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Volumn 117, Issue , 2016, Pages 356-370

Two-dimensional multi-scale dendrite needle network modeling and x-ray radiography of equiaxed alloy solidification in grain-refined Al-3.5 wt-%Ni

Author keywords

Dendrite needle network modeling; Directional solidification; Equiaxed growth; X ray radiography

Indexed keywords

ALUMINUM; COMPUTATIONAL EFFICIENCY; NEEDLES; NICKEL; NUCLEATION; PARAMETER ESTIMATION; SOLIDIFICATION; UNDERCOOLING;

EID: 84989953059     PISSN: 13596454     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.actamat.2016.06.005     Document Type: Article
Times cited : (12)

References (58)
  • 1
    • 0004130692 scopus 로고
    • Fundamentals of Solidification
    • third ed. Trans Tech Publications Aedermannsdorf
    • [1] Kurz, W., Fisher, D.J., Fundamentals of Solidification. third ed., 1989, Trans Tech Publications, Aedermannsdorf.
    • (1989)
    • Kurz, W.1    Fisher, D.J.2
  • 2
    • 55749099721 scopus 로고    scopus 로고
    • Solidification
    • EPFL Press Switzerland
    • [2] Dantzig, J.A., Rappaz, M., Solidification. 2009, EPFL Press, Switzerland.
    • (2009)
    • Dantzig, J.A.1    Rappaz, M.2
  • 3
    • 84958873936 scopus 로고    scopus 로고
    • Recent advances in grain refinement of light metals and alloys
    • [3] Easton, M.A., Qian, M., Prasad, A., StJohn, D.H., Recent advances in grain refinement of light metals and alloys. Curr. Opin. Solid State Mat. Sci. 20 (2016), 13–24, 10.1016/j.cossms.2015.10.001.
    • (2016) Curr. Opin. Solid State Mat. Sci. , vol.20 , pp. 13-24
    • Easton, M.A.1    Qian, M.2    Prasad, A.3    StJohn, D.H.4
  • 4
    • 84908294232 scopus 로고    scopus 로고
    • Growth competition of columnar dendritic grains: a phase-field study
    • [4] Tourret, D., Karma, A., Growth competition of columnar dendritic grains: a phase-field study. Acta Mater 82 (2015), 64–83, 10.1016/j.actamat.2014.08.049.
    • (2015) Acta Mater , vol.82 , pp. 64-83
    • Tourret, D.1    Karma, A.2
  • 5
    • 33747164548 scopus 로고    scopus 로고
    • Columnar to equiaxed grain transition in as solidified alloys
    • [5] Spittle, J.A., Columnar to equiaxed grain transition in as solidified alloys. Int. Mater. Rev. 51 (2006), 247–269, 10.1179/174328006X102493.
    • (2006) Int. Mater. Rev. , vol.51 , pp. 247-269
    • Spittle, J.A.1
  • 7
    • 84892371572 scopus 로고    scopus 로고
    • Structures in directionally solidified Al–7 wt% Si alloys: benchmark experiments under microgravity
    • [7] Liu, D.R., Mangelinck-Noel, N., Gandin, Ch. -A., Zimmermann, G., Sturz, L., Nguyen-Thi, H., Billia, B., Structures in directionally solidified Al–7 wt% Si alloys: benchmark experiments under microgravity. Acta Mater 64 (2014), 253–265, 10.1016/j.actamat.2013.10.038.
    • (2014) Acta Mater , vol.64 , pp. 253-265
    • Liu, D.R.1    Mangelinck-Noel, N.2    Gandin, C.-A.3    Zimmermann, G.4    Sturz, L.5    Nguyen-Thi, H.6    Billia, B.7
  • 8
    • 84883741669 scopus 로고    scopus 로고
    • Multiscale dendritic needle network model of alloy solidification
    • DOI: 10.1016/j.actamat.2013.07.026 and corrigendum Acta Mater. 87 (2015) 411. DOI: 10.1016/j.actamat.2015.01.026
    • [8] Tourret, D., Karma, A., Multiscale dendritic needle network model of alloy solidification. Acta Mater 61 (2013), 6474–6491 DOI: 10.1016/j.actamat.2013.07.026 and corrigendum Acta Mater. 87 (2015) 411. DOI: 10.1016/j.actamat.2015.01.026.
    • (2013) Acta Mater , vol.61 , pp. 6474-6491
    • Tourret, D.1    Karma, A.2
  • 10
    • 12244269743 scopus 로고    scopus 로고
    • X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy
    • [10] Mathiesen, R.H., Arnberg, L., X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy. Acta Mater 53 (2005), 947–956, 10.1016/j.actamat.2004.10.050.
    • (2005) Acta Mater , vol.53 , pp. 947-956
    • Mathiesen, R.H.1    Arnberg, L.2
  • 11
    • 39549097741 scopus 로고    scopus 로고
    • X-ray radioscopic visualization of the solutal convection during solidification of a Ga-30 Wt Pct in alloy
    • [11] Boden, S., Eckert, S., Willers, B., Gerbeth, G., X-ray radioscopic visualization of the solutal convection during solidification of a Ga-30 Wt Pct in alloy. Metall. Mater. Trans. A 39A (2008), 613–623, 10.1007/s11661-007-9462-5.
    • (2008) Metall. Mater. Trans. A , vol.39A , pp. 613-623
    • Boden, S.1    Eckert, S.2    Willers, B.3    Gerbeth, G.4
  • 12
    • 29544452608 scopus 로고    scopus 로고
    • Stray crystal formation in Al–20 wt% Cu studied by synchrotron X-ray video microscopy
    • [12] Mathiesen, R.H., Arnberg, L., Stray crystal formation in Al–20 wt% Cu studied by synchrotron X-ray video microscopy. Mat. Sci. Eng. A 413 (2005), 283–287, 10.1016/j.msea.2005.08.160.
    • (2005) Mat. Sci. Eng. A , vol.413 , pp. 283-287
    • Mathiesen, R.H.1    Arnberg, L.2
  • 13
    • 34250872185 scopus 로고    scopus 로고
    • In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy
    • [13] Ruvalcaba, D., Mathiesen, R.H., Eskin, D.G., Arnberg, L., Katgerman, L., In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy. Acta Mater 55 (2007), 4287–4292, 10.1016/j.actamat.2007.03.030.
    • (2007) Acta Mater , vol.55 , pp. 4287-4292
    • Ruvalcaba, D.1    Mathiesen, R.H.2    Eskin, D.G.3    Arnberg, L.4    Katgerman, L.5
  • 14
    • 84899728218 scopus 로고    scopus 로고
    • Situ and real-time observation of the solidification process of Al-20 mass%Cu alloy by synchrotron x-ray radiography
    • [14] Kang, M., Gao, H., Shu, D., Wang, J., Li, F., Fu, Y., Ling, L., Sun, B., Situ and real-time observation of the solidification process of Al-20 mass%Cu alloy by synchrotron x-ray radiography. Mater. Trans. 55 (2014), 774–778.
    • (2014) Mater. Trans. , vol.55 , pp. 774-778
    • Kang, M.1    Gao, H.2    Shu, D.3    Wang, J.4    Li, F.5    Fu, Y.6    Ling, L.7    Sun, B.8
  • 15
    • 84938856616 scopus 로고    scopus 로고
    • In situ study the effect of refiner on the microstructure evolution of variable cross-section structure by synchrotron X-ray radiography
    • [15] Li, F., Zhang, J., Dai, Y., Bian, F., Fu, Y., Yin, F., Sun, B., In situ study the effect of refiner on the microstructure evolution of variable cross-section structure by synchrotron X-ray radiography. J. Cryst. Growth 428 (2015), 1–7, 10.1016/j.jcrysgro.2015.07.016.
    • (2015) J. Cryst. Growth , vol.428 , pp. 1-7
    • Li, F.1    Zhang, J.2    Dai, Y.3    Bian, F.4    Fu, Y.5    Yin, F.6    Sun, B.7
  • 16
    • 84879411744 scopus 로고    scopus 로고
    • Influence of natural convection during upward directional solidification: a comparison between in situ X-ray radiography and direct simulation of the grain structure
    • [16] Reinhart, G., Gandin, Ch.-A., Mangelinck-Noel, N., Nguyen-Thi, H., Spinelli, J.-E., Baruchel, J., Billia, B., 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 (2013), 4765–4777, 10.1016/j.actamat.2013.04.067.
    • (2013) Acta Mater , vol.61 , pp. 4765-4777
    • Reinhart, G.1    Gandin, C.-A.2    Mangelinck-Noel, N.3    Nguyen-Thi, H.4    Spinelli, J.-E.5    Baruchel, J.6    Billia, B.7
  • 17
    • 84873087203 scopus 로고    scopus 로고
    • Growth and interaction of dendritic equiaxed grains: in situ characterization by synchrotron X-ray radiography
    • [17] Bogno, A., Nguyen-Thi, H., Reinhart, G., Billia, B., Baruchel, J., Growth and interaction of dendritic equiaxed grains: in situ characterization by synchrotron X-ray radiography. Acta Mater 61 (2013), 1303–1315, 10.1016/j.actamat.2012.11.008.
    • (2013) Acta Mater , vol.61 , pp. 1303-1315
    • Bogno, A.1    Nguyen-Thi, H.2    Reinhart, G.3    Billia, B.4    Baruchel, J.5
  • 18
    • 77955506987 scopus 로고    scopus 로고
    • Analysis of an equiaxed dendrite growth model with comparisons to in-situ results of equiaxed dendritic growth in an Al-Ge alloy
    • [18] McFadden, S., Schaffer, P.L., Mathiesen, R.H., D.J Browne, Analysis of an equiaxed dendrite growth model with comparisons to in-situ results of equiaxed dendritic growth in an Al-Ge alloy. Mat. Sci. Forum 654–656 (2010), 1359–1362, 10.4028/www.scientific.net/MSF.654-656.1359.
    • (2010) Mat. Sci. Forum , vol.654-656 , pp. 1359-1362
    • McFadden, S.1    Schaffer, P.L.2    Mathiesen, R.H.3    D.J Browne4
  • 20
    • 84858258539 scopus 로고    scopus 로고
    • CET during the solidification of refined Al-3.5wt%Ni alloys and characterization of the subsequent grain structure
    • [20] Reinhart, G., Nguyen-Thi, H., Mangelinck-Noël, N., Billia, B., Schenk, T., Baruchel, J., CET during the solidification of refined Al-3.5wt%Ni alloys and characterization of the subsequent grain structure. IOP Conf. Ser. Mater. Sci. Eng., 27, 2011, 012011, 10.1088/1757-899X/27/1/012011.
    • (2011) IOP Conf. Ser. Mater. Sci. Eng. , vol.27 , pp. 012011
    • Reinhart, G.1    Nguyen-Thi, H.2    Mangelinck-Noël, N.3    Billia, B.4    Schenk, T.5    Baruchel, J.6
  • 21
    • 84906539136 scopus 로고    scopus 로고
    • In situ study on columnar-equiaxed transition and an axial columnar dendrite growth of Al-15%Cu alloy by synchrotron radiography
    • [21] Li, F., Dong, Q., Zhang, J., Dai, Y., Xie, H., Yin, F., Sun, B., In situ study on columnar-equiaxed transition and an axial columnar dendrite growth of Al-15%Cu alloy by synchrotron radiography. Trans. Nonferrous Met. Soc. China 24 (2014), 2112–2116, 10.1016/S1003-6326(14)63320-3.
    • (2014) Trans. Nonferrous Met. Soc. China , vol.24 , pp. 2112-2116
    • Li, F.1    Dong, Q.2    Zhang, J.3    Dai, Y.4    Xie, H.5    Yin, F.6    Sun, B.7
  • 22
    • 84958952682 scopus 로고    scopus 로고
    • Atomistic to continuum modeling of solidification microstructures
    • [22] Karma, A., Tourret, D., Atomistic to continuum modeling of solidification microstructures. Curr. Opin. Solid State Mater. Sci. 20 (2016), 25–36, 10.1016/j.cossms.2015.09.001.
    • (2016) Curr. Opin. Solid State Mater. Sci. , vol.20 , pp. 25-36
    • Karma, A.1    Tourret, D.2
  • 23
    • 84938994315 scopus 로고    scopus 로고
    • Solidification in a supercomputer: from crystal nuclei to dendrite assemblages
    • [23] Shibuta, Y., Ohno, M., Takaki, T., Solidification in a supercomputer: from crystal nuclei to dendrite assemblages. JOM 67 (2015), 1793–1804, 10.1007/s11837-015-1452-2.
    • (2015) JOM , vol.67 , pp. 1793-1804
    • Shibuta, Y.1    Ohno, M.2    Takaki, T.3
  • 24
    • 0141507002 scopus 로고    scopus 로고
    • Atomistic and continuum modeling of dendritic solidification
    • [24] Hoyt, J.J., Asta, M., Karma, A., Atomistic and continuum modeling of dendritic solidification. Mater. Sci. Eng. R. 41 (2003), 121–163, 10.1016/S0927-796X(03)00036-6.
    • (2003) Mater. Sci. Eng. R. , vol.41 , pp. 121-163
    • Hoyt, J.J.1    Asta, M.2    Karma, A.3
  • 25
    • 84905366628 scopus 로고    scopus 로고
    • Diffusion and interdiffusion in binary metallic melts
    • [25] Kuhn, P., Horbach, J., Kargl, F., Meyer, A., Voigtmann, Th., Diffusion and interdiffusion in binary metallic melts. Phys. Rev. B, 90, 2014, 024309, 10.1103/PhysRevB.90.024309.
    • (2014) Phys. Rev. B , vol.90 , pp. 024309
    • Kuhn, P.1    Horbach, J.2    Kargl, F.3    Meyer, A.4    Voigtmann, T.5
  • 26
    • 84921029687 scopus 로고    scopus 로고
    • A review of quantitative phase-field crystal modeling of solid–liquid structures
    • [26] Asadi, E., Zaeem, M.A., A review of quantitative phase-field crystal modeling of solid–liquid structures. JOM 67 (2015), 186–201, 10.1007/s11837-014-1232-4.
    • (2015) JOM , vol.67 , pp. 186-201
    • Asadi, E.1    Zaeem, M.A.2
  • 27
    • 4243457001 scopus 로고    scopus 로고
    • Quantitative phase-field modeling of dendritic growth in two and three dimensions
    • [27] Karma, A., Rappel, J.W., Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57 (1998), 4323–4349, 10.1103/PhysRevE.57.4323.
    • (1998) Phys. Rev. E , vol.57 , pp. 4323-4349
    • Karma, A.1    Rappel, J.W.2
  • 28
    • 84989893804 scopus 로고    scopus 로고
    • [28] http://web.micress.de.
  • 29
    • 0033524596 scopus 로고    scopus 로고
    • Three-dimensional modeling of equiaxed dendritic growth on a mesoscopic scale
    • [29] Steinbach, I., Beckermann, C., Kauerauf, B., Li, Q., Guo, J., Three-dimensional modeling of equiaxed dendritic growth on a mesoscopic scale. Acta Mater 47 (1999), 971–982, 10.1016/S1359-6454(98)00380-2.
    • (1999) Acta Mater , vol.47 , pp. 971-982
    • Steinbach, I.1    Beckermann, C.2    Kauerauf, B.3    Li, Q.4    Guo, J.5
  • 30
    • 84959567833 scopus 로고    scopus 로고
    • Three-dimensional mesoscopic modeling of equiaxed dendritic solidification of a binary alloy
    • [30] Souhar, Y., De Felice, V.F., Beckermann, C., Combeau, H., Založnik, M., Three-dimensional mesoscopic modeling of equiaxed dendritic solidification of a binary alloy. Comp. Mater. Sci. 112 (2016), 304–317, 10.1016/j.commatsci.2015.10.028.
    • (2016) Comp. Mater. Sci. , vol.112 , pp. 304-317
    • Souhar, Y.1    De Felice, V.F.2    Beckermann, C.3    Combeau, H.4    Založnik, M.5
  • 31
    • 0027543331 scopus 로고
    • Probabilistic modelling of microstructure formation in solidification processes
    • [31] Rappaz, M., Gandin, C.-A., Probabilistic modelling of microstructure formation in solidification processes. Acta Metall. Mater 41 (1993), 345–360, 10.1016/0956-7151(93)90065-Z.
    • (1993) Acta Metall. Mater , vol.41 , pp. 345-360
    • Rappaz, M.1    Gandin, C.-A.2
  • 32
    • 84255167781 scopus 로고    scopus 로고
    • 3D CAFE modeling of grain structures: application to primary dendritic and secondary eutectic solidification
    • [32] Carozzani, T., Digonnet, H., Gandin, C.-A., 3D CAFE modeling of grain structures: application to primary dendritic and secondary eutectic solidification. Model. Simul. Mater. Sc, 20, 2012, 015010, 10.1088/0965-0393/20/1/015010.
    • (2012) Model. Simul. Mater. Sc , vol.20 , pp. 015010
    • Carozzani, T.1    Digonnet, H.2    Gandin, C.-A.3
  • 33
    • 0030245380 scopus 로고    scopus 로고
    • Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling
    • [33] Wang, C.Y., Beckermann, C., Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling. Metall. Mater. Trans. A 27A (1996), 2754–2764, 10.1007/BF02652369.
    • (1996) Metall. Mater. Trans. A , vol.27A , pp. 2754-2764
    • Wang, C.Y.1    Beckermann, C.2
  • 34
    • 0042062337 scopus 로고    scopus 로고
    • A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification
    • [34] Martorano, M.A., Beckermann, C., Gandin, Ch.-A., A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification. Metall. Mater. Trans. A 34A (2003), 1657–1674, 10.1007/s11661-003-0311-x.
    • (2003) Metall. Mater. Trans. A , vol.34A , pp. 1657-1674
    • Martorano, M.A.1    Beckermann, C.2    Gandin, C.-A.3
  • 35
    • 77957957824 scopus 로고    scopus 로고
    • Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – part I: model description
    • [35] Wu, M., Fjeld, A., Ludwig, A., Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – part I: model description. Comput. Mater. Sci. 50 (2010), 32–42, 10.1016/j.commatsci.2010.07.005.
    • (2010) Comput. Mater. Sci. , vol.50 , pp. 32-42
    • Wu, M.1    Fjeld, A.2    Ludwig, A.3
  • 37
    • 84939549912 scopus 로고    scopus 로고
    • Three-dimensional dendritic needle network model with application to Al-Cu directional solidification experiments
    • [37] Tourret, D., Karma, A., Clarke, A.J., Gibbs, P.J., Imhoff, S.D., Three-dimensional dendritic needle network model with application to Al-Cu directional solidification experiments. IOP Conf. Ser. Mater. Sci. Eng., 84, 2015, 012082, 10.1088/1757-899X/84/1/012082.
    • (2015) IOP Conf. Ser. Mater. Sci. Eng. , vol.84 , pp. 012082
    • Tourret, D.1    Karma, A.2    Clarke, A.J.3    Gibbs, P.J.4    Imhoff, S.D.5
  • 38
    • 84938969827 scopus 로고    scopus 로고
    • Three-dimensional multiscale modeling of dendritic spacing selection during Al-Si directional solidification
    • [38] Tourret, D., Clarke, A.J., Imhoff, S.D., Gibbs, P.J., Gibbs, J.W., Karma, A., Three-dimensional multiscale modeling of dendritic spacing selection during Al-Si directional solidification. JOM 67 (2015), 1776–1785, 10.1007/s11837-015-1444-2.
    • (2015) JOM , vol.67 , pp. 1776-1785
    • Tourret, D.1    Clarke, A.J.2    Imhoff, S.D.3    Gibbs, P.J.4    Gibbs, J.W.5    Karma, A.6
  • 39
    • 84877904478 scopus 로고    scopus 로고
    • Multi-scale needle-network model of complex dendritic microstructure formation
    • [39] Tourret, D., Karma, A., Multi-scale needle-network model of complex dendritic microstructure formation. IOP Conf. Ser. Mater Sci. Eng., 33, 2012, 012095, 10.1088/1757-899X/33/1/012095.
    • (2012) IOP Conf. Ser. Mater Sci. Eng. , vol.33 , pp. 012095
    • Tourret, D.1    Karma, A.2
  • 40
    • 84989886965 scopus 로고    scopus 로고
    • Numerical investigation of the columnar-to-equiaxed transition using a 2D needle network model, TMS 2016 145th Annual Meeting, Nashville, TN, 15 – 17 February 2016
    • [40] P.A. Geslin, A. Karma, Numerical investigation of the columnar-to-equiaxed transition using a 2D needle network model, TMS 2016 145th Annual Meeting, Nashville, TN, 15 – 17 February 2016.
    • Geslin, P.A.1    Karma, A.2
  • 41
    • 0022709519 scopus 로고
    • Theory of microstructural development during rapid solidification
    • [41] Kurz, W., Giovanola, B., Trivedi, R., Theory of microstructural development during rapid solidification. Acta Metall. 34 (1986), 823–830.
    • (1986) Acta Metall. , vol.34 , pp. 823-830
    • Kurz, W.1    Giovanola, B.2    Trivedi, R.3
  • 42
    • 0342583796 scopus 로고
    • Instabilities and pattern forestation in crystal growth
    • [42] Langer, J.S., Instabilities and pattern forestation in crystal growth. Rev. Mod. Phys. 52 (1980), 1–30, 10.1103/RevModPhys.52.1.
    • (1980) Rev. Mod. Phys. , vol.52 , pp. 1-30
    • Langer, J.S.1
  • 43
    • 37649029615 scopus 로고    scopus 로고
    • Quantitative phase-field model of alloy solidification
    • [43] Echebarria, B., Folch, R., Karma, A., Plapp, M., Quantitative phase-field model of alloy solidification. Phys. Rev. E, 70, 2004, 061604, 10.1103/PhysRevE.70.061604.
    • (2004) Phys. Rev. E , vol.70 , pp. 061604
    • Echebarria, B.1    Folch, R.2    Karma, A.3    Plapp, M.4
  • 44
    • 84980287971 scopus 로고
    • A path independent integral and the approximate analysis of strain concentration by Notches and Cracks
    • [44] Rice, J.R., A path independent integral and the approximate analysis of strain concentration by Notches and Cracks. J. Appl. Mech. 35 (1968), 379–386.
    • (1968) J. Appl. Mech. , vol.35 , pp. 379-386
    • Rice, J.R.1
  • 45
    • 0031212077 scopus 로고    scopus 로고
    • Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys
    • [45] Bouchard, D., Kirkaldy, J.S., Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys. Metall. Mater. Trans. B, 28B, 1997, 651, 10.1007/s11663-997-0039-x.
    • (1997) Metall. Mater. Trans. B , vol.28B , pp. 651
    • Bouchard, D.1    Kirkaldy, J.S.2
  • 46
    • 0000328150 scopus 로고
    • Columnar dendrite growth: experiments on tip growth
    • [46] Esaka, H., Kurz, W., Columnar dendrite growth: experiments on tip growth. J. Cryst. Growth 72 (1985), 578–584, 10.1016/0022-0248(85)90208-8.
    • (1985) J. Cryst. Growth , vol.72 , pp. 578-584
    • Esaka, H.1    Kurz, W.2
  • 47
    • 0000465774 scopus 로고
    • Development of side-branching in dendritic crystal growth
    • [47] Dougherty, A., Kaplan, P.D., Gollub, P., Development of side-branching in dendritic crystal growth. Phys. Rev. Lett. 58 (1987), 1652–1655, 10.1103/PhysRevLett.58.1652.
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 1652-1655
    • Dougherty, A.1    Kaplan, P.D.2    Gollub, P.3
  • 48
    • 0032626408 scopus 로고    scopus 로고
    • Evolution of the sidebranch structure in free dendritic growth
    • [48] Li, Q., Beckermann, C., Evolution of the sidebranch structure in free dendritic growth. Acta Mater 47 (1999), 2345–2356, 10.1016/S1359-6454(99)00115-9.
    • (1999) Acta Mater , vol.47 , pp. 2345-2356
    • Li, Q.1    Beckermann, C.2
  • 49
    • 0001342033 scopus 로고
    • Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise
    • [49] Langer, J.S., Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise. Phys. Rev. A 36 (1987), 3350–3358, 10.1103/PhysRevA.36.3350.
    • (1987) Phys. Rev. A , vol.36 , pp. 3350-3358
    • Langer, J.S.1
  • 50
    • 0001541731 scopus 로고
    • A note on the generation of random normal deviates
    • [50] Box, G.E.P., Muller, M.E., A note on the generation of random normal deviates. Ann. Math. Stat. 29 (1958), 610–611.
    • (1958) Ann. Math. Stat. , vol.29 , pp. 610-611
    • Box, G.E.P.1    Muller, M.E.2
  • 52
    • 43049166966 scopus 로고    scopus 로고
    • Comparative study of the influence of natural convection on directional solidification of Al–3.5 wt% Ni and Al–7 wt% Si alloys
    • [52] Zhou, B.H., Jung, H., Mangelinck-Noel, N., Nguyen-Thi, H., Billia, B., Liu, Q.S., Lan, C.W., Comparative study of the influence of natural convection on directional solidification of Al–3.5 wt% Ni and Al–7 wt% Si alloys. Adv. Space Res. 41 (2008), 2112–2117, 10.1016/j.asr.2007.06.038.
    • (2008) Adv. Space Res. , vol.41 , pp. 2112-2117
    • Zhou, B.H.1    Jung, H.2    Mangelinck-Noel, N.3    Nguyen-Thi, H.4    Billia, B.5    Liu, Q.S.6    Lan, C.W.7
  • 53
    • 44449149148 scopus 로고    scopus 로고
    • Microstructural development in Al-Ni alloys directionally solidified under unsteady-state conditions
    • [53] Canté, M.V., Spinelli, J.E., Ferreira, I.L., Cheung, N., Garcia, A., Microstructural development in Al-Ni alloys directionally solidified under unsteady-state conditions. Metall. Mater. Trans. A, 39A, 2008, 1712, 10.1007/s11661-008-9536-z.
    • (2008) Metall. Mater. Trans. A , vol.39A , pp. 1712
    • Canté, M.V.1    Spinelli, J.E.2    Ferreira, I.L.3    Cheung, N.4    Garcia, A.5
  • 54
    • 4243341006 scopus 로고
    • Predictions of dendritic growth rates in the linearized solvability theory
    • [54] Barbieri, A., Langer, J.S., Predictions of dendritic growth rates in the linearized solvability theory. Phys. Rev. A 39 (1989), 5314–5325, 10.1103/PhysRevA.39.5314.
    • (1989) Phys. Rev. A , vol.39 , pp. 5314-5325
    • Barbieri, A.1    Langer, J.S.2
  • 55
    • 13744260952 scopus 로고    scopus 로고
    • Three-dimensional crystal-melt Wulff-shape and interfacial stiffness in the Al-Sn binary system
    • [55] Napolitano, R.E., Liu, S., Three-dimensional crystal-melt Wulff-shape and interfacial stiffness in the Al-Sn binary system. Phys. Rev. B, 70, 2004, 214103, 10.1103/PhysRevB.70.214103.
    • (2004) Phys. Rev. B , vol.70 , pp. 214103
    • Napolitano, R.E.1    Liu, S.2
  • 56
    • 84859916957 scopus 로고    scopus 로고
    • Comparison of results from low-gravity and normal gravity experiment “Trace” on the columnar-equiaxed transition in the transparent alloy system neopentylglycol-camphor
    • [56] Sturz, L., Zimmermann, G., Comparison of results from low-gravity and normal gravity experiment “Trace” on the columnar-equiaxed transition in the transparent alloy system neopentylglycol-camphor. 20th ESA Symposium on European Rocket and Balloon Programmes and Related Research Book Series: ESA SP-700, 2011, 459–466.
    • (2011) 20th ESA Symposium on European Rocket and Balloon Programmes and Related Research Book Series: ESA SP-700 , pp. 459-466
    • Sturz, L.1    Zimmermann, G.2
  • 57
    • 84939495479 scopus 로고    scopus 로고
    • Benchmark experiments and numerical modelling of the columnar-equiaxed dendritic growth in the transparent alloy Neopentylglycol-(d)Camphor
    • [57] Sturz, L., Wu, M., Zimmermann, G., Ludwig, A., Ahmadein, M., Benchmark experiments and numerical modelling of the columnar-equiaxed dendritic growth in the transparent alloy Neopentylglycol-(d)Camphor. IOP Conf. Ser. Mat. Sci. Eng., 84, 2015, 012086.
    • (2015) IOP Conf. Ser. Mat. Sci. Eng. , vol.84 , pp. 012086
    • Sturz, L.1    Wu, M.2    Zimmermann, G.3    Ludwig, A.4    Ahmadein, M.5
  • 58
    • 84893520790 scopus 로고    scopus 로고
    • Results from low-gravity and normal gravity experiment “Trace+” on dendritic growth and the columnar-equiaxed transition in the transparent alloy system NPG-DC
    • [58] Sturz, L., Zimmermann, G., Results from low-gravity and normal gravity experiment “Trace+” on dendritic growth and the columnar-equiaxed transition in the transparent alloy system NPG-DC. 21th ESA Symposium on European Rocket and Balloon Programmes and Related Research Book Series: ESA SP-721, 2013, 285–292.
    • (2013) 21th ESA Symposium on European Rocket and Balloon Programmes and Related Research Book Series: ESA SP-721 , pp. 285-292
    • Sturz, L.1    Zimmermann, G.2


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