Scattering functions of Platonic solids

Journal Article · Sat Jan 01 00:00:00 EST 2011 · Journal of Applied Crystallography

DOI:https://doi.org/10.1107/S0021889811011691· OSTI ID:1023336

Li, Xin ^[1]; Shew, Chwen-Yang ^[2]; He, Lilin ^[3]; Meilleur, Flora ^[3]; Myles, Dean A A ^[3]; Liu, Emily ^[1]; Zhang, Yang ^[3]; Smith, Greg ^[3]; Herwig, Kenneth W ^[3]; Pynn, Roger ^[3]; Chen, Wei-Ren ^[3]

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1. Rensselaer Polytechnic Institute
2. City University of New York (CUNY)
3. ORNL

The single-particle small-angle scattering properties of five Platonic solids, including the tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, are systematically investigated. For each given geometry, the Debye spatial autocorrelation function, pair distance distribution function and intraparticle structure factor (form factor) are calculated and compared with the corresponding scattering function of a spherical reference system. From the theoretical models, the empirical relationship between the dodecahedral and icosahedral structural characteristics and those of the equivalent spheres is found. Moreover, the single-particle scattering properties of icosahedral and spherical shells with identical volume are investigated, and the prospect of using different data analysis approaches to explore their structural differences is presented and discussed.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1023336
• Journal Information: Journal of Applied Crystallography, Vol. 44, Issue 3; ISSN 0021--8898
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
DATA ANALYSIS
DISTRIBUTION FUNCTIONS
GEOMETRY
SCATTERING
STRUCTURE FACTORS