Effect of Microstructure on Thermal-Transport Properties of UO 2 Simon Phillpot

1. Effect of Microstructure on Thermal-Transport Properties of UO2 Simon Phillpot Department of Materials Science and Engineering University of Florida Gainesville FL 32611 sphil@mse.ufl.edu 1

2. Taku Watanabe Aleksandr Chernatynskiy Susan Sinnott Department of Materials Science and Engineering, University of Florida Daniel Vega James Tulenko Department of Nuclear and Radiological Engineering, University of Florida Robin Grimes Department of Materials, Imperial College London Patrick Schelling Department of Physics and AMPAC, University of Central Florida Srinivasan Srivilliputhur Department of Materials, U. North Texas 2

3. Pressurized-Water Reactor http://www.nrc.gov/reading-rm/basic-ref/students/animated-pwr.html 4

4. http://coto2.files.wordpress.com/2011/03/2-fuel-pellet-assembly.jpghttp://coto2.files.wordpress.com/2011/03/2-fuel-pellet-assembly.jpg http://www.kntc.re.kr/openlec/nuc/NPRT/module2/module2_2/module2_2_2/2_2_2.htm 5

5. FRAPCON: Unirradiated Fuel Pellet FRAPCON Model http://www.peakoil.org.au/news/does_nuclear_energy_produce_no_co2.htm 6

6. Motivation • Maximize thermodynamic efficiency • h = 1 – Tcold/Thot •  Highest possible fuel temperature • There is a maximum temperature at which the fuel can be used in normal performance •  Carefully control heat flow • Must understand heat transport in UO2 fuel 7

7. Outline • Phenomenology of Thermal Transport in Solids • Phonon Mediated Thermal Transport • Effects of Microstructure on Thermal Transport in UO2 • Phonon-phonon interactions • Phonon-point defect interactions • Phonon-dislocation interactions • Phonon-grain boundary interactions • Bringing It All Together 8

8. Part 1 Phenomenology of Thermal Transport in Solids 9

9. Heat Transfer Mechanisms Three fundamental mechanisms of heat transfer: • Convection • Conduction • Radiation • Convection is a mass movement of fluids (liquid or gas) rather than a real heat transfer mechanism (heat transfer is with convection rather than by convection) • Radiative heat transfer is important at high temperatures • Conduction is heat transfer by molecular or atomic motion • Heat conduction dominates in solids 10

10. Thermal Conduction Transfer of heat through a material not involving mass transfer or emission of electromagnetic radiation 11

11. Thermal Conduction 12

12. Thermal Conduction Why does his tongue stick to a metal pole? Would it stick to a wooden pole? Dumb and Dumber 13

13. T heat source x Phenomenology of Thermal Conductivity Fourier’s Law J = - kdT/dx Heat current Thermal conductivity 14

14. Units Fourier’s Law J = -k dT/dx [k] = Wm-2 / K m-1 = Wm-1K-1 J = Heat Flux (Density) = Heat per unit time per unit area [J] = J s-1 m-2 = Wm-2 [dT/dx] = K m-1 Also: [k] = BTU-inch/hour-square foot-°F 1 BTU-inch/hour-square foot-°F = 0.14Wm-1K-1 15

15. Thermal Conductivity of Solids • Log – log plot • Only 6 order of magnitude range • Some increase with power-law dependence and then decay • Amorphous materials increase slowly 16

16. Solids vs. Liquids Low k materials W/mK Water 0.6 Ethylene Glycol 0.25 PTFE 0.2 Wood 0.2 – 0.4 Engine Oil 0.15 Fiberglass 0.04 Air 0.03 Snow 0.05 – 0.25 (T < 0C) Silica Aerogel 0.003 Liquid Na - 72 W/mK 17

17. Heat Carriers • Electrons – metals only • Lattice vibrations / phonons – all systems 18

18. Part 2: Phonon-mediated Thermal Transport 19

19. Mechanisms of Thermal Conductivity 1 10 100 1000 Thermal conductivity (W/mK) YSZ Diamond Alumina Oriented polymers Copper Isotropic polymers Amorphous materials Phonons /vibrations phonons electrons phonons Electrical conductivity s(Cu ) ~ 5 105 (W cm)-1 s(diamond) ~ 10-16 (W cm)-1 20

20. Mechanisms of Thermal Conductivity 1 10 100 1000 Thermal conductivity (W/mK) YSZ Diamond Alumina Oriented polymers Copper Isotropic polymers Amorphous materials Phonons /vibrations phonons electrons phonons 21

21. Thermal Conductivity of Oxides Courtesy of D. R. Clarke 22

22. Advantages high melting point (~3000K) radiation stability chemical compatibility Disadvantages difficulty of fabrication low thermal conductivity low fuel density UO2 for Nuclear Fuel Figure from “Lecture notes on crystal structure”, ASU Intro to materials 23

23. Crystalline Materials: From Solids to Springs Heat transport from atomic vibrations Vibration of spring system similar to vibrations in solids 24

24. Long Wavelength Longitudinal Acoustic Phonon 25

25. Short Wavelength Longitudinal Acoustic Phonon 26

26. Longitudinal Optical Phonon 27

27. Acoustic vs. Optical Which has lower energy? Why? Lower Energy Less Compression of Springs 28

28. Transverse Phonons 29

29. Longitudinal vs. Transverse Phonons Which has lower energy? Why? Lower Energy Less Compression of Springs 30

30. Phonons Eigenmodes of harmonic potential Schematic dispersion curves for diamond http://physics.ucsc.edu/groups/condensed/moseley/simulations 31

31. Phonon-defect Phonon-boundary Phonon-phonon Phonon-electron Phonon Scattering Mechanisms Macroscale ***** *** * 32

32. Water Waves Water scattering from island defect Water waves scattering from each other http://learn.uci.edu/media/OC08/11004/OC0811004_Difraction.jpg 33

33. Thermal Conductivity Phonon mean free path Thermal conductivity k ~ 1/3CvvL Velocity of sound Specific heat 34

34. Temperature Dependence L=7mm • High T: • Phonon-phonon scattering • L ~ T-a • ~ 1  k ~ T-a Low T Quantum Solid Cv ~ T3  k ~ T3 L=1mm Surface Scattering k ~ 1/3cvvL LiF 35

35. How Large is the Mean Free Path? • = 1/3 Cv v L • k ~ 30 W/m.K • v ~5000 m/s • Cv ~ 3kB = 1.9 106 J/m3K •  • L ~ 10nm 36

36. Part 3 Effect of Microstructure on Thermal Transport in UO2 37

37. Phonon-defect Phonon-boundary Phonon-phonon Phonon-electron Phonon Scattering Mechanisms 38

38. Thermal transport in UO2 Experiment (ORNL) Simulations Triple axis spectrometer HB-3 at HFIR Fundamental theory test Phonon dispersions And line widths Different levels of theory Line width is affected by the microstructure Thermal conductivity from BTE 40

39. UO2: Phonon Dispersion and Lifetimes Phonon dispersion: Phonons lifetimes Experiment (ORNL) Acoustic modes Optical modes Simulations: 4 2 3 1 LA TA Arima et at., J. Alloys Compounds, 400 43 (2005) 41

40. Thermal Conductivity of UO2 42

41. Temperature Scaling k ~ T-a aExpt = 0.79 aBusker = 1.30 aYamada = 1.14 43

42. Atomistic Simulations of Thermal Conductivity 40% is coming from optical modes (at 1000K)! Detailed information about contribution to thermal conductivity from different phonons 44

43. Application to UO2 Force constants: Classical potentials - more than 20 is available (Govers, et al. 2007). Experimental Data: R.L. Gibby, J. Nucl. Mater. 166, 223 (1989). Potentials: Arima1, Busker, Grimes, Morelon and Walker (Nomenclature is from Govers, et al (2007)). 45

44. UO2: Potentials Sensitivity Thermal conductivity from different potentials: Good thermal conductivity <> good phonons and vice-versa: Very sensitive 46

45. Phonon/Point Defect Scattering Four steps: structure creation initial phonon wave packet generation well-defined longitudinal acoustic phonon MD simulation energy analysis doped region 48

46. doped region Point Defect Scattering • Incident phonon frequency: 2.96THz • 1.56% dopants in doped region • Δz = 200 unit cell 49

47. Snapshots t=0 t=26.3 ps t=60.1 ps t=201.3 ps -3000 -100 100 3000 z [a] Energy trapped in the defect region becomes negligible by ~200 ps  Defects decrease efficiency of heat transport 50

48. Effects of Off-stoichiometry UO2+x -0.05 < x < 0.25 Lattice Expansion Thermal Conductivity Prototype for point defects of various types 51

49. Thermal Conductivity of UO2+x κ falls rapidly with increasing defect concentration Reaches plateau by x=0.10 800K and 1600K the same for x>0.10 Very similar to yttria-stabilized zirconia 52

50. What do Vibrational Modes Look Like? x=0 (x< 0.1) x=0.125 (x > 0.1) • Non-Debye DOS at low f • Weakly structured DOS • no wave vectors, no polarization •  diffuse vibrational modes • similar to amorphous phase • Debye DOS at low f • Highly structured DOS • wavevectors, define polarization •  phonons • crystalline 53