ISSN:
1573-4870
Keywords:
Fractals
;
solid state reaction
;
kinetics
;
nucleation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract In the present research we theoretically studied the kinetics of nucleation-limited solid state reactions as influenced by the fractal properties of solid reagent. We consider the model of equal-sized primary particles assembled in fractal cluster. The geometry of such an object is assumed to be described solely by its fractal dimension D and by upper (R max) and lower (R min) cutoffs of fractality further identified with the overall size of the object and the size of the primary particle correspondingly. Depending on the ratio between R max, R min and the radius of the critical nucleus R nucl the following cases are considered: (1) R max ∼ R nucl. In this case the reaction kinetics is described by the equation: α = 1 − B{ln(k′ τ + 1)}D/(D−3), where B, k′ are constants. Numerical solution of this equation gives rise to n-order reaction kinetics with n & 1. (2) R min ≪ R nucl ≪ R max. In this case under certain conditions there can exist non-trivial critical density ρcrit ≠ 0, 1 that favors the formation of the critical nuclei of the new phase. The asymptotic kinetic equation for large times corresponds to n-order reaction with n = (D + 3)/(D + 1). (3) R min ≪ R nucl ∼ R max′. In this case the reaction follows the first-order kinetics with D-dependent rate constant.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022643008915
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