Experimental determination of the stability diagram of a lamellar eutectic growth front

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 1 SUPPL. B, 1997, Pages 780-796

  Ginibre, Marie ^a   Akamatsu, Silvère ^a   Faivre, Gabriel ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001311105     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.56.780     Document Type: Article

References (62)

1. J. D. Hunt and K. A. Jackson, Trans. AIME 236, 843 (1966).
2. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
3. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
4. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
5. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
6. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
7. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
8. The morphological instabilities of the lamellar eutectic growth fronts present profound similarities with those of other one-dimensional periodically modulated fronts. The general, phenomenological reasons for this fact are now well known [M. R. E. Proctor and C. A. Jones, J. Fluid Mech. 188, 301 (1988); P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990)]. The experimental illustrations of it are too numerous to be quoted here. We refer the interested reader to P. Oswald, J. Bechhoefer, and A. Libchaber [ibid. 58, 2318 (1987)] and J.-M. Flesselles, A. J. Simon, and A. Libchaber [Adv. Phys. 40, 1 (1991)] as concerns directionally solidified liquid crystals; to M. Rabaud, S. Michalland, and Y. Couder [Phys. Rev. Lett. 64, 184 (1990)] as concerns directional viscous fingering; and to F. Giorgiutti, A. Bleton. L. Limat, and J. E. Weisfried [ibid. 74, 538 (1995)] as concerns the dynamics of one-dimensional arrays of liquid columns. In all these systems save the last one, the basic state is planar, and the stationary periodic state, i.e., the state having the same symmetries as the basic state of lamellar eutectics, results from a primary bifurcation from the planar state, as shown a long time ago by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] in the case of directionally solidified dilute alloys. For this reason, the bifurcations called "primary" in this paper are considered "secondary" by the authors studying the above-mentioned systems.
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12. 1/2 are often large. R. Trivedi, J. T. Mason, J. D. Verhoeven, and W. Kurz [Metall. Trans. A 22, 2523 (1991)] determined the histogram of the local values of λ in a number of lead-based eutectic alloys, and found that the width of this histogram is typically of 20% of the average value, and often more.
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