Coarsening of complex microstructures following spinodal decomposition

Park, C. -L.; Gibbs, J. W.; Voorhees, P. W.; Thornton, K.

doi:10.1016/j.actamat.2017.03.020

Title: Coarsening of complex microstructures following spinodal decomposition

Journal Article · Thu Mar 16 00:00:00 EDT 2017 · Acta Materialia

DOI:https://doi.org/10.1016/j.actamat.2017.03.020· OSTI ID:1533470

Park, C. -L. ^[1];

^[2]; Voorhees, P. W. ^[2];

^[1]

Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Materials Science and Engineering
Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering

Coarsening plays a pivotal role in materials engineering, but our understanding of the dynamics of coarsening in morphologically complex systems is still limited. In this paper, we examine the correlations between the interfacial velocity and interfacial morphologies, and then predict the evolution of mean curvature based on the correlations. Three simulated structures with varying volume fractions, two bicontinuous and one nonbicontinuous, are generated using the Cahn-Hilliard equation. We find general correlations between interfacial velocity and mean curvature, as well as between interfacial velocity and the surface Laplacian of the mean curvature. Furthermore, we find that the probability of finding a patch of interface with a given normal velocity and the same local principal curvatures is described well by a Gaussian distribution, independent of the principal curvature values and the volume fractions of the structures. We also find that average interfacial velocity is described by a polynomial of the mean curvature and the net curvature. Based on this finding, we develop a semi-analytical approach to predicting the rate of change of the mean curvature, which determines the morphological evolution of complex microstructures.

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Research Organization:: Northwestern Univ., Evanston, IL (United States); Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-99ER45782; SC0015394

OSTI ID:: 1533470

Alternate ID(s):: OSTI ID: 1550565

Journal Information:: Acta Materialia, Vol. 132; ISSN 1359-6454

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 15 works

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References (41)

Ostwald ripening in concentrated alloys Calderon, H. A.; Voorhees, P. W.; Murray, J. L. Acta Metallurgica et Materialia, Vol. 42, Issue 3 https://doi.org/10.1016/0956-7151(94)90293-3	journal	March 1994
The coarsening of γ' in Ni-Al alloys Ardell, A. J.; Nicholson, R. B. Journal of Physics and Chemistry of Solids, Vol. 27, Issue 11-12 https://doi.org/10.1016/0022-3697(66)90110-7	journal	November 1966
Directional coarsening in nickel-base single crystals with high volume fractions of coherent precipitates Pollock, T. M.; Argon, A. S. Acta Metallurgica et Materialia, Vol. 42, Issue 6 https://doi.org/10.1016/0956-7151(94)90011-6	journal	June 1994
Modeling the recrystallized grain size in single phase materials Wang, Shengyu; Holm, Elizabeth A.; Suni, Jaakko Acta Materialia, Vol. 59, Issue 10 https://doi.org/10.1016/j.actamat.2011.03.011	journal	June 2011
Spontaneous pinning of domain growth during spinodal decomposition of off‐critical polymer mixtures Hashimoto, Takeji; Takenaka, Mikihito; Izumitani, Tatsuo The Journal of Chemical Physics, Vol. 97, Issue 1 https://doi.org/10.1063/1.463562	journal	July 1992
Coarsening Effects on Microstructure Formation in Isopycnic Polymer Solutions and Membranes Produced via Thermally Induced Phase Separation Song, Seung-Won; Torkelson, John M. Macromolecules, Vol. 27, Issue 22 https://doi.org/10.1021/ma00100a024	journal	October 1994
Interference of spinodal waves in thin polymer films Krausch, Georg; Dai, Chi An; Kramer, Edward J. Macromolecules, Vol. 26, Issue 21 https://doi.org/10.1021/ma00073a006	journal	October 1993
Domain growth and wetting in polymer mixtures Wiltzius, Pierre; Cumming, Andrew Physical Review Letters, Vol. 66, Issue 23 https://doi.org/10.1103/PhysRevLett.66.3000	journal	June 1991
Geometric characterization of nanoporous metals Erlebacher, Jonah; McCue, Ian Acta Materialia, Vol. 60, Issue 17 https://doi.org/10.1016/j.actamat.2012.07.059	journal	October 2012
Morphological and topological analysis of coarsened nanoporous gold by x-ray nanotomography Chen, Yu-chen Karen; Chu, Yong S.; Yi, JaeMock Applied Physics Letters, Vol. 96, Issue 4 https://doi.org/10.1063/1.3285175	journal	January 2010
Germanium “quantum dots” embedded in silicon: Quantitative study of self-alignment and coarsening Kienzle, O.; Ernst, F.; Rühle, M. Applied Physics Letters, Vol. 74, Issue 2 https://doi.org/10.1063/1.123277	journal	January 1999
Self-Assembly of Two-Dimensional Islands via Strain-Mediated Coarsening Liu, Feng; Li, Adam H.; Lagally, M. G. Physical Review Letters, Vol. 87, Issue 12 https://doi.org/10.1103/PhysRevLett.87.126103	journal	August 2001
Coarsening of Self-Assembled Ge Quantum Dots on Si(001) Ross, F. M.; Tersoff, J.; Tromp, R. M. Physical Review Letters, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevLett.80.984	journal	February 1998
Electrical conductivity versus strength in a precipitation hardened alloy Miyake, J.; Fine, M. E. Acta Metallurgica et Materialia, Vol. 40, Issue 4 https://doi.org/10.1016/0956-7151(92)90015-7	journal	April 1992
Simulation of coarsening in three-phase solid oxide fuel cell anodes Chen, Hsun-Yi; Yu, Hui-Chia; Scott Cronin, J. Journal of Power Sources, Vol. 196, Issue 3 https://doi.org/10.1016/j.jpowsour.2010.08.010	journal	February 2011
Phase wettability and microstructural evolution in solid oxide fuel cell anode materials Davis, Ryan; Abdeljawad, Fadi; Lillibridge, Jeffrey Acta Materialia, Vol. 78 https://doi.org/10.1016/j.actamat.2014.06.037	journal	October 2014
Experimental and Theoretical Investigation of Degradation Mechanisms by Particle Coarsening in SOFC Electrodes Tanasini, P.; Cannarozzo, M.; Costamagna, P. Fuel Cells, Vol. 9, Issue 5 https://doi.org/10.1002/fuce.200800192	journal	October 2009
Topology-dependent scaling laws for the stiffness and strength of nanoporous gold Mangipudi, K. R.; Epler, E.; Volkert, C. A. Acta Materialia, Vol. 119 https://doi.org/10.1016/j.actamat.2016.08.012	journal	October 2016
The theory of Ostwald ripening Voorhees, P. W. Journal of Statistical Physics, Vol. 38, Issue 1-2 https://doi.org/10.1007/BF01017860	journal	January 1985
The dependence of ostwald ripening kinetics on particle volume fraction Brailsford, A. D.; Wynblatt, P. Acta Metallurgica, Vol. 27, Issue 3 https://doi.org/10.1016/0001-6160(79)90041-5	journal	March 1979
Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction Marqusee, J. A.; Ross, John The Journal of Chemical Physics, Vol. 80, Issue 1 https://doi.org/10.1063/1.446427	journal	January 1984
The kinetics of precipitation from supersaturated solid solutions 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	journal	April 1961
Ostwald Ripening of Two-Phase Mixtures Voorhees, P. W. Annual Review of Materials Science, Vol. 22, Issue 1 https://doi.org/10.1146/annurev.ms.22.080192.001213	journal	August 1992
Review Progress in Ostwald ripening theories and their applications to nickel-base superalloys Part I: Ostwald ripening theories Baldan, A. Journal of Materials Science, Vol. 37, Issue 11, p. 2171-2202 https://doi.org/10.1023/A:1015388912729	journal	January 2002
The dendrite arm spacings of aluminum-copper alloys solidified under steady-state conditions Young, K. P.; Kerkwood, D. H. Metallurgical Transactions A, Vol. 6, Issue 1 https://doi.org/10.1007/BF02673688	journal	January 1975
On the ageing of dendrites Kahlweit, Manfred Scripta Metallurgica, Vol. 2, Issue 5 https://doi.org/10.1016/0036-9748(68)90115-4	journal	May 1968
A model for isothermal dendritic coarsening Reeves, J. J.; Kattamis, T. Z. Scripta Metallurgica, Vol. 5, Issue 3 https://doi.org/10.1016/0036-9748(71)90013-5	journal	March 1971
Evolution of interfacial curvatures of a bicontinuous structure generated via nonconserved dynamics Park, C. -L.; Voorhees, P. W.; Thornton, K. Acta Materialia, Vol. 90 https://doi.org/10.1016/j.actamat.2015.02.037	journal	May 2015
On the theory of normal and abnormal grain growth Hillert, M. Acta Metallurgica, Vol. 13, Issue 3 https://doi.org/10.1016/0001-6160(65)90200-2	journal	March 1965
Overview No. 98 I—Geometric models of crystal growth Taylor, J. E.; Cahn, J. W.; Handwerker, C. A. Acta Metallurgica et Materialia, Vol. 40, Issue 7 https://doi.org/10.1016/0956-7151(92)90090-2	journal	July 1992
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening Allen, Samuel M.; Cahn, John W. Acta Metallurgica, Vol. 27, Issue 6 https://doi.org/10.1016/0001-6160(79)90196-2	journal	June 1979
Phase-Field Models for Microstructure Evolution Chen, Long-Qing Annual Review of Materials Research, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.matsci.32.112001.132041	journal	August 2002
Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method Warren, J. A.; Boettinger, W. J. Acta Metallurgica et Materialia, Vol. 43, Issue 2 https://doi.org/10.1016/0956-7151(94)00285-P	journal	February 1995
On spinodal decomposition Cahn, John W. Acta Metallurgica, Vol. 9, Issue 9 https://doi.org/10.1016/0001-6160(61)90182-1	journal	September 1961
Free Energy of a Nonuniform System. I. Interfacial Free Energy Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 28, Issue 2 https://doi.org/10.1063/1.1744102	journal	February 1958
Morphology and topology in coarsening of domains via non-conserved and conserved dynamics Kwon, Yongwoo; Thornton, K.; Voorhees, P. W. Philosophical Magazine, Vol. 90, Issue 1-4 https://doi.org/10.1080/14786430903260701	journal	January 2010
The dynamics of interfaces during coarsening in solid–liquid systems Fife, J. L.; Gibbs, J. W.; Gulsoy, E. B. Acta Materialia, Vol. 70 https://doi.org/10.1016/j.actamat.2014.01.024	journal	May 2014
Evolution of Geometric Statistics Drew, Donald A. SIAM Journal on Applied Mathematics, Vol. 50, Issue 3 https://doi.org/10.1137/0150038	journal	June 1990
Application of the level-set method to the analysis of an evolving microstructure Park, C. -L.; Voorhees, P. W.; Thornton, K. Computational Materials Science, Vol. 85 https://doi.org/10.1016/j.commatsci.2013.12.022	journal	April 2014
The morphological evolution of dendritic microstructures during coarsening Mendoza, R.; Alkemper, J.; Voorhees, P. W. Metallurgical and Materials Transactions A, Vol. 34, Issue 3 https://doi.org/10.1007/s11661-003-0084-2	journal	March 2003
Theory of Thermal Grooving Mullins, W. W. Journal of Applied Physics, Vol. 28, Issue 3 https://doi.org/10.1063/1.1722742	journal	March 1957

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Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition Vidyasagar, A.; Krödel, S.; Kochmann, D. M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2218 https://doi.org/10.1098/rspa.2018.0535	journal	October 2018

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coarsening
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