Commercially pure α-Ti was serial sectioned using a Xe plasma focused ion beam (PFIB) scanning electron microscope and orientation maps were obtained on the parallel layers by electron backscatter diffraction. The orientations and shapes of 13900 grains and 92100 grain faces were characterized. The mean number of faces per grain was 14.2. The grain boundaries were classified according to the three misorientation parameters and two grain boundary orientation parameters. There were more grain boundaries with 180°-twist and 180°-tilt character than expected in a random distribution. Furthermore, grain boundary planes with prismatic orientations were more common than those with basal orientations. The grain boundary with the greatest relative area had a 28°/[0001] misorientation and (314 � 0) and �72 � 5 � 0� grain boundary planes. Compared to earlier instruments with Ga-ion sources, the milling speed of the PFIB makes it possible to collect ten times more data in a comparable time.

Grain boundary distributions in the space of macroscopic boundary parameters are basic statistical characteristics of boundary networks. To avoid artifacts caused by the currently used computation method, it is proposed to utilize the kernel density estimation technique and to determine boundary distributions based on metric functions defined in the boundary space. A distribution is calculated at points of interest by summing areas of boundaries that fall within specified distances from these points. The new method is illustrated on experimental data of a nickel-based superalloy.DOI: 10.1007/s11661-014-2325-y Ó The Author(s) 2014. This article is published with open access at Springerlink.com A variety of properties of polycrystalline materials are affected by grain boundaries. To explore relationships between boundary structures and material properties, the boundaries need to be investigated at both atomic and ''macroscopic'' levels. Studies at the atomic scale are limited by experimental capabilities, but the macroscopic boundary parameters (i.e., misorientations between neighboring grains and directions of boundary plane normals [1] ) can be relatively easily determined. Experimental methods of three-dimensional microstructure characterization have been improved greatly over the last decade, and large sets of boundary parameters are being collected, e.g., References 2, 3. The sizes of resulting data sets allow for statistical analyses of boundaries.One of the most basic statistical characteristics of a boundary network is the distribution of grain boundaries with respect to the macroscopic boundary parameters. In relevant reports published so far (e.g., References 4 through 8), the distributions have been computed using a method [4] based on partition of a certain domain in the boundary parameter space into equivolume bins. Although this method has been successfully applied to various materials, it has deficiencies leading to artifacts in computed distributions, and complicating estimation of the reliability of the distributions.This note presents an alternative approach to computation of the boundary distributions. Suggestions given in Reference 9 are followed to adapt the kernel density estimation technique and to replace the partition of the boundary space by probing the distributions at selected points and counting boundaries that are not farther from those points than an assumed limiting distance defined in the boundary space. It is shown that this change of the computation method leads to significant improvements in the quality of resulting distributions. The new method also allows for a direct estimation of the reliability of the distributions. In the following, deficiencies of the hitherto used approach are discussed. Then, the new approach is described and confronted with the old one. Both methods are applied to grain boundary data of a nickel-based superalloy. For simplicity, only cubic ðm " 3mÞ crystal symmetry is considered; similar analysis can be performed for other holohedral symmetries.The gra...

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Five macroscopic boundary parameters can be extracted from three-dimensional orientation maps. Serial sectioning, which includes consecutive steps of material removal, and electron backscatter diffraction (EBSD) measurement were employed to extract a stack of two-dimensional sections of a pure nickel sample. The EBSD patterns were collected from large millimetre scale areas and mechanical polishing was applied to prepare the sections. The three-dimensional microstructure was then reconstructed from these sections. A new alignment algorithm based on the minimization of misorientation between two adjacent sections has been developed to accurately align the sections. Differently from the conventional alignment methods, the new algorithm corrects not only the translational misalignment but also rotational and plane parallelity misalignments. The aligned three-dimensional microstructure exhibits smooth grain boundary planes and continuous orientation gradients inside the grains as experimental scatter induced by misalignment was largely removed. Grain boundaries were reconstructed from the aligned three-dimensional map, and the distribution of boundaries in the domain of five macroscopic boundary parameters was computed using kernel density estimation. Methods for estimating the reliability of the distributions are demonstrated. This distribution is compared with the distributions obtained previously for other face-centered cubic materials, including a different pure nickel sample.