In three dimensions the primitive reciprocal lattice vectors are related to the real space lattice { "'a, b, c "'} in the following way:
22.
The reciprocal lattice points are the values of momentum transfer where the Bragg diffraction condition is satisfied and for diffraction to occur the scattering vector must be equal to a reciprocal lattice vector.
23.
The vectors " G " are the reciprocal lattice vectors, and the discrete values of " k " are determined by the boundary conditions of the lattice under consideration.
24.
The reciprocal lattice plays a fundamental role in most analytic studies of periodic structures, particularly in the Laue conditions the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector.
25.
When a single crystal is examined in an X-ray Diffractometer such that the diffraction intensity is measured cylindrically around the crystal, it is convenient to use cylindrical coordinates to define the reciprocal lattice vectors and their terminal points.
26.
A reciprocal lattice vector can be represented by two mutually perpendicular vectors \ zeta ( along the rotation axis ) and \ xi in the horizontal plane ( the plane perpendicular to the rotation axis ) containing the X-ray beam.
27.
Just the direction changes by a reciprocal lattice vector \ vec G = \ vec Q = \ vec k _ f-\ vec k _ i with the relation to the lattice spacing G = 2 \ pi / d.
28.
There are also " ad hoc " schemes ( e . g . in the transmission electron microscopy literature ) for indexing hexagonal " lattice vectors " ( rather than reciprocal lattice vectors or planes ) with four indices.
29.
In this equation, G is the reciprocal lattice vector, q is the length of the reciprocal lattice vector, k is the momentum transfer vector, ? is half of the scattering angle, and ? is the wavelength of the radiation.
30.
In this equation, G is the reciprocal lattice vector, q is the length of the reciprocal lattice vector, k is the momentum transfer vector, ? is half of the scattering angle, and ? is the wavelength of the radiation.
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