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Particle Form Factors in Physical Modeling

Learn about form factors for spheres, core-shell structures, cylinders, and rods with special cases. Understand their significance in scattering and molecular modeling.

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Particle Form Factors in Physical Modeling

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  1. Chapter 27 – SINGLE PARTICLE FORM FACTORS 27:2. FORM FACTOR FOR A UNIFORM SPHERE 27:3. SPHERICAL CORE-SHELL 27:5. FORM FACTORS FOR CYLINDRICAL SHAPES 27:8. PAIR CORRELATION FUNCTIONS

  2. 27:2. FORM FACTOR FOR A UNIFORM SPHERE Definition of the form factor: Uniform density sphere: Spherical Bessel function: Final result:

  3. FORM FACTOR FOR A SPHERE

  4. case 2 case 1 case 3 R T R T 27:3. SPHERICAL CORE-SHELL

  5. z Q q y f x 27:5. FORM FACTORS FOR CYLINDRICAL SHAPES Form factor: Uniform density cylinder: Longitudinal: Perpendicular: Cylindrical Bessel functions: Therefore: But: Result for perpendicular form factor: Final result:

  6. FORM FACTOR FOR A ROD

  7. FORM FACTOR FOR A ROD

  8. SPECIAL CASES Disk of radius R and negligible thickness: Infinitely thin rod of length L: Sine integral function:

  9. R r r’ FORM FACTOR FOR A SPHERE Density-density correlation function: Fourier transform: Radial pair correlation function:

  10. COMMENTS -- Single-particle form factors dominate scattering for dilute systems. -- Form factors are an essential component for molecular models used for data analysis.

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