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