Epitaxial crystallization analysis

Analysis of Helical Hand Selection in Epitaxially Crystallized Films. 23... 

In Figure 13, a typical high resolution contact mode SFM scan of uniax-ially oriented POM is shown together with the corresponding 2-D fast Fourier transform filtered image (139). Since the polymer chain direction is in this particular case known a priori, the observed periodicities can be related to the well-established hexagonal crystal structure of POM in a straightforward manner. Uniaxially oriented or epitaxially crystallized specimens thus help in the analysis of the data, as has been discussed in recent review articles (140,141). 

A new crystal modification, y-form, was produced by Cartier and coworkers [37] via epitaxial crystallization on a hexamethylbenzene (HMB) substrate. The structure of this crystal has been confirmed by electron diffraction and packing energy analysis and is shown in Figure 6.14 [37]. Two antiparallel helices were packed in an orthorhombic unit... 

The first order analysis of epitaxial crystallization usually centers on the standard lattice matching criterion, namely near-matching of cell dimensions in corresponding orientations of the contact plane. This is indeed a useful test of any epitaxial crystallization. 

The epitaxial crystallization of iPP on benzoic acid is not amenable to the same in-depth analysis using diffraction data only. In that case, it is necessary to resort to AFM analysis of the iPP contact face, after dissolution of the benzoic acid substrate [32,33]. Here again, the contact face displays the four pattern of methyl groups (cf. Fig. 8.5a). It might be questioned whether a substrate that is more flat would favor the five face of odPP, that is, also less bumpy. No experimental evidence has been collected so far on this issue. 

The correct analysis of epitaxial crystallization of polymers cannot merely rely on global investigation techniques. Whereas the latter are suitable for screening, epitaxy takes place at a very different length scale, namely at the unit-cell level. It is therefore mandatory to use techniques that can read the molecular organization at a local scale. Moreover, in case a metastable crystal form is produced, the impact of epitaxy may be lost beyond only a few nanometers away from the interface. This contribution has developed some of... 

In order to establish such a correlation, however, a statistical analysis of a very large number of patterns would be necessary. This is one possible area for application for the pattern recognition techniques mentioned above. For thin single crystal substrates, any epitaxial relationship of the metal particles to the support is clearly evidenced because the patterns are superimposed in nanodiffraction. A comparison can be made of the patterns obtained with the beam on and just off the particle. 

The use of constraints and restraints arise from unrealistic bond lengths and angles. It is a reasonable use of statistical analysis to include prior information in a refinement procedure, and geometry is one such restraint/constraint. Poor geometries are often a consequence of missing data down one axis, invariably the result of the missing cone or lack of an epitaxially grown crystal. This lack of data has a profound effect on the refinement process... 

Zhang, W.P. and Dorset, D.L. (1990). Epitaxial growth and crystal structure analysis of perfluorotetracosane Macromolecules, 23, 4322-4326. 

We now assume that we have properly recorded rocking curves available, and that a substrate with a single epitaxial layer >0.5 //m thick (and less than, say, 5 m) is measured. This will result in two peaks, one each from the substrate and layer. The same analysis will apply to multiple peaks (other than those from superlattices) provided that they are well separated so that interference effects are minimised. The basic parameters are derived as follows, with the symmetric reflection used unless otherwise specified. The examples are given for (001) substrates and layers, but are quite general (with the caution that if the Poisson ratio is required, the value appropriate to the crystal orientation should strictly be used). 

The structural form of brookite (TiO ) is expected to be bounded by 210 and 111, both being F faces by PBC analysis, but the actual growth form observed is platy Habitus bounded by largely developed 100, which is an S face. The misfit ratio between the PBC on the (0110) face of quartz and that on (100) ofbrookite is the smallest among any misfit ratios between the two crystal species. From this, it was found that the platy Habitus ofbrookite arose because quartz adsorbed in an epitaxial relation on 100 ofbrookite, thus diminishing thegrowthratekof(lOO) [30]. 

The corresponding relation between the host and guest crystals when evaluating the misfit ratio may be a one-to-one lattice relation in the same direction (a X b to a xb axes), or in different axial directions (aX b axes versus aX <110> axes), or on the basis of one unit cell versus a few unit cell sizes (see Fig. 7.13). Royer s misfit ratio is generally a two-dimensional correspondence, but Hartman [13] extended this relation to the misfit ratio in PBCs (see Section 4.2), which is a one-dimensional correspondence. Royer s epitaxial relations correspond to a relation between the F faces of the host and guest crystals containing more than two PBCs, and an epitaxial relation is not allowed between S faces or K faces. In Hartman s analysis, rela-... 

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