Modeling grain growth dependence on the liquid content in liquid-phase-sintered materials

Abstract

A model for grain growth during liquid-phase sintering (LPS) is presented. A Rayleigh grain size distribution is assumed based on both experimental and theoretical results. This asymmetric distribution provides a continuous driving force for coarsening. The model uses the solid grain contiguity to calculate the relative solid-state and liquid-phase contributions to coarsening. The level of grain agglomeration affects both the mean diffusion distance and interface area over which diffusion occurs. A cumulative grain growth rate is calculated assuming independent solid and liquid contributions to coarsening. Consequently, only the liquid volume fraction and solid-liquid dihedral angle are required to predict the change in grain coarsening rate with solid-liquid ratio. A prior empirical correlation between the grain growth rate constant and the liquid volume fraction is compared to the resulting analytic form, showing excellent agreement. The new model is projected to be generically applicable to microstructure coarsening in multiple phase materials, including porous structures.

Review: liquid phase sintering

“…63. This figure plots the experimental grain growth rate constant as a function of the inverse liquid fraction to the two-thirds power [15,91,166].…”

“…A two-way mathematical technique allows extraction of the 3D grain size distribution [90]. When the median 2D intercept is known, the cumulative distribution is given by a Raleigh distribution [91]: Fig. 22 Liquid shape and connectivity changes (for the condition of no pores) as a function of the liquid content and dihedral angle.…”

“…However, DeHoff [164] developed a model that included interactions between neighboring grains while Takajo et al [165] assumed all coarsening was by coalescence, resulting in a broad grain size distribution. German and Olevsky [91,166] showed how contiguity alters the relative solid-state and liquidphase contributions to coarsening and their model was later extended to include pores in LPS [167].…”

“…Thus, trials with changes in the solid volume fraction are useful for assessing the grain growth mechanism. In doing this, LPS data support a grain growth rate constant dependence on the liquid volume fraction raised to the -2/3 power [15,91,166]. Often the grain growth rate constant is normalized to the Ostwald ripening model where the grain growth rate constant is given as…”

Influence of handling and heating cycle on the morphology and flexural strength of glass-infiltrated alumina bars

“…Guo et al [18] lattice might occur, mainly due to the wetting of alumina particles by the glass phase. In this case, solutionprecipitation mechanism as proposed by German [20] could occur. If this mechanism is operative, the dissolution of alumina in the glass phase from high stress regions and precipitating at low stress regions could be the most feasible.…”