Simulated diffraction pattern

Figure 1-12) [30], This pattern was extended by Alan Mackay into the third dimension and he even produced a simulated diffraction pattern that showed 10-foldedness (Figure 1-13) [31], It was about the same time that Dan Shechtman was experimenting with metallic phases of various alloys cooled with different speeds and observed 10-foldedness in an actual electron diffraction experiment (Figure 1-14) for the first time. The discovery of quasicrystals has added new perspective to crystallography and the utilization of symmetry considerations. 

Alan Mackay made the connection with crystallography [139], He designed a pattern of circles based on a quasi-lattice to model a possible atomic structure. An optical transformation then created a simulated diffraction pattern exhibiting local tenfold symmetry (see, in the Introduction). In this way, Mackay virtually predicted the existence of what was later to be known as quasicrystals, and issued a warning that such structures may be encountered but may stay unrecognized if unexpected ... 

Independent of Mackay s predictions and Shechtman s experiments, there was another line of research by Steinhardt and Levine, leading to a model encompassing all the features of shechtmanite (the original quasiperiodic alloy was eventually named so) and other materials that are symmetric and icosahedral, but nonperiodic [143], It was a perfect timing that as soon as they built up their model and produced its simulated diffraction pattern, they could see its proof from a real experiment. 

The final stage in any polymorphic simulation is to check the reliability of the simulated data. This can be achieved by comparing a variety of data, e.g., density, lattice energies, etc. With the advent of reliable software, a simulated diffraction pattern is now used as the primary comparison with the experimental data. Prior research has shown that computer simulations can successfully predict the structure of an unknown polymorph or determine the potential for polymorphisim (37). 

The superposition of the diffraction patterns of Pt[0lT] zone axis and La-AbOj simulated diffraction pattern shows that the relations between platinum and the support could be of epitaxial type, (scale expansion 2)... 

The easy electron migration from platinum crystallites to the biphasic support clearly indicates that a coherent interface between the metal and the substrate must also be considered. Fig.8 shows the superposition of the electron diffraction pattern from the [Oil] zone axis of platinum with a simulated diffraction pattern for the support. The good matching between several reciprocal vectors of the two structures indicates that the relationship between the platinum and the support is similar to that noted in previous observations on the epitaxial relationship between Pd[0lT] zone axis and Y-AI2O3 [110] zone axis (Ref. 23). According to Dexpert et al. (Ref. 23), the resistance to sintering can, therefore, be interpreted as the result of the strength of the epitaxial interactions which is intermediate between chemical bonds and Van der Waals forces. 

Big. 7 Simulated diffraction patterns of the high-(340 K) and low-temperature phases (98 K) of DCPS resulting from the MD calculations. 

A second approach uses the unimodal model-independent method. Here, one begins with the assumption that the size distribution consists of a finite number of fixed size classes. The detector response expected for this distribution is simulated, and then the weight fractions in each size class are optimized through a minimization of the sum of squared deviations from the measured and simulated detector responses. The third system uses the multimodal model-independent method. For this, one simulates diffraction patterns for known size distributions, superimposes random noise on the patterns, and then calculates the expected element responses for the detector configuration. The patterns are inverted by the same minimization algorithm, and these inverted patterns compared with known distributions to check for qualitative correctness. 

Prosa et al. initially reported an orthorhombic tmit cell for form I [89]. In a later study, Tashiro et al. proposed other possible structures that are consistent with both experimental and simulated diffraction patterns [90]. Using electron diffraction, Brinkmann and Rannou found a monoclinic tmit cell for form I P3HT [91]. This structure was challenged by Dudenko et al. [92]. Although it has not been possible to grow single crystals in form 1 (which makes the structure determination difficult). 

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