On the accessibility of the disclination tensor from spatially mapped orientation data

Disclinations, defects that accommodate rotational incompatibilities in a crystal lattice, have been described in detail in the literature, but rarely observed in solid materials. Recently, a method has been described by which it is proposed that disclination densities can be estimated using spatially resolved orientation data generated from electron backscatter diffraction or precession electron diffraction. Herein, a rigorous evaluation of this approach is performed. In this work, a series of constructed and real data sets are used to evaluate the methodology for estimating disclination densities from spatially mapped orientation data and demonstrate the inherent error associated with this approach. It is shown that the outcome of this analysis is heavily dependent on the how numerical approximations are implemented. If a self-consistent method is used, then the disclination tensor will always be zero and if an inconsistent method is used then the error in the estimation of the disclination tensor is unbounded. Therefore, although the theory behind the disclination tensor is sound, the inputs needed to calculate it are not experimentally accessible through the application of numerical approximation methods to orientation maps and a different methodology is needed.

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