A method is constructed that uses ultrasonic experiments to evaluate the parameters of the Jahn-Teller (JT) effect in impurity centers in crystals. The method is based on measurements of temperature dependent attenuation and phase velocity and does not require assumptions about mechanisms of relaxation. The results are illustrated by measurements performed on the impurity system ZnSe:Cr(2+), in which the Cr(2+) ion has a threefold degenerate T term in the ground state, subject to the [Formula: see text] JT problem. Ultrasound propagation anomalies show that the main JT distortions of the tetrahedral environment of the Cr(2+) ion are of tetragonal E type and hence the lowest branch of the adiabatic potential energy surface (APES) is formed in accordance with the [Formula: see text] problem. With dopant concentration 3.8 × 10(18) cm(-3) the modulus of the constant of linear vibronic coupling to tetragonal E type vibrations is determined by two independent experiments: |F(E)| = 5.49 × 10(-5) dyn revealed from attenuation measurements, while a slightly different value |F(E)| = 5.57 × 10(-5) dyn emerges from phase velocity measurements. Contributions of other active vibronic modes to the elastic modulus C(l) = (C(11) + C(12) + 2C(44))/2 are analyzed and it is shown that the influence of the totally symmetric mode is negligible. Using additional information about this system obtained from independent sources, we also estimated the primary force constant in the E direction (K(E)≈(1.4-4.2) × 10(4) dyn cm(-1)) and orthorhombic and trigonal saddle points of the APES in the five-dimensional space of the tetragonal and trigonal coordinates, their stabilization energies being E(JT)(O)≈81-450 cm(-1) and E(JT)(T)≈48-417 cm(-1), respectively (the variations of the K(E), E(JT)(O) and E(JT)(T) values are due to different literature data for E(JT)(E)). With these data the APES of the JT linear [Formula: see text] problem for the Cr(2+) ion in the ZnSe:Cr(2+) system is revealed.

New research results on phenomena due to the existence of electronic resonance energy levels and hybridized states at impurities of transition elements in semiconductors are presented. The data show that the thermal conductivity and ultrasonic parameters of mercury selenide containing iron impurities have resonance anomalies due to the influence of these impurities. A consistent and detailed interpretation is offered for the set of observed effects of hybridized states in mercury selenide with iron impurities. The proposed interpretation of the data obtained on other systems is discussed.

Temperature dependences of phase velocity and absorption of ultrasound were investigated in ZnSe crystal doped with ${\mathrm{Cr}}^{2+}$ ions at the frequencies $32–158\mathrm{MHz}$. Absorption peak and variation of phase velocity found in the temperature interval $10–20\mathrm{K}$ were interpreted as manifestation of the Jahn-Teller effect. Temperature dependences of relaxation time, relaxed, and unrelaxed moduli $C=\frac{1}{2}(C_{11}+C_{12}+2C_{44})$ were restored. The dependences were compared with the results of such investigations in $\mathrm{Zn}\mathrm{Se}:{\mathrm{Ni}}^{2+}$ and analyzed regarding lattice stability of the crystals. Fitting of the temperature dependence of the relaxation time was done with account of thermal activation over the potential barrier, quantum tunnelling with phonon emission, and two phonon process analogous to Raman scattering. Thermal activation proved to be the dominant mechanism of relaxation above $6\mathrm{K}$ and quantum tunnelling—below this temperature.

Temperature dependences of elastic moduli and ultrasonic attenuation were investigated in $\mathrm{Zn}\mathrm{Se}:{\mathrm{V}}^{2+}$ and $\mathrm{Zn}\mathrm{Se}:{\mathrm{Mn}}^{2+}$ crystals as functions of temperature in the interval of $1.4–100\mathrm{K}$ for frequencies of $52–270\mathrm{MHz}$. A peak in the attenuation was found in $\mathrm{Zn}\mathrm{Se}:{\mathrm{V}}^{2+}$ below $4\mathrm{K}$ for fast shear and longitudinal waves propagating along the [110] crystallographic axis. We interpret it to be a manifestation of a relaxation process related to the Jahn–Teller effect in the $3d$ electron system of the impurity. Softening of the elastic moduli $C_{44}$ and $C_{\ell }=(C_{11}+C_{12}+2C_{44})∕2$ were observed below $40\mathrm{K}$. Temperature dependences were deduced for relaxation time and relaxed and unrelaxed $C_{44}$ and $C_{\ell }$ moduli. The temperature dependence of relaxation time shows that $\mathrm{Zn}\mathrm{Se}:{\mathrm{V}}^{2+}$ has potential barrier $V_0=5.6{\mathrm{cm}}^{-1}$. Softening of the $C_{44}$ modulus indicates that the local distortions have a trigonal character. Neither attenuation anomalies nor softening of the elastic moduli was observed in $\mathrm{Zn}\mathrm{Se}:{\mathrm{Mn}}^{2+}$, which has a singlet orbital ground state of the $3d$ impurity.