F(000): Difference between revisions
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The expression for a [[structure factor]] evaluated in the zeroth-order case <math>h=k=l=0</math> yields the result | 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} | <center><math>F(000) = [ (\sum f_{r} )^{\,2} + (\sum f_{i} | ||
)^{\,2} ]^{1/2}</math> | )^{\,2} ]^{1/2}</math></center> | ||
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. | 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. | ||
Latest revision as of 19:49, 24 October 2026
The expression for a structure factor evaluated in the zeroth-order case [math]\textstyle{ h=k=l=0 }[/math] yields the result
where [math]\textstyle{ f_{r} }[/math] is the real part of the scattering factors at [math]\textstyle{ \theta = 0^\circ }[/math], [math]\textstyle{ f_{i} }[/math] is the imaginary part of the scattering factors at [math]\textstyle{ \theta = 0^\circ }[/math], [math]\textstyle{ \theta }[/math] is the Bragg angle, and the sum is taken over each atom in the unit cell.
[math]\textstyle{ F(000) }[/math] is computed without dispersion effects in electron-density calculation by Fourier inversion. In all cases, non-dispersive [math]\textstyle{ 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]\textstyle{ 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]\textstyle{ F(000) }[/math] is either positive or negative and counts the total nuclear scattering power in the cell.