Dendritic growth of undercooled nickel-tin: Part II

High-speed optical temperature measurements were made of the solidification behavior of levitated metal samples within a transparent glass medium. Two undercooled Ni-Sn alloys were examined, one a hypoeutectic alloy and the other of eutectic composition. Recalescence times for the 9 mm diameter samples studied decreased with increasing undercooling from the order of 1.0 second at 50 K under-cooling to less than 10⁻³ second for undercoolings greater than 200 K. Both alloys recalesced smoothly to a maximum recalescence temperature at which the solid was at or near its equilibrium composition and equilibrium weight fraction. For the samples of hypoeutectic alloy that recalesced above the eutectic temperature, a second nucleation event occurred on cooling to the eutectic temperature. For samples which recalesced only to the eutectic temperature, no subsequent nucleation event was observed on cooling. It is inferred in this latter case that both the α and β phases were present at the end of recalescence. The thermal data obtained suggest a solidification model involving (1) dendrites of very fine structure growing into the melt at temperatures near the bulk undercooling temperature, (2) thickening of dendrite arms with rapid recalescence, and (3) continued, much slower recalescence accompanying dendrite ripening.     

High-Speed imaging and analysis of the solidification of undercooled nickel melts

Rapid solidification of undercooled pure nickel has been imaged at sufficiently high spatial resolution (64 ×X 64 pixels) and temporal resolution (40,500 frames/s) to observe interface shape and motion at solidification velocities exceeding 45 m/s. Imaging was of 8 g, quartz-enclosed melts at undercoolings of 70 to 300 K. Dendrite velocities within the melt were calculated from the surface velocities observed employing a simple geometric model of growth. Solidification was found to proceed invariably from a single nucleation point; growth velocity then followed an approximate power-law relationship with respect to undercooling up to some critical value ΔT*, where 150 K < ΔT* < 180 K. At higher undercoolings, velocity increased less rapidly than predicted by the power-law relationship and the interface morphology changed in appearance from angular to macroscopically smooth.     

Dendrite growth processes of silicon and germanium from highly undercooled melts

The crystal growth behavior of a semiconductor from a very highly undercooled melt is expected to be different from that of a metal. In the present experiment, highly pure undoped Si and Ge were undercooled by an electromagnetic levitation method, and their crystal growth velocities (V) were measured as a function of undercooling (ΔT). The value of V increased with ΔT, and V=26 m/s was observed at ΔT=260 K for Si. This result corresponds well with the predicted value based on the dendrite growth theory. The growth behaviors of Si and Ge were found to be thermally controlled in the measured range of undercooling. The microstructures of samples solidified from undercooled liquid were investigated, and the amount of dendrites immediately after recalescence increased with undercooling. The dendrite growth was also observed by a high-speed camera.     

Solidification of highly undercooled Sn- Pb alloy droplets

Experimental work is described on undercooling and structure of tin-lead droplets emulsified in oil. The droplets, predominantly in the size range of 10 to 20 μm, were cooled at rates (just before nucleation) ranging from about 10^-1 K per second to 10⁶ K per second. The higher cooling rates were obtained by a newly developed technique of quenching the emulsified droplets in a cold liquid. Measured undercoolings (at the lower cooling rates) ranged up to about 100 K. Structures obtained depend strongly on undercooling, cooling rate before and after nucleation, and alloy composition. Droplets containing up to 5 wt pct Pb were apparently single phase when undercooled and rapidly quenched. Droplets in the composition range of about 25 wt pct to 90 wt pct Pb solidified dendritically, even at the most rapid quench rates employed, apparently because these alloys undercooled only slightly before nucleation of the primary phase. Formerly Graduate Research Assistant and Postdoctoral Associate in the Department of Materials Science and Engineering, Massachusetts Institute of Technology.     

Direct observation of the crystal-growth transition in undercooled silicon

Using an electromagnetic levitation facility with a laser heating unit, silicon droplets were highly undercooled in the containerless state. The crystal morphologies on the surface of the undercooled droplets during the solidification process and after solidification were recorded live by using a high-speed camera and were observed by scanning electron microscopy. The growth behavior of silicon was found to vary not only with the nucleation undercooling, but also with the time after nucleation. In the earlier stage of solidification, the silicon grew in lateral, intermediary, and continuous modes at low, medium, and high undercoolings, respectively. In the later stage of solidification, the growth of highly undercooled silicon can transform to the lateral mode from the nonlateral one. The transition time of the sample with 320 K of undercooling was about 535 ms after recalescence, which was much later than the time where recalescence was completed.     

Containerless solidification of highly undercooled mullite melts: Crystal growth behavior and microstructure formation

A mullite (3Al₂O₃·2SiO₂) sample has been levitated and undercooled in an aero-acoustic levitator, so as to investigate the solidification behavior in a containerless condition. Crystal-growth velocities are measured as a function of melt undercoolings, which increase slowly with melt undercoolings up to 380 K and then increase quickly when undercoolings exceed 400 K. In order to elucidate the crystal growth and solidification behavior, the relationship of melt viscosities as a function of melt undercoolings is established on the basis of the fact that molten mullite melts are fragile, from which the atomic diffusivity is calculated via the Einstein-Stokes equation. The interface kinetics is analyzed when considering atomic diffusivities. The crystal-growth velocity vs melt undercooling is calculated based on the classical rate theory. Interestingly, two different microstructures are observed; one exhibits a straight, faceted rod without any branching with melt undercoolings up to 400 K, and the other is a feathery faceted dendrite when undercoolings exceed 400 K. The formation of these morphologies is discussed, taking into account the contributions of constitutional and kinetic undercoolings at different bulk undercoolings.     

Heat Flow during Rapid Solidification of Undercooled Metal Droplets

The solidification of undercooled spherical droplets with a discrete melting temperature is analyzed using both a Newtonian and a non-Newtonian (Enthalpy) model. Relationships are established between atomization parameters, the growth kinetics, the interface velocity and undercooling, and other important solidification variables. A new mathematical formulation and solution methodology is developed for simulating the solidification process in an undercooled droplet from a single nucleation event occurring at its surface. The computational mesh used in the enthalpy model is defined on a superimposed bispherical coordinate system. Numerical solutions for the solidification of pure aluminum droplets based on the enthalpy model are developed, and their results are compared to the trends predicted from the Newtonian model. The implications of single vs multiple nucleation events are also discussed. In general, the results indicate that when substantial undercoolings are achieved in a droplet prior to nucleation, the thermal history consists of two distinct solidification regimes. In the first, the interface velocities are high, the droplet absorbs most of the latent heat released, and the external cooling usually plays a minor role. The second regime is one of slower growth, and strongly depends on the heat extraction at the droplet surface. The extent of “rapid solidification”, as determined from the fraction of material solidified at temperatures below a certain critical undercooling, is a function of the nucleation temperature, the particle size, a kinetic parameter, and the heat translow as 10~4. Formerly a Research Associate at the University of Illinois,     

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.     

Rapid dendrite growth in undercooled alloys

The theory of dendritic growth into undercooled alloy melts is extended to the case of large undercoolings, i.e. to high growth rates. This is done by applying the results of the complete stability analysis of a plane interface to the tip of an Ivantsov dendrite. For small Péclet numbers this model corresponds to a model published previously. For large Péclet numbers i.e. large undercoolings, however, the stability parameters become functions of Péclet numbers and cause drastic changes in the growth behaviour of the dendrite. Furthermore the limit of absolute stability is predicted when the undercooling is equal to the sum of the thermal unit undercooling and the equilibrium freezing range of the alloy.     

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     

Crystal-Growth Transition and Homogenous Nucleation Undercooling of Bismuth

The cross-sectional and surface morphologies of highly undercooled bismuth samples are investigated by optical microscopy and scanning electron microscopy. It is found that the grain morphology can be classified into three types. When the undercooling is less than 49 K (49 °C), flaky grains with pronounced edges and faces are arranged parallel to each other, showing the feature of lateral growth. When the undercooling is over 95 K (95 °C), refined equiaxial grains with several smooth bulges on the surface of each grain are randomly arranged, showing the feature of continuous growth. In the undercooling region from 49 K to 95 K (49 °C to 95 °C), the features of both lateral and continuous growth are observed. The microstructures within the sample grains obtained at different undercooling regions are dissimilar, but they all show features of anisotropic growth. Based on the critical growth-transition undercoolings, direct expressions that express the relationship between the solid-liquid interface energy and temperature are determined. Homogenous nucleation undercooling is also predicted according to the solid-liquid interface energy obtained from the critical growth-transition undercooling. The predicted results of homogenous nucleation undercooling for bismuth are in good agreement with the experimental results.     

The effect of undercooling on the cellular precipitation reaction in Cu-3 Pct Ti

The effect of undercooling on the morphology of the cellular precipitation reaction in Cu-3 Pct Ti is examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and serial sectioning experiments. The reaction front formed at small undercooling, which exhibits strong faceting of the precipitate growth interfaces, gradually changes with increasing undercooling to a smoothly curved reaction front with concave precipitate growth interfaces and convex grain boundary segments. This concealment of the faceted reaction front appears to be due to the rapid accumulation of growth ledges with increasing undercooling. This study also indicates that the cellular precipitation reaction, at small undercooling, is initiated by Widmanstätten precipitation. At larger undercoolings, a second mechanism is responsible for cellular genesis. Finally, contrary to accepted models of colony development, serial sectioning experiments show that nucleation of additional lamellae may occur at the faces of existing lamellae, from where they extend laterally to achieve the characteristic interlamellar spacing for that temperature.     

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.     

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.     

Mechanical behavior of cast single phase alloys solidified from undercooled melts

Several ingots (0.0254 m in diam × 0.10 m long) of nickel-30 wt pct copper, nickel-10 wt pct cobalt and iron-25 wt pct nickel were solidified with various undercoolings up to about 200 K, prior to nucleation of the solid. The materials were mechanically tested in the ascast condition. In nickel-30 wt pct copper and iron-25 wt pct nickel alloys the 0.2 pct offset yield strength, ductility and fatigue strength increased with undercooling. A linear relationship was established between 0.2 pct offset yield strength and the square root of secondary dendrite arm spacing in dendritic alloys (undercooled less than 170 K) or that of grain diameter in nondendritic alloys (undercooled more than 170 K). In iron-25 wt pct nickel limited testing indicated improvements in Charpy V-notch impact strength and in fracture toughness with undercooling. No improvement of tensile properties with undercooling was observed in nickel-10 wt pct cobalt, an alloy which solidified normally with very low microsegregation.     

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).     

Undercooling-Induced macrosegregation in directional solidification

The accepted primary mechanism for causing macrosegregation in directional solidification (DS) is thermal and solutal convection in the liquid. This article demonstrates the effects of under-cooling and nucleation on macrosegregation and shows that undercooling, in some cases, can be the cause of end-to-end macrosegregation. Alloy ingots of Pb-Sn were directionally solidified upward and downward, with and without undercooling. A thermal gradient of about 5.1 K/cm and a cooling rate of 7.7 K/h were used. Crucibles of borosilicate glass, stainless steel with Cu bottoms, and fused silica were used. High undercoolings were achieved in the glass crucibles, and very low undercoolings were achieved in the steel/Cu crucible. During under-cooling, large, coarse Pb dendrites were found to be present. Large amounts of macrosegregation developed in the undercooled eutectic and hypoeutectic alloys. This segre-gation was found to be due to the nucleation and growth of primary Pb-rich dendrites, continued coarsening of Pb dendrites during undercooling of the interdendritic liquid, Sn enrichment of the liquid, and dendritic fragmentation and settling during and after recalescence. Eutectic ingots that solidified with no undercooling had no macrosegregation, because both Pb and Sn phases were effectively nucleated at the start of solidification, thus initiating the growth of solid of eutectic composition. It is thus shown that undercooling and single-phase nucleation can cause significant macrosegregation by increasing the amount of solute rejected into the liquid and by the movement of unattached dendrites and dendrite fragments, and that macrosegregation in excess of what would be expected due to diffusion transport is not necessarily caused by convection in the liquid.     

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.     

Dendritic Growth of Undercooled Nickel-Tin: Part III

Studies were made of structure and solute distribution in undercooled droplets of nickel-25 wt pct tin alloy and the eutectic nickel-32.5 wt pct tin alloy. Structures of levitation melted droplets of the Ni-25 wt pct Sn alloy showed a gradual and continuous transition from dendritic to fine-grained spherical with increasing initial undercooling up to about 180 K. Results suggest that all samples solidified dendritically and that the final structures obtained were largely the result of ripening. Experimental data on minimum solute composition in the samples produced are bounded by two calculated curves, both of which assume equilibrium at all liquid-solid interfaces during recalescence and subsequent cooling. One assumes complete diffusion in the solid during recalescence; the other assumes limited diffusion, but partial remelting to avoid superheating of the solid. Several observations support the view that the eutectic alloy solidifies dendritically, much as the hypoeutectic alloy does. Surface dendrites were seen in regions of surface shrinkage cavities and a coarse “dendritic” structure can be discerned on polished sections, which seems to correspond to the large surface “dendrites” seen by high-speed photographs of the hypoeutectic alloy. The structure of highly undercooled eutectic samples is composed fully of an anomalous eutectic. Samples solidified with intermediate amounts of undercooling possess some lamellar eutectic which, it is believed, solidified after recalescence was complete.