Microstructure equilibrium shapes

Thus far, our results are primarily formal. As an exercise in exploiting the formalism, we will first examine the fields associated with spherical inclusions, and then make an assessment of the elastic strain energy tied to such inclusions. These results will leave us in a position to consider at a conceptual level the nucleation, subsequent evolution and equilibrium shapes associated with inclusion microstructures. 

The sequence just outlined provides a salutary lesson in the nature of explanation in materials science. At first the process was a pure mystery. Then the relationship to the shape of the solid-solubility curve was uncovered that was a partial explanation. Next it was found that the microstructural process that leads to age-hardening involves a succession of intermediate phases, none of them in equilibrium (a very common situation in materials science as we now know). An understanding of how these intermediate phases interact with dislocations was a further stage in explanation. Then came an nnderstanding of the shape of the GP zones (planar in some alloys, globniar in others). Next, the kinetics of the hardening needed to be... 

Grain boundaries (and boundaries between phases) are elements of the microstructure of crystalline solids, being characterized by their number, shape, and topological arrangement. The microstructure is a non-equilibrium property. In the next section we discuss grain boundaries. 

Application As is well-known in the industry, any microporous material which is formed through a nonequilibrium process is subject to variability and nonuniformity, and thus limitations such as block thickness, for example, due to the fact that thermodynamics is working to push the system toward equilibrium. In the present material, the microstructure is determined at thermodynamic equilibrium, thus allowing uniformly microporous materials without size or shape limitations to be produced. As an example, the cubic phase consisting of 44.9 wt% DDAB, 47.6% water, 7.0% styrene, 0.4% divinyl benzene (as cross-linker), and 0.1% AIBN as initiator has been partially polymerized in the authors laboratory by themal initiation the equilibrated phase was raised to 8S°C, and within 90 minutes partial polymerization resulted S AXS proved that the cubic structure was retained (the cubic phase, without initiator, is stable at 65°C). When complete polymerization by thermal initiation is accomplished, then such a process could produce uniform microporous materials of arbitrary size and shape. 

To truly control crystallization to give the desired crystalline microstructure requires an advanced knowledge of both the equilibrium phase behavior and the kinetics of nucleation and growth. The phase behavior of the particular mixture of TAG in a lipid system controls both the driving force for crystallization and the ultimate phase volume (solid fat content) of the solidified fat. The crystallization kinetics determines the number, size, polymorph, and shape of crystals that are formed as well as the network interactions among the various crystalline elements. There are numerous factors that influence both the phase behavior and the crystallization kinetics, and the effects of these parameters must be understood to control lipid crystallization. 

Let us consider the three additional examples just mentioned. First, we need to identify the features, in each case, that define the microstructural state. In the case of the emulsion or blend, the most important microscale feature that can be influenced by the flow is the orientation and shape of the disperse-phase bubbles or drops (the mean drop size and drop-size distribution will also generally be important and can be influenced by flow-induced drop breakup and coalescence events, but we will ignore this extra complication for purposes of our current discussion). At equilibrium, the drops will be spherical and the microstructure isotropic. For polymeric liquids, it is the statistical configuration of the polymer molecules... 

Figure 3a shows the microstructure of the initial parent metal the structure of d-phase inclusions (CuAh intermetallic compound-based solid solution) is shown in Fig. 3b. As a result of the welding heat effect, most of the inclusions of the intermetallic phase in the HAZ were subjected to partial local melting and were converted into clusters and interlayers of eutectics (Figs. 3c, 3d, 4a, and 4b), while others changed shape only slightly. This is probably explained by the fact that in the condition of nonequilibrium primary solidification, they had a composition considerably different from that prescribed by the equilibrium diagram [%...

The needle-like grain shape seems to be kinetically determined and therefore not the equilibrium crystal shape [30,38], The estimated equilibrium aspect ratio (ratio of grain length to thickness) is 1.3, not as high as 20, as was found to be the case for the silicon nitride materials. The microstructural formation must therefore be explained on the basis of growth mechanisms. 

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