Relationship between mean grain face curvature and number of faces in normal grain growth: The meaning of normalized integral mean curvature

This paper describes the physical meaning of M_S norm ( =M_S/ V 1 / 3 ) , the unitless grain size normalized integral mean curvature of grain faces, as a descriptor of the effect of face number on grain shape, affecting grain boundary velocity in curvature driven grain growth. M_S norm has consistently been found to have a linear relationship with face class, f, among diverse experiments with real materials and simulations. Analysis of M_S norm in terms of the effects of grain size and number of faces on its components, the average mean curvature H ¯ and surface area S, show that combined, they reduce to a unitless term that is a function only of grain shape. Values of H ¯ , approximated as M_S / V 2 / 3 are shown for the first time as a function of f and grain scale. Plots of H ¯ versus f show positive values at low face classes, decreasing rapidly towards zero at f∼15, and becoming increasingly negative at a decreasing rate with increasing f. Plotted versus linear grain scale, V 1 / 3 , the value of H ¯ for each face class decreases in magnitude with increased scale during growth. Plots of Ms vs. face class show a continuous decrease as with H ¯ . Independent plots of Ms vs. linear grain scale for individual face classes were found to be linear through the origin, with slopes equal to M_S norm.