Acoustic mismatch

In 1941, Kapitza [54] reported his measurements of the temperature drop at the boundary between helium and a solid (bronze) when heat flows across the boundary. More than ten years later, Khalatnikov (1952) presented a model, an approximation to what is now known as the acoustic mismatch model , to explain that a thermal resistance Rk (thermal boundary resistance) occurs at boundaries with helium [55],... 

The acoustic mismatch model, essentially in its modern form, was first written down by Mazo and Onsager (1955) [56], independently of Khalatnikov s earlier version. The model is currently known as Mazo and Onsager model. The citation Mazo (1995) is a post-doc thesis and L. Onsager is the supervisor. 

As can be noted in Fig. 4.4, even if for 0.01 K < T < 0.2K, experimental data confirm the theory of acoustic mismatch with A - Rk T3 10 2 [m2K4/W] the good thermal contact at higher temperatures is not yet explained, in spite of the studies of the problem [57,61-68], Referring to Fig. 4.4, data of Rc between solids are only indicative of the temperature dependence, since the pressure on the contact is not known. 

In 1959, Little [69] extended the acoustic mismatch model to interfaces between solids. The experiments have revealed that in this case, the thermal contact resistance between solids is higher than that evaluated from the model and that data are less reproducible. 

Fig. 4.3. Thermal resistance Rk multiplied by surface area A between 3He and Ag sintered powder. Experimental data from [70]. The dashed line represents the prediction of the acoustic mismatch theory for bulk Ag. The full line is the prediction for the coupling of (zero) sound modes of liquid 3He with modes with a characteristic... 

The different behaviour of contact resistance in the two cases can be examined through the two models the just described acoustic mismatch model and the diffuse mismatch model which suppose that all the phonons are scattered at the interface. Hence these two models define two limits in the behaviour of phonons at a discontinuity. 

Some experiments outlined the frequency dependence of phonon scattering on surfaces [74]. Thus, Swartz made the hypothesis that a similar phenomenon could take place at the interface between solids and proposed the diffuse mismatch model [72]. The latter model represents the theoretic limit in which all phonons are heavily scattered at the interface, whereas the basic assumption in the acoustic mismatch model is that no scattering phenomenon takes place at the interface of the two materials. In the reality, phonons may be scattered at the interface with a clear reduction of the contact resistance value as calculated by the acoustic model. 

Although the term electron-phonon coupling is used here, the discussion applies equally to coupling with an electro-magnetic source. In any event, in order to retain the coherence of the electrons at the given T, the system has to be sufficiently small. At the same time, the strength of the acoustic source is assumed to be such that the additional decoherence it causes is not detrimental. The precise parameter windows in which this can be achieved will be sensitive to acoustic mismatch, details of the sample geometries, etc. 

To obtain the absolute sound attenuation in the coal slurry, the diffraction loss, the acoustic mismatch loss, the attenuation due to the Teflon window, and the oil coupling must be calculated. Thus, it is difficult to accurately determine the absolute attenuation. In practice, one measures the relative attenuation with respect to a standard. The attenuation of ultrasonic waves in a solid suspension is attributed to three major factors, namely, scattering, viscosity, and thermal effects. Although the presence of particles affects the fluid viscosity and thermal conductivity, the primary source of attenuation may be due to particle scattering. Hence, one may define the relative attenuation of the HYGAS coal slurry by comparing the slurry attenuation with that of the carrier fluid, i.e., the toluene/benzene mixture. This can be expressed by the equation... 

The d imensionality o f t he p honon d istribution a 11 ow t emperature may d iffer from 3D in thin films or layers. In our case we consider the acoustic mismatch between the film and the substrate to be negligible and therefore it is reasonable to assume that electrons interact with 3D phonons, and the electron-phonon interaction relaxation time te-ph is supposed to be proportional to T. ... 

If there exists some acoustic mismatching at surfaces and/or interfaces, the ultrasonic waves are reflected to some degree at these interfaces and they may be described by the following convolution chain [13] ... 

Phonon scattering depends on the acoustic mismatch between the two media. These phenomena are accentuated if sound velocities and densities are very different. Diamond could give the best efficiency, but alumina is better than glass and is more readily available. 

From a theoretical point of view, the scattering of phonons in mnltiphase systems is determined by the existence of an interfacial thermal barrier from acoustic mismatch. In a simplified model, the transmission of a phonon between two phases is affected by the presence of common vibration frequencies for the two phases. Thus, it... 

Organic piezo-polymers such as polyvinylidene fluoride along with trifluoroethylene and their copolymers can be made ferroelectric by poling the crystalline regions of these polymers. Because the density of these materials is close to that of human tissue, they have foimd use as transducers for ultrasound imaging with no acoustic mismatch. 

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