Motivation:

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)
hG30µm hS15µm (SF 50) h(Al2O3)7.5µm TEM00
mode
6
Sample Filling and Temperature Distribution
Optically thin sample l gtgt 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
Laser Heating Mode and Temperature Gradients
TEM00 TEM01
9
Analytical Prediction of the Axial Temperature
Gradient
?TTmax - T(r0,zhS/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 gtgt 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) Microf
urnace (Chudinovskikh and Boehler 2001)
Optically thin sample l gtgt hs and kS/kPM
10 kc/T TEM00 heating mode
12

• Future Work
• Effect of functional form of the thermal
  conductivity. Deviations from k1/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.