Linear absorption coefficient effective

It is important to recognize that an effective linear absorption coefficient, Peff, has been introduced into Eq. 2.72 to account for a lower density of dusted or packed powder when compared with the linear absorption coefficient, p, of the bulk. The latter is usually used in diffraction from single crystals. 

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... 

The investigated CuPc in solution showed a good combination of a relatively high absorption cross section /c, a relatively high effective NL absorption coefficient /3eff> a very low energy-dependent saturation FsaU and a low linear absorption coefficient a0. The excellent combination of these values makes CuPc a very good candidate as an OL material [58]. 

The requirements of high-energy resolution are well met by Si and Ge. The photoelectric effect increases with Z to Z, where Z is the atomic number of the substance, and the linear absorption coefficient for lOOkeV y rays in Ge is higher than in Si by a factor of about 40. Therefore, Ge crystals are better suited for measuring y radiation. Semiconductors with still higher atomic numbers, such as CdTe and Hgl2, have been investigated with respect to their suitability as detector materials, but they are not commonly used. 

The isolation of Cu Kv. radiation may be taken as an example. Its wavelength is 1.542 A, which means that cobalt and nickel can be used as filter materials since their K absorption edges (1.608 and 1.488 A, respectively) effectively bracket the Cu Kti line. Their linear absorption coefficients p are plotted in Fig. 7-29(a), which shows that balancing can be obtained by making the nickel filter somewhat thinner than the cobalt one. When their thicknesses. v are adjusted to the correct ratio, then = l co co except in the pass band, and a plot of //.y versus /. has... 

Note that fi , the linear absorption coefficient of the mixture and an unknown quantity, drops out. Physically, this means that variations in absorption, due to variations in the relative amounts of B, C, D,..., have no effect on the ratio IJIs since they affect and in the same proportion.)... 

Microabsorption and extinction, if present, can seriously decrease the accuracy of the direct comparison method, because this is an absolute method. Fortunately, both effects are negligible in the case of hardened steel. Inasmuch as both the austenite and martensite have the same composition and only a 4 percent difference in density, their linear absorption coefficients are practically identical. Their average particle sizes are also roughly the same. Therefore, microabsorption does not occur. Extinction is absent because of the very nature of hardened steel. The change in specific volume accompanying the transformation of austenite to martensite sets up nonuniform strains in both phases so severe that both kinds of crystals can be considered highly imperfect. If these fortunate circumstances do not exist, and they do not in most other alloy systems, the direct comparison method should be used with caution and checked by some independent method. 

Absorption means diminution of coherent x-ray intensity in the crystal through inelastic processes such as atomic absorption and fluorescence, photoelectron emission, and Compton effect extinction means intensity diminution due to loss through diffraction by fortuitously oriented mosaic blocks. The simple extinction expression due to Darwin, given in Eq. (18), is only a rough approximation more accurate treatments will be mentioned in what follows. In Eq. (17) the absorption factor is expressed in terms of the linear absorption coefficient /inn (calculated from tabulated values of the elemental atomic or mass absorption coefficients, updated values of which will appear in Vol. IV of International Tables,2 the path length f, of the incident ray from the crystal surface to the point of diffraction r, and the path length t2 of the diffracted ray from that point to the crystal surface. 

The effective absorption coefficient, eff, and threshold fluence, Fth, were calculated according to Eq. 1 and are summarized in Table 1. The aeff values calculated at low fluences are much larger than those obtained at high flu-ences. The effective absorption coefficients do not correlate with the linear absorption coefficients (Table 1), maybe with the exception of PI. A difference between the values of aeff and aan is observed for most polymers. An important feature is the similarity of aeff for all designed polymers, including PE (%54,000 5000 cm1), while PI reveals a much higher value (Table 1). 

Many of the above described features are quite different to published and our own data for polyimide. Polyimide (PI) has a linear absorption coefficient at 308 nm similar to the designed polymers (around 95,000 cm-1). The first pronounced differences between the ablation characteristics between PI and our polymers are the higher threshold of ablation (three times), lower etch rates, and an effective absorption coefficient which is similar to the linear absorption coefficient. A comparison of the ablation quality between a designed polymer (TP) and the standard polymer (PI) is shown in Fig. 74. 

Avalanche coefficient Linear absorption coefficient Effective absorption coefficient Ablation depth per pulse (=ablation rate) Diameter of ablated (modified) area Thermal diffusivity... 

Ablation Parameters The main parameters that describe polymer ablation are the ablation rate, d(F), and the ablation threshold fluence, b]h. which is defined as the minimum fluence where the onset of ablation can be observed. A third important parameter is the effective absorption coefficient, aeff, which yields information on the mechanisms that take place in the ablation process when compared to the linear absorption coefficient, a]m, that is measured on thin unirradiated polymer films. 

A ). By means of the to -2 6 scanning technique, 2034 independent reflections at less than sin 6 / A =0.589A were colleted and used for the structure determination. Corrections were made for Lorentz and polarization effects. Although the linear absorption coefficient of this crystal is relatively large [ /x (Cu-X,)= 33.56 cm1], absorption correction was not made because of the small size of the crystal used. The structure was solved by a combination of the heavy atom and direct... 

Absorption coefficients define the X-ray attenuation effect from a given solids. We use both mass absorption coefficients, //m, and linear absorption coefficients, p, with these being related by ju = j.umpx, where p is the density of a given solid and x is the X-ray path length. The mass absorption for any material can be calculated from the elemental mass absorption coefficients by the relation pm = Z/ / where the f and the are the weight fraction and linear absorption coefficients, respectively, for each element in the material. 

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