Specific heat
description
Transcript of Specific heat
![Page 1: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/1.jpg)
![Page 2: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/2.jpg)
Specific heat
![Page 3: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/3.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 4: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/4.jpg)
Thermal expansion
![Page 5: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/5.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 6: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/6.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 7: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/7.jpg)
![Page 8: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/8.jpg)
![Page 9: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/9.jpg)
![Page 10: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/10.jpg)
![Page 11: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/11.jpg)
![Page 12: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/12.jpg)
Once have F(V.T) -- can get everything
![Page 13: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/13.jpg)
![Page 14: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/14.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 15: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/15.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 16: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/16.jpg)
![Page 17: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/17.jpg)
![Page 18: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/18.jpg)
![Page 19: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/19.jpg)
![Page 20: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/20.jpg)
![Page 21: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/21.jpg)
![Page 22: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/22.jpg)
M-G EOS Parameters -- from Stixrude et al, 2005 with modifications
![Page 23: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/23.jpg)
![Page 24: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/24.jpg)
High pressure experiments
![Page 25: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/25.jpg)
2) Anvil Devices: 2 broad types
Static Measurements:
i) Large volume multi-anvil press
(MAP)
ii) Symmetric opposed anvil design (many different designs e.g. DAC)
![Page 26: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/26.jpg)
Types of Large Volume Presses
• Piston-Cylinder- 4-6 Gpa
• Multi-Anvil- 25GPa
• Paris-Edinburgh- 12GPa
![Page 27: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/27.jpg)
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
![Page 28: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/28.jpg)
Large volume multi anvil cells:
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
3 orders of magnitude higher than DACs!
![Page 29: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/29.jpg)
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.
![Page 30: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/30.jpg)
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: ,
![Page 31: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/31.jpg)
Creating Temperature:
3 ways:
1) External heating
2) Internal heating
3) IR Laser Heating
![Page 32: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/32.jpg)
unheated ruby chips
Sample size
Optics to enlarged image
Pressure medium
P-T gradient
![Page 33: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/33.jpg)
![Page 34: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/34.jpg)
Laser heating - use black body radiationT: temperatureI: intensity: wavelengthCs: constants: emissivity
Perfect black body: = 1Grey body: < 1
is wavelength dependent
But dependence not known for many materials! (known for Fe)
![Page 35: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/35.jpg)
![Page 36: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/36.jpg)
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
![Page 37: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/37.jpg)
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
![Page 38: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/38.jpg)
Pressure gradients
![Page 39: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/39.jpg)
Synchrotron Radiation
• Bi-product of particle accelerators
• Transverse emission of EM radiation tangential to ring
• Advantages: 1) Focussing (on small samples)2) Bandwidth3) Strength to penetrate high pressure
vessels4) Polarized - elasticity, structure,
density of states
Now: ‘3rd generation’ synchrotron radiation
![Page 40: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/40.jpg)
• 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
In-Situ X-Ray DiffractionMeasuring Material Parameters…
€
=2d sin(q)
![Page 41: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/41.jpg)
![Page 42: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/42.jpg)
X-Ray Spectrography• Use polychromatic X-rays and Be gaskets• Observe absorption freq.• Absorption changes with phase
• Observe:– Atomic Coordination– Structures– Electronic/Magnetic Properties
Measuring Material Parameters…
![Page 43: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/43.jpg)
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 keV+
• Diamonds allow hard X-rays. 12 keV+
![Page 44: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/44.jpg)
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
Measuring Material Parameters…
![Page 45: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/45.jpg)
Need higher pressure
![Page 46: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/46.jpg)
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
![Page 47: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/47.jpg)
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
Measuring Material Parameters…
![Page 48: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/48.jpg)
Elastic Moduli:, , Vp, Vs
3 ways to get these:
1) Static compression (no info on shear properties)2) Shock compression3) Acoustic vibration (frequencies 10^13 Hz) (applicability?)
![Page 49: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/49.jpg)
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)
![Page 50: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/50.jpg)
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!
![Page 51: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/51.jpg)
![Page 52: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/52.jpg)
Blue=olivine, green=MgO, orange=forsterite, black=Al2O3, brown=grossular, purple=pyrope, red=CaO
![Page 53: Specific heat](https://reader036.fdocuments.in/reader036/viewer/2022062520/56815d46550346895dcb4baf/html5/thumbnails/53.jpg)
Raman Spectroscopy