An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy

Intermetallic γ′ precipitates typically strengthen nickel-based superalloys. The shape, size and spatial distribution of strengthening precipitates critically influence alloy strength, while their temporal evolution characteristics determine the high-temperature alloy stability. Combined ultra-small-, small- and wide-angle X-ray scattering (USAXS–SAXS–WAXS) analysis can be used to evaluate the temporal evolution of an alloy’s precipitate size distribution (PSD) and phase structure during in situ heat treatment. Analysis of PSDs from USAXS–SAXS data employs either least-squares fitting of a preordained PSD model or a maximum entropy (MaxEnt) approach, the latter avoiding a priori definition of a functional form of the PSD. However, strong low-q scattering from grain boundaries and/or structure factor effects inhibit MaxEnt analysis of typical alloys. This work describes the extension of Bayesian–MaxEnt analysis methods to data exhibiting structure factor effects and low-q power law slopes and demonstrates their use in an in situ study of precipitate size evolution during heat treatment of a model Ni–Al–Si alloy.