The driving force for limited thermal stability of Nano-Poly-Crystals is a high concentration of internal energy. This makes their microstructures and properties to undergo significant changes when exposed to temperatures exceeding 30% of the melting points of their conventional material counterparts. Two processes are expected to take place under such temperatures, which reduce the internal energy: (a) reduction in the total grain boundary (GB) surface area or GB volume fraction and (b) reduction of the GB energy per unit surface area. The first one leads to the so called grain growth, as the reduced surface of grain boundaries divides the material in question into smaller number of grains with larger sizes. The second process equilibrates the grain boundaries and this can be achieved via reduction of the content of linear and point defects in the grain boundaries or by rotation of grains towards orientations implying lower (specific) misorientation configuration.

This present paper couples the knowledge from energy method with that from theory of stochastic differential equations to study the energy released from nanometals during grain growth. The energy method is used in determining, practically, the important stress (and, hence, energy) distributions in loaded materials, while the theory of stochastic differential equations deals with the analysis of the (temporal) evolutions of the constituent structures in nanomaterials.

The proposed model is tested on polycrystalline nano-aluminium samples. Results reveal that the coupling of the work energy method with the theory of the stochastic differential equation offer a reverberating tool for studying the energy evolved from nanomaterials during grain growth. The impact of annealing time, mean grain size, grain size dispersion and annealing temperatures on the on the internal energy concentrations of the Nanocrystalline aluminium samples are also revealed. Results also demonstrate that a considerable amount of energy is released from the nanomaterials during grain growth. It is also revealed that the energy released from nanomaterials as a result of increase in grain size by GBM and GRC mechanisms is smaller than the energy released from the material during grain growth. The energies involved in T2 events where grains translate after exchanging neighbours and the energy involved in rotating the grain before coalescence in which cases the grain sizes do not change have also been dealt. The energy evolved due to T1 events where smaller grains instantaneously disappear is also dealt with. It is also revealed that the rate of release of the energy is initially very high when the grain sizes are small, but this rate reduces approaching zero as grains grow larger. Thus, it may be concluded from the principle of stationary potential energy that the nanomaterial attains energy equilibrium and as such, the driving force for grain growth at larger micro-sizes is not more the grains’ internal energy concentration.

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1. Stochastic Approach To The Changes In The Mechanical Properties Of Nano-Crystalline Materials Induced By Grain Growth
2. The effect of grain size distribution on mechanical properties of nanometals
3. Statistical model of grain growth in polycrystalline nanomaterials