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I heard today that there's not really any true amorphous materials; that the theoretical concept (no level of ordering whatsoever) exists of course, but that no materials are 100% truly random and always have some crystallites, even if they're really small.

Is that true, let's say, in the case of a typical glass microscope slide? (I know there are different grades and makes of glass, but the slide is probably a fairly standard type.) I briefly Googled "is glass actually amorphous" and "crystallite size in glass slide" but that didn't answer my question.

So what's probably the order of magnitude of the largest dimension of the average crystallite, if it has any to speak of?

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Ordinary silica glass really is amorphous.

You can study the short range order of a material by measuring its radial distribution function. That is, take any atom and plot the density as a function of distance from that atom. This is easily measured using X-ray or neutron scattering.

In a crystal the RDF is just a function of the crystal structure and is easy to calculate, so we can compare the experimental RDF with the theoretical one and we find they are a perfect match. You could do this with quartz, which is just crystalline silicon dioxide i.e. crystalline glass.

However if you look at the RDF of e.g. a microscope slide you find the RDF is different. The first peak in the RDF is the nearest neighbour peak i.e. the Si-O distance, and this is the same as quartz because the Si atom is tetrahedrally coordinated by oxygen in both quartz and glass. However when you look at the second peak you already see differences between quartz and glass i.e. even at the second nearest neighbour scale the glass differs from a crystal.

Glass is truly amorphous because of the way it solidifies. If you take a metal then it solidifies by forming nuclei and growing crystals from those nuclei. The so called amorphous metals are made by extremely rapid cooling so the nuclei don't have time to grow very big, but even so you have a crystalline nucleus with a finite size.

However in molten silica the SiO$_2$ molecules polymerise with each other to form random chains. These chains start small and grow in a random fashion as the temperature falls. These chains tangle up with each other, and because they are large polymers they can't relax and crystallise as the temperature falls. It is possible to crystallise glass, but it requires very, very slow cooling. For example quartz crystals can form from the melt in granite.

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