期刊
JOURNAL OF APPLIED CRYSTALLOGRAPHY
卷 48, 期 -, 页码 565-577出版社
WILEY-BLACKWELL
DOI: 10.1107/S1600576715002964
关键词
polyhedra; subunits; scattering functions; small-angle scattering; form factors
资金
- US DOE [DE-AC02-06CH11357]
Herein, a general method to calculate the scattering functions of polyhedra, including both regular and semi-regular polyhedra, is presented. These calculations may be achieved by breaking a polyhedron into sets of congruent pieces, thereby reducing computation time by taking advantage of Fourier transforms and inversion symmetry. Each piece belonging to a set or subunit can be generated by either rotation or translation. Further, general strategies to compute truncated, concave and stellated polyhedra are provided. Using this method, the asymptotic behaviors of the polyhedral scattering functions are compared with that of a sphere. It is shown that, for a regular polyhedron, the form factor oscillation at high q is correlated with the face-to-face distance. In addition, polydispersity affects the Porod constant. The ideas presented herein will be important for the characterization of nanomaterials using small-angle scattering.
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