Estimation of systematic errors committed when approximating length of grain boundaries using edges of rectangular or...

Area of Science:

• Materials Science
• Crystallography
• Computational Methods

Background:

• Grain boundary (GB) characterization is crucial in materials science.
• Approximating GB length using digital grids can introduce overestimation errors.
• Accurate GB length measurement is essential for understanding material properties.

Purpose of the Study:

• To develop a method for calculating the overestimation error of grain boundary length.
• To quantify these errors for both square and hexagonal grids.
• To validate the use of average errors as correction coefficients for experimental data.

Main Methods:

• Mathematical derivation of overestimation error for straight grain boundary segments.
• Analysis of errors on rectangular (square) and hexagonal grids.
• Comparison of calculated errors with experimental data from Electron Backscatter Diffraction (EBSD).

Main Results:

• Relative errors for square grids range from 0% to 41.42%.
• Relative errors for hexagonal grids range from 15.47% to 33.33%.
• The average overestimation error for both grid types is 27.32%.

Conclusions:

• The calculated average overestimation errors provide a quantitative measure of grid approximation inaccuracies.
• These average errors can serve as correction coefficients to refine experimental grain boundary length measurements.
• Applying these corrections enhances the accuracy of data obtained from techniques like EBSD.