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We find that when this growth front nucleation process is prevalent, singlecrystal growth is transformed into polycrystalline growth

A general mechanism of polycrystalline growth.

NATURE MATERIALS, no. 9 (2004): 645-650

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摘要

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 particul...更多

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简介
  • M any everyday materials, ranging from plastic grocery bags to airplane wings and cast-iron supporting beams for highway bridges, are fabricated by freezing liquids into polycrystalline solid structures.
  • The authors' work extends previous treatments of crystallization by accounting for the freezing-in of local orientational fluctuations at the growth front that create new grains.
重点内容
  • M any everyday materials, ranging from plastic grocery bags to airplane wings and cast-iron supporting beams for highway bridges, are fabricated by freezing liquids into polycrystalline solid structures
  • We find that when this growth front nucleation (GFN) process is prevalent, singlecrystal growth is transformed into polycrystalline growth
  • In the absence of GFN, far from equilibrium, crystallization normally leads to symmetric dendrites similar to the structures of snowflakes
  • Our goal is to determine what role GFN plays in determining this type of morphological variation
  • The duality between the effects of dynamic heterogeneities as they influence χ versus static heterogeneities provides a fundamental insight into the prevalence of polycrystalline growth in polymeric materials, and the similarity of these growth patterns to those of small-molecule liquids containing ‘dirt’
结果
  • The authors' previous study of polycrystalline growth in fluids having static heterogeneities indicated that the essential mechanism of this type of growth was the stabilization of new crystal grains having the crystallographic orientation preferred by the particles rather than the parent crystal[9].
  • This argument implies that static heterogeneities and the mobility asymmetry (χ << χ0) of supercooled liquids should give rise to a common tendency towards polycrystalline growth.
  • Field theoretical models have proved successful in describing phase separation and a wide range of pattern-formation processes involving critical dynamics[2].Similar advances have been made extending this type of coarse-grained description to crystallization.
  • The phase-field model used here[28,29] builds on previous work for multigrain solidification[32,33], homogeneous crystal nucleation[28,29] and the modification of dendritic growth by particulate additives[9].
  • Influence of mobility asymmetry quantifies the energetic cost of misorientation[36], and p(φ), following the procedure commonly used in phase-field theory[28,37], varies smoothly from 0 to 1 as φ changes from the solid to the liquid; p(φ) = φ3(10 – 15φ + 6φ2).A similar approach has been used recently to investigate grain-boundary dynamics and multigrain growth[32,33,36].
  • Whereas the concentration mobility is directly related to the chemical diffusion coefficient, the phase-field mobility Mφ and orientational mobility Mθ must be chosen to capture properly the essential properties of a dynamically heterogeneous liquid.
  • Previous work has established that the crystallization patterns that form insuchmisciblemixturesunderconditionsof highsupersaturationand constant T are essentially equivalent to those formed in singlecomponent fluids at high undercooling[37].The authors choose the Ni–Cu system here because this is a classic case for which many of the model parameters are known.
  • The orientation dependence of the molecular attachment kinetics is taken into account using an anisotropy function for the phase-field mobility,Mφ = Mφ,0{1 + δ0cos[m(ψ – θ)]},where δ0 is a parameter characterizing the magnitude of the mobility anisotropy (δ0 = 0 for the isotropic case),and ψ is the inclination of the liquid–solid interface in the laboratory frame.
结论
  • The duality between the effects of dynamic heterogeneities as they influence χ versus static heterogeneities provides a fundamental insight into the prevalence of polycrystalline growth in polymeric materials, and the similarity of these growth patterns to those of small-molecule liquids containing ‘dirt’.
  • The authors' simulations imply that nucleating agents introduced to control the size and distribution of crystallites nature materials | VOL 3 | SEPTEMBER 2004 | www.nature.com/naturematerials may very well yield a variety of unanticipated polycrystalline growth morphologies.
总结
  • M any everyday materials, ranging from plastic grocery bags to airplane wings and cast-iron supporting beams for highway bridges, are fabricated by freezing liquids into polycrystalline solid structures.
  • The authors' work extends previous treatments of crystallization by accounting for the freezing-in of local orientational fluctuations at the growth front that create new grains.
  • The authors' previous study of polycrystalline growth in fluids having static heterogeneities indicated that the essential mechanism of this type of growth was the stabilization of new crystal grains having the crystallographic orientation preferred by the particles rather than the parent crystal[9].
  • This argument implies that static heterogeneities and the mobility asymmetry (χ << χ0) of supercooled liquids should give rise to a common tendency towards polycrystalline growth.
  • Field theoretical models have proved successful in describing phase separation and a wide range of pattern-formation processes involving critical dynamics[2].Similar advances have been made extending this type of coarse-grained description to crystallization.
  • The phase-field model used here[28,29] builds on previous work for multigrain solidification[32,33], homogeneous crystal nucleation[28,29] and the modification of dendritic growth by particulate additives[9].
  • Influence of mobility asymmetry quantifies the energetic cost of misorientation[36], and p(φ), following the procedure commonly used in phase-field theory[28,37], varies smoothly from 0 to 1 as φ changes from the solid to the liquid; p(φ) = φ3(10 – 15φ + 6φ2).A similar approach has been used recently to investigate grain-boundary dynamics and multigrain growth[32,33,36].
  • Whereas the concentration mobility is directly related to the chemical diffusion coefficient, the phase-field mobility Mφ and orientational mobility Mθ must be chosen to capture properly the essential properties of a dynamically heterogeneous liquid.
  • Previous work has established that the crystallization patterns that form insuchmisciblemixturesunderconditionsof highsupersaturationand constant T are essentially equivalent to those formed in singlecomponent fluids at high undercooling[37].The authors choose the Ni–Cu system here because this is a classic case for which many of the model parameters are known.
  • The orientation dependence of the molecular attachment kinetics is taken into account using an anisotropy function for the phase-field mobility,Mφ = Mφ,0{1 + δ0cos[m(ψ – θ)]},where δ0 is a parameter characterizing the magnitude of the mobility anisotropy (δ0 = 0 for the isotropic case),and ψ is the inclination of the liquid–solid interface in the laboratory frame.
  • The duality between the effects of dynamic heterogeneities as they influence χ versus static heterogeneities provides a fundamental insight into the prevalence of polycrystalline growth in polymeric materials, and the similarity of these growth patterns to those of small-molecule liquids containing ‘dirt’.
  • The authors' simulations imply that nucleating agents introduced to control the size and distribution of crystallites nature materials | VOL 3 | SEPTEMBER 2004 | www.nature.com/naturematerials may very well yield a variety of unanticipated polycrystalline growth morphologies.
基金
  • 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
研究对象与分析
single-pixel-sized orientation pinning centres: 400000
Growth morphologies observed during crystallization of pure isotactic polystyrene films (17 ± 2 nm thick) as a function of temperature[7].Note the transition between the dendritic,disordered dendritic and seaweed morphologies with increasing undercooling.From left to right the temperature of crystallization is T = 463,443,433 and 423 K, respectively.The scale bars are 10 μm. The seaweed morphology may develop either as a single crystal[40,41,42,43,44,45] or as a polycrystalline object6,39,46,47,as recovered by our phase-field simulations. Single-crystal seaweed (top) forms when both the interface free energy and kinetic coefficient are isotropic or close to isotropic.Polycrystalline seaweed can be obtained by either introducing foreign particles (400,000 single-pixel-sized orientation pinning centres; centre row) or by reducing the orientational mobility (by a factor of 50; bottom). The calculations were performed with isotropic interface free-energy and kinetic coefficient with a supersaturation,S = 0.78.The colouring is the same as for Fig. 2.Note that similar morphologies occur in the anisotropic case,if the growth form consists of a large number of fine grains (see Fig. 2). 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. In the bottom row, χ has been reduced by a factor of 5 to mimic the effect of high supercooling. N = 250,000 single-pixel-sized orientation pinning centres have been introduced into the simulation shown in the centre row. The interfacial free-energy is isotropic whereas the anisotropy of the phase-field mobility is 99.5%, and has a twofold symmetry (m = 2). The colouring of the orientation map is an adaptation of the scheme shown in Fig. 2 for twofold symmetry:When the fast growth direction is upwards, 60, or 120 degrees left, the grains are coloured red, blue or yellow, respectively, and the intermediate angles are denoted by a continuous transition among these colours. Owing to twofold symmetry, orientations that differ by 180-degree multiples are equivalent

single-pixel-sized orientation pinning centres: 250000
The seaweed morphology may develop either as a single crystal[40,41,42,43,44,45] or as a polycrystalline object6,39,46,47,as recovered by our phase-field simulations. Single-crystal seaweed (top) forms when both the interface free energy and kinetic coefficient are isotropic or close to isotropic.Polycrystalline seaweed can be obtained by either introducing foreign particles (400,000 single-pixel-sized orientation pinning centres; centre row) or by reducing the orientational mobility (by a factor of 50; bottom). The calculations were performed with isotropic interface free-energy and kinetic coefficient with a supersaturation,S = 0.78.The colouring is the same as for Fig. 2.Note that similar morphologies occur in the anisotropic case,if the growth form consists of a large number of fine grains (see Fig. 2). 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. In the bottom row, χ has been reduced by a factor of 5 to mimic the effect of high supercooling. N = 250,000 single-pixel-sized orientation pinning centres have been introduced into the simulation shown in the centre row. The interfacial free-energy is isotropic whereas the anisotropy of the phase-field mobility is 99.5%, and has a twofold symmetry (m = 2). The colouring of the orientation map is an adaptation of the scheme shown in Fig. 2 for twofold symmetry:When the fast growth direction is upwards, 60, or 120 degrees left, the grains are coloured red, blue or yellow, respectively, and the intermediate angles are denoted by a continuous transition among these colours. Owing to twofold symmetry, orientations that differ by 180-degree multiples are equivalent.

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