Growth of Real Crystals

Frank [5.50] was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). 

During the growth of real crystals the strain relief must take place continuously, and some of the anelastic strain most probably remains in the epilayer rather than in the interface. Furthermore, the final state of strain is observed to depend on the growth temperature (Dodson and Tsao 1987, Tsui and Flyrm 1995, Tsui 1992) which indicates... 

Crystals are solid materials having regular arrangements of atoms, ions, or molecules. Crystal forms are determined not only by structure but also by the factors involved in growth. The same crystal species may therefore appear in various forms. In this chapter, the external forms of real crystals are systematically classified. 

Figure 7.6. Morphological variation expected in twins of real crystals. The symbols indicate dislocations. Only similar forms or unidirectional growth are expected.

If, at ambient temperature, the slow growth of a crystal is attempted, then, against a background of thermal agitation, the systematic assembly of a perfect crystal turns out to be impossible. Dislocations and interstitial atoms are unavoidable. The second law is obeyed, in that entropy growth is unavoidable. Hence fuel cell materials are real and imperfect, and will need careful optimisation. 

In contrast to the growth kinetics of real crystals where dislocations and defects play a dominant role (cf. Section 5.3), the growth mechanism of crystallographic faces free of defects and particularly free of screw dislocations is completely different. The... 

The impedance behavior of real crystal faces has been investigated by different authors [5.29, 5.84-5.93]. The results show that the impedance is characterized by various low frequency features (inductive loop and hysteresis) which are related to the non-steady state conditions of the electrochemical crystal growth process. 

The fifth part deals with growth mechanisms of single crystal faces. The growth by 2D nucleation of quasi-perfect faces as well as the spiral growth mechanism of real crystal faces are discussed. Experimental verification is presented for the case of silver electrocrystallization. 

The difference between the observed and theoretical growth rates has been reconciled by the Frank screw-dislocation theory. Actual space lattices of real crystals are far from perfect and crystals have imperfections called dislocations. Planes of particles on the surfaces and Mtliin the crystals are displaced, and several kinds of dislocations are known. One common dislocation is a screw dislocation (Fig- 27.9), where the individual particles are shown as cubical building blocks. The dislocation is in a shear plane perpendicular to the surface of the crystal, and the slipping of the crystal creates a ramp. The edge of the ramp acts like a portion of a two-dimensional nucleus and provides a kink into which particles can easily fit, A complete face never can form, and no nucleation is necessary, As growth... 

Experimental studies of crystallization indicate that in real systems there is no significant kinetic retardation present in the case when crystal growth takes place at low saturations. This is related to those defects that are present in the structure of real crystals, and in particular to the presence of a... 

Like different buildings constructed of identically shaped bricks, real crystals do not necessarily look like the crystal lattices or unit cells of which they are composed. The shape of real crystals is determined in large part by their relative rates of growth in different directions. For example, a fece-centered cubic structure may grow to form a cube, an octahedron, or a cube with its comers cut off. These forms are shown in Fig. 9.8. 

It is emphasized that the delta L law does not apply when similar crystals are given preferential treatment based on size. It fails also when surface defects or dislocations significantly alter the growth rate of a crystal face. Nevertheless, it is a reasonably accurate generahzation for a surprising number of industrial cases. When it is, it is important because it simphfies the mathematical treatment in modeling real crystallizers and is useful in predicting crystal-size distribution in many types of industrial crystallization equipment. 

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimensional systems. Secondly, two-dimensional dynamics make it an easy (sometimes trivial) task to compare the time behavior of such CA systems to that of real physical systems. Indeed, as we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

The growth of ECC under equilibrium conditions is too slow. Moreover, no macroscopic orientation appears and a structure of the type shown in Fig. 3 c is formed. Therefore this procedure cannot be used in practice. Usually, under real conditions, macroscopically oriented ECC are obtained from the melt stretched to the values of > /3cr at relatively low crystallization temperatures. Under these conditions, the formation of ECC proceeds by another mechanism. 

Real polymer processes involved in polymer crystallization are those at the crystal-melt or crystal-solution interfaces and inevitably 3D in nature. Before attacking our final target, the simulation of polymer crystallization from the melt, we studied crystallization of a single chain in a vacuum adsorption and folding at the growth front. The polymer molecule we considered was the same as described above a completely flexible chain composed of 500 or 1000 CH2 beads. We consider crystallization in a vacuum or in an extremely poor solvent condition. Here we took the detailed interaction between the chain molecule and the substrate atoms through Eqs. 8-10. 

U. Gasser, E. Weeks, A. Schofield, P.N. Pusey, and D.A. Weitz Real-Space Imaging of Nucleation and Growth in CoUoidal Crystallization. Science 292, 258 (2001). 

SOLUTION BEHAVIOR. Biomineralization is dominated by physical chemical considerations , and we begin with a discussion of real electrolyte solutions in which the concentration of a substance exceeds its thermodynamically defined solubility. In such a case, the presence of a coexisting crystal surface will lead to crystal growth. 

All real crystals deviate more or less from their equilibrium habits since all grow at finite velocities Rj. Hartman and Betmema (4) and Hartman (5.61 showed how the empirical law of Dotmay-Harker can be explained on the basis of current molecular theories of crystal growth. The energy required to split a crystal along the plane A--B parallel to the plane (hkl) is the sum... 

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