Form Factor

The Form Factor is the scattering which results from the shape of a particle.

Form Factor Equations

• Sphere
• Cube

Form Factor Equations in the Literature

The following is a partial list of form factors that have been published in the literature:

• NCNR SANS solution form factors:
  • Sphere
  • PolyHardSphere
  • PolyRectSphere
  • CoreShell
  • PolyCoreShell
  • PolyCoreShellRatio
  • Cylinder
  • HollowCylinder
  • CoreShellCylinder
  • Ellipsoid
  • OblateCoreShell
  • ProlateCoreShell
  • TwoHomopolymerRPA
  • DAB
  • TeubnerStrey
  • Lorentz
  • PeakLorentz
  • PeakGauss
  • PowerLaw
  • BE_RPA

• IsGISAXS, Born form factors (see also Gilles Renaud, Rémi Lazzari,Frédéric Leroy "Probing surface and interface morphology with Grazing Incidence Small Angle X-Ray Scattering" Surface Science Reports, 64 (8), 31 August 2009, 255-380 doi:10.1016/j.surfrep.2009.07.002):
  • Parallelepiped
  • Pyramid
  • Cylinder
  • Cone
  • Prism 3
  • Tetrahedron
  • Prism 6
  • cone 6
  • Sphere
  • Cubooctahedron
  • Facetted sphere
  • Full sphere
  • Full spheroid
  • Box
  • Anisotropic pyramid
  • Hemi-ellipsoid

• Scattering functions of Platonic solids Xin Li, Roger Pynn, Wei-Ren Chen, et al. Journal of Applied Crystallography 2011, 44, p.1 doi:10.1107/S0021889811011691
  1. Tetrahedron
  2. Hexahedron (cube, parallelepiped, etc.)
  3. Octahedron
  4. Dodecahedron
  5. Icosahedron

• Pedersen Review: Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting Jan Skov Pedersen, Advances in Colloid and Interface Science 1997, 70, 171. doi: 10.1016/S0001-8686(97)00312-6
  1. Homogeneous sphere
  2. Spherical shell
  3. Spherical concentric shells
  4. Particles consisting of spherical subunits
  5. Ellipsoid of revolution
  6. Tri-axial ellipsoid
  7. Cube and rectangular parallelepipedons
  8. Truncated octahedra
  9. Faceted sphere
  10. Cube with terraces
  11. Cylinder
  12. Cylinder with elliptical cross section
  13. Cylinder with spherical end-caps
  14. Infinitely thin rod
  15. Infinitely thin circular disk
  16. Fractal aggregates
  17. Flexible polymers with Gaussian statistics
  18. Flexible self-avoiding polymers
  19. Semi-flexible polymers without self-avoidance
  20. Semi-flexible polymers with self-avoidance
  21. Star polymer with Gaussian statistics
  22. Star-burst polymer with Gaussian statistics
  23. Regular comb polymer with Gaussian statistics
  24. Arbitrarily branched polymers with Gaussian statistics
  25. Sphere with Gaussian chains attached
  26. Ellipsoid with Gaussian chains attached
  27. Cylinder with Gaussian chains attached

• Supplementary Information of: Matthew R. Jones, Robert J. Macfarlane, Byeongdu Lee, Jian Zhang, Kaylie L. Young, Andrew J. Senesi, and Chad A. Mirkin "DNA-nanoparticle superlattices formed from anisotropic building blocks" Nature Materials 9, 913-917, 2010. doi: 10.1038/nmat2870
  1. Pyramid
  2. Cube
  3. Cylinder
  4. Octahedron
  5. Rhombic dodecahedron (RD)
  6. Triangular prism

• Other:
  • This tutorial lists sphere, rod, disk, and Gaussian polymer coil.
  • Block-Copolymer Micelles Scattering Form Factor of Block Copolymer Micelles Jan Skov Pedersen* and Michael C. Gerstenberg, Macromolecules, 1996, 29 (4), pp 1363–1365 DOI: 10.1021/ma9512115
  • Capped cylinder Scattering from cylinders with globular end-caps. H. Kaya. J. Appl. Cryst. (2004). 37, 223-230 doi: 10.1107/S0021889804000020
  • Lens-shaped disc Scattering from capped cylinders. Addendum. H. Kaya and N.-R. de Souza. J. Appl. Cryst. (2004). 37, 508-509 doi: 10.1107/S0021889804005709