Energy Transmission across Acoustically Mismatched Solid Junctions

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We derive expression for energy flux in terms of lattice normal mode coordinates. Energy transmission across solid junctions from lattice dynamic point of view is given and its relation with atomic masses, lattice constants, and group velocities is clarified. A scattering boundary method (SBM) is proposed for calculating the amplitude transmission across solid junctions. The phonon transmission coefficients and thermal conductance are calculated for two kinds of acoustically mismatched junctions: different chirality nanotubes (11,0) to (8,0), and Si-Ge interface structure. Our calculation shows a mode-dependent transmission in nanotube junction due to the high symmetry vibrating motions for nanotube atoms, indicating its possible important role in nanotube mixture thermal conductance. Energy transmission and Kapitza conductance across the Si-Ge interface [001] are calculated for the Si-Ge diamond-type structure. It is shown that the energy transmission across the Si-Ge interface depends on the incident angle and on the interface mode conversion. A critical incident angle about 42 degrees numerically found for waves incident from Ge to Si. Our numerical result of the Kapitza conductance at temperature T=200K is Gₖ=4.6x10⁸ W/(Km²) We find numerically scaling law Gₖ proportional to T².⁸⁷ for [001] interface at low temperature.