Crystal phenomenological

M. Catti, Chapter 10, Physical properties of crystals phenomenology and modelling, in C. Giacovazzo, H. L. Monaco, G. Artioli, D. Viterbo, G. Ferraris, G. Gilli, G. Zanotti and M. Catti, Fundamentals of Crystallography, 2nd edition, Oxford University Press, Oxford, (2002). 

The chapters of this book expand on the ideas mentioned here, as well as others that have arisen from the efforts of many talented scientists studying this rather unusual phenomenon over the past 40 years. To get the most out of this book, the reader should be familiar with the basics of liquid crystal phenomenology, including molecular structure, phases, textures, and typical sample geometries, as well as theoretical concepts, including curvature elasticity theory and some elements of the fluid dynamics of liquid crystals. 

Sipe J E, Moss D J and van Driel H M 1987 Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals Phys. Rev. B 35 1129-41... 

By 1969, when a major survey (Thompson 1969) was published, the behaviour of point defeets and also of dislocations in crystals subject to collisions with neutrons and to the eonsequential collision cascades had become a major field of researeh. Another decade later, the subjeet had developed a good deal further and a highly quantitative body of theory, as well as of phenomenological knowledge, had been assembled. Gittus (1978) published an all-embracing text that eovered a number of new topics chapter headings include Bubbles , Voids and Irradi-ation(-enhanced) Creep . 

In order to anticipate problems and to interpret observations under the extreme conditions of shock compression, it is necessary to consider structural and electronic characteristics of PVDF. Although the phenomenological piezoelectric properties of PVDF are similar to those of the piezoelectric crystals, the structure of the materials is far more complex due to its ferroelectric nature and a heterogeneous mixture of crystalline and amorphous phases which are strongly dependent on mechanical and electrical history. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

In the next section we shall give a brief account of the crystal structure of the hydroquinone clathrates and of the gas hydrates, as far as is needed for a proper understanding of the subsequent parts. The reader who is interested in the phenomenology of other clathrate compounds should consult one of the many review articles7,8 39 on inclusion compounds. 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

An essential requirement for device applications is that the orientation of the molecules at the cell boundaries be controllable. At present there are many techniques used to control liquid crystal alignment which involve either chemical or mechanical means. However the relative importance of these two is uncertain and the molecular origin of liquid crystal anchoring remains unclear. Phenomenological models invoke a surface anchoring energy which depends on the so-called surface director , fij. In the case where there exists cylindrical symmetry about a preferred direction, hp the potential is usually expressed in the form of Rapini and Popoular [48]... 

Mars, W.V. and Fatemi, A., A phenomenological model for the effect of R ratio on fatigue of strain crystallizing rubbers. Rubber Chem. Tech., 76, 1241, 2003. 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

The dependence of the proton resonance integral J for the unexcited vibrational states on the vibrations of the crystal lattice was taken into account recently in Ref. 47 for proton transfer reactions in solids. The dependence of J on the nuclear coordinates was chosen phenomenologically as an exponential Gaussian function. 

Ab Initio Versus Phenomenological Crystal Field Theory for Lanthanides... 

Pettifor s structure maps additional remarks. We have seen that in a phenomenological approach to the systematics of the crystal structures (and of other phase properties) several types of coordinates, derived from physical atomic properties, have been used for the preparation of (two-, three-dimensional) stability maps. Differences, sums, ratios of properties such as electronegativities, atomic radii and valence-electron numbers have been used. These variables, however, as stressed, for instance, by Villars et al. (1989) do not always clearly differentiate between chemically different atoms. 

Nowadays attention is turned also to the supermolecular level, that is, to the morphologic aspects, to the nature of interfaces, to the formation of new phases, or of particular aggregates (liquid crystals, gels, etc.). Interest has also been directed to the study of chain mobility for its influence on frictional properties of polymers. In recent years there have been many successful approaches to a microscopic theory (in contrast to a phenomenological approach) of the physi-comechanical behavior of macromolecular materials. 

A sublattice phase can be envisaged as being composed of interlocking sublattices (Fig. 5.3) on which the various components can mix. It is usually crystalline in nature but the model can also be extended to consider ionic liquids where mixing on particular ionic sublattices is considered. The model is phenomenological in nature and does not define any crystal structure within its general mathematical formulation. It is possible to define internal parameter relationships which reflect structure with respect to different crystal types, but such conditions must be externally formulated and imposed on the model. Equally special relationships apply if the model is to be used to simulate order-disorder transformations. 

Before addressing these fundamental questions, we present a brief review on phenomenology, classical thermodynamics, and kinetic models of polymer crystallization. Advances made recently (as of 2003) using molecular modeling are reviewed next. 

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