Material-dependent attenuation coefficient

In materials which are highly attenuating, the particle velocity and particle displacement are out of phase, so the elastic modulus and density of the material are complex and dynamic ( .e. frequency dependent). For many materials, the attenuation coefficient is fairly small ( .e. a co/c), so the particle velocity and displacement are in phase and Eq. 9.4 can be replaced with ... 

The radiation protective properties of RubCon with regard to y-radiation are defined by linear attenuation coefficient (LAC) value. LAC is the actual fraction of photons interacting per unit thickness of material. Linear attenuation coefficient values indicate the rate at which photons interact as they move through material. LAC depends on properties of the material and radiant energy. 

Yasui et al. [29] have used solution of wave equation based on finite element method for characterization of the acoustic field distribution. A unique feature of the work is that it also considers contribution of the vibrations occurring due to the reactor wall and have evaluated the effect of different types of the reactor walls or in other words the effect of material of construction of the sonochemical reactor. The work has also contributed to the understanding of the dependence of the attenuation coefficient due to the liquid medium on the contribution of the vibrations from the wall. It has been shown that as the attenuation coefficient increases, the influence of the acoustic emission from the vibrating wall becomes smaller and for very low values of the attenuation coefficient, the acoustic field in the reactor is very complex due to the strong acoustic emission from the wall. 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

In practice ultrasound is usually propagated through materials in the form of pulses rather than continuous sinusoidal waves. Pulses contain a spectrum of frequencies, and so if they are used to test materials that have frequency dependent properties the measured velocity and attenuation coefficient will be average values. This problem can be overcome by using Fourier Transform analysis of pulses to determine the frequency dependence of the ultrasonic properties. 

A complete analysis is made by acquiring a number of radiographs (typically about 1000) of the same sample under different viewing angles (one orientation for each radiograph). A final computed reconstruction step is required to produce a 3D map of the linear attenuation coefficients in the material. This 3D map indirectly gives a picture of the structure density. In the X-ray-computed tomography, the X-ray source and detector are placed at the opposite sides of the sample. The spatial resolution of the attenuation map depends on the characteristics of both the detector and number of X-ray projections. 

According to Evans (1995), differentiation of features within the materials is possible because p at each point directly depends on the electron density of the material in that point (pe), the atomic number (Z) of the chemical components of the materials in that point, and the energy of the incoming X-ray beam (/0). In particular, the linear attenuation coefficient can be approximately considered as the sum of the Compton scatter and photoelectric contributions ... 

In the case of conventional sources, the ability to discriminate among materials with closely similar linear attenuation values (or bulk density) strongly depends on the accuracy of the /(voxc value determination (Denison et al., 1997). For each individual object voxel within a digital image, it is possible to compute a normalized attenuation coefficient known as CT number from the linear attenuation ... 

Like the ultrasonic velocity and attenuation coefficient, the acoustic impedance is a fundamental physical characteristic which depends on the composition and microstructure of the material concerned. Measurements of acoustic impedance can therefore be used to obtain valuable information about the properties of materials. 

A wave can be characterized by an amplitude, frequency, and wavelength which may change with time or distance traveled from the source. We can express both the storage and loss properties of a sonic wave moving in a material concisely as the real and imaginary parts of a complex wavenumber k = co/c + ia, where c is the speed of sound, co is the angular frequency (=2 Jt/),/is frequency, / = V - 1, and a is the attenuation coefficient. Ultrasonic properties are often frequency dependent so it is necessary to define the wavelength at which k is reported. The dependency of k on frequency is the basis of ultrasonic spectroscopy. 

The specific Compton mass attenuation coefficient (p) is a material constant. It depends on the energy of the gamma rays and on the ratio (Z/A) of the number of electrons (Z) to the atomic mass (A) of the material (Ellis 1987). For most sediment and rock forming minerals this ratio is about 0.5, and for a Cs source the corresponding mass attenuation coefficient (p ) for sediment grains is 0.0774 cm g. However, for the hydro-... 

The attenuation coefficient. The total cross section of interaction of a gamma radiation photon with an atom is equal to the sum of all three mentioned partial cross sections a = Oc+Of+o. Depending on the photon energy and the absorber material, one of the three partial cross sections... 

As already mentioned, the total attenuation coefficient is the sum of the attenuation coefficients for each interaction process (eqn [1]). The percentage contribution of each process to the total attenuation changes with photon energy and depends on the atomic number of a single element absorber or the so-called effective atomic number in case of complex materials. 

Here fi is they-ray linear attenuation coefficient, usually measured in cm units. It is a sum of the interaction terms described in O Chap. 6 in this Volume, hence it is also called total attenuation coefficient. Its inverse is called the mean free path, while the thickness reducing the photon beam by half is the half-thickness di/y, both are measured in cm. Frequently the mass attenuation coefficient pip is used, because it does not depend on the physical state of the material. Its dimension is cm /g if the density p is given in g/cm units. Another important quantity is the mass-energy absorption coefficient p Jp, measured in the same units, which characterizes the energy deposition by photons. AH these quantities, their units and usage have been defined by the International Commission on Radiation Units and Measurements (ICRU) in ICRU Report 33 (ICRU 1980), which has recently been superseded by two new ones (ICRU 1993c, 1998). 

X-ray and neutron imaging are complementary techniques for materials research. X-rays interact mainly with the electronic shell of atoms whereas neutrons as charge-neutral particles interact with the nuclei (Figure 18.1a,b). The different interaction mechanisms yield different beam attenuation properties. Figure 18.1c shows the values for the attenuation coefficients of X-rays and neutrons for different element numbers. In the case of X-rays, the attenuation increases with the number of electrons in the atom and, therefore, with the element number. In case of neutrons, no clear dependence on the amount of nuclei within the atomic core can be found. In contrast to X-rays, some light elements such as H and Li have a very... 

Since the attenuation coefficient depends on (he atomic number and the density of the examined material, it is possible to differentiate between different materials (DIN Deutsches Institut fur Normung e.V., 1997). 

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