Testing the validity of the Wiedemann–Franz law for metals and alloys at high pressures

The Wiedemann–Franz (WF) law is a fundamental, empirical law that originally relates the electronic thermal conductivity (Λe) of a metal to its electrical resistivity (ρ) via the Lorenz number L = ρΛe/T, where T is the absolute temperature. Conventionally as ρ is measured or calculated, it has often been used to infer the Λe through the WF law at a wide range of pressure (P)–temperature (T) conditions. However, since the WF law was originally formulated based on a simple electron gas model with L being approximately the Sommerfeld value L0 = 2.44 × 10−8 W Ω K−2, its validity to transition metals involving correlated d-orbital electrons at a variety of P-T conditions has been questioned, not to mention to metallic alloys. Here, we report experimental measurements on the thermal conductivity and electrical resistivity of platinum (Pt), iron (Fe), as well as Fe0.85Si0.15 and FeS alloys at high pressures and room temperature. We demonstrate that the L of Pt and Fe both reasonably agree with L0 from ambient to ∼60 GPa, except for Fe around the pressures where a structural transition (∼12 GPa) and an electronic topological transition (∼30–40 GPa) occur. The L of Fe0.85Si0.15 and FeS alloys, however, both considerably deviate from L0, presumably due to significant inelastic scatterings between carriers and impurities. Our results suggest that using the WF law with ideal L0 to convert ρ of metallic alloys to Λe (and vice versa) at high pressures could lead to a large discrepancy from that obtained by direct measurements.