The response of the statistics of the cumulative features on grains in nanomaterials to different grain growth phenomena

Abstract

Each nanomaterial grain has some number of features, such as faces or triple junctions, on it. The sum of all the features on all grains in nanomaterials, herein called cumulative feature, can be obtained. During grain growth both the number of features per grain and the cumulative features on all grain in nanomaterials evolve randomly with time. Different mechanisms are responsible for grain growth in nanomaterials. This includes Grain Boundary Migration, Grain Rotation-Coalescence, T1 and T2 events. Evolution models for number of features per grain are known already, and not model for evolution of cumulative features. The present paper uses the tools of stochastic theory given by Random Marked Point Field to propose models for the temporal and thermal evolutions of the statistics of the random cumulative features on grains in nanomaterials under different grain growth mechanisms. The resulting differential equations are solved simultaneously using data from nanocrystalline aluminium. It is observed that the mean number of features per grain increases and density of grains in nanomaterials decreases during grain growth. It is revealed that grain growth results in decrease in moments of the cumulative features. It is shown that an increase in annealing temperature results in relatively higher increase in mean number of features per grain, further decrease in grain density, relative increase in mean cumulative features on grain and variable dispersions of cumulative features. It is also observed that the evolution of the statistics of the cumulative features depends on the nature of Galzier-diffusion term, the form of the critical number of faces per grain and the type of grain growth mechanisms. For some choices of the Glazier diffusion term, the dispersion of the cumulative feature evolves in a manner similar to that of the nanomaterials mechanical properties given by the Hall–Petch to Reversed-Hall–Petch Relationship. The variables results are explained to be consequences of different grain growth mechanisms, temperature and the diffusion termed. Thus, it can be concluded that processing route, processing conditions and the nature of evolution of the constituents of nanomaterials are simultaneously vital when designing or characterising nanomaterials.