Monte Carlo simulations for sintering of particle aggregates
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I. INTRODUCTION It has been recognized for some time that the packing geometry and the topological features of particle aggregates have a significant influence on the kinetics and densification of the aggregates during sintering. While models of sintering based on simple geometric arrangements (such as two touching spheres, sphere-plane or cylinder-plane arrangements, and the like) are necessary and have been very useful for guiding the development of theories of sintering and sintering mechanisms, they are clearly inadequate by themselves as a basis for studying the densification, void formation, possibility of crack development, and related phenomena in randomly packed multiparticle assemblies. In fact, very careful experimental studies using model arrangements of copper spheres and glass spheres have been performed by Exner and co-workers1"4 and others5 to demonstrate the consequences of topology of packing on the sintering kinetics of multiparticle assemblies; some of the observations recorded by Exner are discussed later in this paper. Although the simpler two-body approaches are insufficient in the general case, they can be combined with computer simulations for providing a basis for following the sintering behavior of randomly packed particle aggregates. The pioneering studies of Hare6 and Ross et al.7 have in fact shown that very useful information on the statistics of rearrangement of particles and densification of random packings can be obtained through a judicious combination of two-particle sintering kinetics and computer simulation of multiparticle collections. Hare and co-workers have demonstrated recently (see Leu et al.8) that it may also be possible to include other mechanical considerations (such as minimization of elastic energy in the compact and deformation of the compact due to internal stresses) in computer simulations in a self-consistent manner to project the mechanical behavior of compacts under sintering.
The objective of the present paper is to outline a new, Monte Carlo computer experiment for the early stage of sintering of multiparticle assemblies. (The explanation for choosing the label "Monte Carlo" is presented at the end of Sec. II.) The procedure is designed to be sufficiently simple so that simulations can be used more readily as probes of densification mechanisms and kinetics of real compacts. However, despite the simplicity, the basic elements of the present simulation scheme allow extensions of the procedure for accommodating more complex phenomena and mechanical effects of rearrangements of particles during sintering. For instance, the procedure allows localization of internal stresses due to particle rearrangements by assigning probabilities for the development of localized cracks. Alternatively, stress propagation to distant parts of the compact can also be introduced by modifying the sintering rule appropriately. In addition, by relating the local changes in surface areas, thermodynamic properties, or deformation characteristics to the assigned probabilities, one can att
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