A computer simulation of strain energy from rotation to promote protonic conduction across grain boundaries

A computer simulation indicated that both differences in strain energy and the presence of stress in a direction opposite to ion movement could facilitate hydrogen ion motion across grain boundaries. The simulation used an ellipse to represent a grain and calculated elastic stresses that arose when the grain rotated slightly within the material matrix under a uniaxial load provided by the hydrogen ions themselves. The length, aspect ratio, and tilt angle with respect to the applied load were varied in the computer programs. Starting at the grain boundary, the percent of a 60 nm path traversed as a function of tilt angle is presented for grains both 200 μm and 200 nm in length and for aspect ratios of 4/3, 2 and 20. Results are also shown for an ion starting near the upper end, center line and lower end of the grain. When simple criteria of compression and shear in the direction opposite to ion movement were used, it was found that the stress criterion itself and not the aspect ratio primarily determined how much of the entire boundary was traversed.