Absorption factor

Throughout the passage through materials, x-rays undergo an attenuation of intensity as a result of their absorption. In this regard, the Lambert-Beer law [20,26] 

The Physical Chemistry of Materials Energy and Environmental Applications 

In the case of testing a powdered sample in a Bragg-Brentano diffractometer, the sample has the shape of a flat plate located parallel to the reflecting plane, making equal angles with the incident and diffracted beams then, if we have a single phase in the sample, the absorption factor is given by [21] 

It must be noted that this factor is independent of the diffraction angle 0. This fact is caused by the precise equilibrium between two opposite effects, that is, when 0 is small, the sample area irradiated by the incident beam of fixed cross section is large, but the penetration depth of the beam is small. On the contrary when 0 is large, the area irradiated is small but the penetration depth is high, since volume is area multiplied by depth, then the effective volume irradiated is almost constant and, therefore, independent of 0. 

Still another factor affecting the intensities of the diffracted rays must be considered, and that is the absorption which takes place in the specimen itself. We allow for this effect in intensity calculations by introducing the absorption factor A, which is a number by which the calculated intensity is to be multiplied to allow for absorption. The calculation of A depends on the geometry of the diffraction method involved, and we will consider below the two most-used methods. 

The specimen in the Debye-Scherrer method has the form of a very thin cylinder of powder placed on the camera axis, and Fig. 4-18(a) shows the cross section of such a specimen. For the low-an le reflection shown, absorption of a particular ray in the incident beam occurs along a path such as AB at 5 a small fraction of the incident energy is diffracted by a powder particle, and absorption of this diffracted beam occurs along the path BC. Similarly, for a high-angle reflection, absorption of both the incident and diffracted beams occurs along a path such as DE -I- EF). The net result is that the diffracted beam is of lower intensity than one would expect for a specimen of no absorption. 

A calculation of this effect shows that the relative absorption increases as 6 decreases, for any given cylindrical specimen. That this must be so can be seen from Fig. 4-18(b) which applies to a specimen (for example, tungsten) of very high absorption. The incident beam is very rapidly absorbed, and most of the diffracted beams originate in the thin surface layer on the left side of the specimen backward-reflected beams then undergo very little absorption, but forward-reflected beams have to pass through the whole specimen and are greatly absorbed. Actually, the forward-reflected beams in this case come almost entirely from the top and bottom 

Exact calculation of the absorption factor for a cylindrical specimen is often difficult, so it is fortunate that this effect can usually be neglected in the calculation of diffracted intensities, when the Debye-Scherrer method is used. Justification of this omission will be found in Sec. 4-11. 

The calculation of A( ) for a cylindrical specimen proceeds as follows. In Fig. 4-18(a) the path length (AB + BC), for a given value of 0, is expressed as a function of the position x, y of the point B relative to coordinate axes fixed relative to the specimen. The absorption factor A(0) is then given by the function integrated over the 

Taking into account Eq. 2.8, the following integral equation expresses the reduction of the diffracted intensity, A, as the result of absorption  

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. 

72 can be solved analytically for all geometries usually employed in powder diffraction. For the most commonly used Bragg-Brentano focusing geometry the two limiting cases are as follows  

The material has low linear absorption or the sample is thin so that the incident beam is capable of penetrating all the way through the sample. The absorption correction in this case is a function of Bragg angle as shown in Eq. 2.74. Once again, the constant coefficient l/2peff is usually omitted since it becomes a part of the scale factor  

In single crystal diffraction, absorption correction is usually applied to the observed intensities and therefore, A is sometimes called the transmission factor, while the corresponding absorption correction sA = IA. 

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Pharmacokinetics is the study of how the body affects an adiriinistered dmg. It measures the kinetic relationships between the absorption, distribution, metaboHsm, and excretion of a dmg. To be a safe and effective dmg product, the dmg must reach the desired site of therapeutic activity and exist there for the desired time period in the concentration needed to achieve the desired effect. Too Htde of the dmg at such sites yields no positive effect ( MTC) leads to toxicity (see Fig. 1). For intravenous adininistration there is no absorption factor. Total body elimination includes both metabohc processing and excretion. 

In the rectifying section, the equilibrium relationship for component at any stage n can be expressed in terms of component flow rate in the distillate d = Dxd and component absorption factor A = hjKiS... 

Note that the absorption factor is the reciprocal of the expression given in Eq. (14-4) for packed columns. 

Algebraic Method for Concentrated Gases When the feed gas is concentrated, the absorption factor, which is defined in general as A = where K = y°/x, can vary throughout the tower owing... 

For systems in which the absorption factor A for each component is not constant throughout the tower, an effective absorption factor for use in the equations just presented can be estimated by the Edmister formula... 

This procedure is a reasonable approximation only when no pinch points exist within the tower and when the absorption factors vary in a regular manner between the bottom and the top of the tower. 

Both factors depend on the respective partial vapor pressures of water and carbon dioxide and upon the distance to the radiation source. The partial vapor pressure of carbon dioxide in the atmosphere is fairly constant (30 Pa), but the partial vapor pressure of water varies with atmospheric relative humidity. Duiser (1989) published graphs plotting absorption factors (a) against the product of partial vapor pressure and distance to flame (Px) for flame temperatures ranging from 800 to 1800 K. 

Absorbed Dose Equivalent to intake multiplied by an absorption factor... 

A = absorption factor, i.e.,the fraction of carcinogen absorbed by the human body ED = exposure duration... 

Determine the action level in pg/iiv for an 80 kg person with a life expectancy of 70 years exposed to benzene over a 15-year period. The "acceptable risk is one incident of cancer per 1 million persons or lO ". Assume a breathing (intake) rate of 15 m /d and an absorption factor of 75%. The potency factor for benzene is 1.80 (mg/kg-d)." ... 

Afii = absorption factor for each component at conditions of bottom tray. 

Effective Absorption Factor for n-C4. The total rich oil out is estimated as... 

Edmister s effective absorption factor Outside surface area of absorber, ft ... 

Absorption factor, average Effective absorptive factor... 

Surfaces will absorb radiant heat and this factor is expressed also as the ratio to the absorptivity of a perfectly black body. Within the range of temperatures in refrigeration systems, i.e. - 70°C to + 50°C (203-323 K), the effect of radiation is small compared with the conductive and convective heat transfer, and the overall heat transfer factors in use include the radiation component. Within this temperature range, the emissivity and absorptivity factors are about equal. 

The parameters were then further refined by four successive least-squares procedures, as described by Hughes (1941). Only hk() data were used. The form factor for zinc was taken to be 2-4 times the average of the form factors for magnesium and aluminum. The values of the form factor for zinc used in making the average was corrected for the anomalous dispersion expected for copper Kot radiation. The customary Lorentz, polarization, temperature, and absorption factors were used. A preliminary combined scale, temperature, and absorption factor was evaluated graph-... 

In EPMA, X-rays are produced over a range of depths from the surface before their energy falls below Ec. In order to derive the effective absorption factor, an integration must be carried out which requires a knowledge of the shape of the depth distribution of X-ray production. 

If j/ is the X-ray takeoff angle in the instrument, then the absorption factor f(x), where x = pcosec, may be written (Reed 1993) ... 

The amount of a component absorbed or stripped in a column is dependent on the column design (the number of stages), the component solubility, and the gas and liquid rates. The fraction absorbed can be estimated using the absorption factor method, attributed to Kremser (1930) (see Volume 2, Chapter 12). If the concentration of solute in the solvent feed to the column is zero, or can be neglected, then for the solute component the fraction absorbed =... 

The group L/VKj is known as the absorption factor Ah and is the ratio of the mols of any component in the liquid stream to the mols in the vapour stream. 

The group VKi/L is called the stripping factor S, and is the reciprocal of the absorption factor. 

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