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Title: An in situ 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 duringin situheat 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 avoidinga prioridefinition of a functional form of the PSD. However, strong low-qscattering from grain boundaries and/or structure factor effects inhibit MaxEnt analysis of typical alloys. Lastly, this work describes the extension of Bayesian–MaxEnt analysis methods to data exhibiting structure factor effects and low-qpower law slopes and demonstrates their use in anin situstudy of precipitate size evolution during heat treatment of a model Ni–Al–Si alloy.

Authors:
 [1];  [2];  [2];  [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Vehicle Technologies Office (EE-3V)
OSTI Identifier:
1366390
Grant/Contract Number:  
AC05-00OR22725; AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Applied Crystallography (Online)
Additional Journal Information:
Journal Volume: 50; Journal Issue: 3; Journal ID: ISSN 1600-5767
Publisher:
International Union of Crystallography
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ultra-small-angle X-ray scattering; small-angle X-ray scattering; wide-angle X-ray scattering; USAXS–SAXS–WAXS; precipitation hardening; Bayesian inverse transformation

Citation Formats

Andrews, Ross N., Serio, Joseph A., Muralidharan, Govindarajan, and Ilavsky, Jan. An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy. United States: N. p., 2017. Web. doi:10.1107/S1600576717006446.
Andrews, Ross N., Serio, Joseph A., Muralidharan, Govindarajan, & Ilavsky, Jan. An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy. United States. doi:10.1107/S1600576717006446.
Andrews, Ross N., Serio, Joseph A., Muralidharan, Govindarajan, and Ilavsky, Jan. Tue . "An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy". United States. doi:10.1107/S1600576717006446. https://www.osti.gov/servlets/purl/1366390.
@article{osti_1366390,
title = {An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy},
author = {Andrews, Ross N. and Serio, Joseph A. and Muralidharan, Govindarajan and Ilavsky, Jan},
abstractNote = {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 duringin situheat 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 avoidinga prioridefinition of a functional form of the PSD. However, strong low-qscattering from grain boundaries and/or structure factor effects inhibit MaxEnt analysis of typical alloys. Lastly, this work describes the extension of Bayesian–MaxEnt analysis methods to data exhibiting structure factor effects and low-qpower law slopes and demonstrates their use in anin situstudy of precipitate size evolution during heat treatment of a model Ni–Al–Si alloy.},
doi = {10.1107/S1600576717006446},
journal = {Journal of Applied Crystallography (Online)},
issn = {1600-5767},
number = 3,
volume = 50,
place = {United States},
year = {2017},
month = {5}
}

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Works referenced in this record:

Ultra-small-angle X-ray scattering at the Advanced Photon Source
journal, April 2009

  • Ilavsky, Jan; Jemian, Pete R.; Allen, Andrew J.
  • Journal of Applied Crystallography, Vol. 42, Issue 3
  • DOI: 10.1107/s0021889809008802

Global optimization of statistical functions with simulated annealing
journal, January 1994


Small-Angle Scattering of Interacting Particles. I. Basic Principles of a Global Evaluation Technique
journal, August 1997


Simultaneous estimation of the form factor and structure factor for globular particles in small-angle scattering
journal, March 2008


Trans-interface diffusion-controlled coarsening
journal, March 2005

  • Ardell, Alan J.; Ozolins, Vidvuds
  • Nature Materials, Vol. 4, Issue 4
  • DOI: 10.1038/nmat1340

Ultra-Small-Angle X-ray Scattering Instrument at the Advanced Photon Source: History, Recent Development, and Current Status
journal, October 2012

  • Ilavsky, J.; Zhang, F.; Allen, A. J.
  • Metallurgical and Materials Transactions A, Vol. 44, Issue 1
  • DOI: 10.1007/s11661-012-1431-y

Factors affecting particle-coarsening kinetics and size distribution
journal, September 1989

  • Jayanth, C. S.; Nash, Philip
  • Journal of Materials Science, Vol. 24, Issue 9
  • DOI: 10.1007/bf01139016

Microstructural stability at elevated temperatures
journal, October 1999


BayesApp : a web site for indirect transformation of small-angle scattering data
journal, May 2012


Ostwald Ripening of Two-Phase Mixtures
journal, August 1992


The kinetics of precipitation from supersaturated solid solutions
journal, April 1961


Experimental evaluation of particle coarsening theories
journal, May 1990


Light scattering of a concentrated multicomponent system of hard spheres in the Percus–Yevick approximation
journal, August 1978

  • Vrij, A.
  • The Journal of Chemical Physics, Vol. 69, Issue 4
  • DOI: 10.1063/1.436750

Update for BayesApp : a web site for analysis of small-angle scattering data
journal, July 2014


The effect of the shape function on small-angle scattering analysis by the maximum-entropy method
journal, October 1994


Structure and interaction in dense colloidal systems: evaluation of scattering data by the generalized indirect Fourier transformation method
journal, August 2006


A new method for the evaluation of small-angle scattering data
journal, October 1977


Bayesian estimation of hyperparameters for indirect Fourier transformation in small-angle scattering
journal, December 2000


Irena : tool suite for modeling and analysis of small-angle scattering
journal, February 2009


Coarsening kinetics of coherent γ′ precipitates in ternary Ni–based alloys: the Ni–Al–Si system
journal, January 2000


Determination of the regularization parameter in indirect-transform methods using perceptual criteria
journal, August 1992


Application of Bayesian analysis to indirect Fourier transformation in small-angle scattering
journal, November 2006


The theory of Ostwald ripening
journal, January 1985

  • Voorhees, P. W.
  • Journal of Statistical Physics, Vol. 38, Issue 1-2
  • DOI: 10.1007/BF01017860