A methodology is worked out to retrieve the numerical values of all the main parameters of the six-dimensional adiabatic potential energy surface (APES) of a polyatomic system with a quadratic T-term Jahn-Teller effect (JTE) from ultrasound experiments. The method is based on a verified assumption that ultrasound attenuation and speed encounter anomalies when the direction of propagation and polarization of its wave of strain coincides with the characteristic directions of symmetry breaking in the JTE. For the SrF2:Cr crystal, employed as a basic example, we observed anomaly peaks in the temperature dependence of attenuation of ultrasound at frequencies of 50-160 MHz in the temperature interval of 40-60 K for the wave propagating along the [110] direction, for both the longitudinal and shear modes, the latter with two polarizations along the [001] and [110] axes, respectively. We show that these anomalies are due to the ultrasound relaxation by the system of non-interacting Cr 2+ JT centers with orthorhombic local distortions. The interpretation of the experimental findings is based on the T2g ⊗ (eg + t2g) JTE problem including the linear and quadratic terms of vibronic interactions in the Hamiltonian and the same-symmetry modes reduced to one interaction mode. Combining the experimental results with a theoretical analysis we show that on the complicated six-dimensional APES of this system with three tetragonal, four trigonal, and six orthorhombic extrema points, the latter are global minima, while the former are saddle points, and we estimate numerically all the main parameters of this surface, including the linear and quadratic vibronic coupling constants, the primary force constants, the coordinates of all the extrema points and their energies, the energy barrier between the orthorhombic minima, and the tunneling splitting of the ground vibrational states. To our knowledge, such a based-on-experimental-data numerical reconstruction of the APES of a JTE problem in the five-dimensional space of all active tetragonal and trigonal displacements is realized here for the first time.
We show that the structure, properties, and concentration of vacancies in crystals can be studied by ultrasonic experiments previously employed for impurity centres only. Measurements of the temperature dependence of attenuation and phase velocities of ultrasonic shear waves of 52 MHz propagating along the crystallographic axis [110] of nominally pure ZnSe single crystals (grown by the seeded physical vapour transport method) show strong anomalies which are typical for relaxation processes in system with isolated Jahn–Teller (JT) centres. The observed JT distortion mode is trigonal, subject to a threefold orbitally degenerate T‐term interaction with trigonal and tetragonal nuclear displacements. In the absence of sufficiently high concentrations of impurity atoms with such properties we attributed the observed JT centres to zinc vacancies. The temperature dependence of the isothermal and adiabatic forms of the appropriate elastic modulus and the relaxation time show that the relaxation mechanism changes from thermal activation at higher temperatures to tunnelling through a potential energy barrier below 18 K. We provide an estimate of the magnitude of the potential barrier, as well as the pseudorotation frequency and concentration of vacancies. Also we determine the extremum points of the adiabatic potential energy surface of the vacancy centre.
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