Growth real crystals

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. 

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... 

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. 

The structural and equilibrium forms of crystals are predicted assuming that the crystal is perfect and that the ambient phase is isotropic. Growth forms, however, describe real crystals containing lattice defects growing in a real ambient phase. We should therefore consider the following factors, which may affect the growth forms. 

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

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... 

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). 

The above considerations show that real crystal faces exhibit different growth patterns depending on degree of perfection and growth conditions. 

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 process of crystallization or precipitation involves the nucleation and growth of crystals (particles) from a supersaturated solution and is often followed by the agglomeration of crystals. Supersaturation is the driving force for precipitation, which is defined by the difference between the real solute concentration c and equilibrium solute concentration c P,T) at given pressure and temperature. The strict definition of supersaturation is linked to the difference of chemical potential Ap ... 

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... 

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