Usually the minimum thermal conductivity (kmin)indicates the high temperature thermal conductivity of an insulator when the mean phonon free path is close to the interatomic distance. The minimum thermal conductivity of Clark and then modified by Liu have been widely used to predict the kmin of a number of oxides. (1.D. R. Clarke, “Materials Selection Guidelines for Low Thermal Conductivity Thermal Barrier Coatings,” Surf. Coat. Technol., 163–164, 67–74 (2003). 2.B. Liu et al “Theoretical Elastic Stiffness, Structure Stability and Thermal Conductivity of La2Zr2O7 Pyrochlore,” Acta. Mater., 55, 2949–57 (2007).)
However, I just read a paper published in Chin. Phys. B, see the attached, that calculates the kmin of electrical conducting materials of M4AlC3. Since there is electronic contribution to the thermal conductivity, my question is :are these authors calculated are real minimum thermal conductivity?
Hi Yanchun,
they are calculating only the phonon component of the thermal conductivity and obtain numbers in the ball-park 1-2 W/(m*K). I'd expect the electronic contribution to be dominant, say 5-10 times larger than that.
The approach they used only works for materials where the phonon thermal conductivity is dominant.
Per
Dear Yanchun,
It depends on the material under investigation.
Thermal barrier coatings are insulating in nature. So, the thermal conductivity of crystalline insulating material follows inverse relation with temperature. If the thermal conductivity vs temperature shows inverse relation (upto 1000 C) then we call it as conduction is due to phonon. As, it is insulating in nature, electron don't take part in conduction process. In case of metal or cermet, you may find electronic contribution.
Prof. Clarke reported the thermal conductivity of ceramics where only phonon conduction is expected. However, the M4AlC3 phase is one type of MAX phase which is cermet in nature. Hence, electronic contribution comes and the expression changes.
Regards,
SN
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