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Assessment of Silver and Tin Atomic Mobilities in Polycrystalline Magnesium Alloys

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Title:
Assessment of Silver and Tin Atomic Mobilities in Polycrystalline Magnesium Alloys
Creator:
Wagner, Joshua S
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (123 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Materials Science and Engineering
Committee Chair:
MYERS,MICHELE V
Committee Co-Chair:
HENNIG,RICHARD
Committee Members:
PHILLPOT,SIMON R

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Subjects / Keywords:
database -- dictra -- diffusion -- magnesium -- optimization
Materials Science and Engineering -- Dissertations, Academic -- UF
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Materials Science and Engineering thesis, M.S.

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Abstract:
In an effort to increase fuel efficiency and decrease carbon dioxide emissions, the automotive industry is considering low-weight alternatives to the current structural materials. Magnesium (Mg) alloys are of particular interest due to Mg being the lightest structural metal. However, current Mg alloys have limited elevated-temperature applications due to poor creep resistance. The advent of computational thermodynamic and kinetic techniques allows faster and focused alloy development at a fraction of its previous cost. As an integral part of Mg alloy development, the kinetics of the Magnesium-Silver (Mg-Ag), Magnesium-Tin (Mg-Sn), and Magnesium-Silver-Tin (Mg-Ag-Sn) polycrystalline solid-solution systems were investigated. Diffusion couples were prepared to study Ag diffusion in Mg and in Mg-Sn and Sn diffusion in Mg and in Mg-Ag, and each of these were annealed at 450, 500, and 550 degrees Celsius. Concentration profiles were extracted from the diffusion couples using electron probe microanalysis, and interdiffusion coefficients were calculated using the Sauer-Friese-den Broeder modification of the Boltzmann-Matano analytical method. These interdiffusion coefficients were iteratively optimized to yield kinetic data in the form of atomic mobility parameters, and were validated using additional diffusion couple experiments. It was shown that the addition of Sn to Mg-Ag decreased the activation energy of Ag diffusion in Mg, and the addition of Ag to Mg-Sn increased the activation energy of Sn diffusion in Mg. This increase in activation energy slows Sn diffusion in Mg at temperatures below 500 degrees Celsius, which can improve the creep resistance of Mg-Ag-Sn alloys for use in elevated-temperature applications. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2017.
Local:
Adviser: MYERS,MICHELE V.
Local:
Co-adviser: HENNIG,RICHARD.
Statement of Responsibility:
by Joshua S Wagner.

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ASSESSMENT OF SILVER AND TIN ATOMIC MOBILITIES IN POLYCRYSTALLINE MAGNESIUM ALLOYS By JOSHUA STEVEN WAGNER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR TH E DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2017

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2017 Joshua Steven Wagner

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To Al

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4 ACKNOWLEDGMENTS First and foremost, I would like to t hank God for all the blessings h e has bestowed on my life, in particular the opportunity to return to the University of Florida to tes Air Force for covering the entire cost of sending me back to school I want to thank my supervisors at Eglin Air Force Base, Cleo and Jack, for their patience and understandi ng throughout I would also like to thank my co workers at Egli I would like to thank my advisor, Dr. Michele Manuel, for all that she has done for me during both my undergraduate and graduate career here at the University of Florida. m grateful for all her guidance and mentorship throughout my time here, especially in professional development and i n this project I would also like to thank my committee members, Dr. Simon Phillpot and Dr. Richard Hennig, for their feedback and guidance. I n addition, I would like to thank s research group, Sujeily, Wesley, David, Oscar, Flavia Andrew, Ellie Brittani, Ian, and Dr. Monica Kapoor, for their help and friendship. Specifically I would like to thank Ian for the numerous hours he spent working this project alongside me and teaching me all the techniques I needed to work on thi s project. I would also like to thank Dr. Kapoor for numerous hours she spent helping me edit my thesis and my thesis presentation. I would also like to thank my longtime mentor, Dr. Rachel Abrahams, for all of her help and support over the years. From int roducing me to the field of materials science

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5 and engineering as a senior in high school to all her advice and wisdom that she gave me while I pursued graduate studies, she has been incredibly supportive and helpful. I would like to thank my parents, grand mother, and my brother, Alex, for their always constant love and support. here at the University of Florida for their support, encouragement and friendship. This project would not have been possible without each and every one of you

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FI GURES ................................ ................................ ................................ .......... 8 LIST OF TERMS ................................ ................................ ................................ ........... 12 ABSTRACT ................................ ................................ ................................ ................... 17 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 19 2 LITERATURE REVIEW ................................ ................................ .......................... 27 3 MATERIALS AND METHODS ................................ ................................ ................ 49 4 RESULTS AND DISCUSSION ................................ ................................ ............... 59 5 SUMMARY AND CONCLUSIONS ................................ ................................ .......... 80 6 FUTURE WORK ................................ ................................ ................................ ..... 83 APPENDIX A PHASE DIAGRAMS OF MG ALLOYS ................................ ................................ .... 84 B CUBIC B SPLINE INTERPOLATION OF CONCENTRATION PROFILES ............. 89 C CONCENTRATION DEPENDENT INTERDIFFUSION COEFFICIENTS ............. 101 D CONCENTRATION PROFILES COMPARED TO DICTRA SIMULATIONS ......... 105 LIST OF REFERENCES ................................ ................................ ............................. 117 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 123

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7 LIST OF TABLES Table page 1 1 D ensities and mechanical properties of automotive steels Al alloys, and Mg alloys ................................ ................................ ................................ .................. 26 3 1 Compositions of cast Mg alloys ................................ ................................ .......... 54 3 2 Grinding an d polishing steps for Mg alloys ................................ ......................... 54 3 3 D iffusion couple heat treatments ................................ ................................ ........ 54 3 4 Diffusion couple line scan length and step size ................................ .................. 55 3 5 Smoothing factor and R 2 centration profile ................................ ................................ ................................ .................. 55 3 6 Validation d iffusion couple heat treatments ................................ ........................ 55 3 7 Validation diffusi on couple line scan length and step size ................................ .. 56 4 1 Optimized atomic mobility parame ters used in DICTRA simulations .................. 67

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8 LIST OF FIGURES Figure page 2 1 Schematic of vacancy diffusion mechanism ................................ ....................... 40 2 2 Schematic of i nterstitial diffusion mechanism ................................ ..................... 41 2 3 Temperature dependence of the diffusion coefficient in solids, as described by th e Arrhenius relationship ................................ ................................ .............. 42 2 4 Schematic of an HCP lattice with the two possible atomic jump directions hig hlighted with blue lines ................................ ................................ ................... 43 2 5 Example of a concentration profile ex tracted from a diffusion couple ................. 44 2 6 Example of a Matano plane ................................ ................................ ................ 45 2 7 Data from literature of the diffusion coef ficien t of Ag in Mg ................................ 46 2 8 Data from literature of the diffus ion coefficient of Sn in Mg ................................ 47 2 9 Temperature dependent diffusion coefficients of all relevant solutes i n Mg, as 1 atomic mobility database ................................ ..... 48 3 1 An en capsulated diffusion couple jig ................................ ................................ .. 57 3 2 Schematic of diffusion couple sectioning f or EPMA WDS ................................ .. 57 3 3 Example of cubic b spline concentration profile curve fitting in Origin ................ 58 4 1 Concentration dependent interdiffusion coefficients of Mg/Mg 5Ag diffusion couples and the c orresponding DICTRA simulations ................................ ......... 68 4 2 Temperature dependent diffusion coefficients of Ag in Mg ................................ 69 4 3 Concentration profile of Mg/Mg 2Ag validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation ................................ ................... 70 4 4 Conc entration dependent interdiffusion coefficients of Mg/Mg 5Sn diffusion couples and the c orresponding DICTRA simulations ................................ ......... 71 4 5 Te mperature dependent diffusion coefficients of Sn in Mg ................................ 72 4 6 Concentration profile of Mg/Mg 2Sn validation diffusion couple annea led at 525 o C with corresponding DICTRA simulation ................................ ................... 73 4 7 Concentration dependent interdiffusion coefficients of Mg/Mg 2Sn 5Ag diffusion couples and the c orresponding DICTRA simulations ........................... 74

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9 4 8 Temperature dependent diffusion coefficie nts of Ag in Mg and Ag in Mg Sn ..... 75 4 9 Concentration profile of Mg/Mg 2Sn 5Ag validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation ................................ ............... 76 4 10 Concentration dependent interdiffusion coefficients of Mg/Mg 2Ag 5Sn diffusion couples and the c orresponding DICTRA simulations ........................... 77 4 11 Temperature dependent diffusion coefficie nts of Sn in Mg and Sn in Mg Ag ..... 78 4 12 Concentration profile of Mg/Mg 2Ag 5Sn validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation ................................ ............... 79 5 1 Temperature dependent diffusion coefficients of all relevant solutes in MGMOB 1 with results of this study ................................ ................................ ..... 82 A 1 Mg Ag phase diagram ................................ ................................ ........................ 84 A 2 Mg Sn phase diagram ................................ ................................ ........................ 85 A 3 Mg Ag Sn phase diagram at 450 o C ................................ ................................ .... 86 A 4 Mg Ag Sn phase diagram at 500 o C ................................ ................................ .... 87 A 5 Mg Ag Sn phase diagram at 550 o C ................................ ................................ .... 88 B 1 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diff usion couple annealed at 450 o C ................................ ................................ .... 89 B 2 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diffusion couple annealed at 500 o C ................................ ................................ .... 90 B 3 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diffusion couple annealed at 5 50 o C ................................ ................................ .... 91 B 4 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 450 o C ................................ ................................ .... 92 B 5 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 500 o C ................................ ................................ .... 93 B 6 Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 550 o C ................................ ................................ .... 94 B 7 Concentration profile fit with cubic b spline interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 450 o C ................................ ............................. 95 B 8 Concentration profile fit with cubic b spline interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 500 o C ................................ ............................. 96

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10 B 9 Concentration profile fit with cubic b spline interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 550 o C ................................ ............................. 97 B 10 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 450 o C ................................ ............................. 98 B 11 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 500 o C ................................ ............................. 99 B 12 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 550 o C ................................ ........................... 100 C 1 Concentration dependent interdiffusion coefficient for Mg/Mg 5Ag diffusion couples annealed at 450 o C, 500 o C, and 550 o C ................................ ................ 101 C 2 Concentration dependent interdiffusion coefficient for Mg/Mg 5Sn diffusion couples annealed at 450 o C, 500 o C, and 550 o C ................................ ................ 102 C 3 Concentration dependent interdiffusion coefficient for Mg 2Sn/Mg 2Sn 5Ag diffusion couples annealed at 450 o C, 500 o C, and 5 50 o C ................................ .. 103 C 4 Concentration dependent interdiffusion coefficient for Mg 2Ag/Mg 2Ag 5Sn diffusion couples annealed at 450 o C, 500 o C, and 550 o C ................................ .. 104 D 1 Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 450 o C with corresponding DI CTRA simulation ................................ ................................ ... 105 D 2 Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 500 o C with corresponding DICTRA simulation ................................ ................................ ... 106 D 3 Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 550 o C with corresponding DICTRA simulation ................................ ................................ ... 107 D 4 Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 450 o C with corresponding DICTRA simulation ................................ ................................ ... 108 D 5 Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 500 o C with corresponding DICTRA simulat ion ................................ ................................ ... 109 D 6 Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 550 o C with corresponding DICTRA simulation ................................ ................................ ... 110 D 7 Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 450 o C with corresponding DICTRA simulation ................................ ................. 111 D 8 Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 500 o C with corresponding DICTRA simulation ................................ ................. 112

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11 D 9 Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 550 o C with corresponding DI CTRA simulation ................................ ................. 113 D 10 Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 450 o C with corresponding DICTRA simulation ................................ ................. 114 D 11 Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 500 o C with corresponding DICTRA simulation ................................ ................. 115 D 12 Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 550 o C with corresponding DICTRA simulation ................................ ................. 116

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12 L IST OF TERMS Interaction parameter Interaction parameter of Ag in Mg Ag Interaction parameter of Ag in Mg Sn Interaction parameter of Sn in Mg Sn Interaction parameter of Sn in Mg Ag AE Magnesium Aluminum Rare Earth Ag Silver Al Aluminum AM Magnesium Aluminum Manganese Ar Argon AS Magnesium Aluminum Silicon AZ Magnesium Aluminum Zinc BTU British Thermal Unit Concentration o C Degrees Celsius Concentration at distance Concentration at the terminal ends of the diffusion couple Concentration of component Concentration at the Matano plane CO 2 Carbon Dioxide CAFE Corporate Average Fuel Economy CALPHAD Calculation of Phase Diagrams Cd Cadmium

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13 Ce Cerium Cu Copper Diffusion coefficient Chemical diffusion coefficient of component Pre exponential factor Tracer diffusion coefficient of component Diffusion coefficient of component Intrinsic diffusion coefficient of component Intrinsic diffusion coefficient of component Lattice fixed frame of reference diffusion coefficient Volume fixed frame of reference diffusion coefficient Interdiffusion coefficient of at concentration Change in concentration Change in the concentration of component Change in Boltzmann transformation variable Change in distance Partial derivative of concentration of component Partial derivative of time Partial derivative of distance Partial derivative of the square distance Partial derivative of the mole fraction of component Partial derivative of the chemical potential of component Partial derivative of the mole fraction of diffusing species Second order derivative of the concentration of component

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14 Kronecker delta function DFT Density Function Theory DICTRA Diffusion Controlled Transformations EDS Energy Dispersion Spectroscopy EISA Energy Independence and Security Act EPMA Electron Probe Microanalyzer Fe Iron Interfacial free energy g Gram g/cm 3 Grams per cubic centimeter g/km Grams per kilometer Ga Gallium GPa Gigapascal HCP Hexagonal close packed In Indium Flux density of component K Kelvin kg Kilogram La Lanthanum LSW Lifshitz Slyozov Wagner Log Logarithm Atomic mobility of component Atomic mobility of component in gradient Atomic mobility frequency factor

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15 m Micrometer Mg Magnesium mm Millimeter Mn Manganese MPa Megapascal mpg Miles per gallon mTorr MilliTorr Boltzmann transformation variable Ni Nickel O 2 Oxygen gas Origin Origin Graphing and Analysis Software Concentration ratio Para Parallel to c axis Perp Perpendicular to c axis ppm Parts per million PX Polycrystalline Activation energy for diffusion Activation energy for diffusion of component Activation energy for diffusion of component in pure component Average radius of all particles Radius at the onset of coarsening Universal gas constant R 2 Coefficient of determination RE Rare Earth

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16 Sb Antimony SEM Scanning Electron Microscope SiC Silicon Carbide Sn Tin Time Temperature Ta Tantalum U Uranium Kirkendall (marker) velocity Molar volume of the precipitate VASP Vienna Ab Initio Simulation Package WDS Wavelength Dispersive Spectroscopy wt % Weight percent Distance Matano plane Mole fraction of component Mole fraction of component Solubility Mole fraction of component Mole fraction of component Mole fraction of component Mole fraction of component Zn Zinc

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17 Ab stract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for th e Degree of Master of Science ASSESSMENT OF SILVER AND TIN ATOMIC MOBILITIES IN POLYCRYSTALLINE MAGNESIUM ALLOYS By Joshua Steven Wagner December 2017 Chair: M ichele Viola Myers Major: Materials Science and Engineering In an effort to increase fuel efficiency and decrease carbon dioxide emissions, the automotive industry is considering low weight alternatives to the current structural materials. Magnesium (Mg) alloys are of particular interest due to Mg being the lightest structural metal. However, current Mg alloys have limited elevated temperature applications due to poor creep resistance. The advent of computational thermodynamic and kinetic techniques allows faster and focused alloy development at a fraction of its previous cost. As an integral part of Mg alloy development, the kinetics of the Magnesium Silver (Mg Ag), Magnesium Tin (Mg Sn), and Magnesium Silver Tin (Mg Ag Sn) polycrystalline solid solution s ystems were investigated. Diffusion couples were prepared to study Ag diffusion in Mg and in Mg Sn and Sn diffusion in Mg and in Mg Ag, and each of these were annealed at 450, 500, and 550 o C. Concentration profiles were extracted from the diffusion couples using electron probe microanalysis, and interdiffusion coefficients were calculated using the Sauer Friese den Broeder modification of the Boltzmann Matano analytical method. These interdiffusion coefficients were iteratively optimized to yield kinetic da ta in the form of atomic mobility parameters, and were validated using additional diffusion couple

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18 experiments. It was shown that the addition of Sn to Mg Ag decreased the activation energy of Ag diffusion in Mg, and the addition of Ag to Mg Sn increased t he activation energy of Sn diffusion in Mg. This increase in activation energy slows Sn diffusion in Mg at temperatures below 500 o C, which can improve the creep resistance of Mg Ag Sn alloys for use in elevated temperature automotive applications.

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19 CHAPTER 1 INTRODUCTION In 2003 it was determined that rely on petroleum based fuels [1] As a result transportation systems account for about 40% of the w 75 million barrels of oil per day [1] In 2016 the United States transportation sector alone consumed 27.934 quadrillion British thermal units ( BTU ) of energy over the course of the year, 26.424 quadrillion BTU (roughly 95%) of which was fossil fuels such as petroleum and natural gas [2] This consumption has been ste adily increasing from the 1950s up until 2008 [2] Within that time span, vehicle ownership in the United States has grown from about 74.4 million total vehicles in 1960 to more than 239 million vehicles in 2002, with an average annual growth rate of 3% [3] The increased use of petroleum and other fossil fuels presents sustainability problems to the transportation sector because fossil fuels are nonrenewable sources of energy Additionally, increased fossil fuel consumption results in increased greenhouse gas emissions. In 2015, the transportation sector account ed for 27.5% of such greenhouse gas emissions in the United States [4] With the effect of greenhouse gas emissi ons on global warming understood steps must be taken to reduce the amount of greenhouse gas emissions by the transportation industry [5] Rec ently, there has been a push by the United States government to improve fuel efficiency and reduce the amount of greenhouse gases produced by the transportation industry. In 2007, the Energy Independence and Security Act (EISA) was passed, which establishe d more stringent Corporate Average Fuel Economy ( CAFE ) standards [6] CAFE standards set the minimum gas mileage that every automotive

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20 United States. Since the passing of EISA CAFE standards for pass enger cars and light trucks have increased to 35 miles per gallon (mpg) by the year 2020 and are proje cted to increase to 54.4 mpg by the year 2025 [7 8] To meet these demands of improved fuel efficiency, automotive companies have looked at improving a variety of factors. The fuel efficiency of a vehicle depends on mu ltiple variables such as vehicle power vehicle speed, engine and transmission efficiencies, and fuel type [9] The vehicle power requirement, in turn, is t he sum of the power needed for vehicle acceleration, driv ing on a grade, overcoming resistance at the tire road interface, overcoming aerodynamic drag, a nd operating in car accessories [9] Of these, the vehicle acceleration, drivin g on a grade, and overcoming resistance at the tire road interface power requirements are directly proportiona l to the vehicle weight [9] As a result, reducing vehicle weigh t can lead to large reductions in the vehicle power requirement, which in turn can improve fuel efficiency. A 10% reduction in vehicle weight can result in an increase of 5 8% in fuel efficiency, and a 100 kilogram (kg) reduction in vehicl e weight can lead to a 12.5 grams per kilometer (g/km) reduction in carbon dioxide ( CO 2 ) emissions [9 11] Additionally, when vehicle weight is reduced, the power needed for acceleration and braking is also reduced, which allows car manufacturers to design smaller engines, transmissions, and braking systems [9] In order for a material to be considered as a weight reducing alternative in automotive design, it must have a lower density than the material currently being used At the same time, it should also achieve or improve upon the mechanical properties of the material currently being used Of particular im portance in automotive applications

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21 are the bending stiffness and bending strength of a material [9 11 12] These can be determined from a s elastic modulus and yield strength [12] Currently, steel is used for a majorit y of the pa rts in a car, and accounts for around 55 67% of the total weight of the car [9 11] However, the density of steel is about 7.8 grams per cubic centimeter (g/cm 3 ), making it a limiting factor in improving the fuel efficiency of automobiles [9 11 13] Aluminum (Al) alloys, in comparison currently make up 8.5% of the total weight of cars, and are used in parts such as the engine block and the steering wheel [9] Al uminum alloys have densities around 2.7 g/cm 3 which is a third of the density of steel [9 11 13] Although Al alloys have a lower elastic modulus and yield strength th an typica l automotive steels, their low density gives them a comparable specific modulus (elastic modulus divided by density ) and improved specific strength (yield strength divided by density ) when compared to automotiv e steels, as seen in Table 1 1 As a result, a part made out of an Al alloy will need to be about 1.43 times thicker than an automotive steel part if designing to achieve e qual bending stiffness, and 1.12 times thicker to achieve equal bending strength [9 12] This results in a to tal weight decrease of 51% and 62 %, respectively [12] In addition, Al alloys offer improved extrusion properties compared to automotive steels, but have lower formability and cost 3 4 times more than steel [9] Magnesium (Mg) alloys, on the other hand, have been used sparingly in automotive design, with most of their uses being in the interior of cars [9 14] Mg alloys, with densities around 1.8 g/cm 3 are the lightest structural metal s [9 11 13] As s een in Table 1 1 the elastic modulus and yield strength of Mg alloys is lower than both that of

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22 Al alloys and automotive steel, but the specific modulus of Mg alloys is comparable to that of both steel and Al alloys. In addition, the specific strength of Mg alloys is greater than that of steel and Al alloys. As a result, a n automotive part made out o f a Mg alloy will need to be 1.67 times thicker than an automotive steel part when designing to achieve an e qual bending stiffness, and 1.12 times thicker when designing for equal bending strength [9 12] This results in a total weigh t decrease of 61% when designing for equal bending sti ffness and 74% when designing for equal bending strength Addition ally, if Mg alloys were to be substituted in place of Al alloys, it would result in a 9% total weight decrease when designing to achieve an equal bending stiffness, and a 25% total weight decrease when designing for equal bending strength [12 15] These potential weight savings have resulte d in a stronger push by the automotive industry to introduce Mg alloys into automotive designs [12 14 15] In addition to being lightweight, Mg alloys also have improved fluidity, machining, and vibration damping properties over Al alloys and ste el [16 18] However, Mg alloys curr ently have several limitations including limited cold workability and toughness, limited strength and creep resistance above 12 0 d egrees Celsius ( o C) limited corrosion resistance high chemical reactivity and higher alloy cost compared to steel or Al alloys [9 14] In particular the limited strength and creep resistance above 120 o C must be addressed, as car parts such as the powertrain reach temperatures above 120 o C [9] For commonly used Mg based alloy series such as the Magnesium Aluminum Zinc (AZ) and the Magnesium Aluminum Manganese (AM) series, the limited strength and creep resistance above 120 o C results from the discontinuous precipitation of the Mg 17 Al 12

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23 phase [19 21] However, the Mg 17 Al 12 precipi tate acts as the primary strengthening phase for the AZ and AM series at room temperature. The desire to improve creep resistance while maintaining Mg 17 Al 12 as the primary strengthening phase in Mg alloys has led to the study of additional Mg Al based tern ary systems [22 24] Studies have shown that the Magnes ium Aluminum Si licon (AS ) and Magnesium Aluminum Rare Earth (AE ) series have improved creep resistance, but each series has its ow n limitations [22 24] In particular, the AS series has poor corrosion resistance, and the AE series has high alloy cost due to the use of Rare Earth (RE) elements [22 24] Due to the above limitations of Al containing Mg alloys, c urrent research has turned towards the developme nt of Mg alloys without Al [25 26] Studies have shown that Magnesium Tin (Mg Sn) alloys are a promising alternative because of their improved thermal stability over Mg Al alloys. The improved thermal stability is attributed to the precipitation of the Mg 2 Sn phase, which has a melting point of 770 o C [27 28] Additionally, Sn has a solubility of 14.5 weight percent (w t %) at the Mg Sn eutectic temperature of 561 o C and a room temperature solubility of less than 1 wt %, giving Mg Sn alloys great potential to be precipitation hardened by Mg 2 Sn [28 29] However, the higher thermal stability achieved by Mg Sn alloys comes with lower ductility and corrosion resistance [30] Recent studies have shown that adding small amounts of silver (Ag) to Mg Sn alloys can improve the ductility while still forming the desired Mg 2 Sn precipitate [31 32] However the additio n of Ag also resulted in the formation of Mg Ag and Mg Ag Sn phases some of which may be undesirable phases [31 32] In

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24 order to control the precipitates that form in the Mg Ag Sn system, the kinetics of the Mg Ag Sn system must first be understood. In 2011, President Obama launched the Materials Genome Initiative, focused on developing advanced materials at a faster rate for a fraction of the current cost [33] This has created a need to incorporate predictive models into the design process in order to lower the number of experiments needed and thereby speed up the design p rocess and lower design cost [34] One such example is the Calculation of Phase Diagrams (CALPHAD) approach to materials design, which focuses on using the experimental descriptions of lower alloy systems in conjunction with thermodynamic and kinetic databases to predict the thermodynamics and kinetics of higher order systems where limited experimental data exists [35 36] There have been a significant number studies on Mg alloys to develop thermodynamic descriptions and implement this data into pha se equi libria software such as FactSage, Pandat, and Thermo Calc [37 38] However, kinetic databases for Mg alloys remain underdeveloped. Recently, kinetic database s were developed for both Thermo Calc and Pandat [39 40] Of thes e, the only commercial ly available kinetic databases are in Thermo (DICTRA) [40 41] Howe ver, much of the diffusion data of the binary systems, including Mg Sn, were calculated from experiments u sing single crystals Only one ternar y system, Magnesium Aluminum Zinc ( Mg Al Zn ) has an experimental dataset from which atomic mobility values can be calculated [40] This thesis focuses on the experi mental calculation of diffusion coeffici ent values for polycrystalline Mg Ag, Mg Sn, and Mg Ag Sn systems. This experimental diffusion data was then optimized using the

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25 DICTRA module of Thermo Calc, and will be available commercially in Thermo Mg based alloy kinetic database for commercia l alloy design.

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26 Table 1 1 D ensities and mechanical properties of automotive steels, Al alloys, and Mg alloys [13] Material Density ( g/cm 3 ) Elastic M odulus (GPa ) Yield Strength (MPa ) Specific Modulus cm 3 /g) Specific Strength cm 3 /g) Galvanized Steel 7.8 210 200 26.9 25.6 5000 Series Al Alloy 2.7 71 159 26.3 58.9 AZ91 Mg Alloy 1.8 45 160 25.0 88. 9

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27 CHAPTER 2 LITERATURE REVIEW Diffusion can be defined as the spo ntaneo us mixing of atoms due to random thermal motion [42] This thermal motion of atoms can be found in solids, liquids, and gases, and can be described as a flux of atoms passing through an area over a period of time [43] T s First Law ( Equation 2 1 ). (2 1) In Equation 2 1 is the flux density of component is the chemical diffusion coefficient is the change in concentration of component and is the change in distance [43] It is important to note that assumptions about the solution in question. applies only to thermodynamically ideal solutions such as a Copper (Cu) and Nickel (Ni) solid solution [42] Additionally the diffusion coefficient hange with composition. In solids, there exist two common mechanisms by which atoms diffuse: vacancy and interstitial [42 44] The mechanism by which an atom diffuses is dependent on the atomic size of the solvent in comparison to the atomic size of the solute it is diffusing through. For atoms that are a similar size as the atoms making up the lattice of the solid solution, the atoms diffuse by the vacancy mechanism In order for atoms to diffuse using the vacancy mechanism, the neighboring lattice site of the diffusing atom should be vacant Then, upon receiving the requisite amount of activation energy, the diffusing atom will jump from its current lattice site to the vacant lattice site, as seen in Figure 2 1

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28 The activation energy needed for this to take plac e is the sum of the energy for the atom to jump as well as the energy needed t o form a vacancy [42] For atoms that are much smaller in size than the atoms making up the lattice of the solid solution, the interstitial mechanism is the method by which they diffuse. This mechanism occurs by an atom moving in between lattice sites, as seen in Figure 2 2 As no activation energy is needed to create a vacancy for the atom to jump to, the activation energy needed for interstitial diffusion is typically less than that for vaca ncy diffusion [42] Diffusion in the sold state is st rongly dependent on temperature due to the high density of the solid state compared to liquid and gases The higher density requires greater thermal energy for atoms to jump to a neighboring vacant site [42] The temperature dependence of diffusion coefficients fits an Arrhenius model, as seen in Equation 2 2 [44] (2 2) In Equation 2 2 is the diffusion coefficient, is the pre exponential factor, is the activation energy for diffusion, is the temperature, and is the universal gas constant. When the diffusion coefficient is plotted on a logarithmic (log) scale against the inverse of temperature, this produces a straight line from which the activation energy and pre exponential factor can be calculated, as seen in Figure 2 3 For a hexag onal close packed (HCP) Mg lattice, the majority of atoms diffuse using the vacancy mechanism. In the HCP Mg lattice, this mechanism can occur in two ways: the jumping of the diffusing atom to the nearest neighbor vacant site within the same basal plane (or a axis) or the jumping of the diffusing atom from one basal plane

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29 into the nearest neighbor vacant site in an adjacent basal plane (along the c axis) [45] This is illustrated in Figure 2 4 Since the Mg HCP lattice is 1.62 times longer in the c axis than it is in the a axis the diffusion coefficients for the two me thods of atomic jump in the Mg HCP lattice will be different [46] Therefore, for single crystals, the diffusion coefficien t will need to be calculated both perpendicular and parallel to the c axis [45] However, calculating the diffusion coefficie nt of a polycrystalline Mg alloy will have a variety of grain orientations, and therefore diffusion in both jump directions. As a result, calculating the diffusion coefficient of a polycrystalline Mg alloy can be used to determine an effective average diff usion coefficient of the two atomic jump directions [40] In many practical applications, the solid solution in question is no t thermodynamically ideal, the driving force for diffusion becomes very large or the diffusion coefficient changes with composition In such ger applies. For non ideal solid solutions, the diffusion coefficient can be calculated by three methods: tracer diffusion, interdiffusion, and intrinsic diffusion [44] Tra cer diffusion is measured experimentally using radioactive isotopes [44] While more difficult to obtain experimentally diffusion coefficients calculated using tracer diffusion are independent of a thermodynamic factor This eliminates having to use a thermodynamic database in conjunction with diffusion experiments and any errors that would potentially aris e from doing so. The tracer diffusion coefficient can be calculated using the Einstein Equation ( Equat ion 2 3 ) [44] (2 3 )

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30 In Equation 2 3 is the tracer diffusion coefficient of component is the atomic mobility of component is the universal gas constant, and is the temperature In many cases however, tracer diffusion experiments are not practical or possible. A more practical way to measure diffusion coefficients is throu gh diffusion couples, which consists of two dissimilar materials placed in contact with each other and heated t o elevated temperatures to accelerate diffusion [42] This method can be used to calculate the interdiffusion or intrinsic diffusion coefficient of each of the components of the diffusion couple [42 44] The diffusion coefficient can be described using Second Law ( Equation 2 4 ) [43] (2 4 ) In Equation 2 4 is the partial derivative of the concentration of component is the partial derivative of time, is the partial derivative of distan ce, and is the diffusion coefficient of component By assuming can be simplified to Equation 2 5 [44] (2 5 ) In Equation 2 5 is the second order partial derivative of the concentration of component and is the partial derivative of the square distance. Boltzmann further transformed equation into an ordinary differential equation using a transformation variable ( Equation 2 6 ) [47] (2 6 )

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31 In Equation 2 6 is the Boltzmann transformation variable, is the distance and is the t ime. aw makes it possible to extract from an exp erimentally observed concentration profile such as in Figure 2 5 by using Equation 2 7 [47] (2 7 ) In Equation 2 7 is the chang e in and is the change in concentration of component It is important to note that Equa tion 2 7 is only useful if the initial conditions can be described in terms of Matano applied Equation 2 7 to solve for for diffusion couples with constant volume, also known as the volume fixed frame of reference [48] Matano defined the initial conditions of the diffusion couple in terms of resulting in Equation 2 8 (2 8 ) In Equation 2 8 is the inter diffusion coefficient at concentration is the concentration at distance is the concentration at the terminal ends of the diffusion couple and is the Matano plane In order for valu es calculated using Equation 2 8 to be accurate, the Matano plane must first be located. The location of the Matano plane, or the plane of mass balance indicated as is determined by Equation 2 9 [48 49] An example o f this can be seen in Figure 2 6 (2 9 ) In Equation 2 9 is the concentration is the concentration at the terminal ends of the diffusion couple, and is the concentration at the Matano plane However, finding

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32 the Matano plane is a time consuming process with large amounts of error [50] As previously stated, each of the components of a solid solution has their own unique diffusion coefficient [42 44] As a result, in a d iffusion couple with two dissimilar components on either side, the faster diffusin g component will shift the boundary between the two components towards the side of the slower diffusion component, while leaving porosity behind on the side of the faster diffusing component [51 52] This phenomenon is known as the Kirkendall Effect, and can make it difficult to find the point at which the mass of both sides of the diffusion couple is balanced. Additionally, th e Matano plane may not lie at a point of experimental data collection. Sauer, Friese, den Broeder, and Wagner modifie d Equ ation 2 9 so that the Matano plane no longer needed to be found in order to calculate [53 55] This resulted in Equation 2 10 (2 10 ) In Equation 2 10 is the interdiffusion coefficient at concentration is the time, is the change in distance at is the change in concentration at is the concentration at distance is the concentration at the terminal ends of the diffusion couple and is a concentration r atio as defined in Equation 2 11 (2 11 ) Without having to find the Matano plane, the errors in calculating using the Boltzmann Matano method are greatl y reduced [56] While the Boltzmann Matano method can measure diffusion in the volume fixed frame of reference, it cannot measure the rates of diffusion of individual components

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33 relative to local lattice planes [57] diffusion couple experiments with brass, it was found that a net flux of atoms across any lattice plane exists, and the lattice plane shifts accordingly to conserve the density of lattice sites [52] This shift of lattice planes is observed as a movement of inert markers placed on the diffusion couple [52] This movement of markers can be measured by Equation 2 12 [52] (2 12) In Equation 2 12 is the Kirkendall (marker) velocity is the distance, and is the time If interdiff usion coefficient and Kirkendall velocity values are known from experiment for a binary system, the intrinsic diffusion coefficient in the lattice fixed frame of referen quation ( Equation 2 13 ) [58] (2 13) In Equation 2 13 is the mole fraction of component is the intrinsic diffusion of component is the mole fraction of component and is the intrins ic diffusion of component The marker velocity can then be measured using Equation 2 14 [58] (2 14) In Equation 2 14 is the partial derivative of the mole fraction of component Understanding the kinetics of an alloy system can assist in controlling the microstructure of the alloy. In particular, the diffusion coefficients of each component in an alloy have a significant effect on the coarsening rate of precipitates in the alloy, as seen in Lifshi tz Slyozov Wagner (LSW) model ( Equation 2 15 ) [59 60] (2 15) In Equation 2 15 is the average radius of all particles, is the radius at the onset of coarsening, is the diffusion coefficient, is the interfacial free energy, is the

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34 molar volume of the precipitate, and is the solubility. By understanding the diffusion coefficients of all the components in an alloy, the coarsening rate of precipitates in the alloy can be controlled, which in tu rn allows for properties such as strength, ductility, and creep resistance to be controlled. To accelerate the process of materials design and to lower the cost of the materials design process, predictive modeling software is being integrated throughout the design process [34] Three such programs that are currently used to model phase equilibria of materials syste ms are FactSage, Pandat, and Thermo Calc [61 63] All three programs utilize databases containing thermodynamic descri ptions of elements and compounds to calculate phase diagrams, solidification models, and other thermodynamic properties of higher order systems that are experimentally unavailable [61 63] In all three programs, th e databases can be appended to experimental data f rom lower order systems that have been optimized using i n program optimization module s [61 63] However, FactSage only has thermodynamic databases, and therefore does not have the capability to model the kinetics of material sy stems [61] Both Pandat and Thermo Ca lc on the other hand, have thermodynamic and kinetic databases [62 63] These kinetic databases, like their thermodynamic counterp arts, can be appended to experimental data from lower order systems that have been optimized using in program optimization modules [62 63] However, a kinetic database developed using diffusion coefficient values would be im practical. Since most solid solutions are not thermodynamically ideal, the effect of composition of all the components of the solid solution must be taken into account. As a result, a kinetic database developed using diffusion coefficient values would requ ire a separate diffusion

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35 coefficient for every possible composition of solid solutions being examined. This would make the database overly complex. Therefore, atomic mobility values are stored in the kinetic database [64] This r elationship between the experimental diffusion coefficient and atomic mobility depends on the ty pe of diffusion experiment used and the frame of reference [65] The preferred type of experimental diffusion data for optimizing atomic mobility values is tracer diffusion ( Equation 2 3 ), as it does not require data from a thermodynamic database [44 65] This reduces the potential for error when calculating the atomic mobility values to store in the database. When tracer diffusion data cannot be obtained, i nterdiffusion data in the volume fixed frame of reference can be related to the atomic mobility assuming diffusion by the vacancy mechanism th rough Equation 2 16 [65] (2 16 ) In Equation 2 16 is the volum e fixed frame of reference diffusion coefficient, is the Kronecker delta function, is the mole fraction of component is the mole fraction of component is the partial derivative of the chem ical potential of component and is the partial derivative of the mo le fraction of component Unlike tracer diffusion interdiffusion coefficients require input from a thermodynamic database, and therefore are dependent on the accuracy of the thermodynamic database [65] Finally, intrinsic diffusion data in the lattice fixed frame of reference can be related to the atomic mobility assuming diffusion by the vacancy mechanism through Equation 2 17 [65]

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36 (2 17 ) In Equation 2 17 is the lattice fixed frame of reference diffusion coefficient and is the atomic mobility of component in gradient Like with interdiffusion coefficients, intrinsic diffusion coefficients require input from a thermodynamic database [65] In these atomic mobility matrices utilized by both programs, only the diagonal atomic mobility terms are modeled, and the off diagonal terms are assumed to be equal to zero [65] This assumption is reasonable because the atomic jump correlation effects that are associated with off diagonal atomic mobility terms are almost indistinguishable from experimental data scatter [64] With this in mind, the kinetic databases used by Thermo C alc and Pandat solve for ato mic m obility using Equation 2 18 [65] (2 18 ) In Equation 2 18 is the atomic mobility frequency factor and is the activation energy for diffusion of component Whe n there is no magnetic effect on is set to one, and only the composition and temperature effects on are considered [65] Following the CALPHAD approach to thermodynamic free energy modeling, the effec t of composition on the activation energy can be determined using the Redlich Kister polynomial ( Equation 2 19 ) [35 65 66] (2 19 ) In Equation 2 19 is the activation energy for diffusion of component in pure component is the mole fraction of component is the mole fraction of component and is an interaction parameter Although studies have been done on only Thermo Calc

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37 has a commercially available kinetic database for Mg alloys [39 41] As a result, Thermo Calc and its corresponding kinetic modelin g software, DICTRA, were utilized in this study. Diffusion in the Mg Ag system has been investigated by two experimental studies and three computational studies [40 67 70] Lal studied tracer diffusion of 110 Ag in polycrystalline Mg in the temperature range of 476.5 621 o C [67] The samples were sectioned using a precision lathe and their activity measured using a scintillator [67] Combronde, on the other hand, studied tracer diffusion of 110 Ag in single crystal Mg in th e temperature range of 479 639 o C [68] This was done by abrading fixed amounts of materials and measuring the activity penetration curves [68] Recently, Bryan optimized ng software, and added the resulting optimized atomic mobility parameter values to [40] Finally, both Wu and Zhou calculated the diffusion of Ag in single cry stal Mg using first principles Density Function T heory (DFT) in the Vienna Ab In itio Simulation Package (VASP) [69 70] The diffusion coefficients of all the studies are plotted in Figure 2 7 and are discussed below. Diffusion of Ag in Mg has been thoroughly studied, with experimental data sets for both single crystal and polycrystall ine diffusion, and multiple computational studies. However, there is a wide variety of results between the experimental and computational studies. The single crystal experimental study done by Combronde showed that diffusion coefficient val ues were 1.56 2.37 times larger parallel to the c axis than perpendicular to the c axis [68] On the other hand VASP model had larger diffu sion coefficient values perpendicular to the c axis than parallel to the c axis while

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38 achieving similar diffusion coefficient values as those determined experimentall y by Combronde [69] perpendicular to the c axis than parallel to the c axis [ 70] However VASP model produced diffusion coefficient values that are much lower than found experimentally by Combronde or Lal [70] ndicular single crystal values [67] Bryan datasets to optimize the atomic mobility parameters in DICTRA led to diffusion coefficient values that sit s experimental data, representing an effectiv e average diffusion coefficient [40] Diffusion i n the Mg Sn system has been investigated by one experimental study and four computational studies [40 68 71] Combronde studied tracer diffusion of 113 Sn in single crystal Mg in th e temperature range of 475 629 o C [68] Concentration profiles were determined by radioactivity measurements of cuttings made with a precision lathe [68] However, the diffusion coefficient was only measured at two different temperatures perpendicular t o the c axis compared to four different temperatures parallel to the c axis [68] optimizing software, and added the resulting optimized atomic mobility parameter [40] Finally, Ganeshan, Wu, and Zhou calculated the diffusion of Sn in single crystal Mg using first princ iples DFT in VASP [69 71] The diffusion coefficients of all the studies are plotted in Figure 2 8 and are discussed below. Diffusion of Sn in Mg has been insufficiently studied experimentally, but has multiple computational studies.

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39 coefficient measurements perpendicular to the c axis ar e similar in value to diffusion coefficient measurements parallel to the c axis at the same temperature, more experimental data points would be needed to show whether there is a significant difference bet ween the two atomic jump directions for Sn in Mg [68] coeffi cient measurements parallel to the c axis [40] Using VASP models, Ganeshan, Wu and Zhou were able to calculate diffusion coefficient values both parallel and perpendicula r to the c axis [69 70] diffusion coefficient values were slightly larger parallel to the c axis than perpendicular to the c axis [71] VASP model produced diffusion coefficient values that are much lower than those calculated experimentally by Combronde [71] other hand, are larger perpendicular to the c axis than paralle l to the c axis [69] experimentally by Combronde. Likewise, s diffusion coefficient values are larger perpendicular to the c axis than parallel to the c axis and are similar to the values determined experimentally by Combronde [70] Diffusion in the Mg Ag Sn system has currently not been investigated by any studies in literature. Addi tionally, in the commercially available MGMOB 1 database, there exists only one ternary system, the Mg Al Zn system, as seen in Fig ure 2 9 [40 67 68 72 74] This necessitates the kinetic study of additional Mg based ternary systems so that kinetic descriptions of these systems will be co mmercially available in databases for materials development and design.

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40 Figure 2 1. Schematic of vacancy diffusion mechanism

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41 Figure 2 2. Schematic of interstitial diffusion mechanis m

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42 Figure 2 3. Temperature dependence of the diffusion coefficient in solids, as described by the Arrhenius relationship In Figure 2 3 the x axis is the inverse of temperature in Kelvin (K)

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43 Figure 2 4. Schematic of an HCP lattice with the two possible atomic jump direction s highlighted with blue lines. In Figure 2 4 the red lines indicate the a axis and c axis.

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44 Figure 2 5. Example of a concentration profile extracted from a diffu sion couple.

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45 Figure 2 6. Example of a Matano plan e.

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46 Figure 2 7. D ata from literature of the diffusion coefficient of Ag in Mg [40 67 70] In the le gend of Figure 2 7 Perp represents diffusion perpendicular to the c axis, Para represents diffusion parallel to the c axis, and PX represents diffusion in polycrystalline Mg.

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47 Figure 2 8. Data from literature of the diffusion coefficient of Sn in Mg [40 68 71] In the legend of Figure 2 8 Perp represents diffusion perpendicular to the c axis, Para represents diffusion parallel to the c axis, and PX represents diffusion in polycrystalline Mg.

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48 Figure 2 9. Temperature dependent diffusion coefficients of all relevant solutes in Mg, as found in the MGMOB1 atomic mobility database [40 67 68 72 74]

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49 CHAPTER 3 MATERIALS AND METHODS All Mg alloys were cast using a resistive furnace built into an argon (Ar) backfilled glove box. Magnesium granules (99.8% purity), Sn shot (99.8% purity ), and Ag powder (99.95% purity ) were used as initial materials. The raw materia ls were weighed to the desired composition and placed into a graphite crucible coated with boron nitride. The boron nitride coating on the crucible was used to minimize sticking after casting. The crucibles were then placed into the resistive furnace in th e glove box at 750 o C and covered with a graphite lid. To prevent the highly exothermic reaction of molten Mg with oxygen gas (O 2 ), the O 2 level in the glove box was maintained at a concentration less than 100 parts per million ( ppm ) A Mg Ag master alloy was prepared by melting Mg and Ag for 1 hour While in the furnace, the molten metal was stirred twice using a graphite rod coated in boron nitride. This was then cast into a 60 gram (g) rectangular mold coated in boron nitride, and allowed to air cool. The composition of the alloy was verified with e nergy dispersive x ray s pectroscopy (EDS) in a TESCAN MIRA3 scanning electron m icroscope (SEM) and can be seen in Table 3 1 The rema ining alloys were prepared by melting Mg, Sn, and the Mg Ag master alloy for 25 minutes. At the 20 minute point, the molten alloys were stirred while still in the furnace using a graphite rod coated in boron nitride. After 25 minutes, the alloys were cast into a 60 g rectangular mold coated in boron nitride and allowed to air cool The composition of each alloy was verified using wavelength dispersive s pectroscopy (WD S ) in a CAMECA SXFiveFE electron probe m icroanalyzer (EMPA), and can be seen in Table 3 1

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50 To ensure that all alloys were a single phase, ea ch of the alloys went through a solutionizing heat treatment step after casting. To prepare the alloys for heat treatment, each was cut into four approximately equal sections using a silicon carbide (SiC) abrasive saw. Each section was then placed into 1 inch diameter Pyrex tubes and e vacuated to less than 40 millitorr (mTorr) and purged with Ar three times. After the final purge, the section was then encapsulated in the Pyrex tube using a hydrogen oxygen torch. The encapsulated samples we re then heat treated in an open air resistive furnace at 450 o C for 24 hours. Rectangular sections of each solutionized alloy were cut into sections approximately 5 millimeters (mm) wide, 10 mm long, and 3 mm thick using a low speed diamond saw. The surfaces of each section that were going to be in contact in the diffusion couple were ground and polished to 1 micrometer ( m ) using a series of SiC a brasive papers and a cloth polishing pad. A summary of all the steps in this process can be seen in Table 3 2 After completion of the 600 grit SiC planing step, each sample was attached to a lapping fixture using Crystalbond adhesive. The lapping fixture was used to ensure that all sides of each sample were completely flat. After completion of the 1 m polishing step, each sample was removed from the lapping fixture and residual Crystalbond was removed using acetone. The polished surfaces of both ends of the diffusion couple were then placed in contact with each other and the diffusion couple was wrapped in tantalum (Ta) foil. The Ta foil was used as an oxygen getter to limit Mg alloy oxidation. The diffusion couple was then placed in a Kovar jig and tightened with a torque wrench such that the pressure on the bolts was 5 ft lbs Assembled diffusion couples with the jig were then

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51 encapsulated in Pyrex tubes under a vacuum below 40 mTorr using a hydrog en oxygen torch. An example of an encapsulated diffusion couple jig can be seen in Figure 3 1 All diffusion couples were annealed in an open air resistive furnace. The temperature of the furnace was v erified daily using a thermocoup le. The ends of each diffusion couple, along with annealing time and temperature, can be seen in Table 3 3 The annealing t emperatures were chosen to ensure that the combination of tempe rature and composition was in the single phase Mg region, as well as to avoid any liquid regions of the phase diagram. The phase diagrams for all of the alloys used can be seen in Appendix A Additionally, the annealing times were selected so that each diffusion couple would have diffusion through the initial interface between the two metals After the heat treatment was completed, each diffusion couple was water quench ed to stop diffusion. Each was then rinsed in ethanol and mounted in 1 inch diameter acrylic mounts. T he mounts were then sectioned in half perpendicular to the diffusion interface, and each half was remounted in acrylic. A schematic of this sectioning process can be seen in Figure 3 2 Each mounted sample was ground and polished to 1 m using the steps in Table 3 2 As the acrylic mount was already flat on both sides, the lapping fixture was not needed for polishing. Each mounted and polished diffusion couple was then placed in a vacuum box to degas the acrylic mount for at least 12 hours. After degassing, the diffusion couples were analyzed using EPMA WDS. Element calibrations were performed with pure element standards, and a diffusion profile line scan was performed perpendicular to the diffusion interface. Th e length of the line scan and the step size between points for each diffusion couple was chosen so that there would be at least 100 points on each end that were outside the diffusion zone.

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52 This was done so that there would be enough points on either end of the concentration profile to accurately determine the values of and for Equation 2 10 and Equation 2 11 Each diffusion couple and its corresponding line scan length and step size can be seen in Table 3 4 Each concentration profile was smoothed using a cubic b spline interpolation function in Origin Graphing and Data Analysis Software (Origin) [75] This was done to reduce the data scatter when calculating and to achieve a more precise calculation of the diffusion profile integrals as well as the differential found in Equation 2 10 An example of this can be seen in Figure 3 3 The number of points in the cubi c b spline function was set to equal the number of po ints in the original concentration profile, and the s moothing factor varied between 5 10, depending on the number of points, length of the line sc an, and the original composition To verify the accuracy of the cubic b spline to the original concentration profile, a coefficient of determination (R 2 ) was calculated for each concentration profile and corresponding smoothed profile. The smoothing factor used and the resulting R 2 values for each concentration profile can be found in Table 3 5 The concentration dependent interdiffusion coefficient of each diffusion coupl e was extracted from each concentration profile in Origin using Equation 2 10 and Equation 2 11 This data was then sorted by diffusion couple composition and put into experimental data files for use in DICTRA. Thermo the interdiffusion experimental data for the Mg Sn, Mg Ag, and Mg Ag Sn systems calculated using Equation 2 10 and Equation 2 11 The experimental interdiffusion c oefficient data was optimized using the Parro t optimization module of DICTRA, whi ch

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53 yielded optimized atomic mobility parameters This was done using a least squares method in which the atomic mobility parameters were iteratively rescaled and optimized until the sum of squares difference between the experimental data input and the simu lation was minimized Simulations of the concentration dependent interdiffusion coefficients and concentration profiles were then performed using DICTRA under the same time, temperature, and composition parameters as used for the original diffusion couple experiments. These were then compared to their experimental counterparts to determine the accuracy of the optimized atomic mobility values. These optimized atomic mobility parameters were validated using independent diffusion couples that used different en d members, annealing time s and annealing temperature s than w ere used in the atomic mobility optimization. The diffusion couple ends, annealing times and temperatures, and the atomic mobility parameters validated by each of these diffusion couples can be seen in Table 3 6 These validation diffusio n couples were sectioned, ground and pol ished using the same steps as used before in Figure 3 2 and Table 3 2 Each validation diffusion couple was degassed and analyzed with EPMA WDS using the same techniques as used for the original diffusion coupl es. Each validation diffusion couple and its corresponding line scan length and step size can be found in Table 3 7 Each validation concentration profile was t hen c ompared to DICTRA simulations calculated under the same time, temper ature, and composition parameters as the validation diffusion couples to validate the atomic mobility values.

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54 T able 3 1. Compositions of cast Mg alloys. Alloy Wt% Ag, A ctual Wt% Sn, Actual Wt % Mg Mg Ag Master Alloy 44.3 0 Balance Mg 5Ag 5 .72 Balance Mg 5Sn 5.9 0 Balance Mg 2Ag 2.6 7 Balance Mg 2Sn 2.2 5 Balance Mg 2Ag 5Sn 2. 53 5. 59 Balance Mg 2Sn 5Ag 6. 13 2.3 9 Balance Table 3 2. Grinding and polishing steps for Mg alloys. Pad Type Suspension Polishing Time Cleaning Procedure 120 grit SiC paper Sink water Until plane Ethanol 320 grit SiC paper Sink water Until plane Ethanol 600 grit SiC paper Sink water Until plane Ethanol 800 grit SiC paper Sink water Until plane Ethanol 1200 grit SiC paper Sink water Until plane Ethanol 1 m polishing cloth 1 m Alumina (Al 2 O 3 ) 15 seconds Deionized water cotton swab, Ethanol cotton swab Table 3 3. Diffusion couple heat treatments. Diffusion Couple Temperature ( o C) Time (hours) Mg/Mg 5Ag 450 24 Mg/Mg 5Ag 500 24 Mg/Mg 5Ag 550 24 Mg/Mg 5Sn 450 48 Mg/Mg 5Sn 500 24 Mg/Mg 5Sn 550 24 Mg 2Ag/Mg 2Ag 5Sn 450 192 Mg 2Ag/Mg 2Ag 5Sn 500 24 Mg 2Ag/Mg 2Ag 5Sn 550 24 Mg 2Sn/Mg 2Sn 5Ag 450 48 Mg 2Sn/Mg 2Sn 5Ag 500 24 Mg 2Sn/Mg 2Sn 5Ag 550 24

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55 Table 3 4. Diffusion couple line scan length and step size. Diffusion Couple Anneal Temperature ( o C) Line Scan Length ( m) Step Size ( m) Mg/Mg 5Ag 450 1000 1 Mg/Mg 5Ag 500 1339 1 Mg/Mg 5Ag 550 2000 2 Mg/Mg 5Sn 450 1000 1 Mg/Mg 5Sn 500 989 1 Mg/Mg 5Sn 550 1000 1 Mg 2Ag/Mg 2Ag 5Sn 450 10 00 1 Mg 2Ag/Mg 2Ag 5Sn 500 1000 1 Mg 2Ag/Mg 2Ag 5Sn 550 1500 1 Mg 2Sn/Mg 2Sn 5Ag 450 1000 1 Mg 2Sn/Mg 2Sn 5Ag 500 1000 1 Mg 2Sn/Mg 2Sn 5Ag 550 3000 3 Table 3 5. Smoothing factor and R 2 values of eac concentration profile. Diffusion Couple Anneal Temperature ( o C) Smoothing Factor R 2 Mg/Mg 5Ag 450 9 0.943 Mg/Mg 5Ag 500 10 0.988 Mg/Mg 5Ag 550 7 0.993 Mg/Mg 5Sn 450 6 0.975 Mg/Mg 5Sn 500 7 0.989 Mg/Mg 5Sn 550 7 0.992 Mg 2Ag/Mg 2Ag 5Sn 450 7 0.979 Mg 2Ag/Mg 2Ag 5Sn 500 5 0.994 Mg 2Ag/Mg 2Ag 5Sn 550 8 0.995 Mg 2Sn/Mg 2Sn 5Ag 450 8 0.989 Mg 2Sn/Mg 2Sn 5Ag 500 7 0.993 Mg 2Sn/Mg 2Sn 5Ag 550 7 0.990 Note: Diffusion couples with Mg as an end member used 99.95% purity Mg rod. Table 3 6. Validation diffusion couple heat treatments. Diffusion Couple Anneal Temperature ( o C) Anneal Time (hours) Mobility Parameter Validated Mg/Mg 2 Ag 525 18 Mg/Mg 2Sn 525 18 Mg/Mg 2Sn 5 Ag 525 18 Mg/Mg 2Ag 5 Sn 525 18

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56 Table 3 7. Validation diffusion couple line scan length and step size Diffusion Couple Line Scan Length ( m) Step Size ( m) Mg/Mg 2 Ag 1000 1 Mg/Mg 2 Sn 1000 1 Mg/Mg 2Sn 5 Ag 1000 1 Mg/Mg 2Ag 5Sn 1000 1

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57 Figure 3 1. A n encapsulated diffusion couple jig. Figure 3 2. Schematic of diffusion couple sectioning for EPMA WDS.

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58 Figure 3 3. Examp le of cubic b spline concentration profile curve fitting in Origin.

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59 CHAPTER 4 RESULTS AND DISCUSSION All of the concentration profiles used in this study and the cubic b spline interpolation curve s fitted to each can be seen in Appendix B The cubic b spline interpolation function was used as it allows for a more precise calculation of the diffusion profile integrals as well as the differential found in Equation 2 10 which are critical to a ccurately assess the concen tration depen dent interdiffusion coefficient [76] The accuracy of each of the cubic b spline curve fits of all the diffusion zone s was found to be good, with 0.943 being the lowest R 2 value as seen in Table 3 5 The interdiffusion coefficient was calculated using the modification of the Boltzmann Matano method first used by Sauer, Friese, den Broeder, and Wagn er better known as the Sauer Friese den Broeder Method ( Equation 2 10 Equation 2 11 ) [53 55] This method was utilized as opposed to the Boltzmann Matano method ( Equation 2 8 ) as it eliminates the errors associated with finding the Matano plane such as the Matano plane not lying on an experimentally observed point on the concentration profile ( Equation 2 9 ) [56] The conce ntration dependent interd iffusion coefficient s of Ag in Mg, Sn in Mg, Ag in Mg Sn, and Sn in Mg Ag can be found in Appendix C Because of errors associated with the Sauer Friese den Broeder Method from calculations near the ends of the concentration profile, the concentration dependent interdiffusion coefficients are displayed from 1 4 wt %, instead of 0 5 wt %. The first system assessed was the Mg Ag binary system. Two mobility parameters were used to fit the experimen tal diffusion data of Ag in Mg. The primary mobility parameter for Ag in Mg is while a secondary interaction parameter, is used to improve fit by introducing a mobility term which evaluates the effect

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60 of Ag concentration on Ag diffusion in Mg. The optimized atomic mobility values for Ag diffusion in Mg can be found in Table 4 1 The se optimized atomic mobility parameters were then used to model the concentration dependent interdiffusion coefficient of Ag in Mg in DICTRA. A comparison of the concentration dependent interdiffusion coefficients produced by the DICTRA simulations and the corresponding experimental data can be seen in Figure 4 1 It can be observed that there i s good correlation between the DICTRA simulations and the experimentally observed concentration dependent interdiffusion coefficients This can be attributed to the addition of the interaction parameter, which helped to improve the fit of the DICTRA simulations to the experimentally observed data The experimental ly observed conc entration profiles for the Mg/Mg 5Ag diffusion couples as well as the corresponding DICTRA concentration profile simulations can be seen in Appendix D I t can be observed that there is good correlation betwee n the experimentally observed concentration profiles and the DICTRA concentration profile simulations With confirmed correlation back to the ex perimentally observed concentration d ependent interdiffusion coefficients, the optimized atomic mobility parameters for Ag in Mg can now be used to simulate the temperature dependent diffusion coefficient for Ag in Mg. These results, along with any previous literature data, can be seen in Figure 4 2 In Figure 4 2 it can be observed that the temperature dependent diffusion c oefficient s calculated in this study correlates well to previous experimental studies done by Combronde and Lal [67 68] This helps c onfirm the accuracy of the atomic mobility parameters calculated in this study

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61 polycrystalline Mg [67] Additionally, tracer diffusion studies measured the diffusion of Ag in both atomic jump directions in Mg [68] To validate the atomic mobility parameters of Ag in Mg, a diffusion couple was created with different end members, anneal time, and an neal temperature than the initial Ag in Mg diffusion experiments used to calculate the atomic mobility parameters The resulting experimental ly observed concentration profile was compared to a DICTRA simulation run with the same parameters, as seen in Figure 4 3 It can be observed that the DICTRA simulation correlates well to the experimentally observed concentration profile. This confirms the accuracy o f the Ag in Mg mobility parameters and shows that the interacti on parameter was successful in improving the fit of the DICTRA simulations to the experimentally observed diffusion data Next, diffusion in the Mg Sn binary system was assessed. Two mobility parameters were used to fit the experimental diffusion data of S n in Mg. The principal mobility parameter for Sn in Mg is while a secondary interaction parameter, is used to improve fit by introducing a mobility term which evaluates the effect of Sn concentration on Sn diffusion in Mg. The optimized atomic mobility values for Sn diffusion in Mg can be found in Table 4 1 The se optimized atomic mobility parameters were then used to model the concentration dependent interdiffusion coefficient of Sn in Mg in DICTRA. A co mparison of the concentration dependent interdiffusion coefficients produced by the DICTRA simulations and the corresponding experimental data can be seen in Figure 4 4 It can be observed that there is good correlation between the DICTRA simulations and the experimentally observed concentration dependent interdiffusion coefficients This can be attributed to the interaction parameter,

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62 which helped to improve the fit of the DICTRA simulations to the experimentally ob served data The experimental ly observed conc entration profiles for the Mg/Mg 5Sn diffusion couples as well as the corresponding DICTRA concentration profile simulations can be seen in Appendix D It can be observed that there is good correlation between the experimental and the DICTRA simulation concentration profiles With confirmed correlati on back to the experimentally observed concentration dependent interdiffusion coefficients the optimized atomic mobility parameters fo r Sn in Mg can now be used to simulate the temperature dependent diffusion coefficient for Sn in Mg. These results, along with results of previous studies can be seen in Figure 4 5 It can be observed that the temperature dependent diffusion coefficient s calculated in this study differ significantly from the temperature dependent diffusion coefficients determined by Combronde [68 ] In particular, the temperature dependent diffusion coefficient line generated in this study appears to have a lower activation energy than the temperature dependent diffusion coefficient data determined by Combronde. This could be attributed to the fact that performed on single crystal Mg On the other hand, the current study calculates temperature dependent diffusion coefficient s for the diffusion of Sn in polycrystalline Mg, which is desired for materials design applications. studies calculated the diffusion coeffic ient at only two different temperatures in the jump direction perpendicular to the c axis as compared to four different temperatures parallel to the c axis Therefore, the effect diffusion perpendicular to the c axis on the diffusion coefficient is unclear [68]

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63 To validate the atomic mobility parameters of Sn in Mg, a dif fusion couple was created with different end members, anneal time, and anneal temperature than the initial Sn in Mg diffusion experiments used to calculate the atomic mobility parameters. The resulting experimental ly observed concentration profile was comp ared to a DICTRA simulation run with the same p arameters, as seen in Figure 4 6 It can be observed that the DICTRA simulation correlates well to the experimentally observed concentration profile. This confirms the accuracy o f the Sn in Mg mobility parameters, and shows that the interaction parameter was successful in improving the fit of the DICTRA simulations to the experimentally observed diffusion data. With diffusion in both the Mg Ag and M g Sn systems assessed, diffusion in the Mg Ag Sn ternary system was then assessed. One mobility parameter, was used to fit the experimental diffusion data of Ag in Mg Sn, as the other mobility parameters, and were already evaluated an d optimized. The opti mized atomic mobility parameter for Ag diffusi on in Mg Sn can be found in Table 4 1 The se optimized atomic mobili ty parameters were then used to model the concentration dependent interdiffusion coefficient of Ag in Mg Sn in DICTRA. A comparison of the concentration dependent interdiffusion coefficients produced by the DICTRA simulations and the corresponding experimental data can be seen in Figure 4 7 It can be observed that there is ge nerally good correlation between the DICTRA simulations and the experimentally observed concentration dependent interdiffusion coefficients However, t here are some discrepancies between the DICTRA simulations and the experimental ly observed concentration dependent interdiffusion coefficients especially at 500 o C for concentrations of Ag between 1 2 wt % This could be due to the use of

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64 only one atomic mobility parameter , to fit the experimental data. Using one atomic mobility parameter in stead of multiple parameters lowers the fit accuracy. However, with the other atomic mobility parameters for Ag diffusion in Mg, and already evaluated and optimized, only needed to be optimized. Additionally, the experimental ly observed concent ration profiles for the Mg 2Sn/Mg 2Sn 5Ag system as well as the corresponding DICTRA concentration profile simulations can be seen in Appendix D It can be observed that there is good correla tion between the experimental ly observed concentration profiles and the DICTRA simulations With confirmed correlation back to the experimental ly observed concentration dependent interdiffusion coefficients the opti mized atomic mobility parameter for Ag in Mg Sn can be used to simulate the temperature dependent diffusion coefficient for Ag in Mg Sn. To understand the effect of Sn on Ag diffusion in Mg, the temperature dependent di ffusion coefficient of Ag in Mg Sn can be compared to the temperature depend ent d iffusion coefficient of Ag in Mg as seen in Figure 4 8 It can be observed that the addition of Sn decreases the activation energy needed for Ag diffusion in Mg. As a result, for temperatures below 550 o C, the presence of Sn inc reases the diffusion rate of Ag in Mg. To validate the a tomic mobility parameter of Ag in Mg Sn, a diffusion couple was created with different end members, anneal time, and anneal temperature than the initial Ag in Mg Sn diffusion experiments used to calculate the atomic mobility parameters. The resulting experimental ly observed conce ntration profile was compared to a DICTRA simulation run with the same parameters, as seen in Figure 4 9 It can be observed in Figure 4 9 that the DICTRA simulation correlates well to the experimentally

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65 observ ed concentration profile confirming the accuracy of the Ag in Mg Sn atomic mobility parameter One mobility parameter, was used to fit the experimental diffusion data of Sn in Mg Ag, as the other mobility parameters, and were already evaluated and optimized. The opti mized atomic mobility parameter for Sn diffusion in Mg Ag can be found in Table 4 1 The optimized atomic mobilities were then used to model the concentrati on dependent interdiffusion coefficient of Sn in Mg Ag in DICTRA. A comparison of the concentration dependent interdiffusion coefficients produced by the DICTRA simulations and the corresponding experimental data can be seen in Figu re 4 10 It can be observed that there is generally good correlation between the DICTRA simulations and the experimentally observed concentration dependent interdiffusion coefficients However, t here are some discrepancies between the DICTRA simulations an d the experimental data, especially at 500 o C for concentrations of Sn between 3 4 wt % This could be due to the use of only one atomic mobility par ameter , to fit the experimental data. Using one atomic mobility parameter instead of multi ple parameters lowers the fit accuracy. However, with the other atomic mobility parameters for Sn diffusion in Mg, and already evaluated and optimized, only needed to be optimized. Additionally, the experimental ly observed concent ration profiles for the Mg 2Ag/Mg 2Ag 5Sn diffusion couples as well as the corresponding DICTRA concentration profile simulations can be seen in Appendix D It can be observed that there is good correlation between the experimental ly observed concentration profiles and the DICTRA simulations

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66 With confirmed correlati on back to the experimentally observed concentration dependent interdiffusion coefficients the optimized atomic mobility parameter s for Sn in Mg Ag can be used to simulate the temperature dependent diffusion coefficient for Sn in Mg Ag. To understand the effect of Ag on Sn diffusion in Mg, the temperature dependent diffusion coefficient of Sn in Mg Ag can be compared to the temperatu re dependent diffusion coefficient of Sn in Mg, as seen in Figure 4 11 It can be observed that the addition of Ag increases the activation energy needed for Sn diffusion in Mg. As a result, for temperatures below 500 o C, the presenc e of Ag decreases the diffusion rate of Sn in Mg. With slower kine tics, the coarsening kinetics of precipitates can be better controlled as seen in Equation 2 15 Controlling coarsening rates, in turn, can improve elevated temperature mechanical properties and creep resistance. To validate the atomic mobility parameter of Sn in Mg Ag a diffusion couple was created with different end members, anneal time, and anne al temperature than the initial Sn in Mg Ag diffusion experiments used to calculate the atomic mobility parameters. The resulting experimental ly observed concentration profile was compared to a DICTRA simulation run with the same parameters, as seen in Figure 4 12 It can be observed that the DICTRA simulation correlates well to the experimentally observed concentration profile confirming the accuracy of the Sn in Mg Ag atomic mobility parameter

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67 Table 4 1. Optimized atomic mobility parameters used in DICTRA simulations. DICTRA Notation Mobility Parameter Value (J/mol) Ag diffusion MQ(HCP&AG,MG:VA) 1.74087927E5+R*T*LN(9.96234977E 2) MQ(HCP&AG,AG,MG:VA) 2.917 48810E6+3.31001602E3*T MQ(HCP&AG,SN,MG:VA) 1.15310759E7 1. 44608837 E4*T Sn diffusion MQ(HCP&SN,MG:VA) 9.509 6 4086E4+R*T*LN(1.47064452E 7) MQ(HCP&SN,SN,MG:VA) 5.66233992E6+6.75973214E3*T MQ(HCP& SN,AG,MG:VA) 5.10579233E6+6.34046674 E3*T

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68 Figure 4 1. Concentration dependent interdiffusion coefficients of Mg/Mg 5Ag diffusion couples and the correspond ing DICTRA simulations.

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69 Figure 4 2 Temperature dependent diffusion coefficients of Ag in Mg [40 67 70] In the legend of Figure 4 2 Perp represents diffusion perpendicular to the c axis, Para represents diffusion parallel to the c axis, and PX represents diffusion in polycrystalline Mg.

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70 Figure 4 3. Concentration profile of Mg/Mg 2Ag validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation.

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71 Figure 4 4. Concentration dependent interdiffusion coefficients of Mg/Mg 5Sn diffusion couples and the corresponding DICTRA simulations.

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72 Figure 4 5. Temperature dependent diffusion coefficients of Sn in Mg [40 68 71] In the legend of Figure 4 5 Perp represents diffusion perpendicular to the c axis, Para represents diffusion parallel to the c axis, and PX represents diffusion in polycrys talline Mg.

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73 Figure 4 6. Concentration profile of Mg/Mg 2Sn validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation.

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74 Figure 4 7. Concentration dependent interdiffusion coefficients of Mg/Mg 2Sn 5Ag diffusion couples and the corresponding DICTRA simulations.

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75 Figure 4 8. Temperature dependent diffusion coefficients of Ag in Mg and Ag in Mg Sn.

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76 Figure 4 9. Concentration profile of Mg/Mg 2Sn 5Ag validation diffusion c ouple annealed at 525 o C with corresponding DICTRA simulation.

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77 Figure 4 10. Concentration dependent interdiffusion coefficients of Mg/Mg 2Ag 5Sn diffusion couples and the corresponding DICTRA simulations.

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78 Figure 4 11. Temperature dependent diffusion c oefficients of Sn in Mg and Sn in Mg Ag.

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79 Figure 4 12. Concentration profile of Mg/Mg 2Ag 5Sn validation diffusion couple annealed at 525 o C with corresponding DICTRA simulation.

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80 CHAPTER 5 SUMMARY AND CONCLUSIONS In an effort to increase fuel efficiency and decrease CO 2 emissions, the automotive industr y is considering low weight alternatives to current structural materials [11] Magnesium alloys are being considered for such applications, as Mg is the lightest structural metal [11] However, commonly used Mg alloys such as the AZ series h a ve limited strength and creep resistance above 120 o C, which limits their use in automotive applications [14] The main cause of this poor performance at elevated temperatures is the discontinuous precipitation of the Mg 17 Al 12 phase [1 9] To address th is, alloy development for Mg alloys without Al as an alloying element has begun [25 26] Studies have identified the Mg Sn system as a promisi ng candidate for automotive applications as the Mg 2 Sn phase is stable at elevated temperatures [27 28] However, the hi gher thermal stability achieved by Mg Sn alloys comes with lower ductility and corrosion resistance [30] Recent studies have shown that adding small amounts of Ag to Mg Sn alloys can improve the ductility while still forming the desired Mg 2 Sn precipitate, but much of the kinetics of the system is still not understood [31 32] With the advent of improved computational methods and government efforts such as the Materials Genome Initiative, a focus has been placed on incorporating predictive computational models early on in the materials desi gn process to reduce the number of experiments [33 34] One example of such an approach is the CALPHAD methodol o gy to materials design, which focuses on using the experimental descriptions of lower alloy systems in conjunction with thermodynamic and kinetic databases to predict the thermodynamics and kinetics of higher order systems where limited experimental data exi sts [35 36] Following this CALPHAD approach, this study focused

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81 on the development of kinetic experimental descripti ons of the polycrystalline Mg Ag, Mg Sn and the ternary Mg Ag Sn systems for use in Thermo DICTRA Solid soli d diffusion couple experiments were performed and characterized with EPMA to quantify the concentration dependent interdiffusion coefficient of Ag in Mg, Sn in Mg, Ag in Mg Sn, and Sn in Mg Ag The interdiffusion coefficient data was extracted using the Sa uer Friese den Broeder Method, and the data was optimized using the Parrot module of DICTRA. This yielded opti mized atomic mobility parameters from each system, namely , , and A summary of all the solutes in the MGMOB1 database, along with the data from this study, can be found in Figure 5 1 It is important to note from Figure 5 1 that, as a result of this study, th e kinetics of two additional ternary systems will be available for comme rcial use in Thermo based alloy kinetic database It was also shown t hat adding Sn to Mg Ag and vice versa has a significant effect on the activation energy of the diffusing species. In particular, adding Ag to Mg Sn was found to increase the activation energy of Sn diffusion, which decreased the diffu sion coefficient of Sn in Mg for temperatures below 500 o C. Slower kinetics leads to greater coarsening resistance of precipitat es, which allows the coarsening rate to be better controlled Greater control of the coarsening rate in turn, can lead to improved elevated temperature mechanical properties and creep resistance making the Mg Ag Sn alloy system a promising candidate for use in weight reducing automotive applications.

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82 Figure 5 1. Temperature dependent diffusion coefficients of all relevant solute s in MGMOB1 with results of this stud y [40 67 68 72 74]

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83 CHAPTER 6 FUTURE WOR K With the kinetics of the Mg Ag Sn system better understood, future work could include more diffusion couple experiments with the Mg Ag Sn system to further validate the atomic mobility parameters generated in this study. As the DICTRA database now contains only three ternary systems, future work could include kinetic assessments of other Mg based ternary systems to add to the DICTRA database. Fi nally, with the kinetic assessment of the Mg Ag Sn system done in this study, the kinetics of quarternary systems containing Mg Ag Sn could be assessed. This would be done in conjunction with DICTRA, similar to this study.

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84 APPENDIX A PHASE DIAGRAMS OF MG ALLOYS Figure A 1. Mg Ag phase diagram.

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85 Figure A 2. Mg Sn phase diagram.

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86 Figure A 3. Mg Ag Sn phase diagram at 450 o C.

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87 Figure A 4. Mg Ag Sn phase diagram at 500 o C.

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88 Figure A 5. Mg Ag Sn phase diagram at 550 o C.

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89 APPENDIX B CUBIC B SPL INE INTERPOLATION OF CONCENTRATION PROFILES Figure B 1. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diffusion couple annealed at 450 o C.

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90 Figure B 2. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diffusion couple annealed at 500 o C.

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91 Figure B 3. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Ag diffusion couple annealed at 550 o C.

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92 Figure B 4. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 450 o C.

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93 Figure B 5. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 500 o C.

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94 Figure B 6. Concentration profile fit with cubic b spline interpolation for Mg/Mg 5Sn diffusion couple annealed at 550 o C.

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95 Fig ure B 7 Concentration profile fit with cubic b spline interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 450 o C.

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96 Figure B 8 Concentration profile fit with cubic b spline interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 500 o C.

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97 Figure B 9 Concentration profile fit with cubic b spl ine interpolation for Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 550 o C.

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98 Figure B 10 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 450 o C.

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99 Figure B 11 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 500 o C.

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100 Figure B 12 Concentration profile fit with cubic b spline interpolation for Mg 2Ag/Mg 2Ag 5Sn diffusion couple annealed at 55 0 o C.

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101 APPENDIX C CONCENTRATION DEPENDENT INTERDIF FUSION COEFFICIENTS Figure C 1. Concentration dependent interdiffusion coefficient for Mg/Mg 5Ag diffusion couples annealed at 450 o C, 500 o C, and 550 o C.

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102 Figure C 2. Concentration dependent interdiffusion coefficient for Mg/ Mg 5Sn diffusion couples annealed at 450 o C, 500 o C, and 550 o C.

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103 Figure C 3. Concentration dependent inter diffusion coefficient for Mg 2Sn/Mg 2Sn 5Ag diffusion couples annealed at 450 o C, 500 o C, and 550 o C.

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104 Figure C 4. Concentration dependent inter diffusion coefficient for Mg 2Ag/Mg 2Ag 5Sn diffusion couples annealed at 450 o C, 500 o C, and 550 o C.

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105 APPENDIX D CONCENTRATION PROFILES COMPARED TO DICTRA SIMULATIONS Figure D 1. Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 450 o C with corresponding DICTRA simulation.

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106 Figure D 2. Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 500 o C with corresponding DICTRA simulation.

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107 Figure D 3. Concentration profile of Mg/Mg 5Ag diffusion couple annealed at 550 o C with corresponding DICTRA simulation.

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108 Figure D 4. Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 450 o C with corresponding DICTRA simulation.

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109 Figure D 5. Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 500 o C with corresponding DICTRA simulation.

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110 Figure D 6. Concentration profile of Mg/Mg 5Sn diffusion couple annealed at 550 o C with corresponding DICTRA simulation.

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111 Figure D 7. Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 450 o C with corresponding DICTRA simulation.

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112 Figure D 8. Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 50 0 o C with corresponding DICTRA simulation.

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113 Figure D 9. Concentration profile of Mg 2Sn/Mg 2Sn 5Ag diffusion couple annealed at 550 o C with corresponding DICTRA simulation.

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114 Figure D 10. Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion coupl e annealed at 4 50 o C with corresponding DICTRA simulation.

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115 Figure D 11. Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion coupl e annealed at 50 0 o C with corresponding DICTRA simulation.

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116 Figure D 12. Concentration profile of Mg 2Ag/Mg 2Ag 5Sn diffusion coupl e annealed at 55 0 o C with corresponding DICTRA simulation.

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117 LIST OF REFERENCES [1] J.W. McAuley, Global sustainability and key needs in future automotive design, Environ. Sci. Technol. 37 (2003) 5 414 5416. [2] U.S. Energy Information Administration, Monthly Energy Review, March 2017, Washington, D.C., 2017. [3] A. Mayyas, A. Qattawi, M. Omar, D. Shan, Design for sustainability in automotive ind ustry: A comprehensive review, Renew. Sustain. Energy Rev. 16 (2012) 1845 1862. [4] U.S. Environmental Protection Agency, Inventory of U.S. Greenhouse Gas Emissions and Sinks, 1990 2015, Washington, D.C., 2017. [5] Intergovernmental Panel on Climate Change, Climate Change 2014 Synthesis Report Summary Chapter for Policymakers, Geneva, 201 4. [6] The United States Congress, Energy Independence and Security Act of 2007, United States, 2007. [7] National Highway Traffic Safety Administration, Average Fu el Economy Standards Passenger Cars and Light Trucks Model Year 2011, United States, 2009. [8] National Highway Traffic Safety Administration, 2017 and Later Model Year Light Duty Vehicle Greenhouse Gas Emissions and Corporate Average Fuel Economy Standar ds, United States, 2012. [9] P.K. Mallick, Overview, in: P.K. Mallick (Ed.), Mater. Des. Manuf. Light. Veh., 1st ed., Woodhead Publishing, Cambridge, 2010: pp. 1 32. [10] A. Birky, D. Greene, T. Gross, D. Hamilton, K. Heitner, L. Johnson, J. Maples, J. A Fifty Year Perspective, Washington, D.C., 2001. [11] M. Hakamada, T. Furuta, Y. Chino, Y. Chen, H. Kusuda, M. Mabuchi, Life cycle inventory study on magnesium alloy substitu tion in vehicles Energy. 32 (2007) 1352 1360. [12] A.A. Luo, Materials comparison and potential applications of magnesium in automobiles, in: H.I. Kaplan, J.N. Hryn, B.B. Clow (Eds.), Magnes. Technol. 2000, John Wiley and Sons, Hoboken, 2000: pp. 25 34. [13] J.R. Davis, Metals Handbook: Desk Edition, 2nd ed., ASM International, Materials Park, 1998.

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123 BIOGRAPHICAL SKETCH Joshua Wagner was born in 1993 in San Antonio, TX. In 2011, he graduated from the Collegiate High School at Northwest Florida State College in N iceville, FL. He obtained a Bachelor of Science degree in Materials Science and Engineering from the University of Florida in 2015. Joshua then accepted a Science and Engineering Palace Acquire position with the United States Air Force. He worked at Eglin Air Force Base from 2015 to 2016 before being sent back to the University of Florida to pursue a Master in Materials Science and Engineering degree at the University of Florida. His m k focused on the kinetic assessment of Mg Sn, Mg Ag, and Mg Ag Sn alloys for improved creep resistance. Joshua received his Master of Science in Materials Science and Engineering degree from the University of Florida in December 2017.