Pelce, 1986, Dendrites in the Small Undercooling Limit, Stud Appl Math, 74, 245, 10.1002/sapm1986743245
Lipton, 1984, Dendritic growth into undercooled alloy metals, Mater Sci Eng, 65, 57, 10.1016/0025-5416(84)90199-X
Trivedi, 1994, Dendritic growth, Int Mater Rev, 39, 49, 10.1179/imr.1994.39.2.49
Glicksman, 1994, Dendritic Growth Velocities in Microgravity, Phys Rev Lett, 73, 573, 10.1103/PhysRevLett.73.573
Melendez, 2012, Measurements of dendrite tip growth and sidebranching in succinonitrile–acetone alloys, J Cryst Growth, 340, 175, 10.1016/j.jcrysgro.2011.12.010
Bouissou, 1989, Influence of an external flow on dendritic crystal growth, Phys Rev A, 40, 509, 10.1103/PhysRevA.40.509
Kahlweit, 1970, On the dendritic growth of NH4CI crystals from aqueous solutions. II, J Cryst Growth, 7, 74, 10.1016/0022-0248(70)90118-1
Huang, 1981, Fundamentals of dendritic solidification—I. Steady-state tip growth, Acta Metall, 29, 701, 10.1016/0001-6160(81)90115-2
Bogno, 2013, Growth and interaction of dendritic equiaxed grains: In situ characterization by synchrotron X-ray radiography, Acta Mater, 61, 1303, 10.1016/j.actamat.2012.11.008
Martorano, 2003, A Solutal Interaction Mechanism for the Columnar-to-Equiaxed Transition in Alloy Solidification, Metall Mater Trans A, 34, 1657, 10.1007/s11661-003-0311-x
Mirihanage, 2019, Non-steady 3D dendrite tip growth under diffusive and weakly convective conditions, Materialia, 5, 10.1016/j.mtla.2019.100215
Ruvalcaba, 2007, In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy, Acta Mater, 55, 4287, 10.1016/j.actamat.2007.03.030
Buffet, 2010, Measurement of solute profiles by means of synchrotron X-ray radiography during directional solidification of Al - 4 wt% Cu alloys, Mater Sci Forum, 649, 331, 10.4028/www.scientific.net/MSF.649.331
Shevchenko, 2015, The effect of natural and forced melt convection on dendritic solidification in Ga–In alloys, J Cryst Growth, 417, 1, 10.1016/j.jcrysgro.2014.11.043
Becker, 2016, In-situ solute measurements with a laboratory polychromatic microfocus X-ray source during equiaxed solidification of an Al-Ge alloy, Scripta Mater, 124, 34, 10.1016/j.scriptamat.2016.06.032
Reinhart, 2013, Influence of natural convection during upward directional solidification: A comparison between in situ X-ray radiography and direct simulation of the grain structure, Acta Mater, 61, 4765, 10.1016/j.actamat.2013.04.067
Dupouy, 1998, Effects of gravity on columnar dendritic growth of metallic alloys: flow pattern and mass transfer, J Cryst Growth, 183, 469, 10.1016/S0022-0248(97)00415-6
Rerko, 2003, Effect of melt convection and solid transport on macrosegregation and grain structure in equiaxed Al–Cu alloys, Mater Sci Eng A, 347, 186, 10.1016/S0921-5093(02)00592-0
Murphy, 2016, Direct observation of spatially isothermal equiaxed solidification of an Al–Cu alloy in microgravity on board the MASER13 sounding rocket, J Cryst Growth, 454, 96, 10.1016/j.jcrysgro.2016.08.054
Murphy, 2015, Equiaxed dendritic solidification and grain refiner potency characterised through in situ X-radiography, Acta Mater, 95, 83, 10.1016/j.actamat.2015.04.060
Olmedilla, 2019, Three-dimensional mesoscopic modeling of equiaxed dendritic solidification in a thin sample: effect of convection flow, IOP Conf Ser: Mater Sci Eng, 529, 10.1088/1757-899X/529/1/012040
Becker, 2019, Dendrite orientation transition in Al-Ge alloys, Acta Mater, 165, 666, 10.1016/j.actamat.2018.12.001
McFadden, 2012, A generalised version of an Ivantsov-based dendrite growth model incorporating a facility for solute measurement ahead of the tip, Comput Mater Sci, 55, 245, 10.1016/j.commatsci.2011.12.011
Karma, 1998, Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys Rev E, 57, 4323, 10.1103/PhysRevE.57.4323
Takaki, 2013, Unexpected selection of growing dendrites by very-large-scale phase-field simulation, J Cryst Growth, 382, 21, 10.1016/j.jcrysgro.2013.07.028
Steinbach, 1999, Three-dimensional modeling of equiaxed dendritic growth on a mesoscopic scale, Acta Mater, 47, 971, 10.1016/S1359-6454(98)00380-2
Souhar, 2016, Three-dimensional mesoscopic modeling of equiaxed dendritic solidification of a binary alloy, Comput Mater Sci, 112, 304, 10.1016/j.commatsci.2015.10.028
Murphy, 2016, XRMON-SOL: Isothermal equiaxed solidification of a grain refined Al–20wt%Cu alloy, J Cryst Growth, 440, 38, 10.1016/j.jcrysgro.2016.01.032
Rappaz, 1993, Probabilistic modelling of microstructure formation in solidification processes, Acta Metall Mater, 41, 345, 10.1016/0956-7151(93)90065-Z
Wang, 1996, Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling, Metall Mater Trans A, 27A, 2754, 10.1007/BF02652369
Wu, 2010, Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – Part I: Model description, Comput Mater Sci, 50, 32, 10.1016/j.commatsci.2010.07.005
Tourret, 2012, A. Karma Multi-scale needle-network model of complex dendritic microstructure formation, IOP Conf Ser: Mater Sci Eng, 33, 10.1088/1757-899X/33/1/012095
Tourret, 2013, Multiscale dendritic needle network model of alloy solidification, Acta Mater, 61, 6474, 10.1016/j.actamat.2013.07.026
Tourret, 2015, Corrigendum: Multiscale dendritic needle network model of alloy solidification, Acta Mater, 87, 411, 10.1016/j.actamat.2015.01.026
Tourret, 2016, Three-dimensional dendritic needle network model for alloy solidification, Acta Mater, 120, 240, 10.1016/j.actamat.2016.08.041
Tourret, 2019, Multiscale dendritic needle network model of alloy solidification with fluid flow, J Comp Mat, 162, 206
Isensee, 2020, Three-dimensional needle network model for dendritic growth with fluid flow, IOP Conference Series: Materials Science and Engineering, 861
Fleurrisson, 2019, Modélisation multi-échelle paralléliseé pour la prédiction de structure de grains dendrititque couplant les éléments fini, un automate cellulaire et un réseau des paraboles
Sturz, 2016, Two-dimensional multi-scale dendrite needle network modeling and x-ray radiography of equiaxed alloy solidification in grain-refined Al-3.5 wt-%Ni, Acta Mater, 356, 10.1016/j.actamat.2016.06.005
Geslin, 2016, Numerical investigation of the columnar-to-equiaxed transition using a 2D needle network model, TMS 145th Annual Meeting, 15
Tourret, 2015, Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification, JOM, 67, 1776, 10.1007/s11837-015-1444-2
Tourret, 2015, Three-dimensional Dendritic Needle Network model with application to Al-Cu directional solidification experiments, IOP Conf Ser: Mater Sci Eng, 84, 10.1088/1757-899X/84/1/012082
Tourret, 2017, From Solidification Processing to Microstructure to Mechanical Properties: A Multi-scale X-ray Study of an Al-Cu Alloy Sample, Metall Mater Trans A, 48A, 5529, 10.1007/s11661-017-4302-8
Becker, 2018, Free dendritic tip growth velocities measured in Al-Ge, Phys Rev Mater, 2
Becker, 2017, Solidification kinetics in Al-Cu and Al-Ge alloys investigated by in-situ X-ray radiography
Islam, 2006, A computational thermodynamic model of the Mg–Al–Ge system, J Alloy Compd, 425, 129, 10.1016/j.jallcom.2006.01.050
Becker, 2015, Near-isothermal furnace for in situ and real time X-ray radiography solidification experiments, Rev Sci Instrum, 86, 10.1063/1.4922359
Klein, 2016, X-RISE - A Multifunctional X-ray Radiography Device for Parabolic Flights and Laboratory Use, Int J Microgravity Sci Appl, 33
W.S. Rasband, https://imagej.nih.gov/ij/, National Institutes of Health, Bethesda, Maryland, USA, 1997-2018.
F. Cordelières, https://imagej.nih.gov/ij/plugins/track/track.html, Institut Curie, Orsay, France, 2005.
Boukellal, 2018, Scaling laws governing the growth and interaction of equiaxed Al-Cu dendrites: A study combining experiments with phase-field simulations, Materialia, 1, 62, 10.1016/j.mtla.2018.04.008
Velayutham, 2017, Quantification of Equiaxed Dendrite Motion during Spatially Isothermal Solidification of an Al-Cu Alloy in Microgravity, 296
Barbieri, 1989, Predictions of dendritic growth rates in the linearized solvability theory, Phys Rev A, 39, 5314, 10.1103/PhysRevA.39.5314
Yan, 2011, Crystal Growth in Al72.9Ge27.1 Alloy Melt under Acoustic Levitation Conditions, Chinese Phys Lett, 28, 10.1088/0256-307X/28/7/078101
Kurz, 1992
Dantzig, 2016
J.A. Dantzig, (unpublished research).
Morris, 2002, Complete mapping of the anisotropic free energy of the crystal-melt interface in Al, Phys Rev B, 66, 10.1103/PhysRevB.66.144104
Rebow, 2007, On the dendritic tip stability parameter for aluminium alloy solidification, Scripta Mater, 56, 481, 10.1016/j.scriptamat.2006.11.025
Xu, 2017, Heterogeneous nucleation and grain growth of inoculated aluminium alloys: An integrated study by in-situ X-radiography and numerical modelling, Acta Mater, 140, 224, 10.1016/j.actamat.2017.08.053
Athreya, 2006, On the role of confinement on solidification in pure materials and binary alloys, Philos Mag, 86, 3739, 10.1080/14786430500157060
Boukellal, 2019, Isothermal solidification of Si and Al-Cu: 3D phase-field simulations