An Investigation of Tertiary γ′ Precipitation in a Powder-Metallurgy, γ-γ′ Nickel-Base Superalloy

The kinetics of precipitation of tertiary γ′ during continuous cooling of a powder-metallurgy, nickel-base superalloy were established via a series of laboratory-scale heat treatments and fast-acting numerical simulations. Using induction- and direct-resistance-heating methods, cylindrical rods of the superalloy LSHR were supersolvus solution treated, cooled at a constant rate, and quenched at various intermediate temperatures in the tertiary-γ′-precipitation range. Additionally, small cubes were solutioned in an indirect-resistance furnace followed by either free-convection (air) cooling, oil quenching, or water quenching. The microstructures so developed were determined via scanning electron microscopy and selected transmission electron microscopy. These observations revealed a non-linear dependence of the logarithm of the average size on the logarithm of the cooling rate as well as a spatial variation of precipitate size. Coarser and finer tertiary precipitates were located respectively far from or near to the interfaces between secondary γ′ precipitates and matrix γ. The experimental findings were interpreted in the context of two different models, both assuming homogeneous nucleation and growth of precipitates. These models were based on either (1) a conventional “mean-field” approach in which concentration gradients within the gamma matrix developed during growth of secondary γ′ are neglected or (2) a novel “local-field” model in which matrix concentration gradients developed during secondary growth prior to nucleation of tertiary γ′ are taken into account in an approximate fashion. The latter model demonstrated that the source of the spatial variation in tertiary γ′ was related to variations in local supersaturation and thus the local temperature at which nucleation occurs during cooling. Average sizes and size variations predicted by the “local-field” model provided semi-quantitative agreement with experimental measurements.