The correlation between dielectric losses in submillimeter band and attenuation of high frequency acoustic waves

A series of crystalline isomorphic solid solutions of Yttrium-Lutetium Aluminum Garnets (Y_1-cLu_c)₃ Al₅O₁₂ (c=0-1) has been studied. The measurements of dielectric loss (DL) tangent tgδ has been performed at electromagnetic wavelengths 1-0.6 mm and temperature T=300 K. The results obtained has been compared with longitudinal acoustic waves (AW) attenuation data for frequencies f=1÷9.4 GHz, T=4.2÷300 K. The correlation between the DL and the AW attenuation is observed. The dependencies of DL (at T=300 K) and AW attenuation (at T⩾77 K) on concentration c are qualitatively identical in the whole interval c=0÷1. From comparison with theory it follows that the observed DL is due to the two-phonon intrinsic lattice loss. It is caused by the lattice anharmonicity as well as the AW attenuation at not too low temperatures. The prediction for concentration dependence of DL at very low temperatures is discussed that follows from comparison with the results of “heat pulse” propagation experiments for the same samples at T=2 K