513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
of Elements

      

Rhombohedral unit cell

Consider a rhombohedral lattice. All primitive lattice vectors have a length a and the angles between the primitive lattice vectors are all the same α = β = γ. Show that the primitive lattice vectors in real space can be chosen to have the form,

Here a and b are constants.

Find the primitive reciprocal lattice vectors and show that the reciprocal lattice is again of rhombohedral type.

Additionally show that the angle α* between any pair of the primitive reciprocal lattice vectors is cosα* = -cosα/(1 + cosα).