Shrinkage effect

Viberg, U., Freuler, S., Gekas, V., and Sjoholm, I. 1998. Osmotic pretreatment of strawberries and shrinkage effects. J. Food Engineer. 35, 135-145. 

ED - estimated from shrinkage effect SP - matrix isolation infrared spectroscopy... 

Fig. 6. Illustration for the origin of the shrinkage effect in MXj moiecuies is the equilibrium X X distance, r is the instantaneous X X distance during vibration. Because of the perpendic-uiar (bending) vibrations, the average internuciear distance, fg = / r i)P(y) d7 is less than the equilibrium distance here P(y)dy expresses the protebility that the angle X-M-X lies between y and y + dy...

The shrinkage effect1 is treated in more detail elsewhere in the present article. Due to molecular vibrations interatomic distances observed by electron diffraction do not correspond to a set of distances calculated from a rigid geometrical model. Usually the shrinkage effect is routinely included in electron-diffraction least-squares refinement. In order to do so, it has been found appropriate to introduce a third distance type r defined as the distance between mean positions of atoms at a particular temperature. If the harmonic force field is known, iQ may be calculated from ra according to Eq. (12) ... 

The shrinkage effect is now quantitatively well understood for small amplitude vibrations17 8S. The phenomenon is thoroughly studied by Cyvin in a series of articles. The result of his own work and that of others is described in detail in Cyvin s book4. ... 

As earlier indicated carbon suboxide has attracted considerable interest as to the study of shrinkage effect and large molecular motion. The molecule has been submitted to four independent electron-diffraction studies at this laboratory81,82,, 2c. The large shrinkage effect of carbon suboxide could not be explained from the known vibrational frequency at the time when the shrinkage effect was first ob-... 

Since the a //-distance varies so little with framework vibration, particularly in high barrier cases 09). The anti-peak is accordingly not suited for direct determination of 00. On the other hand, the torsional motion leads to an asymmetry in the anti-peak due to the functional relation between r and . For a low barrier case this asymmetry may be appreciable, while in a high barrier case it may be observed only as a shrinkage effect for the anti-distance. The asymmetry or the shrinkage may be used to derive a value for 00. 

Concerning the molecule (W03)3 shrinkage has been calculated418 The inclusion of the shrinkage effect does not change the conclusion that the ring has a puckered conformation. 

However, in some cases, a discrepancy with respect to Burstein-Moss theory has been experimentally observed Roth et al. [41,42] have studied absorption effects in heavily-doped ZnO hlms. They observed that for N > 3 x 1019 cm-3, a shrinkage effect of the gap occurs in addition to the Burstein-Moss effect. This shrinkage of the gap is due to the merging of the donor and... 

On the other hand, there is a technological trend towards a high solid content of polymer formulations, e.g., to minimize shrinkage effects or to shorten processing times. A high polymer content at reasonable processing viscosities can only be obtained by polymer dispersions, either in water or hydrocarbon solvents. 

The mean square amplitude of vibrations have been calculated for these ions 550), and Bastiansen-Morino shrinkage effects reported 767, 768). 

In the case of spray drying, liquid-vapor menisci also exist in the pores, but the material is divided in very small particles (d == 150 pm) leading to a very short drying duration (20 to 30 seconds), which, combined to a low drying temperature (solid temperature 90 °C), results into less detrimental shrinkage effects. 

As we will see, the conversation in Holmenkollen had a very important conceptual impact on the GED method. This phenomenon is known as the Bastiansen-Morino shrinkage effect or more simply as the shrinkage effect . 

Shrinkage effect is a direct consequence of the molecular vibrations and it shows that the bonded and non-bonded interatomic distances measured by GED are not self-consistent, i.e., they do not correspond to a set of distances calculated from a rigid geometrical model. This phenomenon is illustrated on a simplified diagram below for a linear triatomic molecule AB2 (simplification in this case means that for this type of vibration while two B atoms move up, atom A moves down which is ignored in this diagram). 

According to Robiette [166], there are three major topics that comprise the main areas of interplay between spectroscopy and GED the amplitudes of vibration, the shrinkage effect and the inter-relation of molecular structures obtained from spectroscopic and electron-diffraction data. The first two topics were discussed in the previous subsection while this subsection concentrates on the third topic. 

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