Tham khảo tài liệu 'waves in fluids and solids part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 114 Waves in Fluids and Solids Fig. 5. Relationship of the temperature dependence of the Debye temperature part b to the character of the long-wavelength phonons propagation in a crystal part a . Then using the definition of roD the ratio of the phonon density to the squared frequency can be expressed by the dispersion of sound velocities Si ro tlsl 13 ro2 roD ro 6k2 i 1 S3 ro where vo is the unit cell volume. Thus the occurrence of the maximum on the ratio v ữ Ị ữ2 is caused by the additional dispersion of sound velocities. This dispersion is caused by the heterogeneity of the structure which is the source of quasi-localized vibrations. Such additional sound velocity dispersion must be manifested in the behavior of the temperature dependence D . On the curve D T a low-temperature minimum should appear see curve 5 Fig. 5b deeper than those on curves 1-4 in Fig. 5b. This curve corresponds in addition to the quasi-localized perturbations on the frequency of the first van Hove singularity in the phonon spectrum with the density of states vappr ro to the presence of an additional resonance level with the frequency s ro-ro 5 see Fig. 5a . Curves 6 in both parts of correspond to the 5 solution of a heavy isotope impurity in the FCC crystal. The formation of the QLV leads to a significant deepening of the D T low-temperature minimum and to be shifting of its temperature below that of the perfect crystal. In the first section it was shown that heavy or weakly bound impurities form QLV caused by their motion. On these vibrations the fast acoustic phonons associated with the displacements of atoms of the host lattice are scattered. This leads to kinks in the contribution to the phonon spectral density see curve 6 in Fig. 3 which are a manifestation of the Ioffe-Regel crossover. On the background of large quasi-local maxima it is difficult to distinguish their influence on the vibrational characteristics of the crystal. The study of this effect is possible in .
