The growth rate of dendrites in undercooled tin

The dendrite growth velocity has been determined for tin in melts undercooled as much as 40°C (approximately twice the maximum undercooling reported previously). The results can be represented approximately asV = 0.8 (ΔT) ² WhereV is the growth velocity in mm s⁻¹ and ΔT is the undercooling in degrees centrigrade.     

Microstructure of Y3Al5O12 garnet solidified from the melt undercooled beyond the hypercooling limit

The microstructural evolution of Y₃Al₅O₁₂ garnet (YAG) in a wide undercooling range beyond the hypercooling limit (ΔT _hyp) was investigated by containerless solidification processing. The dendrite to cellular-dendrite transition at high-growth velocity was observed at the undercooling beyond ΔT _hyp. This transition may be explained by the hypothesis that it is difficult to form the well-developed secondary-dendritic arms from the hypercooled melt because of no remaining melt in the interdendritic regions. With a further increase in undercooling beyond ΔT _hyp, a cellular microstructure disappeared, and copious amounts of small particles appeared at an undercooling of approximately 1000 K, which is near the glass-transition temperature where the viscosity is approximately 10¹² Pas. It is suggested that multiple nucleation occurred in the highly viscous undercooled melt because of the high nucleation rate. The grain size of YAG, which was analyzed as a function of undercooling, gradually decreased with increasing undercooling even beyond ΔT _hyp, and no fragmentation of dendrites was observed.     

Microstructural characteristics of Ni-Sb eutectic alloys under substantial undercooling and containerless solidification conditions

Both Ni-36 wt pct Sb and Ni-52.8 wt pct Sb eutectic alloys were highly undercooled and rapidly solidified with the glass-fluxing method and drop-tube technique. Bulk samples of Ni-36 pct Sb and Ni-52.8 pct Sb eutectic alloys were undercooled by up to 225 K (0.16 T _E ) and 218 K (0.16 T _E ), respectively, with the glass-fluxing method. A transition from lamellar eutectic to anomalous eutectic was revealed beyond a critical undercooling ΔT ₁*, which was complete at an undercooling of ΔT ₂*. For Ni-36 pct Sb, ΔT ₁*≈60 K and ΔT ₂*≈218 K; for Ni-52.8 pct Sb, ΔT ₁*≈40 K and ΔT ₂*≈139 K. Under a drop-tube containerless solidification condition, the eutectic microstructures of these two eutectic alloys also exhibit such a “lamellar eutectic-anomalous eutectic” morphology transition. Meanwhile, a kind of spherical anomalous eutectic grain was found in a Ni-36 pct Sb eutectic alloy processed by the drop-tube technique, which was ascribed to the good spatial symmetry of the temperature field and concentration field caused by a reduced gravity condition during free fall. During the rapid solidification of a Ni-52.8 pct Sb eutectic alloy, surface nucleation dominates the nucleation event, even when the undercooling is relatively large. Theoretical calculations on the basis of the current eutectic growth and dendritic growth models reveal that γ-Ni₅Sb₂ dendritic growth displaces eutectic growth at large undercoolings in these two eutectic alloys. The tendency of independent nucleation of the two eutectic phases and their cooperative dendrite growth are responsible for the lamellar eutectic-anomalous eutectic microstructural transition.     

Solid-Liquid Interface Energy between Silicon Crystal and Silicon-Aluminum Melt

By examining the surface morphologies of undercooled Si-20 at. pct Al alloy during and after the solidification process, it is determined that the critical undercooling for silicon to grow from lateral mode to intermediary mode ΔT* and that from intermediary mode to continuous mode ΔT** are 131 and 239 K, respectively. A method that predicts the solid-liquid interface energy of binary lateral growth materials on the basis of ΔT* and ΔT** has been developed. Formulas between the physical parameters and the solid-liquid interface energy have been obtained. The interface energy between silicon crystal and Si-Al melt predicted from ΔT* is almost equal to that from ΔT**. The present results of the solid-liquid interface energy predicted according to ΔT* and ΔT** obtained in Si-20 at. pct Al alloy are in very good agreement with the reported results of the grain-boundary method and the critical undercooling method from ΔT* and ΔT** obtained in pure silicon.     

The solidification of undercooled melts <Emphasis Type="Italic">via</Emphasis> twinned dendritic growth

The solidification of undercooled Cu-x wt pct Sn (x=1, 2, 3, or 4) alloys has been studied by a melt-encasement (fluxing) technique. It was found that below undercoolings of ΔT≈90 K, the preferred dendrite growth orientation in each of these alloys was along the 〈111〉 direction: moreover, the 2 and 3 wt pct Sn alloys also displayed evidence of twinned growth. Above ΔT≈90 K, the preferred growth direction returned to the more usual 〈100〉 orientation.     

The velocity of solidification of highly undercooled nickel

At large undercoolings (τ;10 pctT _M, present theories relating solidification velocity to degree of undercooling do not agree well with reported experimental data for the solidification velocity of nickel as a function of undercooling. The present work shows that this discrepancy is due to two factors. First, the majority of previously reported results overestimate the solidification velocity of nickel at large undercoolings. Second, the scatter in experimental data is so large that a functional relationship between undercooling and velocity is not evident. In this study, the solidification velocity of undercooled nickel was measured using a linear array of 38 photodiodes. The results indicate that the velocity of the thermal field generated by the solid/liquid interface approaches a maximum velocity of 20 m s⁻¹ atΔT} ≈ 10 pctT _M (173 K) and men remains constant with increasing undercooling. This suggests that the velocity of the solid/liquid interface, at undercoolings greater than 10 pctT _M, could be limited by attachment kinetics at the interface. GABRIEL CARRO, formerly Research Associate, Department of Applied and Engineering Sciences, Vanderbilt University     

Further analysis of dendritic growth data for succinonitrile

Data reported by Glicksman, Schaefer and Ayers¹ on dendritic growth kinetics in undercooled succinotrile have been reanalyzed using the Trivedi model of dendritic growth, after relaxation of the arbitrary requirement that the dendrite grows with a tip radius, ρ max, that gives the maximum velocity, V_max The experimental results, for both tip radius and growth velocity, fit the Trivedi model with a tip radius some 2 to 4 times greater than ρ_max. The tip radius adopted by a dendrite growing in liquid at a given undercooling, appears to correspond to the radius which gives relative instability of a sphere growing in liquid with the same undercooling. The experimental results also give qualitative support to the model recently proposed by Cantor and Vogel for the influence of fluid flow on dendritic growth.     

Fragmentation of faceted dendrite in solidification of undercooled B-doped Si melts

The fragmentation of the faceted dendrite of B-doped Si solidified from the undercooled melt was investigated using an electromagnetic levitator. The 〈110〉 dendrites, which grew at ΔT <∼100 K, never fragmented because they were composed of {111} planes with the lowest interface energy. On the other hand, the 〈100〉 dendrites, which grew at ΔT>∼100 K, showing fourfold axial symmetry, broke up into small pieces at undercoolings of more than 200 K. It was suggested that the capillary force acts on the interface with a relatively high energy to break up the dendrite into small pieces, since the 〈100〉 dendrites are composed of {110} and {100} planes with interface energies larger than that of the {111} plane. Moreover, striations of concentric circles formed by the segregation of B revealed that the remaining melt solidifies from the surface toward the center to engulf the fragmented dendrites. This solidification process seems different from those of typical metallic materials, in which the fragmented dendrites are randomly distributed throughout the sample and the remaining liquid solidifies from the fragmented dendrites. This solidification characteristic was discussed in relation to the influence of electromagnetic force on the microstructure of Si.     

Effect of the primary phase on grain coarsening in undercooled Fe-Co alloys

Fe-Co alloy melts with Co contents of 10, 30, and 60 at. pct were undercooled to investigate the dependence of the primary phase on grain coarsening. A pronounced characteristic is that the metastable fcc phase in the Fe-10 at. pct Co alloy and the metastable bcc phase in the Fe-30 at. pct Co alloy will primarily nucleate when undercoolings of the melts are larger than the critical undercoolings for the formation of metastable phases in both alloys. No metastable bcc phase can be observed in the Fe-60 at. pct Co alloy, even when solidified at the maximum undercooling of ΔT = 312 K. Microstructural investigation shows that the grain size in Fe-10 and Fe-30 at. pct Co alloys increases with undercoolings when the undercoolings of the melts exceed the critical undercoolings. The grain size of the Fe-60 at. pct Co alloy solidified in the undercooling range of 30 to 312 K, in which no metastable phase can be produced, is much finer than those of the Fe-10 and Fe-30 at. pct Co alloys after the formation of metastable phases. The model for breakage of the primary metastable dendrite at the solid-liquid interface during recalescence and remelting of dendrite cores is suggested on the basis of microstructures observed in the Fe-10 and Fe-30 at. pct Co alloys. The grain coarsening after the formation of metastable phases is analyzed, indicating that the different crystal structures present after the crystallization of the primary phase may play a significant role in determining the final grain size in the undercooled Fe-Co melts.     

Nucleation and phase selection in undercooled Fe-Cr-Ni melts: Part II. Containerless solidification experiments

The solidification behavior of undercooled Fe-Cr-Ni melts of different compositions is investigated with respect to the competitive formation of δ-bcc (ferrite) and γ-fcc phase (austenite). Containerless solidification experiments, electromagnetic levitation melting and drop tube experiments of atomized particles, show that δ (bcc) solidification is preferred in the highly undercooled melt even at compositions where δ is metastable. Time-resolved detection of the recalescence events during crystallization at different undercooling levels enable the determination of a critical undercooling for the transition to metastable bcc phase solidifcation in equilibrium fcc-type alloys. Measurements of the growth velocities of stable and metastable phases, as functions of melt undercooling prior to solidification, reveal that phase selection is controlled by nucleation. Phase selection diagrams for solidification processes as functions of alloy composition and melt undercooling are derived from two types of experiments: X-ray phase analysis of quenched samples and in situ observations of the recalescence events of undercooled melts. The experimental results fit well with the theoretical predictions of the metastable phase diagram and the improved nucleation theory presented in an earlier article. In particular, the tendency of metastable δ phase formation in a wide composition range is confirmed.     

Crystal multiplication in undercooled Cu + 2 Pct Sn alloy

The effects of undercooling (AT) from 10 to 175° on grain structure were observed in a Cu + 2 wt pct Sn alloy, in which grain refinement does not occur at large degrees of under-cooling. Quenching soon after recalescence retained transient grain structures not previ-ously reported in the literature. Crystal multiplication by dendrite fragmentation occur-red when undercooling below the liquidus lay in the range △T = 10 to 70°, and resulted in complete grain refinement in the range △T = 50 to 70°. Fragmentation affected primary, secondary and tertiary dendrite arms during and after recalescence. At △T = 70° a sharp transition occurred to a radiating fan-shaped structure of twin-related grains ori-ginating from a single point of nucleation, with no evidence of fragmentation. It is pro-posed that the transition results from a change in the free dendritic growth mode, the new shape being a wholly primary form without side-arms. The absence of fragmentation in this range (△T > 70°) suggests that self-buckling contributes to fragmentation in the other range (△T < 70°) and could be at least equal in importance to remelting. Formerly with the University of Queensland, Australia, and the National Research Council of Canada, Ottawa     

Numerical analysis of the rapid solidification of gas-atomized Al-8 Wt Pct Fe droplets

A numerical analysis of the microstructural evolution of microcellular and cellular α-Al phase in gas-atomized Al-8 wt pct Fe droplets was represented. The two-dimensional (2-D) non-Newtonian heat transfer and the dendritic growth theory in the undercooled melt were combined, assuming a point nucleation on the droplet surface and the macroscopically smooth solid-liquid interface enveloping the cell tips. It reproduced the main characteristic features of the reported microstructures quite well and predicted a considerable volume fraction of thermal dendritic growth region in a droplet smaller than 10 μm if an initial undercooling was larger than 100 K. The volume fractions of the microcellular region, g_A, and the sum of the microcellular and cellular region, g_α, were predicted as functions of the heat-transfer coefficient, h, and the initial undercooling, ΔT. It was shown that g_A and g_α, in the typical atomization processes with h = 0.1 to 1.0 W/C.M²K, are dominated by ΔT and h, respectively, but for h larger than 4.0 W/C.M² K, a fully microcellular structure can be obtained irrespective of the initial undercooling.     

Nonequilibrium Solidification,Grain Refinements,and Recrystallization of Deeply Undercooled Ni-20 At. Pct Cu Alloys: Effects of Remelting and Stress

Grain refinement phenomena during the microstructural evolution upon nonequilibrium solidification of deeply undercooled Ni-20 at. pct Cu melts were systematically investigated. The dendrite growth in the bulk undercooled melts was captured by a high-speed camera. The first kind of grain refinement occurring in the low undercooling regimes was explained by a current grain refinement model. Besides, for the dendrite melting mechanism, the stress originating from the solidification contraction and thermal strain in the FMZ during rapid solidification could be a main mechanism causing the second kind of grain refinement above the critical undercooling. This internal stress led to the distortion and breakup of the primary dendrites and was semiquantitatively described by a corrected stress accumulation model. It was found that the stress-induced recrystallization could make the primary microstructures refine substantially after recalescence. A new method, i.e., rapidly quenching the deeply undercooled alloy melts before recalescence, was developed in the present work to produce crystalline alloys, which were still in the cold-worked state and, thus, had the driven force for recrystallization.

     

Microstructures of undercooled Germanium droplets

Small liquid Ge droplets (0.3–0.5 mm diameter) have been undercooled 150–415 ± 20°C below T_m in B₂O₃ flux before solidifying to the diamond cubic phase. A correlation was found between initial undercooling and final grain size. Droplets undercooled <300°C exhibited a coarse grain structure. At greater undercoolings, the grain size became progressively finer. This correlation may be subsidiary to the dependence of grain size on interfacial undercooling. Ge droplets lightly doped with Sn solidified dendritically for undercoolings greater than 250°C. Twinned dendrites have been observed at small undercoolings (~ 10°C) in other experiments. It appears that larger interfacial undercoolings are necessary to grow the twin-free dendrites which we have observed. The correlation between grain size and the presence of dendrites suggests that the grain refinement observed in Ge samples undercooled > 300°C stems from dendritic break-up during solidification.     

Last-stage solidification of alloys: Theoretical model of dendrite-arm and grain coalescence

Hot tearing in castings is closely related to the difficulty of bridging or coalescence of dendrite arms during the last stage of solidification. The details of the process determine the temperature at which a coherent solid forms; i.e., a solid that can sustain tensile stresses. Based on the disjoining-pressure concept used in fluid dynamics, a theoretical framework is established for the coalescence of primary-phase dendritic arms within a single grain or at grain boundaries. For pure substances, approaching planar liquid/solid interfaces coalesce to a grain boundary at an undercooling (ΔT _b ), given by

Criterion for judging the homogeneous and heterogeneous nucleation

A criterion for judging the nucleation form in highly undercooled liquid has, respectively, been derived from the nucleation and structure of liquid. It is found that the nucleation form of a highly undercooled liquid can be judged by determining the S _v in the liquid (where S _v is the surface area of the supposed catalyst in a unit volume of the liquid). When the determined value of S _v is equal to 10^10±1 m⁻¹, the liquid has nucleated homogeneously; it has nucleated heterogeneously if the determined value of S _v is less than 10^10±1 m⁻¹. By calculating the values of S _v in highly undercooled aluminum, copper, and silver, it is found that only silver melted under a slag has been undercooled to its undercooling of homogeneous nucleation.     

Phase Selection and Microstructure Evolution in Nonequilibrium Solidification of Fe40Ni40B20 Alloy

Phase selection and microstructure evolution in nonequilibrium solidification of ternary eutectic Fe₄₀Ni₄₀B₂₀ alloy have been studied. It is shown that γ-(Fe, Ni) and (Fe, Ni)₃B prevail in all the as-solidified samples. No metastable phase has been found in the deeply undercooled samples. This is explained as resulting from the size effect of undercooled solidification. At small and medium undercoolings, the dendrite γ-(Fe, Ni) appears as the leading phase. This is ascribed to the existence of the skewed coupled growth zone in FeNiB alloy. With increasing undercooling, the amount of dendrites first increases and then decreases, accompanied by a transition from regular eutectic to anomalous eutectic. The formation mechanisms of the anomalous eutectics are discussed. Two kinds of microstructure refinement are found with increasing undercooling in a natural or water cooling condition. However, for melts with the same undercooling, the as-solidified microstructure refines first, and then coarsens with an increasing cooling rate. The experimental results show that the nanostructure eutectic cell has been obtained in the case of Ga-In alloy bath cooling with an initial melt undercooling of approximately 50 K (50 °C).