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A general mechanism of polycrystalline growth

Nature Materials volume 3, pages 645–650 (2004)Cite this article

Abstract

Most research into microstructure formation during solidification has focused on single-crystal growth ranging from faceted crystals to symmetric dendrites. However, these growth forms can be perturbed by heterogeneities, yielding a rich variety of polycrystalline growth patterns. Phase-field simulations show that the presence of particulates (for example, dirt) or a small rotational–translational mobility ratio (characteristic of high supercooling) in crystallizing fluids give rise to similar growth patterns, implying a duality in the growth process in these structurally heterogeneous fluids. Similar crystallization patterns are also found in thin polymer films with particulate additives and pure films with high supercooling. This duality between the static and dynamic heterogeneity explains the ubiquity of polycrystalline growth patterns in polymeric and other complex fluids.

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Figure 1: Thin-film polycrystalline growth morphologies.
Figure 2: The effect of particulate additives (left two columns) and reducing the orientational-translational mobility ratio χ (right two columns) on the growth morphology.
Figure 3: Growth morphologies observed during crystallization of pure isotactic polystyrene films (17 ± 2 nm thick) as a function of temperature7.
Figure 4: The seaweed morphology may develop either as a single crystal40,41,42,43,44,45 or as a polycrystalline object6,39,46,47, as recovered by our phase-field simulations.
Figure 5: Single-crystal needle (top) and polycrystalline 'fungi' produced by introducing foreign particles (centre) or by reducing χ (bottom) as predicted by the phase-field theory.

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References

  1. Cahn, R.W. The Coming of Materials Science (Pergamon, Oxford, 2001).

    Google Scholar 

  2. Gunton, J.D., San Miguel, M. & Sahni, P. in Phase Transitions and Critical Phenomena Vol. 8 (eds Domb, C. and Lebowitz, J.L.) 267–466 (Academic, London, 1983).

    Google Scholar 

  3. Ferreiro, V., Douglas, J.F., Warren, J.A. & Karim, A. Nonequilibrium pattern formation in the crystallization of polymer blend films. Phys. Rev. E 65, 042802 (2002).

    Article  Google Scholar 

  4. Ferreiro, V., Douglas, J.F., Warren, J.A. & Karim, A. Growth pulsations in symmetric dendritic crystallization in polymer blend films. Phys. Rev. E 65, 051606 (2002).

    Article  Google Scholar 

  5. Woodward, A.E. Atlas of Polymer Morphology (Hanser, New York, 1988).

    Google Scholar 

  6. Fleury, V. Branched fractal patterns in non-equilibrium electrochemical deposition from oscillatory nucleation and growth. Nature 390, 145–148 (1997).

    Article  CAS  Google Scholar 

  7. Beers, K.L., Douglas, J.F., Amis, E.J. & Karim, A. Combinatorial measurement of crystallization growth rate and morphology in thin films of isotactic polystyrene. Langmuir 19, 3935–3940 (2003).

    Article  CAS  Google Scholar 

  8. Keith, H.D. & Padden, F.J. Crystallization of polymers from the melt and the structure of bulk semicrystalline polymers. J. Appl. Phys. 34, 2409–2421 (1963).

    Article  CAS  Google Scholar 

  9. Gránásy, L. et al. Growth of 'dizzy dendrites' in a random field of foreign particles. Nature Mater. 2, 92–96 (2003).

    Article  Google Scholar 

  10. Ryshchenkow, G. & Faivre, G. Bulk crystallization of liquid selenium. J. Non-Cryst. Solids 87, 221–235 (1988).

    Google Scholar 

  11. Magill, J.H. Spherulites: A personal perspective. J. Mater. Sci. 36, 3143–3164 (2001).

    Article  CAS  Google Scholar 

  12. Tracht, L. et al. Length scale of dynamic heterogeneities at the glass transition by multidimensional nuclear magnetic resonance Phys. Rev. Lett. 81, 2727–2730 (1998).

    Article  CAS  Google Scholar 

  13. Russell, E.V. & Israeloff, N.E. Direct observation of molecular cooperativity near the glass transition. Nature 408, 695–68 (2000).

    Article  CAS  Google Scholar 

  14. Ediger, M.D. Spatially heterogeneous dynamics in supercooled liquids. Ann. Rev. Phys. Chem. 51, 99–128 (2000).

    Article  CAS  Google Scholar 

  15. Chang, I. & Sillescu, H. Heterogeneity at the glass transition: Translational and rotational self-diffusion. J. Phys. Chem. B 101, 8794–8801 (1997).

    Article  CAS  Google Scholar 

  16. Weeks, E.R., Crocker, J.C., Levitt, A.C., Schofield, A. & Weitz, D.A. Three dimensional imaging of structural relaxation near the colloidal glass transition. Science 287, 627–631 (2000).

    Article  CAS  Google Scholar 

  17. Kegel, W.K. & van Blaaderen, A. Direct observation of dynamical heterogeneities in colloidal hard-sphere suspensions. Science 287, 290–293 (2000).

    Article  CAS  Google Scholar 

  18. Bennemann, C., Donati, C., Baschnagel, J. & Glotzer, S.C. Growing range of correlated motion in a polymer melt on cooling towards the glass transition. Nature 399, 246–249 (1999).

    Article  CAS  Google Scholar 

  19. Mel'cuk, A.I., Ramos, R.A., Gould, H., Klein, W. & Mountain, R.D. Long-lived structures in fragile glass-forming liquids. Phys. Rev. Lett. 75, 2522–2525 (1995).

    Article  CAS  Google Scholar 

  20. Donati, C. et al. Stringlike cooperative motion in a supercooled liquid. Phys. Rev. Lett. 80, 2338–2341 (1998).

    Article  CAS  Google Scholar 

  21. Ngai, K.L., Magill, J.H. & Plazek, D.J. Flow, diffusion and crystallization of supercooled liquids: Revisited. J. Chem. Phys. 112, 1887–1892 (2000).

    Article  CAS  Google Scholar 

  22. Rössler, E. Indication for a change in diffusion mechanism in supercooled liquids. Phys. Rev. Lett. 65, 1595–1598 (1990).

    Article  Google Scholar 

  23. Masuhr, A., Waniuk, T.A., Busch, R. & Johnson, W.L. Time scales for viscous flow, atomic transport, and crystallization in the liquid and supercooled liquid states of Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 . Phys. Rev. Lett. 82, 2290–2293 (1999).

    Article  CAS  Google Scholar 

  24. Swallen, S.F., Bonvallet, P.A., McMahon, R.J. & Ediger, M.D. Self-diffusion of tris-naphthylbenzene near the glass transition temperature. Phys. Rev. Lett. 90, 015901 (2003).

    Article  Google Scholar 

  25. Oxtoby, D.W. Density functional methods in the statistical mechanics of materials. Annu. Rev. Mater. Res. 32, 39–52 (2002).

    Article  CAS  Google Scholar 

  26. Boettinger, W.J., Warren, J.A., Beckermann, C. & Karma, A. Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163–194 (2003).

    Article  Google Scholar 

  27. Hoyt, J.J., Asta, M. & Karma, A. Atomistic and continuum modeling of dendritic solidification. Mater. Sci. Eng. Rep. R 41, 121–163 (2003).

    Article  Google Scholar 

  28. Gránásy, L., Börzsönyi, T. & Pusztai, T. Nucleation and bulk crystallization in binary phase field theory. Phys. Rev. Lett. 88, 206105 (2002).

    Article  Google Scholar 

  29. Gránásy, L., Börzsönyi, T. & Pusztai, T. Crystal nucleation and growth in binary phase field theory. J. Cryst. Growth 237–239, 1813–1817 (2002).

    Article  Google Scholar 

  30. Gránásy, L. & Pusztai, T. Diffuse interface analysis of crystal nucleation in hard-sphere liquid. J. Chem. Phys. 117, 10121–10124 (2002).

    Article  Google Scholar 

  31. Gránásy, L. et al. Phase field theory of crystal nucleation in hard sphere liquid. J. Chem. Phys. 119, 10376–10382 (2003).

    Article  Google Scholar 

  32. Kobayashi, R., Warren, J.A. & Carter, W.C. Vector-valued phase field model for crystallization and grain boundary formation. Physica D 119, 415–423 (1998).

    Article  CAS  Google Scholar 

  33. Kobayashi, R., Warren, J.A. & Carter, W.C. Modeling grain boundaries using a phase-field technique. Physica D 140, 141–150 (2000).

    Article  Google Scholar 

  34. Huisman, W.J. et al. Layering of a liquid metal in contact with a hard wall. Nature 390, 379–381 (1997).

    Article  CAS  Google Scholar 

  35. Davidchack, R.L. & Laird, B.B. Simulation of the hard-sphere crystal-melt interface. J. Chem. Phys. 108, 9452–9462 (1998).

    Article  CAS  Google Scholar 

  36. Warren, J.A., Kobayashi, R., Lobkovsky, A.E. & Carter, W.C. Extending phase field models of solidification to polycrystalline materials. Acta Mater. 51, 6035–6058 (2003).

    Article  CAS  Google Scholar 

  37. Warren, J.A. & Boettinger, W.J. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Met. Mater. 43, 689–703 (1995).

    Article  CAS  Google Scholar 

  38. Hoyt, J.J. & Asta, M. Atomistic computation of liquid diffusivity, solid-liquid interfacial free energy, and kinetic coefficient in Au and Ag. Phys. Rev. B 65, 214106 (2002).

    Article  Google Scholar 

  39. Grier, D., Ben-Jacob, E., Clarke, R. & Sander, L.M. Morphology and microstructure in electrochemical deposition of zinc. Phys. Rev. Lett. 56, 1264–1267 (1986).

    Article  CAS  Google Scholar 

  40. Kobayashi, R. Modeling and numerical simulation of dendritic growth. Physica D 63, 410–423 (1993).

    Article  Google Scholar 

  41. Ihle, T. & Müller-Krumbhaar, H. Fractal and compact growth morphologies in phase transitions with diffusion. Phys. Rev. E 49, 2972–2991 (1994).

    Article  CAS  Google Scholar 

  42. Taguchi, K. et al. Growth shape of isotactic polystyrene crystals in thin films. Polymer 42, 7443–7447 (2001).

    Article  CAS  Google Scholar 

  43. Utter, B. & Bodenschatz, E. Dynamics of low anisotropy morphologies in directional solidification. Phys. Rev. E 66, 051604 (2002).

    Article  CAS  Google Scholar 

  44. Akamatsu, S., Faivre, G. & Ihle, T. Symmetry-broken double fingers and seaweed patterns in thin-film directional solidification of a nonfaceted cubic crystal. Phys. Rev. E 51, 4751–4773 (1995).

    Article  CAS  Google Scholar 

  45. Lovinger, A.J. & Cais, R.E. Structure and morphology of poly(trifluoro-ethylene). Macromolecules 17, 1939–1945 (1984).

    Article  CAS  Google Scholar 

  46. Ben-Jacob, E., Deutscher, G., Garik, P., Goldenfeld, N.D. & Lareah, Y. Formation of dense branching morphology in interfacial growth. Phys. Rev. Lett. 57, 1903–1906 (1986).

    Article  CAS  Google Scholar 

  47. Lereah, Y. et al. Morphology of Ge:Al thin films: Experiments and model. Phys. Rev. E 49, 649–656 (1994).

    Article  CAS  Google Scholar 

  48. Dudowicz, J., Freed, K.F. & Douglas, J.F. Flory-Huggins model of equilibrium polymerisation and phase separation in the Stockmayer fluid. Phys. Rev. Lett. 92, 045502 (2003).

    Article  Google Scholar 

  49. Kumar, S.K. & Douglas, J.F. Gelation in physically associating polymer solutions. Phys. Rev. Lett. 87, 188301 (2001).

    Article  Google Scholar 

  50. Bedrov, D., Smith, G.D. & Douglas, J.F. Influence of self-assembly on dynamical viscoelastic properties of telechelic polymer solutions. Europhys. Lett. 59, 384–390 (2002).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank Vincent Ferreiro (CNRS), Kathryn Beers (NIST) and Vincent Fleury (CNRS) for providing the images shown in Figs 1 and 4. This work has been supported by contracts OTKA-T-037323, ESA PECS No. 98005, and by the EU Integrated Project IMPRESS. T.P. acknowledges support by the Bolyai János Scholarship.

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Authors and Affiliations

  1. Research Institute for Solid State Physics and Optics, PO Box 49, Budapest, H-1525, Hungary

    László Gránásy, Tamás Pusztai & Tamás Börzsönyi

  2. Metallurgy, National Institute of Standards and Technology, Gaithersburg, 20899, Maryland, USA

    James A. Warren

  3. Polymers Divisions, National Institute of Standards and Technology, Gaithersburg, 20899, Maryland, USA

    Jack F. Douglas

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Correspondence to László Gránásy.

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Gránásy, L., Pusztai, T., Börzsönyi, T. et al. A general mechanism of polycrystalline growth. Nature Mater 3, 645–650 (2004). https://doi.org/10.1038/nmat1190

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