Generally, pure metals are expected to exhibit lower thermal conductivity with increasing temperature (lattice vibration-induced scattering and a decrease in the mean free path).
1. What about alloys/solid solutions? Can anyone explain the basic physics?
2. Can Fe/Ni-based high-temperature capable alloys show increasing thermal conductivity with temperature (13 W/mK to 26 W/mK)
Minor variations in the trend may be acceptable in alloy systems due precipitation and dissolution mechanisms. But this increase appears very significant to me. Why?
The thermal conductivity of Fe/Ni super alloys increases with temperature because the phonons that carry heat travel faster as the temperature increases. As atoms vibrate faster, their interaction increases and thus more energy is transferred more quickly throughout the material, resulting in a higher thermal conductivity. The increasing strength of atomic bonds at higher temperatures also contributes to this effect.
Hello Venkateswaran Chinnu ,
Re your statement that "Generally, pure metals are expected to exhibit lower thermal conductivity with increasing temperature (lattice vibration-induced scattering and a decrease in the mean free path)." According to Table A.1 in [1], the following metallic elements exhibit an increase in their thermal conductivity with increasing temperature, ¶, or a decrease followed by an increase in their thermal conductivity with increasing temperature, §, over the range 100 to 2,500K: niobium (§), palladium (§), platinum (§), tantalum (§), thorium ( (§), uranium (¶), vanadium (§), and zirconium (§).
Re your statement that "Can Fe/Ni-based high-temperature capable alloys show increasing thermal conductivity with temperature (13 W/mK to 26 W/mK)"? Different alloys show different behaviors with respect to the their thermal conductivity verus increasing temperature. For example, according to Table A.1 in [1], Aluminum alloys 2024-T6 and 195 (cast) show increasing thermal conductivity from 100 to 600K; Commercial bronze, Phosphor gear bronze, and Cartridge brass show increasing thermal conductivity from 100-600K; Nichrome and Inconel X-750 show increasing thermal conductivity from 100-1,500K; and Stainless steels AISI 302, 304, 316 & 347 all show increasing thermal conductivity from 400-1,000K. On the other hand, regular steels (6 different types) all show decreasing thermal conductivity from 400-1,000K.
Why there is this difference in behaviors amongst different elements, and amongst different alloys is hard to understand. Most textbooks on solid state physics or materials do not really address this odd behavior, see for example [2]. Simply giving hand-waving explanations about how heat can be carried by delocalized electrons and/or phonons does not work because such arguments don't address one particular element's or alloy's behavior from first principles. Many of the elements and alloys with odd behavior are transition elements or have transition elements in their solid solutions, and all transition metals have very complicated electronic structures.
[1] Frank P. Incropera, David P. De Witt; Fundamentals of Heat and Mass Transfer, Second Edition; John Wiey & Sons, Inc.; 1985; pp. 755-758, Table A.1.
[2] Robert M. Rose, Lawrence A. Shepard, John Wulff; The Structure and Properties of Materials, Volume IV, Electronic Properties; John Wiley & Sons, Inc.; 1966; pp. 65-69.
Regards,
Tom Cuff
Heat can be conducted by both the free electrons and phonons. When the metal is pure, the heat is dominantly conducted by the electrons and electrons are scattered more with increasing temperature because of the shorter mean free path due to the lattice vibrations and vacancies as you explained. Although increased lattice vibration means increased phonon activity, this increase cannot compensate the decrease in the thermal conductivity because of scattering of the electrons.
For alloys, the mechanism of thermal conduction is already phonon-dominated as dissimilar atoms naturally create scattering sites for electrons. This is why solid solution of two elements of similar thermal conductivity creates an alloy with less thermal conductivity as in the example of Fe (79 W/mK) and Ni (91 W/mK). Since thermal conductivity is already phonon-dominated in this case, an increase in temperature increases the lattice vibrations and therefore increases the thermal conductivity.
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