Journal
JOURNAL OF APPLIED CRYSTALLOGRAPHY
Volume 50, Issue -, Pages 734-740Publisher
INT UNION CRYSTALLOGRAPHY
DOI: 10.1107/S1600576717006446
Keywords
ultra-small-angle X-ray scattering; small-angle X-ray scattering; wide-angle X-ray scattering; USAXS-SAXS-WAXS; precipitation hardening; Bayesian inverse transformation
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Funding
- US Department of Energy, Energy Efficiency and Renewable Energy, Office of Vehicle Technologies as part of the Propulsion Materials Program [DE-AC05-00OR22725]
- DOE Office of Science by Argonne National Laboratory [DE-AC02-06CH11357]
- Department of Energy
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Intermetallic gamma' 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.
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