Paracrystalline theory

It has also been suggested that the strain associated with a high concentration of such microscopic precipitates could be described by paracrystallinity theory,51 which would imply that the diffraction pattern of a catalyst containing such precipitates would have a characteristic form which would... 

The mean crystallite length as well as lattice distortion is also obtained by X-ray line broadming analysis based on the paracrystalline theory. 

In summary, the EXAFS results show that there is no difference between pure iron and the catalyst in the average local structure. Furthermore, there are no iron atoms present in the catalyst in significant quantities which exhibit a different geometric environment to the average, i.e., there is only one type of iron atom present. This is strong evidence against the paracrystallinity theory and is more consistent with a macroscopic distribution of the promoter phases, which affects fewer iron atoms than can be detected with the X-ray absorption technique. The porosity of the reduced catalyst may account for a certain lack of EXAFS amplitude. Any significant reduction in the coordination number of the iron in the catalyst would require a cluster-like microstructure for which no evidence has yet been found. 

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

Szwarc discovers the living polymers by anionic polymerisation Theory of paracrystallinity developed by Hosemann... 

Lindenmeyer and Hoseman [139] applied the theory of paracrystallinity to the acrylic fiber diffraction pattern and concluded that the diffuse scattering could arise as the net result of having different conformations distributed along the chain, with no single conformation persisting over a long distance. 

The small angle reflections were analyzed with respect to the dependence of their width on the order of the reflections. From this analysis information on structural defects of the layer arrangement can be obtained. According to the theory of paracrystalline distortionsthe integral width of the reflec-... 

If one examines Figure 6a closely, one will notice that the rings are not really homogeneous rather they are composed of numerous spots, indicating that the liquid crystalline domains are of considerable size. The dependence of the reflection width on the order of the reflection was analyzed according to the theory of paracrystalline distortions of the second kind. Information about the crystallite or domain size and distortion parameter can be obtained from such analysis. The breadth due to instrumental... 

Before beginning with the qrstematic theory in Chap. I, we will give a short historical view of the literature. Literature can be subdivided into two main groups. The first of these can be termed crystalline, for its roots lie in classical crystallography. The other can be termed paracrystalline. Its roots lie in X-ray studies of liquids and gases. 

The fruitful concept of autocorrelation functions thus appesatd. Calculations of the autocorrelation function, called Q-function, proved to be more adequate to paracrystalline problems than intensities. Hosemann s perfect com etion of the theory used the Q-function extensively. 

The concept of paracrystallinity introduced by Hosemann et al. in 1966 was used earlier to describe the phenomenon of ammonia iron. They developed the theory of paracrystallinity from XRD data which seemed to explain the special properties of the activated iron catalyst. A three-dimensional, endotactic incorporation of hercynite (FeAl204) motives into the a-iron lattice was thought to create substitutional point defects in the crystal lattice leading to a modified bulk and surface structure of the activated catalyst material. The interplanar spacings change... 

The average d-spacings of the iron diffraction peaks are very close to those of pure elemental iron as indicated in Fig. 2.15. This result is in good agreement with the conclusions reached from the other two methods of structural analysis discussed above. There is one difference, however, between the diffraction patterns of pure iron powder and that of the catalyst, namely, the line shape is significantly and reproducibly different. The theory of paracrystallinity was developed " from this line shape effect, which is the only experimental evidence in support of the idea that the bulk of an active ammonia synthesis catalyst may be different from iron powder. 

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