Order long-, short-range

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Order No Short range Long range Perfect... 

Liquids are systems devoid of both long-range translational and orientational order whereas short-range order still remains at molecular scales resulting from the subtleties of forces acting on their constituent molecules. In turn, rotator-phase (plastic) crystals are liquid-like in the sense that molecules... 

Figure 1.1 (a) Long-range order (b) short-range order. 

Orientational long-range order, positional short-range order... 

Fig. 5.7.1. (a) The structure of the hexatic phase of a two-dimensional lattice. The orientation of the lattice vectors a and b is preserved over a long range, but the molecular positions are correlated only over a short distance p. b) The orientational order as well as the positional order are short range. (After Litster... 

The important role of random fields in the disordered systems is confirmed by the form of their phase diagram, schematically represented in Fig. 1.11 [26]. It is seen that the boundaries of phases (paraphase (P), phase with long-range order (F), short-range order (SG) and mixed phase (FSG)) are defined by the ratio of mean value of random field Jo (mean field) to its dispersion J. In the disordered ferroics the nonzero mean field originates from fixed sign part of dipole-dipole or spin-spin interaction while alternative sign part defines the dispersion of the random field. 

The resulting order is referred to as quasi-long-range order. It provides a marginal case between true long-range positional order and short-range order. These various types of order are illustrated in Fig. 8. 

Fig. 8 Representation of correlation function, G(r), and X-ray intensity, /( ), for long-range order, algebraically decaying quasi-long-range order, and short-range order...

LRO=long-range order SRO = short-range order the SmC phase has quasi-LRO of the tilt direction. 

Figure Al.3.28. Examples of disorder (a) perfeet erystal, (b) eompositional disorder, (e) positional disorder whieh retains the short-range order and (d) no long-range or short-range order.

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