Specific heat

2. Specific heat

3. Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO

4. Thermal expansion

5. Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO

6. Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO

12. Once have F(V.T) -- can get everything

14. Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO

15. Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO

22. M-G EOS Parameters -- from Stixrude et al, 2005 with modifications

24. High pressure experiments

25. Static Measurements: 2) Anvil Devices: 2 broad types • Large volume multi-anvil press (MAP) • ii) Symmetric opposed anvil design (many different designs e.g. DAC)

26. Types of Large Volume Presses • Piston-Cylinder- 4-6 Gpa • Multi-Anvil- 25GPa • Paris-Edinburgh- 12GPa

27. A large-volume high-pressure and high-temperature apparatus for in situ X-ray observation, ‘SPEED-Mk.II’ By Katsura et al SPEED-Mk.II’ is a multi-anvil KAWAI-type press

28. Large volume multi anvil cells: 3 orders of magnitude higher than DACs! Large volume: House probes, synthesize larger specimens, some experiments require large V (e.g. ultrasonic interferometry) Hydrostatic Pressure: Closer, since squeezing from 8 directions, But, not easily used with gas pressure medium Pressures: Top of lower mantle at best with sintered diamonds and synchrotron radiation

29. P/T Measurement • Pressure can be measured by calibrating the machine to a sample with well known diffraction patterns, such as NaCl. • Since this is a large volume press, temperature can be measured directly with thermocouples.

30. Diamond Anvil Cells: Why Diamonds? Can use:Steel, tungsten carbide, boron carbide, sapphire, cubic zirconia, sintered diamond, or single-crystal diamond Single crystal diamond: 1)Strongest material known 2) Transparent (IR, optical, UV, and X-ray) 3)Non-magnetic insulator: , 

31. Creating Temperature: 3 ways: 1) External heating 2) Internal heating 3) IR Laser Heating

32. unheated ruby chips Sample size Optics to enlarged image Pressure medium P-T gradient

34. Laser heating - use black body radiation T: temperature I: intensity : wavelength Cs: constants : emissivity • is wavelength dependent But dependence not known for many materials! (known for Fe) • Perfect black body:  = 1 Grey body:  < 1

36. Advances in laser heating… • Double sided laser heating • - split beam and heat from both ends • Or mix 2 lasers at different modes - flat T distribution • Can now get temps ~3000K (+/- 10K) at high P • Bottom line: use caution when trusting results from laser heating experiments prior to 1996-98

37. Pressure media • low shear strength • Chemical inertness • Low thermal conductivity • Low emissivity • Low absorption of laser light • Ar 8GPa, Ne 20GPa, He >100GPa • Draw back: high fluorescence, high compressibility

38. Pressure gradients

39. Synchrotron Radiation • Bi-product of particle accelerators • Transverse emission of EM radiation tangential to ring • Advantages: • Focussing (on small samples) • Bandwidth • Strength to penetrate high pressure vessels • Polarized - elasticity, structure, density of states • Now: ‘3rd generation’ synchrotron radiation

40. Measuring Material Parameters… In-Situ X-Ray Diffraction • Provides Crystal Structure, Density and melting points • Synchrotron Radiation provides highly collimated x-ray source • Braggs Law: 2q = angle of diffraction d = spacing of crystal planes  = wavelength of X-ray

42. Measuring Material Parameters… X-Ray Spectrography • Use polychromatic X-rays and Be gaskets • Observe absorption freq. • Absorption changes with phase • Observe: • Atomic Coordination • Structures • Electronic/Magnetic Properties

43. For X-ray studies: • Know temp gradients • Suitable pressure mediums • Angular Diffraction method • Monochromatic X-rays used • Best for quantitative intensity • Precision Lattice Parameter measurement • Energy Diffraction method • Fastest method • Gasket Selection • Be allows trans-gasket measurements at 4 keV+ • Diamonds allow hard X-rays. 12 keV+ X-ray detected lattice parameters during a phase transformation

44. Measuring Material Parameters… Measurement of Pressure • Ruby Chips Fluorescence Method • Freq. shift of ruby with increasing pressure • Linear to 30 GPa • Calibrated to 100 GPa by Raman Spec. • Calibrated to >200 GPa by Gold • Accurate to 15-20% at 200 GPa • Diffuses with temperature (>700K) • Ruby and Diamond Fluorescence overlap between 120-180 GPa • KEY: Allows sampling at multiple points in pressure medium

45. Need higher pressure

46. Optical Probes • Optical Absorption • High pressure melting, crystallization, phase transitions • Infrared Spectroscopy • Detailed bonding properties • Raman Spectroscopy (10-1000cm-1) • Most definitive diagnostic tool for the identification of specific molecules • Diagnostic evidence for phase transition in simple molecular compounds • Brillouin Spectroscopy (<1cm-1) • Wave velocities and elasticity tensor • New primary pressure standard • Fluorescence Spectroscopy • Electronic states

47. Measuring Material Parameters… Raman Spectroscopy • Raman Techniques • Measures scattering of monochromatic light due to atomic vibrations. • Provides vibration frequencies in a solid • Temperature = noise : most samples temperature quenched. • Synchrotron radiation: a powerful, narrow beam of highly collimated light source. • Parameters Measured • Entropies • Specific Heats • Grüneisen Parameters • Phase Boundaries

48. Elastic Moduli: , , Vp, Vs 3 ways to get these: Static compression (no info on shear properties) Shock compression Acoustic vibration (frequencies 10^13 Hz) (applicability?)

49. Extending elastic observations to higher P-T: • Brillouin Spectroscopy - • Optical beam scattered by an acoustic wave • Compression and dilatation by acoustic wave results in change in refractive index of material • Look at Doppler shift of laser frequency - get wave velocity of the acoustic wave • can get up to ~60GPa • at ~2500K in DAC with laser • (mid lower mantle)

50. Some conclusions • Early DAC measurements suspect because non-hydrostatic • Still very hard to do simultaneous high T and P – very few elasticity measurements at high T • Pressure calibrations improving and becoming more consistent – but take care when using older measurements!