THE ROLE OF STRUCTURAL LEDGES AT PHASE BOUNDARIES .1. INTERFACES WITHRECTANGULAR ATOMIC NETS

Misfitting crystal interfaces are examined as to the mechanisms of min imizing interfacial energy. A comparison between the energetics of pla nar and stepped interphase boundaries is made. Structural ledge interf aces with terrace patches of (dimensions l(x) x l(y)) are examined by employing, with increased sophistication, the rigidlike or purely geom etrical 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 t his manner the average misfit parallel to the interface is minimized a nd the necessity for the introduction of misfit dislocations to accomm odate this misfit eliminated. Since the atomic plane spacings parallel to the terraces are different on the two sides of the interface, misf it also exists in a direction normal to the terraces. This misfit is a ccommodated by a tilt type misfit dislocation in every superperiod. Th e present paper proposes models for calculating the energies associate d with (i) the interaction between opposing terrace patches (including elastic relaxation), (ii) the line energy of misfitting opposing rise rs 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 in terface containing conventional misfit dislocations. The calculations predict the regimes of crystal parameters for which misfit accommodati on by either planar or stepped interfaces are energetically favored. I n general it is shown that steps become more favorable as the misfit d ecreases. The calculated resolved and normal stresses associated with steps are a significant fraction of the shear modulus and may contribu te to the plasticity of metals.