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

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D(∞)(T)[1 − exp(−bL)]. When L is several mm, D(∞)(T) = FT(−G) + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0....

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Autor principal: Hofmeister, Anne M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7831911/
https://www.ncbi.nlm.nih.gov/pubmed/33477677
http://dx.doi.org/10.3390/ma14020449
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author Hofmeister, Anne M.
author_facet Hofmeister, Anne M.
author_sort Hofmeister, Anne M.
collection PubMed
description Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D(∞)(T)[1 − exp(−bL)]. When L is several mm, D(∞)(T) = FT(−G) + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D(∞)(−0.477) at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(c(P))/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.
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spelling pubmed-78319112021-01-26 Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics Hofmeister, Anne M. Materials (Basel) Article Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D(∞)(T)[1 − exp(−bL)]. When L is several mm, D(∞)(T) = FT(−G) + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D(∞)(−0.477) at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(c(P))/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light. MDPI 2021-01-18 /pmc/articles/PMC7831911/ /pubmed/33477677 http://dx.doi.org/10.3390/ma14020449 Text en © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Hofmeister, Anne M.
Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title_full Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title_fullStr Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title_full_unstemmed Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title_short Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics
title_sort dependence of heat transport in solids on length-scale, pressure, and temperature: implications for mechanisms and thermodynamics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7831911/
https://www.ncbi.nlm.nih.gov/pubmed/33477677
http://dx.doi.org/10.3390/ma14020449
work_keys_str_mv AT hofmeisterannem dependenceofheattransportinsolidsonlengthscalepressureandtemperatureimplicationsformechanismsandthermodynamics