For the obtained structure, a precise packing analysis was performed by reciprocal lattice
The topics are crystal lattices from one to three dimensions, crystal structures of elements and important binary compounds, the reciprocal lattice
, direct and reciprocal lattices
, and X-ray diffraction.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [??] are magnetic field vector, electric field vector, 2D reciprocal lattice
vector, and plane wave vector, respectively.
In Equations (3) and (4) [beta] = 2[pi][[epsilon].sup.1/2.sub.0]/[lambda] where [[epsilon].sub.0] = [epsilon](G = 0) is the averaged dielectric permittivity ([[epsilon].sup.1/2.sub.0] corresponds to averaged refractive index n), [alpha] an averaged gain in the medium, K(G) the coupling constant, [lambda] the Bragg wavelength, G = (m[b.sub.1], n[b.sub.2]) the reciprocal lattice
vector, and m and n the arbitrary integers.
Color space is determined on the basis of physical characteristics of color chips, the reciprocal lattice
on the basis of logical properties of set-theoretic objects.
The scattering of x-rays on a crystal structure with spatially distributed heterogeneities depends on the phase factor of the lattice [phi](x, z) = exp (ihu(x, z)), where u(x,z) is the vector of atomic displacement, h is the vector of the reciprocal lattice
. This factor is written in the form of the sum: [phi](x, z) = [bar.[phi]](x, z) + [delta][phi](x, z), where the term [bar.[phi]](x, z) = exp (ih(u(x,z))) describes the non-random large-scale deformation in the crystal.
where the neutron-electron coupling constant in parenthesis is -0.27 X [10.sup.-12] cm, [tau] and M are unit vectors in the direction of the reciprocal lattice
vector [tau] and the spin direction, respectively, and the orientation factor <1-[([tau] * M).sup.2]> must be calculated for all possible domains.
She begins with the fundamentals such as unit cell calculation, point groups reciprocal lattice
, properties of X-rays, and electron density maps.
Special attention is given to the possibilities of numerical characterisation of the parameters of the pores on the basis of the analysis of sections and charts of the two-dimensional distribution of the intensity of diffraction reflection--reciprocal space mapping (RSM) around the node of the reciprocal lattice
But whereas diffraction from a periodic object forms a reciprocal lattice
that can be indexed with a set of d reciprocal basis vectors, where d is the dimension, the diffraction pattern from a quasiperiodic object requires a finite number, D > d, independent basis vectors.
It was found that all reciprocal lattice
vectors of (110), (040), and (130) planes aligned perpendicular to the direction of rolling with preferential orientation in the film normal direction.