## Quick Reference

A quantity denoted *F _{hkl}*, where

*h*,

*k*, and

*l*are the Miller indices of the crystal, which occurs in X-ray crystallography and other experiments involving scattering in crystals.

*F*is defined by the equation:

_{hkl}*F*=Σ

_{hkl}*f*

_{i}exp[2πi(

*hx*

_{i}+

*ky*

_{i}+

*lz*

_{i})], where the sum is over all atoms of the unit cell and

*f*

_{i}is the scattering factor for atom i defined by:

*f*

_{i}=4Π

^{∞}

_{0}(ρsin

*kr*/

*kr*)

*r*

^{2}d

*r*Here

*k*=4Πsinθ/λ, where θ is the Bragg angle (see Bragg's law), λ is the wavelength of the X-rays, and ρ is the electron density distribution of the atom i. The structure factor is used in Patterson synthesis.

*F _{hkl}*=Σ

*f*

_{i}exp[2πi(

*hx*

_{i}+

*ky*

_{i}+

*lz*

_{i})]

*f*_{i}=4Π^{∞}_{0}(ρsin*kr*/*kr*)*r*^{2}d*r*

*Subjects:*
Chemistry.

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