TY - JOUR
T1 - Scattering functions of Platonic solids
AU - Li, Xin
AU - Shew, Chwen Yang
AU - He, Lilin
AU - Meilleur, Flora
AU - Myles, Dean A.A.
AU - Liu, Emily
AU - Zhang, Yang
AU - Smith, Gregory S.
AU - Herwig, Kenneth W.
AU - Pynn, Roger
AU - Chen, Wei Ren
PY - 2011/6
Y1 - 2011/6
N2 - 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.
AB - 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.
KW - Platonic solids
KW - small-angle scattering
KW - spatial autocorrelation functions
UR - http://www.scopus.com/inward/record.url?scp=79956331227&partnerID=8YFLogxK
U2 - 10.1107/S0021889811011691
DO - 10.1107/S0021889811011691
M3 - Article
AN - SCOPUS:79956331227
SN - 0021-8898
VL - 44
SP - 545
EP - 557
JO - Journal of Applied Crystallography
JF - Journal of Applied Crystallography
IS - 3
ER -