Order, short-range

The order parameter, defined by Equation (2.2) and its variants such as Equations (2.4) and (2.8), is an average over the whole system and therefore provides a measure of the long-range orientation order. The smaller the fluctuation of the molecular axis from the director axis orientation direction, the closer the magnitude of S is to unity. In a perfectly ahgned hquid crystal, as in other cry stalhne materials, cos 0 = 1 and S= 1 on the other hand, in a perfectly random system, such as ordinary Uquids or the isotropic phase of hquid crystals, cos 0) = i and S = 0. 

An important distinction between liquid crystals and ordinary anisotropic or isotropic hquids is that, in the isotropic phase, there could exist a so-called short-range order, - that is, molecules within a sliort distance of one another are correlated by intermolecular interactions. These molecular interactions may be viewed as renmants of those existing in the nematic phase. Clearly, the closer the isotropic hquid crystal is to the phase transition temperature, the more pronounced the short-range order and its manifestations in mar physical parameters will be. Short-range order in the isotropic phase gives rise to interesting critical behavior in the response of the liquid crystals to externally apphed fields (electric, magnehc, and ophcal) (see Section 3.2). 

As pointed out at the begirming of this chapter, the physical and ophcal properhes of hquid crystals may be roughly classified into two types one pertaining to the ordered phase, characterized by long-range order and crystalline like physical properhes the 

ORDER PARAMETER, PHASE TRANSITION, AND FREE ENERGIES 

Other pertaining to the so-called disordered phase, where a short-range order exists. All these order parameters show critical dependences as the temperature approaches the phase transition temperature from the respective directions. 

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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.

Onsager L and Kaufman B 1949 Orystal statistics III. Short range order in a binary Ising lattice Phys. Rev. 65 1244... 

The integral under the heat capacity curve is an energy (or enthalpy as the case may be) and is more or less independent of the details of the model. The quasi-chemical treatment improved the heat capacity curve, making it sharper and narrower than the mean-field result, but it still remained finite at the critical point. Further improvements were made by Bethe with a second approximation, and by Kirkwood (1938). Figure A2.5.21 compares the various theoretical calculations [6]. These modifications lead to somewhat lower values of the critical temperature, which could be related to a flattening of the coexistence curve. Moreover, and perhaps more important, they show that a short-range order persists to higher temperatures, as it must because of the preference for unlike pairs the excess heat capacity shows a discontinuity, but it does not drop to zero as mean-field theories predict. Unfortunately these improvements are still analytic and in the vicinity of the critical point still yield a parabolic coexistence curve and a finite heat capacity just as the mean-field treatments do. 

The major role of TOF-SARS and SARIS is as surface structure analysis teclmiques which are capable of probing the positions of all elements with an accuracy of <0.1 A. They are sensitive to short-range order, i.e. individual interatomic spacings that are <10 A. They provide a direct measure of the interatomic distances in the first and subsurface layers and a measure of surface periodicity in real space. One of its most important applications is the direct determination of hydrogen adsorption sites by recoiling spectrometry [12, 4T ]. Most other surface structure teclmiques do not detect hydrogen, with the possible exception of He atom scattering and vibrational spectroscopy. 

Short-range order parameter a Standard enthalpy of activa- m... 

The short-range order in a material is important in determining optoelectronic properties. For instance, x-ray and electron diffraction experiments performed on amorphous siHcon (i -Si) and germanium (a-Ge) have revealed that the nearest neighbor environments are approximately the same as those found in their crystalline counterparts (6) photoemission experiments performed on i -Si show that the DOS in valence and conduction bands are virtually identical to the corresponding crystal with the exception that the singularities (associated with periodicity) present in the latter are smeared out in the former. 

The ability of XPD and AED to measure the short-range order of materials on a very short time scale opens the door for surface order—disorder transition studies, such as the surface solid-to- liquid transition temperature, as has already been done for Pb and Ge. In the caseofbulkGe, a melting temperature of 1210 K was found. While monitoring core-level XPD photoelectron azimuthal scans as a function of increasing temperature, the surface was found to show an order—disorder temperature 160° below that of the bulk. 

EXPERIMENTAL STUDY OF THE SHORT RANGE ORDER IN THE PT-V SYSTEM EFFECTIVE PAIR INTERACTIONS AS A FUNCTION OF THE CONCENTRATION... 

To summarize we have reproduced the intricate structural properties of the Fe-Co, Fe-Ni and the Fe-Cu alloys by means of LMTO-ASA-CPA theory. We conclude that the phase diagram of especially the Fe-Ni alloys is heavily influenced by short range order effects. The general trend of a bcc-fcc phase transition at lower Fe concentrations is in accordance with simple band Ailing effects from canonical band theory. Due to this the structural stability of the Fe-Co alloys may be understood from VGA and canonical band calculations, since the common band model is appropriate below the Fermi energy for this system. However, for the Fe-Ni and the Fe-Cu system this simple picture breaks down. 

Figure 2 Time sequence of th< spin configuration on a (100) plane at 50% when the system at T=2.5 (snapshot a) is quenched down to T—1.7 and is subject to an isothermal aging. Snapshots demonstrated in figs, b, c and d correspond to time t=20,000, 43,000 and 50,000. The long range and short range order parameters input from the PPM calculations and resultant ones in the simulated lattice are also demonstrated [22, 24, 28]. ...

Above 390°C a small decrease of resistivity with increasing temperature (compare insert) signals the presence of short-range order (SRO), which is accompanied by a decrease of resistivity with decreasing degree of SRO in this system. 

J.B. Gibson, The effect of short-range order on residual resistivity, J. Phys. Chem. Solids 1 27 (1956). 

Behaviour in short-range ordered alloys, Phys. Rev. Lett. 70 3311 (1993). 

T. Doppler and W Pfeiler, Resistometric investigation of short-range order kinetics in gold-silver alloys, phys. slot. sol. (a) 131 131 (1992). 

W Garlipp, M Migschitz and W Pfeiler, Short-range ordering in AgZn alloys for various states of defect... 

M. Migschitz, F. Langmayr and W Pfeiler, Atomic short-range ordering in Au-Fe alloys a resistometric... 

M. MigscUtz and W Pfeiler, Short-range order kinetics in a-AuFe after deformation and recrystallization,... 

R. Clad, R. Kuentzler and W. Pfeiler, Atomic short-range order and spin-glass behaviour in concentrated... 

M. Migschitz, W GarUpp and W. Pfeiler, Short-range order Kinetics in a-AgZn for various states of post-... 

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