Microabsorption of X-ray Intensity in Fractal Microstructures

Abstract

Analytical models for isotropic random surface fractals with tunable fractal dimension, d/; and variable microstructural parameters are used to investigate the microabsorption of X-rays scattered symmetrically from planar samples. The models characterize homogeneous materials the constituents of which differ by their linear absorption coefficients. The absorption contrast between the fractal scattering phase and the mean value of the material is assumed to be small. It is shown that the microabsorption is maximum if the fractality of the internal surface is low (df ~ 2) whereas it vanishes for df ~ 3 irrespective of other microstructural parameters and the absorption contrast. For one of the models, a simple analytical expression is presented describing the microabsorption effect of surface fractals with an accuracy of about 20% for arbitrary fractal dimension and volume fraction.

Microabsorption of X-rays in Planar Powder Samples in the Non-Symmetric Reflection Case

“…Formula (37) is in accordance with the result of Hermann & Collazo (1995). Here again, the bulk contributions to microabsorption for spherical and polyhedral grains differ only weakly by a numerical factor.…”

“…0 whereas for spherical grains go(r) --(3df ) [a 0 + alr/[~ -a2(r/[~) 3 -a3(r/[O3-dQ, a 0 = 1/(3 -df),a I = (3/2) [1/(df-2)],a 2 = 1/2df, a 3 = a o + a, -a 2 = 3/[df(df -2)(3df)], 0<r</~ (34) (Hermann & Collazo, 1995). Here, /~ denotes the maximum mean breadth of grains.…”

Calculation of the Penetration Depth of X-rays in Intact Pharmaceutical Film-Coated Tablets by Microdiffractometory

“…The magnitude of absorption of X-rays in the tablets will depend not only on the spatial distribution of the particles of microcrystalline cellulose and cerium oxide but also on their linear attenuation coefficient values (22). The linear attenuation coefficients of microcrystalline cellulose and cerium oxide are 9.4 and 391.7 cm 2 /g (CuKa radiation), respectively.…”

Dielectric Reliability for Future Logic and Non-Volatile Memory Applications: a Statistical Simulation Analysis Approach

“…Once oxide defects have been generated, the total leakage current I OX is calculated by summing both defect-assisted (I PTAT ) and direct-FN tunneling (I TUNN ) contributions. The PTAT model adopted (3,5) accounts for electron coupling to oxide phonons, which results in a series of virtual states in the oxide energy band-gap. The leakage current flowing through each randomly generated trap is automatically calculated, checking if multi-trap conductive paths are formed within the oxide.…”