Some questions regarding crystallography

[Petrichor728]

Hello Prof. Seto,

The recent updated versions of ReciPro are very easy to use.
May I ask if you are considering adding a button in the Theoretical Spots module to display specific angles, similar to “d”?
I am currently working on monoclinic ZrO₂, and some spots such as (130) are not shown on the scale (Fig. 1).

There is another question I would like to ask you.
When labeling crystal directions in spherical aberration–corrected STEM images (similar to the labeling shown in Fig. 2), I have some confusion.

For cubic crystals, (130) ⊥ [130].
However, in the monoclinic system, (130) is not ⊥ [130]; there is an included angle between them.
Recently I have been struggling with the angle and its direction.

Does ReciPro have this function?
If not, could it be added to the Theoretical Spots module?
I determine the zone axis and crystal planes from the FFT or SAED pattern of STEM, and then deduce the crystal directions in STEM.

Fig.1
Fig.2

[seto77]

Hello @Petrichor728,

Thank you for the kind words about ReciPro, and for the interesting questions!

1. Displaying angles in the Diffraction Simulator

That is a good suggestion. I have implemented new label options in the Diffraction Simulator that display the scattering angle 2θ and the azimuthal angle χ of each spot, in the same way as the existing "d" labels (χ is measured clockwise from the 12 o'clock direction, consistent with the radial scale lines). These will be included in the next release, so you will be able to read off the angles of spots like (130) that do not fall on the scale lines.

2. Labeling crystal directions in STEM images

This point needs a little care. What you actually see in a high-resolution STEM image are lattice planes (their edge-on fringes), so their orientation is intrinsically characterized by the plane indices (hkl) — it is not something that can, in essence, be expressed by a direction index [uvw]. In cubic crystals, [hkl] happens to be parallel to the normal of (hkl), but this is a degenerate, special case. Carrying that intuition over to other crystal systems, such as monoclinic ZrO₂, is a little dangerous.

I believe what you want to do can be achieved with the existing functions of ReciPro: the Diffraction Simulator, together with the "Symmetry Information" window, which can calculate the angles between planes and between directions/axes.

I hope this helps, and thank you again for using ReciPro!