Kinetic-diffusion controlled growth

A dispersed-element model for kinetic-diffusion controlled growth. Assuming that a total number ns of spherical crystals are nucleated per unit volume at a supercooling of A Tsc =Tm-T(, then these crystals can grow to final grain radius of Rc... 

Kinetic expressions for appropriate models of nucleation and diffusion-controlled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to (Dt),/2]. (This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [77], who considers the possibilities that nucleation is (i) instantaneous (0 = 0), (ii) constant (0 = 1) and (iii) deceleratory (0 < 0 < 1), for nuclei which grow in one, two or three dimensions (X = 1, 2 or 3, respectively). All expressions found are of the general form... 

Nielsen, A. E. 1964. Diffusion controlled growth. Kinetics of Precipitation. Pergamon Press, Oxford, UK. p. 34. 

Many high-pressure reactions consist of a diffusion-controlled growth where also the nucleation rate must be taken into account. Assuming a diffusion-controlled growth of the product phase from randomly distributed nuclei within reactant phase A, various mathematical models have been developed and the dependence of the nucleation rate / on time formulated. Usually a first-order kinetic law I =fNoe fi is assumed for the nucleation from an active site, where N t) = is the number of active sites at time t. Different shapes of the... 

Leubner, I. H. Crystal formation (nucleation) under kinetically controlled and diffusion-controlled growth conditions. J. Phys. Chem. 91,6069-6073 (1987). 

Another approach for determining the growth rate g is based on considerations of supersaturation, growth kinetics, and crystal number density. For diffusion-controlled growth systems, like AgBr, eq (9) was derived, which relates the growth raty to the supersaturation ratio, S, and crystal number density, p. 

Nielsen, A.E. (1961) Diffusion controlled growth of a moving sphere. The kinetics of crystal growth in potassium perchlorate precipitation. J. Phys. Chem., 65, 46-49. 

Nonequilibrium Treatment of Solidification. In the following, as examples of nonequilibrium treatments of solidification in a binary system, a kinetic-diffusion controlled dendritic crystal growth and a buoyancy-influenced dendritic crystal growth are examined. 

Phase formation kinetics based on surface diffusion-controlled growth processes have been suggested for 2D monolayers of camphor-lO-sulfonate on mercury [182], physisorbed uracil films on Au(hkl) [183], as well as the commensu-rate/incommensurate transition c( 2 x 2y2)R45 c(p X 2y2)R45° of bromide on Au(lOO) [51]. 

For diffusion-controlled growth kinetics it can be shown (Nielsen, 1964 Hanitzsch and Kahlweit, 1969) that the linear growth velocity approximates to... 

The diffusion-controlled growth morphology and kinetics of E. coli colonies under different experimental conditions have been studied by Das et al. [70]. Fractal dimension... 

In the review [2004Tak], two models of the overall kinetics of the bainite transformation, one of which is the diffusion controlled growth model of the bainitic laths and the other is the nucleation of bainite ferrite plates controlled model, have been discussed. It was shown that formation and competition of bainitic ferrite and cementite can be predicted quantitatively. 

Reaction of N2 with liquid Th spheres has been investigated. Five-mm diameter spheres of Th supported on a bed of ThN powder grow a dense protective scale of ThN when reacted with an N2 atmosphere [8]. For the kinetics of the diffusion-controlled growth of scale thickness, see p. 24. 

Since the Cu substrate/Sn-based solder interface is planar in nature, the growth of Cu-Sn interfacial IC layers in the solid state occurs in a planar manner. Tin and copper diffuse in opposite directions, and then react with each other. The growth kinetics of the interfacial IC layers is modeled in many studies by assuming a diffusion-controlled growth [32] ... 

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

Wagner (1961) examined theoretically the growdr kinetics of a Gaussian particle size distribution, considering two growth mechanisms. When the process is volume diffusion controlled... 

The account of the formal derivation of kinetic expressions for the reactions of solids given in Sect. 3 first discusses those types of behaviour which usually generate three-dimensional nuclei. Such product particles may often be directly observed. Quantitative measurements of rates of nucleation and growth may even be possible, thus providing valuable supplementary evidence for the analysis of kinetic data. Thereafter, attention is directed to expressions based on the existence of diffuse nuclei or involving diffusion control such nuclei are not susceptible to quantitative... 

An unusual variation in kinetics and mechanisms of decomposition with temperature of the compound dioxygencarbonyl chloro-bis(triphenyl-phosphine) iridium(I) has been reported by Ball [1287]. In the lowest temperature range, 379—397 K, a nucleation and growth process was described by the Avrami—Erofe ev equation [eqn. (6), n = 2]. Between 405 and 425 K, data fitted the contracting area expression [eqn. (7), n = 2], indicative of phase boundary control. At higher temperatures, 426— 443 K, diffusion control was indicated by obedience to eqn. (13). The... 

Curve 1 in Fig. 6.9 shows the influence of constant k, (or of parameters or which are proportional to it) on the current density at constant potential for a reaction with an intermediate value of k°. Under diffusion control (low values of/) the current density increases in proportion to/ . Later, its growth slows down, and at a certain disk speed kinetic control is attained where the current density no longer depends on disk speed. The figure also shows curves for the kinetic current density 4 and the diffusion current density /. 

Nielsen, A.E. (1959b) The kinetics of crystal growth in barium sulphate precipitation. 111. Mixed surface reaction and diffusion-controlled rate of growth. Acta Chem. Scand., 13, 1680-1686. 

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