Relaxation in $\mathrm{Zn}\mathrm{Se}:{\mathrm{Cr}}^{2+}$ investigated with longitudinal ultrasonic waves

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.

Figure 1

Temperature dependences of $[f\left(T\right)-f\left(4.2\right)]∕f\left(4.2\right)$ (open circles) and attenuation of ultrasound (filled circles), respectively, the level at $T=4.2\mathrm{K}$ measured at $54.4\mathrm{MHz}$. Ultrasound passage $\ell =0.717\mathrm{cm}$.

Figure 2

Real (filled circles) and imaginary (open circles) components of the complex wave number versus inverse temperature obtained at $54.4\mathrm{MHz}$. $\Delta k=k\left(T^{-1}\right)-k\left(\infty \right)$.

Figure 3

Relaxation time versus inverse temperature. Circles represent experimental data obtained at fixed frequency $\omega ∕2\pi =54.4\mathrm{MHz}$ and processed with Eq. (16), triangles represent the maxima of absorption obtained at 32.5 and $157\mathrm{MHz}$, solid curve represents the result of fitting done on the basis of Eqs. (9, 10, 11, 12).

Figure 4

Temperature dependences of ultrasonic absorption. Triangles represent dependence measured at $32.5\mathrm{MHz}$, solid curve represents dependence calculated for $32.5\mathrm{MHz}$ using the data on $\tau \left(T\right)$ and $ϵ$ obtained at $54.4\mathrm{MHz}$.

Figure 5

Temperature dependence of elastic moduli. Filled circles for dynamic modulus $[\mathrm{Re}C\left(T\right)-C_0]∕C_0$, open circles for relaxed modulus $[C^R\left(T\right)-C_0]∕C_0$, and open triangles for unrelaxed modulus $[C^U\left(T\right)-C_0]∕C_0$ obtained at $54.4\mathrm{MHz}$. Filled triangles for dynamic modulus obtained at $43\mathrm{MHz}$. The inset shows the curves in the dashed square.

Figure 6

Elastic moduli versus inverse temperature obtained for $54.4\mathrm{MHz}$. Filled circles represent the dynamic modulus $\mathrm{Re}\Delta C∕C_0$, open circles represent the relaxed modulus $(C^R-C_0)∕C_0$, and open triangles represent the unrelaxed modulus $(C^U-C_0)∕C_0$.

Figure 7

Relaxation rate and its summands versus temperature calculated with the use of Eqs. (9, 10, 11, 12). Solid curve for ${\tau }^{-1}$, dashed curve for ${\tau }_T^{-1}$, dashed-dotted curve for ${\tau }_t^{-1}$, and dashed-dotted-dotted curve for ${\tau }_R^{-1}$.