I am usually working with electron microscopy images of macromolecules, and we use reciprocal distance units [1/Angstrom] for units in Fourier Space. A repeating signal every e.g. 10 Angstrom would correspond to a Fourier Space signal at 1/10 [1/Angstrom].
I was surprised to find out that the q-value in small angle X-ray scattering (SAXS) is not defined in the same way. Units are the same [1/nm] or [1/Angstrom], but there is a factor of 2pi in there.
Can a person in the SAXS field explain me the reason for this convention, which seems overly complicated to interpret the actual values in scattering curves in terms of real-space distances?
Dear Stefan T. Huber ,
you are right, unfortunately there are two different definitions:
please see the 'crystallography definition' and the 'physics definition' of the wave vector k in:
https://en.wikipedia.org/wiki/Wave_vector.
wave vector k= 1/lambda , but also k= 2*pi/lambda
To my opinion that is a historical issue.
Relation to the physical momentum is via Planck's constant h and ħ = h/(2pi)
In SAXS we have for the magnitude lql of the momentum transfer q at the angular positions theta of the diffraction peaks hkl:
lql= 4*pi*sin(theta)/lambda=2*pi/dhkl
Please see for example page 3 of:
https://www-ssrl.slac.stanford.edu/conferences/workshops/scatter2006/talks/hufnagel.pdf
So please pay always attention whether the 2pi is included (or not) in the q scale.
I know, my answer is not really satisfying...
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