Coherent to semi-coherent transition of precipitates in Van der Merwe epitaxial films

Abstract The interplay of stresses of two coherent systems, specifically a coherent precipitate within an epitaxial film (in Van der Merve growth mode), gives rise to an interesting scenario; wherein the configurational effects and the strain energy landscape are enriched. This leads to an interdependent evolutionary pathway for the coherent to semi-coherent transition. The transition of the film-substrate interface to the semi-coherent state occurs beyond a critical thickness ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) which arises from energy minimization. Using the model example of the precipitation of NbH 0.5 precipitate in a Nb/Sapphire epitaxial system, the critical radii ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>r</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>film</mml:mtext> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> ) for model geometries have been computed. 3D finite element models have been used to compute the stress state and energetics of precipitates growing in an epitaxial film. The following important observations can be made based on the simulations. (1) The epitaxial stresses can lead to the stabilization of the coherent precipitate. (2) The transition to a semi-coherent film interface, characterized by an array of interfacial misfit dislocations, can energetically favor the semi-coherent state of the precipitate over the coherent state. The magnitude of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>r</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>film</mml:mtext> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> depends on the spatial coordinates within the film. (3) The presence of Nb–H coherent precipitates can stabilize the coherent state of the film interface.