I like how the definition of the crystal (from lecture) had to be redefined to be that the crystal exhibits discrete x-ray diffraction peaks and no longer requires a periodic arrangement of atoms.
It reminds us that how we see and understand the world changes as we continue to undermore more.
The definition of periodic arrangement of atoms seems intuitive and if you were to crack a crystal small enough, that is what you would get.
X-rays were only discovered just before 1900.
Before then, I'd imagine that it'd be incomprehensible to even suggest that discrete x-ray diffraction peaks should be used to identify crystals.
The distinction between sufficient and necessary (or if and only if ☺) certainly makes me more careful of my interpretation of what I read. Particualarly in everyday language, I note that I have become a little sloppy with my language.
Few instances would be when we have a derivation and we say suffice when we mean suffices and necessitates, although that still holds. Main issue would be when we say necessitate when we actually mean suffices.
I'll make sure I am more careful now.
Sidenote: below is a simulation of five fold symmetry from an icosohedral quasicrystal from http://www.alienscientist.com/quasicrystals.html. Makes you think about what other patterns exhibit 5-fold symmetry...and it looks pretty ☺
Another sidenote: this diffraction stuff of lattices with recirocal space etc reminds me of fraunhofer diffraction. Anyone else see that?
Actually, your comment about how crystals were defined before 1900 got me wondering how much was known about them up to then as it were. The Drude model for solids was only established that year, so I'm not sure a firm understanding of what a crystal is was established at that stage.
ReplyDeleteI mean, obviously crystals have been known for millenia, but as far as I can tell crystal structure only started being revealed in the 1920's, with Linus Pauling in particular. He performed a lot of xray diffraction experiments to determine the structure, so they have somewhat gone hand in hand since the beginning.
Fun fact, Pauling is only one of 4 people to receive multiple Nobel prizes, and only one of 2 to receive them in different fields (thanks wiki!)
Good point!
ReplyDeleteSomewhere in there though, someone would have noticed that if you break up something, it forms its own shape, e.g. salt, quartz have their own shape, even snowflakes.
However, a periodic arrangement of atoms...we'd first need to establish that atoms exist then that they contribute to the structure.
Also, from maths, how old are symmetry groups?
I suppose also, when was maths standardised s.t. it's in its current reasonably understandable form today?
Oh wikipedia...