^{1}, Michael Wong

^{1,2}, D. Allen Dalton

^{1}, J. G. O. Ojwang

^{1}, Viktor V. Struzhkin

^{1}, Zuzana Konôpková

^{3,4}and Peter Lazor

^{3}

### Abstract

Knowledge of the thermal conductivity of Ar under conditions of high pressures and temperatures (*P-T*) is important for model calculations of heat transfer in the laser heated diamond anvil cell(DAC) as it is commonly used as a pressure transmitting medium and for thermal insulation. We used a modified transient heating technique utilizing microsecond laser pulses in a symmetric DAC to determine the *P-T* dependent thermal conductivity of solid Ar up to 50 GPa and 2500 K. The temperature dependent thermal conductivity of Ar was obtained by fitting the results of finite element calculations to the experimentally determined time dependent temperature of a thin Ir foil surrounded by Ar. Our data for the thermal conductivity of Ar are larger than that theoretically calculated using the Green-Kubo formalism, but they agree well with those based on kinetic theory. These results are important for ongoing studies of the thermal transport properties of minerals at pressures and temperatures native to the mantle and core.

We thank R. S. McWilliams for important comments and suggestions on the manuscript. We acknowledge support from NSF EAR 0711358 and EAR 1015239, Carnegie Institution of Washington, Army Research Office, STINT IG2010-2 062, and DOE*/*NNSA (CDAC).

I. INTRODUCTION

II. EXPERIMENTAL PROCEDURE

III. COMPUTATIONAL METHODS

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Thermal conductivity
- 48.0
- High pressure
- 27.0
- Diamond anvil cells
- 11.0
- Temperature measurement
- 11.0
- Chemical thermodynamics
- 9.0

## Figures

The DAC sample schematic. Ar sample fills the volume above and below the Ir foil (coupler). Since the coupler has a rectangular shape, Ar can freely move between the upper and the lower pockets.

The DAC sample schematic. Ar sample fills the volume above and below the Ir foil (coupler). Since the coupler has a rectangular shape, Ar can freely move between the upper and the lower pockets.

Representative radiometric time-resolved temperature measurements. The temperature is determined as an inverse slope of the linear lines fitted to the data. The data represent the thermal emission spectra (I_{λ}) transformed as shown and plotted as a function of an energetic variable. *C* _{1} and *C* _{2} are first and second radiation constant with values of *C* _{1} = 119.1044 (Wnm^{2}), *C* _{2} = 1.4388 × 10^{7} (nm K), respectively.

Representative radiometric time-resolved temperature measurements. The temperature is determined as an inverse slope of the linear lines fitted to the data. The data represent the thermal emission spectra (I_{λ}) transformed as shown and plotted as a function of an energetic variable. *C* _{1} and *C* _{2} are first and second radiation constant with values of *C* _{1} = 119.1044 (Wnm^{2}), *C* _{2} = 1.4388 × 10^{7} (nm K), respectively.

The distances between the Ir foil and diamond culets measured using the spectral distance between the interference fringes. The fits applied to the data are used for the sample cavity dimensions in the FE calculations.

The distances between the Ir foil and diamond culets measured using the spectral distance between the interference fringes. The fits applied to the data are used for the sample cavity dimensions in the FE calculations.

Temperature history of the DAC for pulse laser heating at 43 GPa. Many such plots were constructed for pressures up to 50 GPa. Radiometric data from the Wien’s fits (the error bars are the temperature determination uncertainties) illustrate an increase in the sample temperature corresponding to the front edge of the laser pulse and then plateaus before decaying below the detection limit. The thick solid line is the results of the FE calculations, which represent the best fit to these data yielding the following parameters for the temperature dependent thermal conductivity of Ar: K_{300} = 72 W/(K m), m = 1.35—see Table I for the description of parameters. The best fit to the data calculated in the assumption that the emissivity of Ir decreased by 10% at 43 GPa essentially coincides with this curve (not shown); the parameters yielded are K_{300} = 79 W/(K m), m = 1.7. The thermal history, calculated taking into account the isobaric changes in density of Ar and Ir and the isobaric change in the thermal heat capacity of Ir with temperature, is shown by a thin dashed line. The temporal profile (a.u. of intensity) of the incident laser pulse (measured via a photodiode) is also included.

Temperature history of the DAC for pulse laser heating at 43 GPa. Many such plots were constructed for pressures up to 50 GPa. Radiometric data from the Wien’s fits (the error bars are the temperature determination uncertainties) illustrate an increase in the sample temperature corresponding to the front edge of the laser pulse and then plateaus before decaying below the detection limit. The thick solid line is the results of the FE calculations, which represent the best fit to these data yielding the following parameters for the temperature dependent thermal conductivity of Ar: K_{300} = 72 W/(K m), m = 1.35—see Table I for the description of parameters. The best fit to the data calculated in the assumption that the emissivity of Ir decreased by 10% at 43 GPa essentially coincides with this curve (not shown); the parameters yielded are K_{300} = 79 W/(K m), m = 1.7. The thermal history, calculated taking into account the isobaric changes in density of Ar and Ir and the isobaric change in the thermal heat capacity of Ir with temperature, is shown by a thin dashed line. The temporal profile (a.u. of intensity) of the incident laser pulse (measured via a photodiode) is also included.

Thermal conductivity as a function of temperature. Dashed lines show the uncertainty interval. The points indicate thermal conductivity results from MD simulations from Ref. 22 and the corresponding line is the fit to these results.

Thermal conductivity as a function of temperature. Dashed lines show the uncertainty interval. The points indicate thermal conductivity results from MD simulations from Ref. 22 and the corresponding line is the fit to these results.

Thermal conductivity as a function of pressure at 300 K. The data points (closed circles) are those determined in this work at 300 K with the corresponding errors. The separate solid and dashed lines show the results of the MD calculations using the Green-Kubo method and kinetic theory, respectively.^{22} The squares and the thin dashed line show the Leibfried-Schlömann equation (1) fit to our data.

Thermal conductivity as a function of pressure at 300 K. The data points (closed circles) are those determined in this work at 300 K with the corresponding errors. The separate solid and dashed lines show the results of the MD calculations using the Green-Kubo method and kinetic theory, respectively.^{22} The squares and the thin dashed line show the Leibfried-Schlömann equation (1) fit to our data.

## Tables

Thermochemical parameters of materials used in model FE calculations.

Thermochemical parameters of materials used in model FE calculations.

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