Thermal conductivity of iron and nickel during melting - Implication to the planetary liquid outer core
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-12-13 |
| Journal | Pramana |
| Authors | Pinku Saha, Goutam Dev Mukherjee |
| Institutions | Indian Institute of Science Education and Research Kolkata |
| Citations | 4 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: Direct measurements of the thermal conductivity ($\kappa$) of pure iron (Fe) and nickel (Ni) were successfully performed across their melting transitions at high pressures (up to 22 GPa) and high temperatures (up to 2250 K).
- Methodology: The study utilized a Laser Heated Diamond Anvil Cell (LHDAC) combined with finite-element simulations (COMSOL) to accurately model and measure the temperature gradient across the sample surface.
- Melting Signature: A sharp, significant drop (25-40%) in $\kappa$ was consistently observed at the melting temperature for both Fe and Ni, providing a robust method for determining the high-pressure melting curve.
- Liquid Core Constraint: The thermal conductivity of the molten metals was found to be low (Fe: 60-70 W/mK; Ni: 65-70 W/mK) and, critically, remained constant (invariant) along the melting boundary across the tested pressure range.
- Geophysical Implication: These low, constant $\kappa$ values provide essential constraints for geodynamo models, suggesting a lower heat flux from planetary cores (like Mercury and Mars) than previously estimated by some high-end theoretical calculations (160-200 W/mK).
- Material Physics: The constant $\kappa$ in the liquid state is attributed to the loss of long-range order while maintaining a local closed-packed hard-sphere structure, a phenomenon linked to the unfilled d-band transition metals.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Fe Thermal Conductivity (Liquid) | 60-70 ± 20 | W/m-1K-1 | At melting, 5-8 GPa (Mercury core conditions) |
| Ni Thermal Conductivity (Liquid) | 65-70 ± 20 | W/m-1K-1 | At melting, 4-22 GPa |
| Observed $\kappa$ Drop upon Melting | 25-30% (Fe); 30-35% (Ni) | % | Sharp transition from solid to liquid phase |
| Maximum Pressure Tested (Ni) | 22 | GPa | Highest pressure point for Ni $\kappa$ measurement |
| Fe Melting Temperature Range | 1975 to 2098 | K | Observed melting points at 5 to 8.5 GPa |
| Ni Specific Heat (Cp) | 420 | JKg-1K-1 | Used in heat energy calculation (Eqn. 3) |
| Fe Specific Heat (Cp) | 450 | JKg-1K-1 | Used in heat energy calculation (Eqn. 3) |
| Sample Thickness (Fe/Ni) | ~15 | ”m | Initial thickness of compacted metal plates |
| PTM Material | NaCl | - | Used for pressure transmission and thermal insulation |
| NaCl Thermal Conductivity | 6 | W/m-1K-1 | Used in COMSOL simulation [49] |
| Laser Wavelength | 1.070 | ”m | Diode-pumped Ytterbium fiber optic laser |
| Total $\kappa$ Uncertainty | ~30 | % | Estimated total error due to propagation of errors |
Key Methodologies
Section titled âKey Methodologiesâ- Sample Preparation and Loading: Thin plates (~15 ”m) of polycrystalline Fe and Ni were compacted. These metal plates were sandwiched between NaCl discs (~12 ”m thick), which served as both the Pressure Transmitting Medium (PTM) and thermal insulation.
- High-Pressure Apparatus: A single-sided Laser Heated Diamond Anvil Cell (LHDAC) was employed, utilizing 300 ”m culet diamond anvils and a T301 stainless steel gasket.
- Heating Source: A continuous wave (CW) diode-pumped Ytterbium fiber optic laser (1.070 ”m) was used to heat the sample, creating a localized hotspot.
- Steady-State Confirmation: The system was allowed 5-10 minutes to stabilize after heating initiation to ensure steady-state heat flow conditions were achieved before measurement.
- Temperature Gradient Measurement: The temperature profile across the sample surface was measured by translating a 50 ”m pinhole attached to a spectrometer across the magnified image of the sample. Temperature was determined by fitting Planckâs radiation function (650-900 nm range).
- Heat Energy Calculation: The heat energy ($Q$) absorbed by the metal foil at the hotspot was calculated using the thermodynamic equation: $Q = m C_{p} (T_{hotspot} - T_{room}) \nu$, where $m$ is the mass, $C_{p}$ is the specific heat capacity, and $\nu$ is the modulation frequency (50 kHz).
- Thermal Conductivity Simulation: The finite-element software COMSOL Multiphysics was used to simulate the steady-state temperature distribution based on the heat conduction equation. The thermal conductivity ($\kappa$) of the sample was determined iteratively by varying $\kappa$ until the computed temperature profile matched the experimentally measured temperature gradient.
- Melting Point Determination: The melting temperature ($T_{m}$) at a given pressure was identified by the sudden, sharp drop in the calculated $\kappa$ value, marking the solid-to-liquid phase transition.
Commercial Applications
Section titled âCommercial ApplicationsâThe findings are primarily relevant to fundamental research in planetary science and high-pressure physics, providing critical data for large-scale geophysical models and simulations:
- Planetary Geophysics and Core Modeling:
- Geodynamo Lifetime: The low, constant thermal conductivity of liquid Fe and Ni directly impacts the thermal evolution and cooling rate of planetary cores (Earth, Mercury, Mars). A lower $\kappa$ implies a slower heat loss, which is essential for sustaining the magnetic field (geodynamo) over geological timescales.
- Core-Mantle Boundary Heat Flux: Providing accurate, experimentally derived $\kappa$ values for Fe and Ni at conditions relevant to the Mercury core-mantle boundary (5-8 GPa, 1850-2200 K) to refine models of Mercuryâs weak dynamo.
- High-Pressure Materials Science:
- Transport Property Prediction: Establishing reliable experimental benchmarks for the thermal transport properties of transition metals (Fe, Ni) across phase transitions under extreme pressure, validating or challenging ab initio theoretical calculations.
- Alloy Design for Extreme Environments: The observed invariance of $\kappa$ in the liquid state provides insight into electron scattering mechanisms in molten transition metals, which is valuable for designing alloys intended for high P-T applications where thermal management is critical.