Elimination of an isolated pore: Effect of grain size
- PDF / 1,680,066 Bytes
- 16 Pages / 576 x 792 pts Page_size
- 0 Downloads / 205 Views
The effect of grain size on the elimination of an isolated pore was investigated both by the Monte Carlo simulations and by a scaling analysis. The Monte Carlo statistical mechanics model for sintering was constructed by mapping microstructures onto domains of vectors of different orientations as grains and domains of vacancies as pores. The most distinctive feature of the simulations is that we allow the vacancies to move. By incorporating the outer surfaces of the sample in the simulations, sintering takes place via vacancy diffusion from the pores to the outer sample surfaces. The simulations were performed in two dimensions. The results showed that the model is capable of displaying various sintering phenomena such as evaporation and condensation, rounding of a sharp corner, pore coalescence, thermal etching, neck formation, grain growth, and growth of large pores. For the elimination of an isolated pore, the most salient result is that the scaling law of the pore elimination time tp with respect to the pore diameter dp changes as pore size changes from larger than the grains to smaller than the grains. For example, d2p for dp > G with in sample-size-fixed simulations, tp ~ dp for dp < G and tp the crossover pore diameter dc increasing linearly with G where G is the average grain diameter. For sample-size-scaled simulations, tp ~ d4p for dp < G and tp ~ dp for dp > G. That tp has different scaling laws in different grain-size regimes is a result of grain boundaries serving as diffusion channels in a fine-grain microstructure such as those considered in the simulations. A scaling analysis is provided to explain the scaling relationships among tp, dp, and G obtained in the simulations. The scaling analysis also shows that these scaling relationships are independent of the dimensionality. Thus, the results of the two-dimensional simulations should also apply in three dimensions. I. INTRODUCTION Materials processing by sintering of powder compacts has been a central issue in the field of ceramics and metallurgy. With increasing emphasis on nanostructural design, an aspect of sintering that requires more adequate understanding is the densiflcation of nanometer-sized particles without grain growth beyond 100 nm. This is the size range where the pores and the particles are of similar size and thus the spatial distribution of the porosity plays an increasingly significant role on the evolution of structure. In this size range, due to the formation of particle agglomerates, powder compacts often exhibit hierarchical pore-size distributions and thus while some pores are smaller than or equal to the particles, others are much larger than the particle size.1 Individual particles can be polycrystalline as well,2 adding to the complexity of the structure and the densification kinetics. With increasingly complicated structures, it is important to know how sintering is affected by the difference in the 1000 http://journals.cambridge.org
J. Mater. Res., Vol. 10, No. 4, Apr 1995
Downloaded: 18 Mar 2015
structures. For example
