Benchmark microgravity experiments and computations for 3D dendritic-array stability in directional solidification

Medjkoune, Mehdi; Lyons, Trevor; Mota, Fátima L.; Tian, Jiefu; Ji, Kaihua; Littles, Louise; Karma, Alain; Bergeon, Nathalie

doi:10.1016/j.actamat.2025.120954

Benchmark microgravity experiments and computations for 3D dendritic-array stability in directional solidification

Journal Article · Sat Mar 29 00:00:00 EDT 2025 · Acta Materialia

DOI:https://doi.org/10.1016/j.actamat.2025.120954· OSTI ID:2555944

Medjkoune, Mehdi ^[1]; Lyons, Trevor ^[2]; Mota, Fátima L. ^[1]; Tian, Jiefu ^[2]; Ji, Kaihua ^[3]; Littles, Louise ^[4]; Karma, Alain ^[2]; ^[1]

Aix Marseille University (France)
Northeastern University, Boston, MA (United States)
Northeastern University, Boston, MA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
NASA Marshall Space Flight Center (MSFC), Huntsville, AL (United States)

In this study, we present a comprehensive quantitative analysis of stability bands for dendritic arrays during directional solidification of a transparent succinonitrile-0.46 wt % camphor alloy, spanning a broad range of pulling velocities. Taking advantage of the microgravity environment aboard the International Space Station where most convection effects are suppressed, we obtain unique measurements that quantify the stable primary spacing range of spatially extended three-dimensional dendritic array structures under purely diffusive growth conditions. Through carefully designed velocity jump experiments and detailed examination of sub-grain boundary dynamics, we characterize key instabilities, including elimination and tertiary branching, shedding new light on the mechanisms governing dynamic dendritic spacing selection in extended 3D arrays. Phase field simulations are performed to characterize the stability limits of dendritic array structures for quantitative comparison with the flight experiments. Although the simulations capture general trends, significant deviations are noted at the upper stability boundary, indicating the influence of additional, unexplored factors. These findings contribute to a deeper understanding of dendritic growth dynamics and offer valuable benchmark data that could aid in refining predictive models and improving control of dendritic microstructures in metallurgical applications.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Aeronautics and Space Administration (NASA); French Space Agency (CNES)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2555944

Report Number(s):: LLNL--JRNL-2001408

Journal Information:: Acta Materialia, Journal Name: Acta Materialia Vol. 292; ISSN 1359-6454

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (100)

Phase-Field Methods in Materials Science and Engineering Provatas, Nikolas; Elder, Ken Wiley‐VCH Verlag GmbH & Co. https://doi.org/10.1002/9783527631520	book	January 2010
Nonlinear Preconditioning for Diffuse Interfaces Glasner, Karl Journal of Computational Physics, Vol. 174, Issue 2 https://doi.org/10.1006/jcph.2001.6933	journal	December 2001
Effect of dendritic arm spacing on mechanical properties and corrosion resistance of Al 9 Wt Pct Si and Zn 27 Wt Pct Al alloys Osorio, Wislei R.; Goulart, Pedro R.; Garcia, Amauri Metallurgical and Materials Transactions A, Vol. 37, Issue 8 https://doi.org/10.1007/BF02586225	journal	August 2006
Solidification processing Flemings, M. C. Metallurgical Transactions, Vol. 5, Issue 10 https://doi.org/10.1007/BF02643923	journal	October 1974
Interdendritic Spacing: Part I. Experimental Studies Somboonsuk, K.; Mason, J. T.; Trivedi, R. Metallurgical and Materials Transactions A, Vol. 15, Issue 6 https://doi.org/10.1007/BF02644688	journal	June 1984
Interdendritic Spacing: Part II. A Comparison of Theory and Experiment Trivedi, R. Metallurgical and Materials Transactions A, Vol. 15, Issue 6 https://doi.org/10.1007/BF02644689	journal	June 1984
Numerical modeling of cellular/dendritic array growth: spacing and structure predictions Hunt, J. D.; Lu, S. Z. Metallurgical and Materials Transactions A, Vol. 27, Issue 3 https://doi.org/10.1007/BF02648950	journal	March 1996
Permeability for flow of interdendritic liquid in columnar-dendritic alloys Poirier, D. R. Metallurgical Transactions B, Vol. 18, Issue 1 https://doi.org/10.1007/BF02658450	journal	March 1987
Flow of interdendritic liquid and permeability in pb-20 Wt Pct Sn alloys Nasser-Rafi, R.; Deshmukh, R.; Poirier, D. R. Metallurgical Transactions A, Vol. 16, Issue 12 https://doi.org/10.1007/BF02670426	journal	December 1985
Scaling of intragranuiar dendritic microstructure in ingot solidification Bouchard, D.; Kirkaldy, J. S. Metallurgical and Materials Transactions B, Vol. 27, Issue 1 https://doi.org/10.1007/BF02915081	journal	February 1996
In situ characterization of interface-microstructure dynamics in 3D-Directional Solidification of model transparent alloys Trivedi, Rohit; Bergeon, Nathalie; Billia, Bernard Microgravity - Science and Technology, Vol. 16, Issue 1-4 https://doi.org/10.1007/BF02945963	journal	March 2005
Dynamics of interface pattern formation in 3D alloy solidification: first results from experiments in the DECLIC directional solidification insert on the International Space Station Bergeon, Nathalie; Ramirez, Anthony; Chen, Liang Journal of Materials Science, Vol. 46, Issue 19 https://doi.org/10.1007/s10853-011-5382-2	journal	February 2011
Solidification researches using transparent model materials — A review Huang, WeiDong; Wang, LiLin Science China Technological Sciences, Vol. 55, Issue 2 https://doi.org/10.1007/s11431-011-4689-1	journal	December 2011
Modeling of primary spacing selection in dendrite arrays during directional solidification Ma, Dexin Metallurgical and Materials Transactions B, Vol. 33, Issue 2 https://doi.org/10.1007/s11663-002-0007-4	journal	April 2002
Response of primary dendrite spacing to varying temperature gradient during directional solidification Ma, Dexin Metallurgical and Materials Transactions B, Vol. 35, Issue 4 https://doi.org/10.1007/s11663-004-0013-9	journal	August 2004
Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification Tourret, Damien; Clarke, Amy J.; Imhoff, Seth D. JOM, Vol. 67, Issue 8 https://doi.org/10.1007/s11837-015-1444-2	journal	May 2015
Convection Effects During Bulk Transparent Alloy Solidification in DECLIC-DSI and Phase-Field Simulations in Diffusive Conditions Mota, F. L.; Song, Y.; Pereda, J. JOM, Vol. 69, Issue 8 https://doi.org/10.1007/s11837-017-2395-6	journal	May 2017
Interferometric method for the analysis of dendrite growth and shape in 3D extended patterns in transparent alloys Bergeon, N.; Weiss, C.; Mangelinck-Noël, N. Transactions of the Indian Institute of Metals, Vol. 62, Issue 4-5 https://doi.org/10.1007/s12666-009-0061-6	journal	October 2009
The redistribution of solute atoms during the solidification of metals Tiller, W. A.; Jackson, K. A.; Rutter, J. W. Acta Metallurgica, Vol. 1, Issue 4 https://doi.org/10.1016/0001-6160(53)90126-6	journal	July 1953
Transparent compounds that freeze like metals Jackson, K. A.; Hunt, J. D. Acta Metallurgica, Vol. 13, Issue 11 https://doi.org/10.1016/0001-6160(65)90061-1	journal	November 1965
Dendrite growth at the limit of stability: tip radius and spacing Kurz, W.; Fisher, D. J. Acta Metallurgica, Vol. 29, Issue 1 https://doi.org/10.1016/0001-6160(81)90082-1	journal	January 1981
Measurements of cell and primary dendrite arm spacings in directionally solidified aluminium alloys McCartney, D. G.; Hunt, J. D. Acta Metallurgica, Vol. 29, Issue 11 https://doi.org/10.1016/0001-6160(81)90111-5	journal	November 1981
Overview 12: Fundamentals of dendritic solidification—I. Steady-state tip growth Huang, S. -C.; Glicksman, M. E. Acta Metallurgica, Vol. 29, Issue 5 https://doi.org/10.1016/0001-6160(81)90115-2	journal	May 1981
Dynamical studies of dendritic growth Somboonsuk, K.; Trivedi, R. Acta Metallurgica, Vol. 33, Issue 6 https://doi.org/10.1016/0001-6160(85)90198-1	journal	June 1985
Pattern formation during the directional solidification of binary systems Trivedi, R.; Somboonsuk, K. Acta Metallurgica, Vol. 33, Issue 6 https://doi.org/10.1016/0001-6160(85)90199-3	journal	June 1985
Theory of microstructural development during rapid solidification Kurz, W.; Giovanola, B.; Trivedi, R. Acta Metallurgica, Vol. 34, Issue 5 https://doi.org/10.1016/0001-6160(86)90056-8	journal	May 1986
Numerical finite difference model for steady state cellular array growth Hunt, J. D.; McCartney, D. G. Acta Metallurgica, Vol. 35, Issue 1 https://doi.org/10.1016/0001-6160(87)90216-1	journal	January 1987
Cellular spacings—I. Steady-state growth Eshelman, M. A.; Seetharaman, V.; Trivedi, R. Acta Metallurgica, Vol. 36, Issue 4 https://doi.org/10.1016/0001-6160(88)90169-1	journal	April 1988
Cellular spacings—II. Dynamical studies Seetharaman, V.; Eshelman, M. A.; Trivedi, R. Acta Metallurgica, Vol. 36, Issue 4 https://doi.org/10.1016/0001-6160(88)90170-8	journal	April 1988
Cellular and dendritic growth. II Burden, M. H.; Hunt, J. D. Journal of Crystal Growth, Vol. 22, Issue 2 https://doi.org/10.1016/0022-0248(74)90127-4	journal	April 1974
Theory of dendritic growth during the directional solidification of binary alloys Trivedi, R. Journal of Crystal Growth, Vol. 49, Issue 2 https://doi.org/10.1016/0022-0248(80)90157-8	journal	June 1980
Primary dendrite spacing I. Experimental studies Mason, J. T.; Verhoeven, J. D.; Trivedi, R. Journal of Crystal Growth, Vol. 59, Issue 3 https://doi.org/10.1016/0022-0248(82)90372-4	journal	October 1982
Effects of crystal-melt interfacial energy anisotropy on dendritic morphology and growth kinetics Glicksman, M. E.; Singh, N. B. Journal of Crystal Growth, Vol. 98, Issue 3 https://doi.org/10.1016/0022-0248(89)90142-5	journal	November 1989
A numerical analysis of dendritic and cellular array growth: the spacing adjustment mechanisms Lu, Shu-Zu; Hunt, J. D. Journal of Crystal Growth, Vol. 123, Issue 1-2 https://doi.org/10.1016/0022-0248(92)90006-5	journal	September 1992
Primary spacing selection of constrained dendritic growth Weidong, Huang; Xingguo, Geng; Yaohe, Zhou Journal of Crystal Growth, Vol. 134, Issue 1-2 https://doi.org/10.1016/0022-0248(93)90015-O	journal	November 1993
Permeability for flow parallel to primary dendrite arms Ganesan, S.; Chan, C. L.; Poirier, D. R. Materials Science and Engineering: A, Vol. 151, Issue 1 https://doi.org/10.1016/0921-5093(92)90186-5	journal	April 1992
A numerical analysis of time dependent isolated dendritic growth for conditions near the steady state Hunt, J. D. Acta Metallurgica et Materialia, Vol. 38, Issue 3 https://doi.org/10.1016/0956-7151(90)90146-8	journal	March 1990
A numerical analysis of dendritic and cellular growth of a pure material investigating the transition from “array” to “isolated” growth Hunt, J. D. Acta Metallurgica et Materialia, Vol. 39, Issue 9 https://doi.org/10.1016/0956-7151(91)90182-Z	journal	September 1991
Solidification microstructures: A conceptual approach Trivedi, R.; Kurz, W. Acta Metallurgica et Materialia, Vol. 42, Issue 1 https://doi.org/10.1016/0956-7151(94)90044-2	journal	January 1994
Primary spacing selection in directionally solidified alloys Han, S. H.; Trivedi, R. Acta Metallurgica et Materialia, Vol. 42, Issue 1 https://doi.org/10.1016/0956-7151(94)90045-0	journal	January 1994
Cellular and dendritic growth in rapidly solidified AlFe and AlCu alloys Lu, Shu-Zu; Hunt, J. D.; Gilgien, P. Acta Metallurgica et Materialia, Vol. 42, Issue 5 https://doi.org/10.1016/0956-7151(94)90375-1	journal	May 1994
Solidification of aluminium–lithium alloys near the cell/dendrite transition-influence of solutal convection Drevet, B.; Nguyen Thi, H.; Camel, D. Journal of Crystal Growth, Vol. 218, Issue 2-4 https://doi.org/10.1016/S0022-0248(00)00567-4	journal	September 2000
Dendritic array growth in the systems NH4Cl–H2O and [CH2CN]2–H2O: steady state measurements and analysis Hansen, George; Liu, Shan; Lu, Shu-Zu Journal of Crystal Growth, Vol. 234, Issue 4 https://doi.org/10.1016/S0022-0248(01)01679-7	journal	February 2002
Prediction of average spacing for constrained cellular/dendritic growth Ding, Guolu; Huang, Weidong; Lin, Xin Journal of Crystal Growth, Vol. 177, Issue 3-4 https://doi.org/10.1016/S0022-0248(96)01081-0	journal	June 1997
On the solidification of dendritic arrays: An asymptotic theory for the directional solidification of slender needle crystals Spencer, Brian J.; Huppert, Herbert E. Acta Materialia, Vol. 45, Issue 4 https://doi.org/10.1016/S1359-6454(96)00281-9	journal	April 1997
History-dependent selection of primary cellular/dendritic spacing during unidirectional solidification in aluminum alloys Lin, X.; Huang, W.; Feng, J. Acta Materialia, Vol. 47, Issue 11 https://doi.org/10.1016/S1359-6454(99)00166-4	journal	September 1999
Pattern formation in solidification Hunt, J. D. Science and Technology of Advanced Materials, Vol. 2, Issue 1 https://doi.org/10.1016/S1468-6996(01)00040-7	journal	January 2001
Microstructure development in the directionally solidified Al–4.0 wt% Cu alloy system Trivedi, R.; Liu, S.; Mazumder, P. Science and Technology of Advanced Materials, Vol. 2, Issue 1 https://doi.org/10.1016/S1468-6996(01)00062-6	journal	January 2001
Lamellar eutectic growth with anisotropic interphase boundaries: Experimental study using the rotating directional solidification method Akamatsu, S.; Bottin-Rousseau, S.; Şerefoğlu, M. Acta Materialia, Vol. 60, Issue 6-7 https://doi.org/10.1016/j.actamat.2012.02.033	journal	April 2012
Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure Reinhart, G.; Gandin, Ch. -A.; Mangelinck-Noël, N. Acta Materialia, Vol. 61, Issue 13 https://doi.org/10.1016/j.actamat.2013.04.067	journal	August 2013
Multiscale dendritic needle network model of alloy solidification Tourret, D.; Karma, A. Acta Materialia, Vol. 61, Issue 17 https://doi.org/10.1016/j.actamat.2013.07.026	journal	October 2013
Growth competition of columnar dendritic grains: A phase-field study Tourret, D.; Karma, A. Acta Materialia, Vol. 82 https://doi.org/10.1016/j.actamat.2014.08.049	journal	January 2015
Initial transient behavior in directional solidification of a bulk transparent model alloy in a cylinder Mota, F. L.; Bergeon, N.; Tourret, D. Acta Materialia, Vol. 85 https://doi.org/10.1016/j.actamat.2014.11.024	journal	February 2015
In situ observation of solidification patterns in diffusive conditions Akamatsu, Silvère; Nguyen-Thi, Henri Acta Materialia, Vol. 108 https://doi.org/10.1016/j.actamat.2016.01.024	journal	April 2016
Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study Tourret, D.; Song, Y.; Clarke, A. J. Acta Materialia, Vol. 122 https://doi.org/10.1016/j.actamat.2016.09.055	journal	January 2017
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. Acta Materialia, Vol. 129 https://doi.org/10.1016/j.actamat.2017.02.047	journal	May 2017
Thermal-field effects on interface dynamics and microstructure selection during alloy directional solidification Song, Y.; Tourret, D.; Mota, F. L. Acta Materialia, Vol. 150 https://doi.org/10.1016/j.actamat.2018.03.012	journal	May 2018
Effect of sub-boundaries on primary spacing dynamics during 3D directional solidification conducted on DECLIC-DSI Mota, F. L.; Pereda, J.; Ji, K. Acta Materialia, Vol. 204 https://doi.org/10.1016/j.actamat.2020.116500	journal	February 2021
Multiscale prediction of microstructure length scales in metallic alloy casting Bellón, B.; Boukellal, A. K.; Isensee, T. Acta Materialia, Vol. 207 https://doi.org/10.1016/j.actamat.2021.116686	journal	April 2021
Effect of convection on directional solidification in transparent succinonitrile–2.2wt.%(d)camphor alloy Witusiewicz, V. T.; Sturz, L.; Viardin, A. Acta Materialia, Vol. 216 https://doi.org/10.1016/j.actamat.2021.117086	journal	September 2021
Influence of macroscopic interface curvature on dendritic patterns during directional solidification of bulk samples: Experimental and phase-field studies Mota, F. L.; Ji, K.; Littles, L. Strutzenberg Acta Materialia, Vol. 250 https://doi.org/10.1016/j.actamat.2023.118849	journal	May 2023
The roles of macrosegregation and of dendritic array spacings on the electrochemical behavior of an Al–4.5wt.% Cu alloy Osório, W. R.; Spinelli, J. E.; Ferreira, I. L. Electrochimica Acta, Vol. 52, Issue 9 https://doi.org/10.1016/j.electacta.2006.10.004	journal	February 2007
The effect of the dendritic microstructure on the corrosion resistance of Zn–Al alloys Osório, Wislei Riuper; Freire, Célia Marina; Garcia, Amauri Journal of Alloys and Compounds, Vol. 397, Issue 1-2 https://doi.org/10.1016/j.jallcom.2005.01.035	journal	July 2005
An experimental method for the in situ observation of eutectic growth patterns in bulk samples of transparent alloys Bottin-Rousseau, Sabine; Perrut, Mikaël; Picard, Christian Journal of Crystal Growth, Vol. 306, Issue 2 https://doi.org/10.1016/j.jcrysgro.2007.05.035	journal	August 2007
Correlation between thermal parameters, structures, dendritic spacing and corrosion behavior of Zn–Al alloys with columnar to equiaxed transition Ares, A. E.; Gassa, L. M.; Gueijman, S. F. Journal of Crystal Growth, Vol. 310, Issue 7-9 https://doi.org/10.1016/j.jcrysgro.2007.11.169	journal	April 2008
Top-view approach for in-situ observation of growth morphology in bulk transparent organic alloys Witusiewicz, V. T.; Hecht, U.; Rex, S. Journal of Crystal Growth, Vol. 353, Issue 1 https://doi.org/10.1016/j.jcrysgro.2012.04.040	journal	August 2012
Permeability of interdendritic channels Santos, R. G.; Melo, M. L. N. M. Materials Science and Engineering: A, Vol. 391, Issue 1-2 https://doi.org/10.1016/j.msea.2004.08.048	journal	January 2005
Cell invasion during competitive growth of polycrystalline solidification patterns Song, Younggil; Mota, Fatima L.; Tourret, Damien Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-37458-0	journal	April 2023
Stability of a Planar Interface During Solidification of a Dilute Binary Alloy Mullins, W. W.; Sekerka, R. F. Journal of Applied Physics, Vol. 35, Issue 2 https://doi.org/10.1063/1.1713333	journal	February 1964
Solidification furnace for in situ observation of bulk transparent systems and image analysis methods Mota, F. L.; Medjkoune, M.; Littles, L. Strutzenberg Review of Scientific Instruments, Vol. 94, Issue 6 https://doi.org/10.1063/5.0150391	journal	June 2023
Evolution of dendritic patterns during alloy solidification: From the initial instability to the steady state Losert, W.; Shi, B. Q.; Cummins, H. Z. Proceedings of the National Academy of Sciences, Vol. 95, Issue 2 https://doi.org/10.1073/pnas.95.2.439	journal	January 1998
Progress in modelling solidification microstructures in metals and alloys. Part II: dendrites from 2001 to 2018 Kurz, Wilfried; Rappaz, Michel; Trivedi, Rohit International Materials Reviews, Vol. 66, Issue 1 https://doi.org/10.1080/09506608.2020.1757894	journal	May 2020
Phase-field models in materials science Steinbach, Ingo Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 7 https://doi.org/10.1088/0965-0393/17/7/073001	journal	July 2009
Surface-tension-anisotropy measurements of succinonitrile and pivalic acid: Comparison with microscopic solvability theory Muschol, M.; Liu, D.; Cummins, H. Z. Physical Review A, Vol. 46, Issue 2 https://doi.org/10.1103/PhysRevA.46.1038	journal	July 1992
Testing shape selection in directional solidification Bechhoefer, John; Libchaber, Albert Physical Review B, Vol. 35, Issue 3 https://doi.org/10.1103/PhysRevB.35.1393	journal	January 1987
Oscillatory-nonoscillatory transitions for inclined cellular patterns in three-dimensional directional solidification Mota, Fatima L.; Bergeon, Nathalie; Karma, Alain Physical Review E, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevE.102.032803	journal	September 2020
Experimental characterization and theoretical analysis of cell tip oscillations in directional solidification Pereda, J.; Mota, F. L.; Debierre, J. -M. Physical Review E, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevE.102.032804	journal	September 2020
Prediction of dendritic spacings in a directional-solidification experiment Warren, James A.; Langer, J. S. Physical Review E, Vol. 47, Issue 4 https://doi.org/10.1103/PhysRevE.47.2702	journal	April 1993
Quantitative phase-field modeling of dendritic growth in two and three dimensions Karma, Alain; Rappel, Wouter-Jan Physical Review E, Vol. 57, Issue 4 https://doi.org/10.1103/PhysRevE.57.4323	journal	April 1998
Three-dimensional dendrite-tip morphology at low undercooling Karma, Alain; Lee, Youngyih H.; Plapp, Mathis Physical Review E, Vol. 61, Issue 4 https://doi.org/10.1103/PhysRevE.61.3996	journal	April 2000
Quantitative phase-field model of alloy solidification Echebarria, Blas; Folch, Roger; Karma, Alain Physical Review E, Vol. 70, Issue 6 https://doi.org/10.1103/PhysRevE.70.061604	journal	December 2004
Quantitative phase-field modeling of two-phase growth Folch, R.; Plapp, M. Physical Review E, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevE.72.011602	journal	July 2005
Phase-field study of three-dimensional steady-state growth shapes in directional solidification Gurevich, Sebastian; Karma, Alain; Plapp, Mathis Physical Review E, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevE.81.011603	journal	January 2010
Onset of sidebranching in directional solidification Echebarria, Blas; Karma, Alain; Gurevich, Sebastian Physical Review E, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevE.81.021608	journal	February 2010
Phase-field study of spacing evolution during transient growth Gurevich, Sebastian; Amoorezaei, Morteza; Provatas, Nikolas Physical Review E, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevE.82.051606	journal	November 2010
Oscillatory cellular patterns in three-dimensional directional solidification Tourret, D.; Debierre, J. -M.; Song, Y. Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.042401	journal	October 2015
Experimental observation of oscillatory cellular patterns in three-dimensional directional solidification Pereda, J.; Mota, F. L.; Chen, L. Physical Review E, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevE.95.012803	journal	January 2017
Spatiotemporal Dynamics of Oscillatory Cellular Patterns in Three-Dimensional Directional Solidification Bergeon, N.; Tourret, D.; Chen, L. Physical Review Letters, Vol. 110, Issue 22 https://doi.org/10.1103/PhysRevLett.110.226102	journal	May 2013
Pattern Selection in Dendritic Solidification Ben-Jacob, E.; Goldenfeld, Nigel; Kotliar, B. G. Physical Review Letters, Vol. 53, Issue 22 https://doi.org/10.1103/PhysRevLett.53.2110	journal	November 1984
Needle-crystal solution in three-dimensional dendritic growth Brener, Efim Physical Review Letters, Vol. 71, Issue 22 https://doi.org/10.1103/PhysRevLett.71.3653	journal	November 1993
Theory of pattern selection in three-dimensional nonaxisymmetric dendritic growth Ben Amar, Martine; Brener, Efim Physical Review Letters, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevLett.71.589	journal	July 1993
Dendritic Growth Velocities in Microgravity Glicksman, M. E.; Koss, M. B.; Winsa, E. A. Physical Review Letters, Vol. 73, Issue 4 https://doi.org/10.1103/PhysRevLett.73.573	journal	July 1994
Phase-Field Formulation for Quantitative Modeling of Alloy Solidification Karma, Alain Physical Review Letters, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevLett.87.115701	journal	August 2001
Localized Microstructures Induced by Fluid Flow in Directional Solidification Jamgotchian, H.; Bergeon, N.; Benielli, D. Physical Review Letters, Vol. 87, Issue 16 https://doi.org/10.1103/PhysRevLett.87.166105	journal	October 2001
Instabilities and pattern formation in crystal growth Langer, J. S. Reviews of Modern Physics, Vol. 52, Issue 1 https://doi.org/10.1103/RevModPhys.52.1	journal	January 1980
Analysis of gravity effects during binary alloy directional solidification by comparison of microgravity and Earth experiments with in situ observation Bergeon, Nathalie; Reinhart, Guillaume; Mota, Fatima L. The European Physical Journal E, Vol. 44, Issue 7 https://doi.org/10.1140/epje/s10189-021-00102-0	journal	July 2021
Modelling of macrosegregation: applications and future needs Beckermann, C. International Materials Reviews, Vol. 47, Issue 5 https://doi.org/10.1179/095066002225006557	journal	October 2002
Dendritic growth Trivedi, R.; Kurz, W. International Materials Reviews, Vol. 39, Issue 2 https://doi.org/10.1179/imr.1994.39.2.49	journal	January 1994
On Directional Dendritic Growth and Primary Spacing—A Review Strickland, Joel; Nenchev, Bogdan; Dong, Hongbiao Crystals, Vol. 10, Issue 7 https://doi.org/10.3390/cryst10070627	journal	July 2020
Effects of the Interface Curvature and Dendrite Orientation in Directional Solidification of Bulk Transparent Alloys Weiss, Cedric; Bergeon, Nathalie; Mangelinck-Noël, Nathalie Materials Science Forum, Vol. 508 https://doi.org/10.4028/www.scientific.net/MSF.508.337	journal	March 2006

Figures / Tables (19)

Similar Records

Dendritic growth tip velocities and radii of curvature in microgravity

Journal Article · Tue Nov 30 23:00:00 EST 1999 · Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science · OSTI ID:20005984

Three-dimensional dendritic needle network model for alloy solidification

Journal Article · Thu Sep 01 00:00:00 EDT 2016 · Acta Materialia · OSTI ID:1458925

Related Subjects

36 MATERIALS SCIENCE
Dendritic spacing
Directional solidification
Microgravity experiment
Phase field simulations
Transparent alloy

Benchmark microgravity experiments and computations for 3D dendritic-array stability in directional solidification

Citation Formats

References (100)

Figures / Tables (19)

Similar Records

Related Subjects