Modelling of the grain size probability distribution in polycrystalline nanomaterials

Tengen, Thomas Bobga; Iwankiewicz, R.

doi:10.1016/j.compstruct.2009.04.012

Cited by 6 publications

(12 citation statements)

References 11 publications

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“…To be consistent with previous results obtained using grain sizes in nanomaterials [[ 21 - 23 ], and references therein], the radius vector should be used to describe the contour of the grains as opposed to the use of tangent-angle functions, support functions or cross-section functions. The use of radius-vector functions should lead to Fourier series with Fourier coefficients serving as parameters.…”

Section: Methodsmentioning

confidence: 64%

“…The evolution of the mean grain size (i.e. size may be radius, area or volume) during grain growth has been extensively studied [[ 21 - 23 ], and references therein]. The evolution of grain size due to curvature-driven grain boundary migration [GBM], mis-orientation angle-driven grain rotation coalescence [GRC] mechanism and a combination of both mechanisms (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…To be able to identify the issues raised in the previous paragraph, one has to study the evolution/deformation (either during refinement or growth) of grains in nanomaterials. The enormous success previously obtained [ 9 - 11 , 21 - 23 ] from designing and modelling different mechanisms of grain growth and mechanical properties of nanomaterials is used in the present paper. Considering the fact that grain size is related to grain strain, grain elongation and grain yield stress, the approach presented in this report leads to simultaneous or transitional relationships between grain strain, shapes/elongations and the mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

“…From the definitions of form, strain, strain rate and Hall-Petch Relationship (HPR) to Reversed Hall-Petch Relationship (RHPR), data obtained for grain size and overall properties are sufficient for the current analysis. The proposed extended models are solved simultaneously and tested with the data from grain growth in nanocrystalline aluminium samples [ 21 - 23 ]. Theoretical analyses are done so as to anticipate how the evolution of some grain shapes towards and away from spherical grains impacts the materials' mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

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Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

Tengen

2011

Nanoscale Res Lett

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Grain shapes are acknowledged to impact nanomaterials' overall properties. Research works on this issue include grain-elongation and grain-strain measurements and their impacts on nanomaterials' mechanical properties. This paper proposes a stochastic model for grain strain undergoing severe plastic deformation. Most models deal with equivalent radii assuming that nanomaterials' grains are spherical. These models neglect true grain shapes. This paper also proposes a theoretical approach of extending existing models by considering grain shape distribution during stochastic design and modelling of nanomaterials' constituent structures and mechanical properties. This is achieved by introducing grain 'form'. Example 'forms' for 2-D and 3-D grains are proposed. From the definitions of form, strain and Hall-Petch-Relationship to Reversed-Hall-Petch-Relationship, data obtained for nanomaterials' grain size and conventional materials' properties are sufficient for analysis. Proposed extended models are solved simultaneously and tested with grain growth data. It is shown that the nature of form evolution depends on form choice and dimensional space. Long-run results reveal that grain boundary migration process causes grains to become spherical, grain rotation coalescence makes them deviate away from becoming spherical and they initially deviate away from becoming spherical before converging into spherical ones due to the TOTAL process. Percentage deviations from spherical grains depend on dimensional space and form: 0% minimum and 100% maximum deviations were observed. It is shown that the plots for grain shape functions lie above the spherical (control) value of 1 in 2-D grains for all considered grain growth mechanisms. Some plots lie above the spherical value, and others approach the spherical value before deviating below it when dealing with 3-D grains. The physical interpretations of these variations are explained from elementary principles about the different grain growth mechanisms. It is observed that materials whose grains deviate further away from the spherical ones have more enhanced properties, while materials with spherical grains have lesser properties. It is observed that there exist critical states beyond which Hall-Petch Relationship changes to Reversed Hall-Petch Relationship. It can be concluded that if grain shapes in nanomaterials are constrained in the way they evolve, then nanomaterials with desired properties can be designed.

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Section: Methodsmentioning

confidence: 64%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

Tengen

2011

Nanoscale Res Lett

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“…The resulting equation is solved simultaneously with the equations for moments of expressions (4) and (5), using lognormal distribution of grain size [12].…”

Section: Methodsmentioning

confidence: 99%

The evolution of internal energy released from nanomaterials during grain growth

Tengen

Iwankiewicz

2010

Phys. Status Solidi (c)

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The driving force for limited thermal stability of Nano‐Poly‐Crystals is high concentration of internal energy. This makes them to undergo significant changes when exposed to temperatures exceeding one‐third their melting points. Two processes are expected to take place under such temperatures which reduce the internal energy: (a) grain growth i.e. reduction in total grain boundary (GB) surface area or GB volume fraction and (b) reduction of GB energy per surface area. This paper proposes a theoretical approach that couples knowledge from energy method with that from stochastic differential equations to study the energy released from nanometals during grain growth. The basic Physics of the mechanisms leading to grain growth in nanomaterials is applied. The proposed model is tested on polycrystalline nano‐aluminium samples. The impacts of annealing time, mean grain size, grain size dispersion and annealing temperatures are tested. It is anomalously revealed that on comparing the various mechanisms of grain growth, the greatest amount of energy is released from nanomaterial if grain growth is due to Grain Rotation‐Coalescence (GRC) mechanism only, followed by that due to simultaneous GRC and Grain Boundary Migration (GBM) processes and least by that due to GBM only. The energies involved in T1 events, T2 events and in rotating the grains before coalescence during GRC have also been dealt with. On comparing the different physical activities taking place during growth, it is revealed that the largest amount of energy is released from materials in which grains rotate, translate and grow at constant force. This is followed by the amount of energy involved with rotating or translating the grains at constant size and least by the energy released due to changing grain size at constant force. It is also found that the rate of release of energy initially decreases rapidly, and then very slowly approaching zero during grain growth. Thus, one may conclude from the principle of stationary potential energy that the nanomaterial attains energy equilibrium in the long run. Thus, the driving force for grain growth at larger grain sizes is not more the grains' internal energy concentration. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Kinetics of nanocrystalline MgO growth by the sol–gel combustion method

Bueno

Oman

Jardim

et al. 2014

Microporous and Mesoporous Materials

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Modelling of the grain size probability distribution in polycrystalline nanomaterials

Cited by 6 publications

References 11 publications

Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

The evolution of internal energy released from nanomaterials during grain growth

Kinetics of nanocrystalline MgO growth by the sol–gel combustion method

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