Structure-forming factors

Understanding Structure-forming Factors and Theory-guided Exploration of Structure-Property Relationships in Intermetallics... 

Barrat and Boyer did the only other calculation of the structure (form) factor. Since these simulations neglect the counterions, one expects the q dependence should hold over a range of wavevectors. At 2a-/D, the... 

The structure-forming factor in the formation of stacks is likely intermolecular contacts between the endocyclic nitrogen atom N7 in the acridine nucleus and the central nitrogen atom N2 of the azido group (which is displaced out of the molecular plane see below) the distances between these atoms are 3.29 and 3.25 A in stacks A and B, respectively. 

The band-structure code, called BAND, also uses STO basis sets with STO fit functions or numerical atomic orbitals. Periodicity can be included in one, two, or three dimensions. No geometry optimization is available for band-structure calculations. The wave function can be decomposed into Mulliken, DOS, PDOS, and COOP plots. Form factors and charge analysis may also be generated. 

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

During this stage of the qualitative analysis, a PIF analysis is performed that considers those factors which will determine the probability of error for the type of task under consideration. A structured form of PIF analysis such as the HFA tool described in Section 2.7.2 will facilitate this process. 

Buoyancy in some form is employed in nearly all categories of underwater and surface systems to support them above the ocean bottom or to minimize their submerged weight. The buoyant material can assume many different structural forms utilizing a wide variety of densities. The choice of materials is severely restricted by operational requirements, since different environmental conditions exist. For example, lighter, buoyant liquids can be more volatile than heavier liquids. This factor can have a deleterious effect on a steel structure by accelerating stress corrosion or increasing permeability in reinforced plastics. 

The parameters reported by Zintl Hauke were taken as the starting point of the parameter determination. Using these parameters, structure factors were calculated for all of the planes in the sphere of reflection. The atomic form factors of James Brindley (1935) were used. (Subsequent calculations made with two... 

There is one other factor contributing to the overall symmetries of the lattice structure. This factor involves the local symmetry of the atomic groups which actually form the structure. Examples are the "solid-state building blocks" given above, e.g.- the tetrahedon - the group, P043-, and... 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

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