The effects of particle size distribution and induced unpinning during grain growth
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The effects of particle size distribution and induced unpinning during grain growth G. S. Thompson, J. M. Rickman, and M. P. Harmer Department of Materials Science and Engineering and the Materials Research Center, Lehigh University, Bethlehem, Pennsylvania 18015-3195
E. A. Holm Sandia National Laboratories, Albuquerque, New Mexico 87185 (Received 7 August 1995; accepted 3 January 1996)
The effect of a second-phase particle size distribution on grain boundary pinning was studied using a Monte Carlo simulation technique. Simulations were run using a constant number density of both whisker and rhombohedral particles, and the effect of size distribution was studied by varying the standard deviation of the distribution around a constant mean particle size. The results of present simulations indicate that, in accordance with the stereological assumption of the topological pinning model, changes in distribution width had no effect on the pinned grain size. The effect of induced unpinning of particles on microstructure was also studied. In contrast to predictions of the topological pinning model, a power law dependence of pinned grain size on particle size was observed at T 0.0. Based on this, a systematic deviation to the stereological predictions of the topological pinning model is observed. The results of simulations at higher temperatures indicate an increasing power law dependence of pinned grain size on particle size, with the slopes of the power law dependencies fitting an Arrhenius relation. The effect of induced unpinning of particles was also studied in order to obtain a correlation between particle/boundary concentration and equilibrium grain size. The results of simulations containing a constant number density of monosized rhombohedral particles suggest a strong power law correlation between the two parameters.
I. INTRODUCTION
The incorporation of inert, second-phase particles is recognized as an effective method for controlling grain size in ceramics and metals and, thus, the physical properties of these materials. For example, the addition of a small volume fraction of second-phase particles is used to increase strength and hardness by reducing the average grain size. A knowledge of the relationship between the grain size and various processing parameters, such as particle size, distribution, and volume fraction, is key to the design of materials with specific properties. In an attempt to better understand these relationships, many experimental studies of the pinning of grain boundaries by second-phase particles have been conducted. While many theories have been proposed to describe the physics of the pinning process, the results of most of these experimental studies have been interpreted thus far in terms of a model proposed by Zener.1 According to the Zener model, particles remove boundary area from migrating grain boundaries and thereby lower the energy of the boundary. The subsequent unpinning of these grain boundaries from particles would result in an u
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