Crystallographic Distribution of Internal Interfaces in Spinel Polycrystals

Measurements of the grain boundary character distribution in MgAl2O4 (spinel) as a function of lattice misorientation and boundary plane orientation show that at all misorientations, grain boundaries are most frequently terminated on {111} planes. Boundaries with {111} orientations are observed 2.5 times more frequently than boundaries with {100} orientations. Furthermore, the most common boundary type is the twist boundary formed by a 60° rotation about the [111] axis. {111} planes also dominate the external form of spinel crystals found in natural settings, and this suggests that they are low energy and/or slow growing planes. The mechanisms that might lead to a high population of these planes during solid state crystal growth are discussed. Introduction Five parameters are needed to characterize grain boundaries in polycrystalline solids: three can be associated with the lattice misorientation and two with the orientation of the boundary plane. Using electron backscattered diffraction (EBSD) mapping, it is possible to measure four of the five parameters from a single section plane. The fifth parameter, the inclination of the boundary with respect to the section plane, can be determined either by serial sectioning [1,2] or stereological analysis [3,4]. Recent measurements of the distribution of grain boundaries in polycrystalline MgO indicate that grains are most frequently bounded by low energy {100} surface planes [2,5]. Furthermore, the variation of the grain boundary energy with type is, to first order, simply proportional to the variation of the sum of the energies of the two surfaces that comprise the boundary. A more recent study of SrTiO3 (cubic, perovskite structure) also showed that the lowest energy surfaces dominate the grain boundary plane distribution [6]. These observations have two implications. The first is that the surface energy anisotropy, which depends on two parameters, is sufficient for predicting the anisotropy of the grain boundary energy. This is useful because surface energies are easier to measure than grain boundary energies. The second is that the elimination of interfacial area during grain growth is biased toward higher energy grain boundaries so that the population of boundaries is dominated by the lower energy boundaries. This was substantiated by recent three dimensional grain growth simulations of MgO which, when using anisotropic grain boundary energies that approximated the measured energy anisotropy, reproduced the main features of the observed distribution of grain boundary planes [7]. The purpose of the present paper is to examine the distribution of grain boundary planes in MgAl2O4 (cubic, spinel structure). In the prior work, MgO and SrTiO3 both have low energy {100} planes and these planes dominated the grain boundary population. Spinel was selected because it typically exhibits an octahedral growth form bounded principally by {111} faces and it is therefore expected to show grain boundaries that are most frequently terminated by these same planes. This 2 Title of Publication (to be inserted by the publisher) expectation proved to be correct and in the final section of this paper, possible mechanisms for the predominance of the low energy planes are discussed. Experimental A sintered disk of spinel, obtained from RCS technologies, was annealed in air at 1600°C for 48 hours. After this treatment, the average grain size was 12 mm. Crystal orientation maps on a planar section were obtained using an EBSD mapping system (TexSEM Laboratories, Inc.) integrated with a scanning electron microscope (Phillips XL40 FEG). Sixteen maps were obtained, each with an area of 400 mm x 400 mm. Within each map, orientations were recorded at an interval of 2 mm. When combined, these maps contained ~8500 grains. The distributions of grain orientations and misorientations were determined from these data. The five parameter grain boundary character distribution was determined by a stereological analysis of grain boundary traces observed where the grain boundary plane meets the specimen surface [3,4]. Using a procedure described by Wright and Larsen [8], 28,000 traces were extracted from the orientation maps. The traces were analyzed using a previously described procedure to determine the grain boundary character distribution, l(Dg, n), which we define as the relative areas of grain boundaries distinguished by their lattice misorientation (Dg) and orientation (n) [2,4]. By separating the three misorientation parameters and the two interface plane parameters, the distribution of grain boundary planes at each misorientation, l(n|Dg), can be plotted on a stereographic projection. Here, the misorientations are selected according to the axis-angle convention by specifying the common axis of rotation, [uvw] and the angle about that axis, w. The results are presented in multiples of a random distribution (MRD); values greater than one indicate planes observed more frequently than expected in a random distribution. The resolution of the distribution is approximately 10 °. Results Based on the EBSD data, the sample exhibited negligible grain orientation texture and only a weak misorientation texture. Grain boundaries with misorientations of less than 10° occurred with a higher than random frequency, as did boundaries with the S3 misorientation (a 60° rotation about [111].) The maximum in the misorientation distribution was about 2 MRD and occurred at S3. The distribution of grain boundary plane orientations, averaged over all misorientations, is illustrated in Fig. 1. Note that the distribution peaks at the {111} orientation. The data show that the ratio of {111} area to {100} area is approximately 2.5. At specific axis-angle combinations, the anisotropy in l(n|Dg) is larger than in the misorientation averaged plot. The distribution of grain boundary orientations for boundaries with misorientations of 20°, 40°, and 60° about the [111] axis are shown in Fig. 2. The schematic stereogram in 2a is provided as the key, and the symbols have the same meaning as in Fig. 1. Boundary planes perpendicular to the [111] misorientation axis have a pure twist character. The pure tilt boundaries lie along the great circle 90° from the [111] axis and these positions are marked by the black arc in Fig. 2a. The maximum in Fig. 2b corresponds to a pure twist boundary terminated on both sides of the interface by (111) planes. The smaller peaks at