Order-disorder transitions phenomena

At low temperatures, rj will be unity because all of the Cu atoms will be localized on A sites. 1 But the degree of disorder increases as the temperature increases until the Cu and Zn atoms are mixed randomly on the two sublattices and 77 = 0. This process, called a positional (order + disorder) transition, is often described as a cooperative phenomenon because it becomes easier to produce additional disorder once some disorder is generated. In the vicinity of a critical temperature, the order parameter rj behaves like the density difference (pi — pg) near the gas-liquid critical point. Thus,... 

Heteropolymers can self-assemble into highly ordered patterns of microstructures, both in solution and in bulk. This subject has been reviewed extensively [1,123-127]. The driving force for structure formation in such systems is competing interactions, i.e., the attraction between one of the monomer species and the repulsion between the others, on the one hand, and covalent bonding of units within the same macromolecule, on the other hand. The latter factor prevents the separation of the system into homogeneous macroscopic phases, which can, under specific conditions, stabilize some types of microdomain structures. Usually, such a phenomenon is treated as microphase separation transition, MIST, or order-disorder transition, ODT. 

A well-explored example of this phenomenon in the crystalline state is naphthazarin C, where single crystal neutron diffraction studies indicate an order-disorder transition at 100 K. At 60 K, the hydroxyl groups are ordered, whereas at 300 K, the analysis shows a disordered 0-( )H- -( )H-O hydrogen-bond structure [395]. 

Order-disorder, or rod-to-coil , transitions in dilute solution have been reported for polydiacetylenes (2, 5-11), polysilylenes (12-15), and alkyl-substituted polythiophenes (16). The interpretation of the experimental observations has been the subject of considerable controversy with respect to whether the observations represent a single-polymer-molecule phenomenon or a many-chain aggregation or precipitation process (3-16). Our own experimental evidence (12, 13) and that of others (5-8, 10, 16) weigh heavily in favor of the single-chain interpretation. In our theoretical interpretation, we will assume that the order-disorder transitions observed in dilute pol-ysilylene solutions represent equilibrium, single-chain phenomena. 

Tlie coupling between the displacements and the amplitude of the density wave manifests itself in a long-wavelength instability in ordered phases with soft directions (such as LAM and HEX) upon a temperature quench (Qi and Wang, 1999). This phenomenon is most easily illustrated using the example of the LAM phase in the weak segregation limit. At a temperature To below the order-disorder transition temperature, the density wave can be represented as a simple sinusoidal wave ... 

X-ray diffraction analysis reveals two different vacancy distributions without the detection of a two-phase domain in every system. For low values of y S 0.25, the symmetry of the perovskite remains which indicates that the vacancies are apparently disordered. At higher values of y = 0.25 X-ray patterns give evidence of a distortion. For y = 0.25, they can be indexed with the theoretical parameters (orthorhombic symmetry) deduced from the vacancy ordering previously described. As a consequence, an order-disorder transition takes place around y 0.25. This phenomenon is illustrated in Fig. 4, which shows a discontinuity of the unit cell volume Vm around this value for each system. 

Order-disorder transition in the arrangement of defects is an interesting phenomenon in high temperature solid chemistry, but little work has been done in this domain except on the transitions of U409 and UjOg-, which will be described in the ensuing sections. Need is felt for further studies on transitions due to order-disorder arrangement of defects. 

We know that another interesting phenomenon occurs when the temperature increases up to the bulk transition Tj. Previous studies have shown that the APB is wetted by the disordered phase a large layer of disordered phase develops in between the two ordered domains. In other words, the APB is splitted into two order-disorder interfaces, whose separation diverges as In(T), - T). We display in Fig. 5 the 2-dlmensional maps for T=1687 K, i.e. very close to the first-order transition. As expected, we see that the APB separates into two order-disorder interfaces. Moreover, the width of the penetrating disordered layer varies along the APB. This means that each order-disorder interface develops its own transverse fluctuations and that the APB begins to behave as two separate objects. 

Pressure-induced amorphization of solids has received considerable attention recently in physical and material sciences, although the first reports of the phenomenon appeared in 1963 in the geophysical literature (actually amorphization on reducing the pressure [18]). During isothermal or near isothermal compression, some solids, instead of undergoing an equilibrium transition to a more stable high-pressure polymorph, become amorphous. This is known as pressure-induced amorphization. In some systems the transition is sharp and mimics a first-order phase transition, and a discontinuous drop in the volume of the substance is observed. Occasionally it is strictly not an amorphous phase that is formed, but rather a highly disordered denser nano-crystalline solid. Here we are concerned with the situation where a true amorphous solid is formed. 

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