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The break-down in the Hall-Petch trend has been attributed to different deformation mechanisms that become dominant once the grain size is reduced down to below a critical value [ 45 ]. The major interest involving the studies of strength has been to see if the HP relation holds at the smallest grain sizes. In this section, we present the results of recently observed IHP in the intermetallic Al 5 Fe 2 , and various deformation models in the present context of grain size softening will be discussed.

The expansion of the understanding of deformation of conventional polycrystalline materials to materials with grain sizes on the scale of nanometre is, at present, an evolving process. The experimental finding on inverse Hall-Petch has prompted various researches to propose models pertaining to their mechanism of deformation.

Of the proposed models, different deformation mechanisms for nanocrystalline Al 5 Fe 2 intermetallic are discussed subsequently. It is pertinent to point out that dislocation activities [ 46 ] have been shown to exist in some nanocrystalline materials. Nevertheless, the dislocation activity can be considered virtually absent in nanostructured materials where the grain size is lower than the minimum required distance to be maintained between the two dislocations. Therefore, the HP relation is expected to witness a transition below a critical grain size, d c.

TEM and molecular dynamics MD simulation have also demonstrated that the grain boundaries can act as a source and a sink for dislocations. In nanomaterials, Hall-Petch behaviour breaks down because the grain is too small for dislocations to pile-up. In a polycrystalline sample, each individual grain will no longer be able to support more than one dislocation [ 48 ]. Using the concept proposed by Nieh and Wadsworth, Farghalli and co-workers [ 47 , 48 ] developed a relationship between the critical grain size and hardness for the critical grain size below which softening occurs.

Assuming that the stress field of a dislocation is valid at the nanoscale, and on the suggestion that fine grain sizes affect dislocation self-energy, a mathematical analysis was proposed and it leads to Eq. Therefore, it is clear that dislocation-mediated process is not operative in these nanocrystalline intermetallics. It is clearly evident that the models based on dislocation pile-up could not account for grain size softening.


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For such fine grains, the deformation based on dislocation mechanisms becomes less dominant, and the mode of deformation based on grain boundary phase via grain boundary shearing comes into picture [ 51 ]. This would lead to a decrease in hardness and strength, since strain hardening due to dislocation will be absent and the grain boundary will be softer [ 52 ].

Conrad and Narayan [ 29 ] considered the thermally activated deformation and proposed a rate-controlling equation, which is given as. The parameters in Eq. The values of activation volume can be obtained from the slope of the best fit straight line from plot of H versus ln d. In view of the above and by taking logarithm, Eq. The model was validated for IHP regime of the current experimental data, and the experimentally observed and calculated hardness values of this system are shown in Figure The degree of fit, as described by coefficient of correlation, for all the three expressions H v versus ln L , H v versus L these two describe the rigorous and approximate forms of the relationship in the model by Conrad and Narayan [ 29 ] and H v versus L-L 0 0.

On this basis, both the models are acceptable. However, in nanocrystalline materials at room temperature, the value of m is in the range of 0. The following observations are interesting: the relative change in hardness as one goes from the HP to the IHP region is much less in intermetallics than in nanocrystalline materials. This aspect needs further study.

However, it is clear that the observed IHP effect in intermetallics also could be explained in terms of the mesoscopic grain boundary sliding controlled flow process, as with the other classes of materials. The activation energy for grain boundary diffusion of this type of intermetallics [ 29 ] was found to be slightly higher compared to the present activation energy obtained from this analysis.

The results are somewhat in accordance with the previous work on nano-quasicrystalline materials, which proposed a similar approach for the observed softening related to inverse Hall-Petch behaviour [ 51 ]. Using this model, the predicted and the current experimental data were plotted, and it was shown that qualitatively the fit is acceptable Figure The detailed examination showed that the correlation coefficient calculated based on grain boundary sliding using Hv versus d 0.

Despite the abovementioned similarity, manifest difference exists in the activation energy for the rate-controlling process due to their atomistic approach in the rate-controlling process. In case of grain boundary shearing approach, the effective stress is considered as the applied stress, that is, the strain-rate sensitivity index, m, equals 1.

In general, it was pointed out that some of the approximations made in atomistic grain boundary shearing model to explain are questionable [ 34 ]. Hardness versus grain size in IHP regime observed values and calculated values obtained using Eq.


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The average shear strain in the basic unit of sliding, the number of grain boundaries that align to form a plane interface during mesoscopic boundary sliding and the free energy of activation for the rate-controlling GBS process reprinted with kind permission from reference [ 53 ], copyright , Elsevier.

In this section, the recent progress in the synthesis of Al-Fe intermetallics and their softening behaviour using various deformation mechanisms is discussed. Monoclinic Al 3 Fe and triclinic Al 2 Fe phase was found to be unstable under high-energy milling condition and transformed to orthorhombic Al 5 Fe 2 phase.

Microhardness measurements of single Al 5 Fe 2 nanocrystalline intermetallic phase produced by mechanical milling resulted in Hall-Petch HP break-down and showed two distinct behaviours. The break-down of HP for the averaged microhardness measurements was found to be due to the transition of deformation mechanism from dislocation activity to grain boundary sliding.


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Dislocation models could not intend the critical grain size at which the HP relation breaks down, and so models based on grain boundaries were considered. Detailed analysis showed that models based on grain boundaries namely grain boundary sliding and thermally activated grain boundary shearing seem to be reasonable in explaining the IHP effect.

Grain boundary sliding is ascribed to be a viable deformation mechanism resulting in a softening behaviour observed in this system. The authors are thankful to Dr. Srivastava and Prof. Padmanabhan for many stimulating discussions. One of the authors Raviathul Basariya gratefully acknowledges the financial support by L. Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.

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Introduction Intermetallics represent a manifold class of materials that possess intermediate properties between metallic and non-metallic materials. Intermetallics An increased need for new and novel materials with specified properties and particular application has attracted greater attention of metallurgists and material scientists in recent years. Al-Fe intermetallics Considering all excellent physical and mechanical properties of aluminium, it has become an important element in intermetallics.

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Phases Symbol Crystal structure Stability range at. Table 1. Alloy Phases formed References Al Table 2. List of phases formed in Al-Fe alloy. Nanostructured materials Nanostructured materials are an important class of metastable materials that are produced by ball milling. Effect of process parameters on mechanical properties Despite the same composition of initial powder mixture, various structures can evolve depending on the parameters of the milling process. Table 3. Express and low-cost microwave synthesis of the ternary Chevrel phase Cu 2 Mo 6 S 8 for application in rechargeable magnesium batteries.

Journal of Solid State Chemistry , , Microwave synthesis and sintering of TiNiSn thermoelectric bulk. Fabrication of tungsten—copper alloys by microwave hot pressing sintering.

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Physical Metallurgy and Advanced Materials

Microwave ignition of the combustion synthesis of aluminides and field-related effects. Zhou Shu-cai. Leaching of palladium and rhodium from spent automobile catalysts by microwave roasting. Influences of temperatureson tungsten copperalloy prepared bymicrowave sintering. Shanbogh, Sebastian C. Effect of ordered and disordered phases of unsupported Ag 3 In nanoparticles on the catalytic reduction of p -nitrophenol.