It is therefore indexed with direct lattice-indices, instead of with Miller-indices.
2.
Direct lattice-vectors have components measured in distance units, like meters or & Aring; ngstroms.
3.
We let "'R "'be a vector in the direct lattice, which we can express as a linear combination of " its " primitive vectors.
4.
Due to the definition of \ mathbf { G }, when \ mathbf { K } is the direct lattice vector \ mathbf { R }, we have the same relationship.
5.
In normal usage, this first lattice ( whose transform is represented by the reciprocal lattice ) is usually a periodic spatial function in real-space and is also known as the " direct lattice ".
6.
Now, any periodic potential V ( "'r "') which shares the same periodicity as the direct lattice can be expanded out as a Fourier series whose only non-vanishing components are those associated with the reciprocal lattice vectors.
7.
While the Bragg formulation assumes a unique choice of direct lattice planes and specular reflection of the incident X-rays, the Von Laue formula only assumes monochromatic light and that each scattering center acts as a source of secondary wavelets as described by the Huygens principle.
8.
"' Zone axis "', a term sometimes used to refer to " high-symmetry " orientations in a crystal, most generally refers to " any " direction referenced to the direct lattice ( as distinct from the reciprocal lattice ) of a crystal in three dimensions.
9.
A useful and quite general rule of crystallographic " dual vector spaces in 3D " is that the condition for a direct lattice-vector [ uvw ] to have a direction ( or zone-axis ) perpendicular to the reciprocal lattice-vector [ hkl ] is simply hu + kv + lw = 0.
10.
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.
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