不同金属（含铱、锇）趋肤效应深度与频率关系的数据源及计算方法问询

Great question—this is a common need for high-frequency engineering and materials optimization projects. Let’s break this down into data sources, derivable formulas, and practical tips for your least-square fitting work:

• NIST Physical Measurement Laboratory (PML): Their materials property database includes experimentally measured electrical conductivity and magnetic permeability for a wide range of metals, including iridium and osmium, across different frequency bands. Most entries provide discrete data points (not just bulk average values) which are perfect for least-square fitting.
• CRC Handbook of Chemistry and Physics: While it’s more focused on general properties, the latest editions have curated high-frequency electromagnetic data for rare metals. For iridium and osmium, you’ll find sections on AC conductivity at specific frequencies, which you can convert to skin depth using core formulas.
• Peer-Reviewed Engineering Journals: Publications like IEEE Transactions on Microwave Theory and Techniques or Journal of Applied Physics often feature studies on high-frequency behavior of noble/rare metals. Many of these papers include raw experimental data points (e.g., skin depth measurements at 1GHz, 10GHz, etc.) for iridium and osmium, especially for applications like RF shielding or high-temperature electronics.
• University Materials Databases: Some leading materials science labs maintain open datasets of electromagnetic properties for exotic metals. These are often peer-validated and include the granular data you need for fitting.

The classic skin depth formula for good conductors (where electrical conductivity σ >> angular frequency ω × permittivity ε) is:

δ = √(2 / (ωμσ))

Where:

• δ = skin depth (m)
• ω = angular frequency = 2πf (rad/s, f is frequency in Hz)
• μ = absolute magnetic permeability = μ₀μᵣ (μ₀ = 4π×10⁻⁷ H/m, μᵣ = relative magnetic permeability of the metal)
• σ = electrical conductivity (S/m)

Notes for Fitting: #

• Since δ is proportional to √(1/f), you can transform your data to plot δ vs. 1/√f—this should give a linear relationship. The slope of the fitted line will let you solve for the combined parameter √(2/(2πμσ)), which you can use to back-calculate σ if you know μᵣ (most non-ferromagnetic metals like iridium and osmium have μᵣ ≈ 1).
• For extremely high frequencies (e.g., terahertz range), metals may exhibit dispersion (σ and μ change with frequency). In this case, use the generalized formula with complex conductivity and permeability:

  δ = √(2 / (ω |μ*σ*|))
  

  Where |μ*σ*| is the magnitude of the product of complex magnetic permeability (μ*) and complex electrical conductivity (σ*).

• Segment Data by Frequency Bands: Conductivity can shift at certain frequency thresholds (e.g., near the metal’s plasma frequency), so fit your data in distinct frequency ranges for more accurate equations.
• Combine Calculated and Measured Data: If direct skin depth measurements for iridium/osmium are scarce, use measured σ and μ values to compute δ, then treat those computed points as pseudo-experimental data for fitting.
• Integrate Optimization Parameters: Once you have your fitted skin depth equations, you can build a multi-objective optimization framework that balances skin depth performance with density, cost, and electronegativity. For example, use a weighted scoring system where you prioritize skin depth requirements while penalizing high cost or density.

内容的提问来源于stack exchange，提问作者CoryG