In order to study the development of texture and boundary character during annealing, threedimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite tempcrnture Monte Carlo model for grain growth. Randomly textured microstructures evolve nonnally, with growth exponent n = 0.96. While texture remains random, the steady-state boundary misorientation distribution favors low-angle boundaries. To first order, low-angle boundaries increase by lengthening, not by proliferating. In contrast, microstructures with a strong single-component texture develop four-grain junctions and highly curved grain boundaries, which alter evolution. The boundary misorientation distribution narrows and shifts to low angles, and no steady state is observed. The accompanying decrease in mean boundary mobility causes growth to slow, resulting in a growth exponent n = 0.62. The dependence of the growth exponent on average boundary mobility may explain experimental observations of exponents less than unity.

A Monte Carlo model for simulating final-stage sintering has been developed. This model incorporates realistic microstructural features (grains and pores), variable surface diffusivity, grain-boundary diffusivity, and grain-boundary mobility. A preliminary study of a periodic array of pores has shown that the simulation procedure accurately reproduces theoretically predicted sintering kinetics under the restricted set of assumptions. Studies on more realistic final-stage sintering microstructure show that the evolution observed in the simulation closely resembles microstructures of real sintered materials over a wide range of diffusivity, initial porosity, and initial pore sizes. Pore shrinkage, grain growth, pore breakaway, and reattachment have all been observed. The porosity decreases monotonically with sintering time and scales with the initial porosity and diffusivity along the grain boundary. Deviations from equilibrium pore shapes under slow surface diffusion or fast grain-boundary diffusion conditions yield slower than expected sintering rates. [

An efficient serial algorithm for finite temperature, quenched Potts model simulations of domain evolution has been developed. This ‘‘n-fold way’’ algorithm eliminates unsuccessful spin flip attempts a priori by flipping sites with a frequency proportional to their site activity, defined as the sum of the probability of success for every possible spin flip at that site. Finite temperature efficiency for high-spin degeneracy systems is achieved by utilizing a new, analytical expression for the portion of the site activity due to flips to non-neighbor spin values. Hence, to determine the activity of a site, only flips to the nearest neighbor spin values need be considered individually; all other flips are evaluated in a single expression. A complexity analysis of this algorithm gives the dependence of computing time on system parameters and on simulation progress. While a conventional Potts model algorithm has a constant computing time per simulation timestep, the n-fold way algorithm increases in efficiency as domain coarsening progresses. Computer experiments confirm the complexity analysis results and indicate that the n-fold way algorithm is much more efficient than the conventional algorithm even at high fractions of the critical temperature.

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InerL second-phase particles are often dispersed in metallic and ~c materials to control grain mo.rphology and size [1,2]. The microstructure imposed by the particles affects the final properties of the material. For Instance, diversions of particles have long been known to pin grain boundaries and inhibit grain growth [3].Many theoretical studies have examined the grain boundary pinning effect of randomly dispersed, monosized, isou'opic particles. Most of these studies are based on the Zoner approach to inhibited grain growth, in which the pinning force exerted by spherical particles on a randomly positioned grain boundary is equated with the grain boundary curvature driving force for grain growth [4]. For particle inhibited grain growth in three dimensions, the Zcner equation may be generalized as I04 INHIBITED GRAIN GROWTH Vol. 24, No. I ~ * / ~c~ J Figure 3. Computer generated pinned microstructmres for f=O.02 with various particle sizes. (a) r=2.67 Co) r---4.59 (c) r=6.22. The grain boundaries are strongly pinned by the particles, so as r increases the grain diameter increases.

A two-dimensional Monte Carlo simulation procedure has been used to investigate the effect of the initial pore size on the microstructural evolution and the kinetics of final-stage sintering. The sintering time scales with rt/Dgb and the grain-growth time scales with ri/D,,,. Pores are found to effectively pin the grain boundaries from the beginning of final-stage sintering at a porosity of 6 = 0.09 until 6 = 0.03.For 6 I 0.03, the remaining pores do not effectively retard grain-boundary migration and normal grain growth occurs. Small pores were found to be less effective at retarding grain growth than expected on the basis of a simple graingrowth pinning model. The mean pore size was found to be nearly constant throughout the simulations. [