Using Fast Fourier Transforms, one can work with plane-wave basis sets in reciprocal space in which not only the aforementioned integrals, such as the kinetic energy, but also derivatives are computationally less demanding to be carried out.
42.
Wombat will concentrate on " in-situ " studies and time critical investigations, such as structure determinations, texture measurements and reciprocal space mapping of single crystals in most different sample environments serving the physics, chemistry, materials, minerals and earth-science communities.
43.
To measure the intensity along a CTR, the sample must be rotated in the X-ray beam so that the origin of the Ewald sphere is translated and the sphere intersects the rod at a different location in reciprocal space.
44.
In " Sea at New Year " ( 1937 ), the reciprocal spaces of silvery ocean and sky are separated by irregular hills that are subtly darker but no more solid than the atmosphere and dissolve into swaths of mist.
45.
To collect all the necessary information, the crystal must be rotated step-by-step through 180? with an image recorded at every step; actually, slightly more than 180?is required to cover reciprocal space, due to the curvature of the Ewald sphere.
46.
The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points ( see the derivation of the Wigner-Seitz cell ).
47.
The phonon dispersion relation gives all possible phonon modes within the Brillouin zone ( zone within the primitive cell in reciprocal space ), and the phonon density of states " D p " ( the number density of possible phonon modes ).
48.
After determination of \ beta the distance between sample and detector is computed using known crystallographic data of the reference reflexion, a uniformly gridded map for the representative fiber plane in reciprocal space is constructed and the diffraction data are fed into this map.
49.
The origin refinement part of CIP relies on the definition of the plane symmetry group types as provided by the International Tables of Crystallography, where all symmetry equivalent positions in the unit cell and their respective site symmetries are listed along with systematic absences in reciprocal space.
50.
Substituting this in the expression for the heat capacity and again applying that the sum over \ mathbf { k } in the reciprocal space can be replaced by an integral in \ epsilon multipied by the density of states D ( E _ f ) this yields:
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