Layer spacing

In many materials, the relaxations between the layers oscillate. For example, if the first-to-second layer spacing is reduced by a few percent, the second-to-third layer spacing would be increased, but by a smaller amount, as illustrated in figure Al,7,31b). These oscillatory relaxations have been measured with FEED [4, 5] and ion scattering [6, 7] to extend to at least the fifth atomic layer into the material. The oscillatory nature of the relaxations results from oscillations in the electron density perpendicular to the surface, which are called Eriedel oscillations [8]. The Eriedel oscillations arise from Eenni-Dirac statistics and impart oscillatory forces to the ion cores. 

The atomic structure of a surface is usually not a simple tennination of the bulk structure. A classification exists based on the relation of surface to bulk stnicture. A bulk truncated surface has a structure identical to that of the bulk. A relaxed surface has the synnnetry of the bulk stnicture but different interatomic spacings. With respect to the first and second layers, lateral relaxation refers to shifts in layer registry and vertical relaxation refers to shifts in layer spacings. A reconstructed surface has a synnnetry different from that of the bulk synnnetry. The methods of stnictural analysis will be delineated below. 

Figure 5 Summary plot of the transition temperatures (lower), inverse of the smectic layer spacing (middle), and temperature of the a relaxation (upper) of polybibenzoates as a function of the number of methylene units in the spacer Ti, [Ref. 9] T, , [Ref. 9] A I/d, [Ref. 7] T T , [Ref. 9] open symbols our results.

One of the key quantities for a smectic phase is the scaled layer spacing, and this was determined from the periodicity in the longitudinal distribution function gj (r ). This distribution is unattenuated over the distances available from the simulation for the two smectic phases and the periodicity is the same although the width of the distribution is smaller in the smectic B than the... 

The smectic phases Ai, A2 and A have the same macroscopic symmetry, differing from each other in the wavelength of spacing. Hence it is possible to go from Ai to Aa or from Aa to A2 by varying only the layer periodicity in a continuous or discontinuous way(with the jump in the layer spacing d). Smectic-smectic transition lines of first order may terminate at a critical point, where the differences between the periodicities of the smectic A phases vanish, providing a continuous evolution from an Aa to bilayer A2 phase [12]. 

If Lp = Lh, the monolayer smectic Ai phase is formed. In the case that Lp > Lh, the layer spacing d exceeds the molecular length L, which corresponds to the formation of the smectic A phase (Fig. lla,b). In the opposite case, Lp < Lh, the layer spacing is less than L, and the flexible hydrocarbon chains just All the space which is determined by the fluorinated tails (Fig. 10c). 

The smectic X phase in the pure compound I shows additionally to the smectic C layering the two-dimensional (modulated) structure in which the smectic C layers are periodically shifted with a respect to one another by half a layer spacing. 

The layer spacing for smectic Ad and Cd phases significantly exceeds the molecular length (d/L = 1.35-1.65) and increases as the Ad<= Cd transition is approached from above. However, the temperature variations of the layer spacing in the Cd phase are very small in comparison to the classical smectic A-smectic C transition (Fig. 14). This unique behaviour results from the fact that both the tilt angles for different molecular moieties and the relative... 

Fig. 14. Temperature dependences of the layer spacing in the smectic Ad and Cd phases for terminally polar polyphilic compounds F4H11OCB (squares), FsHnOCB (circles), FgHioOCB (triangles) and FioHnOCB (diamonds). The arrows indicate the smectic Ad - smectic Cd phase transition points (Ostrovskii et al. [45])...

The nano-scale structures in polymer layered-silicate nano-composites can be thoroughly characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). XRD is used to identify intercalated structures. XRD allows quantification of changes in layer spacing and the most commonly used to probe the nano-composite structure and... 

---