Growth isotherm

Numerical Analysis of Interfacial IMC Growth. Isothermal growth data were used to predict the IMC layer thickness ensuing a non-isothermal reflow (Ref22,58). The temperaturetime reflow profile was divided into a differential time interval At, during which the temperature was considered as constant. The... 

Fig. 16.18 Optical inhomogeneities of ruby crystals as a function of the growth isotherms (concave, flat, convex) and annealing temperature T. i, is the optical resolution power.

To confirm that the matrix is amorphous following primary solidification, isothermal dsc experiments can be performed. The character of the isothermal transformation kinetics makes it possible to distinguish a microcrystalline stmcture from an amorphous stmcture assuming that the rate of heat released, dH/dt in an exothermic transformation is proportional to the transformation rate, dxjdt where H is the enthalpy and x(t) is the transformed volume fraction at time t. If microcrystals do exist in a grain growth process, the isothermal calorimetric signal dUldt s proportional to, where ris... 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

This approach is an alternative to quantitative metallography and in the hands of a master gives even more accurate results than the rival method. A more recent development (Chen and Spaepen 1991) is the analysis of the isothermal curve when a material which may be properly amorphous or else nanocrystalline (e.g., a bismuth film vapour-deposited at low temperature) is annealed. The form of the isotherm allows one to distinguish nucleation and growth of a crystalline phase, from the growth of a preexisting nanocrystalline structure. 

K. Ohno, H. Trinkaus, H. Muller-Krumbhaar. Simulation of non-isothermal nucleation. J Cryst Growth 99 68, 1990. 

It is usually assumed in the derivation of isothermal rate equations based on geometric reaction models, that interface advance proceeds at constant rate (Chap. 3 Sects. 2 and 3). Much of the early experimental support for this important and widely accepted premise derives from measurements for dehydration reactions in which easily recognizable, large and well-defined nuclei permitted accurate measurement. This simple representation of constant rate of interface advance is, however, not universally applicable and may require modifications for use in the formulation of rate equations for quantitative kinetic analyses. Such modifications include due allowance for the following factors, (i) The rate of initial growth of small nuclei is often less than that ultimately achieved, (ii) Rates of interface advance may vary with crystallographic direction and reactant surface, (iii) The impedance to water vapour escape offered by... 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

Isothermal a—time curves for the decomposition of U02(CH3C02)2 in air (513—573 K) [1018] showed two approximately linear regions, 0.0 < a < 0.2 and 0.2 < a < 0.9, for which the values of E were 107 and 165 kJ mole-1, respectively. In nitrogen, the earlier portion of the curve was not linear and E = 151 kJ mole-1 for the later interval. The zero-order kinetic behaviour was explained by growth of nuclei in thin, plate-like crystals, which were shown by microscopic and surface area measurements to fragment when a > 0.85. The proposed initial step in the decomposition was fission of bonds between the U02+ and the (OCO CH3) species [1018]. 

The predominant gaseous products of the decomposition [1108] of copper maleate at 443—613 K and copper fumarate at 443—653 K were C02 and ethylene. The very rapid temperature rise resulting from laser heating [1108] is thought to result in simultaneous decarboxylation to form acetylene via the intermediate —CH=CH—. Preliminary isothermal measurements [487] for both these solid reactants (and including also copper malonate) found the occurrence of an initial acceleratory process, ascribed to a nucleation and growth reaction. Thereafter, there was a discontinuous diminution in rate (a 0.4), ascribed to the deposition of carbon at the active surfaces of growing copper nuclei. Bassi and Kalsi [1282] report that the isothermal decomposition of copper(II) adipate at 483—503 K obeyed the Prout—Tompkins equation [eqn. (9)] with E = 191 kJ mole-1. Studies of the isothermal decompositions of the copper(II) salts of benzoic, salicylic and malonic acids are also cited in this article. 

Figure 4. Effect of Inlet flow rates on Isotherms, flow streamlines and relative deposition rates of GaAs (a) 70 cc/sec (standard conditions) (b) 140 cc/sec (c) 210 cc/sec. The absolute growth rates scale as 1 (a) 2.6 (b) 3.1 (c).

At different types of adsorption isotherms plotted for adsorption of donor particles on oxides (see section 1.5) expressions (1.112) - (1.115) provide the rise in and decrease in with the growth of partial pressure of gas P, the functions themselves being different. Thus, in case of applicability of the Henry isotherm at small P we have the function oi - exp const-P becoming a power function <7s P with the rise in P which is often observed in experiments [154, 155, 169]. 

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