One of the very basic results of the physical chemistry of solids is the insight that most properties of solids depend on the microstructure. The size of the grains (average grain diameter) in a polycrystalline material has pronounced effects on many of its physical and mechanical properties. A finegrained material, or so-called nanostructured material, is harder and stronger than one that is coarse-grained (Fig. 3.1), since the former has a greater total grain boundary area to impede dislocation motion. For many materials the yield strength, σy, varies with grain size according to:
Eq. (3.1) σy = σ0 + kyd-1/2
In this expression, termed the Hall-Petch equation, d is the average grain diameter, and σ0 and ky are constants for a particular material.
The information for the average grain diameters can be primarily obtained from TEM and/or HRTEM observations, and x-ray line broadening.
It has been reported that composites of amorphous and nanocrystal-line phases have unique properties when compared with those of amorphous
phases.[12]
Amongst the different options for preparations, the mechanical alloying method has been considered the most powerful tool for nanostruc-tured materials[13] because of its simplicity, relatively inexpensive equipment, and the possibility of producing large quantities, that can be scaled up to several tons.[14] The formation of nanocrystalline materials during MA of ceramics or metallic powders is attributed to the intense cold working on the ball milled powders. This leads to a dramatic increase in the number of imperfections (e.g., point and lattice defects) which leads to decreasing the thermodynamic stability of the starting materials. Based on the type of defects applied, different kinds of nanocrystalline materials, with different physical and mechanical properties, can be obtained.[12][15]
It is believed that the reduction in grain size during MA takes place similar to that suggested by the model for nanocrystalline materials fabricated by gas condensation.[6] It is worth noting that the enthalpy stored via high-energy ball milling is far above than that for the conventional cold working technique.[16] For example, the enthalpy stored through cold welding of metals and alloys does not exceed 2 kJ/mol and is only a small fraction of the heat of fusion, ∆Hf.[17] In the MA method, however, the enthalpy is larger and can reach higher values of crystallization enthalpies[17] of a metallic glass, as high as 0.4 times the heat of fusion. We should emphasize that such enthalpy storage, in the form of lattice and point defects, cannot be achieved in traditionally processed materials. Hence, the grain boundary energy of milled nanocrystalline powders is larger than the grain boundary energy of fully equilibrated grain boundary.[18