Three-dimensional growth

Calandra et al. [44] adapted Muller s model to potentiodynamic conditions. Mac Donald [45] corrected a typographical error found in the mathematical expressions in the article. Devilliers et al. [46] developed a general model for the formation of low-conductivity films, considering a process controlled by the solution resistance in the pores of the film. The authors simulated the potentiodynamic curves for the following particular cases constant film thickness (bidimensional growth), three-dimensional growth, and a decomposition/dissolution process coupled to the electrochemical reaction. The potentiodynamic curves simulated for constant thickness are identical to those obtained by Calandra et al. [44]. 

Since faults are zones of inherent weakness they may be reactivated over geologic time. Usually, faulting occurs well after the sediments have been deposited. An exception to this is a growth feu/f (also termed a syn-sedimentary fault), shown in Figure 5.7. They are extensional structures and can frequently be observed on seismic sections through deltaic sequences. The fault plane is curved and in a three dimensional view has the shape of a spoon. This type of plane is called listric. Growth faults can be visualised as submarine landslides caused by rapid deposition of large quantities of water-saturated... 

Growth in the radial direction is assumed to occur at a constant velocity. There is ample experimental justification for this in the case of three-dimensional spherical growth. 

Those exponents which we have discussed expUcitly are identified by equation number in Table 4.3. Other tabulated results are readily rationalized from these. For example, according to Eq. (4.24) for disk (two-dimensional) growth on contact from simultaneous nucleations, the Avrami exponent is 2. If the dimensionality of the growth is increased to spherical (three dimensional), the exponent becomes 3. If, on top of this, the mechanism is controlled by diffusion, the... 

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

The important feature is that a three-dimensional gel network comes from the condensation of partially hydroly2ed species. Thus, the microstmcture of a gel is governed by the rate of particle (cluster) growth and their extent of crosslinking or, more specifically, by the relative rates of hydrolysis and condensation (3). 

Production of net-shape siUca (qv) components serves as an example of sol—gel processing methods. A siUca gel may be formed by network growth from an array of discrete coUoidal particles (method 1) or by formation of an intercoimected three-dimensional network by the simultaneous hydrolysis and polycondensation of a chemical precursor (methods 2 and 3). When the pore Hquid is removed as a gas phase from the intercoimected soHd gel network under supercritical conditions (critical-point drying, method 2), the soHd network does not coUapse and a low density aerogel is produced. Aerogels can have pore volumes as large as 98% and densities as low as 80 kg/m (12,19). 

In most carbon and graphite processes, the initial polymerization reactions occur in the Hquid state. The subsequent stages of crystal growth, heteroatom elimination, and molecular ordering occur in the soHd phase. The result is the development of a three-dimensional graphite stmcture. 

Directed Oxidation of a Molten Metal. Directed oxidation of a molten metal or the Lanxide process (45,68,91) involves the reaction of a molten metal with a gaseous oxidant, eg, A1 with O2 in air, to form a porous three-dimensional oxide that grows outward from the metal/ceramic surface. The process proceeds via capillary action as the molten metal wicks into open pore channels in the oxide scale growth. Reinforced ceramic matrix composites can be formed by positioning inert filler materials, eg, fibers, whiskers, and/or particulates, in the path of the oxide scale growth. The resultant composite is comprised of both interconnected metal and ceramic. Typically 5—30 vol % metal remains after processing. The composite product maintains many of the desirable properties of a ceramic however, the presence of the metal serves to increase the fracture toughness of the composite. 

Laminar flame instabilities are dominated by diffusional effects that can only be of importance in flows with a low turbulence intensity, where molecular transport is of the same order of magnitude as turbulent transport (28). Flame instabilities do not appear to be capable of generating turbulence. They result in the growth of certain disturbances, leading to orderly three-dimensional stmctures which, though complex, are steady (1,2,8,9). 

A continuous lipidic cubic phase is obtained by mixing a long-chain lipid such as monoolein with a small amount of water. The result is a highly viscous state where the lipids are packed in curved continuous bilayers extending in three dimensions and which are interpenetrated by communicating aqueous channels. Crystallization of incorporated proteins starts inside the lipid phase and growth is achieved by lateral diffusion of the protein molecules to the nucleation sites. This system has recently been used to obtain three-dimensional crystals 20 x 20 x 8 pm in size of the membrane protein bacteriorhodopsin, which diffracted to 2 A resolution using a microfocus beam at the European Synchrotron Radiation Facility. 

Monitoring surface structures, especially during thin-film epitaxial growth can distinguish two- and three-dimensional defects... 

Figure 10.5. The three modes of growth of films (a) Frank and van der Merwe s monolayer (two-dimensional) mode (b) the Volmer-Weber three-dimensional mode (c) the Stranski-Krastanov mode involving two-dimensional growth followed by three-dimensional growth.

G. Dziuk. A boundary element method for curvature flow. Application to crystal growth. In J. E. Taylor, ed. Computational Crystal Growers Workshop, AMS Selected Lectures in Mathematics. Providence, Rhode Island American Mathematical Society, 1992, p. 34 A. Schmidt. Computation of three dimensional dendrites with finite elements. J Comput Phys 125 293, 1996. 

R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physica D (55 410, 1993 R. Kobayashi. A numerical approach to three-dimensional dendritic solidification. Exp Math 5 59, 1994. 

A. Em, V. Giovangigli, M. D. Smooke. Detailed modeling of three-dimensional chemical vapor deposition. J Cryst Growth 180 610, 1997. 

J. Holuigue, O. Bertrand, E. Arquis. Solutal convection in crystal growth effect of interface curvature on flow structuration in a three-dimensional cylindrical configuration. J Cryst Growth 180 591, 1997. 

M. C. Liang, C. W. Fan. Three-dimensional thermocapillary and buoyancy convections and interface shape in horizontal Bridgman crystal growth. J Cryst Growth 180 5% , 1997. 

The two isozymes are both homodimers, composed of approximately 600 amino acids and possess approximately 60% homology. The three-dimensional structures of COX-1 and COX-2 are very similar. Each one consists of three independent units an epidermal growth factor-like domain, a membrane-binding section and an enzymic domain. The catalytic sites and the residues immediately adjacent are identical but for two small but crucial variations that result in an increase in the volume of the COX-2-active site, enabling it to accept inhibitor-molecules larger than those that could be accommodated in the COX-1 molecule. 

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