How can I calculate the opacity of a crystal as function of its lattice orientation?

I would like to plot the opacity of a crystal (when radiated by an ion beam) with $[100]$ orientation as a function of the tilt angle $\theta$ from $0^\circ$ to $90^\circ$. So far I've been doing it using Vesta, a program in which I can model the crystal structure in 3D. I insert the reference atomic radii for each atom, then rotate the whole thing for different angles and measure the free projected area for each angle using Photoshop.

Obviously that's very tedious, so I do it only in steps of $5^\circ$ or even $10^\circ$. I would like to find a more systematic way (or a program that can simulate the channeling for me?), since I now have to do it for different crystal structures and for another degree of freedom (azimuthal angle) as well.

Julien.

Edit: I've attached a picture to make sure I expressed myself correctly. The top picture shows a [100] plane of gallium oxide (the black lines show the unit cell). The bottom picture shows the same rotated by about $27.4^\circ$ "sideways" ([101]). The calculations I describe above relate to the free area/area of projected unit cell for each orientation.

• You'll have to tell us more about the crystal and its structure. For most crystals, there won't be any angle dependence. Commented Apr 6, 2018 at 17:05
• @garyp Well the one I'm looking at at the moment is beta gallium oxide, so a monoclinic structure with a complex unit cell, but I'll also do it for silicon, copper and others. But isn't it quite rare that there is no angle dependency? When you rotate most crystals there are less free paths for photons (or ions, which is my interest in this query) to pass through the crystal than at the planes of high symmetry I think.
– Pxx
Commented Apr 6, 2018 at 17:48
• Ions? Is your interest to calculate the transmission of ions through a crystal? If so, you should state that in the question. "Opacity" will make people think that you are interested in light. Commented Apr 6, 2018 at 17:51
• @garyp Sorry, I've just edited the question to include that information.
– Pxx
Commented Apr 6, 2018 at 17:58
• Your approach is totally unsuitable for calculating ion channeling effects. For that you will need to dig into the literature. One place to start is the classic "Ion Beam Handbook for Material Analysis", edited by J.W. Mayer and E. Rimini, Academic Press (1977). Commented Apr 6, 2018 at 18:03