Advancing small-angle X-ray scattering for complex metallic systems: Ti₂Cu precipitation in a martensitic near-$α$ Ti alloy

Small-angle X-ray scattering (SAXS) experiments performed at synchrotronradiation sources enable the in situ study of precipitation behaviour, providingcrucial information for alloy design. Numerous studies have demonstrated thesuccessful use of SAXS to investigate precipitation phenomena across a widerange of complex metallic systems. Nevertheless, despite its advantages, theapplication of SAXS remains often overlooked owing to the challenges asso-ciated with data analysis, especially under non-isothermal conditions in which ametal matrix is continuously evolving due to simultaneous phase transforma-tions and microstructural coarsening. This work presents a novel SAXSmodelling approach developed for the quantitative evaluation of precipitateformation in metallic systems exhibiting scattering signals superimposed ondirectionally streaked signals originating from the embedding matrix, ascommonly found in martensitic microstructures. Two-dimensional synchrotrondata recorded during a continuous in situ heating experiment on a Cu- and Si-containing near-� Ti alloy are used to demonstrate how the evolving SAXSsignal can be separated into matrix- and precipitation-related contributions. AGuinier–Porod function linked to a grain coarsening model was used to describethe background signal from the matrix, while Ti2Cu precipitates were modelledusing an ellipsoidal model function combined with a lognormal size distribution.This combined approach enabled the evaluation of precipitate volume fractionand size distribution throughout the heat treatment. The SAXS results werevalidated through complementary transmission electron microscopy and atomprobe tomography experiments, showing excellent agreement in both size andphase fraction. The presented methodology allows the successful capture ofearly-stage precipitation and provides an adaptable solution to backgroundmodelling challenges in non-isothermal SAXS experiments. This approachexpands the applicability of SAXS for precipitation studies in structurallycomplex alloy systems.