Texture effects

In the foregoing it is assumed that the powder sample is ideally random, i.e. all crystallite orientations are equally probable so that the diffraction rings are of 

A complete description of the texture (or preferred orientation) is formulated as a probability for finding a particular crystallite orientation within the sample this is the orientation distribution function (ODF). For an ideally random powder the ODF is the same everywhere (ODF=l) while for a textured sample the ODF will have positive values both less and greater than unity. This ODF can be used to formulate a correction to the Bragg intensities via a fourdimensional surface general axis equation) that depends on both the direction in reciprocal space and the direction in sample coordinates  

In a diffraction experiment the crystal reflection coordinates (cj), p) are determined by the reflection index (h) while the sample coordinates (ij/, y) are determined by the orientation of the sample on the diffractometer. This formulation assumes that the probability surface is smooth and can be described by a sum of spherical harmonic terms, kfl and kjf, that depend on h and sample orientation, respectively, to some maximum harmonic order, L (ref. 25). The coefficients Cf then determine the strength and details of the texture. Notably, only the even order, L = 2n, terms in these harmonic sums affect the intensity of Bragg reflections the odd order terms in the ODF are invisible to diffraction. 

While the general axis equation in Equation (64) can be used to describe the effect of texture on diffraction intensities in the most general case, most powder diffraction experiments are performed to simplify the problem. Rotation of the sample about an axis (normal to the surface in a Bragg Brentano experiment or about the capillary axis for a Debye-Scherrer experiment) will simplify Equation (64) via symmetry to  

A further simplification of the texture correction can be made if the form of the ODF is assumed to be cylindrically symmetric (e.g. from spirming the sample) and ellipsoidal. If the unique ellipsoid axis is parallel to the diffraction vector (s) and perpendicular to a flat sample surface as it is in a Bragg-Brentano experiment, the general axis equation (commonly referred to as the March-Dollase equation) is  

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Fig. 8. Neutron irradiation induced dimensional changes for GraphNOL N3M graphite irradiated a 600 or 875 °C [61]. Note that the radial dimensional changes exceed the axial changes due to textural effects.

Brye KR, Rogers CW, Smartt AD, Norman RJ. Soil texture effects on methane emissions from direct-seeded, delayed-flood rice production in Arkansas. Soil Sci. 2013 178 519-529. 

Tregunno, N.B. and Goff, H.D. 1996. Osmodehydrofreezing of apples Structural and textural effects. 

Tabakova, Idakiev, Andreeva, and coworkers—Zr a highly efficient support for supported, well-dispersed Au textural effects and mesoporous support preparation. 

Phase identification was performed by X-ray diffraction in Bragg-Brentano geometry with Cu-Ka radiation and a secondary monochromator. A rotating sample holder was used in order to minimize texture effects in the x-y plane and to offset the effects of the rather large grain size. Diffractograms were taken as a function of depth after stepwise removal of layers with an abrasive diamond disk. 

When a variety of found objects such as buttons, cloth, and leather, which supply actual textures, are combined with painted or drawn textural effects on a two-dimensional ground, a collage is created. 

To add a textured effect, choose three or more (but not all) of the units and wrap nylon thread around them, securing the thread with glue. Wrap the units in various directions. If preferred, shapes may be wrapped before the units are attached to one another. 

But the important thing is to be able to make patterns like them without the necessity of direct mechanical stimulus.35 Modern Caricature and Impressionism argued likewise for nature s legitimacy as an object , producing textures, effects, forms, rather than a pictorial subject. 

Mclnerney M. and Bolger T. (2000b) Temperature, wetting cycles and soil texture effects on carbon and nitrogen dynamics in stabilized earthworm casts. Soil Biol. Biochem. 32(3), 335-349. 

The combined importance of the chemical nature and the porous texture of a carbonaceous adsorbent was emphasized in the study of Petrov et al. [189], who examined the uptakes of copper, zinc, cadmium, and lead on as-received and oxidized anthracite. A subsequent study by the same group 1190, using the same adsorbates but different adsorbents, ignores the porous texture effects, reemphasizes the great significance of the chemical nature of the carbon surface, and also highlights the different effects observed for different metals by switching from one adsorbent to another. 

The measurements presented here illustrate impressively that it is essential to consider the effect of substrate heterogeneities on passive film growth. Measurements of passive films on macroscopic surfaces can, in principle, not be quantitatively understood in terms of classical models without taking texture effects into account, as macroscopic measurements can yield only averaged values. 

Those interested mostly in structure determination from powder diffraction see the texture problem differently. The presence of the preferred orientation makes a good pattern fitting difficult or even impossible and, consequently, a procedure is needed to correct for the texture effect in the Rietveld codes. For that it is not necessary to find the ODF, but to have a reliable model of the pole distribution whose parameters are refined together with the structure and other parameters. 

The number of crystals comprising the sample has to be very large and their orientation has to be random (see section 4.2). It sometimes happens, however, that this condition is impossible to fulfill, resulting in discrepancies between the integrated intensities of the peaks in the pattern and the values strictly related to structural parameters. When the nature of this preferential orientation is known, it is possible to take it into account in the refinement. This led several authors [ALT 96, PES 95] to incorporate, into their Rietveld refinement programs, preferential orientation parameters based on the use of the March function which was first introduced by Dollase [DOL 86], Nonetheless, it is still better to avoid any texture effects. 

Mixed EHD film lubrication is encountered during the transition from full EHD film to boundary lubrication. In this region, surface roughness (texture) effects are particularly critical. A common method of accounting for surface roughness effects is through the use of the film parameter (A) ... 

One final experiment addressed to the question of the egg box model and textural effects was to determine the ability of cadmium ions to reverse the effect of calcium ions on softening. Cadmium ion did not inhibit softening (Fig. 7) even though Kohn (29) has demonstrated that it binds to pectate with greater affinity than calcium. It also has an ionic radius nearly the same as calcium... 

Texture effects were suggested by Rancourt et al. (1992) to be the main cause of artifacts attributed to by Dyar (1990), a suggestion that was disputed by Dyar... 

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