Paracrystalline peak

We will now consider three cases where satisfactory peak resolution was much more difficult to achieve. Case (a), a specimen of PET fibre used for texturising, having poorly defined crystalline peaks and possibly an additional peak due to an intermediate phase (11) case (b), a specimen from a range of PET fibres with different shrinkages (.12.), again an additional intermediate phase peak was a possibility case (c), cold drawn polypropylene fibres (13). an additional paracrystalline peak was most likely here. 

Resolution of polyester specimen PET 06 into three crystalline peaks, and three crystalline peaks and a paracrystalline peak... 

Figure 8. Paracrystalline peak resolution. Corrected and smoothed equatorial trace of a PET fiber specimen resolved into three crystalline peaks, 010, 110, 100, a paracrystalline peak and the new best-fit background.

The three case studies outlined here give some indication of the worst difficulties that have been experienced with peak resolution, and have one factor in common the presence of an additional amorphous or paracrystalline peak was suspected in each case. All three optimization programs worked well when the input parameters were well chosen, but constraints were necessary in the more difficult cases and when broad peaks were present. Judicious choice of input parameters always speeds the ultimate solution and the use of BASELINE is most helpful. 

Figure 11. Good resolution with constrained optimization and addition of a paracrystalline peak. Corrected equatorial trace of a polypropylene fiber specimen cold drawn X-5.5. Total theoretical trace now comprised of realistic crystalline peaks 110, 040, 130, 111, 131, 041, and paracrystalline peak at 15.5°. Compare...

Resolution of cold drawn polypropylene specimens into crystalline and paracrystalline peaks... 

It is worth to be noted that these definitions of first- and second-order distortions according to Warren-Averbach are model-free. From a linear or a quadratic increase of peak breadths it can neither be concluded in reverse that strain broadening, nor that paracrystalline disorder were detected. 

On the other hand, lattice distortions of the second kind are considered. Assuming [127] that ID paracrystalline lattice distortions are described by a Gaussian normal distribution go (standard deviation ay, its Fourier transform Gd (.S ) = exp (—2n2ols2) describes the line broadening in reciprocal space. Utilizing the analytical mathematical relation for the scattering intensity of a ID paracrys-tal (cf. Sect. 8.7.3 and [127,128]), a relation for the integral breadth as a function of the peak position s can be derived [127,129]... 

Peak resolution is usually easier if well chosen background parameters are input and if constrained optimization methods are utilised. Misleading results can be obtained if the constraints are too limited and tests with unconstrained optimization are desirable if at all possible. In particular, the possible presence of paracrystalline or intermediate phase peaks must be tested with extreme care in order to avoid ambiguity. It is not sufficient to have a good mathematical resolution alone, all peaks must be significant in crystallographic or structural terms. The incidental measurement of peak-area crystallinity is considered to be of secondary importance to the resolution of overlapping peaks. 

The term crystalline itself may be somewhat misleading when applied to CPs. Well-defined Bragg peaks can be obtained under less stringent conditions of order for instance, in the paracrystalline state [26] (see also Ref. 12, Vol. 1, p. 438), and this applied to all CPs, with the exception of PDAs, which form crystals in the usual sense of the word. 

Because of the presence of structural disorder, the X-ray diffraction patterns of mesophases show a large amount of diffuse scattering and need a special care for a quantitative evaluation. Paracrystalline distortions of the lattice [59,60] usually affect the shape and the width of the diffraction peaks to a large extent. The analysis of disorder necessarily implies a multidisciplinary approach, in order to unravel the complicated nature of disorder in disordered crystalline materials [61]. 

Interference function scattering was modelled by using a paracrystalline lattice model as a basis, with the adoption of the equations for X-ray scattering from low molecular weight crystalline materials. Thus the Bragg peaks essentially result from a powder diffraction pattern from the block copolymers. Reasonable agreement... 

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. 

Modeling the Interface Distribution Function for a ID Lamellar Stack As demonstrated in the last section, the nonideality of a real semicrystalline polymer can lead to a broadening and overlapping of the peaks in K (z), which makes it difficult to extract the correct structure parameters simply from the peak positions. The one-dimensional paracrystalline stack has been suggested as an analytical model for the semicrystalline structure [2,13,16], We here present a procedure that allows simulating and modeling the measured IDF based on this model. A simulated IDF... 

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