Thermal Structure of the Laser-Heated Diamond Anvil Cell B. Kiefer and T. S. Duffy
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Transcript of Thermal Structure of the Laser-Heated Diamond Anvil Cell B. Kiefer and T. S. Duffy
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Thermal Structure of the Laser-HeatedDiamond Anvil Cell
B. Kiefer and T. S. DuffyPrinceton University; Department of Geosciences
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135
24
14
Pressure,
GPa
Pressure, Depth and Temperature Conditions of the Earth’s Mantle
Schubert et al., 2001 (after Jeanloz and Morris, 1986)
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Models of the Heat Transfer in the Laser-Heated DAC
Analytical/ Semi-Analytical Models
Bodea and Jeanloz (1989) -- Basic description of radial and axial gradients
Li et al (1996) -- Effect of external heating on radial gradient
Manga and Jeanloz (1996, 1997) -- Axial T gradient, no insulating medium
Panero and Jeanloz (2001a, 2001b) -- Effect of laser mode and insulation on
radial gradients
Panero and Jeanloz (2002) -- Effects of T gradients on X-ray diffraction patterns
Finite Element and Finite Difference Calculations
Dewaele et al. (1998) -- temperature field and thermal pressures with insulated samples
Morishima and Yusa (1998) -- FD method, non-steady state, low resolution.
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Heat Flow Models for the Laser-Heated DAC:
What Can We Learn?
Sample filling fraction (sample thickness/gasket thickness)
Sample/insulator thermal conductivity ratio
Laser mode (Tem00 vs Tem01)
Optically thin vs optically thick samples
Single-sided heating vs double-sided heating
Complex sample geometries (double hot plate, micro-furnace)
Thermal structure at ultra-high pressures
Asymmetric samples
Diamond heating
Time Dependent calculations (cooling speed, pulsed lasers)
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zrFTz
kz
Tr
krrr
,1
Background
• Steady-State calculations.• Axi-symmetric problem.
Interfaces: • Temperature and heatflow are continuous.• Outermost boundary fixed at T=300K.
Thermal conductivity: k(P,T)=g(P)*300/T.Only sample absorbs: Absorption length l=200 μm.
lzRrQzrF W /exp/exp, 20
mFWHMFWHMRW 20;83.0
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Temperature Dependence of the Thermal Conductivity
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Predicted Thermal Conductivities Along a 2000K - Isotherm
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Basic Geometry of a DAC(FWHM = 20 m)
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Gasket
InsulationDiamond
Diamond
Sample
Al2O3
The Computational Grid
Finite element modeling (Flexpde) * Local refinement of mesh. * 1600-4000 nodes
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Temperature (K/1000)
Insulation
Sample
Al2O3
Temperature Distribution in LHDAC
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30 GPa: Gasket: Thickness = 30 mu; Diameter = 100mu Sample: Diameter = 60 mu Absorption length = 200 mu
Culet Temperature in LHDAC-Experiments
Tmax=2200 K
100%
50%
Filling=100*hS/hG
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Sample Filling and Thermal Gradients
30 GPa: Gasket: Thickness = 30 mu; Diameter = 100mu Sample: Radius = 60 mu Absorption length = 200 mu
10%
25%
50%
75%
90%100%
Filling=100*hS/hG
Sample conductivity = 10 x insulator conductivity
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Axial and Radial Temperature variations
Tave in R=5 μmaligned cylinder
ΔT=Tmax-T(r=0,z=hS/2)T
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;G
S
hh
X )300,()300,(KPkKPk
YM
S
)1(21
1
0max 1
XY
M
axialTT
TT
Approximate solution
Assumption: Radial temperature gradient << axial temperature gradient
hS=sample thickness; hG=gasket thicknessT0=Temperature the center of the culetTM=Peak-Temperature
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ΔTaxial (K)
Predicted Axial Temperature Drop
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TEM00 and TEM01 Heating Modes
TEM01
TEM00TEM01
TEM00
LaserPower
FWHM
30 GPa: Gasket: Thickness = 30 mu; Diameter = 100mu Sample: Thickness = 15 mu; Diameter = 60 mu FWHM = 20 mu; Absorption length = 200 mu
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Heating Geometry and Axial Gradients inLHDAC-Experiments with Ar
Homogeneous absorption + external heating 800 K
Single-sided hotplate(1mu Fe-platelet)Al2O3-support
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Double-sided hotplate (2x 1mu Fe-platelets)Microfurnace (Chudinovskikh and Boehler; 2001)
Heating Geometry and Axial Gradients inLHDAC-Experiments with Ar
Diamond
Diamond
Laser
InsulatingGasketSample
Micro-furnace medium
Microfurnace
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Conclusions:• FE-modeling can be an important tool for the design and the analysis of LHDAC experiments.
•Axial temperature gradients controlled bysample/insulator conductivity ratio and filling fraction.
• Microfurnace assemblage and double-sided hotplate technique can yield low axial gradients.
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Thermal Conductivity of Some LHDAC-Components
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