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Thermal Structure of the Laser-Heated Diamond Anvil Cell B. Kiefer and T. S. Duffy Princeton University; Department of Geosciences. Pressure, Depth and Temperature Conditions of the Earth’s Mantle. 14. 24. Pressure, GPa. 135. Schubert et al., 2001 (after Jeanloz and Morris, 1986). - PowerPoint PPT Presentation
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Thermal Structure of the Laser-HeatedDiamond Anvil Cell
B. Kiefer and T. S. DuffyPrinceton University; Department of Geosciences
135
24
14
Pressure,
GPa
Pressure, Depth and Temperature Conditions of the Earth’s Mantle
Schubert et al., 2001 (after Jeanloz and Morris, 1986)
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.
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)
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
Temperature Dependence of the Thermal Conductivity
Predicted Thermal Conductivities Along a 2000K - Isotherm
Basic Geometry of a DAC(FWHM = 20 m)
Gasket
InsulationDiamond
Diamond
Sample
Al2O3
The Computational Grid
Finite element modeling (Flexpde) * Local refinement of mesh. * 1600-4000 nodes
Temperature (K/1000)
Insulation
Sample
Al2O3
Temperature Distribution in LHDAC
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
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
Axial and Radial Temperature variations
Tave in R=5 μmaligned cylinder
ΔT=Tmax-T(r=0,z=hS/2)T
;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
ΔTaxial (K)
Predicted Axial Temperature Drop
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
Heating Geometry and Axial Gradients inLHDAC-Experiments with Ar
Homogeneous absorption + external heating 800 K
Single-sided hotplate(1mu Fe-platelet)Al2O3-support
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
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.
Thermal Conductivity of Some LHDAC-Components
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