Physics 489 9/3/15
From last time: Recall that a crystal can be defined by its Bravais lattice + Basis
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Bravais lattice = repeated set of mathematical points, R = n1a1 + n2 a2 + n3 a3 .
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{ R} is the set of “Lattice Vectors.”
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a1 , a2 , a3 : Primitive Lattice Vectors.
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The primitive cell always has volume V = a1 ⋅ a2 × a3 . One option for the cell is the
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parallelepiped with edges equal to a1 , a2 , a3 .
Naming convention for cell dimensions and angles: Lengths are a, b, c, and α = (b-c angle)
etc. as shown below. These are the "lattice parameters".
Cubic lattice parameters are simplified to just a, while for cases such as Hexagonal lattices with
a = b, the 3 lengths are a × a × c.
Primitive and conventional Cubic cells:
Images of two-dimensional tilings: What is the Bravais lattice? The basis?
Close-packed structures: For further reference here is a comparison of the FCC and HCP closepacked structues.
(a) FCC conventional cell, with the layers colored red-green-blue to show the A-B-C-A-B-C
stacking. Structure is the same for each case, but viewed from different angles to show the closepacking layers and how they register.
(b) HCP: Below are similar views of the HCP lattice. In the top two views the A-B-A-B layers
are colored alternating blue and green. In the lower figures the corner atoms and center atom of
one unit cell have been colored red.
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The 14 Bravais lattice distinguished by symmetry:
Wurtzite structure (GaN):