This is so cool – literally! 😁😎
Originally shared by John Baez
A crystal made of electrons
Electrons repel each other, so they don’t usually form crystals. But if you trap a bunch of electrons in a small space, and cool them down a lot, they will try to get as far away from each other as possible – and they can do this by forming a crystal!
This is sometimes called an electron crystal. It’s also called a Wigner crystal, because the great physicist Eugene Wigner predicted in 1934 that this would happen.
Only since the late 1980s have we been able to make Wigner crystals in the lab. A crystal can only form if the electron density is low enough. This is due to the uncertainty principle of quantum mechanics, which implies that even at absolute zero, electrons wiggle around – and they do this more when they’re densely packed! When the density is low, they settle down and form a crystal.
But when an electron gas is rapidly cooled, sometimes it doesn’t manage to form a perfect crystal. It can form a glass! This is called a Coulomb glass.
It’s an amazing world we live in, where people can study a glass made of electrons.
We can do other cool stuff, like create electron crystals in 2 dimensions using electrons trapped on a thin film of metal. That’s what this picture shows. It’s a theoretical picture, but you can trust it, since we understand the laws of physics needed to figure out what electrons do when trapped in a disk. The density here is low enough that the uncertainty principle doesn’t play a significant role – so we can visualize the electrons as dots with a well-defined position.
The lines between the dots are just to help you see what’s going on. In general, a 2-dimensional electron crystal wants to form a triangular lattice. But a triangular lattice doesn’t fit neatly into a disk, so there are defects – places where things go wrong.
Puzzle 1. What is happening at the blue defects?
Puzzle 2. What is happening at the red defects?
Puzzle 3. What can you say about the number of blue defects and the number of red defects? Do these numbers obey some rule?
To know if a uniform electron gas at zero temperature forms a crystal, you need to work out its so-called Wigner-Seitz radius. This is the average inter-particle spacing measured in units of the Bohr radius. The Bohr radius is the unit of length you can cook up from the electron mass, the electron charge and Planck’s constant. (It’s also the average distance between the electron and a proton in a hydrogen atom in its lowest energy state.)
Simulations show that a 3-dimensional uniform electron gas crystallizes when the Wigner-Seitz radius is at least 106. In 2 dimensions, it happens when it’s at least 31.
For more, see:
https://en.wikipedia.org/wiki/Wigner_crystal
The picture here was drawn by Arunas.rv and placed on Wikicommons on a Creative Commons Attribution-Share Alike 3.0 Unported license.
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