Comsol Multiphysics

Finite element based method of Comsol Multiphysics numerial modeling package gives the op-portunity to compute heat transfer in the laser-heated diamond anvill cell. It allows to vary ge-ometries of the system (diamonds, gasket, sample, pressure medium), and materials by settingappropriate values of thermal conductivity, even temperature dependent. The first step is to drawa geometry in real dimensions. Since the model has cylindrical symmetry around the axis thatcorresponds to the centerline of the laser beam we reduce the problem to 2D axisymmetric mode.

Conductive heat transport obeys the heat equation

∇ · (−κ(T )∇T ) = Q

where T is temperature, κ temperature dependent thermal conductivity and Q is heat source. Incase of iron sample, laser power is absorbed in very thin surface layer proportional to skin depthsof metal materials, which is usually of the order of nanometres. Thus, laser heating is modeledas heat flux on the heated side of the sample given by total laser power. Comsol then solves theheat equation with appropriate boundary conditions. The output is temperature distribution fromwhich we can extract radial and axial temperature gradients across the sample as well as totalnormal heat flux.

FIGURE 4: Temperature distribution in the sample as a solution of Comsol Multiphysics

High Temperature

In order to achieve temperature in excess of thousands of Kelvins in our samples we use Nd-dopedYttrium-Aluminum-Garnet laser with suitable wavelength for absorption (YAG, λ = 1.06µm).Temperature of the sample is measured by spectral radiometry technique. The incandescent lightfrom heated iron foil is collected in a spectral range between 500 and 800 nm and brought tospectrograph and CCD detector.

FIGURE 3: Schematics of the laser heating system. DAC-diamond anvil cell, LS-light source,OBJ-objective, PC-computer, L-lens, M-mirrors

FIGURE 2: Diamond Anvil Cell with details of the diamonds and diamond culet

Pressures in laser-heated DAC are measured by the ruby fluorescence method. Ruby has a strongfluorescence spectrum with a large pressure shift, but unfortunately also a large shift with temper-ature. However, pressure can be accurately measured from unheated ruby chips anywhere in thepressure chamber. The ruby scale has been calibrated up to 180 GPa against primary shock-wavestandards.

High Pressure

With decades of development, the diamond-anvill cell (DAC) has emerged as uniquely providingthe capability of a wide range of in situ measurements over the entire P − T range of the Earth.These conditions can be kept constant for long periods of time (hours), and this allows visual,spectroscopic, and X-ray diffraction measurements. The principal components of a diamond cellare two diamonds anvils compressing a gasket. A hole drilled in the center of the gasket serves asa pressure chamber. The pressure chamber is filled with material that thermally isolates the ironsample and prevents it from touching the diamonds.

DAC preparation

• diamonds: type IIa, type I

• gasket: BeCu, Stainless Steel

• sample: 2 µm and 5 µm pure iron foils

• pressure medium: MgO and Al2O3

• pressure chamber ∼ 150µm

Introduction

Iron in the deep interior of the Earth has properties, which are much different from those found atambient conditions. For example, its melting point, chemical affinity, magnetism, and density aredramatically modified at high pressures and temperatures prevailing inside the Earth’s core whereiron represents a dominating phase. Knowledge of these modified properties is required in orderto understand the internal structure and evolution of the Earth as well as other planetary bodiesin the Solar system. These facts have stimulated and driven high-pressure studies on iron aroundthe world, including the geochemistry group at the program of Solid Earth Geology, where, in thepast, research focused on melting, and structural and elastic properties of iron at high pressuresand temperatures.

In the current PhD project, the main focus is on thermal and elastic properties of iron at highpressures and temperatures and their implications for the thermal evolution of the Earth. Highpressure – high temperature experiments in conjunction with theory and numerical modelingprovide powerful tool for determination physical properties od material such as, e.g. thermalconductivity.

FIGURE 1: Research on the Earth’s interior: links between experiment and theory

Zuzana Konopkova, Peter Lazor, Department of Earth Sciences, Villavagen 16, 752 36 Uppsala, Sweden

Physics and Chemistry of Iron in the Earth’s Interior