Total linear absorption coefficient

Briefly, the total linear absorption coefficient n (cm-1) varies as a function of the wavelength and the nature of the absorber as the photon energy is varied across and beyond the absorption edge. The logical setup for an absorption experiment in transmission mode therefore consists of three primary components (Fig. 2a) (i) an X-ray source, (ii) a monochromator (and collimator), and (iii) a detector. In this case Beer s law,... 

The first term in the bracket is the contribution from the primary gamma rays (1.17 and 1.33 Mev.) at the point P, r cm. from the point source and the last term is the contribution from the scattered gamma rays at the point P. d is the dose rate in rads per sec. r is the distance in water from the point isotropic 60Co source of C curies fit = 0.0632 cm."1 is the total linear absorption coefficient in water for 1.25 Mev. photons ... 

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

In concentrated systems obtained in a thin uniform shape, the simplest way to record X-ray absorption data is the transmission mode in which the incident and transmitted photons are directly measured by means of ionisation chambers. However, in dilute systems or for surface characterisations, data are usually recorded using secondary effects resulting from the creation of the core hole during the absorption process and from its subsequent relaxation by radiative or non-radiative decays. These processes are the X-ray fluorescence emission and the total electron yield (TEY) emission, respectively. In these detection modes, the linear absorption coefficient is proportional to the ratio of the fluorescence or TEY intensity to... 

Suppose a beam of cross-sectional area A falls on a sheet sample of thickness t in the symmetrical reflection geometry, as in Figure 2.24a. We assume, for the sake of simplicity, that the rays in the beam are all parallel to each other. Now consider a layer of thickness dx inside the sample, at depth x below the flat surface, where the irradiated volume is equal to dx A/ sin 0. Before reaching this depth the beam has traveled distance Z within the sample, where l is equal to x/sin 0, and has suffered attenuation by a factor exp(—/x/), p being the linear absorption coefficient. The scattered beam must travel the same distance within the sample again on its way out. If i 20) is the intensity of scattering per unit volume of the sample, then the contribution dl(20) to the total scattering intensity by the layer dx at depth x is... 

The dependence of Si(Li) detector efficiency on the X-ray energy is shown in Fig. 12.44. For E < 3 keV, the efficiency drops because of absorption of the incident X-rays by the beryllium detector window. For > 15 keV, the efficiency falls off because of the decrease of the total linear attenuation coefficient of X-rays in silicon (Fig. 12.45). 

The number of photons (the intensity) is reduced but their energy is generally unchanged. The term p is called the mass attenuation coefficient and has the dimension cm g . The product pi = pp is called the linear absorption coefficient and is expressed in cm . p(E) is sometimes also called the total cross section for X-ray absorption at energy E. 

Next, we will briefly discuss methods for separating the linear absorption coefficient ocq and the scattering coefficient So(= Sim + 5op) from the overall attenuation coefficient p (Eq. 11). In principle, this is done by measuring the total amount of transmitted light including scattered components (the overall... 

A total of 6416 reflections was collected. The intensities of three representative reflections which were measured after every 150 reflections remained constant throughout data collection indicating crystal and electronic stability (no decay correction was applied). The linear absorption coefficient for Cu Ka is 25.5 cm"l. An empirical absorption correction, based on azimuthal scans of several reflections, was applied which resulted in transmission factors ranging from 0.82 to 1.00. The data were corrected for Lorentz and polarization effects. 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

An exception, with respect to the photosensitised reactions mentioned so far, is represented by the Diels-Alder addition of maleic anhydride to anthracene in dioxane, carried out under irradiation ( = 365 nm) without sensitisers, at 26-45°C. The rate of removal of anthracene was found to be linearly dependent on the total light absorption. As maleic anhydride quenches the fluorescence (transition from excited singlet to ground state) of anthracene, and in agreement with the kinetic evidence, a mechanism was suggested by which singlet anthracene is responsible for cycloaddition rather than triplet anthracene. According to this mechanism, the reaction of the excited diene with maleic anhydride has a rate coefficient of about 3x 10 l.mole . sec, i.e. of the same order as the reported frequency factor of the thermal reac-... 

The integration limits for 6 and (f> for the case of the annular reactor are described by equations 6.52, 6.53, and 6.54. It must be noticed that the exponential term (attenuation) uses the reacting medium total absorption comment while only the reactant absorption coefficient intervenes, with a linear effect, in the value of the LVRPA. Hence i stands... 

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). 

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