What's the x-ray diffraction pattern of triangular atoms?

[Raziel2701]

What would happen to the XRD pattern if instead of having spherical atoms, we had triangular atoms? I found the optical diffraction pattern for a triangular aperture, but I'm not sure if optical diffraction patterns would be the same as XRD patterns.

 

[mfb]

How would triangular atoms look like in detail? To answer a question in the framework of physics in our universe, you need some (at least theoretical) way to generate the setup.

 

[Jolb]

First you should remember that there are many ways to do x-ray diffraction. For example, there is single-crystal XRD and powder XRD, which yield different kinds of spectra, or as another example, you could take data as a Laue photograph or using a theta-2theta setup, which give different kinds of spectra.

The undergrad-level explanation of XRD, which is usually adequate to understand XRD, is the Bragg's Law picture, although to really treat XRD correctly you would want to use some fancy scattering theory. But in the Bragg's law picture, we approximate the crystal lattice as a bunch of 2-D surfaces layered with a constant interlayer spacing. So it doesn't speak to the shape of the original atoms at all--they could be little balls, point particles, or little pyramids, etc. The only thing the Bragg's law picture would do is say: "okay, let's identify a plane in the lattice and model it as a 2-D partially reflecting surface."

In scattering theory, you could do the calculation for scattering waves off a lattice of little pyramid molecules (I assume you mean with a uniform orientation. If they were randomly oriented I bet their shape wouldn't matter.) My guess is that if you used that kind of crystal and performed a scattering theory calculation corresponding to a single-crystal, normal theta-2theta style of XRD measurement, then you would get a pattern that looks identical to the same lattice of spherical atoms, except there will probably be "missing" peaks due to the fact that the reflection off flat surfaces will "miss" at certain configurations of the theta-2theta setup.