Thermal Conductivity of Helium and Argon at High Pressure and High Temperature

At a Glance

Metadata	Details
Publication Date	2022-09-26
Journal	Materials
Authors	Wen‐Pin Hsieh, Yi‐Chi Tsao, Chun‐Hung Lin
Institutions	Institute of Earth Sciences, Academia Sinica, National Taiwan University
Citations	6
Analysis	Full AI Review Included

Executive Summary

This research utilized Time-Domain Thermoreflectance (TDTR) coupled with an Externally Heated Diamond-Anvil Cell (EHDAC) to precisely determine the thermal conductivity (Λ) of Helium (He) and Argon (Ar) under extreme pressure-temperature (P-T) conditions (up to 55 GPa and 973 K).

He Thermal Behavior: Liquid He exhibits a positive temperature dependence (Λ ~ T^0.45 at 10.2 GPa), consistent with the minimum thermal conductivity model for liquids, where increased temperature enhances energy transfer efficiency.
Ar Thermal Behavior: Crystalline solid Ar shows a typical negative temperature dependence (Λ ~ T^-1.37 at 19 GPa), characteristic of dielectrics where phonon scattering increases with temperature.
Pressure Dependence: Solid Ar displays a strong pressure dependence (Λ ~ P^1.25), significantly higher than that of solid He (Λ ~ P^0.72). Solidification of He at ~12 GPa results in an abrupt ~30% increase in Λ.
Modeling Discrepancy: The Leibfried-Schlömann (LS) equation, a common model for dielectric thermal conductivity, significantly overpredicts the measured Λ for both solid He and solid Ar at high pressures, suggesting the influence of additional phonon scattering mechanisms.
Engineering Impact: The results substantially improve the accuracy of thermal modeling required to determine temperature profiles and heat flow within Diamond-Anvil Cell (DAC) experiments using He or Ar as pressure media.
Planetary Science Relevance: The P-T dependence data for He provides crucial constraints for modeling the structural and thermal evolution dynamics of He-containing gas giant planets (e.g., Jupiter and Saturn).

Technical Specifications

Parameter	Value	Unit	Context
Maximum Pressure (He)	55.2	GPa	Room Temperature
Maximum Pressure (Ar)	49	GPa	Room Temperature
Maximum Temperature	973	K	Fixed Pressure (10.2 GPa He, 19 GPa Ar)
Λ (Liquid He, Start)	0.4	W m^-1 K^-1	1.3 GPa, 300 K
Λ (Solid He, Max)	8.8	W m^-1 K^-1	55.2 GPa, 300 K
Λ (Solid Ar, Max)	30	W m^-1 K^-1	49 GPa, 300 K
He Solidification Jump	~30	% Increase	Across liquid-solid transition (~12 GPa)
Liquid He Pressure Exponent (n_l)	0.86 (±0.048)	Dimensionless	Λ ~ Pⁿ (1.3 GPa to 11.4 GPa)
Solid Ar Pressure Exponent (α)	1.25 (±0.025)	Dimensionless	Λ ~ P^α (2.1 GPa to 49 GPa)
Liquid He Temperature Exponent (m_l)	0.45 (±0.036)	Dimensionless	Λ ~ T^m (10.2 GPa)
Solid Ar Temperature Exponent (β)	-1.37 (±0.005)	Dimensionless	Λ ~ T^β (19 GPa)
TDTR Modulation Frequency	8.7	MHz	Pump beam modulation
TDTR Laser Wavelength	785	nm	Central wavelength
Transducer Film Thickness	~90	nm	Aluminum (Al) film
Estimated Analysis Uncertainty	~13	% Error	Pressure < 30 GPa

Key Methodologies

Substrate and Transducer Preparation: Borosilicate glass (D 263®) was polished to ~10 µm thickness to serve as a low thermal conductivity reference substrate. A ~90 nm-thick Al film was thermally evaporated onto the glass to function as the thermal transducer for TDTR.
DAC Assembly: The coated substrate was loaded into a symmetric DAC (300 µm culet) using a Rhenium (Re) gasket. High-purity He or Ar gas (99.9999%) was loaded as the pressure medium and sample material.
Pressure and Temperature Control: An Externally Heated DAC (EHDAC) was used in conjunction with a gas membrane system to achieve simultaneous high P-T conditions (up to 973 K) while maintaining fixed pressure (e.g., 10.2 GPa for He, 19 GPa for Ar) by minimizing thermal pressure effects.
In Situ Characterization: Pressure was monitored using the pressure-shifted fluorescence or Raman spectrum of ruby balls placed adjacent to the substrate. The phase of He (liquid or solid) was confirmed using time-domain stimulated Brillouin scattering.
Thermal Measurement (TDTR): An ultrafast optical pump-probe setup was used. A modulated pump beam (8.7 MHz) heated the Al transducer, and a probe beam monitored the resulting change in the Al film’s optical reflectivity (measured as the ratio of in-phase V_in and out-of-phase V_out components).
Data Analysis and Modeling: The measured V_in/V_out ratio was fitted using a bi-directional thermal model. Key input parameters included the volumetric heat capacity of all layers (glass, Al, He/Ar). The volumetric heat capacity of liquid He was assumed constant at 4 J cm^-3 K^-1 for high P-T conditions.

Commercial Applications

High-Pressure Research and Metrology:
- DAC Thermal Management: The derived P-T dependencies for He and Ar are essential for accurately calculating the temperature distribution and heat flow within DACs, improving the reliability of high-pressure material property measurements.
- TDTR Calibration Standards: Provides necessary thermal property data for common pressure media, enhancing the precision and calibration of TDTR systems used for characterizing thin films and bulk materials under extreme conditions.
Aerospace and Planetary Modeling:
- Gas Giant Interior Dynamics: The thermal conductivity data for He under relevant P-T conditions is critical for developing accurate computational models of the thermal and structural evolution of gas giant planets (like Jupiter and Saturn), which contain significant amounts of He.
Advanced Materials Science:
- Phonon Engineering: The experimental observation that the Leibfried-Schlömann (LS) model fails to predict Λ for solid He and Ar at high pressures highlights the need for more sophisticated computational studies to identify complex phonon scattering mechanisms in simple crystalline systems.
Cryogenic and High-Density Fluid Systems:
- Heat Transfer Modeling: The unique positive temperature dependence of liquid He’s thermal conductivity informs the design and safety modeling of high-density cryogenic fluid systems where heat transfer efficiency is paramount.

View Original Abstract

Helium (He) and argon (Ar) are important rare gases and pressure media used in diamond-anvil cell (DAC) experiments. Their thermal conductivity at high pressure-temperature (P-T) conditions is a crucial parameter for modeling heat conduction and temperature distribution within a DAC. Here we report the thermal conductivity of He and Ar over a wide range of high P-T conditions using ultrafast time-domain thermoreflectance coupled with an externally heated DAC. We find that at room temperature the thermal conductivity of liquid and solid He shows a pressure dependence of P0.86 and P0.72, respectively; upon heating the liquid, He at 10.2 GPa follows a T0.45 dependence. By contrast, the thermal conductivity of solid Ar at room temperature has a pressure dependence of P1.25, while a T−1.37 dependence is observed for solid Ar at 19 GPa. Our results not only provide crucial bases for further investigation into the physical mechanisms of heat transport in He and Ar under extremes, but also substantially improve the accuracy of modeling the temperature profile within a DAC loaded with He or Ar. The P-T dependences of the thermal conductivity of He are important to better model and constrain the structural and thermal evolution of gas giant planets containing He.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma15196681

References

2012 - The properties of hydrogen and helium under extreme conditions [Crossref]
1993 - Equation of state and phase diagram of solid He from single-crystal [Crossref]
1988 - High-Pressure Phase Diagram and Equation of State of Solid Helium from Single-Crystal X-Ray Diffraction to 23.3 GPa [Crossref]
2009 - Hydrostatic limits of 11 pressure transmitting media [Crossref]
1988 - Equation of state of dense helium [Crossref]
1981 - Equation of state and melting curve of helium to very high pressure [Crossref]
2010 - High-pressure melting curve of helium and neon: Deviations from corresponding states theory [Crossref]
2000 - Extended and accurate determination of the melting curves of argon, helium, ice and hydrogen [Crossref]
2004 - Elasticity of dense helium [Crossref]
2013 - Sound velocities of hexagonal close-packed H2 and He under pressure [Crossref]