Theory of dendritic growth—I. Elements of a stability analysis

Langer, J. S.; Müller‐Krumbhaar, H.

doi:10.1016/0001-6160(78)90078-0

Cited by 690 publications

(233 citation statements)

References 9 publications

Supporting

Mentioning

198

Contrasting

Unclassified

Order By: Relevance

“…For a planar interface  * takes the value [21] 1/(4 2 )  0.0253, while similar values have been found for other shapes, including 2-and 3-D parabolic needles [23] . The apparent validity of these models was supported by the direct simultaneous measurement of V and  for succinonitrile [24] which yielded an experimental value for  * in this system of 0.0195, in close agreement with theory.…”

Section: Introductionsupporting

confidence: 69%

The prediction of tip radius during rapid dendritic growth under coupled thermo-solutal control: What value σ

Mullis

Rosam

Jimack

2009

Trans Indian Inst Met

View full text Add to dashboard Cite

A phase-field model for dendritic growth under coupled thermo-solutal control model is presented. Constructed in the quantitatively valid thin-interface limit the model uses advanced numerical techniques such as mesh adaptivity, multigrid and implicit time-stepping to solve the non-isothermal alloy solidification problem for materials parameters that are realistic for metals. Using this model we demonstrate that the dendrite radius selection parameter,  * , shows a complex dependence on a number of materials properties including undercooling, Lewis number, alloy concentration and partition coefficient, in addition to the known dependence on anisotropy strength. Consequently, we argue that as a predictive tool, at least for non-isothermal alloy solidification away from the limits of vanishing concentration and Peclet number, the concept of  * probably retains little intrinsic value.2

show abstract

Section: Introductionsupporting

confidence: 69%

The prediction of tip radius during rapid dendritic growth under coupled thermo-solutal control: What value σ

Mullis

Rosam

Jimack

2009

Trans Indian Inst Met

View full text Add to dashboard Cite

show abstract

“…13 Equations ͑2͒-͑6͒ describe the undercooling in terms of the product of the growth velocity times the dendrite tip radius. For a unique calculation of V as a function of undercooling, ⌬T, we utilize the criterion of marginal stability 22,23 which gives an independent expression of the dendrite tip radius:…”

Section: A Analysis Of Dendrite Growth Velocitiesmentioning

confidence: 99%

Parameter-free test of alloy dendrite-growth theory

Arnold

Aziz²,

Schwarz³

et al. 1999

Phys. Rev. B

View full text Add to dashboard Cite

In rapid alloy solidification the dendrite-growth velocity depends sensitively on the deviations from local interfacial equilibrium manifested by kinetic effects such as solute trapping. The dendrite tip velocityundercooling function was measured in dilute Ni͑Zr͒ over the range 1-25 m/s and 50-255 K using electromagnetic levitation techniques and compared to theoretical predictions of the model of Trivedi and colleagues for dendritic growth with deviations from local interfacial equilibrium. The input parameter to which the model predictions are most sensitive, the diffusive speed V D characterizing solute trapping, was not used as a free parameter but was measured independently by pulsed laser melting techniques, as was another input parameter, the liquid diffusivity D L . Best-fit values from the pulsed laser melting experiment are V D ϭ26 m/s and D L ϭ2.7ϫ10 Ϫ9 m 2 /s. Inserting these values into the dendrite growth model results in excellent agreement with experiment with no adjustable parameters. ͓S0163-1829͑99͒02101-3͔

show abstract

“…The ability to correctly predict ρ is a problem of fundamental importance to the theory of dendritic growth with an additional dendritic tip selection constant (stability parameter) σ* needed to determine the operating conditions (the combination of radius ρ and growth rate V) at the dendrite tip. Values of the σ* have been calculated based on two main dendritic growth theories: marginal stability [3] and microscopic solvability [4]. The marginal stability estimates the tip selection parameter as constant for all materials under all conditions to be 1/4π 2 ≈ 0.025 which is very close to the numerical value of σ* = 0.025 evaluated by Langer and Müller-Krumbhaar [3] for the symmetric problem in 3D, but approximately twice smaller than a value calculated using 3D phase-field simulations by Oguchi and Suzuki [5] for Al-4.5wt%Cu as a onesided problem (the solute diffusion in the solid phase is negligible).…”

Section: Introductionmentioning

confidence: 99%

“…Values of the σ* have been calculated based on two main dendritic growth theories: marginal stability [3] and microscopic solvability [4]. The marginal stability estimates the tip selection parameter as constant for all materials under all conditions to be 1/4π 2 ≈ 0.025 which is very close to the numerical value of σ* = 0.025 evaluated by Langer and Müller-Krumbhaar [3] for the symmetric problem in 3D, but approximately twice smaller than a value calculated using 3D phase-field simulations by Oguchi and Suzuki [5] for Al-4.5wt%Cu as a onesided problem (the solute diffusion in the solid phase is negligible). Based on the marginal stability theory the KurzGiovanola-Trivedi (KGT) constrained (columnar) dendritic growth model was developed for steady-state conditions with the stability parameter which is equal to 0.0253 [6].…”

Section: Introductionmentioning

confidence: 99%

The role of the dendritic growth model dimensionality in predicting the Columnar to Equiaxed Transition (CET)

Seredyński

Rebow²,

Banaszek

2017

Heat Mass Transfer

View full text Add to dashboard Cite

The dendrite tip kinetics model accuracy relies on the reliability of the stability constant used, which is usually experimentally determined for 3D situations and applied to 2D models. The paper reports authors`attempts to cure the situation by deriving 2D dendritic tip scaling parameter for aluminium-based alloy: Al4wt%Cu. The obtained parameter is then incorporated into the KGT dendritic growth model in order to compare it with the original 3D KGT counterpart and to derive two-dimensional and three-dimensional versions of the modified Hunt's analytical model for the columnar-to-equiaxed transition (CET). The conclusions drawn from the above analysis are further confirmed through numerical calculations of the two cases of Al4wt%Cu metallic alloy solidification using the front tracking technique. Results, including the porous zoneunder-cooled liquid front position, the calculated solutal under-cooling, the average temperature gradient at a front of the dendrite tip envelope and a new predictor of the relative tendency to form an equiaxed zone, are shown, compared and discussed for two numerical cases. The necessity to calculate sufficiently precise values of the tip scaling parameter in 2D and 3D is stressed.

show abstract

Theory of dendritic growth—I. Elements of a stability analysis

Cited by 690 publications

References 9 publications

The prediction of tip radius during rapid dendritic growth under coupled thermo-solutal control: What value σ

The prediction of tip radius during rapid dendritic growth under coupled thermo-solutal control: What value σ

Parameter-free test of alloy dendrite-growth theory

The role of the dendritic growth model dimensionality in predicting the Columnar to Equiaxed Transition (CET)

Contact Info

Product

Resources

About