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Abstract
Brandon’s criterion is frequently used to quantify distribution of coincident site lattice (CSL) boundaries in studies related to grain boundary character distribution. This criterion is based on theoretical considerations and is meant to define a range within which special boundaries may exist. Experiments have repeatedly shown that this range includes boundaries which do not show special properties. A broad aim of this study is to explore if there exists a cut-off in deviation which includes only boundaries with special properties. While most other criteria in literature are based on theoretical dependence of secondary dislocation spacing, in this work we find the cut-off deviation through experimental data of recrystallised microstructures from in situ as well as ex-situ heating experiments. Deviation from structure was considered in terms of both, deviation of misorientation axis-angle as well as deviation of the boundary plane from the symmetric tilt orientation. Our results indicate that the deviation in terms of misorientation angle is more important than boundary plane deviation. We also show that the limiting deviation for various orders of twin boundaries (Σ3n) in a recrystallized microstructure is a constant and approximately 1° which is significantly lower than that defined by Brandon’s criterion. We show that this constant cut-off deviation for various Σ3n CSL boundaries can also be obtained by assuming that the secondary dislocations are spaced proportional to displacement shift complete lattice vector. Similar analysis was also carried out for non-Σ3n boundaries but due to limited statistics, no cut-off value could be deduced for these boundaries.
Acknowledgements
Authors wish to thank Dr. Stuart wright for valuable discussions related to calculations of trace deviation.