The theory of two‐phase interfacial structure

SUMMARY The theory of interfaces between crystals of different structure and/or composition is briefly reviewed. The review is limited to planar semi‐coherent interfaces with an abrupt transition from one crystal to the other. Equilibrium, obeying minimum ( free) energy requirements, is introduced as a governing principle. Thus the energy dependence on misfit, strain, atomic bonding, crystal thickness and other parameters is needed for minimization. The following approaches to this problem are dealt with briefly. The coincidence lattice and ball‐and‐wire models, introduced to describe systems with isotropic and covalent bonding respectively, simply correlate low energy with good matching across the interface. The variational approach uses pairwise interface forces and adjusts the positions of atoms adjoining the interface to minimize the energy. The Volterra approach introduces dislocations explicitly for misfit accommodation and to facilitate energy considerations. The Frank‐van der Merwe model recognizes the lattice periodicity by employing an interfacial periodic interaction potential. In this model the resolution of the interface into a sequence of misfit dislocations is a natural consequence of the analysis. It is believed that the latter model has the widest predictive power, while the variational method has greatest potential for accuracy. Possibly the most prominent prediction is the joint accommodation of misfit by overall strain and misfit dislocations. However, the equilibrium theory failed to predict the correct dependence of the contributions of dislocations and strain to misfit accommodation on increasing film thickness. This is now accounted for in terms of the imperfection and difficulty of acquiring misfit dislocations. Some of the consequences of the interface structure of small epitaxial islands are briefly mentioned.