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The puzzle‐interlayer model: an approach to the analysis of tightly packed arrangements of hard particles
Author(s) -
Gille Wilfried
Publication year - 2007
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/s0021889806055130
Subject(s) - physics , scattering , tessellation (computer graphics) , homogeneous , small angle scattering , geometry , plane (geometry) , chord (peer to peer) , particle (ecology) , space (punctuation) , materials science , molecular physics , crystallography , statistical physics , chemistry , optics , mathematics , distributed computing , oceanography , computer science , geology , linguistics , philosophy
The small‐angle scattering (SAS) structure functions are analyzed for an idealized, random two‐phase system: a stationary arrangement of hard puzzle particles, separated by a relatively thin interspace, which can be approximated by an interlayer. The detailed shape of the interlayer is defined by the shape of the particles themselves: The starting point for producing these initial particles is a three‐dimensional initial puzzle in the state of tessellation. Its pieces, homogeneous particles of random shape, fit together filling the space. In a second step, an expanded puzzle is constructed by translating the initial particles by a certain length (relative to one another). The whole tightly packed particle arrangement depends on . The interlayer region between the particles is a connected, homogeneous region. The SAS intensity of depends on the parameter and on the typical shape and size of the pieces of . Chord length distributions (CLDs) are used in the description. The random shape of the pieces of possesses a CLD 1. The CLD 2 of the intermediate spaces is approximated by that of an idealized layer of constant thickness . The scattering of results in terms of the CLDs of both phases. The approach can be applied to many types of . Two initial tessellations of are studied, a `dead leaves' tessellation produced by spherical primary grains and the Poisson plane mosaic.