Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

Clarke, A. J.; Tourret, D.; Song, Y.; Imhoff, S. D.; Gibbs, P. J.; Gibbs, J. W.; Fezzaa, K.; Karma, A.

doi:10.1016/j.actamat.2017.02.047

Title: Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

Abstract

We study microstructure selection during during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. Here we explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ~V^$$-$$1/2, Λ is observed to increase with V (∂Λ/∂V > 0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. Lastly, we explain the observed inversion of ∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.

Authors:

Clarke, A. J.;

; Song, Y.; Imhoff, S. D.; Gibbs, P. J.; Gibbs, J. W.; Fezzaa, K.; Karma, A.

Publication Date:: Mon May 01 00:00:00 EDT 2017

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC). Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1345148

Alternate Identifier(s):: OSTI ID: 1397797

Report Number(s):: LA-UR-16-22554
Journal ID: ISSN 1359-6454; TRN: US1700525

Grant/Contract Number:: AC52-06NA25396; FG02-07ER46400; AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Acta Materialia

Additional Journal Information:: Journal Volume: 129; Journal Issue: C; Journal ID: ISSN 1359-6454

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Directional solidification, Microstructure selection, X-ray radiography, Phase-field modeling

Citation Formats


                    Clarke, A. J., Tourret, D., Song, Y., Imhoff, S. D., Gibbs, P. J., Gibbs, J. W., Fezzaa, K., and Karma, A. Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations.  United States: N. p., 2017. 
Web.  doi:10.1016/j.actamat.2017.02.047.

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                    Clarke, A. J., Tourret, D., Song, Y., Imhoff, S. D., Gibbs, P. J., Gibbs, J. W., Fezzaa, K., & Karma, A. Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations.  United States.  https://doi.org/10.1016/j.actamat.2017.02.047

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                    Clarke, A. J., Tourret, D., Song, Y., Imhoff, S. D., Gibbs, P. J., Gibbs, J. W., Fezzaa, K., and Karma, A. Mon .  
"Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations".  United States.  https://doi.org/10.1016/j.actamat.2017.02.047.  https://www.osti.gov/servlets/purl/1345148.

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@article{osti_1345148,

  title        = {Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations},

  author       = {Clarke, A. J. and Tourret, D. and Song, Y. and Imhoff, S. D. and Gibbs, P. J. and Gibbs, J. W. and Fezzaa, K. and Karma, A.},

  abstractNote = {We study microstructure selection during during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. Here we explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ~V$-$1/2, Λ is observed to increase with V (∂Λ/∂V > 0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. Lastly, we explain the observed inversion of ∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.},

  doi          = {10.1016/j.actamat.2017.02.047},

  journal      = {Acta Materialia},

  number       = C,

  volume       = 129,

  place        = {United States},

  year         = {Mon May 01 00:00:00 EDT 2017},

  month        = {Mon May 01 00:00:00 EDT 2017}

}

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Works referencing / citing this record:

Propagative selection of tilted array patterns in directional solidification
journal, May 2018

Song, Younggil; Akamatsu, Silvère; Bottin-Rousseau, Sabine
Physical Review Materials, Vol. 2, Issue 5
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Tilted Dendritic Growth Dynamics and Dendrite to Degenerate Seaweed Transition in Directional Solidification: Insights from Phase-Field Simulations
journal, February 2018

Xing, Hui; Dong, Xiang Lei; Wang, Jian Yuan
Diffusion Foundations, Vol. 15
DOI: 10.4028/www.scientific.net/df.15.128

Phase-field–lattice Boltzmann simulation of dendrite growth under natural convection in multicomponent superalloy solidification
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Yang, Cong; Xu, Qing-Yan; Liu, Bai-Cheng
Rare Metals, Vol. 39, Issue 2
DOI: 10.1007/s12598-019-01292-5

Free dendritic tip growth velocities measured in Al-Ge
journal, July 2018

Becker, M.; Klein, S.; Kargl, F.
Physical Review Materials, Vol. 2, Issue 7
DOI: 10.1103/physrevmaterials.2.073405

Primary dendrite spacing selection during directional solidification of multicomponent nickel-based superalloy: multiphase-field study
journal, March 2018

Yang, Cong; Xu, Qingyan; Liu, Baicheng
Journal of Materials Science, Vol. 53, Issue 13
DOI: 10.1007/s10853-018-2236-1

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Title: Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

Abstract

Citation Formats

Dendrites, Viscous Fingers, and the Theory of Pattern Formation journal, March 1989

Atomistic to continuum modeling of solidification microstructures journal, February 2016

Modeling and characterization of grain structures and defects in solidification journal, February 2016

Solidification microstructures: recent developments, future directions journal, January 2000

Solidification microstructures and solid-state parallels: Recent developments, future directions journal, February 2009

Transparent compounds that freeze like metals journal, November 1965

Overview 12: Fundamentals of dendritic solidification—I. Steady-state tip growth journal, May 1981

Overview 12: Fundamentals of dendritic solidification—II development of sidebranch structure journal, May 1981

Constrained dendritic growth and spacing journal, July 1984

Dynamical studies of dendritic growth journal, June 1985

Pattern formation during the directional solidification of binary systems journal, June 1985

Dendrite growth at the limit of stability: tip radius and spacing journal, January 1981

Interdendritic Spacing: Part I. Experimental Studies journal, June 1984

Columnar dendrite growth: Experiments on tip growth journal, September 1985

The effect of convection on the dendrite to eutectic transition journal, June 1986

Primary spacing selection in directionally solidified alloys journal, January 1994

Spatial Period-Doubling Instability of Dendritic Arrays in Directional Solidification journal, July 1996

Time Resolved X-Ray Imaging of Dendritic Growth in Binary Alloys journal, December 1999

Direct observation of stray crystal formation in unidirectional solidification of Sn–Bi alloy by X-ray imaging journal, February 2004

On the interest of synchrotron X-ray imaging for the study of solidification in metallic alloys journal, April 2012

Time-resolved x-ray imaging of aluminum alloy solidification processes journal, August 2002

Preliminary in situ and real-time study of directional solidification of metallic alloys by x-ray imaging techniques journal, April 2003

X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy journal, February 2005

Crystal fragmentation and columnar-to-equiaxed transitions in Al-Cu studied by synchrotron X-ray video microscopy journal, August 2006

X-ray Imaging and Controlled Solidification of Al-Cu Alloys Toward Microstructures by Design: X-ray Imaging and Controlled Solidification of Al-Cu Alloys journal, January 2015

Numerical modeling of cellular/dendritic array growth: spacing and structure predictions journal, March 1996

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy journal, February 1964

The redistribution of solute atoms during the solidification of metals journal, July 1953

Predictions of dendritic growth rates in the linearized solvability theory journal, May 1989

Theory of pattern selection in three-dimensional nonaxisymmetric dendritic growth journal, July 1993

Phase-field study of three-dimensional steady-state growth shapes in directional solidification journal, January 2010

A numerical analysis of dendritic and cellular array growth: the spacing adjustment mechanisms journal, September 1992

Prediction of dendritic spacings in a directional-solidification experiment journal, April 1993

Primary spacing selection of constrained dendritic growth journal, November 1993

Oscillatory Instability, Limit Cycle, and Transition to Doublets in Directional Solidification journal, October 1997

Three-dimensional phase-field simulations of directional solidification journal, May 2007

Spatiotemporal Dynamics of Oscillatory Cellular Patterns in Three-Dimensional Directional Solidification journal, May 2013

Oscillatory cellular patterns in three-dimensional directional solidification journal, October 2015

Eutectic dynamics: A host of new states journal, April 1995

2D and 3D phase-field simulations of lamella and fibrous eutectic growth journal, April 2002

Effect of interface anisotropy on spacing selection in constrained dendrite growth journal, October 2008

Onset of sidebranching in directional solidification journal, February 2010

Modeling of primary spacing selection in dendrite arrays during directional solidification journal, April 2002

Multiscale dendritic needle network model of alloy solidification journal, October 2013

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification journal, May 2015

Cellular spacings—I. Steady-state growth journal, April 1988

Cellular spacings—II. Dynamical studies journal, April 1988

Cellular and dendritic growth: Part I. Experiment journal, October 1985

Evolution of characteristic pattern parameters in directional solidification of thin samples of a dilute AlCu alloy journal, May 1995

Convective and interfacial instabilities during unidirectional solidification of a binary alloy journal, May 1980

Influence of thermosolutal convection on the solidification front during upwards solidification journal, July 1989

Localized Microstructures Induced by Fluid Flow in Directional Solidification journal, October 2001

Chimney Formation in Solidifying Ga-25wt pct In Alloys Under the Influence of Thermosolutal Melt Convection journal, April 2013

In Situ X-Ray Observations of Dendritic Fragmentation During Directional Solidification of a Sn-Bi Alloy journal, September 2015

Natural convection in directional dendritic solidification of metallic alloys—I. Macroscopic effects journal, April 1989

The effect of convection on disorder in primary cellular and dendritic arrays journal, December 2002

Pattern formation in constrained dendritic growth with solutal buoyancy journal, May 2009

In situ analysis of the influence of convection during the initial transient of planar solidification journal, March 2011

Analysis by synchrotron X-ray radiography of convection effects on the dynamic evolution of the solid–liquid interface and on solute distribution during the initial transient of solidification journal, June 2011

Investigation of gravity effects on solidification of binary alloys with in situ X-ray radiography on earth and in microgravity environment journal, December 2011

Phase field model for three-dimensional dendritic growth with fluid flow journal, September 2001

Modeling of free dendritic growth of succinonitrile–acetone alloys with thermosolutal melt convection journal, March 2002

Dendritic growth with fluid flow in pure materials journal, March 2003

Three-dimensional phase-field simulations of the effect of convection on free dendritic growth journal, June 2005

Influence of external flows on crystal growth: Numerical investigation journal, September 2006

Influence of external flows on pattern growth journal, May 2007

Spatio-temporal microstructure evolution in directional solidification processes journal, August 2006

Interaction of Interdendritic Convection and Dendritic Primary Spacing: Phase-Field Simulation and Analytical Modeling journal, March 2006

Quantitative phase-field model of alloy solidification journal, December 2004

Growth competition of columnar dendritic grains: A phase-field study journal, January 2015

Phase-Field Formulation for Quantitative Modeling of Alloy Solidification journal, August 2001

Quantitative phase-field modeling of dendritic growth in two and three dimensions journal, April 1998

Nonlinear Preconditioning for Diffuse Interfaces journal, December 2001

Phase-field model of dendritic sidebranching with thermal noise journal, October 1999

Phase field approach to heterogeneous crystal nucleation in alloys journal, January 2009

Directional solidification of inclined structures in thin samples journal, August 2014

Modeling Melt Convection in Phase-Field Simulations of Solidification journal, September 1999

Dendrites, Viscous Fingers, and the Theory of Pattern Formation
journal, March 1989

Atomistic to continuum modeling of solidification microstructures
journal, February 2016

Modeling and characterization of grain structures and defects in solidification
journal, February 2016

Solidification microstructures: recent developments, future directions
journal, January 2000

Solidification microstructures and solid-state parallels: Recent developments, future directions
journal, February 2009

Transparent compounds that freeze like metals
journal, November 1965

Overview 12: Fundamentals of dendritic solidification—I. Steady-state tip growth
journal, May 1981

Overview 12: Fundamentals of dendritic solidification—II development of sidebranch structure
journal, May 1981

Constrained dendritic growth and spacing
journal, July 1984

Dynamical studies of dendritic growth
journal, June 1985

Pattern formation during the directional solidification of binary systems
journal, June 1985

Dendrite growth at the limit of stability: tip radius and spacing
journal, January 1981

Interdendritic Spacing: Part I. Experimental Studies
journal, June 1984

Columnar dendrite growth: Experiments on tip growth
journal, September 1985

The effect of convection on the dendrite to eutectic transition
journal, June 1986

Primary spacing selection in directionally solidified alloys
journal, January 1994

Spatial Period-Doubling Instability of Dendritic Arrays in Directional Solidification
journal, July 1996

Time Resolved X-Ray Imaging of Dendritic Growth in Binary Alloys
journal, December 1999

Direct observation of stray crystal formation in unidirectional solidification of Sn–Bi alloy by X-ray imaging
journal, February 2004

On the interest of synchrotron X-ray imaging for the study of solidification in metallic alloys
journal, April 2012

Time-resolved x-ray imaging of aluminum alloy solidification processes
journal, August 2002

Preliminary in situ and real-time study of directional solidification of metallic alloys by x-ray imaging techniques
journal, April 2003

X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy
journal, February 2005

Crystal fragmentation and columnar-to-equiaxed transitions in Al-Cu studied by synchrotron X-ray video microscopy
journal, August 2006

X-ray Imaging and Controlled Solidification of Al-Cu Alloys Toward Microstructures by Design: X-ray Imaging and Controlled Solidification of Al-Cu Alloys
journal, January 2015

Numerical modeling of cellular/dendritic array growth: spacing and structure predictions
journal, March 1996

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy
journal, February 1964

The redistribution of solute atoms during the solidification of metals
journal, July 1953

Predictions of dendritic growth rates in the linearized solvability theory
journal, May 1989

Theory of pattern selection in three-dimensional nonaxisymmetric dendritic growth
journal, July 1993

Phase-field study of three-dimensional steady-state growth shapes in directional solidification
journal, January 2010

A numerical analysis of dendritic and cellular array growth: the spacing adjustment mechanisms
journal, September 1992

Prediction of dendritic spacings in a directional-solidification experiment
journal, April 1993

Primary spacing selection of constrained dendritic growth
journal, November 1993

Oscillatory Instability, Limit Cycle, and Transition to Doublets in Directional Solidification
journal, October 1997

Three-dimensional phase-field simulations of directional solidification
journal, May 2007

Spatiotemporal Dynamics of Oscillatory Cellular Patterns in Three-Dimensional Directional Solidification
journal, May 2013

Oscillatory cellular patterns in three-dimensional directional solidification
journal, October 2015

Eutectic dynamics: A host of new states
journal, April 1995

2D and 3D phase-field simulations of lamella and fibrous eutectic growth
journal, April 2002

Effect of interface anisotropy on spacing selection in constrained dendrite growth
journal, October 2008

Onset of sidebranching in directional solidification
journal, February 2010

Modeling of primary spacing selection in dendrite arrays during directional solidification
journal, April 2002

Multiscale dendritic needle network model of alloy solidification
journal, October 2013

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification
journal, May 2015

Cellular spacings—I. Steady-state growth
journal, April 1988

Cellular spacings—II. Dynamical studies
journal, April 1988

Cellular and dendritic growth: Part I. Experiment
journal, October 1985

Evolution of characteristic pattern parameters in directional solidification of thin samples of a dilute AlCu alloy
journal, May 1995

Convective and interfacial instabilities during unidirectional solidification of a binary alloy
journal, May 1980

Influence of thermosolutal convection on the solidification front during upwards solidification
journal, July 1989

Localized Microstructures Induced by Fluid Flow in Directional Solidification
journal, October 2001

Chimney Formation in Solidifying Ga-25wt pct In Alloys Under the Influence of Thermosolutal Melt Convection
journal, April 2013

In Situ X-Ray Observations of Dendritic Fragmentation During Directional Solidification of a Sn-Bi Alloy
journal, September 2015

Natural convection in directional dendritic solidification of metallic alloys—I. Macroscopic effects
journal, April 1989

The effect of convection on disorder in primary cellular and dendritic arrays
journal, December 2002

Pattern formation in constrained dendritic growth with solutal buoyancy
journal, May 2009

In situ analysis of the influence of convection during the initial transient of planar solidification
journal, March 2011

Analysis by synchrotron X-ray radiography of convection effects on the dynamic evolution of the solid–liquid interface and on solute distribution during the initial transient of solidification
journal, June 2011

Investigation of gravity effects on solidification of binary alloys with in situ X-ray radiography on earth and in microgravity environment
journal, December 2011

Phase field model for three-dimensional dendritic growth with fluid flow
journal, September 2001

Modeling of free dendritic growth of succinonitrile–acetone alloys with thermosolutal melt convection
journal, March 2002

Dendritic growth with fluid flow in pure materials
journal, March 2003

Three-dimensional phase-field simulations of the effect of convection on free dendritic growth
journal, June 2005

Influence of external flows on crystal growth: Numerical investigation
journal, September 2006

Influence of external flows on pattern growth
journal, May 2007

Spatio-temporal microstructure evolution in directional solidification processes
journal, August 2006

Interaction of Interdendritic Convection and Dendritic Primary Spacing: Phase-Field Simulation and Analytical Modeling
journal, March 2006

Quantitative phase-field model of alloy solidification
journal, December 2004

Growth competition of columnar dendritic grains: A phase-field study
journal, January 2015

Phase-Field Formulation for Quantitative Modeling of Alloy Solidification
journal, August 2001

Quantitative phase-field modeling of dendritic growth in two and three dimensions
journal, April 1998

Nonlinear Preconditioning for Diffuse Interfaces
journal, December 2001

Phase-field model of dendritic sidebranching with thermal noise
journal, October 1999

Phase field approach to heterogeneous crystal nucleation in alloys
journal, January 2009

Directional solidification of inclined structures in thin samples
journal, August 2014

Modeling Melt Convection in Phase-Field Simulations of Solidification
journal, September 1999

On the scaling analysis of the solute boundary layer in idealized growth configurations
journal, November 1990

Solutal boundary layer concept and scaling analysis: two keys to segregation phenomena in melt crystal growth
journal, May 1993

The Distribution of Solute in Crystals Grown from the Melt. Part I. Theoretical
journal, November 1953