scholarly journals QUASI-LONG RANGE ORDER IN GLASS STATES OF IMPURE LIQUID CRYSTALS, MAGNETS, AND SUPERCONDUCTORS

2001 ◽  
Vol 15 (22) ◽  
pp. 2945-2976 ◽  
Author(s):  
D. E. FELDMAN
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Disordered Systems ◽  
Critical Dimension ◽  
Range Order ◽  
Long Range Order ◽  
Weak Disorder ◽  
Random Anisotropy ◽  
Ordered Phases ◽  
Amorphous Magnets

We consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.

Liquid crystal phases of self-assembled amphiphilic aggregates

1993 ◽  
Vol 344 (1672) ◽  
pp. 357-375 ◽  
Keyword(s):  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Self Assembling ◽  
Ordered Phases ◽  
Aggregate Morphology ◽  
Aggregate Growth ◽  
Nematic Phases ◽  
High Concentrations ◽  
Concentrated Solution

Long-range order in solutions of reversibly self-assembling molecules results from interactions among the asymmetric aggregates. Even for electrically neutral species, repulsions between the aggregates become significant at high concentrations. At the very least, the excluded volume of asymmetric aggregates creates formidable packing constraints which are relieved by orientational and positional alignment. Aggregate growth thus promotes long-range order, and long-range order facilitates growth. Nematic phases occur if aggregate growth is strong enough to induce orientational ordering at concentrations lower than those that induce positional ordering. The symmetry of the positionally ordered phases reflects aggregate morphology: the polydispersity of aggregates that grow in one (two) dimension(s) to form rod-like (plate-like) particles suppresses the smectic (columnar) phase in favour of the columnar (smectic) phase. Because plate-like aggregates pack more easily than rod-like aggregates, increasing concentration induces a rearrangement from rod-like to plate-like aggregates, and a transition from columnar to smectic ordering, in solutions of molecules, such as surfactants, capable of forming both types of aggregates. In mixtures of aggregating and non-aggregating species, the difficulty of packing spherically shaped particles among elongated particles results in dramatic demixing such that a very concentrated solution of very large, highly aligned aggregates coexists with a relatively dilute solution depleted of the aggregating species.

scholarly journals Structural and Energy Characteristics of NiAl Alloys with Deviations from Stoichiometric Composition. Part 2

2020 ◽  
pp. 39-46
Author(s):  
A.I. Potekaev ◽  
A.A. Chaplyginа ◽  
M.D. Starostenkov ◽  
A.A. Klopotov ◽  
V.V. Kulagina
Keyword(s):  
Temperature Dependence ◽  
Long Range ◽  
Structural Phase ◽  
Stoichiometric Composition ◽  
Range Order ◽  
Long Range Order ◽  
Heating And Cooling ◽  
Ordered Phases ◽  
Range Parameter ◽  
The Difference

The analysis of the atomic and phase structure confirmed the difference between the structural-phase states at the heating and cooling stages. Based on the analysis of the influence of the deviation of the atomic composition from the stoichiometric condition of the intermetallic compound during cooling, it is established that the deviation is a significant factor in the area of low-stability pre-transitional structural-phase states before the transformation. The behavior of the long-range parameter temperature dependence curves during the cooling of alloys of non-stoichiometric compositions differs significantly from the behavior of the corresponding alloy curve of a stoichiometric composition alloy. It is shown that in the case of cooling of alloys of non-stoichiometric compositions, a significant supercooling is required to establish a long-range order, and the appearance of ordered phases occurs at significantly lower temperatures. It is found that the temperature dependence curve of the long-range parameter of the Ni45Al55 alloy is significantly lower than the corresponding curve of the Ni55Al45 alloy. This indicates different mechanisms for establishing the long-range order of alloys with non-stoichiometric compositions. It is noted that the deviation of the system composition from the stoichiometric one causes a significant reduction of ordered and disordered regions. This article is a continuation of the work published earlier in the journal Izvestiya AltGU. 2020. №1 (111).

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