Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth

Brener, Efim A.; Müller‐Krumbhaar, H.; Temkin, D. E.

doi:10.1103/physreve.54.2714

Cited by 167 publications

(178 citation statements)

References 20 publications

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“…It is important to note that eq 3, with the boundary conditions at the interface given by eqs 1 and 4, is similar to the equation used by Müller-Krumbhaar and collaborators [10][11][12][13][14][15] 20 That is, if eq 1 would be written as…”

Section: Resultsmentioning

confidence: 98%

Pattern Formation and Morphology Evolution in Langmuir Monolayers

et al. 2006

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We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace's equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.

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Section: Resultsmentioning

confidence: 98%

Pattern Formation and Morphology Evolution in Langmuir Monolayers

et al. 2006

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“…Apparently, we have lost the general picture given by the diffusional model proposing the existence of a diffusion zone, which with eq 7 and the boundary conditions given by eqs 1 and 2, successfully explains the pattern formation and the morphology evolution in LMs. 27,28 In the same way, apparently, we have also lost the connection with the morphology diagram with regions of different morphological structures, [6][7][8][9][10][11] determined by the control parameters ∆ and ε, as explained above. Here, we will assess in what conditions the 2D hydrodynamic eq 4 can recover that picture related to pattern formation and to the morphology diagram.…”

Section: Morphology Evolution In Langmuirmentioning

confidence: 99%

“…27,28 Our experiments agree with the kinetic morphology diagram. [6][7][8][9][10][11] However, the underlying physics involved in LM is different from the underlying physics in the Mullins-Sekerka instability; diffusional processes are not involved. This is a new kind of instability that leads to pattern formation, where Marangoni flow is the key factor.…”

Section: Introductionmentioning

confidence: 99%

Domain Growth, Pattern Formation, and Morphology Transitions in Langmuir Monolayers. A New Growth Instability

2010

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The aims of this study are the following two: (1) To show that in Langmuir monolayers (LM) at low supersaturation, domains grow forming fractal structures without an apparent orientational order trough tip splitting dynamics, where doublons are the building blocks producing domains with a seaweed shape. When supersaturation is larger, there is a morphology transition from tip splitting to side branching. Here, structures grow with a pronounced orientational order forming dendrites, which are also fractal. We observed this behavior in different Langmuir monolayers formed by nervonic acid, dioctadecylamine, ethyl stearate, and ethyl palmitate, using Brewster angle microscopy. (2) To present experimental evidence showing an important Marangoni flow during domain growth, where the hydrodynamic transport of amphipiles overwhelms diffusion. We were able to show that the equation that governs the pattern formation in LM is a Laplacian equation in the chemical potential with the appropriate boundary conditions. However, the underlying physics involved in Langmuir monolayers is different from the underlying physics in the Mullins-Sekerka instability; diffusional processes are not involved. We found a new kind of instability that leads to pattern formation, where Marangoni flow is the key factor. We also found that the equations governing pattern formation in LM can be reduced to those used in the theory of morphology diagrams for two-dimensional diffusional growth. Our experiments agree with this diagram.

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“…Such a "seaweed" morphology might come about due to a competition between differently directed capillary and kinetic anisotropies. Microstructure selection maps (in undercooling-anisotropy space) produced by Brener et al [31] using solvability theory indicate a range of such transitions should occur, while simulations by Haxhimali et al [32] have suggested that many common metals may lay close to the dendritic-"seaweed" transition. One such transition has been observed directly as a function of composition in Al-Zn alloys by Dantzig et al [33].…”

Section: Introductionmentioning

confidence: 99%

The Origins of Spontaneous Grain Refinement in Deeply Undercooled Metallic Melts

Mullis

2014

Metals

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Phase-field modeling of rapid alloy solidification, in which the rejection of latent heat from the growing solid cannot be ignored, has lagged significantly behind the modeling of conventional casting practices which can be approximated as isothermal. This is in large part due to the fact that if realistic materials properties are adopted, the ratio of the thermal to solute diffusivity (the Lewis number) is typically 10 3 -10 4 , leading to severe multi-scale problems. However, use of state-of-the-art numerical techniques, such as local mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, allow these difficulties to be overcome. Here we describe how the application of such a model, formulated in the thin-interface limit, can help to explain the long-standing phenomenon of spontaneous grain refinement in deeply undercooled melts. We find that at intermediate undercoolings the operating point parameter, σ*, may collapse to zero, resulting in the growth of non-dendritic morphologies such as doublons and 'dendritic seaweed'. Further increases in undercooling then lead to the re-establishment of stable dendritic growth. We postulate that remelting of such seaweed structures gives rise to the low undercooling instance of grain refinement observed in alloys.

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Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth

Cited by 167 publications

References 20 publications

Pattern Formation and Morphology Evolution in Langmuir Monolayers

Pattern Formation and Morphology Evolution in Langmuir Monolayers

Domain Growth, Pattern Formation, and Morphology Transitions in Langmuir Monolayers. A New Growth Instability

The Origins of Spontaneous Grain Refinement in Deeply Undercooled Metallic Melts

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