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Motivation: Physical Conditions in LHDAC experiments. Exploration of parameter space:

Finite-Element Modeling of the Thermal Structure in Laser-Heated Diamond Anvil Cell Experiments. Boris Kiefer Physics Department; New Mexico State University, NM, USA. Tom. S. Duffy Department of Geosciences, Princeton University, Princeton, USA. Motivation: Physical Conditions in LHDAC

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Motivation: Physical Conditions in LHDAC experiments. Exploration of parameter space:

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  1. Finite-Element Modeling of the Thermal Structure in Laser-Heated Diamond Anvil Cell Experiments Boris Kiefer Physics Department; New Mexico State University, NM, USA Tom. S. Duffy Department of Geosciences, Princeton University, Princeton, USA • Motivation: • Physical Conditions in LHDAC • experiments. • Exploration of parameter space: • Temperature distribution in LHDAC experiments. Axial and radial Gradients. • Heating modes: TEM00 and TEM01. • Different assemblages. • Identification of key parameters in LHDAC experiments.

  2. Previous Work: • Peak temperature is proportional to sample thickness; axial temperature distribution determined by heat loss through diamonds.(Bodea and Jeanloz, 1989). • Thermal pressure is non neglegible in LHDAC experiments; 20-30% of the nominal pressure (Dewaele et al., 1998). • Thermal structure in DAC can cause peak splitting  apparent phase transitions (Panero and Jeanloz, 2002).

  3. Finite Element Modeling of the Thermal Structure in LHDAC • Boundary Conditions: • Continuous Temperature across Material Boundaries. • Continuous Heatflow Between Different Materials. • Radiative contribution neglected.

  4. Computational Strategy • Complete thermal structure. • Steady State calculations. • Cylindrical symmetry (2-d). • Code: FlexPDE (PDE Solutions Inc.) Heat Conduction Equation:

  5. Geometry Heating Laser Diamond Argon Sample Gasket Al2O3 Diamond T(r,z) in Sample and Insulating Medium Temperature Argon Sample Al2O3 T (1000K) hG=30μm; hS=15μm (SF 50%); h(Al2O3)=7.5μm TEM00 mode

  6. Sample Filling and Temperature Distribution Optically thin sample: l >> hs and kS/kPM = 10 Gasket thickness 30 μm; TEM00 heating mode Axial Filling: 10% 25% 50% 75% 90% 100% Radial

  7. Analytical Model for Optically Thin Samples Boundary conditions: T(hG/2) = T(-hG/2) = 300 k = T0 TM = maximum temperature. T0 = background temperature. kS = cS/T and kM =cM/T

  8. Optically thin sample: l >> hs and kS/kPM = 10 Sample Filling: 50%; hG = 30 μm Laser Heating Mode and Temperature Gradients TEM00 TEM01

  9. Analytical Prediction of the Axial Temperature Gradient ΔT=Tmax - T(r=0,z=hS/2) Temperature Drop (K)

  10. Axial Temperature Gradient and Sample Geometry - I Reference Calculation 800 K External Heating Al – support (2.5 μm thick) Single-sided Fe – platelet (1 μm thick) Optically thin sample: l >> hs and kS/kPM = 10 TEM00 heating mode Sample Filling: 50%; hG = 30 μm

  11. Axial Temperature Gradient and Sample Geometry - II Sample Filling: 50%; hG = 30 μm Double-sided hotplate (2x 1mu Fe-platelets) Microfurnace (Chudinovskikh and Boehler; 2001) Optically thin sample: l >> hs and kS/kPM = 10; k=c/T TEM00 heating mode

  12. Future Work: • Effect of functional form of the thermal conductivity. Deviations from k=1/T behavior. • Radiative component. • Combined TEM00 and TEM01 mode. Multi mode heating. • Time dependent calculations of thermal structure, equilibration times and indeuced temperature fluctuations due to laser heating.

  13. Conclusions: • Thermal Structure Depends Most Strongly on the Thermal Conductivity ratio of sample and insulating medium. • Sample Filling has an Equally Strong Effect on the Thermal Structure. • Microfurnace assemblage and double-sided hotplate technique appear to be most promissing. • FE-modeling can be an important tool for the design and the analysis of LHDAC • experiments.

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