The chemical kinetics of mechanical alloying
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I.
INTRODUCTION
W H I L E the applications of mechanical alloying have been widely extended since the process was first announced in 1970, Ir-6J and the microstructural evolution during milling has been well characterized, 1~,7-~~l studies of the fundamental mechanisms have only recently commenced.l~2 ~51 These have mainly been concerned with the mechanics of mechanical alloying, mathematical and empirical modeling to determine collision frequency, impact velocities, and collision energies, and the temperature rise associated with ball/powder collisions and the effect these parameters have on the rate at which alloying proceeds. However, mechanical alloying may simply be considered as a means to mechanically induce solid-state chemical reactions that occur across welded interfaces, formed when powder particles are impacted in a collision between the grinding media. The nature of these chemical reactions is, therefore, of equal importance as the mechanics in the development of our understanding of the mechanism of mechanical alloying. A defining characteristic of all solid-state reactions is that they involve the formation of product phases that physically displace the reactants. These products constitute a barrier layer opposing further reaction. The reaction interface, defined as the nominal boundary surface between the reactants, is continually diminished during the course of the reaction. Solid-state reaction rates are controlled by the initial reactant geometry and by the diffusion rates of the reactants through product barriers, t~6.~7.jst Such reactions necessarily require elevated temperatures to proceed at reasonable rates. Of particular concern in an understanding of the mechanism of mechanical alloying is, therefore, how solid/solid reactions occur during what is nominally a roomtemperature process. It has been suggested 1~gl that the efficacy of mechanical alloying is a consequence of the continual fracturing and welding of powder particles because this both increases and dynamically maintains the reaction interracial volume during milling, thereby minimizing the deleterious effects of product barriers. Chemical kinetics not only describe the rate of a
chemical reaction but may also be used to determine the mechanism, i.e., kinetic measurements can be used to identify the rate-controlling step in a reaction. Reaction kinetics are usually described by the Arrhenius equation k = A exp ( - Q / R T )
where k is the reaction rate at temperature T, A is the pre-exponential factor (collision frequency), Q is the activation energy of the rate-controlling step, and R is the universal gas constant. The collision frequency has little significance in solid-state reactions, lwl whereas the activation energy is the energy barrier that must be overcome during the rate-limiting step of the reaction. A change in Q during the course of a reaction therefore implies a change in mechanism, i.e., a change in the rate-controlling step. Additionally, the quantitative determination of the activation energy may be used to ide
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