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

Abstract

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 <i>in situ</i> 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 <i>a priori</i> definition of a functional form of the PSD. However, strong low-<i>q</i> 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-<i>q</i> power law slopes and demonstrates their use in an <i>in situ</i> study of precipitate size evolution during heat treatment of a model Ni-Al-Si alloy.