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

Andrews, Ross N.; Serio, Joseph A.; Muralidharan, Govindarajan; Ilavsky, Jan

doi:10.1107/S1600576717006446

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:

Andrews, Ross N. ^[1]; Serio, Joseph A. ^[2]; Muralidharan, Govindarajan ^[2]; Ilavsky, Jan ^[1]

Argonne National Lab. (ANL), Argonne, IL (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Tue May 30 00:00:00 EDT 2017

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.

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                    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.  https://doi.org/10.1107/S1600576717006446

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                    Andrews, Ross N., Serio, Joseph A., Muralidharan, Govindarajan, and Ilavsky, Jan. 2017.  
        "An in situ USAXS–SAXS–WAXS study of precipitate size distribution evolution in a model Ni-based alloy".  United States.  https://doi.org/10.1107/S1600576717006446.  https://www.osti.gov/servlets/purl/1366390.

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@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},

  url          = {https://www.osti.gov/biblio/1366390},
  journal      = {Journal of Applied Crystallography (Online)},

  issn         = {1600-5767},

  number       = 3,

  volume       = 50,

  place        = {United States},

  year         = {Tue May 30 00:00:00 EDT 2017},

  month        = {Tue May 30 00:00:00 EDT 2017}

}

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Works referenced in this record:

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

Goffe, William L.; Ferrier, Gary D.; Rogers, John
Journal of Econometrics, Vol. 60, Issue 1-2
https://doi.org/10.1016/0304-4076(94)90038-8

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

Brunner-Popela, J.; Glatter, O.
Journal of Applied Crystallography, Vol. 30, Issue 4
https://doi.org/10.1107/s0021889896015749

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

Hansen, Steen
Journal of Applied Crystallography, Vol. 41, Issue 2
https://doi.org/10.1107/s0021889808004937

Trans-interface diffusion-controlled coarsening
journal, March 2005

Ardell, Alan J.; Ozolins, Vidvuds
Nature Materials, Vol. 4, Issue 4
https://doi.org/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
https://doi.org/10.1007/s11661-012-1431-y

The theory of Ostwald ripening
journal, January 1985

Voorhees, P. W.
Journal of Statistical Physics, Vol. 38, Issue 1-2
https://doi.org/10.1007/bf01017860

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

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

Ostwald Ripening of Two-Phase Mixtures
journal, January 1992

Voorhees, P.
Annual Review of Materials Research, Vol. 22, Issue 1
https://doi.org/10.1146/annurev.matsci.22.1.197

Microstructural stability at elevated temperatures
journal, October 1999

Ardell, Alan J.
Journal of the European Ceramic Society, Vol. 19, Issue 13-14
https://doi.org/10.1016/s0955-2219(99)00094-1

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

Hansen, Steen
Journal of Applied Crystallography, Vol. 45, Issue 3
https://doi.org/10.1107/s0021889812014318

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

Lifshitz, I. M.; Slyozov, V. V.
Journal of Physics and Chemistry of Solids, Vol. 19, Issue 1-2
https://doi.org/10.1016/0022-3697(61)90054-3

Experimental evaluation of particle coarsening theories
journal, May 1990

Jayanth, C. S.; Nash, P.
Materials Science and Technology, Vol. 6, Issue 5
https://doi.org/10.1179/mst.1990.6.5.405

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
https://doi.org/10.1063/1.436750

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

Hansen, Steen
Journal of Applied Crystallography, Vol. 47, Issue 4
https://doi.org/10.1107/s1600576714013156

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

Jemian, P. R.; Allen, A. J.
Journal of Applied Crystallography, Vol. 27, Issue 5
https://doi.org/10.1107/s0021889894000373

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

Fritz, Gerhard; Glatter, Otto
Journal of Physics: Condensed Matter, Vol. 18, Issue 36
https://doi.org/10.1088/0953-8984/18/36/S14

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

Glatter, O.
Journal of Applied Crystallography, Vol. 10, Issue 5
https://doi.org/10.1107/S0021889877013879

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

Hansen, Steen
Journal of Applied Crystallography, Vol. 33, Issue 6
https://doi.org/10.1107/S0021889800012930

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

Ilavsky, Jan; Jemian, Peter R.
Journal of Applied Crystallography, Vol. 42, Issue 2
https://doi.org/10.1107/S0021889809002222

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
https://doi.org/10.1107/S0021889809008802

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

Muralidharan, G.; Chen, H.
Science and Technology of Advanced Materials, Vol. 1, Issue 1
https://doi.org/10.1016/S1468-6996(00)00005-X

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

Svergun, D. I.
Journal of Applied Crystallography, Vol. 25, Issue 4, p. 495-503
https://doi.org/10.1107/S0021889892001663

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

Vestergaard, Bente; Hansen, Steen
Journal of Applied Crystallography, Vol. 39, Issue 6
https://doi.org/10.1107/S0021889806035291

Ostwald Ripening of Two-Phase Mixtures
journal, August 1992

Voorhees, P. W.
Annual Review of Materials Science, Vol. 22, Issue 1
https://doi.org/10.1146/annurev.ms.22.080192.001213

Works referencing / citing this record:

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journal, December 2019

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Materials, Vol. 12, Issue 24
https://doi.org/10.3390/ma12244083

Quantification of Thermal Oxidation in Metallic Glass Powder using Ultra-small Angle X-ray Scattering
journal, May 2019

Paul, Tanaji; Zhang, Linqi; Biswas, Sourabh
Scientific Reports, Vol. 9, Issue 1
https://doi.org/10.1038/s41598-019-43317-0

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

Abstract

Citation Formats

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

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

The theory of Ostwald ripening journal, January 1985

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

Ostwald Ripening of Two-Phase Mixtures journal, January 1992

Microstructural stability at elevated temperatures journal, October 1999

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

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

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

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

Ostwald Ripening of Two-Phase Mixtures journal, August 1992

Review of the Quench Sensitivity of Aluminium Alloys: Analysis of the Kinetics and Nature of Quench-Induced Precipitation journal, December 2019

Quantification of Thermal Oxidation in Metallic Glass Powder using Ultra-small Angle X-ray Scattering journal, May 2019

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

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

The theory of Ostwald ripening
journal, January 1985

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

Ostwald Ripening of Two-Phase Mixtures
journal, January 1992

Microstructural stability at elevated temperatures
journal, October 1999

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

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

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

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

Ostwald Ripening of Two-Phase Mixtures
journal, August 1992

Review of the Quench Sensitivity of Aluminium Alloys: Analysis of the Kinetics and Nature of Quench-Induced Precipitation
journal, December 2019

Quantification of Thermal Oxidation in Metallic Glass Powder using Ultra-small Angle X-ray Scattering
journal, May 2019