Is there a Lower Limit to the Thermal Conductivity of Solids?
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IS THERE A LOWER LIMIT TO THE THERMAL CONDUCTIVITY OF SOLIDS? DAVID G. CAHILL* and R.O. POHL** Present address: IBM Watson Research Center, Yorktown Heights, NY 10598 Laboratory of Atomic & Solid State Physics, Cornell University, Ithaca NY 148532501 ABSTRACT The thermal conductivity of various systematically disordered crystals has been measured. It has been found that the lowest thermal conductivity above -100 K that can be achieved is equal to that of the amorphous phase. This experimentally observed lower limit of the thermal conductivity can be described with a model proposed by Einstein in which the elastic energy propagates in a random walk among the atoms which are vibrating with random phases, and which is called the minimum thermal conductivity. This heat transport mechanism resembles somewhat that commonly accepted in liquids. INTRODUCTION The figure of merit of thermoelectric devices increases with decreasing thermal conductivity. Thus, significant improvements of the figure of merit have been achieved by increasing the phonon scattering in mixed crystals of silicon and germanium. Fig. 1 shows the thermal conductivity of Gel_,Si,. mixed crystals as measured by Abeles, Cody, and coworkers in their pioneering work', compared to that of pure Ge and Si single crystals 2 . For x = 0.3 and 0.7, a reduction of the thermal conductivity by over one order of magnitude can be achieved near room temperature. This work demonstrated the importance of lattice disorder for improving the figure of merit.
102 _
Si E101
Fig. 1: Thermal conductivity of
Ge
Pure Crystals
"
Abeies et al. - 100
Ge Si
,.
-
0
100
single crystal Ge and Si between 1 and 1000 K after Ref. 2. The
dashedlines are thermal
"conductivities '..-100 0 -E 10-1 "
95 5 92 8 70 30 nAt -7f%
Temperature, K Mat. Res. Soc. Symp. Proc. Vol. 234. ©1991 Materials Research Society
of Ge=Sij,_ measured by Abeles et al. (Ref. 1).
S
28
10-
2
io10-3
"Q10-4 00 10-5
Q 4-
10-6 0.1
1 10 temperature (K)
100
Fig. 2: Thermal conductivity of seven glasses that represent different chemical bonding types. Low temperature data are reviewed by Pohl (Ref. 6). The conductivity of all glasses measured to date falls into the range spanned by the data shown here. The Zro.7 Pdo. 3 data are almost indistinguishable from those of CdGeAs 2 below 1 K. High (>30 K) and low temperature data match up well for all glasses with the exception of those for nitrate glass (Ca, KNO3 , N - G).
In this lecture, we will address the question by how much the lattice thermal conductivity of any solid can be reduced under optimum conditions. We will ignore the thermal conductivity that results from the charge carriers, and will also ignore the effect the disorder may have on the electrical conductivity. These questions will have to be addressed separately. The only condition imposed on the solids we will study is that they are in bulk form, since any porosity will affect the thermal and the electrical conductivity in the same way, and thus will not affect the figure of merit. Sp
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