Investigation of Surface Grooves from Migrating Grain Boundaries
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Investigation of Surface Grooves from Migrating Grain Boundaries Nicole E. Munoz, Shelley R. Gilliss, N. Ravishankar1, C. Barry Carter Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455-01432 1 Now at Materials Research Center, Indian Institute of Science, Bangalore 560 012, India ABSTRACT Visible-light microscopy (VLM) and atomic-force microscopy (AFM) were used to study the progression of grain-boundary grooving and migration in high-purity alumina (LucaloxTM). Groove profiles from the same grain boundaries were revisited using AFM following successive heat-treatments. The grooves measured from migrating grain boundaries were found to have asymmetric partial-angles compared to those measured from boundaries that did not migrate during the experiment. For a moving boundary, the grain with the larger partial-angle was consistently found to grow into the grain with the smaller partial-angle. Migrating boundaries were observed to leave behind remnant thermal grooves. The observations indicate that the boundary may be bowing out during the migration process. INTRODUCTION The theory of grain-boundary grooving developed by Mullins [1] has been used by others to calculate relative surface and boundary energies from thermal groove geometry [2-5]. Sintering is the most common method for processing ceramic materials. During sintering a compact of powders is heated to temperatures near the material’s melting point in order to form a dense solid. At these elevated temperatures, thermal energy exists for mass transport and the reduction of higher energy surfaces, resulting in a net decrease in the surface energy of the system. Since grain-boundary migration and thermal grooving of the surface almost invariably occur during sintering, their study is important to understanding the processing of ceramics in order to produce a desired set of properties. Alumina, both currently and in the past, has been widely investigated [6-9] and is the focus of this study. The driving force for groove formation is the tendency for the grain boundary to reduce its surface area and therefore minimize its energy. For a crystal in equilibrium, the surface energy can be thought of as being equivalent to surface tension [10]. The equilibrium geometry for a groove formed at a boundary that perpendicularly intersects the surface in an isotropic material is determined by a balance of surface tensions at the point of intersection of the three surfaces given by the equation γgb = γ1cos θ1 + γ2cos θ2
[1]
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in which γgb is the surface tension of the grain boundary, and γ1 and γ2 are the surface tensions of each grain on either side of the boundary [11]. The term θ will be referred to as a partial-angle, since the sum θ1 + θ2 is commonly called the dihedral angle. Equation 1 predicts θ1 = θ2 when the boundary intersects the free surface at 90o and the material has isotropic surface energies such that γ1 = γ2. This geometry is shown in Figure 1. The surface mounds that form on either side
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