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The coarsening of polyhedral grains in a liquid matrix was calculated using crystal growth and dissolution equations used in crystal growth theories for faceted crystals. The coarsening behavior was principally governed by the relative value of the maximum driving force for growth (Δgmax), which is determined by the average size and size distribution, to the critical driving force for appreciable growth (Δgc). When Δgmax was much larger than Δgc, pseudonormal grain coarsening occurred. With a reduction of Δgmax relative to Δgc, abnormal grain coarsening (AGC, when Δgmax ≥ Δgc) and stagnant grain coarsening (SGC, when Δgmax < Δgc) were predicted. The observed cyclic AGC and incubation for AGC in real systems with faceted grains were explained in terms of the relative value between Δgmax and Δgc. The effects of various processing and physical parameters, such as the initial grain size and distribution, the liquid volume fraction, step free energy, and temperature, were also evaluated. The calculated results were in good agreement with previous experimental observations.

When pure alumina is sintered at 1620°C, normal grain growth occurs with equiaxial grains and curved grain boundaries. When 100 ppm of SiO 2 together with 50 ppm of CaO is added, abnormal grain growth (AGG) occurs with large grains elongated with straight grain-boundary segments in the direction of the basal planes. Some of the fine matrix grains also have straight grain boundaries, and ϳ10% of the grain boundaries of the matrix grains are faceted when observed by transmission electron microscopy (TEM). Some of these grain boundaries are expected to be singular with low-energy structures corresponding to the cusps in the polar plot of the grain-boundary energy against the inclination angle. No frozen liquid is found at the grain triple junctions and grain boundaries by TEM. When 600 ppm of MgO is added together with 100 ppm of SiO 2 and 50 ppm of CaO normal growth occurs. The grain boundaries are curved when observed via optical microscopy and TEM and show that all the grain boundaries are defaceted, indicating that they become atomically rough. When sintered at 1900°C after adding 150, 300, or 500 ppm of SiO 2 , AGG occurs with straight and faceted grain boundaries, similar to the specimens sintered at 1620°C after CaO and SiO 2 are added. When MgO is added together with SiO 2 and sintered at 1900°C, normal grain growth occurs with rough grain boundaries. High-resolution TEM observation shows no frozen liquid layer at a grain boundary. The results indicate that the occurrence of AGG in alumina with SiO 2 or together with CaO is correlated with the formation of faceted and straight (on large and atomic scales) grain boundaries. It is proposed that these grain boundaries have singular ordered structures with low boundary energies and their growth by lateral step movement can cause the AGG. The addition of MgO causes grain-boundary roughening and, thus, normal grain growth. The grain boundaries in pure alumina also appear to be rough, and, hence, normal grain growth occurs.

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A correlation between grain boundary faceting and abnormal grain growth has been observed in recrystallized polycrystalline Ni at varying annealing temperatures, with or without C added. Carburized Ni specimens deformed to 50 pct show faceted grain boundaries and abnormal grain growth when annealed at temperatures below 0.7 T m , where T m is the melting point of Ni in absolute scale. When annealed at or above 0.7 T m , the grain boundaries are smoothly curved and, therefore, have a rough structure, and normal grain growth is observed. In the specimens annealed in vacuum without carburization, all grain boundaries are faceted at 0.55 T m , and some of them become defaceted at higher temperatures. The specimens annealed in vacuum at temperatures between 0.55 and 0.95 T m show abnormal grain growth. When the grain boundaries have a rough structure and are, therefore, nearly isotropic, normal grain growth is indeed expected, as shown by the simulation and analytical treatment. When all or a fraction of the grain boundaries are faceted, with the facet planes corresponding to the singular cusp directions in the variation of the boundary energy against the inclination angle, abnormal grain growth can occur either because some grain boundary junctions become immobile due to a torque effect, or the growth occurs by a step mechanism.

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Abnormal grain growth (AGG) in alumina with anorthite liquid has been observed with varying anorthite and MgO contents, at 1620°C. When only anorthite is added to form a liquid matrix, the grain–liquid interfaces have either flat or hill‐and‐valley shapes indicating atomically flat (singular) structures. The large grains grow at accelerated rates to produce AGG structures with large grains elongated along their basal planes. This is consistent with the slow growth at low driving forces and accelerated growth above a critical driving force predicted by the two‐dimensional nucleation theory of surface steps. With increasing temperature, the AGG rate increases. The number density of the abnormally large grains increases with increasing anorthite content. The addition of MgO causes some grain–liquid interfaces to become curved and hence atomically rough. The grains also become nearly equiaxed. With increasing MgO content the number density of the abnormally large grains increases until the grain growth resembles normal growth. This result is qualitatively consistent with the decreasing surface step free energy associated with partial interface roughening transition.