Dendrite growth

Crystallization conditions such as temperature, solvent, and concentration can influence crystal form. One such modification is the truncation of the points at either end of the long diagonal of the diamond-shaped crystals seen in Fig. 4.11b. Twinning and dendritic growth are other examples of such changes of habit. 

Conformal coatings are protective coatings appHed to circuit board assembHes. They protect the interconnect conductors, solder joints, components, and the board itself they reduce permeabiHty to moisture, hostile chemical vapors, and solvents in the coating. Use of conformal coatings eliminates dendritic growth between conductors, conductor bridging from moisture condensation, and reduction in insulation resistance by water absorption. 

Test of Dendritic Growth Models. The microgravity environment provides an excellent opportunity to carry out critical tests of... 

The phase-field model and generalizations are now widely used for simulations of dendritic growth and solidification [71-76] and even hydro-dynamic flow with moving interfaces [78,79]. One can even use the phase-field model to treat the growth of faceting crystals [77]. More details will be given later. 

In our treatment of directional solidification above, only one diffusion field was treated explicitly, namely the compositional diffusion. If a simple material grows dendritically (thermal diffusion) one may worry about small amounts of impurities. This was reconsidered [132], confirming a qualitative previous result [133] that impurities may increase the dendritic growth rate. Recently some direct simulation results have been obtained with two coupled diffusion fields, one for heat and one for matter, but due to long computing times they are not yet in the state of standard applications [120,134]. 

E. Brener, T. Ihle, H. Muller-Krumbhaar, Y. Saito, K. Shiraishi. Fluctuation effects on dendritic growth morphology. Physica A 200 96, 1994. 

A. Karma, W.-J. Rappel. Phase field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys Rev E 55 R3017, 1996 A. Karma, W.-J. Rappel. Quantitative phase field modeling of dendritic growth in two and three dimensions. Phys Rev E 57 4111, 1998. 

G. Goldbeck-Wood, Y. Saito, H. Miiller-Krumbhaar. Numerical simulation of dendritic growth. Phys Rev A 5S 2148, 1988. 

L. M. Martyushev, V. D. Seleznev, S. A. Skopinov. Reentrant kinetic phase transitions during dendritic growth of crystals in a two-dimensional medium with phase stratification. Tech Phys Lett 25 495, 1997. 

R. Ananth, W. N. Gill. Dendritic growth in microgravity and forced convection. J Cryst Growth 779 263, 1997. 

The dendritic growth of lithium was suppressed on a lithium electrode surface modified by an ultrathin solid polymer electrolyte prepared from 1,1—difluoro-ethane by plasma polymerization [114]. 

Another complication had to be matched when the zinc electrode was made reversible in a battery with unstirred electrolyte or an electrolyte gel, dendritic growth of the electrolytically deposited metal takes place. The formation of dendrites cannot be fully suppressed by the use of current collectors with large surface areas (grids, wire fabrics). However, by using improved separators combined in multi layer arrangements, the danger of short-circuiting is reduced. 

Occasionally the zinc electrode is wrapped in a polypropylene fleece filled with inorganic substances, such as potassium titanate, in order to reduce the solubility of zinc since the problem of dendrite growth is aggravated even by the metallization of the cellophane separator due to the aforesaid silver reduction and its promoting the generation of shorts. 

Aqueous electrolytes proposed in the literature for cathodic electrodeposition of lead selenide are generally composed of dissolved selenous anhydride and a lead salt, such as nitrate or acetate. Polycrystalline PbSe films have been prepared by conventional electrosynthesis from ordinary acidic solutions of this kind on polycrystalline Pt, Au, Ti, and Sn02/glass electrodes. The main problem with these applications was the PbSe dendritic growth. Better controlled deposition has been achieved by using EDTA in order to prevent PbSeOs precipitation, and also acetic acid to prevent lead salt hydrolysis. 

Bmne H, Roder H, Bromann K, Kem K, Jacobsen J, Stoltze P, Jacobsen K, Nprskov JK. 1996. Anisotropic comer diffusion as origin for dendritic growth on hexagonal substrates. Surf Sci 349 LI 15. 

Fig. 5.52 Pb02 dendrite growth at a lead electrode. Current density 0.3 mA cm-2. (From G. Wranglen, Electrochim. Acta, 2, 130, 1960)... 

A potential source of structural imperfection is the rapid increase of reactive groups as growth is pursued. Their incomplete conversion leads to defects inside the molecule [27]. In convergent-iterative syntheses these problems are avoided by directing the dendritic growth from the surface inwards to a focal point. In a final step several dendrons are connected with a multifunctional core to yield the desired dendrimer (Fig. 9). 

Further, dendritic growths with new multiarmed clusters having more flexibility and various geometries have also been considered by the authors. Thus, the hexato-sylated dipentaerythritol 39 was converted into hexaazide 40, which upon treatment with propargylated mannoside 29 under standard conditions of click chemistry and subsequent O-deacetylation afforded the hexavalent cluster 42 in good (61%) yield over two steps (Scheme 6). 

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