Yeti,
I recently wanted to extract lattice constants from FFT images. I am using
reference values obtained from a commercial software.
Employing the transformation rule from real space to reciprocal space (and vice
versa) I do not succeed in
calculating the correct values. However, when multiplying the fft coordinates
with 2*pi it fits pretty well.
This leads to one of my questions. Did you implement the crystallographic
notation (a_real * a_rec = 1) or the
solid state notation (a_real * a_rec = 2*pi) for reciprocal space? (just to
ensure the correct transformation)
The second question concerns the result's quality. Using the same data from the
commercial software results in two pretty equal
lattice constants of the unit cell. Calculating by hand from the very same FFT
coordinates (peaks) results in two similar but
different values. Using neighbor pixels slightly varies the result, but never
matches.
For example a hexagonal structure:
lattice constant commercial/nm Gwyydion-manually/nm
|a| 1.25 1.29
|b| 1.24 1.22
The question is why does it differ? Do I have to correct the coordinates if the
angle between two vectors of neighbor peaks
is != 60 degree (i.e. hexagonal structure)? Should I calculate the center of
mass of each FFT peak ? Maybe the latter improves
the precision. However, am I overcritical about a difference of 3 % ?
Cheers,
/M
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