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The magnitude of m is much less than the corresponding grain boundary (GB) sliding deformation with m of 0.5.
Further, the distribution of grain number (Fig. 4c) and grain weight for a corresponding grain thickness revealed a significantly shorter peak and a smaller area under the distribution curve for the mutant, with the single grain weight for a corresponding grain thickness significantly smaller in the mutants (Fig. 4d).
Fig. 4 Panicle and grain size analysis for field grown mutants (KO). a Panicle length (n = 29), b grain size parameters of unhulled grain (n = 30), c grain number and weight for corresponding grain thickness, d single grain weight for corresponding grain thickness are shown.
The generalized displacement of the slider, indicating an internal variable, is introduced to describe the local process of the cooperative switching of the corresponding grain group.
By considering creep damage of grain boundary, when the damage variable reaches a critical value, the corresponding grain boundary element is eliminated to describe dynamic intergranular fracture processes.
In the present research, by employing dilatometry experiments two equivalent DP microstructures have been designed which are identical in most primary aspects such as constituents' volume fractions, the corresponding grain sizes and their morphologies.
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Grain length, width and area were determined for ten corresponding grains from each of the three replicate plants for both the WT and the mutant using ImageJ.
Activation energy was found to be 0.06 eV and 0.46 eV corresponding to grain and grain boundary, respectively which proves that the grain boundaries are more resistive than grains.
By using a small paint electrode, five separate relaxation frequencies have been observed corresponding to grain and grain boundary of partially stabilized zirconia (PSZ), Al2O3 in the PSZ matrix, a thermally grown oxide (TGO) layer, and the electrode effect.
For V images, same process was repeated with the major axis corresponding to grain width and minor axis corresponding to grain thickness.
Each phase-field parameter (phi _{alpha }) (corresponding to grain (alpha)) varies smoothly from 0 (outside) to 1 (inside the grain), over a diffuse region that characterizes the interfaces.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com