Isolating lattice from electronic contributions in thermal transport measurements of metals and alloys above ambient temperature and an adiabatic model
Abstract
From femtosecond spectroscopy (fs-spectroscopy) of metals, electrons and phonons reequilibrate nearly independently, which contrasts with models of heat transfer at ordinary temperatures (T>100 K). These electronic transfer models only agree with thermal conductivity (k) data at a single temperature, but do not agree with thermal diffusivity (D) data. To address the discrepancies, which are important to problems in solid state physics, we separately measured electronic (ele) and phononic (lat) components of D in many metals and alloys over ∼290–1100 K by varying measurement duration and sample length in laser-flash experiments. These mechanisms produce distinct diffusive responses in temperature versus time acquisitions because carrier speeds (u) and heat capacities (C) differ greatly. Electronic transport of heat only operates for a brief time after heat is applied because u is high. High Dele is associated with moderate T, long lengths, low electrical resistivity, and loss of ferromagnetism. Relationships of Dele and Dlat with physical properties support our assignments. Although kele reaches ∼20×klat near 470 K, it is transient. Combining previous data on u with each D provides mean free paths and lifetimes that are consistent with ∼298 K fs-spectroscopy, and new values at high T. Our findings are consistent with nearly-free electrons absorbing and transmitting a small fraction of the incoming heat, whereas phonons absorb and transmit the majority. We model time-dependent, parallel heat transfer under adiabatic conditions which is one-dimensional in solids, as required by thermodynamic law. For noninteracting mechanisms, k≅ΣCikiΣCi/(ΣC2i). For metals, this reduces to k=klat above ∼20 K, consistent with our measurements, and shows that Meissner’s equation (k≅klat+kele) is invalid above ∼20 K. For one mechanism with multiple, interacting carriers, k≅ΣCiki/(ΣCi). Thus, certain dynamic behaviors of electrons and phonons in metals have been misunderstood. Implications for theoretical models and technological advancements are briefly discussed.
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