The effects of elastic interactions on precipitate microstructural evolution in elastically inhomogeneous nickel-base alloys

Abstract

The roles of lattice mismatch, ε, Vegard’s Law parameter, η and single crystal elastic constants, C_ij, on the morphologies of γ′-type (Ni₃X, X = Al, Ga, Ge, Si) and γ (Ni–Al and Ni–Ge solid-solution) precipitates in aged binary Ni-X alloys are evaluated over the temperature range 800–1200 K. Using data on the lattice constants and the C_ij of both phases as functions of composition and temperature, informed by phase equilibrium in the γ/(γ + γ′)/γ′ regions of the Ni-X phase diagrams, values of ε, η and the C_ij (and elastic constants derived there from) are estimated for γ and γ′ phases of equilibrium composition. The precipitate microstructures are sensitive to small differences between the C_ij. For example, Ni–Al alloys are nearly elastically homogeneous, but large precipitates in aged normal (Ni-rich) and inverse (Ni₃Al-rich) alloys have very different morphologies, Ni₃Al precipitates being plate-shaped in normal alloys and Ni–Al precipitates being lath-shaped in inverse alloys. The ultimate shapes of precipitates appear to depend primarily on the signs and magnitudes of shear constants δC′ and δC₄₄; C' = (C₁₁ - C₁₂)/2. Coalescence cannot occur when δC′ > 0. When δC′ ≈ 0 coalescence leads to plates or laths depending on the sign of δC₄₄, becoming plates when δC₄₄ > 0 and laths when δC₄₄ < 0. The sign of δK possibly plays a role in determining whether the ultimate shape is plates or laths. Experimental and computer-generated microstructures are presented and discussed in the context of these findings.

Keywords:

• Ni-based superalloys
• microstructure
• shape evolution
• computer modelling

Acknowledgements

This paper is dedicated to my colleague and friend, Armen Khachaturyan, for sharing his insights on the factors that affect microstructures in so many different metallic and ceramic alloys, and for his guidance as a mentor to a generation of gifted students and post-doctoral researchers who continue to contribute new and insightful ideas to the Microstructure Modelling Community. I am grateful to the National Science Foundation for supporting this work during my tenure as Program Director of the Metals and Metallic Nanostructures Program from 2009 through 2011.

Notes

1. The equation published by Ma and Ardell [71] was used to generate the γ solvus for Ni₃Al with T in °C, which was then used to generate as a function of T in K, which was then fitted to produce Equation (4).