So, visualising Bravais lattices.
I'm finding this challenging in that these lattices are infinite, but when you draw/make a model, it's finite and you can't really see the symmetry as the lattice has finished.
There are more infinite pictures of the cubic lattices about halfway down this webpage, which I find makes sense. You can see how the adjacent unit cells fit in with each other and that all vertices in the lattice are the same.
Sidenote: Mathematica recognises input of ==face centered cubic :D
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I agree that challenging to visualize Bravais lattices especially to prove the fact that no matter which site you are at, the arrangement and orientation of other sites from you are identical. Imagining things in 3D is not easy. I am still finding it difficult to imagine fcc as having coordination number of 12 and being identical no matter where you are at. I recall that in one of my chemistry courses in first year, you are allowed to bring in the ball and stick toy models into exam hall. Mathematica continues to amaze me from time to time.
ReplyDeleteI've spent tonight playing with toothpicks and plasticine - get the idea of repeated neighbours - don't think bringing models is going to be useful in a time-limited exam!
ReplyDeleteThe coordination number 12, I think of as 3+6+3, if that helps...
Yeah, I think that Bravais lattices are difficult to model with balls and sticks (or other assorted thingies). The models that Dr Paul has are good but of course, you need to have the right model for the structure; it would be interesting to see how many layers it takes to help you visualise a structure in 3D....
ReplyDeleteThe co-ordination number is a tricky concept too, because we haven't been given a very strict definition of what the 'closest' neighbour is: for body-centred cubic this is quite obvious but it is not so obvious for other structures where the closest neighbour lattice sites are not equidistant.
Just something I saw on Wikipedia as I closed it: for quasi-crystalline systems (e.g. liquid crystals), there is a function for the co-ordination number. Perhaps there is also a function for crystals to make this a less ambiguous definition?
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