6. group associated with a cubic crystal. 0000010523 00000 n
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(3) a3 is the vector to a lattice point nearest, but not on, the a18a2 plane. 0000007569 00000 n
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A concrete … 0000026998 00000 n
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Thus, it is evident that this property will be utilised a lot when describing the underlying physics. trailer
Cubic lattices have the highest degree of symmetry of any Bravais lattice. endstream
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From this general consideration one can already guess that an aspect closely related with the description of crystals will be the topic of mechanical/electromagnetic waves due to their periodic nature. 0000004816 00000 n
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They belong to the (m3m) symmetry group which contains the following symmetry
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Also, an observer sitting on one specific lattice point would see the same
[2] All lattice points are equivalent, i.e. 0000005874 00000 n
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The third index, t, is redundant since u+v+t=0. 0000002128 00000 n
in Problem 4.8) is the following: (1) a1 is the vector to a near est neighbor lattice point. 0000012440 00000 n
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[u v t w], is sometimes used for the hexagonal system. 0000003623 00000 n
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Note that the (m3m) symmetry group is the highest possible symmetry
Accordingly, the physics that occurs within a crystal will reflect this periodicity as well. 0000056315 00000 n
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There are many choices for the primitive vectors of a Bravais lattice. 0000008300 00000 n
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all properties remain invariant under translations by any vector $\vec{T}_{mno}$. Diamond lattice is NOT a Bravais Lattice either Same story as in graphene: We can distinguish two different type of carbon sites (marked by different color) We need to combine two carbon sites (one black and one white) together as a (primitive) unit cell If we only look at the black (or white) sites, we found the Bravais lattice: fcc 0000055435 00000 n
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The Bravais lattices The Bravais lattice are the distinct lattice types which when repeated can fill the whole space. 0000059884 00000 n
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overall symmetry group of the crystal. 0000021666 00000 n
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