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Thermal conductivity in ISOL target materials : development of a numerical approach and an experimental… Au, Mia 2020

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Thermal Conductivity in ISOL Target Materials:Development of a numerical approach and anexperimental apparatusbyMia AuB.Sc. Mechanical Engineering, University of Alberta, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Engineering Physics)The University of British Columbia(Vancouver)July 2020c©Mia Au, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Thermal Conductivity in ISOL Target Materials:Development of a numerical approach and an experimental apparatussubmitted by Mia Au in partial fulfillment of the requirements for the degree ofMaster of Applied Science in Engineering Physics.Examining Committee:Dr. Reiner Kruecken, Deputy Director, Research, TRIUMF. Professor of Physics,University of British ColumbiaSupervisorDr. Alexander Gottberg, Department Head, Targets and Ion Sources, TRIUMF.Adjunct Professor of Physics, University of VictoriaSupervisory Committee MemberiiAbstractThe method of Isotope Separation On-Line (ISOL) is one of the most successfulways to produce rare nuclei. Hitting a target material with accelerated particlesgenerates heat and reaction products which then diffuse and effuse through thetarget material before they are released for ionization and extraction for exper-iments in nuclear physics, astrophysics, materials science, pharmaceuticals, andmany more. The target material temperature dominates the release process and islimiting the primary beam intensity. Heat is dissipated from the beam spot throughthe target material, making the effective thermal conductivity of the target mate-rial critical for the ISOL process. Specifically-engineered microstructures have thepotential to achieve better release properties. To address the thermal challengesin target materials, a deeper understanding of the thermal conductivity of theseengineered materials is required.In this work, a numerical method is developed for evaluating the effective ther-mal conductivity of representative microstructures. A combined parallel and seriesmodel agrees with numerical data of four representative microstructures when ther-mal radiation through pores is considered by fitting a morphological parameter anda parameter describing the portion of series connections. Separately, a steady-stateexperimental-numerical method is used to determine the effective thermal conduc-tivity of porous β -SiC slip-cast material and β -SiC pressed pellet material as afunction of temperature up to 1200◦C and 1050◦C respectively. In addition, a newexperimental apparatus for effective thermal conductivity is presented from con-ceptual design to operation.This thesis works towards understanding thermal transport through target ma-terials. The new numerical method for material analysis, effective thermal conduc-iiitivity measurements on SiC, and the establishment of the CHI system at TRIUMFfor thermal conductivity measurements on target materials help build towards sys-tematic studies of engineered materials in ISOL and beyond.ivLay SummarySpecifically-engineered materials are used as targets to produce rare nuclei. Hittingtarget material with a high-energy beam of particles causes reactions that make rarenuclei and generate heat. Rare nuclei must then be extracted from the target ma-terial. Temperature and heat transport through the material’s engineered structureare critical to the extraction process and central to this research.In this thesis, a computational method for evaluating heat transport is developedand used to compare four material structures with theoretical predictions. Two ce-ramics with different engineered structure are produced and tested beyond 1000◦Cto determine their ability to transport heat. An experimental apparatus is designed,procured, built and installed for systematic studies of new materials. This workprovides a method and experimental approach to understanding and testing heattransport in engineered materials.vPrefaceThis thesis is an intellectual product of the author, M. Au. None of the text of thethesis is taken directly from previously published or collaborative articles. The mo-tivation for this work is based on the targets and ion sources operated at TRIUMF.ISOL target and ion source developments and designs are the product of extensiveinternational collaboration.Chapter 3. The numerical method is my original work. I was responsible for allmaterial models, simulations conducted, data analysis and conclusions with adviceand input from my supervisor A. Gottberg.Chapter 4. The method and apparatus used was developed and built at INFNby Manzolaro et al. and published in 2013 [83]. The POCO-EDM-AF5 graphitedata was taken by M. Sturaro and published in the thesis “Caratterizzazione termo-strutturale di materiali ceramici per applicazioni in fisica e medicina nucleare”, forthe degree requirements of Masters in Mechanical Engineering at the University ofPadova, 2018 [116]. I was responsible for taking data and applying the method us-ing a reference sample to re-calibrate the experimental apparatus. I was responsiblefor the β -SiC material synthesis. I produced the cast β -SiC samples at TRIUMFwith help and guidance from J. Wong and D. Ortiz Rosales, using a procedure de-veloped by M. Dombsky and V. Hanemaayer, published previously and patented[42][63]. I produced the pressed β -SiC samples at SPES with advice and guidancefrom S. Corradetti. I developed a sintering routine for both types of β -SiC ma-terials at the SPES laboratory and used it to produce samples for the experimentsdiscussed in Chapter 4. I conducted experiments and collected data on the β -SiCsamples using the apparatus, then completed the data analysis on the SiC samplesusing the numerical method with advice from M. Ballan and R. Salomoni.viChapter 5. The Chamber for Heating Investigations (CHI) experimental ap-paratus is designed to study target material properties in two ways: the study ofthermal conductivity for this thesis work, and the study of isotope release from tar-get materials for the PhD thesis of L. Egoriti for the degree requirements of Doctorof Philosophy in Chemistry at the University of British Columbia. L. Egoriti andI were equally responsible for the design, procurement, installation, and assemblyof the test infrastructure, with technical assistance from our teammate C. Petersonduring installation and assembly. I was responsible for the design of the controls,data acquisition and interlocks for the system, with assistance from teammate R.Caballero-Folch. L. Egoriti was responsible for design of the target material proce-dure, and handling and transportation equipment with assistance from teammatesM. Cervantes-Smith and C. Peterson. I was responsible for design and prototypingof the thermal conductivity configuration, while L. Egoriti was responsible for thedesign and prototyping of the release configuration.All data analysis and writing was completed by me.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Isotope Separation On-Line . . . . . . . . . . . . . . . . . . . . . 21.1.1 RIB intensity and isotope yield . . . . . . . . . . . . . . . 41.1.2 Target material characterization . . . . . . . . . . . . . . 141.1.3 Existing literature on thermal conductivity of target materials 151.2 The ARIEL target material challenge . . . . . . . . . . . . . . . . 182 Approaches to calculating thermal conductivity . . . . . . . . . . . . 212.1 The building blocks of thermal conductivity . . . . . . . . . . . . 222.1.1 Electron and phonon thermal conductivity . . . . . . . . . 22viii2.1.2 Radiation thermal conductivity . . . . . . . . . . . . . . . 252.2 Real materials, porosity and heterogeneous media . . . . . . . . . 262.2.1 Analytical models of heat transfer through porous media . 272.3 Finite element approaches . . . . . . . . . . . . . . . . . . . . . 302.3.1 Material model generation . . . . . . . . . . . . . . . . . 302.3.2 Numerical transport equations . . . . . . . . . . . . . . . 313 Development of a numerical model for thermal conductivity . . . . 323.1 Constructing the model geometry . . . . . . . . . . . . . . . . . . 323.1.1 Simulation geometry . . . . . . . . . . . . . . . . . . . . 343.1.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 413.2 Numerical model discussion . . . . . . . . . . . . . . . . . . . . 434 A numerical-experimental method to study effective thermal con-ductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.1 Calibration of the numerical-experimental approach . . . . . . . . 544.2 Using the steady-state high temperature method on SiC target ma-terials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . 604.2.2 Experimental method . . . . . . . . . . . . . . . . . . . . 624.2.3 SPES SiC measurements . . . . . . . . . . . . . . . . . . 654.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Development of an experimental apparatus for thermal conductivityinvestigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.1 CHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.1.1 Conceptual design . . . . . . . . . . . . . . . . . . . . . 785.1.2 Detailed design . . . . . . . . . . . . . . . . . . . . . . . 815.1.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . 955.1.4 Commissioning . . . . . . . . . . . . . . . . . . . . . . . 965.2 Future work for CHI . . . . . . . . . . . . . . . . . . . . . . . . 976 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99ixBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102A Numerical approach to thermal conductivity . . . . . . . . . . . . . 116A.1 Uncertainty in the numerical method . . . . . . . . . . . . . . . . 116A.1.1 Mesh dependence study . . . . . . . . . . . . . . . . . . 116A.1.2 Effective conductivity calculation . . . . . . . . . . . . . 117B A numerical-experimental approach . . . . . . . . . . . . . . . . . . 119B.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . 119B.2 Evaluating uncertainties in optimized effective thermal conductivity 122C Design details of CHI . . . . . . . . . . . . . . . . . . . . . . . . . . 125C.1 Go No-Go evaluation . . . . . . . . . . . . . . . . . . . . . . . . 125C.2 Conceptual design . . . . . . . . . . . . . . . . . . . . . . . . . . 129C.2.1 Radial steady state concept . . . . . . . . . . . . . . . . . 129C.2.2 Laser flash . . . . . . . . . . . . . . . . . . . . . . . . . 132C.2.3 Axial steady state . . . . . . . . . . . . . . . . . . . . . . 134C.2.4 Radiating crucible . . . . . . . . . . . . . . . . . . . . . 136C.2.5 Concept decision matrix . . . . . . . . . . . . . . . . . . 138C.2.6 Electron bombardment . . . . . . . . . . . . . . . . . . . 138C.3 Detailed design . . . . . . . . . . . . . . . . . . . . . . . . . . . 140C.3.1 Design iterations . . . . . . . . . . . . . . . . . . . . . . 140C.3.2 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144C.3.3 Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . 145C.3.4 Interlocks and data acquisition . . . . . . . . . . . . . . . 147C.3.5 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 152xList of TablesTable 1.1 ISOL facility power densities . . . . . . . . . . . . . . . . . . 7Table 3.1 Simulation model comparison . . . . . . . . . . . . . . . . . . 36Table 3.2 β and γ fitting parameters . . . . . . . . . . . . . . . . . . . . 44Table 3.3 Variation of fitting parameters with emissivity . . . . . . . . . 47Table 4.1 Measured porosity of SiC samples, using helium pycnometry todetermine density. . . . . . . . . . . . . . . . . . . . . . . . . 63Table C.1 CHI concept go-no go evaluation . . . . . . . . . . . . . . . . 128xiList of FiguresFigure 1.1 Schematic of the ISOL process for isotope production . . . . 2Figure 1.2 TRIUMF layout . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.3 In-target reactions . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 1.4 ISAC production vs. yield . . . . . . . . . . . . . . . . . . . 5Figure 1.5 Proton and electron target geometries . . . . . . . . . . . . . 8Figure 1.6 Proton stopping power in U . . . . . . . . . . . . . . . . . . 9Figure 1.7 Target temperatures from Joule and beam heating . . . . . . . 10Figure 1.8 ISAC high power target . . . . . . . . . . . . . . . . . . . . . 11Figure 1.9 keff of fibrous ISOL materials . . . . . . . . . . . . . . . . . 16Figure 1.10 Experimental thermal conductivity values of UC . . . . . . . 18Figure 1.11 keff of UCx graphite vs. graphene . . . . . . . . . . . . . . . 19Figure 1.12 AETE target beam heating . . . . . . . . . . . . . . . . . . . 20Figure 2.1 keff of UC from DFT . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.2 Effect of porosity on keff of UO2 . . . . . . . . . . . . . . . . 24Figure 2.3 Phonon thermal conductivity of β -SiC . . . . . . . . . . . . . 24Figure 2.4 Schematic of keff . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.5 Parallel and series models . . . . . . . . . . . . . . . . . . . 28Figure 3.1 Representative material model . . . . . . . . . . . . . . . . . 33Figure 3.2 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.3 Simulation models . . . . . . . . . . . . . . . . . . . . . . . 35Figure 3.4 Simulation cell A . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.5 Simulation cell B . . . . . . . . . . . . . . . . . . . . . . . . 38xiiFigure 3.6 Material model for simulation . . . . . . . . . . . . . . . . . 39Figure 3.7 Simulation cell D . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.8 keff vs. |x2− x1| . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.9 Simulation uncertainty vs. T . . . . . . . . . . . . . . . . . . 41Figure 3.10 keff of cell A and fit theory . . . . . . . . . . . . . . . . . . . 45Figure 3.11 keff of cell B and fit theory . . . . . . . . . . . . . . . . . . . 46Figure 3.12 keff of cell C and fit theory . . . . . . . . . . . . . . . . . . . 47Figure 3.13 keff of cell D and fit theory . . . . . . . . . . . . . . . . . . . 48Figure 3.14 keff of all models at emissivity 1 . . . . . . . . . . . . . . . . 49Figure 3.15 Predicted keff of UC . . . . . . . . . . . . . . . . . . . . . . 50Figure 3.16 Predicted keff of UCx . . . . . . . . . . . . . . . . . . . . . . 51Figure 3.17 Predicted keff of UCx vs. d . . . . . . . . . . . . . . . . . . . 51Figure 4.1 SPES thermal conductivity apparatus . . . . . . . . . . . . . 55Figure 4.2 Experimental and numerical model . . . . . . . . . . . . . . 55Figure 4.3 C0, C1 and C2 for graphite . . . . . . . . . . . . . . . . . . . 57Figure 4.4 Values of optimization scheme residuals over 148 iterations . 57Figure 4.5 Numerical and reference keff from the steady-state method . . 58Figure 4.6 Experimental and numerical temperatures for graphite . . . . 59Figure 4.7 Sintering furnace . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 4.8 Cast β -SiC, sintered . . . . . . . . . . . . . . . . . . . . . . 61Figure 4.9 Pressed β -SiC . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.10 EDS spectra of β -SiC . . . . . . . . . . . . . . . . . . . . . 63Figure 4.11 Emissivity of cast β -SiC . . . . . . . . . . . . . . . . . . . . 66Figure 4.12 Emissivity of cast β -SiC . . . . . . . . . . . . . . . . . . . . 67Figure 4.13 keff for cast β -SiC . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 4.14 Experimental and numerical temperatures for cast β -SiC . . . 68Figure 4.15 Cast β -SiC after testing . . . . . . . . . . . . . . . . . . . . . 69Figure 4.16 Emissivity of pressed β -SiC . . . . . . . . . . . . . . . . . . 70Figure 4.17 keff of pressed β -SiC . . . . . . . . . . . . . . . . . . . . . . 71Figure 4.18 Experimental and numerical temperatures for pressed β -SiC . 72Figure 5.1 Conceptual design of CHI . . . . . . . . . . . . . . . . . . . 80xiiiFigure 5.2 Conceptual schematic of CHI . . . . . . . . . . . . . . . . . 81Figure 5.3 CAD model of CHI . . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.4 CAD section of CHI . . . . . . . . . . . . . . . . . . . . . . 83Figure 5.5 CAD model of electron bombardment flange . . . . . . . . . 84Figure 5.6 CAD model of keff configuration . . . . . . . . . . . . . . . . 85Figure 5.7 Competing electron current effects at CHI . . . . . . . . . . . 87Figure 5.8 First prototype of CHI keff configuration . . . . . . . . . . . . 88Figure 5.9 CHI commissioning sparks . . . . . . . . . . . . . . . . . . . 89Figure 5.10 CHI cathode prototype 1 . . . . . . . . . . . . . . . . . . . . 89Figure 5.11 CHI cathode 2 . . . . . . . . . . . . . . . . . . . . . . . . . 90Figure 5.12 CHI cathode 2 prototype . . . . . . . . . . . . . . . . . . . . 91Figure 5.13 CHI with cathode 2 under current . . . . . . . . . . . . . . . 92Figure 5.14 CHI commissioning cathode . . . . . . . . . . . . . . . . . . 93Figure 5.15 CHI commissioning thermocouples . . . . . . . . . . . . . . 94Figure A.1 Mesh refinement . . . . . . . . . . . . . . . . . . . . . . . . 117Figure A.2 Mesh refinement for model A . . . . . . . . . . . . . . . . . 118Figure B.1 Cast β -SiC, wet . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure B.2 Cast β -SiC, green . . . . . . . . . . . . . . . . . . . . . . . . 121Figure B.3 Samples installed in sintering furnace . . . . . . . . . . . . . 122Figure B.4 keff bounds for POCO EDM-AF5 . . . . . . . . . . . . . . . 123Figure B.5 keff bounds for pressed β -SiC . . . . . . . . . . . . . . . . . 124Figure C.1 Radial concept precedence . . . . . . . . . . . . . . . . . . . 130Figure C.2 Radial concept for CHI . . . . . . . . . . . . . . . . . . . . . 130Figure C.3 Laser flash concept for CHI . . . . . . . . . . . . . . . . . . 134Figure C.4 Axial concept for CHI . . . . . . . . . . . . . . . . . . . . . 136Figure C.5 CHI decision matrix . . . . . . . . . . . . . . . . . . . . . . 139Figure C.6 CAD model of early keff concept . . . . . . . . . . . . . . . . 141Figure C.7 Predicted temperatures with wire filament . . . . . . . . . . . 141Figure C.8 Predicted temperatures with flat foil . . . . . . . . . . . . . . 142Figure C.9 ATD0009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Figure C.10 CHI pressure drops . . . . . . . . . . . . . . . . . . . . . . . 145xivFigure C.11 CHI P&ID . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Figure C.12 CHI DAQC2 . . . . . . . . . . . . . . . . . . . . . . . . . . 148Figure C.13 CHI DAQ and interlocks . . . . . . . . . . . . . . . . . . . . 149Figure C.14 CHI current power supply wiring . . . . . . . . . . . . . . . 150Figure C.15 CHI voltage power supply wiring . . . . . . . . . . . . . . . 151xvGlossaryVariablesα thermal diffusivityβ fraction of series connectionscp heat capacity of the material [J kg−1K−1]d largest dimension of the gap parallel to heat flowρ density of the materialηdiff diffusion efficiencyD diffusion coefficient1µs diffusion time constantη total total efficiency of the ISOL processε emissivityE energyγ geometrical or morphological factort1/2 half-lifedEλ (λ ,θ ,φ ,T ) spectral radiance of an emitting surface per unit wavelength(or frequency) [W sr−1m−3]xviIRIB intensity of the radioactive ion beamIdriver intensity of the driver beamk thermal conductivityks thermal conductivity of a solid material with zero porositykp thermal conductivity of a porekeff effective thermal conductivity of a materialkel electron contribution to thermal conductivitykph phonon contribution to thermal conductivitykrad radiation contribution to thermal conductivityNt number density of target nucleiP porosityq energy current or heat fluxQ heat flow [W]R universal gas constant, 8.314 [J mol−1 K−1]σB Stefan-Boltzmann constant, 5.67 ·10−8 [W m−2K−4]φW work functionσi energy-dependent cross-section for the production of adesired isotope i by the interaction of particles with thetarget nucleusAcronymsANSYS ANSYS MechanicalAPDL ANSYS Parametric Design LanguagexviiARIEL Advanced Rare IsotopE LaboratoryBTE Boltzmann Transport EquationCAD Computer Aided DesignCBCF carbon-bonded carbon fibreCERN the European Organization for Nuclear ResearchCHI Chamber for Heating InvestigationsCT computed tomographyDFT Density Functional TheoryEDS Energy Dispersive X-ray SpectroscopyEURISOL European ISOL facilityFEA Finite Element AnalysisFLUKA Monte Carlo particle transport codeFVM Finite Volume MethodGANIL Grand Acce´le´rateur National d’Ions LourdsHIE-ISOLDE High Intensity and Energy ISOLDEHRIBF Holifield Radioactive Ion Beam FacilityINFN National Institute of Nuclear PhysicsISAC Isotope Separator and ACceleratorISOL Isotope Separation On-LineISOLDE Isotope mass Separator On-Line DEviceLED L-edge densitometryLIEBE Liquid Eutectic Lead Bismuth Loop Target for EURISOLxviiiMD molecular dynamicsµCT micro-computed tomographyMYRRHA Multi-purpose hYbrid Research Reactor for High-techApplicationsORNL Oak Ridge National LaboratoryPSB Proton Synchrotron BoosterRIB radioactive ion beamRISP Rare Isotope Science ProjectRVCF reticulated vitreous carbon fibreSCK CEN Studiecentrum voor KernenergieSEM scanning electron microscopySPES Selective Production of Exotic SpeciesSRIM Stopping Range of Ions in MatterTRIUMF Canada’s Particle Accelerator CentreXRD X-ray diffraction spectroscopyXRF X-ray fluorescencexixAcknowledgmentsThank you to my supervisor Alexander Gottberg, for patiently answering ques-tions, teaching, and advising me throughout the project. Thank you to my super-visor Reiner Kruecken, for your consideration and support. You have given me somany opportunities to learn and grow as a student at TRIUMF and UBC.Thank you Luca Egoriti, my partner in the development of CHI. You are aconstant source of support, motivation, insight and fun. To Fernando Maldonado,thank you for all the enthusiastic discussions, simulation advice, and constant will-ingness to offer help and expertise. Thank you to Marla Cervantes-Smith for yourinsight into material properties and synthesis, and all your encouragement and un-derstanding. I am so grateful to have had you as my fellow students, colleagues,and close friends over the past few years.Thank you to Michele Ballan for discussions, collaboration, and all the funtimes in Vancouver and Legnaro. Thank you Riccardo Salomoni, Stefano Cor-radetti, and Mattia Manzolaro for all the assistance with materials, experimentsand analysis. Thank you to the members and staff of the SPES project and atINFN-LNL for invaluable technical support and for the kind and welcoming timeI was able to spend with you.Thank you to my office-mate Allon Messenberg, and the members of the ARIELtrailer, for a fun and productive workplace. Thank you Thomas Day Goodacre,Carla Babcock and Roger Caballero Folch for all your help, advice and support,and for putting up with all my questions. Thank you Aaron Schmidt and DarwinOrtiz Rosales, for technical support and fun conversations. Thank you to ChrisPeterson for all your help with installation and assembly of CHI.Thank you to Tomislav Hruskovec; Adrian Watt and the building servicesxxgroup; Franco Mamarella and the electrical services group; Dan Louie, ArthurLeung and the power supplies group; and the machine shop, electrical shop andscintillator shop. I am lucky to have had help from TRIUMF’s technical experts.To my loved ones, thank you for putting up with me during the two years ofthis thesis work. To my mother, my sisters and my father for always cheering meon. To my aunt Susan and uncle Paul, for feeding and supporting me. To mygrandmother Susan Blackner, for all the visits and precious time. To my room-mates Katrin Schmid and Olivia Adams, you were my support system, friends andfamily for the past two years—I still can’t believe how lucky we got. To QuinnTemmel, thank you for the endless support, patience, and sticking with me throughit all.TRIUMF receives federal funding via a contribution agreement with the Na-tional Research Council of Canada. ARIEL is funded by the Canada Foundationfor Innovation (CFI), the Provinces of AB, BC, MA, ON, QC, and TRIUMF. Iacknowledge additional support from the NSERC CREATE IsoSiM fellowship.xxiChapter 1IntroductionLiving is worthwhile if one can contribute in some small way to thisendless chain of progress.— Paul Dirac (1933)Radioactive isotopes provide many avenues towards understanding the uni-verse. In fundamental nuclear physics, the study of nuclei far from stability is crit-ical for exploring nuclear structure and reactions, looking for physics beyond thestandard model, and developing knowledge of particles and particle interactions.In nuclear astrophysics, studying exotic nuclei gives information on reactions instars and the origins of chemical elements. Radioactive isotopes are additionallyused for experimental studies in materials science and in nuclear medicine andradiopharmaceuticals. To pursue and develop these many fields of science, theinternational research community has invested and is investing significant effortsinto developments for isotope production. Facilities all over the world work toproduce nuclides of interest ranging from exotic short-lived radioactive nuclei, tosuperheavy nuclides on the boundaries of the periodic table of elements, to nucleicloser to stability that give experimental data to fundamental models and calcula-tions or that are used as probes to understand properties and processes of soft andsolid matter. These nuclei are created and then instantly delivered to an experimentin the form of a radioactive ion beam (RIB).The production and extraction of these nuclides is a challenging task requiringyears of research and development. This thesis aims to improve one method ofproducing radioactive isotopes by studying critical material properties.1Figure 1.1: Schematic of the ISOL process for isotope production1.1 Isotope Separation On-LineIsotope Separation On-Line (ISOL) facilities produce exotic nuclei by bombard-ing a target material with energetic particles to produce isotopes up to the targetmaterial mass. Reaction products move through the material matrix by diffusionand effusion until they are released to the ion source, where they can be ionized,extracted and mass separated for an experiment or further acceleration steps. Theprocess is shown schematically in Figure 1.1.In 1951 the earliest use of the ISOL method was published by Kofoed-Hansenand Nielsen, describing simultaneous use of a cyclotron and isotope separator tostudy short-lived krypton isotopes formed in fission of uranium [70]. In 1960 aproposal was made to use proton beam from the synchrocyclotron at the EuropeanOrganization for Nuclear Research (CERN) to produce atomic fragments from anISOL target. This was the start of the Isotope mass Separator On-Line DEvice(ISOLDE) at CERN, which is now the oldest operating ISOL facility. The ISOLmethod was proposed as an avenue to discovering and studying nuclei far fromstability, pushing developments in nuclear spectroscopy, detectors, and theory [11].The Isotope Separator and ACcelerator (ISAC) facility at Canada’s Particle Ac-2Figure 1.2: Layout of TRIUMF isotope production facility and beam lines[1]. The ARIEL facility is highlighted in blue, and the ISAC facilityis highlighted in green with detailed inset (right) of the experimentalfacilitiescelerator Centre (TRIUMF) began operation in 1998 and currently provides a wideselection of isotopes by irradiating thick targets with up to 100 µA of 480 MeVprotons, using a 520 MeV, 300 µA proton cyclotron [6][40]. The Advanced RareIsotopE Laboratory (ARIEL) facility at TRIUMF will use 3.3 mA of 30 MeV elec-trons and add a new 480 MeV, 100 µA proton target. Research in this thesis aimsto address thermal challenges faced by this new facility as well as to improve per-formance at ISAC. ARIEL will triple TRIUMF’s isotope production capabilities.The Selective Production of Exotic Species (SPES) project at Italy’s NationalInstitute of Nuclear Physics (INFN) is an ISOL facility under construction basedon a 40 MeV, 8 kW proton beam, hosting thermal research conducted for this the-sis. In addition to ISOLDE, TRIUMF and SPES, other ISOL projects includeHolifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Lab-oratory (ORNL) [9], the Rare Isotope Science Project (RISP) project in Korea[126], ISOL@MYRRHA at Studiecentrum voor Kernenergie (SCK CEN) in Bel-gium, and SPIRAL II at Grand Acce´le´rateur National d’Ions Lourds (GANIL), in3France [78]. The European ISOL facility (EURISOL) has been proposed as a next-generation ISOL facility exceeding the capabilities of all existing or planned ISOLfacilities worldwide [14][31].Fundamental criteria for qualifying a RIB or ISOL facility include diversityof available beams, beam intensity (yield), and non-degradation of beam inten-sity over time [17]. As research in astrophysics and nuclear structure continuesto develop, including more sensitive detection techniques and more sophisticatedtheoretical models calling for experimental data of more exotic isotopes, require-ments for the ISOL method grow more demanding. Performance regarding thesefundamental criteria is greatly determined by the specifically developed ISOL tar-get materials, driving target development as a critical focus of research for all thesefacilities.ISOL driver beams produce isotopes through various processes including directreactions, fragmentation, spallation, or fission (Figure 1.3). The probability ofeach process occurring depends on the driver beam particle and beam energy. Theresulting diversity of available isotopes depends on these production cross-sectionsand extraction of the specific element.Driver beam upgrades including the upgrade of the Proton Synchrotron Booster(PSB) at ISOLDE to 1.4 GeV in 1999—and potentially an upgrade to 2 GeV fol-lowing High Intensity and Energy ISOLDE (HIE-ISOLDE)—are motivated by thedesire to increase in-target isotope production rates [17], concluding that “a care-ful choice of projectile energy is an important parameter for optimizing productionyield of isotopes” [57]. In Figure 1.4, production yield is compared to radioactiveion beam yield provided by ISAC. Contrasting diversity of produced isotopes anddelivered beams highlights the critical factor limiting beam diversity: the releaseprocess. We can create the isotopes, but we cannot always release them from thetarget. The two main reasons for this will be introduced in the following sections.1.1.1 RIB intensity and isotope yieldThe intensity of the radioactive ion beam (IRIB) describes the quantity of the par-ticular species of interest that can be made available for the experiment. IRIB isgiven by integrating the amount of isotope produced over the travel length x of4Figure 1.3: a) Schematic of fragmentation, spallation, and fission processesinduced by a proton driver beam. b) Schematic of photofission reactionsinduced by high energy gamma rays [19][91]Figure 1.4: Left: Production rates resulting from 10 µA of 500 MeV protonson a uranium carbide target, calculated using FLUKA and presented asa chart of the nuclides [60]. Right: Radioactive ion beam yields at ISACfrom different target and ion source combinations presented as a chartof the nuclides as of 2012 [40].5driver beam particles through the target material as described in Equation 1.1. Toaccommodate growing demand for radioactive isotopes, IRIB should be maximized.IRIB = η totalIproduced = η total∫σi(E)Idriver(E,x)Nt(x)dx (1.1)IRIB in particles per second depends on energy (E) and the energy-dependent cross-section for the production of a desired isotope i by the interaction of particleswith the target nucleus (σi) as discussed in the previous section, but it is evi-dently not the only contributing factor. The others are the intensity of the driverbeam (Idriver), number density of target nuclei (Nt), and total efficiency of the ISOLprocess (η total). η total describes efficiencies of all processes the desired nuclidepasses through, with contributions from extraction/release from the target material,transport from the target material to the ion source, ionization, beam transportation,separation, storage and post-acceleration processes if applicable [60].The number of target nuclei available for reactions Nt depends on the targetmaterial density and the target geometry. The beam loses energy as it interacts withtarget material atoms; the eventual energy degradation of the beam limits the usefulinteraction range. Target lengths are typically optimized for release efficiency orrestricted by technical limitations. From Equation 1.1, this leaves two approachesto improving isotope yields:1. Increasing the primary beam intensity Idriver2. Improving efficiencies η totalOption 1 depends on the primary accelerator’s beam current limit. Increasing beamcurrent comes with additional engineering challenges from corresponding powerdensity increases in the target. Because of thermal challenges, many targets can-not reach the maximum design capability of their accelerator system. In practice,the efficiencies of Equation 1.1 dominate the isotope production. These can betackled by targeting processes that typically contribute the smallest efficiency, par-ticularly the release and extraction processes. The two effects are highly correlatedthrough the unmistakeable dependence on target material temperature. To maxi-mize efficiencies, temperatures must remain homogeneous and as high as possiblewithout degrading the target, requiring careful balance with additional inhomoge-6Table 1.1: ISOL facilities compared by beam energy and power. Resultingpower density given for a UCx (0.2% U-235, 68.8% U-238, 31% C) tar-get with density 2g/cc (TRIUMF) and 3.5g/cm3 (ISOLDE). Values cal-culated using FLUKA with bin size 1 mm3. *For the ARIEL electrontarget (AETE), the maximum is calculated perpendicular to the incidentbeam from the centre pellet, while the minimum is calculated along thecentre pellet diameterISOL facility Energy[MeV]Beampower(limit)[kW]Maximum(minimum)linear powerdensity[W/mm]Maximumpowerdensity[W/cm3]ISOLDE-CERN 1400 2.8 (2.8) 1.5 (1.1) 28.5ISAC-TRIUMF 500 50 (50) 45 (33.7) 884ARIEL-TRIUMF 35 25 (100) 616 (17.6)* 745SPES-INFN 40 8 (16) 762.5 (662.5) [8] –neous beam heating. As this research addresses the thermal conductivity problemthat restricts target operation, these dependencies must always be kept in mind.Hitting the target: increasing driver beam intensityAt first glance, Idriver should directly increase the IRIB (Equation 1.1), but in prac-tice the dependence on temperature and efficiencies complicates this effect. Manydevelopments in accelerator technologies aim to increase power on the target. In2019, Popescu et al. published a current review of worldwide ISOL target devel-opment for heat management with higher power driver beams [95].Heat from beam interaction depends on the driver beam particle, target geom-etry, and atomic density, resulting in different temperature profiles for differentbeams (Figure 1.5). It also depends on beam energy. Higher driver beam energyresults in a more homogeneous profile of deposited power along the target interac-tion length because the stopping power varies less with change in energy, as well asbeing lower in value (Figure 1.6). Because of varying accelerator energies, ISOLfacilities have different considerations for increasing beam current. In-target powerdensities are compared for some facilities in Table 1.1.7Figure 1.5: a) Schematic of temperature on target material induced by a pro-ton driver beam. b) Schematic of temperature on target material fromreactions with a gamma beam generated by bremsstrahlung using anelectron-to-gamma converter. Here, red is used to indicate higher tem-peratures and blue is used to indicate cooler temperatures.For an axial proton beam incident on a cylindrical target, heat is dissipated ra-dially from the beam spot at the centre of the target material by conduction to theperimeter of the cylinder. Higher energy protons (ISOLDE and ISAC) lose lessenergy per unit path length to heat. Protons with lower energy (SPES), deposit amuch larger fraction of their energy as heat into the material. The thermal profiledepends not only on the beam energy, but also on the target geometry as shown inFigure 1.5 and the amount of heat that can be successfully transferred to the heatsink without increasing the thermal gradient. Maintaining homogeneous tempera-tures high enough to promote diffusion thus depends fundamentally on the thermalproperties of the target material.Initially, ISAC operated using 1-3 µA of proton beam. In this low-powerregime, targets are wrapped with layers of heat shields (three 0.025 mm thick Tashields) and DC current resistively heats the target and transfer line. These condi-tions are designed to maintain homogeneous temperatures in the range of 2000◦C8Figure 1.6: Total stopping power of protons in uranium as a function of pro-ton energy, given as the sum of collision (electronic) stopping powerand nuclear stopping power calculated by PSTAR [10].[40] and limit radiative heat loss. During initial operation, the proton beam currentwas increased to 10 µA with observable increases in yields [44]. The developmentof higher power targets at ISAC came by removing heat shields and improving ther-mal contact with the tantalum container, allowing more heat to be dissipated. AtSPES, Ballan et al. have done extensive work using thermal Finite Element Anal-ysis (FEA) and experimental validation to develop homogeneous target materialtemperatures (Figure 1.7) [8].For each material, allowable operating temperature is determined from vapourpressure limits to prevent excessive evaporation of target or container material [45].Beam power limits are then set to keep the maximum predicted temperature in thetarget material below the vapour pressure threshold. For refractory materials withhigh thermal conductivity, including Ta, Nb, W, C, and others, the beam can beoperated at a higher current than for materials with lower thermal conductivity andmelting temperatures [129]. The target design without heat shields later enabledthe ISAC facility to operate up to 40 µA on Ta metal foil refractory targets withgood thermal conductivity and contact, and up to 15 µA on SiC pressed pellet9Figure 1.7: Simulated temperature of the SPES target design cross-sectionusing 40 MeV, 200 µA protons, featuring target material disks spacedto maintain homogeneous temperatures by a) Joule heating and b) beamheating. FEA conducted by M. Ballan and published, reprinted withpermission from [8].ceramic targets with lower thermal conductivity and poorer thermal contact withthe tantalum container. Slip-cast composite ceramics were developed by Hane-maayer, Bricault and Dombsky as an alternative to pressed pellets, featuring thin(0.1-0.3) mm porous ceramic layers bonded to graphite layers with high thermalconductivity [63]. Slip-casting facilitated proton currents up to 40 µA for SiC andincreases for several other materials including TiC, ZrC, and TaC [40]. The ISAChigh-power target shown in Figure 1.8 was developed to go beyond the previouslyexisting limit of proton beam intensity by increasing radiative cooling from thecontainer. The design, described in [41], incorporates tantalum fins to increase thesurface area of the target container. A bare ISAC target was measured to have aneffective emissivity of 0.35±0.01, while the high-power target achieved 0.92±0.2[20]. The increase in effective emissivity allowed ISAC high power targets to beoperated with higher Idriver, up to 100 µA of proton beam current in the case ofhighly conductive, refractory metal foils [43]. In this regime, target material ther-mal conductivity is the limiting factor for heat transport from the beam spot to theradiative heat sink. Graphite layers in slip-cast materials are intended for conduc-10Figure 1.8: Image of the ISAC target container design for high power, fea-turing tantalum fins for increased radiative surface area for the radiativeheat sink. The tube heater and ion source heater currents are shown withblack arrows. Inset photo of target reprinted with permission from [41].tion from the hot beam spot to the radiatively-cooled edge of the target materialdisc, but the layers are thin (0.13 mm) and may delaminate from the ceramic. Sys-tematic studies of these effects are missing, motivating parts of the research donefor this thesis. An alternative approach to homogenize beam power distributionis by rastering the incident proton beam. Using magnetic benders, the beam spotis moved around the sample, providing time-structure to the beam that allows thematerial to cool before the beam returns to the same spot [76][129]. Liquid looptargets have been proposed as a solution capable of withstanding 100 MW of directirradiation at facilities such as EURISOL and ISOL @ MYRRHA (Multi-purposehYbrid Research Reactor for High-tech Applications)[14]. The liquid target con-cept transports beam energy by conduction and forced convection, while circula-tion of target material achieves effects similar to rastering or increasing the size ofthe beam spot. Additional challenges of this approach include cavitation, recircula-tion zone hot spots, corrosion, high voltage, and transient effects from pulsed driverbeams, in designs such as the Liquid Eutectic Lead Bismuth Loop Target for EU-11RISOL (LIEBE) design at EURISOL [66]. There are many predictions for thermalgradients in ISOL targets—but without systematic studies of thermal conductivity.At 100 µA, 480 MeV (48 kW), ISAC is the world-wide highest power ISOL fa-cility operating at the edge of available technology to dissipate beam power fromthe target. Further increase of beam power deposition in ISOL targets requires de-velopment of new heat transfer technologies and further studies of the microscopiccontribution of heat transfer in these porous and multi-phasic materials.Increasing Idriver comes with a transition in operational modes, where the tar-get no longer has to be heated to promote diffusion, but instead must be cooled toavoid exceeding operating temperatures. Thermal gradients from the beam spot tothe radiative heat sink facilitate heat dissipation, but large thermal gradients haveadverse effects on isotope release [43]. The requirement for homogeneous temper-atures rules out other heat sink mechanisms such as active cooling. Regardless ofthe heat deposition profile, additional heat must be dissipated to avoid degradationin hot spots and isotope loss in cold spots. The aim of increasing Idriver and thefundamental importance of understanding thermal gradients in existing operatingconditions are two driving factors motivating models and studies of target materialthermal conductivity.ISOL facilities are no longer limited by the available power that the driver beamaccelerator can provide. Instead, they are limited by the amount of power that theISOL target can accept. This acceptance depends in turn on the maximum amountof power that can be dissipated from the target container, maximum tolerable ther-mal gradients, and peak temperatures in the target. These depend directly on thethermal conductivity of the target material.Improving target efficiencies through microstructureRelease efficiency describes the amount of isotope that exits the target materialcompared to the total amount of the isotope produced. After production, the isotopeundergoes diffusion through material and effusion between surfaces in the target.Time spent in these processes limits the amount of released isotope to an extentdependent on the isotope’s half-life. The product of release efficiency and transferefficiency from the target to ion source can be on the order of 10−6, which can12fully prevent successful extraction of an isotope even if the desired species hasbeen produced [60].Diffusion rates depend primarily on temperature, generally following the Ar-rhenius relation Equation 1.2.D = D0 exp(−EART) (1.2)With the diffusion coefficient (D), maximum diffusion coefficient (D0), activationenergy (EA) and universal gas constant R. The mobility of a species is highlydependent on the properties, chemistry, and morphology of the target material.Nuclei selections available from ISOL facilities are limited by in-target chemistryand radioactive isotope half-lives. This limiting factor motivates in-depth studies ofchemistry, diffusion and effusion processes through target materials. For isotopeswith a half-life (t1/2) shorter than the diffusion time constant ( 1µs ), µs =pi2Dr2 , wherer is the radius of a spherical grain, the diffusion efficiency (ηdiff) can be calculatedusing Equation 1.3 [69].ηdiff =3r√Dt1/2ln2(1.3)ηdiff is inversely proportional to r, motivating development of targets with porousmicro- and nanostructures for higher radioisotope beam intensities. In 2016, Got-tberg described target material criteria and challenges, outlining materials used forISOL and discussing considerations for target material categories including moltenmaterials, solid metals, oxides, carbides, other experimental and specialized mate-rials [60]. Gottberg concluded that “engineering a defined nano or microstructureas well as conserving this structure during the desired operational time, have gen-erated high yields and improved stabilities” [60]. Several other authors [115] [98]have further highlighted the importance of target material structure for isotope re-lease.Following observed successes, many efforts have gone into engineering mate-rial structures with high release efficiencies. At ORNL, matrices of carbon-bondedcarbon fibre (CBCF) and reticulated vitreous carbon fibre (RVCF) were used toproduce fibrous Al2O3, Ni-coated RVCF, and UC2-coated RVCF to study after ir-radiation [80]. In 2013, Czapski et al. pioneered an ice-templating technique to13specifically tailor SiC and Al2O3 microstructures, concluding that the techniquecould successfully be applied to create specific microstructures for ISOL targetmaterials with high release efficiencies [37]. Other studies have explored nano-metric and micrometric ceramic oxides and carbides [52] [97], the use of grapheneas a sintering aid [34], carbon nanofibre backbones [125], and many more. Somestudies go further to examine materials after irradiation to identify sintering andmicrostructure evolution caused by the ISOL target operating environment [52].1.1.2 Target material characterizationIn parallel to ongoing work on target production methods, the community has puteffort into understanding and characterizing ISOL material structures. A selectionof material properties with effects on performance for ISOL targets was publishedin 2019 by Ramos [98]. Links between production method and resulting materialproperties are being studied and reported [24] [62].ISOL target materials have been characterized with approaches such as X-raydiffraction spectroscopy (XRD), helium pycnometry, mercury pycnometry, scan-ning electron microscopy (SEM), X-ray fluorescence (XRF), and L-edge densit-ometry (LED) [52][62][74][98][115][120]. In some cases, nuclear fuel materialcharacteristics overlap with ISOL targets, predominantly with fissile materials in-cluding uranium composites [4], giving information on open porosity, pore distri-bution, morphological features, chemical composition, phases, lattice parametersand bulk density. Engineered materials form an extremely active topic of researchtowards better release properties. Despite the heat dissipation challenges discussedin Section 1.1.1, the topic of heat transfer through these engineered materials isstill largely untouched.Most studies on heat transfer through porous materials define some version ofthe following for characterization of materials:• Volume fraction of pores or porosity P• Pore morphology, closed or connected pores• Emissivity of pore and internal surfaces ε• Thermal conductivity of fully dense solid material ks14Many properties that are characteristic of ISOL target release performance overlapwith material properties that have significant impacts on effective heat transport.Fortunately, extensive work in characterizing engineered target materials providesexisting parameters against which to compare thermal transport properties.To improve isotope release efficiency, it is desirable to further engineer high-release target material morphology for better thermal properties, namely high ther-mal conductivity and high mechanical integrity at high temperatures.1.1.3 Existing literature on thermal conductivity of target materialsOne difficulty of studying thermal properties ISOL materials arises from con-straints imposed by ISOL operating conditions. In 2015, Pietrak and Wis´niewskipublished a review of simple, analytical models for thermal conductivity of het-erogeneous media, noting significant impacts of porosity [94]. In the review, theynote limits of applicability for many models. ISOL materials and operating condi-tions fall outside the range of applicability for many theories. Despite that, some ofthese simple analytical models have been employed in the study and developmentof ISOL targets and target materials, particularly to estimate target temperatureswhen direct temperature measurements are experimentally infeasible. Porous, het-erogeneous, multi-phasic ISOL materials in vacuum, at high temperatures, andmost notably during irradiation, limit the applicability of rigorous thermal con-ductivity models, even though such models have been developed for packed par-ticle beds [67][117][119][127], open-cell foams [30][58][73], insulation [18][101][109], and others.In 1999, Liu and Alton presented a thermal analysis on fibrous Al2O3, usingbeam heating profiles from Stopping Range of Ions in Matter (SRIM) and FEAusing ANSYS Mechanical (ANSYS) to determine target temperatures [79]. Theauthors remarked that radiative heat transfer could be more effective than con-duction for fibrous target materials with low conductive contributions to effectivethermal conductivity of a material (keff) [79]. Alton, Zhang and Kawai noted thatthermal conductivities for highly porous materials increase with increasing temper-ature (Figure 1.9). This behaviour is in complete contrast to the published thermalconductivities of most bulk materials that decrease with increasing temperature.15Figure 1.9: Thermal conductivity of fibrous Al2O3, ZrO2, CBCF and1xRVCF, 2xRVCF and Ni materials measured using a laser flash ap-paratus at ORNL by Zhang and Alton, reprinted with permission from[129].The authors propose that it is likely due to internal radiation by individual fibresinto open channels, allowing beam-deposited heat to effectively conduct throughlonger distances in the material [129] [3]. Following this exciting result, Zhang andAlton fit the experimental data with a model (Equation 1.4) containing a radiativecontribution to effective thermal conductivity, with two fitting constants C1 and C2.keffAlton =C1ρfibreρbulkks+C2εσBAs(T 4−T 40 )1∆r∆T(1.4)Fit results (Figure 1.9) show an increase in keff with T . This highlights theimportance of radiative effects for heat redistribution since radiation dominates theheat transfer for these highly-porous materials, especially at the elevated temper-atures required for fast diffusion release from ISOL targets [129]. The effects oftarget material microstructure on thermal conductivity are still largely unknown,limiting attempts to predict temperatures in porous ISOL materials. To date nosystematic studies have conclusively linked ISOL target material morphology ormicrostructure to thermal transport properties.16Thermal conductivity of UCx target materialsIn 1976, Lewis and Kerrisk presented a comprehensive review of data on uraniumand plutonium carbides [77] (Figure 1.10). Unlike ISOL materials, the nuclearfuels in this study are typically pure and dense. Due to the lack of experimentalor theoretical approaches, nuclear fuel material literature values are often used todescribe ISOL materials despite the differences, or used with some correction.In 2015, Corradetti et al. published experimental data on the thermal con-ductivity of uranium carbide ISOL target material as a function of temperature upto 1200◦C [33] Figure 1.10. This work reports among the first experimental val-ues for the temperature-dependent thermal conductivity of ISOL target materials.In sharp contrast to the data reviewed for nuclear fuel materials, Corradetti et al.identified a decline in thermal conductivity with increase in temperature. Literaturedata reports an increase with temperature [77], exposing a difference between highpurity, dense nuclear UC and porous, multi-phasic ISOL materials. The contrasthighlights the importance of material structure and composition.Because of the difference in materials, studies done for nuclear materials, re-viewing carbon, oxygen, and nitrogen content, and effects of porosity, are likelynot applicable to ISOL materials such as UCx. The data of Corradetti et al. [33]does not follow nuclear material data, or the trends displayed by the measurementsof Biasetto et al. [12] or Alton et al. [3] for more porous ISOL materials. The lackof understanding on ISOL materials highlights the need for further research.The study of thermal transport through target materials is of practical interest tothe international ISOL community. Target temperatures are critical for high-powerdriver beams and continue to be a subject of intense development. Highly porousmicro and nano-structured morphologies are desirable for release characteristicsand are being heavily investigated [120] [115]. For these materials, most modelspredict decreasing thermal conductivity as temperature increases [101][85][51].Low thermal conductivity presents challenges for operational regimes where beamheating dominates target temperatures. Though the ISOL problem of target mate-rial thermal conductivity is acknowledged, work in this field is just beginning.17Figure 1.10: Thermal conductivity of uranium carbide. Experimental liter-ature values shown in grey are recommended values of thermal con-ductivity of nuclear reactor uranium carbides from a literature reviewpublished by Lewis and Kerrisk [77] [29] [122] [88]. TD is used to in-dicate theoretical density. Weight percentage of oxygen was observedto have a significant effect on the effective thermal conductivity. Incomparison, the SPES MM ISOL uranium carbide measured by Cor-radetti et al. shows different behaviour with temperature[33]. The blueshaded region indicates a range of typical operating target tempera-tures, showing a lack of high-temperature data.1.2 The ARIEL target material challengeThe ARIEL electron target station is designed to accept 100 kW of beam poweronto a high-Z converter. The electrons produce bremsstrahlung (braking radiation)as they are decelerated. The resulting flux of photons induces wanted photofissionreactions in the target material and unwanted e-p pair production, leading to heatdeposition. Studying an operational mode of only a quarter of the full power, abeam of 35 MeV electrons will be at 700 µA of beam current, corresponding to25 kW of power. The analysis shows a hot spot on the side with incident gammarays (Figure 1.12). The difference between the hot centre (≈2500◦C) and the sur-rounding target container (≈1300◦C) indicates that heat dissipation is limited bytarget material thermal conductivity. The predicted target temperature is unsustain-18Figure 1.11: Thermal conductivity of uranium carbide synthesized withgraphene and uranium carbide synthesized with graphite for ISOL tar-get materials, measured by Biasetto et al. using a laser flash apparatus.TD is used to indicate theoretical density. Reprinted with permissionfrom [12], copyright c©2018, Springer Nature.able, disqualifying the simple design and prompting more research into the criticalmaterial property of thermal conductivity. The problem of beam power limits onexisting targets is a well-known one and has been explicitly stated several timesregarding ARIEL and the foreseen science projects: “power density inside the Utarget in all of these projects exceeds the present capability of carbide material ther-mal conductivity. A high thermal conductivity target material is mandatory for thesuccess of these projects” [40]. Low target thermal conductivity has been addressedwith additions to the target container [41] and by entirely new designs [14] but notyet by target microstructure. The effects of radiation heat transfer through themicrostructure of typical ISOL materials are unknown. Thermal conductivity forthese materials has to date been predicted using a handful of analytical approachesand existing data for dissimilar materials. If material morphology can be devel-oped to promote radiation heat transfer, at some point the radiative contributionmay dominate the conductive contribution. This unknown territory is particularlypromising for the development of ISOL target materials, since the material pa-19Figure 1.12: Steady state temperatures from FLUKA simulations [15][53]and ANSYS FEA software. Left image: Opposing mechanisms ofbeam heating and resistive (Joule) heating of an ARIEL electron targetassembly. Right image: target geometry pictured with 25 kW beam(700 µA of 35 MeV electrons) 1500 ADC target heating, 600 ADCion source heating using UCx thermal conductivity from [33], showinga non-homogeneous temperature profile with large thermal gradientsand highlighting the importance of material thermal conductivity.rameters that enhance radiation view factors are the same material parameters thatenhance diffusion and release of reaction products from target material matrices,namely open porosity and pore connectivity.The following chapters describe a collection of theoretical/analytical, numeri-cal, and experimental approaches to understand thermal behaviour of target mate-rials and develop knowledge of the effects of material morphology on heat trans-fer. Chapter 2 outlines models for keff and their applicability to specific materials.In Chapter 3, a numerical method for the study of ISOL materials is developedand presented. Chapter 4 describes experiments using the single currently exist-ing method to experimentally determine thermal conductivity of ISOL materials,and Chapter 5 describes the development of parallel test infrastructure at TRIUMFthat will add to the capability for badly-needed measurements. Investigating pos-sibilities of enhanced heat transfer by radiation at high temperatures in porous mi-crostructures is of particular interest.20Chapter 2Approaches to calculatingthermal conductivityIt can scarcely be denied that the supreme goal of all theory is tomake the irreducible basic elements as simple and as few as possiblewithout having to surrender the adequate representation of a singledatum of experience. — Albert Einstein (1933)Thermal conductivity (k) describes the ability of a material to conduct heat.The Fourier Law (Equation 2.1) relates the energy current or heat flux (q) to thelocal temperature gradient ∇T using the k of the material.q =−k∇T (2.1)Incident accelerated particles deposit energy to electrons and atoms of the targetmaterial, causing local heating and temperature gradients. The goal for high powerISOL targets is to dissipate more energy while maintaining a low temperature gra-dient, driving by necessity towards materials with high k. Some qualitative ob-servations have been made for ISOL target thermal conductivity, but systematiccharacterization is lacking. This chapter explores some theories for ISOL appli-cations. These theories can help predict effects of high-release microstructures onthermal conductivity and resulting target temperature inhomogeneity.212.1 The building blocks of thermal conductivityHeat transfer results from interactions between principal energy carriers: phonons,electrons, and photons. Energy is carried through solid crystalline materials by lat-tice vibrations, giving a phonon contribution to thermal conductivity (kph). Elec-tron transport through solids adds an electron contribution to thermal conductiv-ity (kel). These processes combine to describe bulk conductivity, the thermal con-ductivity of a solid material with zero porosity (ks). For porous materials, a radia-tion contribution to thermal conductivity (krad) occurs between internal surfaces ofthe pore phase.There is no unified approach to accurately describe all material morphologiesacross all sets of parameters. For insulating materials, such as ceramics, the phononcontribution may dominate the thermal conductivity. For metals such as copper,the electronic contribution often dominates. For either metals or insulators withporous structures, radiation effects through the pores may dominate, especially athigh temperatures. While extremely relevant for ISOL target materials, the radia-tive contribution is often neglected entirely by fundamental material studies whichfocus on low temperatures. Out of the enormous variety of theories, a very limitedselection will be discussed here.2.1.1 Electron and phonon thermal conductivityFor electrons, simple models predict an approximately temperature-independentcontribution to thermal conductivity above room temperatures [68]. Mankad andShi separately predict thermal conductivity of uranium carbide using Density Func-tional Theory (DFT), concluding that UC, UC2 and U2C3 exhibit approximatelytemperature-independent electronic thermal conductivity above room temperature[82][112]. Some DFT results are compared against experimental data in Figure 2.1,further supporting this prediction. For target materials where electronic contribu-tions dominate, constant high-temperature thermal conductivity suggests a limit onpossible power dissipation using solid-phase conductivity alone.For dielectric materials and semiconductors, phonon contributions are oftenmuch larger than electronic contributions to thermal conductivity. To study phononthermal conductivity, information about the lattice is needed.22Figure 2.1: Thermal conductivity of uranium carbide UC with the rock-saltcrystal structure, calculated by Mankad and Jha [82] shown with theblack line, compared with data measured using a laser flash apparatusby Moser and Kruger and published in reference [88]. Reprinted withpermission from [82].Several authors [84][90][104] (Figure 2.3) studied effects of point defects onlattice conductivity of relevant materials, including UO2 (Figure 2.2) and β -SiC(Figure 2.3). These studies investigate impacts of lattice structure, while illustrat-ing the difficulty in using these methods to study bulk materials with many varieddefects. For real materials at high temperatures, where microstructure on largerscales must be explicitly accounted for, it is necessary to zoom out.Together, electronic and phonon contributions describe conduction. Both needto be understood to describe ks of a particular material. In the studies briefly out-lined above, the expected difference between uranium carbides and silicon carbidesdue to principle energy carrier behaviour can be seen. Through theory, mechanismsof thermal transport can provide information on material lattice structure and cap-ture features such as nanopores, voids, vacancies, interstitials, and point defects.The study of ISOL materials must move beyond solid conductivity to consider theexpected contribution of radiation.23Figure 2.2: Thermal conductivity of uranium dioxide UO2 calculated byNichenko and Staicu [90] and shown with symbols, compared withlines and symbols showing a model of effective thermal conductivity.Reprinted with permission from [90].Figure 2.3: Variation of phonon thermal conductivity of β -SiC with respectto temperature, calculated by Samolyuk et al. and compared to experi-mental data, reprinted with permission from [104]242.1.2 Radiation thermal conductivityThe radiative heat transfer mechanism observed by Zhang, Alton and Kawai (Equa-tion 1.4) [129][3] describes heat transfer across pores and makes the considerationof temperature-dependence not only non-negligible, but likely dominant.Planck’s law describes the spectral radiance of an emitting surface per unitwavelength (or frequency) [W sr−1m−3] (dEλ (λ ,θ ,φ ,T )) (Equation 2.2).dEλ ,blackbody(λ ,T ) =4pi2h¯c2λ 5(exp 2pi h¯cλkBT −1)dλ (2.2)The Stefan-Boltzmann law Equation 2.3 is obtained by integrating Equation 2.2over all wavelengths to obtain the electromagnetic energy emitted from a diffusesurface at temperature T .Eblackbody(T ) = σBT 4 (2.3)With the Stefan-Boltzmann constant, 5.67 · 10−8 [W m−2K−4] (σB). For a realsurface, emissivity takes a non-unit value ε (Equation 2.4).dEλ (λ ,θ ,φ ,T ) = ε(λ ,θ ,φ ,T ) ·dEλ ,blackbody(λ ,T ) (2.4)Geometric constants can be introduced as done by Russell to give Equation 2.5for the effective thermal conductivity of a pore due to radiation [101].kpRussell = 4σBFT3∆x (2.5)Where F is a factor accounting for emissivity and geometry of the radiating sur-faces, and ∆x is the distance across the pore in the direction of the heat flow. Modelsof this form are also referred to as Damko¨hler type equations. Various authors pro-pose different forms of F . Russell suggested F could be considered approximately1 [101], but noted there may be some effect of pore permeability—connectivity.Another solution F = γdε was derived by Loeb, with a geometrical or morpho-logical factor (γ) and the largest dimension of the gap parallel to heat flow (d).Loeb provides geometrical factors for some simple pore shapes [81]. Effective25pore conductivity is then described using (Equation 2.6).kpLoeb = 4γdεσBT3 (2.6)To describe real materials at high temperatures using these building-block ap-proaches, one must quantify contributions of energy carriers: electrons, phonons,and photons. Approaches such as DFT, the Boltzmann Transport Equation (BTE)or molecular dynamics (MD) simulations can provide specific properties for a par-ticular lattice and capture effects of distinct features within the solid, such as peri-odic nanopores or lattice defects. These theories provide large pieces of the pictureand give physical meaning to phenomenological behaviours and dominant trends.The overarching question is: how can these pieces of the picture be combinedto describe how heat moves through a complex engineered material in which allthese processes are at play? The ISOL target challenge requires a general answerthat could be readily applied for systematic studies of the effective properties of amuch larger number of atoms arranged in a real, non-periodic microstructure.2.2 Real materials, porosity and heterogeneous mediaMacroscopic heat transfer can be described using the thermal transport processesconduction, convection, and radiation. Each process relates the thermal gradient inthe material to transported energy current, resulting in a sum of heat fluxes fromeach transport process. Effective or observed thermal conductivity keff is then thesum of conduction kcond through the material matrix—and the fluid in the pores, ifpresent— with radiation krad across the pores as illustrated in Figure 2.4. These the-oretical models build effective conductivity through combinations of solid with ksand pore phase with thermal conductivity of a pore (kp). The effective descriptionof theoretical thermal conductivity is most interesting for ISOL target materials,since it provides an avenue to evaluating heat transfer through different microstruc-tures at high temperature while avoiding the precise description of particles, atoms,crystal lattices, and grain boundaries. As discussed in Section 2.1, it is important toremember that ks and kp are the sum effects of principle energy carrier interactionsand as such depend heavily on temperature and material.An extremely brief selection of analytical models for combining ks and kp into26Figure 2.4: Schematic of a porous material showing conduction processesthat occur through the solid phase and radiation occurring across pores.a keff will be reviewed in the proceeding sections, followed by a collection of newapproaches, developments and advancements in analytical heat transfer models andtheir potential applications for ISOL target materials.2.2.1 Analytical models of heat transfer through porous mediaMany analytical models and approximations of heat transfer in porous media areavailable in literature, and have been solved to some degree with good agreementfrom experiment. The approaches vary widely, incorporating different shape pa-rameters, inputs of specific material properties, and each with different basic un-derlying model assumptions.The parallel model (Equation 2.7) and series model (Equation 2.8) considersimple combinations of solid and pore properties, offering simple upper and lowerbounds for the keff of a composite material while considering only P, ks and kp.keffparallel = ks(1−P)+Pkp (2.7)keffseries =kskp(1−P)kp+ ksP (2.8)27Figure 2.5: Four models of heat transfer through two phase (solid and pore)materials. a) Parallel model, b) Series model, c) Combined series-parallel model with β the fraction of series connections, and d) Maxwellmodel for dilute pores.The parallel and series models can be combined (Equation 2.9) using an additionalparameter fraction of series connections (β ) that describes the fraction of seriesconnections over total connections as illustrated in Figure 2.5.keffseries-parallel = (1−β )((1−P)ks+ kpP)+βkskp(1−P)kp+ ksP (2.9)The oldest and simplest analytical model for keff of heterogeneous materialswas proposed in 1904 by Maxwell in his famous work on electricity and magnetism(Equation 2.10) [85].keffMaxwell = ks(1+3P(kp+2kskp−ks )−P) (2.10)Maxwell’s relation is valid only in the limit of very dilute pores, but due to itssimplicity it is widely used in literature. The Maxwell relation was used to correctthermal diffusivity measurements of ISOL UCx to 100% theoretical density in [12],28giving the data plotted in Figure 1.11.Several models are compared to experimental data for packed beds [119], openand closed-pore ceramics [113], and open-cell foams [73], evaluating model per-formance by experimental agreement. For materials nearing or above the percola-tion limit—the pore volume fraction at which keff begins to rapidly increase due toformation of conductive chains—interactions occur between thermal influences ofneighbouring pores and popular classical models break down [94]. Then empiri-cal percolation models [39] or unit cell approaches [127] for specific materials arerecommended.Care is required to match a keff model to an ISOL material of interest. Modelsof packed beds may be more similar to pressed pellets, or slip-cast ceramic wafers.Models of metal and ceramic foams [16] may be more applicable to highly porouscellular ISOL materials like the CBCF and RVCF matrices studied at ORNL byZhang, Alton, Kawai et al. [129], while models of fibres are more applicable tothe nano-fibrous ceramics developed at TRIUMF by Wong [125] and at ISOLDE.Specifically tailored microstructures [37] may not be well described by any of thesemodels. In all cases, model applicability must be carefully considered before use.Additional model parameters can be added or fit to consider specific materials, butalways the addition of empirical parameters comes with loss of generality.In conclusion, this section reviewed a small number of ways to combine known(or modelled) bulk conductivity ks with models for pore phase heat transfer kp toget a keff. Target materials are operated at high temperatures (2000◦C) and vac-uum atmospheres. In these conditions, conduction through the solid structure ofthe target material dominates at low temperatures, and radiation through the poresdominates at high temperatures. In their study of highly porous ISOL target ma-terials, Zhang and Alton also commented that radiation was the only contributionto pore conductivity [129]. Pore connectivity or permeability may enhance radi-ation contributions near a percolation limit, allowing each internal surface of thematerial to exchange heat by larger view factors with farther surfaces through in-terconnected pores. To successfully apply the formulations of keff given in thissection, a radiative description of kp is essential.292.3 Finite element approachesISOL target materials require another approach. This is especially true for high-release engineered materials for which geometric parameters are not available. Nu-merical approaches have proven useful to study thermal transport in porous, realmaterials. They require mathematical models of specific microstructures to solvediscretized thermal transport equations.2.3.1 Material model generationThe material microstructure of interest must be well characterized. Then a repeat-able method of generating a representative model with acceptable similarity to thematerial is necessary.Perhaps the simplest approach is to observe material microstructure using animaging technique such as SEM. 3D modelling software can use simple geome-tries to approximate a qualitatively similar structure. Depending on the relevantcharacterization parameters of the material, results should be analyzed carefully toensure the desired parameters are studied. Alternatively, random seeding, pack-ing and particle growth codes can be used to represent sintered particles [123][65],while Voronoi tessellations can be used for fibrous materials and open-cell foams[123][36]. These can be compared to SEM or micro-computed tomography (µCT)data using parameters such as porosity, specific surface area, mean pore size, andmean connection point (for sintered-particle materials) or mean strut (for fibrous orfoam-like materials) size and shape. A more rigorous approach is to measure themicrostructure using X-Ray computed tomography (CT) and directly use the datato reconstruct a 3D model [47].Local material impurities within the solid, such as grain boundaries and pointdefects, are captured only in the solid’s effective properties. This is extremely ben-eficial for modelling and computational simplicity, and allows access to effectivematerial properties rather than individual energy carriers and scattering mecha-nisms. If information on the material morphology is available, generated compu-tational models can be compared to the desired morphology for validity.Once a mathematical description of the material has been obtained, the modelis “meshed” into a three-dimensional grid of differential elements. Depending on30the complexity of the model, mesh generation can be difficult. Often, mesh den-sity and quality must be carefully balanced with available time and computationalresources. The mesh can then be used for numerical heat transfer analysis.2.3.2 Numerical transport equationsIn FEA and/or Finite Volume Method (FVM) approaches, a thermal conservationequation is solved over the mesh of differential control elements/volumes. TheFEA solver ANSYS uses a radiosity solver method extended to multiple enclo-sures, implementing radiation between surfaces j, i and a specified ambient tem-perature as defined in Equation 2.11 for N enclosures.N∑i=1(δ jiεi−Fji 1− εiεi )QiAi=N∑i=1(δ ji−Fji)σBT 4 (2.11)Surface-to-surface radiation is implemented by a matrix of view factors Fji be-tween surfaces i and j in the computed geometry, where Fji is computed using thehemicube method as in Equation 2.12 [28][105].Fji =1Ai∫Ai∫A jcosθi cosθ jpir2d(Ai)d(A j) (2.12)Equation 2.11 then uses the view factor matrix to determine heat exchange withinthe model. Additionally, the solver incorporates a surface emissivity εi, which canbe specified as a function of temperature for the bulk material.Computational studies help predict operational temperatures that are difficult tomonitor. Beam-heating profiles from SRIM or Monte Carlo particle transport code(FLUKA) are combined with FEA codes [79][86] and validated experimentallywhen possible [20][8]. These fully-coupled heat transfer models allow the studyof pore-scale processes in specific microstructures. Examples in literature suggestthat numerical methods can capture radiation-enhanced thermal conductivity forporous materials [129]. Numerical methods have the potential to reveal impactsof specifically developed high-release microstructures on heat transfer in ISOLmaterials.31Chapter 3Development of a numericalmodel for thermal conductivityComputers are incredibly fast, accurate and stupid; humans areincredibly slow, inaccurate and brilliant; together they are powerfulbeyond imagination. — UnknownA numerical method was developed for evaluating the effective thermal con-ductivity of representative open-porous microstructures. The method uses ANSYSto connect morphological parameters to theory while adding physical meaning tofitting parameters that have already been used to describe thermal transport be-haviour in ISOL materials [3]. The method is described in Section 3.1, and resultsare analyzed in the context of certain theoretical models in Section 3.2.3.1 Constructing the model geometryBeam interactions generate local heating, causing a three-dimensional temperaturegradient that depends heavily on the beam character and target geometry. Theseconditions can be simulated using FEA, but the beam heat deposition is specificto a particular beam and geometry. The simulation cell for this numerical studywas chosen to generalize the problem by reducing it to one-dimensional heat trans-fer. This approach can then apply to any material with an internal or external heatsource. In the example of ISOL targets, this simulation cell represents zooming into32Figure 3.1: ISOL target material with heat flux caused by beam interactions,approximated as one-dimensional (uniaxial) heat flux through a smallcylindrical representative simulation cellthe familiar thermal gradient problem, considering a small section of material ori-ented perpendicular to the temperature gradient between the hot spot of beam heatdeposition and the radiation-cooled target container, regardless of the temperatureprofile. Thermal gradients are three dimensional and geometry dependent, but thesimulation cell is taken to be small enough that the dominant heat flow is axial andone dimensional, simplifying and generalizing the problem. This concept is shownschematically in Figure 3.1 with the familiar heat profile of the ARIEL electrontarget. Here, simulation cells represent small sections of material oriented with thehot side near the off-centre hot spot and the cold side towards the target container,with the cylinder axis along the temperature gradient. The thermal conductivityproblem then becomes one-dimensional, reducing the difficulty and complexity ofthe problem while keeping it specific to the material in question. Using the modelpresented in this section to estimate thermal conductivity of a microstructure givesan avenue to predicting temperatures for any target geometry during operation andevaluating new material developments for their effects on thermal conductivity.33Figure 3.2: Schematic of setup for thermal conductivity simulation shown asa cross-section of a cylinder with material sample diameter D. The ma-terial sample can be varied to test different microstructure representativemodels, while the guard provides a surface-to-surface radiation bound-ary condition along the direction of heat transfer. Schematic not to scale.3.1.1 Simulation geometryThe simulation setup is outlined in Figure 3.2. It features two main bodies: acylindrical outer radiation “guard”, and an internal material “sample”. For open-porous materials, view factors of distant surfaces within the material structure aresignificant and must be represented using boundary conditions. The external guardfunctions as a mean-field approximation along the cylinder axis (x-axis). Elementsin the microstructure with faces that have a significant view-factor to the guard ex-change thermal radiation according to Equation 2.11, so that the guard representsaverage effects of surrounding material beyond the simulation cell. The guardthus enables the calculation of bulk effective one-dimensional thermal conductiv-ity. The adiabatic conditions on outside surfaces of the guard prevent heat loss byradiation to ambient temperatures. In this way, the cylinder simultaneously func-tions as an insulating “radiation guard” while maintaining the temperature gradientalong the x direction for heat exchange as indicated with small arrows in Figure 3.1and Figure 3.2.34Figure 3.3: Simulation cells and representative schematic for 4 models: A)fibres perpendicular to flux with view factors through B) fibres perpen-dicular to flux with no view factors through C) fibres parallel to heatflux D) representative microstructure of target material. Direction ofheat flow is shown with white arrows.A cylindrical geometry was used for the radiation guard so that the edge con-dition would be axisymmetric. Non-axisymmetric material models were then ex-pected to be dependent only on feature orientation relative to the direction of heatflow and independent of feature orientation about the guard axis of symmetry. Thisallows the simplification of the model to one-dimensional heat transfer. A fixedtemperature Th was applied to nodes on the hot side of the guard and of the sample,and a fixed temperature Tc was applied to nodes on the cold side of the guard andsample. ANSYS R© Workbench Academic Release 19.1 was used for the study.Fixed temperatures were changed to collect data points of thermal conductivity asa function of temperature.To test the method, three different representative models of highly porous,anisotropically oriented fibres were considered, and one representative model of areal, random material microstructure was tested for comparison (Figure 3.3). Thecommercial software SolidWorks, Release 2018 was used to create representative35Table 3.1: Four representative microstructure models compared by poros-ity and available distances for continuous conductive and radiative heattransfer parallel to the direction of heat flowModel Description Porosity[%]Maxconductivedistance[%length]d, maxradiativedistance[%length]A, perpendicular cylindrical fibres 66.9 4 100open view factors throughB, perpendicular cylindrical fibres 54.0 4 28closed reduced view factorsC, parallel cylindrical fibres 53.9 100 100parallel to heatD, real representative 55.0 100 30microstructurematerial geometry. Some key parameters regarding effective thermal conductivitywere identified from the various theories described in Chapter 2, and are tabulatedin Table 3.1 for four different material models.One notable parameter identified in pore-radiation theories is the maximumdistance for radiative heat transfer between surfaces in the structure, representedby d. d captures the effect of pore size on the radiative contribution to thermalconductivity. Another parameter is orientation-specific and should represent theexpected effect of microscopic structure in the direction of the temperature gra-dient, which is expected to increase radiative heat transfer. For this analysis, thegeometric factor will be called γ , after the theory of radiative thermal conductivityacross a pore developed by Loeb (Equation 2.6).In cell A, cylindrical fibres are aligned perpendicular to the direction of heatflow. The cylinders are evenly spaced in a square grid to allow view factors fromcylinders at one end to cylinders at the other end. d was taken to be 44 mm as il-lustrated in Figure 3.4. With the highest porosity, cell A is the most “open-porous”model. Open porosity is expected to enhance radiation contributions to heat trans-fer.36Figure 3.4: Simulation cell A, fibres perpendicular to flux with view factorsthrough. Detail B shows significant view factor between internal sur-faces even at long distances d ≈ L.In cell B, fibrous cylinders are aligned perpendicular to the direction of heatflow, but cylinders are staggered to reduce d as compared to cell A. By comparingthe distances for radiation shown as d in Figure 3.4 and Figure 3.5, it can be seenthat in the “closed” geometry B, the view factor for heat transfer at a radiative dis-tance d of 12 mm is already smaller than the view factor for radiative heat transferthrough the entire geometry of the “open” geometry A.In cell C, fibrous cylinders are aligned parallel to the direction of heat flow.Cells C and B have similar porosity. Comparing effective thermal conductivity ofthese two models should give some information on the effect of morphology atthe same porosity. Cells C and A have the same d, meaning that they should havethe same effects of pore dimensionality, but different porosity and morphology.Comparison should help separate the two effects.To generate a model representative of a real ISOL target material microstruc-ture, a simple model was created featuring both parallel and perpendicular faces.MeshLab2016.12 [27] was then used to create randomized open porosity by Voronoivertex sampling [121]. The mesh was processed in ANSYS; the resulting model37Figure 3.5: Simulation cell B, fibres perpendicular to flux with reduced viewfactors through. Detail views B, C, and D show decreasing view angleswith distance.is compared with SEM images of a sintered uranium carbide ISOL target in Fig-ure 3.6. the presence of strut-like and particle-like structures was observed for boththe real material and the model. Both have very low closed porosity. The radiativedistance d for model D was estimated by measuring maximum radiative distancesfor a number of pores as shown in Figure 3.7.The four simulation cells were meshed using ANSYS. The chosen mesh sizefor each geometry was determined using a mesh dependence study. The mesh el-ement size was systematically reduced and simulation results were observed untilthe results became independent of the mesh size. Simulation data was then col-lected using a mesh size that was large enough to minimize computational timewhile ensuring the model was safely in the mesh-independent regime. Details ofthe mesh dependence study are described in Section A.1.The applied simulation boundary conditions were surface-to-surface radiationon all internal surfaces, including the hot and cold elements. Th, Tc and ε werechanged to obtain different data points of effective thermal conductivity as a func-tion of temperature and internal surface emissivity. The heat flow [W] (Q) was38Figure 3.6: Simulation cell D, real material representation. A) SEM image ofsintered uranium carbide ISOL target material taken by M. Cervantes-Smith [25] B) Enlarged sectioned image of cell D, computational modelapproximating a real microstructureFigure 3.7: Simulation cell D, real material representation with radiative dis-tance between pore walls measured for several gaps in the direction par-allel to heat transfer. Dimensions shown in mm.39Figure 3.8: Effective thermal conductivity of microstructure A) open perpen-dicular fibres shown as a percentage of bulk thermal conductivity ks ataverage temperatures of 150◦C and 2946◦C using different measure-ment locations x1 and x2.recorded for each data point. The effective thermal conductivity of different modelmaterials was then quantified by recording keff at each data point using Equa-tion 3.1.keff =Q(T )(x2− x1)AX−sec(T (x1)−T (x2)) (3.1)For each model, temperatures are recorded in 10 positions x. Effective thermalconductivity can then be calculated from the ∆T between the two points x1 and x2.keff for each set of two points is shown for model A in Figure 3.8. Uncertainties arelarger at smaller (x2− x1). keff converges at larger (x2− x1). keff values from small(x2− x1) are also susceptible to a shift in average temperature if x1 and x2 are notsymmetrically chosen around the midpoint between Th and Tc. This scatter can beseen in Figure 3.8. Additionally, the uncertainty is much larger for higher averagetemperatures.From the 10 positions, x1 and x2 are chosen sufficiently far from the fixed40Figure 3.9: Uncertainty in effective thermal conductivity as a function of av-erage temperature for datasets with emissivity 1. All four models fitwith third order polynomials of T avg.temperature nodes to reduce edge effects. Uncertainty in keff was determined byuncertainties in each of the components of Equation 3.1 (Section A.1). Uncertaintyincreases with T as shown in Figure 3.9, suggesting a relation between radiativeheat transfer and simulation uncertainty. This dependence is likely due to limitingthe hemicube resolution in the radiosity solver. This dependence is additionallysupported by the reduction in uncertainties that was observed as hemicube resolu-tion was increased. Lower emissivity datasets have less uncertainty than displayedin Figure 3.9.3.1.2 AssumptionsAmbient temperature was changed to always match the cold nodes Tc so that anyunaccounted-for view factors generated by numerical artefacts would exchangeheat with surroundings at the same Tc. Heat input Qh and output Qc were recordedfor each T avg. The difference was taken as the discretization uncertainty of thesimulation heat value Q resulting from the enclosure radiation balance.It was assumed that the distance between measurement points (x2− x1) was41sufficiently large to give an effective heat transfer (Figure 3.8). For sufficientlylarge distances, the effects of individual features in the material model are assumedto average out. Because of the temperature gradient along the x direction, mea-surement locations x1 and x2 were placed symmetrically about the simulation cellmidpoint. Symmetric placement helped eliminate shift in effective T avg.The mean-field approximation applied in the radial direction by the guard as-sumes that the element Ai in Equation 2.11 views a temperature on the cylinder thatis approximately the same as that of an infinitely repeated model of the structure,so that thermal radiation along the temperature gradient can be replaced by thermalradiation along the guard. Physically, this means that the temperature of each ele-ment along the guard is assumed to be equivalent to the average temperature of thematerial at that point along the thermal gradient. This approximation is more cor-rect for elements in the centre of the model than elements at the edge. To minimizethe impact of the approximation, local temperatures Tx1 and Tx2 were obtained byaveraging a selection of 50 to 100 elements within equally sized volumes along theaxis of the cylindrical simulation cell. Matching average material temperature withthe guard along x is required for the one-dimensional temperature gradient approx-imation, causing this approach to suffer from larger uncertainties at larger Th−Tcas the gradient grows larger in the x direction. Additionally, this imposes a limit onthe form factor for which the method is considered reliable: the cylinder diametermust be large enough that the guard does not occupy a majority of the view fac-tor for the set of elements over which measured temperatures are averaged. Thisassumption imposes mesh size limitations when scaling down the model to studymicro or nano-structures, since any decrease in dimensionality requires a corre-sponding increase in the diameter of the cylindrical cell as the volume decreasesfaster (r2) than the surface area (r). For this reason, mesh dimensions were stud-ied using millimetre scales, with the implicit assumption that the behaviour of keffwould scale with structure size. Because simulation uncertainty grows with the ∆Tbetween the hot and cold side, the size of mesh at which the simulation becamemesh independent was observably affected by the applied thermal gradient. Todecrease uncertainties, a ∆T of 100◦C was maintained throughout the temperaturerange.Simulation uncertainty, specifically uncertainty in the balance between Qin and42Qout, was also observed to depend strongly on the hemicube resolution, though thetemperature values obtained by averaging were unaffected. To decrease uncertain-ties, hemicube resolution was increased to 100 from the ANSYS default of 10. Thisincreases resolution of the view-factor calculation as in Equation 2.12 and lowersdiscretization uncertainty in the radiative heat transfer equations. The increase inhemicube resolution comes with a significant increase in required computationaltime and resources.3.2 Numerical model discussionEffective thermal conductivity for each microstructure was calculated for a set oftemperatures and emissivities. At first glance, the numerical model qualitativelyappears to reproduce the radiative T 3 dependence expected at high temperatures.For all simulations, a constant ks was assumed. For many materials relevant toISOL, ks is expected to stay constant or decrease as temperature increases—thispoint will be revisited at the end of this section.Internal surface emissivity appears to affect rate of increase of keff with respectto temperature, becoming more noticeable at higher temperatures. Comparing keffof the same microstructure with different internal surface emissivities allows sep-aration of emissivity (ε) from microstructure-dependent geometric factors in theradiative conductivity models. Identifying dependence on geometry then deter-mines the impact of scale and morphology on the thermal transport. For eachmaterial, conduction-only simulations were conducted to display impacts of mate-rial structure on keff without radiation contributions. Assuming bulk conductivityks is homogeneous throughout the structure, effective conduction is expected todominate thermal conductivity near and below room temperature. This is observedin the agreement shown by all emissivity datasets for the same microstructure nearroom temperature.A fit of the numerical data was created using the series-parallel model (Equa-tion 2.9), with the Loeb relation for effective conductivity due to radiation (Equa-tion 2.6). When combined, the resulting model is given by Equation 3.2.43Table 3.2: Fraction of series connections and radiative geometric factor ob-tained for four different material microstructure modelsModel β , fraction ofseries connections[%]γ , Loeb geometricfactor[dimensionless]A, perpendicular open 53.83±0.09 0.20±0.04B, perpendicular closed 66.32±0.04 0.22±0.03C, parallel 3.82±0.02 0.64±0.16D, real 20.9±0.2 2.3±0.6kefftheory = (1− β )((1− P)ks + 4γdεσBT 3P) + βks4γdεσBT 3(1−P)4γdεσBT 3+ ksP(3.2)The factor d in the model, the largest dimension of the gap in the directionof heat flow, was taken to be the largest distance between two faces in the mi-crostructure with a non-negligible view-factor as discussed previously in Table 3.1.The radiation geometric factor γ and the fraction of series connections over totalconnections β were obtained for each microstructure by fitting the theory to thenumerical data. Fitted values of γ and β are compared in Table 3.2.The fitted theory is plotted with the numerical data for all four simulation cellsin, Figure 3.10, Figure 3.11, Figure 3.12 and Figure 3.13. The combination ofseries and parallel models with the Loeb theory of radiation across a pore fits thenumerical data within uncertainty and appears to capture the trend with temperaturefor a set of 4 emissivity values. The conduction-only datasets correspond to a fitwith an emissivity ε = 0, which leads to a flat line with no temperature dependence.Again, it should be noted that the data is represented as a percentage of solid-phaseconductivity ks.In Table 3.2, it can be seen that γA and γB agree within uncertainty. This sup-ports the hypothesis that morphology and dimensionality of a material structurecan be separated into the two parameters γ and d. Both structures have cylindri-cal fibres perpendicular to the direction of heat flow. Different packing arrange-ments allow radiative heat transfer through A, while fibres can only radiate to com-44Figure 3.10: Effective thermal conductivity of microstructure A) open per-pendicular fibres shown as a percentage of solid phase thermal con-ductivity ks. Data points calculated from the numerical model, fittingthe series-parallel model with Loeb kp using two parameters β and γ .The conduction only dataset corresponds to heat transfer through thesolid phase only, with radiation boundary conditions disabled.paratively nearby faces in B. These two structures have different keff because ofthe parameter d, which gives a length scale for heat transfer by radiation. Theyhave the same morphology—cylindrical fibres perpendicular to the direction ofheat transfer—and should have the same morphology-dependent parameter γ . Theagreement suggests that effective thermal conductivity has a T 3 dependence on thematerial dimensionality d, and that qualitatively similar microstructures may havethe same γ . The precise determination of the morphological parameter γ for a par-ticular microstructure is still unclear. For the two perpendicular arrangements offibres, γ was determined to be 0.21±0.02.Expectedly, model C showed the smallest β . The low fraction of series con-nections corresponds to the highest keffks at low T . The parallel fibres also resultedin a larger γ (0.64) than the perpendicular arrangements A and B (0.2), indicatinga morphology more beneficial for radiative heat transfer. Since radiation can occur45Figure 3.11: Effective thermal conductivity of microstructure B) closed per-pendicular fibres shown as a percentage of solid phase thermal con-ductivity ks. Data points calculated from the numerical model, fittingthe series-parallel model with Loeb kp using two parameters β and γ .The conduction only dataset corresponds to heat transfer through thesolid phase only, with radiation boundary conditions disabled.from the hot end of a fibre to the cold end of another, this result was also as ex-pected. It was also noticed that the fitted Loeb morphology parameter γC was unex-pectedly different for different values of emissivity as shown in Table 3.3. Lookingat the numerical keff predicted for the model of parallel fibres (Figure 3.12) showsthat this microstructure is not affected by the emissivity of internal surfaces of thestructure. This suggests that for some microstructures, the emissivity-dependenceindicated in the Loeb model may not be accurate. By contrast, β remained the samewithin uncertainty between emissivity datasets. This emissivity-independence wasobserved only for the parallel model, but more study is needed to quantitativelydetermine the limits for the model. As a continuing hypothesis, it could be that forhighly aligned structures with a a small β , in which radiative and conductive heattransfer act mostly in parallel, the effects of internal surface emissivity on effectivethermal conductivity are negligible.46Figure 3.12: Effective thermal conductivity of microstructure C) parallel fi-bres shown as a percentage of solid phase thermal conductivity ks.Temperature and heat flux data were taken from the numerical model.The conduction only dataset corresponds to heat transfer through thesolid phase only, with radiation boundary conditions disabled.Table 3.3: Fraction of series connections β and radiative geometric factor γ asfitting parameters for model C, parallel cylindrical fibres, with the series-parallel and Loeb model of keffEmissivity β , fraction ofseries connections[%±0.07]γ , Loeb geometricfactor[dimensionless]1 3.85 0.2650.75 3.85 0.3510.5 3.85 0.5210.25 3.85 1.0250 (conduction) 3.73 –47Figure 3.13: Effective thermal conductivity of microstructure D) representa-tive real microstructure shown as a percentage of solid phase thermalconductivity ks. Temperature and heat flux data were taken from thenumerical model. The conduction only dataset corresponds to heattransfer through the solid phase only, with radiation boundary condi-tions disabled.Interestingly, model D showed the largest γ , corresponding to the highest keffat high temperatures. This unexpected result suggests that simple models of cylin-drical fibres may in fact underpredict the contributions of radiative heat transfer inporous, random materials. If true, real porous materials may show lower thermalconductivity near room temperature, but exhibit a sudden increase in thermal con-ductivity at high temperatures. There may be potential to enhance heat transfer forthese materials using radiative contributions at high temperatures, which would beextremely relevant for ISOL materials. Since only one model of a representativemicrostructure was successfully studied, the result may also be dependent on somefeature of the generated microstructure. For a conclusive result, further studiesof random microstructures should be undertaken. The four different models canbe compared in Figure 3.14. One observation that can be noted from this studyis the model’s success in capturing the qualitative trend of the effective thermal48Figure 3.14: Effective thermal conductivity of all four models shown as apercentage of solid phase thermal conductivity ks for the emissivity=1data set. Temperature and heat flux data were taken from the numericalmodel. Fitted lines are third order polynomials.conductivity while agreeing within uncertainty with the quantitative values for allmodels except the highly parallel model. The combination of series and paral-lel models with the Loeb model of radiative pore conductivity is able to capturethe behaviour of morphology, porosity, and radiative heat transfer on the effectivethermal conductivity of perpendicular fibres and a representative real microstruc-ture. This agreement further supports the conclusions of Zhang, Alton, and Kawai[3][129] that effective thermal conductivity of porous ISOL materials can be repre-sented by a conductive term proportional to T and a radiative term proportional toT 3. Comparison of the four carefully chosen models goes beyond the fitting equa-tion used in previous work (Equation 1.4) and adds physical meaning to the fittingcoefficients. The connection between these fitting parameters and real microstruc-ture properties such as the pore dimensionality d is invaluable for predictive studiesof new target materials and probes the link between specific material structures and49Figure 3.15: Hypothetical effective thermal conductivity of porous uraniumcarbide for four different pore sizes d (1µm,10µm, 100µm, 500µm)using ks of 100%TD UC [77], emissivity 1. Parameters β = 0.209 andγ = 2.3 are taken from material model D.thermal transport behaviour.The analytical expression allows for prediction of the impacts of parameterssuch as d, giving some insight into material structures that may have better thermaltransport properties. Some values of effective thermal conductivity are calculatedusing the series-parallel model with Loeb radiation, using literature values of thethermal conductivity for ks. A comparison of four different pore sizes is shownfor two different sets of literature data on uranium carbides in Figure 3.15 andFigure 3.16.The behaviour of the numerical model suggests that in some cases, the relationbetween material structure and effective thermal conductivity can be separated intoa morphological parameter and a pore-dimension parameter. To interpret theseresults in the context of improving the high-temperature thermal conductivity ofISOL target materials, the critical efficiencies of diffusion and subsequently isotoperelease should not be forgotten. Diffusion efficiency is inversely proportional toparticle grain size, while effective thermal conductivity appears to decrease withpore size until d reaches the range of 100s of µm (Figure 3.17). To develop a50Figure 3.16: Hypothetical effective thermal conductivity of porous uraniumcarbide for four different pore sizes d (1µm,10µm, 100µm, 500µm)using ks of hyperstoichiometric UCx [29], emissivity 1. Parametersβ = 0.209 and γ = 2.3 are taken from material model D.Figure 3.17: Hypothetical effective thermal conductivity of porous uraniumcarbide at three different temperatures as a function of pore gap di-mension d, using ks of 100%TD UC [77], emissivity 1. Parametersβ = 0.209 and γ = 2.3 are taken from material model D.51microstructure with good thermal properties while keeping small grain size forgood release properties, anisotropic dimensionality may be needed. An interestingmicrostructure to test would be one with very small dimensionality (nanometric)perpendicular to the thermal gradient, and large dimensionality (≈100 µm) parallelto the thermal gradient.This work builds on previous work done in the field to support the conclusionthat numerical modelling can provide a method to evaluate the impact of morphol-ogy on thermal transport. The work here aims to add meaning to observed fittingparameters, correlating trends with real microstructure characteristics. For the firsttime, a predictive component can be added to the iterative process of ISOL targetmaterial design. This model can potentially be used as a tool for systematicallyevaluating different material microstructures, adding direction to high-temperaturematerials research in and beyond ISOL.52Chapter 4A numerical-experimentalmethod to study effective thermalconductivityIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)In the numerical model presented in the previous chapter, it is necessary to havesome computational representation of the sample morphology. This relies on tech-niques such as SEM, µCT, or at the very least knowledge of porosity, connectivity,and tortuosity of the material. In 2013, Manzolaro et al. developed a novel steady-state method for measuring effective thermal conductivity of ISOL target materialsby combining a numerical model with experimental data [83]. This approach led togroundbreaking data of thermal conductivity taken on ISOL target materials [33].As the first of its kind in the ISOL community, this experimental apparatus wasused to study effective thermal conductivity of several samples for this thesis. Ad-ditionally, the experimental method described in this chapter contributed greatlyto further developments in experimental studies of effective thermal conductiv-ity. Chapter 5 describes the development of a new experimental apparatus for thestudy of effective thermal conductivity, built as a continuation from the approachdescribed in this chapter.534.1 Calibration of the numerical-experimental approachThe experimental apparatus located at INFN, Legnaro National Laboratories (il-lustrated in Figure 4.1) features a resistively heated graphite crucible secured onwater-cooled copper electrodes. A disc of sample material 30-40 mm in diameteris mounted concentrically above the graphite crucible, resting on three tantalumpins with minimal thermal contact. The entire assembly is enclosed in a bell-shaped vacuum chamber. The sample is heated by radiation from the hot graphitecrucible below, producing approximately radial thermal gradients with a hot spotat the sample disc centre and lower temperatures at the disc’s outer edge.In this steady-state approach, a series of thermal-electric simulations are con-ducted by applying current to a model of the apparatus, heating the radiating cru-cible to cause temperature gradients in the sample material disc mounted above.Experimental data is taken by recording temperatures on the sample surface at thecentre and at the edge. A series of data points is then used in the simulations to de-termine function of temperature-dependent sample effective thermal conductivitythat causes the numerical model temperatures to best agree with experimental data(Figure 4.2).To calibrate the test apparatus and demonstrate the reliability and reproducibil-ity of the steady state method, this approach was applied to a material with knownthermal conductivity. The numerical method was calibrated using existing data col-lected on a sample of POCO-EDM-AF5 graphite. The POCO-EDM-AF5 graphitepurchased from POCO graphite is an isotropic graphite with grain size less than1 µm. Temperature-dependent thermal conductivity of POCO-EDM-AF5 graphitehas been reported by the manufacturer.Measurements of the temperature at the centre and the edge of the POCO-AF5sample at a set of heating currents were taken by Matteo Sturaro [116]. An infaredpyrometer was used in dual-color mode for contactless temperature measurements.Assuming that the sample is a grey body with wavelength-independent emissivity,prior knowledge of the value of sample emissivity is not required for temperaturemeasurement taken using this dual colour mode. More details about this approachwill be discussed in Section 4.2.keff was approximated by a second-order polynomial function of temperature54Figure 4.1: 3D model of the experimental apparatus and numerical modelconditions developed by Meneghetti, Manzolaro et al. [83]. a) Sectionview of model showing components and applied heating current at thewater-cooled electrodes (clamps). b) Magnified view of sample discsupported on tantalum pins. c) Image of radial temperature distributionacross sample disc above radiating crucible. Image taken with permis-sion from [83].Figure 4.2: a) Image of experimental apparatus with graphite calibrationsample. b) Image of numerical model with nodal temperature displayedon the sample and heating crucible after optimization.55(Equation 4.1). The ANSYS optimization code described in [86] was then used toperform a least-squares optimization of the coefficients C0, C1 and C2.keffSPES =C0−C1T +C2T 2 (4.1)C0, C1 and C2 were given initial values and limits. A full thermal-electric simula-tion was computed using the initial values with Equation 4.1 to describe the nodaltemperature-dependent thermal conductivity of the sample. In the simulation, nu-merical transport equations were solved for Joule heating, surface-to-surface radia-tive heat transfer, and conduction through solids. The resulting temperature on thecentre and periphery of the sample disk was recorded for each current, and com-pared to experimental data at the same heating current to obtain a residual valuefor the set of thermal conductivity constants. ANSYS Parametric Design Lan-guage (APDL) was then used to find the values of C0, C1 and C2 that minimizedthe residuals. The constants are shown as a function of optimization iterationsfor the EDM-AF5 calibration sample in Figure 4.3. The difference between ex-perimental temperatures (indicated using S) and numerical temperatures (indicatedusing N) were evaluated to give a residual variable RQ as defined in Equation 4.2.RQ =N∑i=1(TCSi−TCNi)2+(T PSi−T PNi)2 (4.2)Jumps in the RQ as shown in Figure 4.4 correspond to changes in the constants atthe start of a new optimization loop. In each iteration, the constants converge torepeatable values showing very little variation from the initial input. It was notedthat if initial values were too far from the optimum, the optimization procedurewas unable to converge. To promote convergence, initial values were obtained byfitting the manufacturer data with a second order polynomial and extracting the fitcoefficients.The set of constants that achieved the lowest RQ was then returned as the op-timized thermal conductivity function. For the graphite calibration sample, theoptimized function is shown compared to thermal conductivity data provided bythe manufacturer in Figure 4.5. The RQ value of 1776.70 obtained for the cali-bration was very low for this application of the optimization function [116][103].56Figure 4.3: Values of C0, C1 and C2 constants of the effective thermal con-ductivity function during the iteration process showing repeated con-vergence over 11 optimization loops and 148 total iterations.Figure 4.4: Values of optimization scheme residuals over 148 iterations57Figure 4.5: Optimized thermal conductivity function provided by the numer-ical method with an RQ of 1776.70, compared to thermal conductiv-ity data provided by the material manufacturer for EDM-AF5 gradegraphite from POCO graphiteThe low RQ corresponds to an excellent match of temperatures corresponding toinput heating current as shown in Figure 4.6. The numeric model with the opti-mized function of effective thermal conductivity produces temperatures very closeto those recorded in the experimental apparatus. The combined numerical and ex-perimental method was successfully calibrated using a commercial material samplewith known thermal conductivity.4.2 Using the steady-state high temperature method onSiC target materialsAfter calibration, the method was applied to porous ISOL target materials withunknown effective thermal conductivity. Two types of material were produced:slip-cast SiC discs and pressed SiC pellets. Slip-cast SiC samples were prepared58Figure 4.6: Values of temperature T measured at the centre (C) and edge (P)of the disc indicated by squares and circles respectively. Experimentalvalues (S) shown in red are compared to numerically calculated val-ues (N) using the optimized function for thermal conductivity shown inblue.for this study using the same materials and procedure regularly used for SiC ISOLtargets online at the TRIUMF ISAC facility. This material is routinely used inoperation at ISAC and studying its properties is intended to provide informationabout relevant ISOL material microstructures. Slip-cast samples for this study wereprepared at TRIUMF and shipped to SPES before sintering. β -SiC powder forthe pressed pellets was sent from TRIUMF to SPES, where the pressed samplesfor this study were produced. The pressed SiC pellets prepared and studied forthis thesis were the first pressed SiC pellets developed at the SPES laboratory,which has produced extensive work on the thermal and mechanical properties ofSiC [103][116]. Pressed SiC pellets are one of the first target materials intendedfor use at the facility for production of aluminum isotopes [32]. The properties ofthe pressed samples are representative of potential ISOL materials for the SPEStarget as well as TRIUMF’s ARIEL electron target, neither of which are currentlyenvisioned to use materials produced with the slip-casting method.After production of the silicon carbide samples, thermal conductivity measure-59Figure 4.7: The sintering vacuum furnace shown with labelled components.Left: the hinged heat shield is shown in the open position, allowingaccess to the tantalum heater. The heating current path is indicated inyellow. Centre: the water-cooled vacuum vessel is shown above thecontrols system. Right: the pyrometer is shown aligned with the furnaceviewport. Images from [7].ments were taken at the INFN SPES facility using the steady-state, radial methodfor taking thermal conductivity measurements at high temperatures developed byManzolaro et al. [83].4.2.1 Sample preparationβ -phase SiC from H.C. Starck (grade B-phase hp) was used to prepare both theslip-cast and pressed samples. The production processes for both sample types aredescribed in more detail in Section B.1.The slip-cast samples were prepared starting from the procedure of Dombskyand Hanemaayer [42] for SiC. Binders and plasticizers are added to the carbidepowder to form a slurry, which is then poured on graphite backing foil, dried, andpunched.A sintering routine was developed for the slip-cast samples:60Figure 4.8: Cast sample of β -SiC shown after sintering. A) Cast SiC waferdelaminated from graphite backing foil. B) Cast SiC wafer withoutgraphite backing installed in thermal conductivity test stand.1. Place samples flat into vacuum chamber and place a graphite disc on top ofthe samples (Figure B.3).2. After establishing vacuum, increase the temperature at a rate of 0.5 K/min3. Hold the temperature constant at 1600◦C for 4 hours.4. Cool back down to room temperature at a rate of approximately 5 K/min.Following this procedure, the slip-cast SiC was sintered into a thin, brittle diskthat was easily separable from the graphite layer as shown in Figure 4.8. The slip-cast SiC wafer was then tested for effective thermal conductivity.Pressed samples were manufactured using the same β -SiC powder from H.C.Starck and a solution of 20% phenolic resin in acetone. The powder mixture wasthen cold pressed in atmosphere using 30 Tons for 10 minutes to form solid pelletswith a diameter of 40 mm and thickness slightly over 1 mm. The pressed pelletswere sintered using the same sintering procedure as the cast samples (Figure 4.9).During the development of the sintering procedure, SEM analysis using En-ergy Dispersive X-ray Spectroscopy (EDS) was applied to the samples to study the61Figure 4.9: Pressed sample of β -SiC shown before sintering (left) and aftersintering (right).composition of Si, C, and observe the quantity of oxygen, if present. The peakfor Si was observed at 1.8 keV, and the peak for C was observed at 0.28 keV asshown in Figure 4.10. Theoretically, EDS can measure trace constituents such asoxygen to limits of detection as low as 200 ppm with spectra containing more than10 million counts [59]. Since the sample surfaces were observed without any stan-dardized preparation, and the spectra contain far fewer counts, it is expected thatdetection limits for the EDS analysis of the SiC samples may be as high as 10 wt%[59].Extra or damaged samples were tested using helium pycnometry to determinethe density of the material as reported in Table 4.1. From the helium pycnometrymeasurements, sample density and porosity were determined.4.2.2 Experimental methodTests were conducted using the steady-state method developed for the SPES projectand presented in [83].Samples were marked using pencil to aid in alignment with the crucible, and sothat the pyrometer could be aligned at the sample disc centre. Samples were placed62Figure 4.10: EDS spectra of β -SiC samples after sintering, showing peaks forSi at 1.8 keV and C at 0.28 keV using 10.0 kV accelerating voltage.Trace amounts of oxygen may be present. Left: Pressed β -SiC pelletwith 10 wt. % phenolic resin. Right: Cast β -SiC waferTable 4.1: Measured porosity of SiC samples, using helium pycnometry todetermine density.Sample Density[g/cc]Porosity[%]Slip cast SiC, standard formula 3.555 ± 0.016 45.7 ± 1.8Slip cast SiC, 10x plasticizer quantity 3.558 ± 0.014 37.3 ± 4.0Pressed SiC, 10wt% 3.228 ± 0.004 64.5 ± 1.8on top of the support bars (three tungsten pins shown in Figure 4.1) so that theywere concentric with the crucible. Care was required to avoid breaking the fragilesamples during the installation process. The vacuum chamber lid was lowered overthe apparatus once the sample was in place, taking care not to bump the interiorcomponents and shift the sample position. The chamber was then evacuated usingthe roughing pump.The emissivity was measured using an Ircon Modeline 5 Series 5R sensor two-colour pyrometer as described by Biasetto et al. [13]. The two-colour mode of63the pyrometer is used to measure the relative intensity of emitted radiation in twowavelength bands. The emissivity slope of the pyrometer was set to 1 as recom-mended by the pyrometer manufacturer for grey bodies with no spectral emissivitydependence. The temperature was then calculated using Equation 4.3.T =hckB( 1λ2 − 1λ1 )lnIλ1Iλ2+ lnελ2ελ1+ ln λ1λ2(4.3)Once the temperature has been found in two-colour mode, the control system ofthe pyrometer automatically adjusts to one-colour (monochromatic) mode and theemissivity is adjusted until the temperature matches the temperature from Equa-tion 4.3 measured in two-colour mode. The emissivity value where the two modesagree is then taken to be the emissivity of the sample at that temperature [13]. Formaterials or surfaces with an emissivity slope not equal to one, the assumption ofemissivity slope should be carefully considered.The pyrometer was mounted on top of the vacuum chamber and aligned withthe sample centre using the pencil markings. The ramping program was then ini-tiated and a specified amount of current was applied to the electrodes, passingthrough the graphite crucible. Pyrometer data was collected at the centre. After theprogram had finished ramping down, the pyrometer spot was moved to the edge ofthe sample and the ramping program was repeated, providing pyrometer data onthe same sample, at the same crucible current, but at the edge (periphery) insteadof the centre. The double measurement sequence may have introduced sourcesof systematic error in the relation of the centre temperature to the edge tempera-ture if the experimental set up was changed in any way between centre and edgemeasurements. This could include a change in surface contact resistivity causedby applying one heating and cooling cycle, or changes in the material or surfaceproperties as a result of coating at high temperatures. 10◦C was added to eachtemperature reading to correct for the window offset [75][55].To determine effective thermal conductivity, the data points of current weretaken with the corresponding centre and edge temperatures on the sample. Aquadratic optimization function was defined as previously described, using theform Equation 4.1 where T is the temperature measured in ◦C, and Ci are the co-64efficients of the thermal conductivity function. The emissivity measured by thepyrometer was recorded and used in the numerical data analysis.4.2.3 SPES SiC measurementsSeveral sets of measurements were taken on slip-cast samples produced with theformula described in Section 4.2.1, after they had been sintered and separated fromthe graphite backing foil. For a set of heating currents, the steady state temperaturesof the centre and periphery were matched. The numerical method was then usedto optimize the coefficients C0, C1, and C2 of the effective thermal conductivityas a function of temperature for the cast samples. Using this method, the effectivethermal conductivity of cast SiC is derived up to 1200◦C, and the effective thermalconductivity of pressed SiC is predicted up to 1055◦C.Slip-cast SiCThe samples produced by slip-casting were thin and very fragile after sintering.Several samples were not perfectly flat or uniform in appearance, with differentthickness observed near the edges. After measurements, dark spots were observedon both the upper and lower surfaces. This could be due to a change in composi-tion from the localized heating at the centre during testing. Heating the SiC castmaterial beyond a certain temperature may have caused a change in the materialleading to a corresponding change in material properties. Though it is unknownhow large an effect this may have had on the effective thermal conductivity, it wasobserved as a hysteresis in the emissivity measurements of the surface, shown inFigure 4.11. Additionally, it was noted that the edge and centre measurements atthe same temperature do not agree. It is possible that the samples were too thinto be entirely opaque to the radiation from the crucible. It is also possible thatthe hysteresis is due to systematic uncertainty between the two different heatingand cooling cycles. The surfaces may have been coated or otherwise changed inradiative properties during the preceding measurement cycle.It was observed that the numerically obtained temperatures were consistentlylower than the experimentally measured ones. This could be explained by theaveraging procedure of the pyrometer, where the average temperature within the65Figure 4.11: Emissivity measurements taken at the centre compared to emis-sivity measurements taken at the periphery of a cast β -SiC materialsample. The measurement of centre emissivity was completed im-mediately after the measurement of edge emissivity. Both sets showsome hysteresis; data taken during heating displays some shift fromdata taken during cooling.pyrometer spot is read and recorded, compared to the numerical temperature whichis a nodal temperature at one point in the material. Since the pyrometer spot on thesample is circular with a diameter of 4 mm, it is likely that the average over thespot is different than the predicted nodal temperature.Emissivity measurements taken on the cast SiC samples showed unusual be-haviour. From Figure 4.11 and Figure 4.12 it can be seen that emissivity measure-ments follow a pattern, with one higher data point followed by several lower ones.This could be due to thermal stabilization during the temperature measurement, asthe sample may have been heating or cooling at the beginning of the temperaturestep. Alternatively, the jump could be due to the switch in pyrometer operationbetween two-colour and single-colour mode. Emissivity values at the edge wereobserved to correspond with the heating current applied to the crucible, while theemissivity values at the centre remained temperature-independent in the range ofscatter. Cast samples may not have been thick enough to be entirely opaque to66Figure 4.12: Emissivity measurements taken at the edge (periphery) of a castβ -SiC material sample on different days. After the first dataset wastaken, a full heating and cooling cycle was completed before the sec-ond data set was taken. A difference in emissivity data can be seen.Both sets show some hysteresis between heating and cooling cycles.Figure 4.13: Optimized thermal conductivity function provided by the nu-merical method with an RQ of 152890. The optimized valuesof the coefficients for cast β -SiC are C0=31.196, C1=0.0010594,C2=1.8731×10−667Figure 4.14: Values of temperature T of cast β -SiC measured at the centre(C) and edge (P) of the sample disc indicated by squares and circlesrespectively. Experimental values (S) shown in red are compared tonumerically calculated temperature (N) using the optimized functionfor thermal conductivity shown in blue.the light emitted from the crucible. This could have caused the pyrometer directedat the sample to register additional light, throwing off the measurements for theemissivity, particularly at the centre. The temperature-dependent emissivity wasnot observed at the centre. It was assumed that the measurement of emissivityobtained from the centre of the sample is more representative of the surface emis-sivity than the measurements obtained from the edge. Alternatively, the observeddifference in emissivity may be due to the formation of an oxide layer on the hotterparts of the sample surface, causing the dark spot at the centre to truly exhibit adifferent surface emissivity.Measurements were taken on the cast SiC samples and analyzed using the op-timization procedure. Difficulty in convergence of the numerical model was at-tributed to additional vibration of the test stand caused by the positioning of thescroll pump. Additional vibration may have caused the thin sample discs to shiftduring the experiment. Dark spots observed on the surface of the discs after testingwere not centred, suggesting that the sample discs did not remain concentric with68Figure 4.15: Images of a cast β -SiC sample after thermal conductivity mea-surements. A) Dark spot observed off-centre on the side facing awayfrom the crucible (top) B) Discoloration on the side facing the crucible(bottom), showing concentric pattern.the crucible during testing. The dark spots further support the possibility of anoxide layer forming during the experiment, giving the disc a different emissivity inthe centre compared to the edge region. This could explain the observed hysteresisand discrepancy between emissivity measurements and the centre and edge. Use ofthe centre-measured emissivity in the numerical optimization procedure could be acontributing factor to the large RQ and the difference in experimental temperaturesfrom the numerically predicted ones.Cold-pressed SiCThe same procedure was carried out for the pressed SiC samples. Like the castsamples, the pressed samples gave a difference between the edge emissivity andthe centre emissivity measurements. Data from the centre more closely agreedwith literature data, shown in Figure 4.16. Since data at the centre more closelyagreed with expected values from literature and remained approximately constantover the temperature range, the centre emissivity was used in the numerical model.The pyrometer measures emissivity at 1000 nm, near the 905 nm of the literature69Figure 4.16: Emissivity measurements taken at the centre compared to emis-sivity measurements taken at the periphery of a pressed β -SiC pellet.Data published for the emittance of β -SiC at a wavelength of 905 nmis plotted for comparison [21].data, further supporting the conclusion that the centre emissivity measurements aremore reliable. As with the cast samples, the formation of a surface oxide layeris possible and may cause the sample to exhibit different surface emissivity at theedge regions compared to the higher temperature centre region. Since the sur-face emissivity used in the numerical model is used to calculate the heat transferthrough each element, it is possible that the model was not able to replicate exper-imental temperatures without considering the differing surface emissivities acrossthe sample. This may be one factor contributing to the RQ value and resultingin a mismatch between numeric and experimental temperatures. The pattern inemissivity measurements where a higher data point was followed by several lowervalues was observed again. As with the cast samples, this could be attributed tothermal stabilization or switching of pyrometer operation mode.The numerical optimization method converged after several iterations, produc-ing the optimized function displayed in Figure 4.17. Since temperature measure-ments were only taken up to 1055◦C, the effective thermal conductivity predictedby the optimized function is likely valid only in the range of temperatures from70Figure 4.17: Optimized thermal conductivity function provided by the nu-merical method with an RQ of 46685. The optimized values of the co-efficients for pressed β -SiC are C0=29.3, C1=0.025598, C2=0.000001room temperature to 1055◦C.4.3 ConclusionsCast and pressed β -SiC target materials were investigated using the high-temperaturesteady-state method developed by Manzolaro et al. [83] to determine their effec-tive thermal conductivity. A numerical method developed using ANSYS was usedto optimize the coefficients of a second order polynomial of temperature to obtaina prediction for thermal conductivity in the temperature range from room temper-ature to 1200◦C for cast SiC and room temperature to 1055◦C for pressed SiC.The numerical method was able to converge with an RQ of 46685 with thepressed pellets, compared to a much higher RQ of 152890 for the slip-cast discs.For future investigations, slip-cast samples should be made thicker to increaseopacity. Another point of interest would be to measure the effective thermal con-ductivity of slip-cast samples bonded to graphite foil to quantify the effects of thegraphite foil on thermal transport. This may require further development of the sin-tering procedure to ensure that the graphite foil and slip-cast ceramic layer remain71Figure 4.18: Values of temperature T of pressed β -SiC measured at the cen-tre (C) and periphery (P) of the sample disc indicated by squares andcircles respectively. Experimental values (S) shown in red are com-pared to numerically calculated temperature (N) using the optimizedfunction for thermal conductivity shown in blue.acceptably bonded. The larger thickness (approximately 1.5 mm) of the pressedpellets compared to the cast discs likely made pressed samples more opaque toradiation from the crucible. Additionally, pressed pellets had more uniform thick-ness, more symmetric diameter, and flatter surfaces than the delaminated cast ma-terials. Due to their larger mass, the pressed samples were also possibly morerobust against vibrations of the stand. Pressed pellets showed a tendency to frac-ture when large thermal gradients were applied radially. Stress-induced failures ofthe pressed samples prevented data collection at higher temperatures, giving an up-per limit to the experimentally determinable effective thermal conductivity for thepressed samples. For future work, more samples of both types should be preparedand tested to reduce the influence of individual sample characteristics such as inter-nal voids or cracks, which may cause differences in effective thermal conductivitybetween samples.The high temperature steady-state method using a radiating crucible has bro-ken ground towards understanding thermal transport through target materials. The72geometry, numerical modelling, and optimization routine impose some constraints,but are able to relate experimental observables to the desired material properties.The geometry provides approximately radial thermal gradients similar to the tem-perature distribution expected for an impinging axial proton beam. The numeri-cal optimization routine requires a set of temperature measurements at the centreand at the periphery, but at present only one temperature may be recorded at atime. To successfully complete both sets of measurements, thermal stresses mustbe kept low enough that the sample does not break during one measurement withoutcompleting the other. The induced thermal failures provide invaluable informationfor the structural integrity of target materials [103], but limit achievable measure-ment temperatures for thermal conductivity to below the failure point. Some of thepressed β -SiC samples failed near 800◦C, preventing higher-temperature measure-ments. Future plans to implement a scanning pyrometer will enable temperatureof the centre and edge to be measured during the same thermal cycle, reducingthe potential for hysteresis caused by the intermediate thermal cycle. This upgradewould enable the method to successfully take data until the point of sample struc-tural failure. Alternatively, using two pyrometers at the same time would enablethese measurements. Unfortunately, this option would require a design change ofthe apparatus. The geometry of the method described in this section provides use-ful information on mechanical performance of materials, but limits evaluation ofthe thermal properties. The second consideration for the method is that the numer-ical modelling of the thermal-electric problem is closely tied to the experimentalresults. The model assumes that the radiating surfaces are diffuse—without anyangular dependence—and grey—without any wavelength dependence. Publishedresults reporting the spectral emissivity of β -SiC suggest that there is a wavelength-dependence of the emissivity [21]. The assumption of a grey body radiating spec-trum and the use of a constant emissivity slope of 1 in the calculation of the sam-ple temperature may need to be reconsidered for the samples investigated in thisthesis. As such, it should be understood that the effective thermal conductivitiesreported in this chapter are based on these assumptions. Despite concerns for theslip-cast and pressed samples, the method has successfully replicated manufac-turer data for materials for which thermal conductivity and emissivity informationis available, such as the EDM-AF5 graphite. The third consideration is that the73optimization procedure requires an initial guess for the coefficients C0, C1 and C2of the thermal conductivity function. The use of a second order polynomial toapproximate the thermal conductivity may become less accurate for porous ma-terials, for which a T 3 dependence is expected as discussed in Chapter 3 and asobserved experimentally by Zhang, Alton, and Kawai [129][3]. Though the opti-mization routine was attempted using a more phenomenological polynomial of theform keff =C0−C1T +C2T 3, no difference was seen in the fit coefficients. Addi-tionally, the method appears to experience difficulties in convergence if the initialvalues are not close enough to an acceptable minimum. For materials where thethermal conductivity is known or given, the model performed exceedingly well, asdisplayed in Figure 4.5. For the slip-cast and pressed SiC materials, it was very dif-ficult to determine with confidence that no other combination of coefficients couldprovide a better optimized function, making it difficult to quantify uncertainty inthe optimized coefficients produced by ANSYS. This could again be due in partto the limited time in which it was possible to conduct experiments. To conclu-sively determine the coefficients and uncertainty of the optimization function foreither material, more data is absolutely required. Taking these three considerationsof method geometry, numerical model-dependence, and optimization function re-strictions into account, the experimental-numerical method described in this chap-ter was calibrated using a commercial graphite sample, then used to measure theeffective thermal conductivity of slip-cast and pressed-powder SiC target materi-als. For the first time, a prediction of effective thermal conductivity of these ISOLmaterials is available.The steady-state high temperature method used in this chapter is the pioneeringadvancement towards experimental understanding of effective thermal conductiv-ity for ISOL targets. This method, and the research of the SPES team at INFN,achieved the first step and provided a base of technical knowledge, setting an ex-perimental foundation on which to base future studies. The identification of limi-tations due to geometry, numerical model-dependence, and optimization functionrestrictions shows conclusively the need for a new approach. The work discussedin this chapter thus inspired the work discussed next in Chapter 5, developed forthis thesis and intended to further pursue systematic studies of the effect of ISOLtarget material structure and composition on the effective thermal conductivity.74Chapter 5Development of an experimentalapparatus for thermalconductivity investigationsThe true method of knowledge is experiment. — William Blake(1788)Experimental data is indispensable for studying thermal conductivity whilecapturing various real effects from the material production process. Engineeredtarget materials are too complex to hope for accurate quantitative property predic-tions, but a combined approach allows modelling to provide direction for experi-mental studies. Some experimental uranium carbide values from literature were re-viewed by Lewis and Kerrisk [77] and discussed in Chapter 1, highlighting impactsof composition and density on effective thermal conductivity. The preferred exper-imental values are shown in Figure 1.10. For a target material of interest, experi-ments can incorporate effects from many contributing factors that are not capturedin numerical models. This chapter takes another step away from reliance on numer-ical models, branching off from the pioneering work of Manzolaro, Meneghetti etal. towards the necessary acquisition of model-independent experimental data. Asthe next extension of the numerical-experimental work, a new experimental appa-ratus was conceptualized, designed, procured, installed and assembled at TRIUMF.75The new test apparatus was named the Chamber for Heating Investigations (CHI).This chapter describes the creation of the CHI, beginning from conceptual designand ending with operation.5.1 CHIIn conjunction with the research conducted at SPES, test infrastructure was de-signed, components were procured or manufactured, assembled and installed atTRIUMF. The purpose of the CHI is to facilitate target material characterizationand to provide dedicated infrastructure for offline systematic studies of two criti-cal target material properties: effective thermal conductivity and isotope release.CHI is intended to experimentally measure effective thermal conductivity, movingbeyond theoretical and numerical model-dependent work presented in the previ-ous chapters. Additionally, the CHI is intended to provide information about themovement of isotopes through a target material. To quantify isotope release, thesample must first be irradiated to create radioactive isotopes. Isotopes of interestare identified and quantified using gamma-ray spectroscopy. Two samples will beirradiated and assessed through gamma spectroscopy. One will be heated usingCHI while the other serves as a reference for changes of background due to themany different half-lives involved. The objective of CHI release study capabil-ity is to quickly heat and keep the irradiated sample at a uniform temperature invacuum for a specified amount of time. The heated sample is then removed andthe specific activity of the isotope of interest is measured again to determine theamount released from the material matrix during heating. By modelling release asthe combined effects of diffusion, effusion through voids, and radioactive decay ofthe species of interest, analysing specific activity over time gives information ondiffusion and effusion characteristics for a specific target material. Fitting param-eters can then extract physically meaningful information by comparison to theseanalytical models and/or simulations such as those done by Egoriti et al. [49] us-ing the Monte Carlo code MolFlow+, or by Garcia using the nuclear transport codeGEANT 4 [56].With the two objectives of studying thermal conductivity and release proper-ties of target materials in mind, the high-level system requirements for CHI were76identified as follows:1. Quantitative thermal conductivity measurements of as-manufactured targetmaterials must be possible. To obtain measurements as a function of temper-ature, temperature measurements of the sample material are required.2. Quantitative isotope release measurements must be possible.3. Possible test conditions must include the offline equivalent of target materialoperating conditions. A vacuum atmosphere is required. Sample tempera-tures in excess of 2000◦C must be possible, giving measurement capabilitiesfrom room temperature to 2200◦C.4. Test infrastructure must accommodate experiments on existing or foreseentarget materials, including reactive materials, actinides, and radioactive irra-diated material samples.5. The system must be operational in the year 2020.6. The system cost must remain below the budget of $60 000.7. The system should minimize reliance on numerical modelling.The design of CHI was then driven by the need to meet these high-level re-quirements. CHI was thus designed to host two configurations: one for studyingthermal conductivity satisfying requirement 1, and the other for investigating iso-tope release properties satisfying requirement 2. To satisfy requirements 3 and 4,both configurations were designed using a vacuum chamber with the capability toheat material samples to at least 2000◦C, and capable of accepting removable sam-ples of target material following the geometry of TRIUMF-ISAC as-made targetmaterials. An exchange system for reactive and/or radioactive actinide or irradi-ated samples was developed to satisfy requirement 4. The following sections willdescribe the work done to develop the thermal conductivity configuration as partof this thesis. The work done in parallel to develop the release configuration is partof the thesis work of L. Egoriti.775.1.1 Conceptual designThere is an impressive variety of existing approaches to measuring thermal con-ductivity. Many methods were evaluated for their ability to meet the high levelrequirements for CHI (Section 5.1). Several steady state methods [54] [72] (Chap-ter 4) were considered, as well as transient measurements such as the laser flash[92] and modulated electron beam [23][29][89][124]. Transient measurements pre-dominantly provide information on the thermal diffusivity (α) Equation 5.1.keff = αcpρ (5.1)From α , the density of the material (ρ) and the heat capacity of the material [Jkg−1K−1] (cp) of the material can be used to determine the keff by Equation 5.1.The conceptual design process is described in further detail in Section C.1 andSection C.2. From these concepts, the electron bombardment design was chosen.In comparison to the other concepts for CHI, the electron bombardment apparatuspresented significant benefits:• The same apparatus could be used for multiple methods (radial/axial, steady/-transient) and could use the benchmarks provided by the SPES method dis-cussed in Chapter 4.• The geometry allows for small, thin discs of as-made target material. Itaccepts a low sample mass, which decreases the amount of activity in thecase of radioactive or irradiated samples.• Measurements should take very little time once the sample is installed. Themeasurement time will depend primarily on the thermal mass of the system,thermal stabilization time and how quickly the system can reach the desiredmeasurement temperature.• For sample exchange, the sample holder can be designed for separate re-moval while leaving the electron source installed. This will likely help re-duce systematic differences between measurements and facilitate removal ofreactive or radioactive samples.78• Contactless measurements are possible. This reduces measurement uncer-tainty compared to contact-based methods such as thermocouples, whichmay undergo reactions with reactive or radioactive samples at high tempera-tures and alter the resulting temperature measurement.The conceptual design of the CHI thermal conductivity configuration features aheated filament and a sample holder. The heating induces thermionic emission, bywhich electrons are emitted from the hot surface of the filament. An accelerationvoltage then accelerates electrons from the filament across a potential to bombardthe sample surface. The accelerated electrons are stopped in the material sample,depositing their energy through interactions with the electrons and nuclei of thesample material. Effective thermal conductivity keff of the sample can then be cal-culated from the temperature difference between the front and back surfaces ofthe sample disc. Electrostatic optics such as lenses or accelerating grids can be in-stalled between the filament and the sample to focus the electrons into a small beamthat impacts a defined spot of a thin cylindrical sample, or to alternatively defocusthe electrons into an approximately uniform heat load over the entire sample face.This flexibility in the electron bombardment concept allows axial or radial heatinggeometry. The accelerating voltage can be modulated to provide a transient mea-surement method in which the phase lag of the temperature response on the otherside of the sample can be used to determine the thermal diffusivity. Alternatively, asteady state method can be employed with the same apparatus by heating a samplewith electron bombardment and measuring the temperature difference between thetwo sides. The electron bombardment radiator design was the cheapest and mostflexible option that satisfied the high-level requirements for the thermal conductiv-ity configuration. A schematic of the concepts is sketched in Figure 5.1.Electron beams have been used in several studies to calculate thermal diffusiv-ity of materials that are relevant for ISOL target developments. HypostoichiometricUO2 [111] as well as uranium carbide [29][124] were studied using a modulatedelectron beam technique. The technique allows for measurements to be taken upto 2000◦C [89]. Documented use of the method in similar conditions helpfullyprovides a precedent and existing design considerations. The design concept isshown in Figure 5.2. Some parameters considered in the conceptual design include79Figure 5.1: Conceptual design of the CHI, showing the vacuum system onthe left and the two configurations of the experimental setup on theright. Top right: configuration of the CHI for thermal conductivity ex-periments. Bottom right: configuration of the CHI for isotope releaseexperiments.the sample preparation, test calibration, installation, testing and analysis proce-dures. In addition to the pros, several cons of the electron bombardment methodwere identified. Use of an accelerating voltage requires design of a high voltagesystem, which comes with additional cost, time, and safety considerations. Themethod requires development of a controls system for the beam modulator and fil-ament heater. While manual control may be acceptable for commissioning and firstmeasurements, a systematic control scheme is eventually required. Transient mea-surements require a temperature sensor with response time < 2% of 0.5 rise time,which may depend on the sample thickness, thermal conductivity and emissivity.Pyrometer use requires knowledge of the sample emissivity. If the sample cannotbe coated with a known emissivity coating, a separate calibration or measurementof emissivity and emissivity slope may be required for confidence in pyrometermeasurements. These downsides to the method had some impact on the detaileddesign, which will be discussed further in the following section.80Figure 5.2: Schematic for the electron beam concept for measuring thermalconductivity showing a top-down view of the vacuum chamber on theright, and an inset of the instrumentation contained on the sample flangefor thermal conductivity measurements.5.1.2 Detailed designAfter refinement of the conceptual design, a Computer Aided Design (CAD) modelwas developed and detailed analysis was performed to inform specific design pa-rameters, using thermal and electric FEA for component temperatures.The design of the CHI vacuum chamber features a stainless steel six-way crosswith a 12” central spherical chamber. The top port of the six-way cross is equippedwith a turbomolecular pump and designed to include a gate valve. The bottom portis designed with an overpressure valve and a vacuum line to a scroll pump. Thecentral chamber provides the vacuum atmosphere for measurements. Two of thefour horizontal ports are used as viewports, and another for a “cluster” flange host-ing two 2-3/4” viewports and two thermocouple feedthroughs. The combination ofviewports and thermocouple feedthroughs was chosen to maximize flexibility withtemperature measurements, providing optical access for pyrometers and electricalaccess for thermocouples. To prevent coating the viewports by off-gassing sam-ples, manual shutters were added to each viewport. The fourth horizontal flange— the sample flange — hosts the sample, sample heater, cooling, and in-vacuum81Figure 5.3: CAD model of CHI, with flange functions indicated and insetshowing the electron bombardment apparatus for thermal conductivitymeasurements (upper left) and the heater apparatus for release measure-ments (lower left), exchangeable instrumentation configurations that aremounted on a sample flange with a sliding exchange system.test apparatus. The chamber is mounted to the table via a steel flange designed tosupport the assembly weight and withstand the failure scenario of the turbo pumpcrashing.The two configurations conceptualized in Figure 5.1 were made interchange-able by designing a separate sample flange to host all instrumentation specific to thedifferent configurations. Both sample flanges are based on 8” conflat (CF) stain-less steel vacuum flanges. The thermal conductivity sample flange has three 2-3/4”CF ports, which are used for services to pass from air into the vacuum chamber.One feedthrough carries two copper electrodes for the DC heating current. Onefeedthrough carries three SHV 5kV (Safe High Voltage 5 kV) plugs to apply ac-celerating voltage. The third has two pipes with VCR connectors for the inlet andoutlet of the cooling water. A rendering of the concept is given in Figure 5.3. Therelease sample flange has two 2-3/4” CF ports, and each one has a single insulatedcopper pipe that carries cooling water and DC heating current. The release appara-tus can be substituted for the electron bombardment apparatus by exchanging the82Figure 5.4: CAD model of CHI shown as a section view, with red arrowsindicating pyrometer access and white arrow indicating sample flangeexchange direction. The instrumentation for each configuration ismounted onto the sample flange and can thus be exchanged to performeither thermal conductivity or release investigations.sample flange. A rendering of the exchangeable concepts is given in Figure 5.3.The design of the thermal conductivity sample flange will be discussed in the fol-lowing sections.Support and cooling designThe support and cooling system of the CHI is required to define the positions ofthe sample with respect to the electron source and any beam optics. The com-ponents must avoid exceeding operating temperatures (0.4 of the material meltingtemperature was used as a rule-of-thumb maximum operating temperature to pre-vent creep) and capture extra radiated heat into cooling water rather than the steelvacuum chamber walls. Additionally, the support and cooling system — and allservices for the apparatus — are required to be supported from the single 8” CFsample flange. The design must facilitate removal from the vacuum chamber inorder to service the components and to enable timely exchange of sample materi-83Figure 5.5: CAD model of support and cooling assembly for thermal conduc-tivity tests configuration of CHI. Labels indicate planned positions forinstrumentation including a modulating grid and lens in addition to theheated cathode and sample holder. Large white arrow shows directionof assembly extraction from the vacuum chamber.als without the need for excessive disassembly. To allow removal through the 8”flange of the vacuum chamber for transformation into the second configuration ofthe test stand, components should be lightweight and fit through the 6” internaldiameter of the flange tube.To support the assembly and fix the distance to each feedthrough from the sam-ple flange without adding excessive weight, three aluminum rods with feet weredesigned to be bolted into the vacuum-side of the flange. A slotted plate was de-signed to support the instrumentation as shown in Figure 5.5. To prevent radiativeheating of the vacuum vessel, a water-cooled copper heat shield was added. Boltingthe heat shield to the support plate cools the support plate by conduction. At first,a catch tray was designed to contain pieces of fragile samples. When the water-cooled heat shield was designed, the catch tray concept was replaced by the bottomof the copper shield. The electron bombardment instrumentation is mounted usingthe support plate. Copper electrodes hold the resistively heated cathode, electron84Figure 5.6: CAD model of support and cooling assembly for thermal conduc-tivity tests configuration of CHI. The design of a separate heat shieldand support plate is shown, in addition to a sample holder with sixclamping tabs instead of four.optics, and the sample holder. Commercial insulating washers provide some con-ductive cooling without providing electrical contact. Slots in the copper supportplate allow distances between the sample holder, cathode and optics to be flexiblyadjusted. The sample holder uses two tantalum pieces to sandwich a disc of targetmaterial. Small tabs on the sample holder are used to minimize thermal contactpoints. The first sample holder design featured four tabs (Figure 5.5) and usedonly compression and friction to hold the material sample. The second sampleholder design features a thicker rim and three clamping bolts, with six contact tabsFigure 5.6. More details of design iterations are outlined in Section C.3.1.Cathode designThe resistively heated cathode provides thermal radiative heating and a well-definedprofile of electrons. The cathode is designed to be resistively heated to above2000◦C with minimal deflection. To satisfy these requirements, tantalum was cho-sen as the cathode material. With a melting temperature around 3000◦C, tantalum85is a refractory metal capable of Joule heating and withstanding the required tem-peratures. Additionally, tantalum has a work function (φW ) of 4.22 eV. Thus, it willmore readily emit electrons than other refractory materials such as carbon [38].The maximum electron current I0 from the cathode was estimated by Child’sLaw [26] for the emission of charged particles from a source anode with radius rainto an acceleration gap d with extraction voltage V0 and permittivity of vacuum(ε0):I0 =4ε09√2qmepir2ad2V 3/20 (5.2)To consider the thermal emission of electrons from the cathode surface, theRichardson-Dushman equation (Equation 5.3) was used [100][48].J =4pimeqh3(kBT )2 exp−φW ∗kBT (5.3)Where φW∗ is φW corrected for the Schottky effect caused by an electric field E atthe surface as in Equation 5.4 [106].φW∗= φW −√eE4piε0(5.4)The Child’s law estimate was then compared to the amount of electrons availablefor extraction from the cathode to determine which of the two effects would limitthe available electron current for the electron bombardment heater. Figure 5.7 sug-gests that with an accelerating voltage of 5 kV and a temperature range below 2600K, the Child’s law estimation remained at least one order of magnitude larger thanthe Richardson-Dushman estimation. It was therefore assumed that the electroncurrent at CHI is likely to be limited by the cathode temperature, not the accel-erating voltage. To maximize the electron heating effects, the tantalum cathodeshould be operated above the rule-of-thumb 0.4 melting temperature, up to a max-imum suggested temperature of 0.75 melting temperature (/2400 K). Near 2400K, Equation 5.3 predicts an electron current of approximately 0.6 A. It was thusassumed that the electron bombardment current with a tantalum cathode at CHIwould reach at maximum 600 mA. It should be noted that the prediction depends86Figure 5.7: Prediction of extracted electrons at CHI using Child’s law foran accelerating voltage of 5 kV compared with prediction of thermallyemitted electrons using the Richardson-Dushman equation.on the distance between the cathode and the anode, as well as the surface area ofthe anode and the emitting hot surface area of the cathode. Here, the distance wastaken to be 5 mm, the anode radius was taken to be 9.5 mm, and the cathode radiuswas taken to be 5 mm.Several designs were investigated for the cathode, using ANSYS thermal sim-ulations to inform the development of prototype designs. Only the designs thatwere developed into prototypes are discussed here (concepts can be found in Sec-tion C.3.1).The design of cathode 1 was intended for low-current (/ 50 A) operation. Aswirl profile was prototyped using a waterjet cutter, with a slightly larger cross-sectional area at the centre to avoid thermal deflection and prevent contact be-tween the sample and cathode at short extraction distances (Figure 5.8). A METISM311 two-colour pyrometer [110] was used to record cathode temperatures duringheating, using emissivity slopes calibrated for tantalum using metals with knownmelting temperatures (vanadium at 1910◦C, platinum-iridium alloy at 1800◦C, andsilver at 962◦C) to obtain emissivity slopes of 1.05 at 1000◦C, 0.91 at 1800◦C, and0.93 at 2000◦C for tantalum [46]. With applied accelerating voltage, unpredictable87Figure 5.8: First prototype for the thermal conductivity tests configuration ofCHI, shown on the left with the cathode, sample holder, and interme-diate electron grid. Shown on the right with the copper heat shield,mounted on the sample flange with no electron optics or sample in-stalled.sparks from the sample were observed (Figure 5.9). Sparking behaviour identi-fied machine protection concerns for the heater power supply. A grounding cablewas thus connected from the negative output terminal of the DC heating powersupply directly to building ground to protect power supply internal componentsagainst sparks. Measurements of grounding cable current confirmed that if anyof the power supply output was directed through the grounding cable, the amountwas negligible. Instability of the current power supply output was observed at lowcurrents (less than 5% of the maximum rated output). The cold spot observed inthe centre of prototype 1 was likely due to the larger cross-section added to preventdeflection.Cathode 2 was designed as a flat sheet with a narrower section at the centre.ANSYS thermal-electric simulations suggested this design had the potential to heatthe sample beyond required measurement temperature (2200◦C) if maximum avail-able current (500 A) was used (Figure 5.11). The larger cross-section compared to88Figure 5.9: Three images captured of high voltage sparks seen during com-missioning of the first prototype for the thermal conductivity tests con-figuration of CHI.Figure 5.10: Image of the cathode, being heated with 20 A of current duringcommissioning of the first prototype for the thermal conductivity testsconfiguration of CHI. Pyrometer readings taken using an emissivityslope of 1.00 [46] report peak temperatures of 950 ◦C in the hot regionsof the cathode.89Figure 5.11: Temperature results using ANSYS to simulate 500 A of resistiveheating current for a flat-foil cathode design with an assumed electronheat load of maximum 600 W on the sample surface. As a conserva-tive estimate of maximum electrode and insulator temperatures, onlyradiative cooling to ambient temperature was assumed.cathode 1 allows the power supply to operate at or above 50 A, reducing currentinstability. To reduce the possibility of sparks from the voltage wire, an Accuglasscoaxial cable rated for 30 kV was stripped of the external Kapton layer and theground sheath, leaving the internal conductor and a layer of electrical insulation.The wire was then connected between the SHV feedthrough and the sample holderelectrode. Two versions of the new design were produced using 0.001” thick tan-talum foil, shown in Figure 5.12.Commissioning of the system with cathode 2 identified quick thermal responseof the cathode temperature to changes in applied heating current as shown in Fig-ure 5.14. Monitoring internal components identified insufficient thermal contactbetween the insulating washers and the copper plate, causing steady-state tempera-tures on the copper electrodes to be quite high (250◦C at 50 A of heater current) asshown in Figure 5.15. The thermal response of the heating components is slower90Figure 5.12: Image of the redesigned cathode 2. The drawing above and theprototype on the left have a width of 20 mm, while the prototype onthe right was made thinner (15 mm at the centre).than the heated cathode, as expected.Though cathode 2 was brought above 1300◦C, no electron current was ob-served. To safely increase heating current and cathode temperature, better thermalcontact is required between the electrodes and support plate to lower electrode andbusbar temperatures.91Figure 5.13: Image from the back of the sample with a graphite sample, be-ing heated with 50 A of current during commissioning of the secondprototype for the thermal conductivity tests configuration of CHI. Py-rometer readings taken using an emissivity slope of 1.00 report peaktemperatures of 1245◦C in the hot region of the cathode.Data acquisition and interlocksFor a pulse of heat, the temperature rise is described in terms of the thermal dif-fusivity α as in Equation 5.5, where l represents the sample thickness. Fitting thethermal response can then give α , from which keff can be determined using Equa-tion 5.1 if the density and specific heat capacity are known or measured. There areseveral approaches published for the determination of thermal diffusivity.Salazar et al. [102] studied keff of aligned circular cylinders embedded in amatrix, concluding that for bulk material samples the values obtained using mod-ulated techniques approaches the steady-state value. Monde and Mitsutake [87]developed a method for determining the thermal diffusivity of solids using an an-alytical inverse solution for unsteady heat conduction. In the laser flash methodproposed in 1961 by Parker, Jenkins, Butler and Abbott [92], a small bulk sample92Figure 5.14: Image of applied cathode heating current and correspondingcathode temperature measured using a METIS M3 pyrometer duringa commissioning run of the CHI shown as a function of time. Datashows large uncertainties in heater current from operating at/ 10% ofthe 500 A maximum rated output.of cylindrical shape is heated by a short energy pulse on the front face and thetime-dependent temperature of the rear face is recorded.T = T0+∆T (1+2∞∑n=1(−1)n exp(−α pi2n2l2t)) (5.5)Equation 5.5 is the form derived for pulse length shorter than the characteristicthermal response time, giving the α and subsequently the keff using Equation 5.1if the material’s ρ and cp are known. The method has since been refined, giv-ing corrections for radiative losses by the front and back faces of the sample andfinite-pulse time effects [5][22][35][64][96][118]. The method has since been stan-dardized (ASTM E1461-13 is a commercial test standard available for purchase)93Figure 5.15: Image of applied cathode heating current and correspondingtemperatures on the CHI busbars and electrodes measured using ther-mocouples (TC) during a commissioning run of the CHI shown as afunction of time. Error bars on the thermocouple temperatures are toosmall to be seen.and has also been adapted to extract properties such as spectral emissivity [71]. Ex-pressions for a variety of other input waveforms have been presented in literature[89] [23] and could be adopted for use at CHI.To enable this variety of measurement capabilities, the CHI is designed to mon-itor the applied heating current, the applied accelerating voltage, and have flex-ibility to accommodate various temperature measurements from an assortment ofthermocouples and/or pyrometer readings. More details on the data acquisition andinterlock configuration for both power supplies can be found in Section C.3.3.At low temperatures and without any accelerating voltage, the sample is heatedentirely by radiation from the hot cathode. In this operating paradigm, it is possibleto use thermocouples to record temperatures on the front and back of the sample.Heating current can be increased and decreased to observe the thermal responsesof thermocouples at the front and back of the sample, which can then be used toextract the thermal diffusivity.94The possibility of obtaining two data points also allows for a calculation ofsteady-state thermal conductivity to be attempted. While it may be possible to an-alytically estimate the power incident on the sample surface, it will be difficult todescribe the radiative losses from the sample with low uncertainty. This approachwill likely depend on the use of an ANSYS model to determine the amount ofpower transferred through the high-temperature sample, approaching the methodof Manzolaro et al. [83]. In this mode, the 3D model developed for the CHI canbe used to develop a thermal-electric model, after which the numerical optimiza-tion procedure can be undertaken. Furthermore, use of the numerical optimizationprocedure provides a nodal value of temperature-dependent thermal conductivity,such that the method can account for complex thermal gradients in the sample.This approach encounters the same restrictions observed in Chapter 4, where it isdifficult both to obtain a good initial guess for the thermal conductivity functioncoefficients and to determine that the optimized minimum is a true global and nota local minimum in the optimization space.At higher temperatures, pyrometer readings of the sample replace the need forthermocouples. The contactless temperature measurement then enables the use ofthe accelerating voltage on the sample. If a steady current of electrons can beextracted from the cathode, the accelerating voltage can be changed (or modifiedwith the addition of a grid) to vary the electron current incident on the samplesurface and subsequently the power transferred through the sample. For sufficientlyfast variations, the analysis method of Parker [92] can be used.5.1.3 InstallationThe tests conducted at CHI require services including water, electrical power, nu-clear ventilation and network connectivity. The test stand was assembled and theninstalled in TRIUMF’s ISAC I experimental hall. For the system to be operational,design of service connections and subsequent installation was required.Both test configurations require cooling water inside and outside the vacuumchamber. For the release flange, the water lines also carry DC current and directlycool the electrodes. A de-ionized water loop with two parallel circuits is to beused one-at-a-time for operation of each sample flange configuration. A chilled95water cooling line was designed for external components, including the turbo pumpand the vacuum chamber. More details of the water system and the piping andinstallation diagram (P&ID) can be found in Section C.3.2.DC current is required for heating using the Joule effect, and the thermal con-ductivity flange requires additional services for acceleration voltage. The designincludes flexibility to bias two elements up to 5 kV and modulate one separatelyfrom the other by biasing an additional power supply. More details of the electricalsystem can be found in Section C.3.3.5.1.4 CommissioningThe accelerating voltage was commissioned by biasing the sample holder on theGlassman power supply output voltage. To protect the Lambda power supply, the4/0 cables were disconnected from its output terminals and were connected di-rectly to ground instead. The configuration prevented any sparks from returningto the Lambda supply during the commissioning process. The CHI was put undervacuum, and then the Glassman power supply voltage was slowly increased. Theheater power supply was then connected, and the process of high voltage condi-tioning was repeated before beginning to heat the cathode.Conditioning was done by slowly increasing the voltage output of the Glass-man voltage power supply until small sparks were seen or heard. The voltage wasthen kept at the same level for a while before the slow ramping was continued.After confirming that the voltage could be operated up to 5 kV without arcing,the voltage power supply output was brought back to 0, and the current (heater)power supply was slowly turned up. Operating procedures for safely energizingthe test stand, taking measurements, and de-energizing the system were developed(Section C.3.5).After the power supplies are on and enabled, the system can be conditioned forvoltage and current. Voltage conditioning is done by keeping the system at highvoltage for a length of time while the system is under vacuum. Some sparks maybe observed during conditioning, especially around insulator-high voltage-vacuuminterfaces. Current conditioning is done by increasing the heating current whilemonitoring critical components with thermocouples, and monitoring the cathode96with a pyrometer. The accelerating voltage and heating current power supplieshave been conditioned and the test stand has been operated with three cathodedesigns. In the low-temperature radiative mode, a temperature difference betweenthe front and back of the sample can be observed using the sample holder to pressthermocouples against the sample surface. This requires a sample material that willnot undergo reactions with the thermocouple material.5.2 Future work for CHIDuring installation, design iterations and troubleshooting, several areas of im-provement were identified for the test stand. These areas of work include increasingthe cathode temperature, adding hardware to control and focus a modulated elec-tron beam, and developing a controls system to allow tests to run autonomously.In the first stages of troubleshooting, the cathode did not reach high enoughtemperatures to emit electrons. The cathode 2 design appears to be the most suc-cessful, reaching temperatures above 1200◦C with a heating current of 50 A whilebusbar and electrode temperatures remain below 400◦C. It is likely that higher tem-peratures are required for the cathode to emit electrons. No steady electron currenthas been observed with these cathode temperatures. To allow the cathode to gethotter without overheating the electrodes and busbars, thermal contact across theelectrode insulators must be improved. This could be done by increasing the ther-mal mass and contact area of the insulating washers, using a custom design out ofa thermally conductive insulator such as aluminum nitride (AlN).The CHI system is designed to include space for a modulating grid and elec-trostatic lens. Additionally, slots on the cooled support plate allow flexibility indefining the distance between components. The lens is intended to provide fo-cusing to more precisely define the profile of bombarding electrons. Installinghardware for biasing the modulating grid will allow refinement of the modulationbeyond varying the accelerating power supply.The Raspberry Pi 3 Model B+ has 3.3 V and 5.0 V capabilities. Therefore,analogue communication using the 0-10 VDC logic on the power supply inputsrequires development of an amplifier circuit. Once this development is completed,the signal can be sent directly to the power supplies to control their outputs. The97CHI test procedure could then be run automatically, saving significant amounts oftime during routine operation.The CHI test stand has been designed, procured, assembled and installed atTRIUMF. The test stand and its two configurations give developmental flexibil-ity for the systematic study of new target materials, with ongoing developmentsenvisioned for improvement of the system and method.98Chapter 6ConclusionsI was taught that the way of progress was neither swift nor easy.— Marie CurieEffective thermal conductivity of ISOL target materials limits the amount ofacceptable beam power to avoid destroying the target. Simultaneously, researchand development initiatives in high-release target materials are moving towardsspecifically tailored microstructures with little understanding of how the materialmorphology may impact the material’s thermal conductivity. Combining mech-anisms of heat transfer through materials is fundamentally interesting for devel-oping understanding of energy carrier behaviour. In applied sciences, effectivethermal conductivity is a topic of interest for many industries in pursuit of high-performance materials. Beyond fundamental interest in heat transfer theory, devel-oping a deeper understanding of the effective thermal conductivity of engineeredmaterials has large implications for nuclear physics, medicine, materials science,astrophysics, and more through the large community of researchers relying on theISOL method for radioisotope production.The work presented in this thesis develops a deeper understanding of how ef-fective thermal conductivity is affected by microstructure. The fundamental heattransfer mechanisms and theories described in Chapter 2 give new approaches todevelopment of theoretical models. For ISOL materials, the most successful modeldescribed keff as a simple analytical function of ks and kp combined in series andparallel with a parameter describing the fraction of series or parallel connections.99Using these effective descriptions gives flexibility to use experimental data or dif-ferent theoretical models for ks and kp depending on the information available forthe material of interest. The numerical method developed in Chapter 3 was suc-cessfully used for testing representative microstructures and evaluating them. Nu-merical results obtained using this method agree with the combination of the par-allel and series models for three out of four representative microstructures whencombined with the Loeb theory for thermal radiation through pores. Different mi-crostructures were successfully compared using a parameter that captures dimen-sionality and two fitting parameters that capture morphology. By fitting data usingfour nonzero values of emissivity (1, 0.75, 0.5, 0.25) the two models of cylindricalfibres perpendicular to the direction of heat flow showed the same morphologicalfactor γ . Using experimental data available from literature for ks(T ) and the fit-ted Loeb model of radiation across pores for kp(T ), the keff(T ) of porous UC andUCx was predicted. By developing a better understanding of the fitting parameters,the combination of theoretical and numerical approaches offers the opportunity topredict effective thermal conductivity from information about morphology suchas the information available from a SEM image. Additionally, trends and predic-tions from these models can inform new developments in target material engineer-ing, suggesting that long pores (large d ≈100 µm) in the direction of the thermalgradient could enhance radiative heat transfer. Since the release process benefitsfrom reducing particle size while thermal conductivity benefits from increasingpore size, these findings suggest that thermal conductivity and release experiencecompeting effects of engineered structures. This poses a challenge for target de-velopments to accomplish both effects with one material. There may be a need todevelop materials with porous features on two different scales.The numerical-experimental method used in Chapter 4 was used to determinethe thermal conductivity of β -SiC ISOL materials. Sintering development for theslip-casting method of sample production allowed delaminated layers of pure β -SiC to be studied and compared to pressed pellets of pure β -SiC. The effectivethermal conductivities of β -SiC slip-cast and cold-pressed material were deter-mined as a function of temperature up to 1200◦C and 1050◦C respectively usingthe high-temperature steady-state method [83]. Using ANSYS and optimizing keffas a second-order polynomial of T , the two sample types were compared. Slip-100cast samples showed overall higher thermal conductivity and a larger second-ordercoefficient C2 than the pressed samples, suggesting that as temperature increases,the effective thermal conductivity of the pressed pellets decreases faster than thatof the slip-cast samples. The method provides invaluable test conditions for radialthermal gradients and mechanical stresses in the pressed SiC materials. Limitationsin the method geometry, numerical model-dependence, and optimization functionconvergence in finding the keff of materials with unknown thermal conductivityidentified a need for more development of the method.Building from the limitations of existing methods, the new experimental appa-ratus discussed in Chapter 5 offers a flexible approach for the measurement of ef-fective thermal conductivity of target materials. The conceptual and detailed designprocess has been completed and the installation and assembly of the CHI systemat TRIUMF is finished. Several prototyping and troubleshooting iterations havebeen conducted, identifying further areas of development. In the low-temperature,steady-state regime, the CHI was able to identify a temperature difference acrossthe thickness of a graphite sample of known thermal conductivity. Due to com-plex radiative heat losses in the steady-state method, thermal conductivity studiedin this regime is likely to remain numerical model-dependent. Extracting electronsfor electron bombardment heating is the next phase of the thermal conductivityconfiguration at CHI. This phase will enable transient thermal conductivity mea-surements and provide the first model-independent approach to routinely studyingeffective thermal conductivity of specifically engineered ISOL target materials.In conclusion, this thesis contributes to a body of work towards understandingthe effective thermal conductivity of porous materials, extending a vibrant fieldof research into applications for ISOL materials and critical research for the an-ticipated beam power at ARIEL. The addition of the new numerical method formaterial analysis, the use of an existing method for effective thermal conductivitymeasurements on ISOL materials, and the establishment of a new test apparatusare key outcomes towards this objective. This body of work aims to help buildtowards applications in the ISOL field and beyond, in the huge field of engineeredmaterials.101Bibliography[1] ISAC Facilities for Rare-Isotope Beams. 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Schlu¨nder. Wa¨rmeleitfa¨higkeit von Schu¨ttungen beima¨ßigen Temperaturen. Chemie Ingenieur Technik, 42(14):933–941, 1970.→ pages 15, 29114[128] J. Zgraja and A. Cieslak. Induction heating in estimation of thermalproperties of conductive materials. COMPEL, The international journal forcomputation and mathematics in electrical and electronic engineering, 36(2):458–468, 2017. → page 126[129] Y. Zhang and G. D. Alton. Design of high-power ISOL targets forradioactive ion beam generation. Nuclear Instruments and Methods inPhysics Research, Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment, 521(1):72–107, 2004. → pages9, 11, 16, 25, 29, 31, 49, 74115Appendix ANumerical approach to thermalconductivityA.1 Uncertainty in the numerical methodThe numerical method gives predictions about phenomenological effects of mi-crostructure on keff. Care must be taken before using the method to estimate abso-lute values of thermal conductivity, as may be the case when using a predicted kefffor thermal simulations to predict in-target temperatures.A.1.1 Mesh dependence studyCartesian mapping was used to generate approximately equal hexahedral elementswith aspect ratios near to 1. The numerical model was generated using a decreasingmesh element size, increasing the number of nodes. Computational time requiredfor the simulation to solve increases corresponding to the number of nodes, butthe discretization error is reduced. A mesh independence study was conductedto identify mesh sizes that produced results within the asymptotic region of meshbehaviour. For meshes that do not fall within the asymptotic region, the Richard-son extrapolation was used to predict uncertainty of the results produced on finermeshes.The study was conducted by systematically decreasing the mesh size as il-116Figure A.1: Four different mesh sizes used for a mesh dependence study ofsimulated heat transfer through a representative model of a real mi-crostructure.lustrated in Figure A.1 and conducting the simulation on the progressively finermeshes. Values of interest, namely local temperatures and total heat fluxes, wererecorded in the same way for each successive mesh refinement. When the changein solution values as a function of mesh nodes became small, the numerical resultwas assumed to be mesh-independent. An example of this is shown for model A,open perpendicular fibres, in Figure A.2.After the mesh independence study was completed, a mesh was chosen withinthe mesh-independent region.A mesh independence study was conducted for a hemicube resolution of 20and for a hemicube resolution of 100.As always, the computational time and resources required to solve a problemare the trade-off for greater resolution and lower uncertainties.A.1.2 Effective conductivity calculationFor each model at each temperature, local temperatures within the microstructurewere recorded at 10 locations xi along the direction of heat flow. At each xi, nodal117Figure A.2: Five different mesh sizes used for a mesh dependence study ofsimulated heat transfer through a representative model of perpendicularcylinders.temperatures within x= xi±∆x, y=±∆y, z=±∆z were averaged. The uncertaintyin the average nodal temperature was determined by the maximum deviation fromaverage within the selection of nodes. The deviation would increase if ∆x, ∆y,or ∆z are increased too much, due to edge effects from the radiating guard, or ifthe nodal selection is decreased too much, due to a smaller sample size of nodes.This process gave T (xi) for each of the 10 xi, from which temperature differences∆T = T (x j)−T (xi) were calculated, each corresponding to a ∆L = x j− xi with anuncertainty calculated from ∆x.With ∆T , ∆L and Q, an effective thermal conductivity value was computed foreach set of nodal selections i and j. The two data points closest to each of the endswere eliminated to reduce edge effects from the fixed temperature boundaries, andvalues of i and j were chosen symmetrically about the midpoint between the hotand cold boundaries. The remaining ten values of effective thermal conductivitywere averaged for each temperature point and the uncertainty was computed usingthe uncertainty in each of the 10 keff values.118Appendix BA numerical-experimentalapproachB.1 Sample preparationβ -phase SiC with minimum purity 99.995% and average particle size 1.7µm wasprocured from H.C. Starck (grade B-phase hp). The same powder was used toprepare both the slip-cast and the pressed samples.The procedure for preparing slip-cast samples was developed from the proce-dure of Dombsky and Hanemaayer [42] for SiC. 25.0 g of SiC powder was com-bined with 14 mL of de-ionized water (solvent) and 0.8 g of ammonium carbonate(dispersant). Two jars were filled with the solution, and 8 tungsten carbide ballswere added to each jar. The jars were then installed in a ball mill and ground at200 rpm for 20 min for 10 cycles, with a 3 minute pause between cycles, to forman initial slurry. It has been noted that the milling process “tends to reduce boththe average particle size and the particle size distribution” [42]. The jars were re-moved from the ball mill. SiC material that had coated the lid and sides of the jarswas scraped back into the mixture. Binders and plasticizers were measured out andweighed for each jar, then added to each jar: 0.75 g PEG 400 (plasticizer), 1.025g glycerol (plasticizer), 16.75 g of 5% PVA solution (binder), 10 mL of de-ionizedwater, 1.6 mL methanol and 2.4 mL butanol (surfactants). The jars were replacedin the ball mill and were ground at 60 rpm overnight to form the final slip. The slip119was then poured over 0.13 mm thick exfoliated graphite backing foil. Particulatesand dust were removed before placing the graphite foil on a flat, clean glass sur-face. The foil was smoothed flat, starting from the centre and smoothing towardsthe edges to avoid air bubbles, which could cause deformation in the cast material.The graphite foil was taped down at the edges to hold it in place. The SiC mixturein the jars was cast onto the graphite foil and allowed to dry overnight in air at roomtemperature, forming a “green” (unsintered) carbide layer on the graphite substrateas shown in Figure B.1. A stainless steel cutting tool was manufactured to punchcircular discs of 39 mm diameter from the cast by gently tapping with a rubbermallet. Figure B.2 shows three samples after drying and punching. Cast sampleswere prepared using different amounts of binders and plasticizers, and were castwith and without the graphite foil. Samples with the same formula described abovewere prepared with and without backing foils. For comparison, samples were alsoprepared using more plasticizers. Since the plasticizers are intended to evaporateout of the material during sintering, the increased amounts of plasticizers were in-tended to change the porosity of the resulting material. Two mixtures were used:5x the plasticizers and 10x the plasticizers. Significant differences were observedbetween the cast samples during drying. Very few samples with more plasticiz-ers were successfully produced. The few produced samples did not display theanticipated effects of increasing the porosity of the cast ceramic layer.The sintering procedure was developed using a vacuum furnace with graphiteinserts as shown in Figure B.3. Heating current is passed through a tantalum tubeheater in which the samples are mounted. The heater is insulated with 8 semicir-cular heat shields to maintain homogeneous temperatures within the tube, main-taining the sample temperature while lowering temperatures on the outside of theassembly. The heat shield assembly has hinges to allow access for sample in-stallation. Slip-cast samples were measured before the experiment, recording thediameter, thickness and mass of the disc after sintering. Several programs for tem-perature increase were attempted. After observing bubbling, delamination, andphase change for unsuccessful sintering procedures, the successful procedure wasidentified. The composite samples had a thickness of 0.4±0.1 mm, and the carbidewafer when separated had a thickness 0.27±0.05 mm.Pressed samples were prepared by mixing using a quartz mortar and pestle. A120Figure B.1: Slip-cast β -SiC drying on a graphite backing foil. Dry regions atthe edges can be seen in the surface quality of the carbide layer.Figure B.2: Cast samples of β -SiC punched using a custom cutting tool,shown before shipping and sintering.121Figure B.3: The sintering vacuum furnace shown during installation of un-sintered samples. The hinged heat shield is shown in the open posi-tion, allowing access to the tantalum tube. Slip-cast β -SiC samples areplaced flat on graphite inserts in the sintering chamber. Graphite discsare placed on top of the slip-cast samples.solution of 20% phenolic resin in acetone was added to the powder as a bindingagent. The acetone evaporated during mixing to add some stickiness to the powdermixture while leaving it dry enough to be cold-pressed. The first attempt used 2wt.% phenolic resin, but the SiC powder did not hold together and pellets crum-bled after pressing. The amount of binding solution was increased to successfullyproduce pellets with 5 wt.% and 10 wt.% phenolic resin. The amount of resin wasnot optimized further.B.2 Evaluating uncertainties in optimized effectivethermal conductivityThe method to evaluate the uncertainty in the predicted form of effective thermalconductivity from the steady-state high-temperature method was developed andpresented by Manzolaro et al. [83]. For each constant Cm, m = 0,1,2 the uncer-tainty is given by the standard deviations of the temperature measurements andthe constants during the optimization procedure, using the residual function J asdefined in Equation B.1.122Figure B.4: Prediction of keff for POCO EDM-AF5 graphite calibration sam-ple shown with upper and lower bounds and manufacturer data.J(f) =N∑i=1[TCNi−TCSi]2+[TPNi−TPSi]2 (B.1)With the vector of unknown coefficients f = { f0, f1, f2} = {C0,C1,C2}, thenthe standard deviation of each constant can be found using Equation B.2.σ f m = σT√√√√{[ ∂ 2J(f)∂ fp∂ fq]−1}mm(B.2)Taking partial derivatives of the residual function is not easy, since TCN and TPNare the results of ANSYS thermal-electric simulations. Additionally, since theresidual function values jump at the start of each iteration loop (as shown in Fig-ure 4.4), the standard deviation may be misleading. Taking the standard deviationof the values of the constants themselves gives a standard uncertainty for each ofC0, C1, C2, which corresponds to uncertainty in the predicted keff.The upper and lower bounds of the POCO EDM-AF5 sample are shown in Fig-ure B.4. In this case the uncertainty is very small, corresponding to the low resid-123Figure B.5: Prediction of keff for pressed β -SiC shown with upper and lowerbounds.uals. Availability of manufacturer data assisted with obtaining these low residualsby choosing an initial set of constants very close to the optimized constants.Convergence of the method and low residuals were much harder to obtain forthe β -SiC samples for which the thermal conductivity was not known in advance.The upper and lower bounds using the same procedure are shown in Figure B.5.124Appendix CDesign details of CHIThis appendix captures some of the thought process and technical work completedfor the development of the CHI test stand described in Chapter 5.Section C.1 and Section C.2 contain information about alternative methods ofmeasuring thermal conductivity that were considered for the test stand. Thoughthis information is not relevant to the existing electron bombardment heater design,details in this section may be relevant for ongoing work in the field.C.1 Go No-Go evaluationMany methods have been used in literature to measure thermal conductivity as afunction of temperature [2]. Steady-state methods involve measuring conditionswhere there is no change in temperature with respect to time. After brainstorming,a list of steady-state methods was produced:• Commercial heat flow meter: purchase a commercial heat flow meter forsmall samples• Axial steady state: heat on one end and measure one-dimensional tempera-ture difference.• Radial steady state: heat/cool on cylinder axis and cool/heat on cylinderradius and measure radial temperature difference. Kubota et al. report two125different apparatuses for thermal conductivity measurements in the rangesroom temperature to 800◦C and ranges 1000◦C and above [72].• Guarded hot plate: encapsulate heater with sample material and measuretemperature. (ASTM standard E1225-13: Standard Test Method for ThermalConductivity of Solids Using the Guarded-Comparative-Longitudinal HeatFlow Technique), [54]• Boil-off calorimetry: boil a liquid and determine conductivity [107][108].• 4-probe technique: determine thermal conductivity from electric resistivitymeasurement, measuring current and voltage with 4 probes.• Radiating crucible: heat a crucible, which radiates to a sample, and measuresample temperature [83].In addition to the steady-state methods, several transient concepts were pro-posed for CHI:• Laser flash method: heat sample with laser pulse and detect temperature onother side, measuring half-rise time [92].• Laser thermoreflectance method: laser causes transient temperature change,probe laser records change in surface reflectivity [2]• Laser photothermal grating: uses pattern caused by two laser beams at thesame wavelength to induce photothermal grating, which is detected by aprobe beam. Probe beam diffraction relaxation time is then related to thermaldiffusivity [2].• Induction furnace: adapt the laser flash method using induction heating [128].• Photoacoustic: Uses incident modulated radiation to induce acoustic wavesin air surrounding the sample.• Photothermal displacement: a pump laser causes distortion of sample sur-face, probe laser senses deformation. Thermal diffusivity is found through amodel of heat diffusion and thermoelastic equations.126• Modulated electron beam: heat one side of the sample, first with constantload and then time-varying load. Measure temperature of both sides of thesample to calculate thermal conductivity, measure phase lag to calculate ther-mal diffusivity [23] [89] [124].• Hot wire: Uses a short pulse to heat a source over a large sample.• 3-Omega: uses a strip heater above a substrate to evaluate the third harmonicvoltage component when applying AC heating current.During the “Go No-Go” evaluation, many of the steady-state methods wereeliminated for their inability to reach ISOL target operating temperatures. Theguarded hot plate approach has been noted in literature to reliably reach temper-atures of 1200 K, with some cases noting uses up to 1400 K [54]. Due to in-creasing radiation heat losses at high temperatures, one-dimensional steady-statemethods become impractical above radiation temperatures (≈1600 K). Successfulapproaches rely on axially heating larger cylindrical samples such as the graphitetube furnace proposed by Rasor and McClelland [99]. The axial method was usedby Kubota et al. for measurements of nuclear fuel materials UO2, UC and UC2,reporting uncertainties of ±15% for thermal conductivity measurements rangingfrom room temperature to 1000◦C [72]. The axial method was used by Grossmanto measure thermal conductivity of dense uranium monocarbide up to 2050 K [61].Of the steady-state approaches, the axial method, radial method, and radiating cru-cible method passed the Go No-Go evaluation.Some transient measurements were eliminated due to budget constraints. Oth-ers including the laser thermoreflectance, photothermal grating, and photothermaldisplacement methods are used to study samples of low dimensionality, and wereeliminated for their inability to use as-made bulk ISOL target materials as samples.Laser-flash instruments are even available commercially, but these machines ex-ceeded the budget for the CHI. Of the transient measurement methods, the custom-made laser-flash concept and the electron bombardment concept passed the “GoNo-Go” evaluation.The heat flow meter failed requirements 3 and 4 because contact plates are re-quired to touch the sample, preventing the use of reactive materials at high temper-atures. Similar reasoning caused the parallel conductance and guarded hot-plate127Table C.1: Go-No go evaluation for methods of measuring thermal conduc-tivity. *ConditionalConcept Requirements Result1. keffasfunc-tion oftem-pera-ture3.vacuum,sampletem-pera-turesto2200◦C4.Reactive,ac-tinide,radioac-tivemateri-als5.Year20206.costbelow$600007.Min-imalmodelre-lianceHeat flowmeterpass fail fail pass pass pass failAxial pass pass pass pass pass pass passRadial pass pass pass pass pass pass passParallelconduc-tancepass pass fail pass pass pass failGuardedhot platepass pass fail pass pass pass failBoil-off pass fail pass pass pass pass fail4 probe pass fail pass pass pass pass failRadiative pass pass pass pass pass pass* passInduction pass pass pass pass pass fail failPhoto-acousticpass fail pass pass pass pass faile-beam pass pass pass pass pass pass passLaserflash ap-paratuspass pass pass pass fail pass failCustomlaserpass pass pass pass pass* pass passTransienthot wirepass pass fail pass pass pass fail3 omega pass pass fail pass pass pass fail128methods to fail requirement 4, as this method requires negligible contact resis-tance between the sample and reference plates. Meanwhile, the boil-off calorimetrymethod is limited to melting temperature of the material used and is unlikely to befeasible for 2200◦C. The four-probe technique also has an upper temperature limit,operating in the range 20 - 1600◦C. For the inductive method, inhomogeneous heatgeneration must be reconstructed using computer modelling, failing requirement 7.The photoacoustic method uses sound waves, requiring gas or air atmosphere andfailing requirement 3. While commercial laser flash apparatuses were quoted to besignificantly above budget, failing requirement 6, there remained a possibility ofconstructing an in-house apparatus that might be below the budget. The laser flashmethod was tentatively passed with this reasoning. The transient hot-wire and 3omega methods assume a “semi infinite” substrate and negligible heater-to-samplesize ratio, as well as requiring the sample to be electrically conductive. These twomethods failed requirement 4. The five passing concepts were investigated beyondthe Go-No Go.C.2 Conceptual designFive conceptual designs were developed for the CHI and evaluated. For each con-cept, a brief procedure was envisioned, including the required sample preparation,calibration, sample installation, testing, data analysis, and potential uncertainties.Out of the five concepts, the electron bombardment apparatus was chosen. The fourconcepts that were developed for comparison but were not chosen are described inthe following sections.C.2.1 Radial steady state conceptThe radial steady state concept features a heater (or heat sink) along sample axis,and external cylindrical heat sink (or heater) to cause a temperature gradient in theradial direction of a cylindrical sample.1. Sample preparation: samples would be prepared using a set of concentricsamples. A central hole would be drilled through multiple pellets, whichwould then be stacked together to make a cylinder of sufficient length toeliminate heat loss from the cylinder ends. Heat shields and insulation would129Figure C.1: A) Radial apparatus developed by Sobon et al. [114] B) Radialapparatus developed by Kubota et al. [72] C) Radial apparatus devel-oped by Rasor and McClelland [99]Figure C.2: Schematic for the radial steady-state concept for measuring ther-mal conductivity130be added around the sample, using a cylindrical insert and outer casing forpyrometer measurements. Heater wire and current connectors would be at-tached through the sample.2. Test stand calibration: Thermocouple and pyrometer calibration would beneeded. Heater wire calibration would be required to estimate power outputas a function of heating current.3. Sample installation: A heater wire would be installed through the axial holein the samples and then connected to current electrodes. The cooling jacketwould need installation around the sample.4. Testing: Heating to measurement temperature could be accomplished by in-creasing the heater current. Pyrometers (and/or differential thermocouples)could be used to record temperature of tube inserts and outer cylinder todetermine the temperature drop across the sample. Sample ambient temper-ature could be measured on heat shields. Inlet and outlet temperature as wellas flow rate of the water would need to be measured for calorimetry.5. Data analysis: Input power could be calculated by referencing the heater wirecalibration. Heat flow could be calculated from the temperature increase ofcooling water. From recording the temperature difference at each sampletemperature, the thermal conductivity could be extracted for a radial heatdistribution.6. Uncertainties: Some heat losses by radiation would occur from the edgesof the sample. Could correct for heat losses by recording temperatures onheat shields and quantifying possible heat loss. Sample contact with heatingwire could also cause chemical reactions and change of resistivity duringmeasurements, particularly for actinides.The radial heating method comes with several pros:• Direct measurement of thermal conductivity131• Two methods of calculating heat flow: measuring the temperature differenceand using the current and resistance of heater wire material, or using a volt-meter to record voltage drop across the sample.• Wire heating likely requires low power, and most power should go into heat-ing the target material.• Temperature measurements taken into a cavity in the material should reducedependence on emissivity.And some cons:• Larger amounts of sample material required, which makes measurements ofirradiated samples difficult.• Samples require an axial hole and good contact with supporting material.Difficult for powdery or nanofibrous materials.C.2.2 Laser flashThe well known laser-flash method uses a laser pulse to heat one side of a thin discsample. The time to rise halfway to maximum temperature on the opposite side ofthe sample is then used to determine the thermal diffusivity. While commerciallyavailable, existing laser-flash apparatuses were beyond the budget for CHI andwere thus ruled out.1. Sample preparation: A sample pellet would be mounted onto a sample holder.Pellet thickness should be considered so that the rise time to half of the max-imum temperature is within 10 to 1000 ms. Samples may need to be coatedwith graphite.2. Test stand calibration: Pyrometer calibration for front/back faces would berequired to determine emissivity slopes of sample materials, or calibratedon coated graphite. The laser pulse would need calibration to determinethe profile of the deposited heat and to determine the required power forthe sample thickness. Calibration using samples of known properties (heatcapacity, conductivity, reference blackbody for emissivity) could be used.1323. Sample installation: The sample would be installed in a sample holder whichmay include an external heater. Mirrors and pyrometers would require align-ment.4. Testing: Heat capacity and emissivity of the sample would be required priorto measurement. Heating to measurement temperature would be done eitherwith the laser power or with an external heater. A pulse from the laser wouldbe applied with a length of < 2% of the rise time required for rear face toreach 0.5 of the maximum temperature. This would be different for differenttypes of samples. Temperature response on the back of the sample would berecorded, as well as laser power and sample temperature.5. Data analysis: from measured or known density, specific heat capacity, andemissivity, the method of Parker can be used [92]. From the thermal diffu-sivity, the thermal conductivity can be calculated.6. Uncertainties: Corrections for radiative heat loss in the method have beenaddressed in literature. Corrections might be required for reflected heat fromthe rest of the apparatus. There would be some uncertainty in the sampleproperties required to use the method.Pros• “thermal diffusivity values ranging from 0.1 to 1000 (mm)2 / s are measur-able by this test method from about 75 to 2800 K”• “experimental uncertainties within +/- 5%” [92].• Works best with small, thin discs – low sample mass required.• Measurements take very little time – installation is simple once test stand isset up• The method is quite standardized and will be useful for comparison to liter-ature. Industrial standards (ASTM E1461-13) are available for purchase.• Could measure surface emissivity in the same apparatus using precedentedmethod [71].133Figure C.3: Conceptual design of the CHI using the laser flash method ofthermal conductivity measurement.Cons• Requires specific heat capacity and density data• Measures thermal diffusivity only, indirect measurement of thermal conduc-tivity.• Requires purchase and setup of laser – controls and additional power.• Requires new temperature sensor: Detector + amplifier with response time< 2% of 0.5 t rise• Requires a separate heater setup to maintain sample temperatures.• Samples may require coating before testing.• Purchase of expensive components like the laser may mean large lead time.C.2.3 Axial steady stateIn the axial steady state method, one side of the sample is heated, the other side iscooled, and the temperature difference between the two faces is measured.1341. Sample preparation: Pellets would be combined into a stack and surroundedwith heat shielding.2. Calibration: The hot plate would need calibration to know the temperatureas a function of heating current. Heat flow through the sample would needto be estimated.3. Sample installation: Sample would be placed in a heat shield between thehot plate and cold plate, and then inside an insulation jacket. Good thermalcontact between pellets and plates would be ensured.4. Testing: Heating to measurement temperature would be done using the hotplate. A differential thermocouple would be used to record temperature ofsample neat the hot plate and near the cold plate, and a thermocouple withinthe insulation could be used to determine the sample temperature. The inletand outlet temperature of cooling plate water could be used to determine theheat flow.5. Data analysis: Input power would be calculated referencing the hot platecalibration. Heat flow could be calculated from the temperature of coolingwater. Thermal conductivity would then be calculated from the temperaturedifference.6. Uncertainties: Heat losses by radiation would be significant. This couldbe corrected by recording temperatures on heat shields and also behind hotplate, and quantifying possible heat loss. Some correction would be neededfor the temperature drop of the cooling water, which would not take intoaccount side losses.Pros• Direct measurement of thermal conductivity.• Simplest calculation of thermal conductivity.• Well known and standardized method.Cons135Figure C.4: Schematic for the axial steady-state concept for measuring ther-mal conductivity• Larger samples are preferred.• Mounting a sample requires establishing good surface contact between theheating/cooling plates and the sample surface.• Heat losses from the hot plate and actual heat flow through the sample arenot easily quantified at high temperatures. Several authors have noted thedifficulty of one-dimensional measurements at high temperatures.• Designing and installing sufficient insulation may be challenging.C.2.4 Radiating crucibleThe radiating crucible concept features a resistively heated radiator, which heatsthe sample non-homogeneously through radiation. The temperature difference be-tween centre and edge of sample is measured using a calibrated pyrometer, andANSYS is used to determine the radiative power heating the sample and fit ther-mal conductivity to measurement data.1. Sample preparation: produce a flat circular pellet with uniform thickness.1362. Test stand calibration: Crucible calibration would require measuring thetemperature of graphite heater as a function of heating current. Tempera-ture measurements would then be used to calibrate ANSYS simulations.3. Sample installation: Place pellet on stand above radiating crucible4. Testing: Heat to measurement temperature. Use pyrometer to record tem-perature of sample at center and at edge. Use thermocouples on crucible andvessel components to get temperature of radiating surfaces5. Data analysis: Calculate input power: referencing calibration measurements,use ANSYS to calculate radiating power to sample. At each ambient temper-ature, use ANSYS to match thermal conductivity to measured temperatures6. Uncertainties: The numerical method will calculate all heat exchange in thevacuum chamber with some uncertainty inherent to the method. There wouldbe some additional uncertainty in each of the material properties used in thesimulation. The thermal conductivity may not be accurately described by thechosen fit, in which case the method may need to be re-evaluated.Pros• Test stand components and operation are simple• The test method has precedented use for ISOL materials at SPES• The radial heat profile most closely mimics the thermal gradients in a realtarget material for proton driver beams such as ISOLDE or ISAC.Cons• Two pyrometers are required, or repeat measurements to get temperature atcentre and edge of sample, introducing hysteresis.• The spectral emissivity is assumed wavelength-independent and emissivityslope is assumed in temperature measurements and also in simulations.• Reliance on ANSYS simulations for input power and also temperature.137• Optimization function has convergence difficulties if input values are too farfrom the final optimized values. Optimization function may converge to alocal instead of global minimum.• Sample geometry requirements such as flat surface, symmetric diameter, andminimum thickness may exclude some sample materials. Sample fracturingdue to radial thermal gradients may prevent high temperature measurements.C.2.5 Concept decision matrixA list of desirable design metrics was developed, encompassing the measurementmethod, test stand design, required devices, and required data analysis. The fiveconcepts were given a weighted score in each category to produce a decision ma-trix.C.2.6 Electron bombardmentThe electron bombardment heater was chosen for CHI.1. Sample preparation: A pellet would be mounted onto a sample holder de-signed to take target materials as-made.2. Calibration: Pyrometer calibration would be needed to determine the emis-sivity slopes of the material, or the material would need to be coated. Theelectron beam shape may need to be calibrated to characterize the heat loadon the sample. One option is to calibrate using samples of known properties.3. Sample installation: The sample holder would be installed into the test setupand positioned. Electron beam optics may need to be aligned and distancebetween components measured.4. Testing: procedures would depend on the choice of transient or steady mea-surement. For transient measurements, pulse or wave forms would be ap-plied by modulating the electron beam. Temperature response over timeon the back of the sample would be recorded. Sample average temperaturewould need to be measured and the power deposited by the electrons could beknown from calibration data or from a direct measurement. For steady-state138Figure C.5: Decision matrix comparing the five conceptual designs usingweighted design metrics. Design metrics are weighted for importance(3:most important/needed, 2:important/wanted, 1:least important/con-sidered) Concepts are ranked from best (5) to worst (1) for each metric,starting from 1 and allowing ties. Subtotals are then added to obtaintotals in the bottom row, with high numbers indicating better perfor-mance.139measurements, numerical modelling may be needed to quantify the radiativeheating from the filament.5. Data analysis: The input power would be calculated from the applied elec-trons and thermal radiation from the electron source. For transient measure-ments, the time to reach half of the maximum temperature would be required,or the phase lag, for a modulated beam. Thermal diffusivity could then becalculated and used to find the thermal conductivity if heat capacity and den-sity are known. Alternatively, the temperature difference between the frontand back faces could be measured to attempt an axial steady-state measure-ment, or the temperature difference between the centre and edge could bemeasured and an optimization routine to used to match numerical and exper-imental data as described in Chapter 4.6. Calibration: Corrections or calibration data would be required for electronbeam power incident on the sample. In the steady state, corrections for ra-diative heat loss and reflected power could be used from existing literatureor numerical simulation.From the scores in Figure C.5, the electron bombardment radiator concept wasidentified as the concept that best met the design requirements.C.3 Detailed designC.3.1 Design iterationsThe first iteration of the support and cooling assembly featured a cylindrical pipethat functioned simultaneously as a cooled heat shield and a supportive connectionto the 8” flange (Figure C.6). Soldered copper pipe was envisioned for cooling thepiece. Once the design decision was made to support the sample and electron beaminstrumentation on the same flange, the heat shield design went through several it-erations before a separate rectangular heat shield and support plate were designed.The first design of the cathode featured a spiral filament. A thermal-electric sim-ulation of the design was used to estimate component temperatures with 120 A140Figure C.6: Thermal simulation results for pipe support and cooling designwith 2 lpm of cooling water, conservatively assuming a filament tem-perature of 2500◦C.Figure C.7: Thermal simulation results for resistively heated spiral wire cath-ode design using 120 A of heating current, assuming a 2000◦C sample141Figure C.8: Thermal simulation results for resistively heated spiral wire cath-ode design using 250 A of heating current, assuming 900 W of electronbeam heating on the front face of the sample.of resistive heating and a contact-cooled support plate (Figure C.7). Private com-munications with experienced team members suggested that at high temperatures,the thin tantalum wire would likely deform under its own weight and the cathodedesign would not maintain its distance or shape.A later design of the cathode featured a simple foil sheet. A thermal-electricsimulation of the design with 250 A of resistive heating and no conductive cool-ing was used as the worst case scenario for component temperatures (Figure C.8).Though the sample became very hot when 900 W of electrons were assumed, itwas observed that even with 250 A of resistive heating, the tantalum cathode wouldlikely be too cold to actually emit electrons, and 900 W would likely not be achiev-able even with the larger cathode surface area (Equation 5.3).142Centre canadien d'accélération des particulesh1gf2345hgfedcba1edc234ba5THIS DRAWING, SUBJECT MATTER AND INFORMATIONCONTAINED THEREIN, IS THE SOLE, EXCLUSIVE ANDCONFIDENTIAL PROPERTY OF  TRIUMF LABORATORY,AND AS SUCH, SHALL NOT BE DISCLOSED, COPIED,REPRODUCED  OR USED,  IN WHOLE  OR IN PART,WITHOUT EXPRESSED WRITTEN PERMISSION OF THETRIUMF LABORATORY  OR  ITS  REPRESENTATIVES.DO NOT COPY, THIS DOCUMENTCONTAINS PROPRIETARY INFORMATIONOFSHEETSIZESUB-ASSYWPN #CHECKEDSCALEDATETOLERANCES UNLESS OTHERWISE SPECIFIEDALL DIMS IN MILLIMETRESDESIGNEDANGULARSURFACE FINISHDECIMALS.XX± 1± 0.11.6 µmDWG NO. REVTHIRD-ANGLE PROJECTION.X ± 0.2± 0.5XASSEMBLYTRACKING #DRAWNCanada's particle accelerator centre4004 Wesbrook Mall, Vancouver, BC,  V6T 2A3, CanadaD 11ATD0009Mia Au2019-04-301:2ELECTRON BOMBARDMENT CONFIGURATIONCHI STANDELECTRON BOMBARDMENT FLANGE ASSEMBLYQuinn TemmelMia AuAO-1421202200633110041011201ITEM WILL BE FABRICATED USING THIS ASSEMBLY AS A GUIDE. SEE NOTE 11101203SEE NOTE 14EXPLODED ISOMETRIC VIEWNOT TO SCALE112131415171NOTES:1. ITEMS 5 , 6  & 7  EACH CONSIST OF TWO MDC#9924003 PUSH-ON CONNECTORS & A LENGTH OF 24 AWG KAPTON INSULATED WIRE. WIRE LENGTH WILL BE DETERMINED BY ROUTING WITHIN THIS ASSEMBLY (ATD0009), AND EACH SEE NOTE 1ISOMETRIC VIEWNOT TO SCALE1810310218272.9457.2202.4A ECO-5198 - CHANGE CONTROL APPLIES Quinn TemmelITEM REF No. DESCRIPTION MATERIAL QTY.1 ATD0010 ELECTRON BOMBARDMENT ASSEMBLY 12 ATD0046 CUSTOM FLANGE ASSEMBLY 13 ATD0067 BUS BAR/CLAMP 1 Copper 14 ATD0068 BUS BAR/CLAMP 2 Copper 15 ATD0069 WIRE ASSEMBLY 1 16 ATD0070 WIRE ASSEMBLY 2 17 ATD0071 WIRE ASSEMBLY 3 1 100  SCREW, SOC HD CAP, M4x0.7-12 SST 3101  M4x0.7X12LG LOW PROFILE SOCKET HD SCREW AISI 304 4102  BOLT, HEX HD, 1/4-20 X 1.50 LG SST 18103  NUT, HEX, 1/4-20 STL 18 200  MDC 2-3/4 CF UHV FLUID 2-TUBE VCR FEEDTHRU OR EQUIV AISI 304 1201  ELECTRICAL FEEDTHROUGH 5000VDC MAX, 3 SHV COAXIAL RECESSED PIN ON CF2.75, MDC9232008  1202 9452008 2.75" CONFLAT POWER FEEDTHRU, 2 PINS, 5KV, 150A, MDC 1203  GASKET, 2.75 CF, SILVER PLATED, LESKER Copper 3REV DATE REVISION DESCRIPTION BY APPDFigure C.9: Assembly drawing of ATD0009, the electron bombardment flange assembly of the CHI stand143C.3.2 WaterConvection coefficients were determined for the water cooling loops in the CHIthermal conductivity design. For a given volumetric flow rate V˙ and pipe diameterd, the convection coefficient was found considering internal forced convection ofwater through a circular pipe. The Reynolds Number (Re) was found using stan-dard properties of water for the kinematic viscosity ν [50]).Re =vDhν=V˙ν pi4 d(C.1)Where Dh is the hydraulic diameter. For Re larger than 5000, the flow was assumedturbulent, and the Dittus-Boelter equation was used to find the average Nusseltnumber Nu:Nu = 0.023Re0.8Prn (C.2)With the Prandtl number Pr and n taking a value of 0.4 for heating. The convectioncoefficient was then approximated usingh =Nu× kd(C.3)Using an iterative process, pipe diameters were then determined based on theamount of cooling required. Pressure drops through each of the lines were cal-culated as shown in Figure C.10.For the thermal conductivity flange, the de-ionized water passes through a 1/4”section into the VCR feedthroughs. For the release flange, the de-ionized waterpasses through a 3/8” section of pipe before entering an adapter to mate with theDC current feedthrough. The de-ionized water system was commissioned, leak-tested and pressure-tested to 60 psi.A chilled water cooling line was designed for external components, includingthe turbo pump and the chamber itself. Because of the chamber and flange geome-try, direct convective cooling was avoided, and instead water-cooled copper blockswere designed to be clamped around the six arms of the cross. The chilled waterline cools the turbo pump and the cross in series. Chilled water is supplied at 15◦Cand 60 psi, then passes through a strainer before entering the CHI system.144Figure C.10: Calculation of pressure drops through the CHI system NALCW(Non-Active Low Conductivity Water) and CHW (Chilled Water)cooling loops.A piping and installation diagram (P&ID) was developed for the CHI watersystem as shown in Figure C.11.C.3.3 ElectricalBoth test configurations required DC current for heating using the Joule effect,and the thermal conductivity flange required additional services for accelerationvoltage.A 480 VAC line was installed to supply a portable 15 KVA transformer toprovide power for CHI. The transformer provides a 480 VAC, 3 phase connection,several 120 VAC outlets, and a 320 VAC outlet.For the heating current, a 500 A, 10 V DC power supply was obtained. A 5 kV,600 mA Glassman power supply provides the acceleration voltage. A groundedSHV receptacle was manufactured for de-energizing the power supply by connect-ing the central pin of the RG-59 cable directly to ground before beginning work onthe test apparatus.Another 1 kV, 1 A power supply was installed to provide an additional bias145Figure C.11: Diagram of the CHI system DI (de-ionized) NALCW (Non-Active Low Conductivity Water) and CHW (Chilled Water) coolingloops.voltage to allow for the addition of an electrostatic lens or a grid, giving more con-figurational flexibility. The power supplies were mounted in a power supply rackand connected to building ground through a copper busbar and grounding cable.Plexiglass shielding was installed for low-voltage electrical safety. An additionalground receptacle was manufactured and attached to the table to provide a shortcircuit for the voltage power supply while de-energizing the system. To leave thesystem unattended, the SHV cable is attached to this ground receptacle to dissipateany energy buildup in the power supply.To deliver the DC power and provide flexibility for extracting the sample flange,4/0 welding cables were used for the DC current power supply. Copper busbarswere designed to attach to the power supply DC current terminals, and two addi-tional sets of busbars were designed and manufactured for the vacuum chamber,one set for the water-cooled copper conductors of the release setup, and the otherfor the thermal conductivity sample flange filament heater feedthrough. The bus-bars were connected each with two cables in parallel to carry a maximum of 500A. A high voltage splitter box was designed and manufactured to take the output of146the Glassman power supply and split it into two RG-59 output plugs. This gives thepossibility of biasing two electrodes and includes flexibility to additionally mod-ulate one bias separately from the other by biasing an additional power supply onthe output voltage. Floating a second modulating power supply may require a highvoltage safety cage but will allow modulation around the 5 kV accelerating voltage.C.3.4 Interlocks and data acquisitionThe current and voltage power supplies are connected to the Raspberry Pi, whichreads the applied current and voltage, and correlates the data with data from thevacuum and reference thermocouples.For data acquisition and interlocks, a Raspberry Pi is used with the addition ofDAQC2 data acquisition plates. The Raspberry Pi 3 Model B+ provides pythonprogramming capabilities, network access, and a quad core 64-bit 1.4 GHz pro-cessor with 1 GB SRAM. The addition of the DAQC2 plate provides digital andanalogue input and outputs as shown in Figure C.12, communicating with the Rasp-berry Pi through the 40 pin GPIO header. Since the DAQC2 plates are limited by atime delay of 0.2 s, an Arduino was added to take data for thermocouples collect-ing time-sensitive thermal responses. The Arduino takes time-stamped data with afiner time resolution than possible with the DAQC2 plates. The data can then becombined with data from the Pi using time-matching. The pyrometer data also hasa finer time resolution than possible with the DAQC2 plates.The Glassman KR600 0-5 kV, 600 mA power supply communicates using aDB25 pin header with input and output read-backs that can be read as analoguesignals into the DAQC2 analogue input pins. The power supply additionally com-municates through USB or Ethernet. The Lambda EMS 0-10 V, 0-500 A powersupply communicates using a set of analogue signals that can be read to the ana-logue input pins of the DAQC2 plate. To implement interlocks, signals includ-ing flow switches and the vacuum gauge controller read-back are taken into theDAQC2 and analysed using a continuously running monitor code in the Pi. Inter-lock criteria are constantly checked in the monitor code to determine if the systemis outside the safe operation regime. Then a relay board is used to short the shut-offpins of the power supplies to the reference (common) ground, disabling the power147Figure C.12: Image of the DAQC2 Pi-plate with board functions indicated.Image taken from [93].supplies. This system provides a rough means of shutting off the power supplies inthe event of a bad vacuum atmosphere or lack of cooling water. Additionally, bothpower supplies have internal shut-off mechanisms for machine protection. The DCcurrent power supply was additionally equipped with a 14 VDC metal oxide varis-tor (MOV) for protection against arcs from the cathode to the sample. The LambdaDC current return was connected to building ground to add additional protectionagainst fast transients caused by sparking.148Figure C.13: Schematic for the data acquisition and interlocks configurationfor the CHI149GPIO 400 24 681012 GPIO1814 GND16 GPIO 2321 GPIO0920 GND22 GPIO2524 GPIO082926 GPIO0731Raspberry Pi DAQC2: addr 0ADC0  AIN01 AIN12 AIN23 AIN34 AIN45 AIN56 AIN67 AIN7GND8 +5VDAC0 DAC01 DAC12 DAC23 DAC34 GND5 GNDRaspberry PiModel 3B+USB0 USB0 1 USB12 USB2 3 USB31 3.3 V5791113 GPIO2715 GPIO2217 3.3 V19 GPIO1021 GPIO09323 GPIO11252830Lambda EMSJ1-D251 +V2 +V REM3 V PROG I4 V AMP IN5 V PROG R6 V PROG R COMMON7 –V REM8 -V9 I PROG I11 I PROG R10 I AMP IN12 –SHUNT (-I)13 INV I AMP IN15 REM V IN14 +SHUNT (+I)17 REM SWEMS 10-500-2-D-08060-10 V0-500 mATB11234567891011121314151617RELAY BOARDNO NC C INRELAY 1NO NC C INRELAY 2+24V IN GND24 VUSB to RS232Pfeiffer gauge controllerGND16 ENABLECHI Current power supplyInterlocks and DAQNO NC C INRELAY 37/23/20NO NC C INRELAY 4LEGENDDAQHV INTERLOCKSCONTROLSCURRENT INTERLOCKSFigure C.14: Schematic for the data acquisition and interlocks configuration for the current power supply at CHI150GPIO 400 24 681012 GPIO1814 GND16 GPIO 2321 GPIO0920 GND22 GPIO2524 GPIO082926 GPIO0731Raspberry Pi DAQC2: addr 0ADC0  AIN01 AIN12 AIN23 AIN34 AIN45 AIN56 AIN67 AIN7GND8 +5VDAC0 DAC01 DAC12 DAC23 DAC34 GND5 GNDRaspberry PiModel 3B+USB0 USB0 1 USB12 USB2 3 USB31 3.3 V5791113 GPIO2715 GPIO2217 3.3 V19 GPIO1021 GPIO09323 GPIO11252830RELAY BOARDNO NC C INRELAY 1NO NC C INRELAY 2GlassmanJ41 GND2 COMMON3 INTERLOCK7 REMOTE I8 SIGNAL COMMON9 V MONITOR10 I MONITOR11 DIGITAL COMMON12 +10 V15 REMOTE HV ON20 HV ENABLE21 HV STATUS22 FAULT STATUS24 ARC STATUS23 MODE STATUS25 GNDKR-6000-5 kV0-600 mA+24V IN GND24 VUSB to RS232Pfeiffer gauge controllerGNDCHI Voltage power supplyInterlocks and DAQ16 REMOTE HV ONNO NC C INRELAY 37/23/20NO NC C INRELAY 4LEGENDDAQHV INTERLOCKSCONTROLSCURRENT INTERLOCKSFigure C.15: Schematic for the data acquisition and interlocks configuration for the voltage power supply at CHI151C.3.5 ProceduresThe CHI can be left under a rough vacuum, with the scroll pump on. Before test-ing, the vacuum level should be checked. If the CHI internal pressure is belowapproximately 1e-2 mbar, the turbo pump can be turned on. Pressure levels dropquite quickly after the turbo pump has been started. The valve connecting the scrollpump to the vacuum chamber must then be closed, so that the scroll pump pulls onthe exhaust pipe of the turbo pump.The interlock system can be started by running the python code. The code readssignals from the vacuum gauge controller to interpret the vacuum levels and pro-vide continuous analog outputs from the ADC of the Pi to a set of relays that enablethe power supplies when powered as illustrated in Figure C.14 and Figure C.15.Starting and stopping waterThe water system must be flowing for the test stand to maintain operational temper-atures. When starting the two cooling loops, any excessive pressure in the supplyhoses should be released before increasing the flow rate to operating conditions.Starting with the CHI system closed off from building water, the procedure to startcooling water is as follows:• Open valve to deionized water return. Open deionized water valves on CHItable. For operation with release flange, leave release flange valves open andclose thermal flange valves. For operation with thermal flange, leave thermalflange valves open and close release flange valves. Pressure gauges on theCHI table should read around 30 psi, and the paddlewheels should be still.• Ensure upper valve (knob) to deionized water supply is closed by turningclockwise. Slowly open the lower supply valve until the supply pressure isaround 30 psi (return pressure).• Slowly turn upper deionized water supply knob counterclockwise until sup-ply pressure gauge reads around 50 psi. The paddlewheels on the CHI tableshould be steadily moving.152Powering upThe CHI must be put in shutdown condition before it can be left alone. In shutdowncondition, power supplies are disconnected from the transformer. Cables for inputAC power are stored safely by coiling on top of the power supplies in the blue rack.The breaker switches 3/4/5 and 8-10 are set in the “off” position. The plexiglassbarrier at the back of the power supplies is in the closed position and secured usingthe doorknob bolt. It is fine to leave the breaker for the roughing pump and valvesin the on position. A safe startup procedure was written for connecting the voltageand current power supplies before turning them on. The HV cable is connected tothe building ground plug on the CHI table.Procedure to energize the system for high voltage using the Glassman (XPPower) KR5R600:1. Unplug the RG-59 cable(s) from the CHI table ground and attach it to thedesired voltage pin(s) on the SHV feedthrough of the CHI sample flange.2. Install plexiglass safety barriers.3. Plug AC power cable for HV power supply into the transformer panel 84. Ensure plexiglass barrier at back of power supply is in place.5. Flip transformer switch 8 into the on position.6. Press the “ON” switch on the front panel of the Glassman power supply. The“ON” switch should glow orange.7. Check polarity. The light above the “POL +” should be green.8. Press the red “HV ON” square button on the front panel of the Glassmanpower supply to enable high voltage. The light underneath the “HV ON”button should turn on.9. Increase the current by manually adjusting the current knob. The powersupply should remain voltage limited, indicated by a green light above the“KILOVOLTS” voltage output shown on the front panel. 10. At this pointthe power supply is enabled and ready to apply an accelerating voltage to theCHI system.15310. Slowly ramp up the voltage using the voltage adjustment knob on the rightside of the power supply front panel.To ramp down the voltage power supply:11. Turn the voltage adjustment knob counterclockwise until the voltage outputon the power supply front panel shows an output of 0.00 kV and 0.00 mA.12. Allow system to rest at zero output for a minimum of 1 second. This allowsany power to dissipate from the voltage power supply. (Voltage decay timeconstant 50 ms for KR5R600)13. Press the “OFF” switch on the front panel of the Glassman power supply.The light in the ON/OFF switch should go off and the power supply frontpanel indicators should turn off.14. Flip switch 8 on the transformer panel into the “OFF” position.15. Disconnect the AC input power cable to the Glassman power supply fromthe transformer and coil it neatly on top of the Glassman power supply in theblue rack.16. Unplug the RG-59 cable(s) from the CHI sample flange voltage feedthroughand into the ground plug on the CHI table.17. Leave plexiglass barriers with visible notice signs in place when leaving thetest stand area.Procedure to energize the CHI system for heating current using the LambdaEMS 10-500 power supply:1. Install plexiglass safety barriers around copper electrodes on the CHI table.2. Plug AC power cable for Lambda EMS power supply into the 480V recep-tacle on the transformer panel 3/4/5.3. Ensure plexiglass barrier at the back of the power supply rack is in place andsecured with the doorknob bolt.1544. Flip transformer switch 3/4/5 into the on position.5. Flip the “ON” switch on the front panel of the Lambda EMS power supply.The light above the “ON” switch should glow red.6. The power supply starts in the voltage-limited mode. The red light above the“VOLTAGE” adjustment knob on the left of the front panel will be on. In-crease the voltage using the voltage adjustment knob until the power supplybecomes current-limited. The light above the “VOLTAGE” adjustment knobwill turn off, and the light above the “CURRENT” adjustment knob will turnon.7. Turn the voltage adjustment knob clockwise again to set a higher voltagelimit. The output current and voltage should not change.8. Once the power supply is current-limited and the voltage limit has been setsufficiently high, the heating current can be gradually increased using thecurrent adjustment knob. Below 20 A, the applied current is difficult to con-trol.To ramp down the current power supply:9. Decrease the applied current by turning the current adjustment knob counter-clockwise until it stops decreasing.10. Decrease the set voltage by turning the voltage adjustment knob counter-clockwise until the power supply becomes voltage-limited. Continue de-creasing until the power supply output is 0.00 V, 0 A.11. Flip the POWER switch on the front panel of the Lambda EMS into the OFFposition.12. Flip the transformer switch 3/4/5 into the OFF position.13. Disconnect the 480 VAC input power cable from the transformer receptacle3/4/5 and store the cable neatly above the Lambda EMS power supply in thepower supply rack.15514. Leave plexiglass barriers with visible notice signs in place when leaving thetest stand area.156

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