Distance shrinkage

Table I. Interatomic distances, shrinkages, and bending vibrational frequencies of first row transition metal dihalides...

We have tried to set up a model for the% effects with the program to be described later, that uses (4.16) to evaluate I pi Table 1 gives model-parameter values for 4 intensities I4,..., Ii corresponding to increasing surface correlation. We have disregarded the intermembrane distance shrinkage in order to simplify the diagram. 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

Figure 4. Change in interlayer distance between Ni02 sheets upon charge for an Li/LiNi02 cell. The gap (shrinkage) of ca.0.3 A in the interlayer distance is associated with the formation of nickel dioxide (kNi02) for 0.75

The next stage is a sol-gel transition that is accounted for by the formation of a three-dimensional network from cross-linked sol nanoparticles. It is apparent that it can happen only when the particles are in direct contact. The association of sol nanoparticles, as shown by Figure 3.7A, will inevitably result in shrinkage of the volume because of a decrease of the distance between them. The larger the initial distance and the denser the arrangement of particles in the gel, that is the larger the difference between the initial and final states in the system, the larger the syneresis. 

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...

Figure 5 gives the variation of the atomic volume in the actinide series, for the room temperature crystal structures as well as for the ccp and bcc high temperature allotropes, which exist for a number of actinides. The graph is based on the lattice parameters of Table 1, which includes also recent results. The marked dip in the curve from Th to Am illustrates the shrinkage of interactinide distance which is linked to the itinerancy of the 5f electrons in this part of the actinide series. 

The most noticeable effect of low temp upon stable deton results from a shrinkage in vol. Because of the higher d at low temps, deton velocities, and consequently deton pressures, are higher. These increases are too small to have practical significance. Where propagation time is critical, and must be synchronized with a process that is independent of temp, this effect, now accentuated by reduction in distance, can be a source of difficulty (Ref 2)... 

Figure 4 Model of the nanopore structure (cut through a (001) plane), evolution of the inter pore distances with treatment at 620 K, involving shrinkage in the direction normal to the substrate surface.

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) ... 

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. 

---