Thermal Structure of the Laser-Heated Diamond Anvil Cell B. Kiefer and T. S. Duffy

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

2. Pressure, Depth and Temperature Conditions of the Earth’s Mantle 14 24 Pressure, GPa 135 Schubert et al., 2001 (after Jeanloz and Morris, 1986)

4. 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.

5. 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)

6. 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.

7. Temperature Dependence of the Thermal Conductivity

8. Predicted Thermal Conductivities Along a 2000K - Isotherm

9. Basic Geometry of a DAC (FWHM = 20 mm)

10. The Computational Grid Finite element modeling (Flexpde) * Local refinement of mesh. * 1600-4000 nodes

11. Temperature Distribution in LHDAC

12. Culet Temperature in LHDAC-Experiments Tmax=2200 K Filling=100*hS/hG 100% 50% 30 GPa: Gasket: Thickness = 30 mu; Diameter = 100mu Sample: Diameter = 60 mu Absorption length = 200 mu

13. Sample Filling and Thermal Gradients Filling=100*hS/hG 25% 10% 50% 75% 100% 90% 30 GPa: Gasket: Thickness = 30 mu; Diameter = 100mu Sample: Radius = 60 mu Absorption length = 200 mu Sample conductivity = 10 x insulator conductivity

14. Axial and Radial Temperature variations ΔT=Tmax-T(r=0,z=hS/2) dT Tave in R=5 μm aligned cylinder

15. Approximate solution Assumption: Radial temperature gradient << axial temperature gradient hS=sample thickness; hG=gasket thickness T0=Temperature the center of the culet TM=Peak-Temperature

16. Predicted Axial Temperature Drop ΔTaxial (K) d

17. TEM00 and TEM01 Heating Modes TEM00 TEM01 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

18. Heating Geometry and Axial Gradients in LHDAC-Experiments with Ar Homogeneous absorption + external heating 800 K Single-sided hotplate (1mu Fe-platelet) Al2O3-support

19. Heating Geometry and Axial Gradients in LHDAC-Experiments with Ar Microfurnace Double-sided hotplate (2x 1mu Fe-platelets) Microfurnace (Chudinovskikh and Boehler; 2001)

20. 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.

24. Thermal Conductivity of Some LHDAC-Components