Some General Crystallization Concepts

The following concepts should be kept in mind when evaluating 

Crystal growth rates are higher at higher temperatures. 

Additives or the level of impurities are only effective within a narrow range. Crystal habit can be poorer at too high a level of impurities and the habit may not be affected at all at too low a level of impurities. 

The incorrect amount or type of impurities can cause cycling of the crystal size. 

Crystals grown contain occlusions. These occlusions can result in a lower product purity and crystals that can be more easily broken. Crystals grown with the right level of impurities present in solution can be less prone to breakage and can be purer. 

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Flexoelectricity - what is it How does it arise in liquid crystals What are its consequences What role does it play in liquid crystal phases, structures, and textures How is it measiu-ed What is its role, both realized and potential, in applications of liquid crystals How was it discovered and what is its history in the context of the development of liquid crystal science and technology in the last 50 years The name flexoelectricity clearly indicates the dual role of curvature distortions and electrical effects in liquid crystals, but just how are these two fundamental sets of concepts related by this phenomenon This book attempts to lay out the answers to these questions, with a combination of broad reviews and focused insights into the role of flexoelectricity in the science and technology of liquid crystals. In this introduction there is first a little informal review of history along with some general comments on the fundamentals and the special challenges presented by this phenomenon, and then there is a brief sketch of the chapters of this book. 

Comparing with conventional systems, such as elemental metals and polyatomic superconductors, the compounds based on tetrachalcogenafiilvalenes and metal 1,2-chalcogenolenes present some advantages in particular they can be easily prepared in a pure single crystal form, stable in air. They constitute therefore a completely different family of compounds with reduced dimensionality, on which the physical theories associated with the cooperative magnetism of the onset or a superconductivity state, can be tested to generalize the concepts involved. 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

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