Signals in thermal conduction produced by frequency cross between resonant scattering centres on the two sides of an interface

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Abstract
Analytical expressions are derived for the size of the frequency crossing signals that should occur in the temperature gradient along each half of a bicrystal carrying a heat current. The crossing occurs when the resonant frequency of a scattering process in one half is made equal to that of a scattering process in the other half. The two cases of resonant scattering strong and weak compared with boundary scattering are treated. In the first case, the signals in each half are in general of different size and the larger is twice that of a homogeneous doubly doped sample of similar concentration. In the second, the signals in each half are equal. The expressions apply when inelastic scattering can be neglected but the role of this scattering is discussed in qualitative terms. It is shown that cross signals should also be seen in the size of heat pulses that have passed through the bicrystal.