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 D ele is associated with moderate T , long lengths, low electrical resistivity, and loss of ferromagnetism. Relationships of D ele and D lat with physical properties support our assignments. Although k ele reaches ∼20 × k lat near 470 K, it is transient. Combining previous data on u with each D This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the https://creativecommons.org/licenses/by/4.0Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. * E. M. Criss is an employee of Panasonic Avionics Corporation, but prepared this paper independent of his employment and without use of information, resources, or other support from Panasonic Avionics Corporation.† Corresponding author. 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 ∼ = ΣC i k i ΣC i /(ΣC 2 i ). For metals, this reduces to k = k lat above ∼20 K, consistent with our measurements, and shows that Meissner's equation (k ∼ = k lat + k ele ) is invalid above ∼20 K. For one mechanism with multiple, interacting carriers, k ∼ = ΣC i k i /(ΣC i ). Thus, certain dynamic behaviors of electrons and phonons in metals have been misunderstood. Implications for theoretical models and technological advancements are briefly discussed.

Temperature-dependent thermal transport properties of carbonate minerals and rocks

“…We used a NETZSCH LFA 427, described by Bräuer et al (1992), to measure thermal diffusivity. For a general descriptions of this method, which is commonly used in industry and materials science, see Maglić and Taylor (1992), Hohenauer (2003, 2005), and Criss and Hofmeister (2017). For procedural details regarding our laboratory, see Pertermann and Hofmeister (2006).…”

Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics

“…These fronts can be distinguished in transient experiments, such as LFA, where T is measured as a function of t , but not in periodic experiments, which average measurements over some time interval [ 4 ] (Chapter 4). Measuring the thermal evolution after a heat perturbation sheds quantitative information on the rate and mechanism by which energy diffuses through a material [ 9 ].…”

“…The resulting nearly isothermal conditions provided insignificant heat transfer, and so reasonable agreement was obtained [ 4 ]. (ii) A factor of 3 error exists in all such models due to assuming that heat is scattered in all directions, which does not describe heat flowing down the temperature gradient, as required by thermodynamic law [ 9 ]. (iii) In solids, heat and mass move independently, but in gas, heat and mass move inseparably.…”

“…To better understand heat transport in solids, a large database was constructed on thermal diffusivity ( D ) above ~298 K on ~200 non-metallic crystals, ~100 silicate glasses, and ~30 metals using laser-flash analysis (LFA) [ 4 , 9 , 10 ]. This contact-free technique was developed in 1961 by Parker et al [ 11 ].…”

“…The focus is thus on silicates and oxides. For summaries, see [ 9 , 10 , 18 ] and [ 4 ] (Chapters 7, 9, 10).…”