Diffusive Propagation of Phonon Beams in Yttrium Aluminum Garnets Containing Substitutional Rare Earth Atoms

The diffusive maxima of phonon signals are studied for a number of solid solutions of rare earth atoms in yttrium aluminum garnets. The used exact formula for the diffusion constants allows for qualitative discussion of the obtained results. The established energy of phonons, forming the diffusive maximum of phonon signal of the temperature T$\text{}_{H}$ arriving at the bolometer, ranges from 3.2k$\text{}_{B}$T$\text{}_{H}$ to 4.2k$\text{}_{B}$T$\text{}_{H}$, which is in reasonable agreement with the existing estimations. The qualitative analysis allows us to estimate the contribution, made by the rare earth ions occupying the octahedral positions of the sixfold oxygen coordination, to the scattering of phonons due to lattice imperfections in yttrium aluminum garnets.