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Quantitatively Connecting the Thermodynamic and Electronic Quantitatively Connecting the Thermodynamic and Electronic Properties of Molten Systems by Charles Cooper Rinzler Submitted to the Department of Materials Science and Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2017 c Massachusetts Institute of Technology 2017. All rights reserved. Author................................................................ Department of Materials Science and Engineering April 9, 2017 Certified by............................................................ Antoine Allanore Associate Professor Thesis Supervisor Accepted by........................................................... Donald Sadoway Chairman, Department Committee for Graduate Students 2 Quantitatively Connecting the Thermodynamic and Electronic Properties of Molten Systems by Charles Cooper Rinzler Submitted to the Department of Materials Science and Engineering on April 9, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract The electronic and thermodynamic properties of noncrystalline systems are inves- tigated and quantitatively connected through the application of theory presented herein. The electronic entropy is confirmed to control the thermodynamics of molten semiconductors. The presented theory is applied to predict the thermodynamic prop- erties of the prototypical Te-Tl molten semiconductor from empirical electronic prop- erty data and the electronic properties from empirical thermodynamic data. The theory is able to answer a question posed in the literature regarding a correlation between features of phase diagrams and molten semiconductivity. The quantitative connection is extended to predict thermodynamic properties of fusion, and a stabil- ity criterion to predict whether a system will behave as a molten semiconductor is developed and verified. The investigation and prediction of electronic transitions, such as metallization of high temperature systems, is enabled by the theory provided herein. The thermo- dynamic bases for key features of phase diagrams in the molten state are explained and quantified. Methods to rapidly collect electronic and entropy data in the molten phase are provided and enable access to key thermodynamic data for high temper- ature systems. The connection of electronic entropy to short-range order allows the detection and prediction of solid-phase compounds through the collection of electronic property data in the molten phase and the prediction of thermodynamic quantities of fusion. An absolute reference for entropy at temperatures substantially above 0◦ Kisproposed. Thesis Supervisor: Antoine Allanore Title: Associate Professor 3 4 Acknowledgments For my parents Denise Denton-Rinzler and Richard Rinzler. You gave everything so that I could have a chance at a life of purpose, fulfillment, and happiness. You have supported and encouraged me in all things. This PhD, and all success I may have in life, is only possible because of your dedication to my education, your commitment to giving me every opportunity by demolishing every obstacle to my wellbeing, and, most importantly, your support in my development as a human being. I love you and am so thankful to have you in my life. To my sister, Marina (Mimi) Rinzler, who has believed in me despite my best efforts to dissuade her and has been the best friend through all times of life to an extremely lucky brother. You have taught me more about how to live my best life than you could ever know. To my mentor, advisor, and friend Professor Antoine Allanore, who has been my thought partner, an intellectual, academic, and moral guide, and who has, along with his family, supported me far beyond any reasonable expectation. Thank you for the opportunity to work, and work with you, on matters that are meaningful, challenging, and rewarding. This thesis is every bit as much yours as it is mine. The Fannie and John Hertz Foundation has supported my work through a Hertz Fellowship. This generous grant enabled me to engage in research on a high-risk, high- impact subject and to work and collaborate with the ideal advisor. More critically, the fellowship has provided support on all axes (intellectual, academic, professional, and personal) in abundance. The Hertz community has become my family and it has been an absolute honor to be a part of such an incredible group of individuals. Our work together is just beginning. I would like to thank and acknowledge Professors Eugene Fitzgerald and Jeffrey Grossman for actively participating on my committee. Professor Grossman has been a continual source of enthusiasm and perspective for this work. Professor Fitzgerald has kept my eye on the prize while enabling me to make the most out of my time at MIT. 5 Thank you to my colleagues in the Allanore Lab for your friendship, support, and for making the day-to-day and month-to-month of this PhD meaningful and engaging. You will be happy to know that I will no longer have a forum to talk at you about how exciting entropy can be in your lives. A special shout-out to Angelita Mireles, Elissa Haverty, and the whole DMSE administration for being complete rockstars, keeping me sane and on task, and al- ways taking the opportunity to make my life better and my PhD smoother. This department does not exist without you - thank you for all that you do for all of us every day. Finally, thank you to all of my friends for keeping me afloat with copious amounts of love, humor, and (liquid) support. You know who you are. You make my life worth living. And to the ones that encouraged me to get this PhD - this is all your fault... 6 Contents 1Introduction 17 1.1 StructureofthePresentWork . 18 1.1.1 Connecting Electronic and Thermodynamic Properties in the MoltenPhase ........................... 18 1.1.2 The Role of Entropy at High Temperature . 19 1.1.3 Connecting Transport Properties and Entropy: a Quantitative Theory............................... 20 1.1.4 Molten Semiconductors as Materials of Focus . 20 1.1.5 Extensibility of the Theory to Other Systems . 21 1.2 BackgroundonMoltenSemiconductors . 22 1.2.1 Electronic Properties of Noncrystalline Systems . 22 1.2.2 MoltenSemiconductors. 22 1.2.3 TheoryofMoltenSemiconductors . 24 1.2.4 PreviousApproaches . 26 1.2.5 Solidvs. MoltenSemiconductors . 32 1.3 Thermodynamics of Molten Semiconductors . 33 1.3.1 PredictionofPhaseDiagrams . 34 1.3.2 Interpretation of Phase Diagrams of Molten Semiconductor Sys- tems . 37 1.4 Connection of Transport Properties to Equilibrium Thermodynamic Variables.................................. 38 1.4.1 TransportEntropy ........................ 38 7 1.4.2 Previous Attempts at Connection . 39 1.5 ElectronicEntropy ............................ 39 1.5.1 FormsofElectronicEntropy . 40 1.5.2 Contribution of Electronic Entropy to Total Entropy . 41 1.6 Summary ................................. 43 2Hypothesis 53 2.1 FeaturesofPhaseDiagrams . 54 2.2 Scientific Gap . 56 2.3 Hypothesis . 56 2.4 ConsequencesforMaterialsModeling . 57 2.5 Framework for Validation of Hypothesis . 59 2.6 Summary ................................. 59 3TheoryRelatingElectronicEntropytoElectronicProperties 63 3.1 Theory................................... 63 3.1.1 Electronic Entropy and Thermopower . 63 3.1.2 Formulation for Use of Empirical Data . 65 3.1.3 Assumptions Used in Application of Theory . 65 3.2 DiscussionofTheoreticalBasis . 66 4PredictionofPropertiesofTe-Tl 71 4.1 AppliedModel .............................. 71 4.2 Results . 72 4.3 Discussion . 72 5ExtensionofFrameworktoPredictingThermodynamicQuantities of Fusion 79 5.1 CalculationoftheEntropyofFusion . 79 5.2 Results . 80 5.3 Discussion . 80 8 6ACriterionforMoltenSemiconductivity 85 6.1 Stability Analysis of Molten State . 85 6.2 ApplicationtotheTe-TlSystem. 87 6.3 Discussion . 90 7PredictionofMetallizationTemperatureofMoltenSemiconductor Systems 95 7.1 Method .................................. 96 7.2 Calculation of the Metallization Temperature of FeS . 97 7.3 Calculation of the Metallization Temperature of the Te-Tl system . 99 7.4 Discussion . 99 8PredictionofFeaturesofPhaseDiagrams 103 8.1 Method .................................. 105 8.2 Calculation of the Excess Entropy of the Fe-S System . 105 8.3 Calculation of the Miscibility Gap of the Fe-S System . 106 8.4 Discussion . 106 9ExperimentalMethodsandResults 111 9.1 Review of Apparatuses from Previous Researchers . 111 9.1.1 QuartzTestCell ......................... 112 9.1.2 BoronNitrideTestCell. 112 9.2 DynamicInductionTestCell. 113 9.2.1 Apparatus Design . 113 9.2.2 Apparatus Performance . 116 9.2.3 ResultsforPb-S.......................... 116 9.3 StaticTestCell .............................. 116 9.3.1 Apparatus Design . 117 9.3.2 Apparatus Performance . 120 9.3.3 Results for Sn-S . 120 9.4 DiscussionoftheExperimentalMethods . 122 9 10 Extension to Metallic and Ionic Systems 127 10.1 ExtensionofTheorytoMetallicSystems . 127 10.2 ExtensionofTheorytoIonicSystems . 129 11 Future Research 133 11.1 Extension of Experimental Methods for Measuring the Entropy of Mix- ing to New Systems . 133 11.1.1 MoltenSemiconductorSystems . 134 11.1.2 Metallic Systems Exhibiting Congruent Melting Compounds . 134 11.1.3 MulticomponentSystems. 134 11.1.4 Ionic Systems . 134 11.2 Integration of Physical Models of Entropy into a CALPHAD Framework135 11.3 Atomistic Modeling of Molten Semiconductors . 135 12 Conclusion 139 12.1 DemonstratedConsequencesofTheory . 139 12.1.1 Modeling of Molten Semiconductors . 139 12.1.2 BeyondMoltenSemiconductors
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