Successive phase transformation

From the texturological point of view, formation of crystallizing PMs is different because of the existence of nucleation stages at each phase transformation, usually more than one. As a result each nucleation gives a new maximum value of specific surface area, which can only decrease until the next transformation. A set of successive phase transformations including both wet and dry stages is characteristic for numerous PMs. Thus, each new phase transformation starts with the maximum possible surface area with its successive decrease directed by the necessity to decrease excess free energy. 

A12°3)i oo (p2°5)2.73 (H2° X x ranging from 42 to 3,600. The pH of the solution was in all experiments lower than 2.5. Under these conditions A1P04-H3 is metastable and appears in the following sequence of successive phase transformations ... 

Zeolites are thermodynamically metastable phases that can be transformed at longer synthesis times into more stable (and more dense) structures [93]. This phenomenon is known as the Ostwald rule of successive phase transformations. 

The transformation toughening mechanism has been most successfully exploited in materials where the phase transformation of interest is... 

Based on the reversibility of their phase transformation behavior, polymorphs can easily be classified as being either enantiotropic (interchange reversibly with temperature) or monotropic (irreversible phase transformation). Enantiotropic polymorphs are each characterized by phase stability over well-defined temperature ranges. In the monotropic system, one polymorph will be stable at all temperatures, and the other is only metastable. Ostwald formulated the rule of successive reactions, which states that the phase that will crystallize out of a melt will be the state that can be reached with the minimum loss of free... 

The introduction of Zr02 plays an important role in changing the thermal behaviour of the composite. However, whether the t —> m Zr02 phase transformation occurs or not is conditional on other factors, such as the particle size of Zr02, chemical composition and the local stress situation. Briefly, it is important to ensure that the t —> m transformation successfully occurs immediately below the softening temperature of the glass during... 

Paramount to the success of this approach is that efficient and reliable methods and multi-step sequences for the total synthesis of natural products and analogues thereof on polymeric supports are available. The corresponding transformations must proceed with a degree of selectivity and robustness typical of related classical solution phase transformations, irrespective of the stringencies and differing demands imposed by the anchoring to the polymeric support. 

In Chapters 6, 7, and 8, the thermodynamic framework is successively apphed to phase transformations of single-component systems, chemical reactions, and ideal solutions. Included are discussions of the thermodynamics of open systems, the phase rule, and colligative properties. Chapter 9 gives the framework for discussing nonideal multicomponent systems and describes a... 

While in volumes 180 and 181 of this series several basic aspects of morphology, inter-phase structure and disorder were addressed, in the present volume, molecular interactions, modeling, phase transformation and crystallization kinetics are considered (see the subject index including keywords from volumes 180 and 181 at the end of the book). Needless to say, in spite of substantial success over 60 years or more we are still far from having a complete and unambiguous picture of polymer crystallization. We firmly believe that a fruitful approach to such a complex problem requires one to give way to many different and sometimes conflicting viewpoints, as we have attempted to do in these volumes. We do hope that they are not only a time-capsule left for... 

Certain subvalent, fourth-group compounds undergo single or a series of first-order phase transformations at increasing temperatures from their expected distorted phases to give successively more symmetrical structures ... 

The Ostwald step rule is, evidently, a particular case of the general requirement (see Section 1.3.3) for a sequential decrease in chemical potentials of the transformation intermediates in the course of a stepwise transformation. In the transformation of the constant composition soHd phases, the said requirement refers to chemical potentials of the soHd phases. If the state diagram of a particular matter comprises several allowed phases (the ones differing, for example, by their crystal structures, etc.), the initial phase transformation into the thermodynamically stable state at a constant temperature will be successively mediated by aU of the phases along the reaction pathway from the initial point to the stable phase. 

The hyperbolic description implies that to a reasonable approximation, tetrahedral water, silicate, silicon and germanium frameworks are characterised by a preferred area per vertex group and a preferred Gaussian curvature. Thus, identical tessellations of isometric surfaces, with equal areas and curvatures at corresponding points on the surface, should offer alternative possibilities for stable frameworks. Indeed this is the case for the zeolite frameworks, faujasite and analcime, which are related to each other through the Bonnet transformation. Within an intrinsic two-dimensional description, these two frameworks are indistinguishable. We have seen in section 2.6 that the Bonnet transformation describes well a number of characteristics of the fee -> bcc martensitic phase transformation in metals and alloys. The success of this model suggests that the hyperbolic picture, intuitive and obvious for zeolites, is also valid for other atomic structures. 

As for krypton hydrate, Desgreniers et aU studied the pressure-induced phase transformations of krypton hydrate at room temperature by using X-ray diffraction measurements. They found that the initial cubic sll of krypton hydrate (KH-I) successively transformed to the cubic si (KH-II), the hexagonal structure (KH-III), and the sO (KH-IV) at 0.3 GPa, 0.6 GPa, and 1.8 GPa, respectively. They also found that the sO phase decomposed at pressures above 3.8 GPa. 

In recent high-pressure X-ray diffraction, neutron diffraction, and Raman studies on methane hydrate, pressure-induced phase transformations of methane hydrate show that the initial si (MH-sl) successively transforms to the sH (MH-II) at about 0.9 GPa and to the sO (MH-III) at about 2.0 GPa. 

Powder diffraction is very well suited for studies at non-ambient conditions. Naturally, one of the early applications of powder diffraction was high temperature studies of phase transformations. Development of equipment for low temperature and high-pressure studies quickly followed. Later, application of powder diffraction for in situ, time-resolved and in operando studies were successfully pursued. 

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