Additional particle analysis of Samp le 1 Mg Dy(r) 18T (4,4)MPa as a function of radial position is presented in Figure 6 9, with micrographs near the crucible, mid radius, and near the center of the sample. Several large particles were found at grain boundaries, with smaller intergranular pa rticles. The particle volume fraction varied minimally across the sample, indicating that the particles were not pushed considerably by the s olidification front (Figure 6 9 D ). Figure 6 10. TEM HAADF micrograph of Sample 1 showing dispersed Dy 2 O 3 nanoro ds (Photo courtesy of Karen Torres and Author) . Working with collaborators Prof. Greg Thompson and Karen Torres at the University of Alabama Tuscaloosa, TEM High Angle Annular Dark Field imaging (HAADF) was used to show an even dispersion of nanoparticles in Figure 6 10. Because there were few rare earth containing particles greater than 1 Âµm (compared to the Er 2 O 3 contaning samples), it can be concluded that most of the Dy 2 O 3 rods were incorporated into the microstructure rather than agglomerating.
96 Fig ure 6 11. Orientation of Dy 2 O 3 rods . A ) Relative orientation distribution of particles in Figure 6 10 and B ) demagnetization energy of Dy 2 O 3 rods of various sizes (diameter*length) at 20T. The orientation of the particles was quantified by fitting ellipses to a binary representation of Figure 6 10 using in ImageJ software. The resulting orientation distribution of the ell ipses is shown in Figure 6 11a, and the particles appear to be aligned, possibly due the magnetic field. However, this result is not suppo rted when taking into account demagnetizing energies of Dy 2 O 3 in relation to the thermal disordering energy (kT) of the system. Following the procedure of M. Li [ 82 ] a nd Equations 2 3 [ 84 ] and 2 4 [ 69 ] , the energy of various sizes of Dy 2 O 3 rods are calculated for a 20 T field in Figure 6 11b. Dy 2 O 3 has a volume susceptibility, v , of 4.859x10 4 at the processing temperature of 1023 K [ 217 ] . The demagnetizing energies for particles near the size of those in the study are much lower than kT, and would not be expected to align based on the energetics. Rather than magnetic energy, reorientation at the solidification front is likely r esponsible for this behavior, as has been seen in other systems [ 218 ] . It should be noted that Dy 2 O 3 exhibits a cubic structure up
97 to 1473 K [ 217 ] , so magnetocryst alline anisotropy will be a minor factor, compared to demagnetization energy. Figure 6 12. Surfaces of the boundary between regions of alignment vs. non alignment for Dy 2 O 3 prolate ellipsoids as a function of volume, aspect ratio, and magnetic field at 300 K and 1000 K. A plot of the boundaries between regions of alignment and non alignment for Dy 2 O 3 rods as a function of magnetic field, aspect ratio, and particle volume is shown in Figure 6 12. This figure was produced with Equations 2 3 and 2 4, simil arly to Figure 6 11b. It can be seen that above an aspect ratio of around 3, the tendency to align becomes relatively independent of aspect ratio. At the volumes of particles visible in Figure 6 10 (~1x10 6 nm 3 ), particles would align in a 20 T field at 300 K, but not at 1000 K. This is primarily due to a temperature dependent reduction in magnetic susceptibility
98 [ 217 ] . In order to thermodynamically align particles 1x10 6 nm 3 in volume at 1000 K, a magnetic field over 60 T would be needed. 6.4 Particle Containment Interaction Throughout the studies, Fe based impurities were observed. This was accompanied by the absence of diamond in the nominally diamond reinforced samples. Samples 4, 5, and 6 provided a suitable comparison for investigating this phenomenon. Sample 4 Mg NA 18T (1.5,0)MPa was sonicated with EMA T with no reinforcement, Sample 5 Mg Dia(s) 18T (1.5,0)MPa contained diamond and was sonicated, and Sample 6 Mg Dia(s) 0T (0,0)MPa contained diamond and was not sonicated. Samples 4 and 5 were not sonicated during solidification, and so received Type 2 tre atment: melt treatment (outlined in Section 5.3). Figure 6 13. Microstructure o f diamond reinforced samples. A ) Sample 4 Mg NA 18T (1.5,0)MPa , B ) Sample 5 Mg Dia(s) 18T (1.5,0)MPa , and C ) Sample 6 Mg Dia(s) 0T (0,0)MPa (Photos courtesy of Author) . Rep resentative microstructures of all three samples can be seen in Figure 6 13. Particles larger than 1Âµm are seen in all samples. EDS point scans revealed these
99 particles contained Fe and Cr (Figure 6 14). In Samples 4 and 5, which were processed by EMAT, la rger particle aligned by dipole dipole interactions in the static magnetic field direction. Because there was no static field in the processing of Sample 6, no alignment is observed. Figure 6 14. Aligned group of particles in Sample 5 Mg Dia(s) 18T (1.5 ,0)MPa A) microstructure and B, C) corresponding EDS analysis of the indicated points (Photo courtesy of Author) . Similarly to the oxide reinforced samples, the primary source of these particles was determined to be the stainless steel (Fe Cr Ni) crucible . The mechanism of production was not identical for each, however. Figure 6 15 shows cross sectional views of the crucible Mg interface for Sample 4, 5, and 6. A significant texturing of the interior surface of the crucible could be seen in the samples tha t contained diamond, regardless of whether the sample was sonicated. This indicates that the diamond reacted with the stainless steel to produce reaction products. Diamond, while normally stable to 1500Â°C, graphitizes in the presence of Fe at 800Â°C [ 219 ] . Once graphi tized, the carbon may react with the components of the steel. Reactions of diamond with steel
100 have been previously seen, and they result in a rough surface textures like those in Figure 6 15b and 6 15c [ 219 ] . Figure 6 15. Crucible morphology of Samples. A ) Sample 4 Mg NA 18T (1.5,0)MPa , B ) Sample 5 Mg Dia(s) 18T (1.5,0)MPa , and C ) Sample 6 Mg Dia(s) 0T (0,0)MPa . The samples that included diamond resulted in a rough crucible surface (Samples 5 and 6), irrespective of magnetic field or sonication (Photos courtesy of Author) . Figure 6 16. Crucible Mg interfaces. A ) Sample 4 Mg NA 18T (1.5,0)MPa , B ) Sample 5 Mg Dia(s) 18T (1.5,0)MPa , and C ) Sample 6 Mg Dia(s) 0T (0,0)MPa (Photos courtesy of Author) .
101 Optical images of the crucible Mg boundary can be seen in Figure 6 16. In the samples that received MAMT treatment (A and B ), small particles can be seen emitting from the crucible wall, whereas less particles are seen local to the wall in C . Morphology changes can be seen in the samples containing diamond, consistent wit h Figure 6 15. The possible products of diamond stainless steel reaction are summarized in Table 6 3. Based on the free energies of formation at 1000K, Cr 7 C 3 and MgNi 2 are most likely to form. The sample with the largest amount of particles was analyzed wi th X ray Diffraction, the results of which are shown in Figure 6 17. In the pattern, there are small Fe (the primary phase of the crucible) and other possible reaction products. Because Fe based particles are present in Sample 4, a long with other samples containing no diamond, it can be deduced that particles are produced in these samples primarily by an abrasion process from sonication. Similarly, since Fe based particles are present in Sample 6, which contains diamond but did not undergo sonication, particles are produced in this sample by a reaction process. Consequently, Fe based products may be produced by sonication and/or reaction with diamond. Figure 6 17. XRD spectrum of Sample 5, post EMAT procesing. Small peaks are visib le that correspond to interaction products with the stainless steel crucible.
102 Table 6 2. Free energies of formation for possible reaction products of Mg, C, (Fe, Cr, Ni) at 1000K [ 220 ] . At equilibrium conditions, Cr 7 C 3 and MgNi 2 are energetically favorable to form. Compound Fe 3 C Cr 3 C 2 Cr 7 C 3 Ni 3 C Mg 2 C 3 MgNi 2 Mg 2 C 3 at 1000K 10.04 93.94 179.56 56.31 90.10 38.36 74.80 Further TEM studies on Samples 5 and 6 revealed that nanoparticles were produced in addition to the previously seen >1 Âµm particles. Figure 6 18 shows a group of nanoparticles, the la rgest of which is cuboidal. One of the particles is analyzed with an EDS linescan, and found to consist of primarily Ni and Fe. Cr was not detected, indicating that it was removed via another reaction. Figure 6 19 shows a group of very small particles (10n m) in Sample 6, only particles smaller than 1Âµm found in Sample 6. These particles contained Ni by EDS point scans. Considering the data in Table 6 2, these particles are identified as Ni 2 Mg, which may have formed as diamond reacted with the Fe and Cr in t he stainless steel because Ni 3 C has a high free energy of formation. A TEM foil was produced from a string of particles similar Figure 6 13 (Sample 5 Mg Dia(s) 18T (1.5,0)MPa ) with site specific Focused Ion Beam (FIB) techniques, and corresponding TEM anal ysis is presented in Figure 6 20. A range of particle sizes and morphologies were evident, which would be consistent with combined abrasion/reaction particle production. The faceted, geometric shapes of some of the particles indicate they are reaction prod ucts, while the large, rounded particle appears to be an abrasion product.
103 Figure 6 18. TEM HAADF micrograph of Sample 5. A) Low magnification, B ) m agnified particle and C,D ) corresponding EDS linescan of Ni and Fe (Photos courtesy of Author) . Figure 6 19. TEM HAADF of Sample 6 at A) low and B) high magnification (Photos courtesy of Author) .
104 Figure 6 20 . TEM HAADF micrograph of a string of particles in Sample 5 (Photo courtesy of Author) . 6.5 Summary Several important observations were made in Chapt er 6. First, the size distribution of rare earth oxide nanoparticles (nominally 50nm) is found to be multi modal , with particles 100 nm, 500 nm and >10 Âµm in diameter. Particles >10 Âµm are visible in the microstructure of the samples and are hypothesized t o be a result of complex particle interlocking. EMAT dispersed >100 nm Dy 2 O 3 rods evenly in the matrix. Additionally, diamond reinforcement was found to interact with the stainless steel
105 crucible to produce complex abrasion/reaction products. MAMT is found to be a capable technology with which to distribute nanoparticles in metal matrix nanocomposites, but consideration of potential reactions between components and control of particle size is required for successful application. Stainless steel abrasion pro ducts were found in all samples that underwent MAMT processing with diamond reinforcement , and this effect should be co ntrolled for in future studies.
106 CHAPTER 7 EFFECT OF MAMT ON MICROSTRUCTURE MAMT can alter cast microstructures by a v ariety of mechanism s, including, but not limited to, acoustic refinement [ 121 ] and magnetic texture alignment [ 82 ] . A critical parameter in determining microstructure is whether or not the sample is held under EMAT power during solidification. The details of this were discussed in detail in Section 5.3. Material that undergoes EMAT power in th e liquid, but not during solidification, will display microstructural features consistent with casting in a magnetic field with no acoustic components. If the material is processed by EMAT during solidification, however, the cast microstructure will exhibi t both magnetic and acoustic consequences. The effect of differing EMAT solidification pressure on grain structure, grain alignment to the field, and the effect of lithium additions were investigated. 7.1 Non MAMT Microstructure Prior to evaluating the eff ect of MAMT, the microstructure of pure Mg cast in cylindrical geometry was measured (Figure 7 1). A shrinkage pipe is centered in the upper portion of the sample, measured to be >5% of the total volume. The theoretical shrinkage volume is given in Equatio n 7 1 [ 221 ] l s are the liquid and solid densities, respectively (1.59 g/cm 3 and 1.73 g/cm 3 for liquid and solid Mg, respectively [ 9 ] ). The shrinkage percentage for Mg is 9%, consistent with that observed in all samples. A coarse, columnar microstructure is evident, in which the grains reorient and become smaller toward the center of the sa mple due to geometric convergence, typical of pure Mg [ 222 ] . This sample solidified in a similar timeframe to the MAMT produced samples (~30 seconds) so the microstructures are experimentally comparable.
107 Figure 7 1 . Sample 0 Mg NA 0T (0,0)MPa , a non MAMT control of air cooled Mg. A) As cast and B ) bisected, polished and etched (Photo s courtesy of Author). (7 1) 7.2 Grain Refinement By EMAT Grain refinement is one of the principle applications of acoustic processing in light metals [ 47 , 53 , 54 , 223 ] . Sonication causes refinement by increasing in the number of crystallization nuclei in the liquid pool by several mechanisms, including remelting and transport of dendrite arms, a smoother temperature distribution in the liquid pool, and enhanced heat conduction at the solidification front [ 55 ] . The samples that are investigated in this section are shown in Table 7 1. Sample 0 Mg NA 0T (0,0)MPa provides a baseline for cast Mg outsid e of the MAMT setup. Sample 1, 2, and 3 were driven with induction power during solidification, so acoustic processes should be active in the samples for which the static magnetic field was active during solidification.
108 Table 7 1. Processing conditions f or the samples analyzed in Section 7.2. Sample Number Matrix Particle Size (nm) Volume Percent Static Field [T] Max P ac to Liquid [MPa] Max P ac During Solidification [MPa] 0 Mg NA 0T (0,0)MPa Mg None N/A N/A 0 0 0 1 Mg Dy(r) 18T (4,4)MPa Mg Dy 2 O 3 25x225 1 18 4 4 2 Mg Dy(r) 18T (1.5,1.5)MPa Mg Dy 2 O 3 25x225 1 18 1.5 1.5 3 Mg Dy(r) 0T (0,0)MPa Mg Dy 2 O 3 25x225 1 0 0 0 4 Mg NA 18T (1.5,0)MPa Mg None N/A N/A 18 1.5 0 5 Mg Dia(s) 18T (1.5,0)MPa Mg Diamond 50 1 18 1.5 0 6 Mg Dia(s) 0T (0,0)MPa Mg Diamond 50 1 0 0 0 7.2.1 Non EMAT Control Figure 7 2 . Microstructure of a cross section of Sample 0 Mg NA 0T (0,0)MPa , unreinforced Mg con trol (Photo courtesy of Author) . To understand the changes due to EMAT processing, it is necessary to first analyze a contro l sample, Sample 0 Mg NA 0T (0,0)MPa , outside of the EMAT setup
109 and establish the cast microstructure for Mg in the cylindrical geometry common to all samples (Figure 7 1). Large columnar grains (2 6 mm width) are apparent in the standard microstr ucture of Sample 0 (Figure 7 2) . The grains change direction and become smaller towards the center due to converging geometry. The upper right portion of the micrograph is the location of shrinkage porosity in the sample. 7.2.2 MAMT at High Power During Solidifica tion Sample 1 was processed by MAMT. It was solidified under the highest EMAT power used in the study, corresponding to a maximum pressure of 4 MPa. The resulting microstructure was highly refined (Figure 7 3) when compared to typically cast Mg in Figure 7 2. While grain refinement was systematic in the sample , the degree of refinement decreased towards the center of the crucible (i.e. as solidification progressed). This sample was reinforced with 1 vol.% of Dy 2 O 3 nanorods, b ut it is not expected that the r einforcement played a significant factor in the grain refinement, since the volume fraction of particles did not vary significantly as a function of radial position in the sample ( this was shown in Figure 6 9). Figure 7 3 . M icrostructure of a cross secti on of Sample 1 Mg Dy(r) 18T (4,4)MPa (Photo courtesy of Author) . Figure 7 4 shows the grain size and distribution of acoustic pressure as a function of solidification distance. The acoustic pressure was calculated according to
110 Equation 3 11. It can be seen that grain size and acoustic pressure are inversely proportional. The cavitation threshold is variable in light metals, from 0.2 1 MPa [ 55 ] , so an average value is given in Figure 7 4. As discussed in Section 3.5, the melt solidifies from the crucible wall inward. Consequently, as solidification progresses, the region where acoustic pressure is p roduced becomes solid. This would tend to decrease the amplitude of acoustic waves since the solid has rigidity [ 105 ] , demonstrated by the inc = 2.5 mm) it was found that the maximum grain fo r EMV of pure Mg [ 121 ] at 200 Âµm. This study found the frequency of maximum n size near 10 kHz to be > 600 Âµm. The disparity between these two results necessitates that more frequencies be tested with MAMT to study changes in grain refinement. Figure 7 4. Acoustic pressure and grain size (G.S) as a function of distance from the crucible wall for Sample 1 Mg Dy(r) 18T (4,4)MPa (Photo courtesy of Author) .
111 Another factor that may contribute to a reduction of acoustic pressure with soli di fication is a transition in acoustic production mode. Shown in Figure 7 5, as Mg solidifies the thickness of solid material (prior to solidification, this was just the crucible discussed in Section 3.1 increases, transitioning the vibration mode from melt vibration to crucible vibration. As the effective crucible thickness becomes large, the stiffness of the structure increases, and the displacement amplitude decreases dramatically. Simultaneously, the maximum intensity of eddy currents reaching the melt decreases, dec reasing the acoustic pressure attained by melt vibration mode. Both of these mechanisms lead to a reduction in overall acoustic pressure with continued outside in solidification, consistent with a reduction in grain refinement in Figure 7 4. This effect ma y be avoided in a MAMT system in which the material solidifies from the centerline outward. Figure 7 5. Top down s chematic of inward sol id ifying material in the MAMT system. As g to a decrease in displacement amplitude.
112 7.2.3 Low Induction Power During Solidification Samples solidified with induction power lower were investigated. Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa , seen in Figure 7 6 , was solidified with a maximum sonic pressure of 1.5 MPa. Sample 3 Mg Dy(r) 0T (0,0)MPa (Figure 7 7 ) was solidified with the same induction power, but no static magnetic field and thus no acoustic power to the melt or during solidification. Comparing Sample 2 to Sample 1, the mechanism of grain refin ement is inactive for Sample 2, indicating that the cavitation threshold was not reached. While the calculated pressure of 1.5 MPa (calculated by Equation 3 11) should be above the cavitation threshold for liquid Mg, it appears that the actual pressure is lower. The pressure calculated by Equation 3 11 is likely artificially high due to assumptions made in development of the model. First, it was assumed that the crucible absorbs no current. In the real sample, the crucible will absorb some current, reducing the maximum current density in the melt. Second, the model did not account for imperfect transmission of the alternating magnetic field through the crucible melt interface, another mechanism that could reduce the current density in the melt [ 168 ] . Sample 3 has similar grain morphology to Sample 2, indicating that the addition of low EMAT power did not affect the grain mor phology significantly. Comparing to Sample 0 Mg NA 0T (0,0)MPa , columnar growth was impeded in both Samples 2 and 3 by melt agitation from low intensity EMAT for Sample 2 and induction stirring in Sample 3 [ 125 ] .
113 Figure 7 6 . Microstructure of a cross section of Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa (Photo courtesy of Author) . Figure 7 7 . Microstructure of a cross section of Sampl e 3 Mg Dy(r) 0T (0,0)MPa (Photo courtesy of Author) . 7.2.4 No Induction During Solidification Samples with no induction, and therefore no EMAT during solidification were also studied. Samples 4 Mg NA 18T (1.5,0)MPa and 5 Mg Dia(s) 18T (1.5,0)MPa (Figures
114 7 8 and 7 9 , respectively) were processed similarly with melt MAMT treatment and no induction during solidification and both include columnar grain growth similar to Sample 0 Mg NA 0T (0,0)MPa . Sample 4 exhibits larger grains, while grains are smaller in S ample 5. This was likely due to two factors: magnetic field and particles. In Sample 4, the static magnetic field was still active during solidification, so melt advection was damped by MHD effects (discussed in Section 2.3.1). This stabilized columnar gro wth, compared to Sample 0. While the magnetic field was still active in Sample 5, the tendency to increase grain size was reversed by the increased level of parti cle inclusions (Figure 6 13b). It is believed that t hese particles pinned grain boundaries dur ing growth and refined the microstructure slightly. Sample 6 Mg Dia(s) 0T (0,0)MPa (Figure 7 10 ) was solidified with no magnetic field, but the microstructure was less columnar than Sample 0. This could be due to a slightly increased solidification speed i n the MAMT system compared to air cooling . Figure 7 8 . Microstructure of a cross section of Sample 4 Mg NA 18T (1.5,0)MPa (Photo courtesy of Author) .
115 Figure 7 9 . Microstructure of a cross section of Sample 5 Mg Dia(s) 18T (1.5,0)MPa (Photo courtesy o f Author) . Figure 7 10 . Microstructure of a cross section of Sample 6 Mg Dia(s) 0T (0,0)MPa (Photo courtesy of Author) . 7.3 Effects of Magnetic Anisotropy The influence of EMAT on microstructural alignment was studied by texture analysis of Sample 1. M icrographs taken by Cody Heitman and Dr. Quadir Zakaria at the Electron Microscopy Unit of the University of New South Whale s in Figure 7 11 show there was a change from (A ) a more random orientation to (B) a more aligned texture moving inward from the cru cible. As discussed in Section 2.1.1, grain alignment
116 is due to a reduction in magnetization energy of the Mg HCP crystal. There is a balance, however, between acoustic intensity and the tendency to align, an effect seen in the literature [ 224 ] . Figure 7 11 . Electron Backscatter Diffraction (EBSD) of the Sample 1 Mg Dy(r) 18T (4,4)MPa A) near the crucible wall and B ) mid radius of the sample. A shift in solidifica tion microtexture is evident (Photos courtesy of Cody PK Heitman) . In Figure 7 11 , the orientation is more random in the region where acoustic intensity was high (see Figure 7 4) and is  oriented (easy axis magnetization) in the region where acousti c intensity was lower. The magnetization energy of differing
117 spheres of Mg is plotted in Figure 7 1 2 using Equation 2 1. The tendency of acoustic orientation to change texture is in addition to the thermal disordering energy (kT). Figure 7 1 2 . Magnetocr ystalline energy of different sized Mg crystals in a 20T magnetic field as a function of c axis to magnetic field misalignment. A general scheme for magnetic alignment of particles in a liquid by a magnetic field can be found in Figure 7 13 . The horizonta l axis is the magnetization potential of the particle, determined by the free energy reduction achieved by alignment. The barrier to alignment is the thermal disordering energy, kT [ 70 ] . If the energy of magnetization is greater than kT, a particle will tend to align, whereas if the energy is lower, Brownian motion will disorder it. In boxes on the axis are the relative influence s of various factors on the tendency of a particle to alig n. Increasing field strength, magnetic susceptibly, particle volume, and magnetic anisotropy all act to align a particle . Conversely, temperature acts to decrease the tendency to align because it generally decreases magnetic susceptibility while also incre asing the magnitude of kT itself. Acoustic intensity is o n the vertical axis of the graph, in acoustic intensity, magnetic alignment will be disrupted. It is likely that the disordering threshold is dependent on magnetization energy, particle size, acoustic frequency, and
118 viscosity, among others. Overall this schematic is roughly divided into four quadrants. The only quadrant in which alignment is expected is quadrant 4, in which the magnetization energy is high, but acoustic disordering is low. In Figure 7 11, it appears that the Mg nuclei have tran sitioned from quadrant 2 in 7 11(a) to quadrant 4 in 7 11 (b). Figure 7 13 . Schematic of the tendency of a particle to align in the presence of magnetic and acoustic fields [ 56 ] . 7.4 Alloying Additions The effect of alloying addition was explored with a series of Mg Li alloys in Samples 9 13. The compositions were chosen to be within the single phase region of the Mg rich side of the phase diagram. The compositions of 7.5 and 15 at.% Li are shown in Figure 7 14 .
119 Figure 7 14 . Mg Li phase diagram [ 225 ] showing the nominal m atrix compositions of Samples 9 through 13. All samples are chosen to be within the single phase HCP region. Table 7 2. Relevant processing conditions for the sample s analyzed in Section 7.4 . p ac is acoustic pressur e, as calculated by Equation 3 11 . A full list of s amples can be found in Table 5 1 . 7.4.1 Microstructural Analysis The microstructures of Samples 9 13 were evaluated with regard to grain size and distrib ution. The summarized grain s ize data is found in Figure 7 15 . Generally, an increase in solute content is associated with a decrease in grain size, as expected from literature [ 222 ] . The grain size of Samples 12 and 13 are refined by a factor of two, Sample Name M atrix Particle Size (nm) Volume Percent Static Field [T] Max P ac to Liquid [MPa] Max P ac During Solidification [MPa] 9 Mg7Li NA 18T (1.5,1.5)MPa Mg 7.5at%Li None N/A N/A 18 1.5 1.5 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa Mg 7.5at%Li Diamond 50 1 18 1.5 1.5 11 Mg7Li Er(s) 18T (1.5,1.5)MPa Mg 7.5at%Li Er2O3 50 1 18 1.5 1.5 12 Mg15Li NA 18T (1.5,1.5)MPa Mg 15at%Li None N/A N/A 18 1.5 1.5 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa Mg 15at%Li Diamond 50 1 18 1.5 1.5
120 compared to cast Mg 15 at.% Li from literature with a grain size of 550 Âµm [ 226 ] . The cooling rate for the data from literature was lower than the MAMT samples. Sonication during solidification possibly refined the microstructure , but the alloying addition was likely a primary contributor to the grain refinement compared to pure Mg . Diamond incorporation had no significant effect on the grain size, a s Samples 9 and 10 (Figures 7 16 and 7 17 ), and Samples 12 and 13 (Figures 7 19 and 7 20 ), are microstructurally indistinct. Sample 11 (Figure 7 16) was refined compared to 9 and 10, likely due to the large Er 2 O 3 agglomerations in the matrix. Throughout all samples except Sample 10, grain size increased away from the crucible wall, similarly to Sample 1 Mg Dy(r) 18T (4,4)MPa . Figure 7 15 . Grain size of Samples 9 13 as a function of distance from the crucible.
121 Fi gure 7 16 . Microstru cture of Sample 9 Mg7Li NA 18T (1.5,1.5)MPa (Photo courtesy of Author) . Figure 7 17 . Microstructure of a cross section of Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa (Photo courtesy of Author) .
122 Figure 7 18 . Microstructure of a cross section of Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa (Photo courtesy of Author) . Figure 7 19 . Microstructure of a cross section of Sample 12 Mg15Li NA 18T (1.5,1.5)MPa (Photo courtesy of Author) .
123 Figure 7 20 . Microstructure of a cross section of Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa (Photo courtesy of Author) . 7.4.2 Compositional Analysis The Li concentrations of each sample were measured with ICP AES according to the procedure in Section 5.5.4. Sections were taken from mid radius and mid height for each sample. Addition ally, a distribution of samples was taken from Sample 12 to measure potential macrosegregation. A schematic of the results is shown in Figure 7 21 . Significant deviations from the nominal compositions could be seen across the samples. The macrosegregation originated either from improper mixing in pre processing and/or enhanced macrosegregation in the melt. A reduction in advection usually reduces macrosegregation during solidification, but if diffusion in the melt is strong, macrosegregation can increase [ 79 , 100 ] . Additionally, the magnetic field could have impeded mixing of the Mg and Li by stabilizing the melt . Future studies with
124 compositional analysis before EMAT processing are necessary to determine which mechanism is responsible for the compositional variation. Figure 7 21 . ICP AES locations and atomic % compositions for Samples 9 13. Significant macroseg regation is present. 7.5 Summary EMAT is found to reduce grain size of pure Mg (with 1 vol.% ex situ particle reinforcement) when the acoustic pressure is above the cavitation threshold, with the maximum refinement occurring within the twice the skin dept h of induction currents. Additionally, pure Mg samples processed at lower acoustic power (mostly below the cavitation threshold) displayed equiaxed growth, but no refinement. Samples solidified with no EMAT power had columnar microstructures comparable to air cooled cast Mg. Potential microstructural alignment to the static magnetic field was investigated, and it was found that the microstructure was aligned in regions that received less acoustic pressure, an effect seen in literature. Mg Li alloys were als o investigated and showed considerable macrosegregation, and magnetic melt damping may be the cause.
125 CHAPTER 8 CONCLUSIONS The experimental goal of this work was to ascertain whether Magneto Acoustic Mixing Technology (MAMT) is an appropriate method to produce metal matrix nanocomposites (MMNCs). In Chapter 1, the motivation for producing MMNCs by MAMT was developed and the process was introduced. Chapter 2 contained descriptions of potential mechanisms active in the presence of magnetic and acoustic fie lds, along with details on MMNC strengthening mechanisms and fabrication technologies. Chapter 3 presented a physical description of MAMT and calculations pertinent to the process. It was found that the skin depth (the depth of induction current in the sa mple) is vitally important to the process, as it controls the vibration mode by which MAMT proceeds. In the case of a large skin depth and melt vibration, a model for acoustic pressure in the melt was developed. A model for the acoustic propagation of wave s in the system was presented, as well as the influence of frequency on acoustic production. Since solidification is an important component of the current studies, two models were employed to estimate solidification front velocity in the materials. Reinfo rcement of Mg with rare earth oxide and diamond was chosen in Chapter 4. Additionally, considerations when choosing particle reinforcement for melt processing of MMNCs were discussed, including thermodynamic stability, mechanical effects of size, volume fr action, coefficient of thermal expansion, and elastic modulus. Chapter 5 contains a description of the experimental techniques, from pre processing to analysis. The specific MAMT setup is characterized, along with the analytical techniques used to investi gate samples. A series of Mg and Mg alloy
126 composites was fabricated to differing processing conditions (varying particle chemistry, acoustic pressure, and solidification treatment) to study the effect of processing on resultant structure. Chapter 6 describ ed the effect of MAMT on particle dispersion. It was found that thermodynamic stability and shape are of primary importance. The rare earth oxides, though partially agglomerated from particle interlocking, were stable in the MAMT system. Non interlocked Dy 2 O 3 nanoparticles were evenly dispersed in the microstructure, demonstrating the dispersion capability of MAMT. Conversely, in samples reinforced with diamond, the particles interacted with the stai nless steel crucible to produce multi modal reaction produ cts (10 nm to 5 Âµm) that were then dispersed in the matrix. Larger particles were gathered into strings by dipole dipole interactions, while smaller particles were found relatively evenly in the microstructure, again displaying the dispersion potential of MAMT. Particles were mobile in the melt, but the melt itself was effectively damped by the static magnetic field. Interaction of the melt with the crucible was found to produce particles in the microstructure for samples sonicated samples. Furthermore, rea ction with diamond accelerated the process. Future studies can alleviate this contamination issue with careful consideration of crucible materials and particle chemistry. Chapter 7 explored the microstructural effects of MAMT processing, including grain re finement and alignment. It was found that reaching the cavitation threshold in light metals is a dominant factor in grain refinement, an observation made in other studies [ 109 , 119 ] . Additionally, it was found that texture alignment to the magnetic field is decreased by the action of sonic waves. The effect of alloying was examined with Li
127 additions to Mg. MAMT wa s found to refine grains, even at low acoustic pressure. Significant macrosegregation was observed. The origin of macrosegregation is either enhanced diffusion in the melt due to magnetic stabilization or incomplete mixing in pre processing. Future studies are needed to elucidate this mechanism. This work makes contributions to several scientific fields. Primarily, it describes a novel technology (MAMT) and establishes it as a viable option for metal matrix nanocomposite processing. Important connections ar e made between input materials, processing conditions, and resulting structures, while relating to physical mechanisms. The description of particle choice for MMNC melt fabrication provides an introduction to important concepts in the field. The theoretica l framework established in Chapter 3 may be adapted to other material systems and applications like sonochemistry. Thus, a foundation has been provided that opens the way for the synthesis of novel materials with the combination of magnetic and sonic field s that would be otherwise unachievable.
128 CHAPTER 9 FUTURE WORK 9.1 MAMT Processing Investigations A primary benefit of MAMT is the flexibility with which sonic energy may be delivered to a sample. However, this flexibility makes for a myriad of experimen tal approaches to understanding how MAMT changes material structures. Many aspects of the process such, as frequency and skin depth, are interdependent and change the process concurrently, so a nuanced approach must be taken to derive a general model for M AMT. In this section, the experimental lines of inquiry will be split into fundamental mechanisms and MAMT configuration variations. 9.1.1 Fundamental Physical Mechanisms MAMT offers the opportunity to study the effect s of acoustic and magnetic fields on materials in ways previously unavailable. One of the primary benefits of MAMT is the widely variable frequencies, unlike in horn based sonication technologies which have one resonant frequency [ 114 ] . This capability could facilitate studies on the frequency dependence of cavitation and other acoustic phenomena. A fundamental difference between horn based sonication and EMAT is that intensity drops away from the source horn based sonica tion in the first and increases away from the source in MAMT [ 56 ] . In this way, MAMT produces convergent acoustic waves. The comparison between intensity distributions was explored in Appendix B, where propagation normal to the emitting surface was assumed for MAMT as an early approximation. The physics of convergent acoustic waves in liquids has received very little attention in the literature [ 227 ] , and MAMT may facilitate studies into this subject.
129 The strong static magnetic field in the MAMT system is a source of unc ertainty in describing the propagation of sound. In the current geometry, sound waves propagate perpendicularly to the field lines of the static magnet (as seen in Figure 3 1). Because this sound wave is longitudinal, the melt displacement is perpendicular to the field lines and is damped, based on the magnetohydrodynamic (MHD) principles outlined in Section 2.1.3. While the melt displacement is likely too small to be completely damped, the propagation behavior could be affected, for instance, by the transf ormation of longitudinal waves into AlfvÃ©n waves [ 228 ] . This could enable studies into MHD sonic dispersion in conductive liquids. 9.1.2 MAMT Specific Inves tigations With the complexity of MAMT, further work needs to be done to improve the predictability of resultant microstructures. One of the most important questions to be resolved is how sonication is produced depending on the skin depth. In this document, induction current in the crucible wall was ignored, as an approximation, to produce the model of sound production given in Section 3.2. This approximation was appropriate because the skin depth was much larger than the crucible thickness, meaning the majo rity of the eddy currents are in the melt. However, depending on the frequency and crucible material, the skin depth may be similar to the crucible thickness in the intermediate region between melt and crucible vibration modes (Section 3.1). This situation , in which the melt and crucible are both being driven by disparate body forces, creates a complex mechanism in which oscillation amplitude or phase difference may cause impacts between the melt and crucible. Sophisticated numerical techniques will likely be necessary to model this interaction, and its effect on sound production, accurately.
130 Another potentially fruitful investigation is the effect of solidification on the production of sound waves in EMAT. As the melt solidifies inwards, it changes the edd y current distribution and apparent stiffness of the crucible, reducing the displacement in response to the Lorentz force. This effect was observed in the microstructure of Sample 1 Mg Dy(r) 18T (4,4)MPa in Section 7.2.2. The scale of this change in acoust ic intensity is currently unknown. Another line of research may be to circumvent this effect by changing the geometry of the apparatus (continuous casting with solidification from the inside outward, for instance). One phenomenon that was not evaluated in the current studies is the effect of using a ferromagnetic crucible on the MAMT process. For diamagnetic or paramagnetic materials (like the stainless steel used in the current study), the Lorentz force is responsible for sound production in MAMT [ 56 ] . However, in a ferromagnetic material, two other processes can produce oscillations: magnetostriction and the magnetization force. Magnetostriction occurs when a ferromagnetic material changes shape in response to a magnetization, and the magnetization force is caused by the interaction of an applied magnetic field and previous magnetization of the ferromagnet [ 128 ] . Magnetostriction is the primary mode by which acoustic waves may be generated. It should be noted that in the case of magnetostriction of a ferromagnetic material, only an alternating magne tic field must be applied to the workpiece for sonication (i.e. no large static field is necessary), unlike sonication by the Lorentz force. Of course, these processes are dependent on the crucible exhibiting ferromagnetic properties, and therefore it must be below the Curie point. At temperatures above the Curie point, ferromagnetic properties give way to paramagnetic behavior , so only the Lorentz force
131 would act to produce sound waves. Cobalt may be a good candidate material for studying these effects in light metals, considering its very high Curie point of 1400Â°C. Another option is to change the geometry of MAMT from the cylindrical geometry described in this document. This geometry would be primarily dependent on design of the induction coils. For examp le, planar coils could inoculate a melt with planar sound waves equal in intensity throughout, simplifying analysis of the effect of MAMT on materials. 9.2 Potential Applications Up to this point, MATM has been an unexplored technique. This document outlin es how it may be used in the fabrication of Light Metal Matrix Nanocomposites, but there are several other applications to which MAMT may be suited. 9.2.1 Other Systems of Interest In this document MAMT was discussed primarily with regard to the fabricati on of light metal matrix composites for weight sensitive applications, but it may be adapted to process other metal matrix composites for other uses. In this respect, one of the primary benefits of MAMT is the potential temperature range. Vacuum induction systems can reach temperatures of 3000Â°C [ 229 ] . While this temperature almost certainly too high to house safely in a magnet bore, materials such as steels (T m = 1200 1600Â°C), can potentially be melted and processed by MAMT. Steels cannot be sonicated with current technology because of temperature limitations on ultrasonic probes, but high power MAMT could facilitate the melt fabrication of steel composites. 9.2.2 Sonochemistry Sonochemistry, the facilitation or acceleration of chemical reactions by sonic energy [ 112 , 116 , 230 ] , is an application to which EMAT may be well suited.
132 Specifically, this process takes advantage of the extreme pressures and temperatures in collapsing cavitation bubbles to drive reactions that would not occur under equilibrium conditions. Figure 9 1 . Schematic of a potential MAMT apparatus for continuous sonochemical applications . Using a similar geometry to the system described in Section 3.1, EMAT may be applied to an aqueous (or other liquid) system to drive sonochemical processes. A sample schematic is shown in Figure 9 1. In this setup, reactants flow by pipe into a contained liquid) is heated and vibrated by coupling induction and static fields. In an aqueous system, vibration mode would need to be crucible vibration, as water is a poor conductor and would not carry induction curren ts well. In the EMAT reaction zone, the desired reaction occurs in a continuous fashion. If implemented in a vertical column, this setup could also be used for gas or solid precipitation and collection. With the advent of persistent switches on superconduc ting magnets (discussed in Section 2.1 ), this application of MAMT has the potential to be economically viable in high throughput operations.
133 9.3 Sonofusion Sonofusion, otherwise known as Bubble Fusion, is a hypothetical process in which nuclear fusion occ urs in collapsing cavitation bubbles in deuterated organic solvents. Experimental evidence for this process has been presented [ 231 , 232 ] , but has been met with a great deal of controversy because of experimental irregularities [ 233 , 234 ] . Despite uncertain initial research, there is still interest in this purported fusion mechanism. The initial research was conducted using piezoelectric drivers, but the MAMT system described in this document may be a good candidate for future investigations. The flexibility of MAMT with regard to frequency and power, compared to sonicating horns, could potentially facilitate more rigorous studies into the existence of sonofusion.
134 APPENDIX A CALCULATION OF ACOUSTIC PRESSU RE AND INTENSITY IN MAMT CRUCIBLE VIBRATION MODE In discussing high power EMAT, it is important to understand how processing and material parameters affect the production of acoustic waves. There are two primary sonication modes in EMAT, melt vibration and crucible vibration, which were discussed in Chapter 3. Which mode is dominant depends on the media carrying the majority of the induced cu rrent, the crucible or the melt. This can be ascertained by inspecting the skin depth with regards to the crucible. M elt vibration was the mode utilized in the current studies, and derivation of acoustic pressure for that mode was contained in Chapter 3. Crucible vibration mode was not used in the studies, but a derivation of acoustic pressure and intensity is provided h ere for future studies. A relationship between induction power, magnetic flux density, material properties and dimensions, and acoustic production will be drawn. Several assumptions are made. The first is that the contained liquid and containment crucible are always in contact. Consequently, physical interactions of the melt with the container (damping) are ignored. Second, the alternating eddy currents high frequencies, both of these assumptions will fail as inertial effects become more dominant. For this calculation, all induction eddy currents are assumed to be in the crucible, so currents within the melt are neglected for computational simplicity. First, the distribut ion of eddy currents in the crucible will be calculated based on transformer equations and skin depth. Second, the body forces due to the Lorentz interaction are calculated. The subsequent deformation of the container is determined, and its amplitude is re lated to sound intensity. For the calculation of container
135 deformation, the container is idealized as an unbound cylinder for simplicity. Since the actual container is bound on one side and consequently more stiff, the calculated displacement amplitude wil l be an over estimate. A concept that arises several times in the derivation is skin depth. In a conductor carrying an alternating current, internally produced eddy currents cause the current density to decrease away from the surface. This profile is de scribed by Equation A 1, where J(d) is the current at a certain depth d, J s is the surface current density and the skin depth [ 235 ] . Th e skin depth (Equation A 2) is a material dependent parameter at which the current density has dropped to 1/ e (or ~37%) of its surface value. Skin r ) of the material, the alternating current frequency ( f 0 ) [ 235 ] . (A 1) (A 2) First, the distribution of current in the crucible is calculated. Since the induction coil is helical and the workpiece is cylindrical, this may be done following the transformer equat ions for induction heating [ 125 ] . Equation A 3 describes the current in the workpiece I w , the number of turns in the induction co il N c and the current in the coil I c . (A 3 ) The total current in the workpiece must be reduced, based on the fact that some of the induced current will be beyond the thickness of the crucible. This is accomplished by multiplying the current by the cumulative distribution function of the skin depth, or the
136 fraction of total current within a certain depth. The cumulative distribution function of a negative exponential like Equation A 1 is given in A crucible thickness t is substituted for d, then Equation A 10 gives the fraction of the total current in the crucible. Factoring A 10 into Equation A 8 gives the crucible current, I cr , in Equation A 11. (A 9) (A 10) (A 11) Having described the distribution of current, the Lorentz force due to the interaction of current and static field is calculated. Equation A 11 gives the vec tor form of the Lorentz force F L , where I is the current, B 0 is the magnetic flux density, and the integral is with respect to traveled distance c [ 236 ] . d c is an infinitesimal circumferential distance over which the current travels. Because c and B 0 are always perpendicular ( B 0 is in the axial direction of the cylinder), the cross product in A 12 can be transformed into a direct multiplic ation in Equation A 13. The total force on the cylinder toward the central axis of the cylinder (F tot ) is now calculated by integrating A 13 from 0 to C w . This resulting total force is given in Equation A 14. (A 12) (A 13) (A 14)
137 The total body force due to the Lorentz interaction may be converted to and alternating hydrost atic pressure on the container, and is calculated by dividing F tot by the external induction area of the crucible, C w h w , in Equation A 11. (A 15) Next, the deflection of the crucible from this pressure must be calculated. Equation A r , as a function of pressure p, [ 172 ] . Substituting A 15 into A 16 gives A 17. (A 16) (A 17) One of the assumptions made fo r this model is constant contact between the crucible and liquid. If this is the case, then the crucible displacement is equal to the 18. (A 18) The spee d of sound in liquid is needed, Equation A 19, where ad is adiabatic compressibility [ 55 ] . P acoustic ) as Equation A l is density of the fluid, c is the speed of sound in the fluid and f is the frequency of the sound (equivalent to the induction frequency) [ 55 ] . Sound pressure is related to acoustic intensity (I acoustic ) by Equation A 21 [ 55 ] .
138 (A 19) (A 20) ( A 21) Substituting A 18 into A 20 and A 21 gives Equations A 22 and A 23, respectively. Finally, A 11 can be substituted into A 22 and A 23 for the final for acoustic pressure and acoustic intensity in terms of input variables in A 24 and A 25. A summary o f the input variables is found in Table A 1. (A 22) (A 23) (A 24) (A 25)
139 Table A 1. Summary of input variables for calculating acoustic pressure and intensity in the EMAT system by Equations A 20 and A 21. Variable Identity Units P acoustic Acoustic Pressure Pa I acoustic Acoustic Intensity W/m 2 P in Input power to i nduction system W I c Induction coil current Amperes N c Number of turns in coil unitless d c Coil diameter (of one turn) m l c Coil Length (top to bottom) m f Induction frequency Hz c Coil resistivity 0 Permeability of free space mÂ·kgÂ·s 2 Â·A 2 c Relative permeability of coil unitless B 0 Magnetic flux density of static magnet T r w Radius of workpiece (the crucible) m w Crucible resitivity E Pa h w Affected height of crucible m t Crucible thickness m l Density of metallic melt kgÂ·m 3 ad Adiabatic compressability of melt Pa 1 Âµ cr Relative permeability of crucible unitless
140 APPENDIX B CALCULATION OF ACOUSTIC INTENSITY DISTRIBUTION FOR HO RN AND EMAT BASED SONICATION When discussing the effect of sonic energy on materials processing, it is useful to understand how sonic energy propagates in the system. High power electromagnetic acoustic transduction (EMAT) and sonotrode based technologies radiate this energy in quite different fashions, and will be discussed individually. It should be noted that sonic energy is assumed to propagate as a plane wave evenly away from the radiating surface in both cases, as is appropriate for the relative lengt h scales of radiator and sound wavelength [ 55 ] . The intensity is calculated based on geometri c spreading of the wavefront, leading to Equation B 1 , where P ac is the acoustic power, A i is the area at a certain distance away from the source, and I i is the intensity (in W/cm 2 ) at that distance. In this analysis, attenuation is neglected, so P ac is in variant and Equation B 2 may be used to compare intensities at the source and a distance away (denoted, respectively, by subscripts 0 and s). The results of this methodology in thi s document are given in Figure 3 5 . (B 1) (B 2) B.1 MAMT Acoustic Intensity Distribution For the instance of MAMT discussed in this document, it is assumed that sonic power is generated evenly over the sides over the cylinder and propagates inward. The intensity is then giv en by a ratio of cylindrical areas, leading to increased intensity towards the center of the sample. The rel ationship is given in Equation B 3 , where I s (s)
141 is the intensity as a function of distance away from the radiating wall, I 0 is the initial wall inte nsity, A 0 is the area of the cylinder wall, A s wall, R is the radius of the cylinder, and h is t he cylinder height. T he initial acoustic intensity must be known for this calculation. If the skin depth of induction i s sufficiently small, the acoustic intensity calculated in Appendix A can be used . It should be noted that this simple relation gives a nonphysical result of infinite intensity at the center of the cylinder , but is limited by both cavitation and the mean f ree path of the material . However, it is still useful for understanding relative intensity across the material. (B 3) B.2 Sonotrode Acoustic Intensity Distribution The case of a sonotrode is more complex than that of MAMT , because of a complex three dimensional propagation. At the relati ve radiator size and wavelength for [ 106 ] spherical, however, since the radiator consists of a disc and not a point source. Here, the area away from the radiator tip is modeled as a series of expanding oblate sphe roids with semi axes a, b, and c increasing by the same distance each timestep. At the source, a and b are the radius of the sonotrode, while c is zero. The intensity decreases as a function of A 0 /A i , where A 0 is twice the area of the radiator tip (the are a of the first spheroid) and A i is the area of a spheroid some distance away from the tip. Visualized in a two dimensional plot (in the plane of semi axes a and c), these spheroids appear to be an expanding set of ellipses. To create a plot of this intensi ty distribution, it is necessary to link these 2D ellipses to their corresponding 3D spheroids
142 in this case). The equation for a n ellipse is given in Equation B 4 , wh ere x and z are axis starts as the radius of the sonotrode, r, Equation B 4 is transformed to Equation B 5 . Since a value of 1mm is chosen, this may be simplified to Equation B 6 , if all distances are given in mm. (B 4) (B 5) (B 6) To begin the plot, crucible shape, crucible size, sonotrode size and sonotrode position must be chosen. Once this is decided, (0,0) is chos en as the center of the performed on Equation B 6 at each relevant (x,z) position. Four solutions are reached, and the largest positive solution is chosen as the r eal value. The result of this The second step is to insert intensity values from the 3D calculation. I 0 is the sonotrode acoustic power divided by the circular surface area of the sonotrode tip. The expa nding sonic power follows the equation o f an oblate spheroid, Equation B 7 , where a is the major semi axis and c is the minor semi axis. The equation is transformed into a series of expanding spheroids in Equation B 8 , following the same methodology as wit h the 2D ellipses. The equation for the surface are of a oblate spheroid is given in Equation B 9 . Again, 10 , which simplifies to Equation B -
143 11 . With I 0 , A 0 , A n , and n as a function of (x,z) known, a plot may be generated wi th I n as a function of (x,z). (B 7) (B 8) , where (B 9) (B 10) (B 11)
144 APPENDIX C INDIRECT COMPOSI TIONAL MEASUREMENTS IN MG LI ALLOYS Experimental studies in which Li may not be homogeneously distributed in an particularly difficult to measure experimentally. Standard microsco py techniques like Energy Dispersive X ray Spectroscopy (EDS), Electron Probe Microanalysis (EPMA) cannot be used to detect Lithium because the X Ray emission energy is too low to be detected. Thus, techniques like Inductively Coupled Plasma (ICP) are need ed. Unfortunately, a single measurement requires a section of material to be dissolved, greatly limiting the spatial distribution information. In this appendix, two indirect methods of Li compositional measurement will be described. The first will give bou nds of composition based on the volume percentage of phases in the microstructure. The second determines the composition based on Vickers hardness. These methods are specifically applied to Mg Li binary alloys, but could be adapted to other systems. C.1 Mi crostructure Based Compositional Measurement This method determines composition based on the local microstructure of a cast alloy. In a microstructure containing a eutectic constituent, it is possible to provide bounds for the local composition based only on the area fraction of eutectic. This is accomplished beginning by calculating the amount of eutectic based on both equilibrium and Scheil solidification of different alloy compositions with thermodynamic software. By inverting the variables of the result ing eutectic dependence of composition, a composition based on microstructure can be deduced. This technique is only useful where there is a phase dependence on composition. Thus, it is unsuitable for compositional measurements in a solid solution material .
145 First, Pandat, a thermodynamic calculation software, is used to create a matrix of BCC phase fraction as a function of Li at.% in Mg under Sheil and equilibrium solidification conditions. These represent the limits of possible BCC phase fraction in a reg ion with a specific Li at.%. This information, gathered from the PanMag databas e in Pandat, is found in Table C 1. Table C 1. Percentage of BCC in the microstructure under Sheil and Equilibrium conditions as a function of Li at.%. Li at.% Fraction BCC (Sh eil) Fraction BCC (Equilibrium) 0 0 0 2 0 0 4 2.20E 5 0 6 8.48E 4 0 8 5.028E 3 0 10 0.0183 0 12 0.0451 0 14 0.0996 0 16 0.1771 0 18 0.2965 0.1916 20 0.4621 0.4623 22 0.7212 0.7330 24 0.9680 1 26 0.9999 1 28 1 1 Next, linear models are fit to the corresponding curves. This is trivial for the equilibrium case, as the fit is linear where 0
146 Figure C 1. Equilibrium BCC volume fraction in Mg Li as a function of Li at.%. The linear fit to the variable model is displayed in black. (C 1) The case for Sheil solidification is slightly more complicated. First, Li at.% is plotted as a function of Fraction BCC and a model is fit ted in Figure C 2. Though the power law provided the best fit, there i s considerable error. This is mitigated by plotting the residual between the data and the power law, and then fitting a linear model th e regression, shown in Figure C 3. Adding the linear fit to the initial power law model in Equation C 2, a superior fit c an be seen in Figure C 4 .
147 Figure C 2. Li at.% as a function of BCC Fraction for the case of Sheil solidification and a power law model. Figure C 3. Difference between Sheil data and the power model in Figure C 2: as a function of BCC Fraction, along w ith a linear fit.
148 Figure C 4. Li at.% as a function of BCC Fraction for the case of Sheil solidification, along with the corr ected model found in Equation C 2. (C 2) Figure C 5. B oundaries of potential Li at.% in MgLi alloys as a function of BCC phase fraction. Since the percentage of BCC in the microstructure must lie between the Sheil and equilibrium cases, a range of potential composition can be found by plotting both the Sheil and equilibrium models si multaneously, found in Figure C 5. The range of
149 possible concent ration is found in Figure C 6. It can be seen that this technique is much more accurate at higher fractions of BCC in the matrix. Figure C 6. Range of possible Li at .% as a function of fraction BCC in MgLi binary alloys. To implement this technique, the fraction of BCC in the microstructure must be measured. This can be accomplished by a number of techniques, including x ray diffraction and neutron diffraction, but th e easiest method is likely optical microscopy. An optical micrograph of a polished and etched microstructure can be thresholded and analyzed by a program such as ImageJ. Depending on the magnification, this will likely output the fraction of eutectic, so a scaling factor from eutectic fraction to BCC fraction may be needed. Whether or not this is necessary can be determined by examining the morphology of the eutectic phase. If lathes are observed, the fraction of eutectic can be multiplied by 0.80 (the frac tion of BCC at the eutectic composition for MgLi [ 225 ] ). If the eutectic is divorced, no factor is necessary.
150 C.2 Hardness Based Compositional Measurement The previous method of indirect compositional measurement is unsuitable for solid solution alloys, so a metho d using hardness is utilized. This is based on hardness measurements by Hibbard [ 237 ] , which are found in Figure C 7. Inverting the axes, Li percent can be determined by hardness measurements using the equations in Figure C 8. If this method is used, care should be taken to understand the level of uncertainty inherent in hardness testing and test numerous sites to compensate with statistical significance. Figure C 7. Vickers hardness as a function of Li at.% and wt.%. [ 237 ]
151 APPENDIX D ADDITIONAL DATA D.1 Mechani cal Testing Data Mechanical tests of Samples 4, 5 and 6 were conducted. The results of the tension tests are found in Figure D 1. Pre and post test microstructures of the samples are shown in Figures D 2, D 3, and D 4. The yield stresses of the materials are low, but are consistent with large grained (1 mm) Mg, as measured by Caceres [ 238 ] . It can be seen that the higher volume fraction of particles in Sample 5, as compared to 4 and 6 contributes to a higher work hardening rate. The particle dispersions in the samples are shown in Figure 6 13. Figure D 1. Tension Curves for Samples 4, 5, and 6. Data for pure Mg with a grain size of 1 mm by Caceres [ 238 ] is shown for comparison.
152 Figure D 2. Etched tension specimen of sample 4 Mg NA 18T (1.5,0)MPa . A) pre and B ) post test (Photos courtesy of Author). Figure D 3. Etc hed tension specimen of sample 5 Mg Dia(s) 18T (1.5,0)MPa . A) pre and B ) post test (Photos courtesy of Author).
153 Figure D 4. Etched tension specimen of sample 6 Mg Dia(s) 0T (0,0)MPa . A) pre and B ) post test (Photos courtesy of Author). Compression tests were also performed on the samples by sectioning 3 mm diameter and 5 mm tall cylinders from the samples. Results of several of the tests can be seen in Figure D 5. They show a wide variability in mechanical response within the same sample. Since the grain size is of the same order of magnitude as the sample size, making single crystal effects dominant in the samples. Figure D 6 shows an etched compression sample in which t winning dominates the deformed microstructure. A shear band is also visible in the sam ple, likely originating at a grain of preferential orientation for slip.
154 Figure D 5. Compression Curves for Samples 4, 5, and 6. Figure D 6. Structure of a compression specimen from 6 Mg Dia(s) 0T (0,0)MPa . A) Post testing overview, B) polished and e tched, and C ) high magnificat ion of the area indicated in B (Photo s courtesy of Author) .
155 D.2 Thermal Profiles This section is a compilation of the thermal profiles for samples discussed in the dissertation. Details on each of the run conditions may be fo und in Table 5 1 . Figure D 7. Temperature and magnetic field profile for Sample 1 Mg Dy(r) 18T (4,4)MPa Figure D 8. Temperature and magnetic field profile for Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa
156 Figure D 9. Temperature and magnetic field profile for S ample 3 Mg Dy(r) 0T (0,0)MPa Figure D 10 . Temperature and magnetic field profile for Sample 4 Mg NA 18T (1.5,0)MPa Figure D 11 . Temperature and magnetic field profile for Sample 5 Mg Dia(s) 18T (1.5,0)MPa
157 Figure D 12 . Temperature and magnetic field p rofile for Sample 6 Mg Dia(s) 0T (0,0)MPa Figure D 13 . Temperature and magnetic field profile for Sample 7 Mg Er(s) 18T (1.5,0)MPa Figure D 14 . Temperature and magnetic field profile for Sample 8 Mg Er(s) 0T (0,0)MPa
158 Figure D 15 . Temperature and magn etic field profile for Sample 9 Mg7Li NA 18T (1.5,1.5)MPa Figure D 16 . Temperature and magnetic field profile for Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa Figure D 17 . Temperature and magnetic field profile for Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa
159 F igure D 18 . Temperature and magnetic field profile for Sample 12 Mg15Li NA 18T (1.5,1.5)MPa Figure D 19 . Temperature and magnetic field profile for Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa D.3 Radiography Data Radiography data relevant to the studies in the current document are compiled in Figures D 15 through D 26. The orthogonal perspectives are shown in figure D 14.
160 Figure D 20 . Orthogonal perspectives for X ray radiography. Figure D 21 . Radiography for Sample 2 Mg Dy(r) 18T (1.5,1.5)MPa Figure D 22 . Radiography for Sample 3 Mg Dy(r) 0T (0,0)MPa
161 Figure D 23 . Radiography for Sample 4 Mg NA 18T (1.5,0)MPa Figure D 24 . Radiography for Sample 5 Mg Dia(s) 18T (1.5,0)MPa Figure D 25 . Radiography for Sample 6 Mg Dia(s) 0T (0,0)MPa
162 Figure D 26 . Radiography for Sample 7 Mg Er(s) 18T (1.5,0)MPa Figure D 27 . Radiography for Sample 8 Mg Er(s) 0T (0,0)MPa Figure D 28 . Radiography for Sample 9 Mg7Li NA 18T (1.5,1.5)MPa
163 Figure D 29 . Radiography for Sample 10 Mg7Li Dia(s) 18T (1.5,1.5)MPa Figure D 30 . Radiography for Sample 11 Mg7Li Er(s) 18T (1.5,1.5)MPa Figure D 31 . Radiography for Sample 12 Mg15Li NA 18T (1.5,1.5)MPa
164 Figure D 32 . Radiography for Sample 13 Mg15Li Dia(s) 18T (1.5,1.5)MPa
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185 BIO GRAPHICAL SKETCH Hunter Henderson was born in Boynton Beach, Florida and grew up in Stuart, Florida. After an undergraduate in m aterials s cience and e ngineering at the University of Florida, he pursued a graduate degree at the same institution.