On the energetics of heterophase interfaces

This dissertation is an attempt to understand the importance of lattice matching criterion in the determination of interfacial energy. We study this through the energetics of orientation relationships in two very different systems: (i) a solder alloy system and (ii) epitaxial systems.; In the first part, to study systems of higher anisotropy, {dollar}eta{dollar}-Cu{dollar}sb6rm Snsb5{dollar} precipitates in a {dollar}beta{dollar}-Sn matrix were thoroughly investigated for the morphology, orientation relationship and the habit plane using a number of Transmission Electron Microscopy techniques. The precipitates were found to be slab-like, and possessing a definite OR, determined as close to ({dollar}-{dollar}111){dollar}sbeta{dollar} // (001){dollar}sbbeta{dollar} with (101{dollar}rbracksbeta{dollar} // (200{dollar}rbracksbbeta{dollar}. They were also found to be faceted and elongated along the {dollar}langle{dollar}100{dollar}ranglesbbeta{dollar} directions with a (001){dollar}sbbeta{dollar} habit.; Geometric models were used to understand the nature of the morphology and crystallography. The stability of the OR was analyzed using the principles of the O-lattice theory. The habit plane was calculated and was further analyzed energetically, by applying for the first time, a formulation that allows calculation of misfit dislocation strain energy through sectioning of the O-lattice by more than a thousand low index planes. Other aspects of the morphology were also rationalized.; In the second part, the validity of the geometric models to predict ORs was tested on epitaxial systems, where the interface is constrained on one side. Specifically, epitaxy on (001) surfaces were analyzed. In an attempt to go beyond the existing models, a new energetic formulation called the Lattice Potential Model was used. This approach, while duplicating the results of the earlier models, was also successful in predicting certain observed epitaxial configurations that the earlier models were unable to predict. The existence of (111)/(001) epitaxy and the alternative (110)/(001) epitaxy were addressed with great success. The concept of "Epitaxial Maps" is introduced, which displays the relationship between the lattice parameter ratio and the possible epitaxy along with the probability of its occurrence.; It is concluded that the strain energy contribution to the interfacial energy, as dictated by geometry is a crucial factor in determining microstructural features.