Structure factor, definition

For arrangements (a) and (b) the structure factor in the first order is 4Ba for planes with hSG even and kSG + lSG even, and 0 for all other planes. These arrangements are definitely eliminated by the experimental data for example, (411)SG is absent, and (521)sg> with smaller interplanar distance, reflects very strongly at the same wave length. Such wide discrepancies cannot be explained as due to the effect of sulfur and oxygen atoms. The barium atoms are, therefore, located as in (c). Because of the presence of other atoms no attempt was made to determine the two parameters involved. 

Motoyuki T, Kaoru K, Hironori N, Akira T, Hajime I, Hideto M. Definition of crucial structural factors of acetogenins, potent inhibitors of mitochondrial complex I. Biochim Biophys Acta 2000 1460 302-310. 

Fig. 4.15 Momentum transfer (Q)-dependence of the characteristic time r(Q) of the a-relaxation obtained from the slow decay of the incoherent intermediate scattering function of the main chain protons in PI (O) (MD-simulations). The solid lines through the points show the Q-dependencies of z(Q) indicated. The estimated error bars are shown for two Q-values. The Q-dependence of the value of the non-Gaussian parameter at r(Q) is also included (filled triangle) as well as the static structure factor S(Q) on the linear scale in arbitrary units. The horizontal shadowed area marks the range of the characteristic times t mr- The values of the structural relaxation time and are indicated by the dashed-dotted and dotted lines, respectively (see the text for the definitions of the timescales). The temperature is 363 K in all cases. (Reprinted with permission from [105]. Copyright 2002 The American Physical Society)...

In analogy to the definition of the total charge density, we define the total structure factor Ftotal(H), which includes both the nuclei and the electrons, and is, excluding thermal effects, given by... 

From their definitions, one may admit that topological indices may code two structural factors, namely, the size and the shape of the molecule. This assumption is proved by calculating 94) the schemes (B) in Figure 2 for the 36 polyalkylcyclohexanes with 6-10 carbon atoms, and for a subseries of 22 polyalkylcyclohexanes with 10 carbon atoms (resulting in scheme (C)). The schemes (A)-(C) corroborated with the... 

What is the definition of the form factor (or intraparticle structure factor) ... 

The self-dynamic structure factor of the solute at all time is calculated from the mean square displacement (MSD) using the following definition ... 

An early strategy was to use measured intensities rather than structure factors as Fourier coefficients. Although the transform of I, known as a Patterson function, must, by definition contain the same information as the... 

In many of these cases the CN group was included in the final analysis with a resulting improvement in the calculated structure factors, but this does not definitely establish the CN position. 

By definition, the structure factor is the sum of single-chain ( bare ) X0 and interchain H structure factors X = X0 + H. The formal solution to the OZ equations ... 

DM are ab initio crystal structure solution techniques able to estimate phases directly from structure factor magnitudes. These methods started in 1948. With the advent of modern computers and the use of sophisticated mathematical approaches, they are able to definitively solve, in practice, the phase problem for small molecules. Protein structures, up to say 2000 non-hydrogen atoms in the asymmetric unit, are today solved ab initio, provided single-crystal diffraction data with resolution better than 1.2 A are available. 

Note that everything except for 5(q) is stmctuic-independent. By expanding the structure factor explicitly in terms of its definition given in eqn (4.22), it is evident that the energy has decomposed into a series of pair terms as... 

By definition, the dynamic structure factor accounts for the correlations between the positions of the particles at different moments of time ... 

The effective interaction represented by b(q) can be considered as the sum of two terms, a direct interaction and an indirect interaction through one or several interacting polymers. The definition of the structure factor and its diagram representation (see Fig. 13.18) shows that b(q) must be defined by the equality... 

Here the structure factor signifies the vectorial sum of the waves scattered by the single atoms which show amplitude f and phase y. Every atom contributes a scattered wave to the whole diffraction effect, the amplitude of which is proportional to the so-called form factor. The phase is thus defined by the position of the atom in the elementary cell, whilst the form factor is a characteristic constant for every sort of atom which represents a measure of its scattering power. Hence no special differences exist in the positions of the diffracted beams, which in both X-ray and electron diffraction cases satisfy the geometric relations between lattice constant and X-ray or material wavelengths, according to the Bragg equation. However, there are definitely differences in their intensities. 

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