While the direct lattice exists in real-space and is what one would commonly understand as a physical lattice, the reciprocal lattice exists in reciprocal space ( also known as " momentum space " or less commonly " K-space ", due to the relationship between the reciprocal lattice of a reciprocal lattice, then, is the original direct lattice again, since the two lattices are Fourier Transforms of each other.
12.
The reciprocal to a simple hexagonal Bravais lattice with lattice constants c and a is another simple hexagonal lattice with lattice constants \ begin { matrix } \ frac { 2 \ pi } { c } \ end { matrix } and \ begin { matrix } \ frac { 4 \ pi } { a \ sqrt { 3 } } \ end { matrix } rotated through 30?about the c axis with respect to the direct lattice.
13.
Since Steno s Law can be further generalized for a single crystal of any material to include the angles between either all identically indexed net planes ( i . e . vectors of the reciprocal lattice, also known as'potential reflections in diffraction experiments') or all identically indexed lattice directions ( i . e . vectors of the direct lattice, also known as zone axes ), opportunities exist for morphological fingerprinting of nanocrystals in the TEM ) by means of transmission electron goniometry.
14.
They are written ( hk ! ), and denote the family of planes orthogonal to h \ mathbf { b _ 1 } + k \ mathbf { b _ 2 } + \ ell \ mathbf { b _ 3 }, where \ mathbf { b _ i } are the basis of the reciprocal lattice vectors . ( Note that the plane is not always orthogonal to the linear combination of direct lattice vectors h \ mathbf { a _ 1 } + k \ mathbf { a _ 2 } + \ ell \ mathbf { a _ 3 } because the reciprocal lattice vectors need not be mutually orthogonal . ) By convention, negative integers are written with a bar, as in for " 3.
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