Premium
Direct analysis of small‐angle smeared intensity tails. I. General results
Author(s) -
Ciccariello Salvino,
Sobry Roger
Publication year - 1999
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/s0021889899000618
Subject(s) - physics , slit , monotonic function , intensity (physics) , optics , momentum transfer , exponent , kernel (algebra) , atomic physics , mathematical analysis , scattering , mathematics , linguistics , philosophy , combinatorics
The leading asymptotic terms of small‐angle slit‐smeared intensities, at large momentum transfer h = (4π/λ)sin (θ/2), are obtained from the pinhole intensities by an integral transform whose kernel is the beam‐height profile determined by the slits used in a Kratky camera. This profile, directly measurable, generally shows a trapezoidal shape characterized by Q 0 , the end point of its horizontal plateau, and Q 1 , the momentum‐transfer value beyond which it vanishes. It results that any pinhole contribution, monotonically decreasing as 1/ h α , after being smeared, decreases as 1/ h (α−1) in the region h < Q 0 , while the power exponent monotonically increases from (α− 1) to α in the outer h region. The actual change explicitly depends on the slit length. On the contrary, the oscillatory damped contributions cos ( h δ)/ h 4 and sin ( h δ)/ h 4 , after being smeared, remain close, whatever the slit length, to those resulting from the smearing with an ideal slit.