Radiation absorption coefficients

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

The condensed phase density p, specific heat C, thermal conductivity A c, and radiation absorption coefficient Ka are assumed to be constant. The species-A equation includes only advective transport and depletion of species-A (generation of species-B) by chemical reaction. The species-B balance equation is redundant in this binary system since the total mass equation, m = constant, has been included the mass fraction of B is 1-T. The energy equation includes advective transport, thermal diffusion, chemical reaction, and in-depth absorption of radiation. Species diffusion d Y/cbfl term) and mass/energy transport by turbulence or multi-phase advection (bubbling) which might potentially be important in a sufficiently thick liquid layer are neglected. The radiant flux term qr... 

Equation (12.5.A-c) expresses that net changes in the radiation intensity result from flue gas absorption and emission, kg is the radiation absorption coefficient [m T Equations for the coefficients A and B in (12.5.A-b) are obtained by integration of (12.5.A-c) over six segments of the total soUd angle... 

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). 

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... 

Thickness. The traditional definition of thermal conductivity as an intrinsic property of a material where conduction is the only mode of heat transmission is not appHcable to low density materials. Although radiation between parallel surfaces is independent of distance, the measurement of X where radiation is significant requires the introduction of an additional variable, thickness. The thickness effect is observed in materials of low density at ambient temperatures and in materials of higher density at elevated temperatures. It depends on the radiation permeance of the materials, which in turn is influenced by the absorption coefficient and the density. For a cellular plastic material having a density on the order of 10 kg/m, the difference between a 25 and 100 mm thick specimen ranges from 12—15%. This reduces to less than 4% for a density of 48 kg/m. References 23—27 discuss the issue of thickness in more detail. 

Sihcon cells are hundreds of micrometers ( -lm) thick in order to faciUtate handling with minimal breakage, although most solar radiation is absorbed in the first 20—30 p.m. Light penetration decreases exponentially, proportional to, where d is the absorption coefficient of a material and T is its thickness. The values of (X for a given material vary with the wavelength of incident radiation in siUcon, (X is 10 —10 /cm over most of the range of usable solar radiation. 

Flere C is the volume concentration of j-phase particles is the mass concentration of the analyte in the j-phase particles w is the x-ray fluorescence radiation yield t. is the mass absorption coefficient of the analyte for the primar y radiation d. is the j-phase particle effective size r fs... 

Assuming the approximate absorption coefficient of solar radiation to be 0.65, for a light-grey external surface, having collected soot and dirt over a period of time, as in ANSI-C-37-24 the approximate temperature rise on account of solar radiation... 

Nx = / nowhere Ix is the radiation flux, n is the number of gas molecules in the path of the beam per cm of projected area, and a is the cross-section of absorption. Alternatively, the absorption coefficient, is defined drrough the Beer-Lambert equation... 

The rate of heat conduction is further complicated by the effect of sunshine onto the outside. Solar radiation reaches the earth s surface at a maximum intensity of about 0.9 kW/ m. The amount of this absorbed by a plane surface will depend on the absorption coefficient and the angle at which the radiation strikes. The angle of the sun s rays to a surface (see Figure 26.1) is always changing, so this must be estimated on an hour-to-hour basis. Various methods of reaching an estimate of heat flow are used, and the sol-air temperature (see CIBSE Guide, A5) provides a simplification of the factors involved. This, also, is subject to time lag as the heat passes through the surface. 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

We have limited our investigations to the action of gamma-rays and fast neutrons on aromatic, alicyclic, aliphatic, and ionic compounds. The absorption coefficients for these types of radiation have an order of magnitude of lO /cm which is particularly adequate. Shallow penetrating radiations would only alter the superficial layers and would obviously not be able to affect the intensity of the quadrupole line substantially. This is for instance the case for ultraviolet light which has been shown to be unable to produce any effect on the resonance line of iodoform (CHI3 3Sg)... 

Fig. 2.3. Schematic variation of absorption coefficient as a function of the frequency of absorbed radiation experimental curve (1) and theoretical curves in Debye approximation (2) and impact approximation (3) (Rocard formula).

The irradiation-induced absorption coefficient // may be a better way of evaluating the radiation hardness and it is expressed as ... 

Complex processes are involved in transmittance and reflectance of scattered radiation, which are theoretically described by Schuster [4]. In an ideal scattering medium all fluxes of light can be summed up as components of two vectors. Vector I stands for the light flux in the direction of the incident light, and the vector J describes the light intensity in the antiparallel direction. With k, the absorption coefficient, and 5", the scattering coefficient, the two Schuster equations are as follows ... 

Mass absorption increases strongly with the atomic number Z. For the 14.4 keV radiation of Fe, the coefficient follows approximately the relation k. 0.003 from oxygen to krypton. Therefore, organic solvents containing sulfur or chlorine are virtually opaque to the Mossbauer radiation. The sulfur component of a 2 mm layer of dimethylsulfoxide (DMSO) absorbs 70% of the Mossbauer radiation (/ = 1.1 g cm ) [35]. Even worse is dichloromethane (CH2CI2), having an absorption coefficient of 16.83 cm g. A layer of 0.1 g cm , which is only 0.75 mm thick (p = 1.33 g cm ), absorbs about 82% of 14.4 keV radiation. For the same reason, chlorinated polymers (PVC) or glass should not be used for... 

Table B.l Mass absorption coefficients for the 14.41-keV Mossbauer radiation of Fe...

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). 

Absorption Coefficient, Linear—A factor expressing the fraction of a beam of x- or gamma radiation absorbed in a unit thickness of material. In the expression I=I0e+l x, I0 is the initial intensity, I the intensity of the beam after passage through a thickness of the material x, and p is the linear absorption coefficient. 

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