Using visible light to get (weak) diffraction information about crystals? If a crystal has diameter roughly 0.25mm containing unit cells (say cubes) of about 1 angstrom on a side, there are about 2.5 million unit cells in the diameter of the crystal. Bragg's law (n$\lambda = 2d\sin\theta)$ applies, and tells us that we would like to use wavelength on the order of 1 angstrom to probe the crystal.
But if $\lambda = 5000$ angstroms (a laser) it seems we could still get refraction of parallel waves separated by about 2500 angstroms, or about $0.25$mm/$2500$ angstrom $= 1000$ reinforcing refractions in the above crystal, considering only the one dimension. Hence my question--
Is it possible that while we cannot resolve structures smaller than a few angstroms without using x-rays, we might get information (albeit attenuated) about identical repeating structures (crystals) using longer wavelengths?
Edit:
The images below may help clarify. Above is radial average intensity calculated in python for the laser diffraction of zircon image (below, with central beam edited out). One one hand I wouldn't try to correlate the calculation with XRD calculations, on the other hand there seems to be some non-random information in the image. If nothing else, this may clarify my misconceptions.

Edit 2
Am adding the
 of ZrO2.
unedited photo of ZrO2.
 A: The following isn't really an answer, rather a rebuttal of sorts.

Using visible light to get (weak) diffraction information about
crystals

would of course a very interesting thing to do, which is why as a chemist it piqued my attention. But I fear that in accordance with common perception it isn't really possible and that which is on display in the question is something else.
I first ran a quick test with a monocrystalline Calcite crystal, about the size of my thumb. I shone a $532\mathrm{nm}$ ($8000\mathrm{mW}$) green pointer laser through it and obtained two weakened central beams and a completely random 'halo' of scattered light. No diffraction pattern whatsoever.
I then finely ground up some kitchen salt (chemically $\text{NaCl}$) in a mortar and pestle and loaded it into a glass capillary tube.
But trying to shine a laser beam through that is a waste of time: like most bulk transparent materials (glass, sucrose crystals, salt crystals etc) their ground up versions simply aren't transparent to VIS.
They would be to X-rays but that would yield circular diffraction patterns. Only monocrystallin materials would show the kind of diffraction pattern the OP shows in his question.
So I don't know what's causing the interesting pattern but I don't think it is diffraction related. But I'd like to know more about the OP's experimental set up to understand what might be producing the observed effect.
