Form-factor

In a scattering experiment, the measured intensities do not give any information on the phase relation between the elementary parts. On the other hand polymers are non homogeneous particles, most of the volume occupied by a chain is filled with the solvent molecules. Therefore the smooth scattering curve observed as a function of q is not very hepfiil if we do not have robust theoretic models describing the chain statistics. The form factor for the chain is 

The intensity of scattered light is the energy of radiation that falls onto a nit area per unit time. It is proportional to the square of the electric field averaged over one oscillation period 1 jv  

The final result used the equation for the product of cosines  

The first term in Eq. (2.134) oscillates exactly two full periods (47t) and its integral over the time interval 0 t l/u is thus equal to zero. The second term (cosine of the phase difference) is time independent and determines the intensity of light scattered by the molecule 

The dependence of the scattered intensity on the size and the shape of the polymer is usually described by the form factor defined as the ratio of intensity scattered at angle 9 (scattering wavevector to that extrapolated to zero angle ( — 0) and therefore, zero scattering wavevector (1 1 - 0)  

All optical paths are the same at zero scattering angle (q = 0) and there is no phase shift (ipj = 0 for all j) because the scattering wavevector q = 0 [Eq. (2.131)]. The intensity of light scattered by the molecule at zero angle. 

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Brown P J 1999 Magnetic form factors International Tables for Crystallography 2n6 edn, vol C, ed A J C Wilson and E Prince (Dordrecht Kluwer) section 4.4.5... 

B2.2.5.5 ATOMIC FORM FACTOR AND GENERALIZED OSCILLATOR STRENGTH... 

The form factor f takes the directional dependence of scattering horn a spherical body of finite size into account. The reciprocal distance s depends on the scattering angle and the wavelength A as given by Eq. (23). 

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. 

Polycarbonates. Currently, all audio CDs (CD-AD), all CD-ROM, and the biggest fraction of substrate disks for WORM and EOD worldwide are manufactured from a modified bisphenol A—polycarbonate (BPA-PC) (3). In 1991, some 1.3 x 10 compact disks were produced, equivalent to an annual amount of about 35,000 t BPA-PC. WORM and EOD disks are manufactured mainly from BPA-PC for sizes of 5.25 in. and below, and glass for larger form factors (eg, 12 in.), partially also from BPA-PC, and in some cases from aluminum or from cross-linked polymers (epoxy resins) (190). 

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. 

The area form factor [176] can be considered as a measure of the gluing efficient surface area based on the volume and is inversely proportional to the thickness of the particles F/V = 2jd = 2x sj 1. 

Indicator lights, fixed pattern, and segmented displays are applications which have been suggested for OLED deployment. Manufacturers of automobile components have shown interest in OLED indicators for the dashboard, where the primary considerations are those of cost, form factor, brightness, and stability over a wide range of ambient conditions. Power consumption is not particularly critical. The possibility of molding a thin light into a curved dashboard is attractive. 

The form factor (2n/ln (L/d)) changes slowly with the aspect ratio (L/d) and can be regarded as constant (k). The total drag on the cylinder is obtained by integration ... 

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... 

The parameters were then further refined by four successive least-squares procedures, as described by Hughes (1941). Only hk() data were used. The form factor for zinc was taken to be 2-4 times the average of the form factors for magnesium and aluminum. The values of the form factor for zinc used in making the average was corrected for the anomalous dispersion expected for copper Kot radiation. The customary Lorentz, polarization, temperature, and absorption factors were used. A preliminary combined scale, temperature, and absorption factor was evaluated graph-... 

The reliability factor B was 0276 after the first refinement and 0-211 after the fourth refinement. The parameters from the third and fourth refinements differed very little from one another. The final values are given in Table 1. As large systematic errors were introduced in the refinement process by the unavoidable use of very poor atomic form factors, the probable errors in the parameters as obtained in the refinement were considered to be of questionable significance. For this reason they are not given in the table. The average error was, however, estimated to be 0-001 for the positional parameters and 5% for the compositional parameters. The scattering power of the two atoms of type A was given by the least-squares refinement as only 0-8 times that of aluminum (the fraction... 

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

Once the wavelength dependence of the molecular form factor F(nqo) is known from the reasonable model of layer organization, the ratios r /ti may be calculated. The value of these ratios (for example, T2/T1, T3/T1) give a good guide to the sharpness of the distribution function f(z) - for an ideal crystal f(z) would be an array of delta-functions and T2 = Ti = = = 1. From the... 

A model with overlapping perfluoroalkyl tail should be excluded, since in this case the difference A is independent of the length of the fluorinated chain. The calculations for the molecular form factor gives a reasonable agreement with the intensities of successive (OOn) harmonics for the model with overlapping aromatic parts of the molecules and the tilt (approximately 35°) of perfloro chains [41c]. This model also satisfies fhe requiremenfs for dense Ailing of space. The smecfic layers in fhe dimeric smecfic phase are well defined (cr = 2.5-3 A) and consisf of fwo sublayers of fhe fluorinafed and aromafic parfs of fhe molecules. 

Due to new opportunities and continued computer min-iaturizations (e.g., laptops replacing desktops and desktops getting smaller), the HDD is in transition to smaller form factors. The 2.5 in. and smaller disk sizes are rapidly growing. In 2004, a quarter of HDD shipments were 2.5 in. or smaller. By 2008 these smaller form factor drives could count for about one-half of HDD shipments. 

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

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