Absorption coefficient,

The spectrophotometric method measures the amount of light transmitted through a film of ethylene polymer containing carbon black. The absorption of the sample is compared with a standard to evaluate carbon black dispersion and the amount of carbon black. 

The efficiency at which an atom absorbs x-rays or an atomic nucleus absorbs neutrons can be expressed several ways. The more fundamental way of expressing it is in terms of the absorption cross section aabs, which is defined as the number of photons (or neutrons) absorbed per second by an atom (or a nucleus), divided by the flux of the incident radiation. Since the flux is the number of particles passing through unit area per second, a abs has the dimension of area, usually given in bams (1(T24 cm2). 

The efficacy of absorption by a material depends on the density of its atoms as well as on the absorption cross section of individual atoms. The absorption cross section Eabs per unit volume of the material is then given, in the case of a monatomic substance, by 

For a given type of radiation (and wavelength), aabs is an intrinsic property of the element, whereas Eabs (= p) is a property of the particular material sample, being dependent on its mass density p and therefore on temperature and whether the sample is crystalline or amorphous, etc. X-Ray literature usually cites, instead of aabs, the mass absorption coefficient /z/p(= aabs Nklm), which is the absorption cross section per unit mass, an intrinsic property of the element. 

The process of absorption of x-rays or neutrons is not affected by the state of bonding of the atoms in the material, and therefore for a material consisting of more than one element, the overall absorption coefficient depends only on the relative numbers of various atoms present in it. Thus the linear absorption coefficient of a sample can be calculated by 

Element Atomic Number Absorption Cross-Section O abs (10 24 Cm2) Mass Absorption Coefficient n/p (cm2/g)  

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The sensitivity of the luminescence IP s in the systems employed here decreases with increasing x-ray energy more strongly than in the case of x-ray film. Therefore, this phenomenon must be compensated by using thicker lead front and back screens. The specific contrast c,p [1,3] is an appropriate parameter for a comparison between IP s and film, since it may be measured independently of the spatial resolution. Since the absorption coefficient p remains roughly constant for constant tube voltage and the same material, it suffices to measure and compare the scatter ratio k. Fig. 2 shows k as a function of the front and back screen thickness for the IP s for 400 keV and different wall thicknesses. The corresponding measured scatter ratios for x-ray films with 0,1 mm front and back screens of lead are likewise shown. The equivalent value for the front and back screen thicknesses is found from the intersection of the curves for the IP s and the film value. 

Fig. 2 shows the response of a C2 film system on a step wedge (wall thickness range 2. .. 18 mm) exposed with a X-ray tube at 160 kV. For the exposure withy-rays (Irl92 or Co60) corresponding linear relationships are obtained. From this linear relationship it is followed, that the influence of the scattered radiation and the energy dependence of the absorption coefficient can be considered by an effective absorption coefficientPcff in equation (1). 

After this calibration step (the effective absorption coefficient is determined from a known wall thickness change and the corresponding variation of the optical film density) the evaluation of local wall thickness changes Aw (corresponding to De,o) from the nominal wall thickness w o , (corresponding to Dnom) can be done according to ... 

After the calibration step an effective absorption coefficient according to equation (3) ofpeir = 1.48 1/em was determined. 

The expression exp(-cxx) describes the reduction of the wave amplitude in absorbing materials. The damping coefficient a can be split into an absorption coefficient Oa and the scattering coefficient Oj. 

The detailed examination of the behavior of light passing through or reflected by an interface can, in principle, allow the determination of the monolayer thickness, its index of refiraction and absorption coefficient as a function of wavelength. The subjects of ellipsometry, spectroscopy, and x-ray reflection deal with this goal we sketch these techniques here. 

The quantity e is called the absorption coefficient or extinction coefficient, more completely the molar decadic absorption coefficient it is a characteristic of the substance and the wavelength and to a lesser extent the solvent and temperature. It is coimnon to take path length in centimetres and concentration in moles per... 

Votsmeier M, Song S, Davidson D F and Hanson R K 1999 Shock tube study of monomethylamine thermal decomposition and NH2 high temperature absorption coefficients int. J. Chem. Kinetics 31 323-30... 

Absorption coefficient, linear decaidic a. K Aqueous solution at infinite dilution aq, CO... 

Magnetic dipole moment of a molecule m, fJL Molar (decadic) absorption coefficient e... 

Table 7.8 Mass Absorption Coefficients for Ka., Lines and WLa-, Line...

Mass Absorption Coefficients. Radiation traversing a layer of substance is diminished in intensity by a constant fraction per centimeter thickness x of material. The emergent radiant power P, in terms of incident radiant power Pq, is given by... 

Table 7.8 contains values of p,/p for the common target elements employed in X-ray work. A more extensive set of mass absorption coefficients for K, L, and M emission lines within the wavelength range from 0.7 to 12 A is contained in Heinrich s paper in T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry (eds.). The Electron Microprobe, Wiley, New York, 1966, pp. 351-377. This article should be consulted to ascertain the probable accuracy of the values and for a compilation of coefficients and exponents employed in the computations. 

TABLE 7.8 Mass Absorption Coefficients for Kai Lines and W Lai Line (Continued)... 

In an EXAFS experiment the measurable quantity is the absorption coefficient a of Equation (8.16). If Qq is the absorption coefficient in the absence of EXAFS, deduced from the steeply falling background shown in Figure 8.32, then x k), the fractional change of a due to EXAFS, is given by... 

Internal redection starts by consideration of an interface between two media, a denser transparent medium with refractive index n, and a rarer medium with a complex refractive index (= where is the absorption coefficient of the medium) as shown in Figure 23. If of the rarer... 

Transmission. The spectral transmission of glass is determiaed by reflectioa at the glass surfaces and the optical absorption within the glass. Overall transmission of a flat sample at a particular wavelength is equal to (1 — R), where P is the absorption coefficient, t the thickness of glass, and... 

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