Phase order-disorder

Incommensurate phases, modulated phases, order-disorder phenomena... 

Ordered phases can form at low temperatures in solid solutions. These will become disordered as the temperature is increased because of the TAS term in the free energy where AS is higher entropy of the disordered phase. Order-disorder transitions are examples of second-order phase transitions that take place over a range of temperatures with no heat of transition. 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

In the examples given below, the physical effects are described of an order-disorder transformation which does not change the overall composition, the separation of an inter-metallic compound from a solid solution the range of which decreases as the temperature decreases, and die separation of an alloy into two phases by spinodal decomposition. 

Some materials undergo transitions from one crystal structure to another as a function of temperature and pressure. Sets of Raman spectra, collected at various temperatures or pressures through the transition often provide useftil information on the mechanism of the phase change first or second order, order/disorder, soft mode, etc. 

M. Schoen, D. J. Diestler, J. H. Cushman. Stratification-induced order-disorder phase transitions in molecular confined films. J Chem Phys 707 6865-6872, 1994. 

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. 

T. Hashimoto, T. Miyoshi and H. Ohtsuka, Investigation of the relaxation process in the Cu3Au-alloy order-disorder phase transition near the transition point, Phys. Rev. B 13.1119 (1976). 

Whereas only a few atomie jumps may be neeessary to enable ehanges in the equilibrium degree of SRO, without atomie movement over long distanees ehanges in LRO may not be suffieient to reaeh equilibrium. This ean lead to a eompetition between inerease of SRO in the matrix and formation of the new LR0-phase when lowering the temperature below an order/disorder phase boundary. In those cases, thermal and/or meehanieal pretreatment of the sample is of erueial importanee for what is observed in the sample. 

G. Foumet, Order-disorder phenomena in solid solutions, in. Phase Stability in Metals and Alloys", P S. 

Phase transition irreversible, 225 order - disorder, 224-228 reversible, 225, 229, Physicochemical properties of ammonium hydrofluoride, 39 deviations from ideal, 149 ideal system, 148 NbF5 and TaFs, 25 niobium containing melts, 150 tantalum containing melts, 151 M5Nb3OFlg, 234-235 Piezoelectric properties, 245-247 Plasma chemical decomposition equipment, 311... 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

For example, 0 describes the temperature dependence of composition near the upper critical solution temperature for binary (liquid + liquid) equilibrium, of the susceptibility in some magnetic phase transitions, and of the order parameter in (order + disorder) phase transitions. 

LeiblerL., Theory of microphase separation in block copolymers. Macromolecules, 13, 1602, 1980. Eoerster S., Khandpur A.K., Zhao J., Bates E.S., Hamley I.W., Ryan A.J., and Bras W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules, 21, 6922, 1994. 

Reactive compatibilization can also be accomplished by co-vulcanization at the interface of the component particles resulting in obliteration of phase boundary. For example, when cA-polybutadiene is blended with SBR (23.5% styrene), the two glass transition temperatures merge into one after vulcanization. Co-vulcanization may take place in two steps, namely generation of a block or graft copolymer during vulcanization at the phase interface and compatibilization of the components by thickening of the interface. However, this can only happen if the temperature of co-vulcanization is above the order-disorder transition and is between the upper and lower critical solution temperature (LCST) of the blend [20]. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

Recently, due to increased interest in membrane raft domains, extensive attention has been paid to the cholesterol-dependent liquid-ordered phase in the membrane (Subczynski and Kusumi 2003). The pulse EPR spin-labeling DOT method detected two coexisting phases in the DMPC/cholesterol membranes the liquid-ordered and the liquid-disordered domains above the phase-transition temperature (Subczynski et al. 2007b). However, using the same method for DMPC/lutein (zeaxanthin) membranes, only the liquid-ordered-like phase was detected above the phase-transition temperature (Widomska, Wisniewska, and Subczynski, unpublished data). No significant differences were found in the effects of lutein and zeaxanthin on the lateral organization of lipid bilayer membranes. We can conclude that lutein and zeaxanthin—macular xanthophylls that parallel cholesterol in its function as a regulator of both membrane fluidity and hydrophobicity—cannot parallel the ability of cholesterol to induce liquid-ordered-disordered phase separation. 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

The structural phase transitions and nature of the Br... N and Br... Br interactions in l-phenyl-2-methyl-4-nitro-5-bromoimidazole have been studied [76], The compound was found to undergo a reversible order-disorder transition over a wide... 

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