# 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

of ZrO2.

unedited photo of ZrO2.

• Comments are not for extended discussion; this conversation has been moved to chat.
– Buzz
Aug 26, 2021 at 0:22
– Gert
Aug 27, 2021 at 14:41
• To clarify: in theory a perfect crystal contains much larger identical subunits--say 5000 unit cells in diameter-- which could interact with longer light wavelengths. So Bragg's relation applies and we get what might be called 5000th order effects. In practice I think there are no effects and there is something wrong with the assumptions. Sep 4, 2021 at 11:28
• Based on the answer below it is likely the photo is of reflection, not diffraction. Oct 6, 2021 at 12:56

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.

• Thanks for your upvote. Look again at Bragg's Law ($\lambda =2d\sin\theta$ for first order spectra) and it's obvious you need rays with pretty small wavelengths to resolve lattices in the order of $0.3\mathrm{nm}$... Pity, really!
– Gert
Aug 27, 2021 at 2:21
• I did this experiment years ago:physics.stackexchange.com/questions/384086/…, which shows it can't only be a case of $d/ \lambda$ ratio.
– Gert
Aug 27, 2021 at 13:31
• And it can't just be about energy either: a VIS laser effortlessly travels through a solid $\text{NaCl}$ crystal. I might raise a ticket myself, intrigued as I am now...
– Gert
Aug 27, 2021 at 13:33