Single crystal Ni-base superalloys are used in the manufacturing of the turbine blades of turbo-engines. The exceptional mechanical properties of these alloys during service at high temperature, originate from their particular microstructure, composed of γ’ precipitates (L12 ordered structure), surrounded by a γ matrix (FCC disordered solid solution). It is therefore essential to understand the formation and evolution of these phases. During heat treatment, the microstructure of superalloys undergoes multiple changes, driven by the competition between the interface energy and the elastic energy. The aim of the present work is to analyze how the volume fraction of precipitates and the slight difference in the elastic constants of the coexisting phases influence the shape, size, and arrangement of the precipitates.
Previous studies have individually investigated the effects of volume fraction, and elastic inhomogeneity on the microstructure of superalloys, both experimentally  and using computer simulations . In this work we use a phase field model and perform simulations in two and three dimensions. The phase field method describes the evolution of microstructures based on the time evolution of continuous fields, which makes it a powerful tool for studying the evolution of complex structures .
We first analyze the effect of the precipitate volumes fraction considering a large range of values, typically from 0.2 to 0.9. For the lowest values, the initial configuration is metastable and a specific methodology is used to initiate the transformation. We then introduce an elastic inhomogeneity between the precipitate and matrix phases, for different volume fractions, in order to illustrate the combined effect of elastic inhomogeneity and volume fraction. Our simulations show a significant impact of the elastic inhomogeneity, especially of the C’ shear modulus, on coalescence and thus on the shape of the precipitates. The morphology and alignment of the precipitates are also seen to change for different values of the volume fraction, and the morphological changes are quantitatively measured.