Linear growth rate, of crystals

Adapted from Reference 22. n, index of Avrami s equation z, rate constant in Avrami s equation C, linear growth rate of crystal sperulite I, sporadic nucleation rate in time d, width of crystal fibril r, crystal radii. 

Figure 1. Nucleation rate and growth rate initially increase with supercooling, then decrease as atomic mobility is reduced by the increasing viscosity of the glass. Typical linear growth rates of crystals are 1-20 pm/min.

The linear growth rates of crystal faces vary enormously. Some approximate examples of the average rate for crystallization from solution are... 

Theoretically, at the constant linear growth rate of crystals and at the constant nucleation rate, n must be equal to 4. The values of n > 4 obtained from the calculations are connected with the growth of the nucleation rate during the initial autocatalytic period of crystallization. 

FIGURE 5.20 Plot of dimensionless linear growth rate of crystallization versus dimensionless temperature. (Reprinted with permission of the publisher from Gandica and Magill, 1972.)... 

Figure 13 Top, plot of linear growth rates of polyfethylene adipate) spherulites as a function of crystallization temperature for indicated molecular weight fractions. Spherulites shown correspond to the indicated range of temperatures. (A) Crystallization at the lower temperature range (B) at intermediate temperatures (C) crystallization at high temperatures. Reproduced with permission from Ref. [216]. Copyright 1956,...

Methods used for the measurement of crystal growth rates are either a) direct measurement of the linear growth rate of a chosen crystal face or b) indirect estimation of an overall linear growth rate from mass deposition rates measured on individual crystals or on groups of freely suspended crystals 35,41,47,48). 

Here the so called ideal growth rate of the crystal layer is a calculated one. It is calculated from the linear dependence between the cooling rate of the surface and the resulting growth rate. The measured growth rate of crystal layer v includes all pos-... 

The growth rates of crystals depend on their instantaneous surface and the linear velocity of solution past the surface as well as the extent of supersaturation, and are thus represented by the... 

Figure 16.5. Supersaturation behavior, (a) Schematic plot of the Gibbs energy of a solid solute and solvent mixture at a fixed temperature. The true equilibrium compositions are given by points b and e, the limits of metastability by the inflection points c and d. For a salt-water system, point d virtually coincides with the 100% salt point e, with water contents of the order of 10-6 mol fraction with common salts, (b) Effects of supersaturation and temperature on the linear growth rate of sucrose crystals [data of Smythe (1967) analyzed by Ohara and Reid, 1973],...

Vc = volume of holdup in the tank n = number of crystals per unit volume L = length of the crystal G = linear growth rate of the crystal t = time... 

Adamski and Klimczyk analyzed cholesteryl pelargonate36) and caproate 37) liquid crystal to fully-ordered-crystal transitions over a temperature range of about 25 K. Again, the appearance of the fully ordered crystals was that of a spherulitic superstructure. The nucleation was time dependent, and the linear growth rate of the spherulites decreased with decreasing temperature by a factor 1/2 to 1/3, in contrast to the nonanoate and acetate. The Avrami exponent was close to 4 as judged from the measurement of the crystallized volume in the field of view under the microscope. 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data that infer a direct relationship between contact nucleation and crystal growth these data showed that the number of nuclei produced by an impact was proportional to the linear growth rate of the impacted face. This could indicate that the effect of supersaturation is to alter growth rates and, concomitantly, the characteristics of the impacted crystal faces alternatively, what appears to be a mechanistic relationship actually could be a result of both nucleation and growth depending upon supersaturation. 

Na = rtf ia the number of particles-II (formed by the growth of the particles of quasicrystalline phase released from the gel during the crystallization process), both contained in a unit mass of zeolite formed at the end of the crystallization process, Kg is the constant of the linear growth rate of zeolite particles and 0 = 6/(q+1)(q+2) (q+3). The numerical values of the constants K0 = G N0Kg and Ka = G BNaK, calculated by the procedure described earlier (25), as well as the ratios Na/ N0 = Ka/0 K0, are listed in Table IV. as functions of time ta of the gel ageing. 

M the mass of one mole of the crystal, p the density of the crystal, and c the concentration of the solute. Equation (31) assumes that the change in concentration of the solution can be solely attributed to the growth of a single characterised solid. The mean linear growth rate of the suspension, R, may then be defined as... 

The incorporation of a TAG molecule into a crystal lattice requires a very large loss in conformational entropy, and thus, a long time is needed for the TAG molecule to ht into the crystalline lattice. In addition, the TAG molecule may be detached before the crystallme lattice before it is fully incorporated into the crystalline lattice. For example, for growth of tristearin (SSS) in triolein (OOO), linear growth rates of the order of 10 to 10 m/s have been observed (41). 

Linear growth rate of a face which is the rate of displacement of a crystal face in a direction perpendicular to the face. 

The linear growth rate of a face can be expressed in terms of the step velocity, step height, and step spacing. Techniques used for in situ measurement of crystal growth rates as a function of supersaturation include the following ... 

If the volume, V, of a solution changes at a rate dV/dt because of solvent evaporation, the linear growth rate of a crystal of area A is ... 

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