A brief intro to the structure of bling

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Oh, crystals! I do love my crystals.

They’re the foundation material for most of my works, but it was not really until I was an undergrad that I really appreciated them.

This was partly because I had not realized that so many of the materials I dealt with on a regular basis were crystalline.

The thing is, when you have a solid material, the atoms have to sit somewhere, but where do they go?! Well, it’s not always easy to answer this, but if you have a general idea of what the atoms are, what sort of traumatic treatments (extreme heat, natural disasters, etc.) they had to face, what other junk got tossed into the mixture, and what the ambient temperature and atmosphere are, you could make some pretty good guesses. For centuries, this is exactly what people did!

Given enough time, energy, and a certain affinity for one another, with all atoms being more or less equal, they will try to sit in an ordered manner with one another. Many of my favorite materials happen to sit in a nice cubic structure, the simplest case being a simple cubic configuration, where one atom occupies each corner:

SC unit cell
It doesn’t get simpler than this.

But that’s just 8 atoms, and what do you care about 8 atoms? That’s practically nothing (seriously)! Well, if you keep propagating that cubic pattern in all the main directions along the cube’s edges (forward-backward, left-right, up-down), you’re going to get a larger crystal.

Crystal building
Yes, this is exactly how crystal structures propagate.

How large you ask? Well, up until you run into a wall.

wall
Well, I guess we’re camping out here. Indefinitely.

And if your atoms just don’t have enough time, energy, or discipline, they just are a mess.

Here’s how this manifests in some real materials you might actually care about:

  1. Some solids are obviously crystalline: diamond, quartz, sapphire, etc. You can tell because they have nice flat surfaces or facets that naturally occur when you try to cut these things into smaller pieces.
  2. Some solids are not so obviously crystalline: metals are the big one. Most metals we deal with are just collections of very tiny crystallites packed tightly enough that you can’t tell the difference between one or the other unless you have a microscope. So unless you’re dealing with something really REALLY special, that hunk of metal you’re working is polycrystalline.
  3. Some solids are not crystalline at all: glass is not just the name of a material but also a structural term. It just so happens that glass is a glass. How about that?

For (1) and (2), you got more or less long-range order, it’s just that for (1) it’s definitely longer than for (2). (2) happens when you have two armies running up against each other to do battle at their boundaries, and yeah, it’s a mess.

As for (3), this is what is known as “amorphous”. I mean, it kind of does have order, it’s just short-range order (OMG, the name of the blog in a blog post!!). It could be just a mess of cubes or polyhedrons randomly oriented with respect to each other, so order is limited to the nearest atoms only (e.g. as far as the cube corners go).

Short-range order
PARTY!

Or it really could be a complete mess, like freezing in time the chaos that ensues when throwing a bunch of primary schoolers into a classroom and ordering them to sit in their seats while candy rains from the ceiling.

Even shorter-range order
CANDY PARTY!

Clearly, order takes time to restore. Likewise, cooling silicon dioxide (SiO2) too quickly from a liquid to a solid does not give time for the atoms to settle into place (like it would in quartz), so it remains chaos (i.e., glass). But frozen.

Given enough time, the sugar and natural hyperactivity will wear off, and all the atoms will settle into their lowest energy state.

image

The end.

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