# F(000)

### From Online Dictionary of Crystallography

##### Revision as of 13:12, 6 February 2012 by BrianMcMahon (talk | contribs)

The expression for a structure factor evaluated in the zeroth-order case [math]h=k=l=0[/math] yields the result

[math]F(000) = [ (\sum f_{r} )^{\,2} + (\sum f_{i} )^{\,2} ]^{1/2}[/math]

where [math]f_{r}[/math] is the real part of the scattering factors at [math]\theta = 0^\circ[/math], [math]f_{i}[/math] is the imaginary part of the scattering factors at [math]\theta = 0^\circ[/math], [math]\theta[/math] is the Bragg angle, and the sum is taken over each atom in the unit cell.

[math]F(000)[/math] is computed without dispersion effects in electron-density calculation by Fourier inversion. In all cases, non-dispersive [math]F(000)[/math] is a structure factor and not a structure amplitude: it has both magnitude and a sign.

For X-rays non-dispersive [math]F(000)[/math] is positive definite and in many cases an integer (but it is not an integer for non-stoichiometric compounds). It counts the number of electrons in the cell.

For neutrons non-dispersive [math]F(000)[/math] is either positive or negative and counts the total nuclear scattering power in the cell.