Growth from the Melt. III. Dendritic Growth

Bolling, G. F.; Tiller, W. A.

doi:10.1063/1.1728359

Cited by 184 publications

(45 citation statements)

References 17 publications

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“…Although the B-F and C-K models assume the uniform distribution of solute elements in liquid phase, Doherty et al, 21) Weinberg et al 27) and Sugiyama et al 30) suggested that during the initial solidification stage near the mold side, the diffusion layer exists ahead of solid-liquid interface and, hence, the effective partition coefficient increases with the cooling rate according to Bolling-Tiller model. 31) Their suggestion results in the less microsegregation in the mold side compared with the center part of the ingot. In addition, other explanations were proposed for the increase in the microsegregation from the mold side to the center.…”

Section: )mentioning

confidence: 99%

As-cast Austenite Grain Structure in Al Added 0.2 wt% Carbon Steel

et al. 2010

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Figure 3 shows a phase diagram of Fe-0.2wt%C-0.035wt%P-0.8wt%Mn-0.2wt%Si-0.006wt%N-xAl system calculated from CALPHAD method. 14) We employed the thermodynamic database, PanIron for all the calculations. 15) The horizontal axis is Al concentration. The liquidus temperature does not substantially change with the Al concentration. It should be noticed that the type of steel changes from hyperperitectic to hypoperitectic one at 0.53 wt% Al. When Al concentration is less than 0.53 wt%, the solidus temperature, in other words, T g decreases very slightly with Al concentration. On the other hand, in the range of Al concentration for hypoperitectic steel, d phase is stabilized at lower temperatures by increasing Al concentration, leading to drastic decrease in T g . As mentioned in the introduction, it has been reported that g grains grow rapidly below T g and, therefore, lowering T g leads to finer g grain structure. However, the decrement of T g up to 0.54 wt% Al is quite small. Therefore, the Al addition does not lead to significant change in the g grain structure during slow cooling process, as is consistent with the result of Figs. 1 and 2. In Fig. 3, also, the temperature for formation of AlN phase increases with the increase in Al concentration. However, the AlN phase forms at much lower temperatures than T g in all samples of the present experiments. Hence, it is considered that the AlN phase precipitates from g phase after g grain growth substantially occurs at the high temperature region. In the present SEM/EPMA analysis, AlN particles were rarely detected. Casting ExperimentFigure 4(a) shows the as-cast g grain structure in the sample with 0.04 wt% Al. As described in the Sec. 2, the g grain boundary is decorated with film-like proeutectoid a phase. The bottom of the micrograph corresponds to the mold side, while the top part represents the center of the ingot. It is seen that the columnar grains develop from the mold side to the center of the ingot along the thickness direction, which coincides with the direction of heat flow in the present casting condition, and the equiaxed grains form in the central region. It is noted that very fine columnar grains form between the columnar grain region and the equiaxed grain region. Therefore, this as-cast g grain structure can be characterized by three regions, Coarse Columnar Grain (CCG) region near the mold side, Equiaxed Grain (EG) region in the central region of the ingot, and Fine Columnar Grain (FCG) region in between the CCG and the EG regions.Figure 4(b) shows the d dendrite structure at the same location. The d dendrite structure consists of columnar dendrites developing from the mold side to the inward of the sample and the equiaxed dendrites in the central region. By comparing the as-cast g grain and d dendrite structures (Figs. 4(a) and 4(b)), the CCG and FCG are found to originate from the columnar dendrites. The cooling rates at various positions from the mold side toward the center can be evaluated by the empirical equation, l 2 ϭ710(60Ṫ) Ϫ0.39 , wher...

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Section: )mentioning

confidence: 99%

As-cast Austenite Grain Structure in Al Added 0.2 wt% Carbon Steel

et al. 2010

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“…Moreover, application of capillarity as the temperature boundary condition on the solid-liquid interface comprises the identical methodology used since the earliest models of dendritic growth were considered over 50 years ago. [7,8] In the next section, we show that the Gibbs-Thomson capillarity effect is much more than just a boundary condition on the surrounding transport field. Capillarity introduces temperature gradients along a dendritic interface-albeit extremely weak ones-so that the GibbsThomson equilibrium temperature distribution acts as an independent energy field during crystal growth, producing, as we shall demonstrate, more important effects on the branching process than recognized previously.…”

Section: E Testing Current Theories Of Dendritic Growthmentioning

confidence: 99%

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] These efforts included precepts and hypotheses on dendritic interfacial physics as varied as the following: Take, for example, item (a), the concept of maximum velocity, which would occur, hypothetically, for a paraboloidal dendrite, the solid-liquid interface of which has interfacial energy, i.e., capillarity. As all interfaces have excess free energy, or surface tension, this idea could, conceivably, have provided a reasonable supposition about the operating state of dendrites: namely, that dendrites grow steadily when they achieve their maximum velocity, as allowed by the thermal conduction field and the level of supercooling specified in the melt.…”

Section: Interfacial Physicsmentioning

confidence: 99%

Mechanism of Dendritic Branching

Glicksman

2011

Metall Mater Trans A

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Theories of dendritic growth currently ascribe pattern details to extrinsic perturbations or other stochastic causalities, such as selective amplification of noise and marginal stability. These theories apply capillarity physics as a boundary condition on the transport fields in the melt that conduct the latent heat and/or move solute rejected during solidification. Predictions based on these theories conflict with the best quantitative experiments on model solidification systems. Moreover, neither the observed branching patterns nor other characteristics of dendrites formed in different molten materials are distinguished by these approaches, making their integration with casting and microstructure models of limited value. The case of solidification from a pure melt is reexamined, allowing instead the capillary temperature distribution along a prescribed sharp interface to act as a weak energy field. As such, the Gibbs-Thomson equilibrium temperature is shown to be much more than a boundary condition on the transport field; it acts, in fact, as an independent energy field during crystal growth and produces profound effects not recognized heretofore. Specifically, one may determine by energy conservation that weak normal fluxes are released along the interface, which either increase or decrease slightly the local rate of freezing. Those responses initiate rotation of the interface at specific locations determined by the surface energy and the shape. Interface rotations with proper chirality, or rotation sense, couple to the external transport field and amplify locally as side branches. A precision integral equation solver confirms through dynamic simulations that interface rotation occurs at the predicted locations. Rotations points repeat episodically as a pattern evolves until the dendrite assumes a dynamic shape allowing a synchronous limit cycle, from which the classic repeating dendritic pattern develops. Interface rotation is the fundamental mechanism responsible for dendritic branching.

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“…It was pointed out that due to the interfacial curvature and interfacial kinetics, the interface is essentially nonisoconcentrational for an isothermal transformation 3,4 and nonisothermal in solidification. 5,6 Approximate treatments were presented therein.…”

Section: Introductionmentioning

confidence: 99%

On the applicability of the Ivantsov growth equation

Liu

Chang

1997

Journal of Applied Physics

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The steady state growth equation for a paraboloid of revolution and a parabolic cylinder, taking the interfacial energy into account, is revisited. Although the consideration of the interfacial energy was necessary, the growth equation was much more complicated than the original equation with a zero interfacial energy, since both the thermodynamics and kinetics of the growth are considered in one equation. In the present work, we take advantage of the development in computational thermodynamics and consider the thermodynamics and kinetics of the process in separate equations, but solve them simultaneously. A consistent framework to describe the phenomena and compare it with previous treatment of the interfacial energy will be presented.

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Growth from the Melt. III. Dendritic Growth

Cited by 184 publications

References 17 publications

As-cast Austenite Grain Structure in Al Added 0.2 wt% Carbon Steel

As-cast Austenite Grain Structure in Al Added 0.2 wt% Carbon Steel

Mechanism of Dendritic Branching

On the applicability of the Ivantsov growth equation

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