Preferred orientation factor

Thki is the preferred orientation factor, i.e. it is a multiplier, which accounts for possible deviations from a complete randomness in the distribution of grain orientations. 

Preferred orientation effects are addressed by introducing the preferred orientation factor in Eq. 2.65 and/or by proper care in the preparation of the powdered specimen. The former may be quite difficult and even impossible when preferred orientation effects are severe. Therefore, every attempt should be made to physically increase randomness of particle distributions in the sample to be examined during a powder diffraction experiment. The sample preparation will be discussed in Chapter 3, and in this seetion we will discuss the modelling of the preferred orientation by various functions approximating the radial distribution of the crystallite orientations. 

The simplest radial function that describes the anisotropic distribution of the preferred orientation factor as a function of angle is an ellipse... 

A different approach has been suggested by Dollase, where the preferred orientation factor is represented by a more complex March-Dollase function ... 

In both cases (Eqs. 2.78 and 2.79) the preferred orientation factor Thu is proportional to the probability of the point of the reciprocal lattice, hkl, to be in the reflecting position (i.e. the probability of being located on the surface of the Ewald s sphere). In other words, this multiplier is proportional to the amount of crystallites with hkl planes parallel to the surface of the flat sample. 

A summary of physical and chemical constants for beryUium is compUed ia Table 1 (3—7). One of the more important characteristics of beryUium is its pronounced anisotropy resulting from the close-packed hexagonal crystal stmcture. This factor must be considered for any property that is known or suspected to be stmcture sensitive. As an example, the thermal expansion coefficient at 273 K of siagle-crystal beryUium was measured (8) as 10.6 x 10 paraUel to the i -axis and 7.7 x 10 paraUel to the i -axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement ia wrought beryUium. 

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 results show that the C5o-Pst star-shaped polymer L-B hlms are hrmly fixed on the surface of the substrate, even after the surface was scanned for many times. The topography, high density, order and preferred orientation of the hlms are dominating factors in friction. The C5o-Pst him could play a signihcant role in microtribological applications. 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor profile function describing the profile of the k h reflection. 

The difference in concerted reactions is large (5.5 kcal/mole) and no additional factor is needed to explain the high selectivity of the reaction. However, charge-transfer from olefin to aromatic should theoretically be an important stabilizing configuration in this reaction, and one should see if inclusion of CT will modify the conclusion. The charges on the atoms are shown in 17 after transfer of one electron. A contribution of a CT configuration would help to stabilize the preferred orientation relative... 

Scheme 6.44). The reaction gave the oxime derivative 38, however, and the expected isoxazoline was not detected, which was attributed to geometric factors that only permit a vertical orientation, not the normal in-plane approach of the nitrile oxide unit with respect to the double bond of ring A. The preferred orientation only allows the cyclization to take place (248). 

Jermy (15) has emphasized the Importance of allomones in the host plant selection process. Although the ovlpositional and phagostimulative kalromones do not appear to be sufficient to account for host specificity by M. sexta in the host plant selection process, the mere avoidance of allomones does not appear to be sufficient either. Rather, the presence of a detectable allomone is sufficient to account for non-selection of a potential host plant. For example, given a choice between esculentum and any other suitable host plant M. sexta moths select 1. excu-lentum (16). No allomones are Involved To account for this preference, the presence of volatile orientation factor(s) may be Involved. In fact, Morgan and Lyon ( ) Isolated amyl salicylate from the host plant Datura stromonlum as an orientation factor for gravid female moths. We have also shown that an orientation factor is present in the steam distillate of esculentum leaves. 

Suppose that the particles in Figure 1.8 were actually oblate ellipsoids (all in their preferred orientation) rather than spheres. Would their volume be over- or underestimated if the particles were assumed to be spheres In terms of their axial ratio, calculate the factor by which the mass is under- or overestimated when the particles are assumed to be spheres. (Consult a handbook for the volume of an ellipsoid.)... 

The result of this crystallization is a harder, less ductile film. The extent or the degree of crystalinity, either before or after heat treatment, is a compound function of phosphorous content, metalizing solution (bath) pH, temperature to which the sample was heated, time of exposure to the highest temperature, and a number of additional factors. By degree of crystalinity we mean here component crystalline sizes, possible preferred orientation and alike. 

Adjustments in other factors must also be made. These may include the lattice parameters, a 20-zero correction parameter, and a preferred orientation parameter. Principal among the non-structural parameters to be adjusted are (1) any adjustable parameters in the expression used for y and (2) the parameters in G(04-0h). G(0.,--0h) is itself a convolution of the instrumental... 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Pj is a preferred orientation correction, which is not included in the previous intensity of a diffraction peak function A is an absorption factor y° is the pattern background function... 

Theoretical Explanation. The major factors of the thermal expansion coefficient of calcined coke are the degree of preferred orientation of the crystallites and void structure (12-14). For example, the thermal expansion coefficient is low for needle coke because it is strongly affected by the preferred orientation of its crystallites. 

Material factors. The main metallurgical properties of importance are alloy composition, distribution of alloying elements and impurities, microstructure and crystal structure, heat treatment, mechanical working, preferred orientation of grains and grain boundaries (texture), mechanical properties (strength, fracture toughness, etc.).31... 

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