The coupling fluid

The echo from the surface of the lens can never be entirely eliminated, and because the reflection from the specimen must pass through the coupling fluid it will suffer attenuation that may well make it smaller than the lens surface 

A resolution coefficient may be defined to compare the shortest wavelength that can be used in different coupling fluids (Attal and Quate 1976 Wickra-masinghe and Petts 1980). For a given pulse length, the minimum focal length q is proportional to the velocity Vo- If the time interval between echoes is required to be to, then 

The maximum frequency / that can be used is determined by the attenuation, which is proportional to the square of the frequency. If the attenuation per unit distance travelled is written as a = do f2, and the acceptable attenuation within the considerations of 3.1 is Oacc, then the constraint on the frequency is 

The shortest wavelength Amin that can be used is therefore 

The velocity has a maximum value v = 1555.147ms 1 which occurs at 74.2°C (Kaye and Laby 1986). 

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Some applications of the coupled fluid flow-reaction model were carried out to the ore-forming process (e.g., Lichtner and Biino, 1992). However, a few attempts to understand quantitatively the precipitations of minerals from flowing supersaturated fluids in the submarine hydrothermal systems have been done (Wells and Ghiorso, 1991). Wells and Ghiorso (1991) discussed the silica behavior in midoceanic ridge hydrothermal system below the seafloor using a coupled fluid flow-reaction model. 

It was attempted to derive the relationships in the precipitated amounts of barite and quartz, flow rate and precipitation rate using the coupled fluid flow-precipitation... 

The coupled fluid flow-precipitation kinetics model calculations indicate the following results ... 

The above-mentioned consideration indicates that important factors controlling the precipitations of barite and silica are surface area/water mass ratio (A/M), temperature, precipitation rate constant (k) and flow rate (u), and the coupled fluid flow-precipitation models are applicable to understanding the distributions of minerals in submarine hydrothermal ore deposits. 

Fig. 1.5. Matrix from human bone-derived cells (a) fixed, after 5 weeks, 1.5 GHz (b) unfixed, after 1 week, 1.3 GHz. Both pictures were taken with the coupling fluid at 37°C and with the substrate at the focus of the lens (photographs courtesy of Roger...

Fig. 2.1. A lens for high-resolution acoustic microscopy in reflection. The central transparent part is a single crystal of sapphire, with its c-axis accurately parallel to the axis of the cylinder. The sandwich structure at the top is the transducer, with the yellow representing an epitaxially grown layer of zinc oxide between two gold electrodes. The pink shaded areas within the sapphire represent the plane-wavefronts of an acoustic pulse they are refracted at the lens cavity so that they become spherical in the coupling fluid. A lens for use at 2 GHz would have a cavity of radius 40f[Pg.8]

The coefficients k are given in Table 3.3 with T in °C. The polynomial expansion is useful in analysis programs to calculate the velocity from the temperature. The attenuation in water decreases with temperature, but the rate of decrease is less at higher temperatures. The attenuation and velocity are plotted against temperature in Fig. 3.1. For practical operation of an acoustic microscope with water as the coupling fluid, the smallest lens radius for routine operation is 40 pm (focal length 46pm). With water at 60°C a lens... 

The optimum lens angle (in the coupling fluid) would be 0opt = sin-1 [n sin tan-1(/jopt/5b) ] ... 

The starting point for the design of lens for surface imaging is the choice of the frequency for which it is to be used. This determines the attenuation per unit distance in the coupling fluid (Table 3.1). In water the attenuation is about... 

In acoustic microscopy, viscous attenuation is most significant in the coupling fluid. In water (and all the other fluids in Table 3.1 except CS2 and superfluid 4He) at the frequencies used in acoustic microscopy, the relaxation time is much less than the period of the wave. Thus cot [Pg.77]

If the specimen is moved away from the focal position, then this will cause a phase shift that depends on 6. If the wavenumber in the coupling fluid is k = 2n/Xo, then the z component of the wavevector is kz = k cos 6. Defocusing the specimen by an amount z causes a phase delay of 2zkz, or 2zk cos 0 (the factor of two arises because both the incident wave and the reflected wave suffer a change in path length). Expressing this phase delay as the complex exponential of a phase angle, the response of the microscope with a defocus z is... 

In most high-resolution lenses, Ft % 1 so that z0, and hence —zmin and zmax, are of the order of Ao. With the further notation that the wavenumber and attenuation in the coupling fluid are k and ( o, respectively, and that the response of the transducer to a uniform field of unit amplitude would be V0> the response to the geometrically reflected field is... 

The inversion procedure is most straightforward when attenuation in the coupling fluid is ignored. This may present problems in high-frequency applications. 

This table gives the accuracy required in each experimental parameter in order to measure a Rayleigh velocity in the vicinity of 3000 m s-1 from V(z) with water as the coupling fluid, assuming the other parameters are exact. If each parameter contributes equal error, then from (8.47) each tolerance must be reduced by 1/ /3. 

If pulses can be generated and detected whose length is short compared with the time difference between reflections from the top and the bottom surfaces of a layer, then the elastic properties of the layer can be deduced from the amplitude and timing of the two echoes. The return pulses from such a situation are illustrated in Fig. 8.10. Figure 8.10(a) is an oscilloscope trace of the reference echo from the substrate at defocus z0 and with nothing on it except the coupling fluid. We can choose to write the reference signal as... 

From the ratio of the magnitude of the reflection A from the top of the layer to the magnitude of the reference signal A0, and knowing the impedance Z0 of the coupling fluid and the impedance Zs of the substrate, the impedance of the cell is... 

If the density pc of the cell is known, then the acoustic velocity in the cell can be immediately deduced, since vc = Zc/pc. Since determination of acoustic velocity by this method depends on the measurement of relative amplitudes, the amplifiers and their gain controls must be accurately calibrated. The combination of reflection and transmission coefficients on the right-hand side of (9.4) can be expressed in terms of the acoustic impedances of the coupling fluid, the cell, and the substrate. 

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