Orientation preferred

Conventional theory of powder diffraction assumes completely random distribution of the orientations among the infinite amount of crystallites in a specimen used to produce a powder diffraction pattern. In other words, precisely the same fraction of the specimen volume should be in the reflecting position for each and every Bragg reflection. Strictly speaking this is possible only when the specimen contains an infinite number of crystallites. In practice it can be only achieved when the number of crystallites is very large (usually in excess of 10 to lO particles). Nonetheless, even when the number of crystallites approaches infinity, this does not necessarily mean that their orientations will be completely random. The external shape of the crystallites plays an important role in achieving randomness of their orientations in addition to their number. 

When the shapes of crystallites are isotropic, random distribution of their orientations is not a problem and deviations from an ideal sample are usually negligible. However, quite often the shapes are anisotropic, e.g. platelet-like or needle-like and this results in the introduction of distinctly non-random crystallite orientations due to natural preferences in packing of the anisotropic particles. The non-random particle orientation is called preferred orientation and it may cause considerable distortions of the scattered intensity. 

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. 

Consider two limiting anisotropie particle shapes platelet-like and needle-like. The platelets, when packed in a flat sample holder, will tend to align parallel to one another and to the sample surface. Then, the amount of plates that are parallel or nearly parallel to the surface will be much greater than the amount of platelets that are perpendicular or nearly perpendicular to the surface. In this case, a specific direction that is perpendicular to the flat 

The needle-like crystallites, when packed into a flat sample, will also tend to align parallel to the surface. However, the preferred orientation axis, which in this case coincides with the elongated axes of the needles, will be parallel to the sample surface. In addition to the nearly unrestricted distribution of needles axes in the plane parallel to the sample surface (which becomes nearly ideally random when the sample spins around an axis perpendicular to its surface), each needle may be freely rotated around its longest direction. Hence, if the axis of the needle coincides, for example, with the vector d. then reflections from reciprocal lattice points with vectors parallel to will be suppressed to a greater extent and reflections from reciprocal lattice points with vectors perpendicular to d / will be strongly increased. This example describes the so-called in-plane preferred orientation. 

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Monte Carlo simulations are an efficient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an efficient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic effects are included. 

The viscosity of a suspension of ellipsoids depends on the orientation of the particle with respect to the flow streamlines. The ellipsoidal particle causes more disruption of the flow when it is perpendicular to the streamlines than when it is aligned with them the viscosity in the former case is greater than in the latter. For small particles the randomizing effect of Brownian motion is assumed to override any tendency to assume a preferred orientation in the flow. 

The stmcture of the polysihcon depends on the dopants, impurities, deposition temperature, and post-deposition heat annealing. Deposition at less than 575°C produces an amorphous stmcture deposition higher than 625°C results in a polycrystalline, columnar stmcture. Heating after deposition induces crystallization and grain growth. Deposition between 600 and 650°C yields a columnar stmcture having reasonable grain size and (llO)-preferred orientation. 

Fig. 1. Orientational order of the molecules in a liquid crystal. 9 is the angle between the long axis of a molecule and the direction of preferred orientation...

AppHcations of soHd-state nmr include measuring degrees of crystallinity, estimates of domain sizes and compatibiHty in mixed systems from relaxation time studies in the rotating frame, preferred orientation in Hquid crystalline domains, as weU as the opportunity to characterize samples for which suitable solvents are not available. This method is a primary tool in the study of high polymers, zeoHtes (see Molecular sieves), and other insoluble materials. 

Powder diffraction patterns have three main features that can be measured t5 -spacings, peak intensities, and peak shapes. Because these patterns ate a characteristic fingerprint for each crystalline phase, a computer can quickly compare the measured pattern with a standard pattern from its database and recommend the best match. Whereas the measurement of t5 -spacings is quite straightforward, the determination of peak intensities can be influenced by sample preparation. Any preferred orientation, or presence of several larger crystals in the sample, makes the interpretation of the intensity data difficult. 

Within the plane of a nonwoven material, the fibers may be either completely isotropic or ia a preferred orientation or alignment, usually with respect to a machine or processiag direction. In the case of thicker, dry-laid nonwovens, fiber orientation may be developed ia the third dimension, ie, that dimension which is perpendicular to the plane of the fabric, by a process known as needle-punching (7). This process serves to biad the fibers ia the nonwoven by mechanical interlocking. Hydroentangling is an alternative to needle-punching (8). 

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. 

The rate of addition depends on the concentration of both the butylene and the reagent HZ. The addition requires an acidic reagent and the orientation of the addition is regioselective (Markovnikov). The relative reactivities of the isomers are related to the relative stabiUty of the intermediate carbocation and are isobutylene 1 — butene > 2 — butenes. Addition to the 1-butene is less hindered than to the 2-butenes. For hydrogen bromide addition, the preferred orientation of the addition can be altered from Markovnikov to anti-Markovnikov by the presence of peroxides involving a free-radical mechanism. 

Fig. 2. Young s modulus corrected for porosity as a function of preferred orientation curve is based on theoretical model where = rayon-based fibers Q — PAN-based fibers and A = pitch-based fibers (2). To convert GPa to psi, multiply by 145,000.

The conformation of heteroethylenic rings. A - and A -pyrazolines, and the nitrogen inversion and preferred orientation of the IV-methyl groups in pyrazolidines (71T123) have been discussed in connection with their NMR spectra (Section 4.04.1.3.3). 

X-ray Diffraction (XRD) is a powerful technique used to uniquely identify the crystalline phases present in materials and to measure the structural properties (strain state, grain size, epitaxy, phase composition, preferred orientation, and defect structure) of these phases. XRD is also used to determine the thickness of thin films and multilayers, and atomic arrangements in amorphous materials (including polymers) and at inter ces. 

Thin-film XRD is important in many technological applications, because of its abilities to accurately determine strains and to uniquely identify the presence and composition of phases. In semiconduaor and optical materials applications, XRD is used to measure the strain state, orientation, and defects in epitaxial thin films, which affect the film s electronic and optical properties. For magnetic thin films, it is used to identify phases and to determine preferred orientations, since these can determine magnetic properties. In metallurgical applications, it is used to determine strains in surfiice layers and thin films, which influence their mechanical properties. For packaging materials, XRD can be used to investigate diffusion and phase formation at interfaces... 

As we have seen, the orientation of crystallites in a thin film can vary from epitaxial (or single crystalline), to complete fiber texture, to preferred orientation (incomplete fiber texture), to randomly distributed (or powder). The degree of orientation not only influences the thin-film properties but also has important consequences on the method of measurement and on the difficulty of identifying the phases present in films having multiple phases. 

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 structure of CBCF is shown in the SEM micrograph in Fig. 4. The crenellated surface of the rayon derived carbon fibers is clearly visible, as is the phenolic derived carbon binder. The preferred orientation of the fibers (resulting from the slurry molding operation) is obvious in Fig. 4, and imparts considerable anisotropy to the material. The molding direction is perpendicular to the plane of the carbon fibers in Fig. 4. 

Crystallography is a very broad science, stretching from crystal-structure determination to crystal physics (especially the systematic study and mathematical analysis of anisotropy), crystal chemistry and the geometrical study of phase transitions in the solid state, and stretching to the prediction of crystal structures from first principles this last is very active nowadays and is entirely dependent on recent advances in the electron theory of solids. There is also a flourishing field of applied crystallography, encompassing such skills as the determination of preferred orientations, alias textures, in polycrystalline assemblies. It would be fair to say that... 

A separate study was the improvement of magnetic permeability in soft alloys such as are used in transformers and motors by lining up the orientations of individual crystal grains, also known as a preferred orientation this became an important subspeciality in the design of transformer laminations made of dilute Fe-Si alloys, introduced more than 100 years ago and still widely used. 

Metallurgists originally, and now materials scientists (as well as solid-state chemists) have used erystallographic methods, certainly, for the determination of the structures of intermetallic compounds, but also for such subsidiary parepistemes as the study of the orientation relationships involved in phase transformations, and the study of preferred orientations, alias texture (statistically preferential alignment of the crystal axes of the individual grains in a polycrystalline assembly) however, those who pursue such concerns are not members of the aristocracy The study of texture both by X-ray diffraction and by computer simulation has become a huge sub-subsidiary field, very recently marked by the publication of a major book (Kocks el al. 1998). 

Kocks, U.F., Tome, C.N. and Wenk, H.-R (1998) Texture and Anisotropy Preferred Orientations in Polycrystals and their Effects on Materials Properties (Cambridge University Press, Cambridge). 

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