What is a ruby and why is it red? Why is the friction so low on a sled? On a plot of P versus T, plot out the the phases of helium-three....
A favorite professor loved to craft simply stated preliminary exam questions that happened rhyme. Parts were often difficult - here the second question is still not fully answered. The ruby question is good as there are layers of depth to show how much you have thought about it.
Sapphire, ruby and corundum are all very stable crystalline forms of Al2O3 - aluminum oxide.1 In ruby and sapphire a percent or so of the aluminum atoms are replaced by something else - chromium in the case of ruby. Chromium is a bit larger and has a different shape than aluminum. The result is a small distortion of the arrangement of oxygens around the chromiums. The most obvious visual difference is how the two crystals absorb light. The distortions change how visual light is absorbed. Pure corundum doesn't strongly absorb, ruby absorbs in the violet and yellow-green making it appear red.2
Structure is one of the features used to categorize solids. A crystal is a solid with a structure of atoms or molecules that repeat in three dimensions with a regular pattern called a lattice - single crystal snowflakes, table salt, diamonds... Groupings of smaller crystals form polycrystals - most metals, large snowflakes, ice and ceramics are polycrystals. Amorphous solids lack such order .. glass and almost anything organic for example.
Impurities in crystals lead to changes in physical properties like the colors of gem stones. But there are many ways to disrupt a pure crystal lattice. Some locations can be empty, filled with some impurity or dislocations to the pattern of the crystal can lead to strong steel. Impurities create different electrical properties that allow semiconductors to exist - without ongoing theoretical and experimental work from the 40s, the integrated circuit wouldn't exist.
Steel is largely iron with a few other things thrown in. Carbon turned out to be a big winner, but you have to get the recipe right and there are tens of thousands of variations giving a wide range of properties. Successful recipes were carefully guarded secrets .. the special steels used in Japanese swords, steels from Toledo and Damascus became legendary. Sometimes there was a bit of odd baggage - one recipe involved adding the urine from red-haired boys. Serious progress had to wait for real science.
It is possible to have two dimensional structures with regular repeating patterns - graphene is a single layer of hexagonally packed carbon atoms. Amazing properties that lead in a recent Nobel prize in physics. You can easily make some yourself with a pencil and a bit of scotch tape.3
But it gets stranger...
It is natural for a physicist to think in more than three dimensions. Space-time, the structure of space and time we live in, has four dimensions. Other more abstract hypotheses have eight, nine, eleven, twenty six. Calculations can have large numbers of dimensions. Sometimes this is practical in the real world - cryptology and cellphone modulation schemes both make use of higher dimensionalities.
So it is natural to think of a four dimensional crystal -- one in space and time. And usually, for a variety of reasons, you quickly rule it out as non-physical. Afew years ago Frank Wilczek didn't throw it away and presented the idea of a time crystal that exists in four dimensions. The physical pattern is be stable, but a property of it repeats in time. Instead of regularly repeating atoms there would be a regularly repeating internal motion.
It was very controversial - it looked like a perpetual motion machine, but loophole was spotted. Properties like electron spin might bunch up in direction at regular intervals in time .. a repeating lattice in time. As crazy as it sounds a few groups tried to make their own time crystals and two appear to have succeeded with papers passing peer review and due out in the near future. Here's one of the early papers and a high level description. Much more is likely to emerge in the next few months.
Apart from being beautiful it has the potential to be incredibly useful. Quantum computing has the fundamental challenge of maintaining entanglement over time in a macroscopic object. It could be that time crystals are a mechanism to successfully address the problem and who knows what else... perhaps years, perhaps decades, perhaps never...
ah the frontier
1 In pure corundum three electrons from each aluminum join with six O2- ions in an octahedral group. The aluminums are left without unpaired electrons and their energy levels are filled. This configuration is exceptionally stable and strong and is also colorless.
2 There is also a fluorescent emission in the red making the crystals beautifully red. This emission property is central to making lasers out of rubies.
3 rather than tell you, just watch this:)
Not a recipe, but a bit of technique. It's Winter and that means reasoning with hard Winter squashes. I find it's much easier if you par-cook (not boil) them for a few minutes. Find a big enough pot and let it simmer for two or three minutes. If the squash is larger than the pot, just turn it over.
That's it. Now it should slice easily. Something frustrating becomes easy.