The role of structural ledges at phase boundaries—I. Interfaces with rectangular atomic nets

Abstract

Misfitting crystal interfaces are examined as to the mechanisms of minimizing interfacial energy. A comparison between the energetics of planar and stepped interphase boundaries is made. Structural ledge interfaces with terrace patches of (dimensions l x × l y ) are examined by employing, with increased sophistication, the rigidlike or purely geometrical energetics, followed by the relaxed energetic properties. For the stepped interface the mismatch which builds up along each terrace pair patch is compensated for by a relative displacement of the atomic patterns of the two terraces (pattern advance) at the next step. In this manner the average misfit parallel to the interface is minimized and the necessity for the introduction of misfit dislocations to accommodate this misfit eliminated. Since the atomic plane spacings parallel to the terraces are different on the two sides of the interface, misfit also exists in a direction normal to the terraces. This misfit is accommodated by a tilt type misfit dislocation in every superperiod. The present paper proposes models for calculating the energies associated with (i) the interaction between opposing terrace patches (including elastic relaxation), (ii) the line energy of misfitting opposing risers at the steps and (iii) the energy of the tilt misfit dislocation in a superperiod. This energy is compared with the energy of a planar interface containing conventional misfit dislocations. The calculations predict the regimes of crystal parameters for which misfit accommodation by either planar or stepped interfaces are energetically favored. In general it is shown that steps become more favorable as the misfit decreases. The calculated resolved and normal stresses associated with steps are a significant fraction of the shear modulus and may contribute to the plasticity of metals.