Recovering Grain-Boundary Inclination Parameters through Oblique Double Sectioning
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BACKGROUND
A. Motivation
THE measurement of grain-boundary inclination parameters in polycrystalline materials can prove to be very challenging as a result of material opacity. Consequently, studies involving the grain-boundary character distribution (GBCD) are often conducted only in terms of the grain-boundary misorientation, and disregard the inclination of the grain boundary. Several studies have illustrated that misorientations related to the coincident site lattice (CSL) boundary theory can exhibit an increased resistance to different modes of failure.[1–4] In contrast, Pan et al. discovered that when both the boundary misorientation and inclination were measured, the boundary inclination played an important role.[5] Low-angle boundaries and S3 CSL boundaries resisted cracking regardless of boundary inclination, while the remaining population of CSL boundaries resisted cracking only when the correct boundary inclination and the more restrictive definition of CSL boundaries by Palumbo and Aust[1] were satisfied.[5] Rohrer et al. indicate that certain materials showed no preference for high coincidence boundaries based on grain-boundary misorientation, beyond the population E.R. HOMER, Graduate Student, formerly with the Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602 is with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. Contact e-mail: [email protected] B.L. ADAMS, Professor, is with the Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA. R.H. WAGONER, Professor, is with the Department of Materials Science and Engineering, Ohio State University, Columbus, OH 43210, USA. Manuscript submitted January 30, 2007. Article published online June 29, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS A
of low-angle and S3 boundaries. Instead, it is suggested that boundaries terminated by low-index planes, which can occur at any misorientation, should be considered special in the population.[6] While the necessity of measuring boundary inclination for accurate determination of the GBCD is arguable, it is evident that grain-boundary inclination can have a large effect on the character of a boundary. For this purpose, the work presented herein describes a new and efficient technique for obtaining the grainboundary inclination parameters of the GBCD. B. Aim and Approach The new method presented in this article, called oblique double sectioning (ODS), provides a new manner through which to recover the GBCD of a material. The ODS method can be best understood as a cross between stereology[7,8,9] and serial sectioning,[10] two methods readily used to recover the GBCD of a material. This hybrid approach utilizes the advantages of serial sectioning’s direct measurement of boundary inclination and stereology’s statistical sampling of a material. A set of samples from a single specimen is serially sectioned twice, giving two parallel layers of data from which the GBCD can be dire
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