THE CONTRIBUTION OF LONGITUDINAL PHONONS TO THE LATTICE THERMAL CONDUCTIVITY

Date of Completion

January 1982

Keywords

Physics, Condensed Matter

Degree

Ph.D.

Abstract

The theory of anharmonic three-phonon interactions predicts an expression for the mean free path of longitudinal phonons which increases rapidly at low frequencies and leads to a divergence of the thermal conductivity integral. In the present treatment this divergence is removed by relaxing the energy conservation condition, thus allowing low-frequency longitudinal phonons to interact with phonons of any frequency. This reduces their mean free path. The contribution of the longitudinal phonons had been disregarded in the commonly used Callaway expression for the thermal conductivity. The present treatment confirms that this contribution is relatively small at low temperatures but shows that it is about one fifth of the total conductivity at ordinary and high temperatures. The temperature dependence of this contribution is approximately T('-1.3) and it may explain part of the deviation of the experimental thermal conductivity from the T('-1) behavior. Also, because this contribution is mainly due to phonons with mean free paths of the order of up to tens of microns, a sensitivity of the thermal conductivity to large defects and to grain size, which is greater than previously expected, may result. The theory is compared to the observed conductivity of sapphire, germanium, silicon, and lithium fluoride over a wide temperature range. The agreement is good at high temperatures (if account is taken of the effect of thermal expansion) with only one adjustable parameter to give the overall magnitude of the conductivity. The fit at low temperatures is not as good, particularly in the region where the conductivity attains its maximum value, because of an inadequacy in the theoretical expression for the umklapp relaxation rate at low temperatures. ^

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