Growth of a crystal

One-dimensional diffusive growth of a crystal of fixed composition For constant... 

Figure 11.5(b) shows that the later-formed calcite crystal has a different Habitus from the earlier-formed prismatic crystal around which it grows, and Fig. 11.5(c) is an example of the growth of a crystal with dog-tooth Habitus on an earlier-formed crystal with rhombohedral Habitus. (See also Fig. 7.10.) By compiling these relations, it is possible to trace systematically how the Habitus of calcite changes from earlier to later stages or as the temperature decreases in the case of contact metasomatism [2], [3]. The Habitus variation with decreasing temperature summarized above is a general trend based on data of this type.

Fig. 7.163. The growth of a crystal, illustrating how a fast-growing face grows out of existence, while the slow-growing crystal faces remain.

When the conditions of growth of a crystal are unknown the evidence of its shape should be regarded with reserve. There are, indeed, cases in which the shape of a crystal is inconsistent with clear X-ray evidence on atomic structure- for instance, cuprite Cu20 (Greenwood, 1924 Bragg, 1937 Miers, 1929). Possibly this is due to the presence of impurities during growdh (see p. 54). 

For growth of a crystal with shape R(z, t) evolving in time, the wetting-angle condition is written in dimensionless form as... 

Really, conducted in present work X-ray diffraction study of HxGaSe crystals at T - 300K shown that parameter Co growth with x and at x = 1.0 increased by 0.031+0.003 A from C0 = 15.94A to Co = 15.971A. It is in 2.5 times greater that one can estimate from our simple pressure extrapolation. At the same time one can observe an unsignificant growth of a crystal lattice parameter a, with x. Thus for... 

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. 

The growth of an ordered colloidal structure is similar to that of the growth of a crystal. In this case, the rate at which particles arrive at... 

If L is a characteristic dimension of a crystal of selected material and shape, the rate of growth of a crystal face that is perpendicular to L is, by definition,... 

As early as 1878, Gibbs concluded that the breakdown or growth of a crystal was not a continuous transformation, as the gas-liquid transition was considered to be. Thomson derived what has come to be known as the Gibbs-Thomson equation, relating the vapor pressure of liquid droplets to the size of the droplets. Ostwald extended the concept to the problem of solubility, but made a numerical error later corrected by Freundlich. Similar to the Gibbs-Thomson equation, the Ostwald-Freundlich equation was expressed by... 

The growth of a crystal in solution probably proceeds similarly to the growth in vapour but growth from supercooled melts needs further study. In all instances a very high supersaturation (1.5 times) is normally needed to initiate growth. 

The conditions for stable growth of a crystal are closely associated with segregation of dopants or impurities. Crystal growth theory includes an expression for the effective segregation coefficient K, for a crystal growing from a medium in which the dopant distribution is characterized by a boundary layer of thickness 5 ... 

Supersaturation. The rate of growth of a crystal face will always increase with the difference in chemical potential A /< between crystal and solution or melt. For crystallization from solution we have... 

Epitaxial growth of a crystal on a substrate crystal is such that the growth follows the crystal axis of the substrate. 

FIGURE 9.28 (a) U nit-cell model of the equiaxed dendritic growth of a crystal. The liquid within the grain envelope and within the element are shown as well as the mass fraction distribution of the species A (b) the idealized phase diagram (c) the mass fraction distribution of the species A for two different elapsed times. (From Rappaz and Thevos, Ref. 152, reproduced by permission 1987 Pergamon.)... 

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