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On the Porod law
Author(s) -
Ciccariello S.,
Goodisman J.,
Brumberger H.
Publication year - 1988
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889887010409
Subject(s) - discontinuity (linguistics) , physics , momentum transfer , plateau (mathematics) , mesoscopic physics , radius , boundary (topology) , mathematics , condensed matter physics , scattering , mathematical analysis , quantum mechanics , computer security , computer science
The Porod law states that i ( h ), the intensity of X‐radiation scattered by an ideal multiphase noncrystalline system, for `large' momentum transfer values (≡ h ) approaches h −4 and that is linearly related to the interphase surface areas. A more general expression is obtained which relates the value of the correlation‐function derivative at the origin to the integral of the discontinuity of the electron density fluctuation along the discontinuity surface. Debye's assumption, by which the continuous electron density of the sample is approximated by a discrete‐valued one, is critically discussed. The validity of the approximation results in the presence of a Porod plateau [ h 4 i ( h ) = constant]. The momentum transfer range where the plateau is observed is related to the scale of lengths where the sharp‐boundary idealization remains essentially unchanged. It is argued that the scattered intensity can show more than one Porod plateau and some examples of correlation functions with this behaviour are reported. The problem of the background subtraction is discussed and the corresponding coefficients are related to the electron densities relevant to the real and to the associated sharp‐boundary sample.