Ultrasonic temperature dependence

Fig. 2.6 Temperature dependence of ultrasonic attenuation at fixed frequency

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

Ultrasonic Thermometers. These are usually designed to respond to the temperature dependence of sound speed. In special cases where only one particular temperature is of interest, such as the temperature of a phase change, or the recrystallization temperature of a substance, the temperature dependence of attenuation may be utilized, Ultrasonic thermometers have found applications in the range —80 to +250 C, where the so-called quartz thermometer offers resolution of 0,1 millidegree and linear superiority to platinum resistance thermometers. 

F. S., Ultrasound characterization of coronary artery wall in vitro using temperature-dependent wave speed, IEEE Trans Ultrason. Ferroelectr. Ereq. Control 50,1474-1485, 2003 Bhardwaj, R Mohanty, A.K., Drzal, L.T. et al.. Renewable resource-based composites from recycled cellulose liber and poly(3-hydroxybutyrate-co-3-hydroxyvalerate) bioplastic. Biomacromolecules 7, 2044-2051, 2006. 

Figure 7. Temperature dependence of quantum yield of chlorine consumption in reaction of methane photochlorination in structurally nonequilibrium glassy mixes of reactants (1) structurally nonequilibrium mix of reactants prepared by rapid spraying at 22 K (2) same mix after thermal annealing at 30-40 K (3) same mix after ultrasonic treatment at 22 K.

Many studies have been performed on optical properties of doped fluoroperovskite lattices searching for new tunable lasers. Dielectric-loss and ultrasonic measurements on KZnFs Li have revealed that the Li+ impurity sits in a <100> off-centre position approximately 0.15 A from a normal K+ site [234]. In the case of Cu in the cubic KMgp3 lattice, from the temperature dependence of the absorption spectra and from MCD measurements a clear indication of the off-centre configuration of Cu ion replacing a K+ ion was obtained [235]. 

Fig. 3 Lowest electronic states (a) for DyV04 crystal, temperature dependence of the energy gap between ground and excited doublets (b) (for comparison Raman scattering results are shown for the DyAs04 crystal with similar electronic and crystal structures), and the ultrasonic measurements (c) of the elastic constant Ci = l/2(Cn-Ci2) for DyV04 crystal...

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

The temperature dependence of ultrasonic attenuation will also have a maximum but its location, Tm, should be shifted with respect to T = T due to the factor /T in the expression (28). 

Note, the tetragonal distortion influence the Cs modulus exclusively, the trigonal - the c/ modulus. This fact can give us an instrument to determine the type of local distortions in an ultrasonic experiment carried out in a zinc-blende crystal the distortions can be pointed out with the help of temperature dependences of the elastic moduli. 

Fig. 2 Temperature dependences of ultrasonic attenuation for longitudinal waves propagating in ZnSe V along the [110] axis, measured at 270 MHz open circles), 156 MHz (filledcircles), and 52 MHz triangles). A a = a (T) - a (To), To = 16 K. The plot for 52 MHz is shifted downward by 0.7 dB for clarity. Concentration of the dopand = 5.6 X lO cm After Fig. 3 in [3]...

Fig. 4 Temperature dependences of ultrasonic attenuation for fast shear mode propagating in ZnSe V + along the [110] axis measured at 52MHz (open circles). Aa = ci(T) — a(7o), To = 8K. Solid curve shows the dependence Aa(T) T. Maximum of this curve corresponds to A(ur = 1. After Fig. 2 in [3]...

If the setup makes it possible to measure the ultrasonic velocity only (or the dynamic elastic modulus), a similar technique can be developed for reconstruction the relaxation time and all other parameters characterizing the Jahn-Teller system. In this case we need two temperature dependences vg (T) (or cg (T)) the first one (denoted without superscript) obtained on the doped specimen and the second (superscript (2)) - on the un-doped. At high enough temperatures these dependences should be identical, while at low temperatures they should differ due to the Jahn-Teller effect. So, contribution of the Jahn-Teller system to the total dynamic modulus Acg may be written as... 

Elastic Properties [1.30,1.31,1.35]. In regard to elasticity, at least below room temperature, tungsten behaves nearly isotropically the anisotropy coefficient at 24 °C is = 1.010 [1.35]. The elastic constants for polycrystalline tungsten at 20 °C are given below. Their temperature dependence as well as the respective values for singlecrystal elastic constants are shown in Fig. 1.10 [1.40], based on ultrasonic measurements [1.30,1.31]. 

The resonance frequency technique has been used for determining the adiabatic Young s moduli in dependence on test temperatures up to 1000 °C. The shear moduli were measured by the pulse-echo ultrasonic technique. The bulk moduli were determined by synchrotron radiation diffraction. The temperature-dependent Young s and shear moduli are plotted in fig. 7. 

Using Eq. (26.1) it is possible to obtain the temperature dependence of the hydrogen jump rate from the experimental data on ultrasonic loss. The Snoek relaxation measurements are especially informative if they are performed at a number of excitation frequencies. It should be noted that the Snoek effect can be observed only for sufficient elastic anisotropy, X -X2, of hydrogen sites. For hydrogen in pure b.c.c. metals, the Snoek effect has not been found [16], in spite of the uniaxial symmetry of tetrahedral sites occupied by hydrogen in these materials. It is believed that the absence of the observable Snoek effect is due to the small value of X1-X2 for hydrogen in the tetrahedral sites of b.c.c. metals. 

Electrical effects. Electrical methods are convenient because an electrical signal can be easily processed. Resistance thermometers (including thermistors) and thermocouples are the most widely used. Other electrical methods include noise thermometers using the Johnson noise as a temperature indicator resonant-frequency thermometers, which rely on the temperature dependence of the resonant frequency of a medium, including nuclear quadrupole resonance thermometers, ultrasonic thermometers, and quartz thermometers and semiconductor-diode thermometers, where the relation between temperature and junction voltage at constant current is used. 

Any increase in temperature will raise the vapor pressure of a medium and so lead to easier cavitation but less violent collapse (see above). This effect will be accompanied by a decrease in viscosity and surface tension. However, at temperatures approaching the solvent boiling point, a large number of cavitation bubbles are generated concurrently. These will act as a barrier to sound transmission and dampen the effective ultrasonic energy from the source which enters the liquid medium. The combination of all these effects shows a shape of maximum and the optimum temperature depends on the experimental conditions used and reaction studied. 

Fig. 5.3.10. Temperature dependence of the elastic constants of the smectic A phase of diethyl 4,4 -azoxydibenzoate determined by ultrasonic velocity measurements open circles, 2 MHz filled circles, 5 MHz triangles, 12 MHz crosses, 20 MHz. (After Miyano and Ketterson. )...

Quite a different appUcation of ultrasonic measurements to amorphous alloys was made by Doussineau et al. (1978). These authors measured the temperature dependence of the ultrasonic attenuation and described their experimental results in terms of a resonant interaction with two-level systems such as were described in section 8. 

S1N Singh, R.K., Singh, M.P., and Chaurasia, S.K., Temperature dependent ultrasonic and conductivity studies in aqueous polymeric solution. Fluid Phase Equil., 284, 10,... 

Figure 10.67 Temperature dependence of the tensile stress at yield (dry) of BASF Ultrason E3010 PES resin [6].

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