Ivantsov Theory Research Articles

In-situ observation of isothermal CaSiO3 crystallization in CaO–Al2O3–SiO2 melts: A study of the effects of temperature and composition

The crystallization behavior of CaSiO3 in different CaO–Al2O3–SiO2 melts was comprehensively investigated in-situ with a confocal scanning laser microscope (CSLM) over a wide range of temperatures. The observations clearly indicate a transition from a faceted to dendritic crystal morphology with decreasing temperature. The undercooling required for dendritic growth increases with decreasing Al2O3 (under same basicity) and increasing basicity. The dendrite structure becomes finer at higher growth rates with a lower Al2O3 and higher basicity. The growth rates of different dendrites are time-independent. With increasing temperature, the growth rate first increases and then decreases. The observed dendrite tip radii are compared with those obtained from Ivantsov theory in 2D and 3D. With decreasing temperature, the growth conditions in the CSLM experiments appeared to shift from 3D (with the dendrite tip below the surface melt) close to 2D (with the dendrite tip on top of the surface melt).

Scaling Theory of Two-Phase Dendritic Growth in Undercooled Ternary Melts

Two-phase dendrites are needlelike crystals with a eutectic internal structure growing during solidification of ternary alloys. We present a scaling theory of these objects based on Ivantsov's theory of dendritic growth and the Jackson-Hunt theory of eutectic growth. The additional introduction of the relationship ρ∼λ (ρ: dendrite tip radius; λ: eutectic interphase spacing) suggested by recent experimental results [S. Akamatsu et al., Phys. Rev. Lett. 104, 056101 (2010)] leads to a complete solution of theselection problem and to the scaling rule ρ∼λ -1/2 (v: dendrite tip growth rate).

Phase-field simulation of Non-Isothermal dendritic growth of NiCu alloy

Phase-field model is used and The dendrite growth of a Ni-40.83%Cu binaryalloy under were simulated by the model coupled with solute field and temperature field.The effects of solidification latent heat on the growth of equiaxed dendrite, distribution of solute field and temperature field in undercooled liquid alloy were analyzed.The results indicate that the dendritic has well-developed secondary arms as undercooling degree increases.Correspondently, the solute Peclet number and the tip speed increases, the tip radius decreases, and the solute segregation in solid-liquid interface increases. The results agree well with Ivantsov theory.

Phase-field modeling of isothermal solidification in binary alloy

A new phase-field model is developed based on the Ginzberg-Landau theory, which is consistent with WBM model and KKS model. The dendritic growth process during the solidification in a Al-65%Cu binary alloy was simulated using the phase-field model. Solute diffusion equation was solved simultaneously. The effects of undercooling on the dendritic growth and solute profile in isothermal solidification of binary alloy were investigated. The results indicate that the dendritic has well-developed secondary arms with the increase of undercooling. Correspondently, the solute Peclet number and the tip speed increases, the tip radius decreases, and the solute segregation in solid-liquid interface increases. The results agree well with Ivantsov theory.

Equiaxed dendritic solidification in supercooled melts

The growth of equiaxed dendrites from a pure supercooled melt is examined. We propose modifications to the classical Ivantsov theory that allow for consideration of multiple interacting dendrites. The modified theory reveals the existence of a steady-state dendritic solidification mode in a frame of reference moving with the dendrite tip. This regime should be valid from the onset of nucleation to the commencement of time-dependent coarsening when the mass of the solid becomes comparable to the liquid mass in the solidification chamber. This regime is characterized by a reduced (relative to the single dendrite case) heat flux leading to slower solidification rates, but with the same level of supercooling. We study the effects of the relative proximity and number of interacting dendrites through a numerical example of solidification of succinonitrile, a common material used in many experiments. The data show that the model predicts a new steady growth regime that is different than the steady growth law of a single dendrite as described by Ivantsov theory.

Anomaly in dendritic growth data — effect of density change upon solidification

We examine recent dendritic growth data obtained by Glicksman and co-workers [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISIJ Int. 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston, MA, 1995, in press; M.E. Glicksman, M.B. Koss, L.T. Bushnell and J.C. LaCombe, in: Modelling of Casting, Welding and Advanced Solidification Processes VII, Eds. M. Cross and J. Campbell, (The Minerals, Metals and Materials Society, 1995); private communication] in microgravity. These authors have pointed out an anomaly in the data, when compared with theoretical predictions. In particular, a systematic deviation of the growth Pe´clet number from an Ivantsov's theory was noted at the intermediate supercooling range. This work considers effects due to density change upon solidification. This requires a careful reexamination of the definition of material parameters, and an evaluation of effects due to the solidification-induced fluid flow (“Stefan wind”). A consistent application of carefully obtained material parameters clearly eliminates the discrepancy between the theory and experimental data. However, the effect of fluid flow due to the solid-melt density change is shown to be of minor importance to the particular experiment and material under consideration. We conclude by presenting an Ivantsov's theory modified for the wall proximity effect and corrected for density change upon solidification that matches the entire range of supercooling levels used in Glicksman's experiments.

On the role of convection in free dendritic growth: experimental measurement of the concentration field

We present an experiment designed to visualise the concentration field during the growth of dendrites. It is used to assess the role of convection by exploring three situations: growth in a gel, growth in a solution and forced imposed external flow. The observations bear on the qualitative concentration field and the quantitative measurement of the supersaturation. We show that the observations in the three cases can be correctly explained by, respectively, diffusion alone (Ivantsov theory), destabilisation of the liquid by natural convection and a uniform flow at the scale of the dendrite.

Dendritic solidification of rare gases

Rare gases form simple liquids and thus they can be used as model substances to study the dendritic solidification of metals and the development of spatial structures at conditions far from equilibrium. The growth of rare gas dendrites into a volume of about 100 cm 3 supercooled melt was investigated using capillary injection technique. Tip growth velocity v tip' tip radius R, the secondary arm spacing S tip and the volume of the whole dendrite V of krypton and xenon dendrites have been measured in the supercooling range 0.005 < ΔT < 0.3 K. The properties of rare gas dendrites are compared with data of succiononitrile. The data hold the scaling laws, which are based on the assumption that thermal diffusion is the only mechanism of heat transport during dendritic solidification. The data of Kr and Xe do not confirm quantitative predictions of Ivantsov theory, nor the assumption v tipR 2=const. The experiments shows that the volume solidification rate increase with supercooling. The dendrites do not have the shape of a rotational paraboliod. The measurement of the volume of dendrites is done by means of the technique of Archimedes. We find that the volume of a dendrite increase with L 3, where L is an overall dimension of the dendrite.

Self-consistent theory of dendritic growth with convection

A theory is described which treats dentritic growth with forced convection in the melt as a free boundary problem. This approach yields self-consistent solutions for the rate of propagation of an isothermal interface and the temperature and velocity fields surrounding it. The solutions to the free boundary problem reduce to Ivantsov's pure conduction solution when the Reynolds number is zero. It is shown that the Oseen, Stokes and potential flow approximation of the Navier-Stokes equations for convection in a subcooled melt yield exact solutions for the shape preserving growth of a parabolic dendrite. The results given here, and our previous results, yield an infinite family of solutions. Therefore microscopic solvability theory is used to separate the growth velocity, V G, and tip radius, R, for a fixed subcooling, Δ T. The theoretical results which include convection and the solvability relationship agree well with the experimental data of Huang and Glicksman and with the results of Ananth and Gill who used the experimental data directly with the convection theory to separate V G and R. In contrast, Ivantsov's theory, which neglects convection, yields large errors when compared with these experiments, which are correlated well by 2αd 0 V GR 2.1 = 0.03 . This implies that the solvability relationship, 2αd 0 V GR 2 = 60 ϵ 7 4 , in contrast to the heat transfer calculation, is not affected profoundly by convection in the melt in the range of the subcooling used in the experiments. However, the value of V G R 2 decreases slightly, for a fixed degree of anisotropy, ϵ, as the subcooling gets smaller and convection increases in intensity. Forced flow experiments in which flow velocities are orders of magnitude larger than those in natural convection, would help to clarify the effect of convection on interfacial stability.

Growth of needle-shaped crystals in the presence of convection.

The motion of the freezing front between a needle-shaped crystal and a supercooled liquid is analyzed for situations where there is forced convection aligned with the crystal axis. It is shown that in the absence of capillary effects the shape of the crystal-melt interface is a paraboloid of revolution, similar to that found in situations where diffusion is the sole heat-transfer mechanism. A relation between the supercooling, the product of tip velocity and tip radius, and the strength of the flow is derived which reduces to the well-known Ivantsov theory in the absence of convection.