Nucleation and phase selection in undercooled Fe-Cr-Ni melts: Part I. Theoretical analysis of nucleation behavior

The selection of the primary solidifying phase in undercooled stainless steel melts is theoretically analyzed in terms of nucleation theory. Nucleation phenomena are considered using different models for the solid-liquid interface energy. The classical nucleation theory for sharp interfaces and an improved modification, the diffuse interface theory, are applied. The influence of deviations of the nucleus composition from the overall alloy composition is also revealed. A preferred nucleation of the metastable bcc phase in fcc equilibrium solidification-type alloys is predicted. The critical undercooling of metastable crystallization as a function of alloy composition is calculated for an isoplethal section at 69 at. pct Fe of Fe₆₉Cr_31-x Ni _x alloys. The results are summarized in a phase selection diagram predicting the primary solidification mode as a function of undercooling and melt composition.     

Phase selection in undercooled ti3sn melts

The solidification of undercooled Ti₃Sn melts was investigated using electromagnetic levitation and electrohydrodynamic atomization experiments followed by extensive microstructural char- acterization. The study was motivated by several reports on the kinetic preference for the body- centered cubic (bcc) phase over more closely packed disordered and ordered structures during competitive crystallization from undercooled melts. At low undercoolings, Ti₃Sn melts yield the equilibrium ordered hexagonal DO₁₉ structure, which is retained without change upon cool- ing. Undercoolings between ~100 and ~300 K yield primary dendrites with hexagonal sym- metry but a final microstructure which is clearly martensitic in origin. Two previously unknown metastable forms of Ti₃Sn were identified: an ordered base-centered orthorhombic derived from the α martensite and an ordered monoclinic phase related to the face-centered orthorhombic martensite observed in the Ti-V system. Both phases are believed to evolve from the solid state transformation of a high temperature β phase, but the dendritic structure clearly indicates the formation of a hexagonal phase different from DO₁₉,i.e., α. The latter forms in preference to β, which has a larger driving force in at least part of the undercooling regime studied. It is proposed that the primary α transforms to β as a consequence of recalescence, which subse- quently transforms martensitically and orders to yield the observed metastable forms of Ti₃Sn.     

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.     

Theoretical treatment of the solidification of undercooled Fe-Cr-Ni melts

The solidification behavior of undercooled Fe-Cr-Ni melts is analyzed with respect to the competitive formation of body-centered cubic (bcc) phase (ferrite) and face-centered cubic (fcc) phase (austenite). The activation energies of homogeneous nucleation and growth velocities for both phases as functions of undercooling of the melt are calculated on the basis of current theories of nucleation and dendrite growth using data of thermodynamic properties available in the literature. As model systems for numerical calculations, the alloys Fe-18.5Cr-11Ni forming primary ferrite and Fe-18.5Cr-12.5Ni forming primary austenite under near-equilibrium solid-ification conditions are considered. Nucleation of the bcc phase is always promoted in the under-cooled primary ferrite alloy, whereas the barrier for bcc nucleation falls below that for fcc nucleation for large undercooling in primary austenite alloys. With rising undercooling, tran-sitions of the fastest growth mode were found from bcc to fcc and subsequently from fcc to bcc for the primary ferrite forming alloy and from fcc to bcc for the primary austenite forming alloy. The results of the calculations provide a basis for understanding contradictory experi-mental findings reported in the literature concerning phase selection in rapidly solidified stainless steel melts for different process conditions. Formerly Visiting Scientist at the Institut fur Raumsimulation     

Electromagnetic Levitation: In‐situ Diagnostics of Non‐Equilibrium Solidification of Undercooled Melts

The electromagnetic leviation technique is applied for undercooling of bulk melts of metallic alloys. Large degrees of undercooling become accessible by avoiding heterogeneous nucleation on container walls and processing the melt under high purity conditions. This article reviews various in‐situ diagnostic methods such as the capacitance proximity sensor technique, high‐speed videometry and in‐situ X‐ray diffraction using synchrotron radiation to study non‐equilibrium solidification phenomena in undercooled melts. Experimental results on metastable phase formation and rapid solidification determined with high accuracy are used to verify theories for nucleation and dendritic growth.     

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.     

Vacuum Electromagnetic Levitation Melting and Undercooling of Peritectic Terfenol-D

For the first time, the undercooling of a magnetostrictive material-a near peritectic Tb0.27TDy0.73Fe1.90 alloy was realized by vacuum electromagnetic levitation melting and 60 K undercooling was obtained. There is one recaleseence be-havior during sol;difieation of the undercooled melt, which can attribute to the priority precipitation of REFe2 phase instead of REFe3 phase, due to preferential nucleation and higher crystal growth rate of REFe2 phase and the suppression of peri-tectic reaction. According to the crystal structural characteristic of REFe2 and REFe3, REFe2 is a Laves phase intermetal-lics with MgCu2 type structure, which has similar polytetrahedral structure wltn short range ordered structure in under-cooled melt and has lower potential barrier for nucleation than that of REFe3, which lead to the preferential nucleation of REFe2 phase directly from the undercooled melt. Also, the similarity of structures between REFe2 phase and undereooled melt leads to higher crystal growth rate of REFe2 phase than that of REFe3.     

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.

     

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).     

Metastable Phase Formation and Its Transformation in Highly Undercooled Ni75B25 Alloy

Ni₇₅B₂₅ alloy was solidified at various undercooling. The formation and subsequent transformation of metastable Ni₂₃B₆ phase were clearly identified. If undercooling prior to nucleation is less than a critical value of 240 K (240 °C), the alloy solidifies completely into Ni₃B phase. At larger undercooling, metastable Ni₂₃B₆ phase primarily forms in the melt but then is decomposed into α-Ni and Ni₃B through a eutectoid reaction. The decomposition simultaneously triggers the rapid solidification of residual liquid, due to which a second temperature recalescence occurs. The α-Ni/Ni₃B eutectoid is partially remelted if temperature exceeds the eutectic temperature during the second recalescence. Then, residual Ni₃B grows into coarse round grains while the remaining liquid re-solidifies into α-Ni/Ni₃B eutectic structure in the remelted region. In the case that the eutectic temperature is not reached, the eutectoid product with dot α-Ni distributing in Ni₃B matrix is retained in the solidification structure. A longer delay time between the two temperature recalescence events means less residual liquid, lower recalescence temperature and thus depressed remelting. The formation competition between Ni₃B and Ni₂₃B₆ phases in the alloy melt is nucleation controlled. The heterogeneous site in Ni₇₅B₂₅ alloy melt is a better nucleation substrate for Ni₂₃B₆ phase than for Ni₃B phase.

Graphical abstract

     

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.     

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.     

Solidification of undercooled Sn-Sb peritectic alloys: Part I. Microstructural evolution

The droplet emulsion technique, which involves dispersal of a bulk liquid alloy into a collection of fine droplets (5 to 30μm), was applied to Sn-Sb alloys to yield high levels of controlled undercooling. The maximum undercooling levels achieved varied from 179 °C for pure Sn to 113 °C for a Sn-16 at. pct Sb alloy. Analysis of hypoperitectic alloy samples (alloys with an Sb content less than that of the liquid at the peritectic temperature) indicates that solute trapping occurs during solidification at the levels of undercooling and cooling rate investigated, yielding nearly homogeneousβ-tin solid solutions with compositions approaching those of the bulk alloys. With increasing undercooling and/or cooling rate, hyperperitectic alloys exhibit a transition from a highly segregated structure consisting of faceted primary intermetallic phase and cellularβ to a structure consisting primarily of a supersaturated tin-rich solid solution. Lattice constant measurements confirm that virtually complete supersaturation ofβ-tin was achieved in emulsion samples cooled at 200 °C s^s−1 for compositions up to approximately 20 at. pct Sb. The development and characteristics of subsequent solid-state precipitation were used to guide the interpretation of the often complex solidification reaction sequences in the hyperperitectic alloys. The formation of supersaturatedβ-tin solid solutions in the undercooled samples is related to the appropriate metastable phase equilibria and the development of solute trapping. Formerly Graduate Student, Department of Materials Science and Engineering, University of Wisconsin-Madison     

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.     

Microstructural transitions during containerless processing of undercooled Fe-Ni alloys

The microstructural development associated with solidification in undercooled Fe-Ni alloys has been reported in different studies to follow various pathways, with apparent dissimilarities existing as a function of sample size and processing conditions. In order to identify the possible hierarchy of microstructural pathways and transitions, a systematic evaluation of the microstructural evolution in undercooled Fe-Ni alloys was performed on uniformly processed samples covering seven orders of magnitude in volume. At appropriate undercooling levels, alternate solidification pathways become thermodynamically possible and metastable product structures can result from the operation of competitive solidification kinetics. For thermal history evaluation, a heat flow analysis was applied and tested with large Fe-Ni alloy particles (1 to 3 mm) to assess undercooling potential. Alloy powders (10 to 150 μm), with large liquid undercoolings, were studied under the same composition and processing conditions to evaluate the solidification kinetics and microstructural evolution, including face-centered cubic (fcc)/body centered cubic (bcc) phase selection and the thermal stability of a retained metastable bcc phase. The identification of microstructural transitions with controlled variations in sample size and composition during containerless solidification processing was used to develop a microstructure map which delineates regimes of structural evolutions and provides a unified analysis of experimental observations in the Fe-Ni system.     

Solidification of undercooled Fe-Cr-Ni alloys: Part III. Phase selection in chill casting

In Parts I and II of this series of articles, it was shown that a range of levitation-melted Fe-Cr-Ni alloys, both hypoeutectic and hypereutectic, all solidified with the hypereutectic phase (bcc) as their primary phase, except for the hypoeutectic alloys at low undercoolings. In this article, the effect of heat extraction on phase formation is studied by chill casting the undercooled alloys before nucleation. Two of the previously studied alloys are examined; one hypoeutectic and the other hypereutectic. Chill substrates employed were copper, stainless steel, alumina, zirconia, and a liquid gallium-indium bath. Contrary to the case of levitation melting and solidification, it is found that the dominant primary phase to solidify in both alloys, independent of chill substrate, is the hypoeutectic phase (fcc). It is concluded that chilling the undercooled melt results in nearly concurrent nucleation of bcc and fcc. Two different mechanisms are considered as possible explanations of the subsequent fcc phase selection during growth. These are termed “growth velocity” and “phase stability” mechanisms. Evidence favors a phase stability mechanism, in which the bcc phase massively transforms to fcc early in solidification so that fcc then grows without competition. It is suggested that this mechanism may also explain structures observed in welds and other rapid solidification processes.     

Solidification of undercooled Fe-Cr-Ni alloys: Part I. Thermal behavior

Solidification of undercooled Fe-Cr-Ni alloys was studied by high-speed pyrometry during and after recalescence of levitated, gas-cooled droplets. Alloys were of 70 wt pct Fe, with Cr varying from 15 to 19.7 wt pct, balance was Ni. Undercoolings were up to about 300 K. Alloys of Cr content less than that of the eutectic (18.1 wt pct) have face-centered cubic (fee) (austenite) as their equilibrium primary phase, and alloys of higher Cr content have body-centered cubic (bcc) (ferrite) as their equilibrium primary phase. However, except at low undercoolings in the hypoeutectic alloys, all samples solidified with bcc as the primary phase; the bcc then transformed to fcc during initial recalescence for the lower Cr contents or during subsequent cooling for the higher Cr contents. The bcc-to-fcc transformation, whether in the semisolid or solid state, was detected by a second recalescence. In the hypoeutectic alloys, the growth of primary metastable bcc apparently results from preferred nucleation of bcc. The subsequent nucleation of fcc may occur at bcc/bcc grain boundaries. Formerly Graduate Student, Department of Materials Science and Engineering, Massachusetts Institute of Technology     

The undercooling of aluminum

An important parameter affecting microstructure development during solidification is the amount of undercooling prior to nucleation. The undercooling potential of aluminum has been assessed by thermal analysis measurements on powder dispersions of the liquid metal. A number of variables have been identified which influence the undercooling of powder Al samples including powder coating, powder size, melt cooling rate, and melt superheat. Surface analysis by Auger electron spectroscopy indicates that changing the medium in which the powders are produced is an effective method of altering the coating chemistry. Factorial design analysis has been employed to quantify the potential of processing variables to increase the undercooling level obtainable in aluminum. The factorial analysis indicates that control of the powder coating through changing the medium in which the powders are produced is most effective in decreasing the nucleation temperature. Additionally, the finest powders produced in the medium which induces the least catalytic coating, when cooled at high rates,T = 500 °C/s, from low superheats,T _s = 710 °C, are found to achieve the deepest undercooling, ΔT = 175 °C. These studies provide the basis for further increases in undercooling and for future investigations into the solidification reactions which produce both stable and metastable structures in aluminum alloys. Formerly Research Assistant in the Department of Metallurgical and Mineral Engineering, University of Wisconsin-Madison     

Nonequilibrium Solidification Behavior of Co-Si Alloys Near the First Eutectic Point

Adopting a fluxing purification and cyclic superheating technique, Co-10 wt pct Si and Co-15 wt pct Si alloys had been undercooled to realize rapid solidification in this work. It was investigated that the solidification modes and microstructures of Co-Si alloys were deeply influenced by the undercooling of the melts. Both alloys solidified with a near-equilibrium mode in a low undercooling range; the peritectic reaction occurred between the primary phase and the remnant liquids, and it was followed by the eutectic reaction and eutectoid transformation. With the increase of undercooling, both alloys solidified with a nonequilibrium mode, and the peritectic reaction was restrained. As was analyzed, a metastable Co₃Si phase was found in Co-10 wt pct Si alloy when a critical undercooling was achieved.