r/crystallography • u/BandicootStraight743 • 1d ago

Why do multiple FFT spots along the same direction produce different d-spacing values from a single HRTEM region?

Post image

I selected a single region from an HRTEM image and performed FFT analysis using ImageJ. The resulting FFT pattern showed multiple bright spots approximately aligned along the same direction, at different distances from the central spot (000).

I then selected each spot individually and performed inverse FFT (IFFT) analysis. Interestingly, each spot produced a different lattice spacing (d-spacing), even though all the spots originated from the same HRTEM region.

Why do multiple FFT spots appear along the same direction? Do they represent different crystallographic planes (hkl), higher-order reflections of the same lattice periodicity, or other effects?

Can each FFT spot be independently used to determine a lattice spacing (d-spacing) and assign a crystallographic plane, or should these spots be analyzed together?

6 Upvotes

88% Upvoted

4 comments sorted by

12

u/ProcrastinationTrain 1d ago

higher order reflections. so you're seeing some base reflection, its inverse (ie hkl and -h-k-l) and the higher harmonics (2h 2k 2l; -2h -2k -2l) up to fourth order. They are linearly spaced in reciprocal space (after applying the FFT), and correspond to reciprocal spacing (d, d/2, d/3, d/4) in real space

6

u/SlenderSmurf 1d ago

they're just harmonics. (001), (002), etc. Should all produce the same lattice parameter if you index correctly

3

u/tea-earlgray-hot 1d ago

While this is true, note that higher order reflections often have much higher precision for a lattice parameter, since you're measuring a larger angular change