Integral mean curvature per unit volume and the grain boundary sweep constant

Abstract

A microstructural property new in application to grain growth, the integral mean curvature per unit volume, MVSgb, has been found to describe the rate of volume sweeping by boundaries throughout the entire structure. It is shown that MVSgb is experimentally obtainable via the sweeping tangent count or from summing the values of MS of all grains within a volume. Measurements on real materials and from computer simulations in the self-similar grain growth regime show that the values of MVSgb and V¯−2/3, where V¯ is the mean grain volume, are essentially equal, though the basis of this experimentally observed similarity remains to be derived. The Rhines/Doherty grain boundary sweep constant, θ*, describing the number fraction of grains lost per volume fraction swept by boundaries, has also been determined for the first time for a 3D grain structure as θ* ≈ −2, constant throughout steady-state grain growth. Combining MVSgb and θ* derives the classic grain growth law expressed as V¯2/3−V¯02/3 = −4/3k(t−t0). Testing shows that the value of the rate constant k from this relationship independently matches the slope k of the plot of dV/dt vs. MS, as theoretically expected. This is the first known time the classic grain growth law of D¯2 ≈ kt, where D¯ is equivalent to the mean linear grain intercept, has been derived using a comprehensive microstructural approach, encompassing the entire structure.