Specific heat Blue olivine green Mg O orange forsterite black Al

Specific heat

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

Thermal expansion

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

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

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

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

High pressure experiments

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

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

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 multianvil KAWAI-type press

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

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

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

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

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

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

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 ~3000 K (+/- 10 K) at high P - Bottom line: use caution when trusting results from laser heating experiments prior to 1996 -98

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

Pressure gradients

Synchrotron Radiation • Bi-product of particle accelerators • Transverse emission of EM radiation tangential to ring • 1) 2) 3) Advantages: Focussing (on small samples) Bandwidth Strength to penetrate high pressure vessels 4) Polarized - elasticity, structure, density of states Now: ‘ 3 rd generation’ synchrotron radiation

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: 2 q = angle of diffraction d = spacing of crystal planes = wavelength of X-ray

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

X-ray detected lattice parameters during a phase transformation 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 ke. V+ • Diamonds allow hard X-rays. 12 ke. V+

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 (>700 K) Ruby and Diamond Fluorescence overlap between 120 -180 GPa – KEY: Allows sampling at multiple points in pressure medium

Need higher pressure

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

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

Elastic Moduli: , , Vp, Vs 3 ways to get these: 1) Static compression (no info on shear properties) 2) Shock compression 3) Acoustic vibration (frequencies 10^13 Hz) (applicability? )

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 ~60 GPa • at ~2500 K in DAC with laser • (mid lower mantle)

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!

Blue=olivine, green=Mg. O, orange=forsterite, black=Al 2 O 3, brown=grossular, purple=pyrope, red=Ca. O

Raman Spectroscopy