Free-surface proximity induced bistability and semi-semicoherency in precipitation systems

Abstract

In systems without a ‘high misfit’ and in the early stage of growth, the precipitates tend to remain coherent with the parent matrix. On further growth beyond a critical size (r*), the precipitates undergo a coherent to semi-coherent transition by formation of interfacial misfit dislocation loops to minimize the total strain energy of the system. The variation of r* with domain size has been studied and the concept of re-entrant interface transition to the coherent state was demonstrated in finite crystals. Dislocations can exist in a state of mechanical equilibrium; but are thermodynamically metastable. In the proximity of ‘interfaces’ dislocations experience a configurational force. The current work pertains to study the stability of an interfacial misfit dislocation loop in the proximity of a free-surface; wherein we evaluate configurational effects in a semi-infinite body. The Cu-2 wt%γFe alloy is used as a model system in this study. In this work we: (i) demonstrate the stabilization of the coherent state (divergence of r*), induced by the proximity of the free-surface; (ii) discover the existence of bistability in materials at the microstructural scale, resulting from the destabilization of the equatorial position of the dislocation loop and arising from symmetry breaking in climb of the interfacial loop due to the vicinity of a free-surface. (iii) identify regimes of ‘equi-bistablity’ and regions with asymmetry in energy wells, (iv) establish the existence of a ‘semi’-semicoherent state. Here, one specific system has been chosen to illustrate the effects; however, we expect the conclusions to have a broader applicability.