The most important concepts we learnt this week are the Bravais lattice and the reciprocal lattice. The Bravais lattice can be imagined physically as coordinates or holes in space where you can place atoms/molecule etc(basis). The reciprocal lattice being in k-space a bit harder, at least for me to imagine physically what it is. It is defined as a set of all wave vectors that yield plane waves with periodicity of a given Bravais lattice so I think each dot in the reciprocal lattice as the coordinate of a vector from the origin. A family of lattice planes correspond to a single wave vector in the reciprocal lattice which is convenient. Defining W-Z cell in real space makes sense but its k-space equivalent the first Brillouin zone, what does it represent?
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Probably sounds strange, but it seems to make more sense to have the reciprocal lattice.
ReplyDeleteWe have electrons which have can only have certain momenta. To have the elctron live within our lattice, it must have momentum which allows its corresponding wave to fit in the lattice.
So, our lattice spacing is related to the momentum of the electrons.
Why not just stay in momentum space?
I would suspect that the FBZ would be the unit cell that we would see in imaging our crystal.
Hang on, defining the W-Z cell in real space tells us physically the repeating structure of our crystal.
Then likewise for our FBZ defining the repeating behaviour of electrons?