Abnormal grain growth in the Potts model incorporating grain boundary complexion transitions that increase the mobility of individual boundaries

The Potts model of grain growth was adapted for the purpose of simulating abnormal grain growth (AGG) resulting from grain boundary complexion transitions. The transition in grain boundary structure between specific complexion types results in changes in properties. Where the transitions decrease energy and increase the mobility of boundaries, AGG occurs provided that such transitions predominantly occur via propagation to adjacent boundaries. Thus the model increases the mobility of selected boundaries on the basis of their adjacency to zero, one, or a multiplicity of boundaries that have already transitioned. The effect of transitions to a high mobility complexion was investigated separately from the effect of changes in energy. The influence of the frequency of complexion transitions with different adjacencies on the occurrence of AGG was explored. The simulations show how propagating complexion transitions can explain the AGG observed in certain ceramic systems. Abnormal grain growth occurs in a wide variety of different materials systems, including alumina [1], yttria [2], barium tita-nate [3], boron carbide [4], tungsten carbides [5], nickel alloys [6], molybdenum alloys [7], and steels [8]. A variety of mechanisms have been proposed to explain AGG, but in the absence of inert particles or pores that pin most boundaries, it is generally agreed upon that the boundaries surrounding an abnormally large grain must have a sustained mobility and/or energy advantage. For example, Rollett et al. [9] used two dimensional Potts model simulations to show that a relatively large grain decreases in size relative to the average grain size unless the grain has a mobility advantage (a greater grain boundary velocity per applied driving force) and energy advantage (a lower grain boundary energy). Similar results were obtained in three dimensions [10]. Rollett and Mullins [11] analyzed relative growth rates of grains assigned a mobility and/or energy advantage and established a simple quad-ratic relationship between the maximum relative size and the two ratios; Humphreys [12] published a similar theory at the same time. A reasonable expectation from these analyses is that the tendency for a grain to grow abnormally should be related both to the mobility (and energy) advantage and to the fraction of the grain surface area that has that advantage. In order, however, for a given grain to grow to a large enough size relative to the average in order to be observable as abnormal, the property advantage must be sustained over a large number of changes in the …