Thermal Structure of the Laser-Heated Diamond Anvil Cell B. Kiefer and T. S. Duffy Princeton University; Department of Geosciences

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 (Tem 00 vs Tem 01 ) 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)

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.

Temperature Dependence of the Thermal Conductivity

Predicted Thermal Conductivities Along a 2000K - Isotherm

Basic Geometry of a DAC (FWHM = 20  m)

The Computational Grid Finite element modeling (Flexpde) * Local refinement of mesh. * nodes

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 T max =2200 K 100% 50% Filling=100*h S /h G

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*h S /h G Sample conductivity = 10 x insulator conductivity

Axial and Radial Temperature variations T ave in R=5 μm aligned cylinder ΔT=T max -T(r=0,z=h S /2) TT

Approximate solution Assumption: Radial temperature gradient << axial temperature gradient h S =sample thickness; h G =gasket thickness T 0 =Temperature the center of the culet T M =Peak-Temperature

ΔT axial (K) Predicted Axial Temperature Drop 

TEM00 and TEM01 Heating Modes TEM01 TEM00 TEM01 TEM00 Laser Power 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 in LHDAC-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 in LHDAC-Experiments with Ar Microfurnace

Conclusions: FE-modeling can be an important tool for the design and the analysis of LHDAC experiments. Axial temperature gradients controlled by sample/insulator conductivity ratio and filling fraction. Microfurnace assemblage and double-sided hotplate technique can yield low axial gradients.

Thermal Conductivity of Some LHDAC-Components