1. Introduction

Following solidification of low-carbon steel in a continu-ous casting mould, the delta-ferrite to austenite phase tran-sition occurs in the thin solid shell in close proximity to themeniscus. It is well known that many casting defects origi-nate in this region and yet, very little is known about themorphological development of this important phase transi-tion. The introduction of high speed continuous castingtechniques has elevated the need to more deeply understandthe mechanism and rate of this important phase change.The lack of knowledge about the mode and mechanism ofthe delta-ferrite to austenite phase transition is due, at leastin part, to the difficulty of making in-situ observations.Direct observation of the phase change has been problemat-ic because of the difficulties of obtaining high resolution inhigh temperature metallography and also because the delta-ferrite to austenite phase transition in Fe–C alloys ismasked by subsequent austenite decomposition preventingthe use of quench-arrest techniques. With the developmentof high-temperature confocal microscopy, a technique bywhich high optical resolution can be obtained at high tem-perature, the interest in studying the d to g phase transitionhas been rejuvenated.1) It is therefore not surprising thatYin et al.1) has employed the technique in their study of thisphase transformation. One of the interesting observationsthey made was that a growing planar d /g interface can de-generate into an unstable growth morphology. They pro-posed that this morphological development could be ex-plained by the application of the Mullins-Sekerka type sta-bility analysis.2,3) These observations of unstable growthmorphology during the d to g phase transformation in alow carbon, aluminium killed steel are reproduced in Fig. 1,highlighting the relevant microstructural features.

In this collage of laser scanning confocal microscopy(LSCM) images, Yin et al.1) digitally enhanced the austen-ite phase to increase the contrast between austenite and thedelta-ferrite matrix. The features of greatest interest to thepresent study are those associated with austenite grains Aand B, which have developed a “finger-like” interphasemorphology. Yin et al. argued that this morphology couldbe described by a Mullins-Sekerka type stability analysis.In regard to the application of the M–S analysis to solid-state phase transformations, Shewmon noted that the stabil-ity of planar transformation interfaces is greater than predicted on the basis of diffusion gradients alone.4)

Widmanstätten ferrite growth, being dependent upon a lim-ited set of crystallographic orientation relationships be-tween the ferrite and the austenite parent phase, was citedas an example. Shewmon concluded that interfacial reac-tion kinetics must play a role in stabilising solid-solid interfaces when semi or full coherency is established be-tween the precipitate and parent phase. The importance ofShewmon’s analysis is that the mobility of a progressing in-terface has a determining influence upon the stability ofthat interface, and hence, the interface stability is not onlydetermined by solute diffusion.

Yin et al.1) argued that the issues raised by Shewmonwere not relevant to the progression of a delta-ferrite/austenite interphase boundary, and that the Mullins-Sekerkainstability analysis could therefore be directly applied toanalyse the stability of such an interface. They contendedthat delta-ferrite/austenite boundaries are incoherent; there-fore the rate of progression of such interfaces should be dif-fusion controlled. Moreover, the delta-ferrite/austenite in-terphase boundary possesses isotropic free energy, and assuch interfacial mobility should be very fast and can be ig-nored. Furthermore, at the high temperatures associated

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Instability of the Delta-ferrite/austenite Interface in Low CarbonSteels: The Influence of Delta-ferrite Recovery Sub-structures

Dominic PHELAN and Rian DIPPENAAR

BHP Steel Institute University of Wollongong Wollongong, NSW, Australia.

(Received on June 27, 2003; accepted in final form on September 5, 2003 )

An in-situ study of the delta-ferrite/austenite phase transformation in low carbon steels utilising laserscanning confocal microscopy has found that the presence of a recovery sub-structure in the delta-ferritephase plays an active role in the apparent instability of delta-ferrite/austenite interfaces. Phase field model-ling conducted in an attempt to quantify the influence of sub-boundaries on the transformation rate of delta-ferrite to austenite in Fe–C and Fe–C–Mn alloys, confirmed the in-situ observations that austenite growspreferentially along delta-ferrite sub-boundaries. The modelling studies also predicted that the transforma-tion kinetics of the delta-ferrite to austenite would be enhanced if a sub-boundary network were present inthe delta-ferrite grains.

KEY WORDS: delta-ferrite; austenite; transformation; instability; steel; phase field; model.

with the delta-ferrite to austenite transformation, the trans-formations stresses will be low, and therefore the stabilisingeffect of stresses due to volumetric changes may be neglect-ed.

The spacing of the observed instability of the delta-fer-rite/austenite interphase boundary in Fig. 1, is 120 mm. Yinet al.1) used the spacing relationship developed by Kurz andFisher,5) Eq (1), to calculate the expected wavelength of theinstabilities for the alloys used in their study, and found it tobe equal to 123 mm. This excellent correlation between ob-served and calculated wavelengths was used to justify theapplication of the Mullins-Sekerka stability analysis to thedelta-ferrite to austenite phase transformation.

.............................(1)

l is the instability wavelength, V the interface velocity, Dthe diffusion coefficient, G the Gibbs–Thomson undercool-ing, and DTo the equilibrium undercooling.

It is important to further analyse the use of this equation.For a given set of experimental conditions where cellulardisturbance of the interface is produced, there is a spectrumof wavelengths that are stable. We have recalculated the re-lationship between perturbation wavelength and the rate ofgrowth of the amplitude for the alloy used in the study ofYin et al., as per the method of Kurz and Fisher, and the re-sults are presented in Fig. 2. The wavelength l i, calculatedby Eq. (1) is that associated with the limit of stability underconditions of directional solidification, that is, the mini-mum wavelength that will be stable under the pertaining ex-perimental conditions. Below l i all perturbations decay dueto capillarity effects and a planar interface is retained. Atlong wavelengths, the rate of growth of the amplitude islimited by long-range diffusion and perturbations will notgrow preferentially, again resulting in the stabilisation of aplanar interface. According to Mullins and Sekerka3) thewavelength that will become stable and which will domi-nate the growth morphology is expected to be the fastestgrowing Fourier component of the spectrum of wave-lengths. This wavelength is that of the perturbation at whichthe highest growth rate is achieved, lm. Mullins andSekerka3) proposed that this maximum wavelength be cal-culated by Eq. (2).

.................................(2)

If this argument is applied to the observations of Yin etal., the spacing between the fingers is expected to be lm

and not l i, i.e. 213 mm rather than 123 mm. Should our in-terpretation be correct, it seems that the inter-‘finger’ spac-ings measured by Yin et al. do not justify the application ofthe Mullins-Sekerka analysis to the interpretation of theirresults. For this reason an attempt was made to further in-vestigate the morphology of the delta-ferrite to austenitephase transition.

2. Experimental

In-situ observations of the delta-ferrite to austenite phasetransformation were made in a laser scanning confocal mi-

croscope to which an infrared heating furnace is attached.Samples, 4.2 mm in diameter and 2.5 mm thick were placedin an alumina crucible and heated under a high purity argonatmosphere (�99.9999). Details of the LSCM techniquehave previously been reported.6,7) A low carbon steel wasselected for this study, containing 0.06 percent carbon bymass and silicon killed, see Table 1. The samples wereheated to a temperature of 1 400°C and held for a period of10 min, before heating at a rate of 100°C/min to 1 450°C.Samples were then held for a further 10 min at this temper-ature before cooling at a designated rate to 1 400°C, whereit was again held isothermally until completion of the d to gphase transition.

3. Results

The microstructure observed in the laser scanning confo-cal microscope (LSCM) following the transformation fromaustenite to delta-ferrite is shown in Fig. 3. A large delta-ferrite grain is delineated by deeply grooved grain bound-aries, and within the delta-ferrite grain, a network of sub-boundaries has formed. Phelan and Dippenaar6) proposed

l lm i� 3

l p�2D

V T

GD o

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Table 1. Composition of the low carbon silicon killed steel.

Fig. 1. Unstable growth morphology of the d to g transforma-tion, Yin et al.1)

Fig. 2. Stability analysis for the Fe–C steel used in the study ofYin et al.1)

that this sub-boundary network forms by a recovery processfollowing the imposition of a strain field caused by the vol-ume change during the austenite to delta-ferrite phase tran-sition. They have also shown that the sub-boundary energyis typically 10 to 20% that of the delta-ferrite grain bound-aries.

A typical example of the observed delta-ferrite to austen-ite phase transformation is shown in Fig. 4. The transfor-mation of delta-ferrite to austenite commences at delta-fer-rite triple points. Austenite grows preferentially along thedelta-ferrite grain boundaries forming the type of “film”shown in frame (a). The subsequent growth of austenite isfollowed in frames (b) and (c) and it is evident that the ad-vancing d /g interphase boundary extends preferentiallyalong the sub-boundaries. In frame (c) two intragranularcells emerge, and in frame (d) they have merged seamlesslywith the austenite that has grown from the grain boundary.

The observation that the newly formed austenite graininitially grows along the high-angle delta-ferrite grain

boundary is in agreement with the observations of Yin etal.1) However, Yin et al. have neither reported the presenceof sub-boundaries nor the preferential growth of the ad-vancing d /g interface along such sub-boundaries. A possi-ble explanation is the differing compositions of the steelsused in that study compared to the present work. It has pre-viously been observed7) that while sub-boundaries areclearly delineated in silicon deoxidised steels, this is not thecase in the aluminium deoxidised steels. In aluminium con-taining steel, sub-boundaries are extremely faint and diffi-cult to observe, and hence, can be easily overlooked. In thestudy of Yin et al.1) aluminium killed steels were used andthis may explain why they have not observed sub-bound-aries. In the present study a silicon deoxidised steel wasused and sub-boundaries in the delta-ferrite phase are clear-ly seen.

The sequence of events following the nucleation ofaustenite on a delta-ferrite grain boundary is further illus-trated with reference to the sub-boundary structure shownin Fig. 5. The progression of the transformation to austeniteis captured in frame 5(b); the location of the interface hav-ing been highlighted digitally. The preferred growth alongsub-boundaries and the appearance of so-called intragranu-lar austenite cells, marked I1 and I2, are evident. Thesecells are clearly located at positions where sub-boundariesintersect. The last image in the sequence, frame (c) hasbeen captured at the completion on the transformation toaustenite. One final pocket of delta-ferrite is in the processof being transformed to austenite, and appears as an isolat-ed circular region. In both Figs. 4 and 5 the appearance ofintragranular austenite is coincident with junctions of delta-ferrite sub-boundaries. The distance between the intersec-tions of sub-boundaries and grain boundaries was measuredand found to have an average value of 106 mm with a stan-dard deviation of 40 mm. In the interpretation of the micro-graphs in Fig. 5, it must be emphasised that due to the na-

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Fig. 3. Delta-ferrite sub-boundary microstructure observed withLSCM.6)

Fig. 4. Transformation of delta-ferrite to austenite in Si-killed steel.7)

ture of imaging in the LSCM, pre-existing boundaries arestill observed even after the phase transformation has oc-curred. Therefore, the ‘sub-boundaries’ shown within thecells I1 and I2 are the thermally etched grooves of thedelta-ferrite sub-boundaries before the d to g transition oc-curred. These grooves remain in position even after thetransition has occurred.

4. Discussion

The presence of a sub-boundary network within delta-ferrite grains poses problems for the application of aMullins-Sekerka type of analysis to the growth morphologyof austenite from delta-ferrite. Enhanced diffusion along in-terfaces results in preferential growth of the austenite alongsub-boundaries compared to growth in the bulk, resulting ina finger like appearance of the advancing d /g interface. Ittherefore seems that the finger like growth morphology ofaustenite is more likely to be due to preferred growth alongsub-boundaries than to destabilisation of the growing d /ginterface.

The presence of a network of sub-boundaries also offersan explanation for the generation of intragranular austeniteislands that merge with grain boundary austenite. The intra-granular austenite which forms at sub-boundary intersec-tions have the same crystallographic orientation, and mustin fact have originated from a singular nucleation event inthe bulk, and not by multiple nucleation events at the freesurface. Such an interpretation is supported by the experi-mental work of Onink et al.8) who studied austenite decom-position by using high temperature transmission electronmicroscopy (TEM). Their study entailed TEM observationsof austenite decomposition in low carbon steel. A disc ofsteel was thinned to less than 100 mm, and further thinnedby the use of electro polishing techniques to produce sam-ples that were transparent to electrons. The field of viewwas restricted to 5�5 mm; samples were heated to tempera-

tures between 827 and 927°C for 5 to 10 min before coolingat approximately 5 to 10°C/s to the transformation tempera-ture. They attempted to observe both nucleation andgrowth, but they were never able to observe nucleation offerrite in the austenite matrix. Their conclusion, though therationale behind it was not elucidated, was that nucleationdid not occur because the free surface in this thin regionsuppressed nucleation. Other studies into the nucleation ofsolid-state phase transformations in Fe–C alloys have high-lighted grain corners as the dominant nucleation site,9–11)

supporting the findings of Onink et al.8)

The sequence of events during the delta-ferrite to austen-ite phase transformation, as observed at the free surfaceusing LSCM, should be interpreted as follows. Sub-bound-aries form a network within the delta-ferrite grains, just asdelta-ferrite grain boundaries form a network in the bulk ofthe specimen. Nucleation of austenite occurs in the bulk ofthe sample at grain boundary corners. Preferential growthoccurs along grain boundaries, and to a lesser extends alongsub-boundaries, leading to austenite first appearing at thefree surface on grain boundary triple points. Growth ofaustenite is observed to rapidly form a film along the grainboundaries on the free surface, but growth into the centre ofthe delta-ferrite grain occurs at a slower rate, due to thelower diffusion rate in the bulk as compared to an interface.At some subsequent time, cells of austenite appear aroundsub-boundary triple points, which then thicken and mergewith the grain boundary austenite films. This seamlessmerging between cells and films indicates they are from thesame nucleation event, hence the presence of a network oflow-angle sub-boundaries provides for a more logical de-scription of the transformation process.

4.1. Phase Field Model

Phase field models have become popular for the simula-tion of microstructural development due to the reduction inassociated computational requirements compared to sharp

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Fig. 5. Preferential growth of austenite on a delta-ferrite substructure.

interface models. In phase field models each phase or grainis described by an order parameter, f , which describes thestate of the phase and is governed by the minimisation offree energy functional, f̂ , as described by Steinbach et al.12)

Eq. (3). Interfaces are defined as regions of finite thickness,h , across which the order parameter changes continuouslyfrom one region to the next. This treatment is shownschematically in Fig. 6 where the change in the phase fieldparameter varies from 1 to 0 across the solid/liquid inter-face.13) The introduction of such a parameter simplifies theboundary conditions of the simulation as the whole domaincan be treated as a continuum and not as a Stefan problemwith a sharp interface between two distinct phases.

...(3)

where e ik is defined as the gradient energy coefficient ofphases i and k, mik is the linear coefficient of deviation fromthermodynamic equilibrium, and e ik, mik and aik are relatedto the interface mobility, surface tension, interface thick-ness, the latent heat of the phase transition and equilibriumtransformation temperature (m ik, s ik, h ik, Lik and Tik respec-tively) by Eqs. (4) to (6).

e2ik�h iks ik ..................................(4)

.........................(5)

................................(6)

A set of kinetic equations, Eqs. (7) and (8), are developeddescribing the phase field parameter and solute distributionin space and time, and hence how the microstructure devel-ops with time. In Eq. (7) the inherent mobility of interfaces,m , is a fitting parameter used to describe interfaces that ex-hibit anisotropy of mobility, for example coherent versusincoherent interfaces in solid state transformations. The in-fluence of curvature on microstructural development is han-dled in Eq. (7) by the first group of terms incorporating theinterfacial energy, s ij. Chemical thermodynamics is incor-porated into Eq. (7) by the second group of terms, relatinginterface thickness, h , entropy of fusion, DSij, and the equi-librium undercooling, DTij.

.........................(7)

The kinetics of the phase transformation is not deter-mined by the minimisation of the free energy functionalalone, but in combination with the kinetics of solute diffu-sion. The phase field equations are coupled to a solute bal-ance through the equilibrium undercooling as defined inEq. (8) and shown schematically in Fig. 7. The solute distri-bution is assumed to be under local equilibrium partitionconditions, with the proviso that concentrations deviatefrom equilibrium values as a function of curvature or kinet-ic undercooling. Interfaces are assessed as regions of phasemixing, and the solute balance is maintained by equatingthe equilibrium solute distribution in each phase at a sharpinterface, with a proportional contribution of each phase asdetermined by the phase field parameter change across a fi-nite interface. Linearised phase diagrams are used to de-scribe the equilibrium solute conditions for all phases beingsimulated and a finite element method is used to solve theequations, conserving both the phase field parameter andsolute concentration.

�ph

f fi j ij ijS TD D˘

˚˙˙

˙ ( , ) ( )f m s f f f fph

f fi ij

j

ij i j j i i jx t � � � � — —Ê

ËÁ

ˆ

¯˜

È

ÎÍÍ

2 22

2

aikik

ik

�h

s72

ma L T T

Tikik ik ik

ik

��6 ( )

� � � � �1

4

1

3

1

32 2 3 2 3 2

am

iki k ik i i k k k if f f f f f f f

Ê

ËÁˆ

¯̃

È

ÎÍÍ

˘

˚˙˙

˘

˚˙˙

ˆ ˆ | |, ( )

f fi k i k

n

ikik

k i i k� � ��

 — —È

ÎÍÍ

ef f f f

22

2

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Fig. 6. Schematic representation of the treatment of an interfacein phase field model Eiken et al.12)

Fig. 7. Link between solute balance and phase field parameter Eiken et al.12)

...................(8)

where Di is the diffusion coefficient of the solute in phase i,k is the partition co-efficient for an interface of curvature R,CR is the equilibrium solute concentration for a interface ofradius R.

Simulations of the delta-ferrite to austenite phase trans-formation were conducted using Micress, a multi-compo-nent/multi-phase commercial simulation software packagebased on the model developed by Steinbach et al.12) In thepresent simulations two phases, delta-ferrite and austenite,and two dissolved components, carbon and manganese, aremodelled. The preceding description of phase field model-ling was of a generic nature, and attention will now begiven to the practicalities of modelling the delta-ferrite toaustenite phase transformation. The first step in establishingsuch a simulation is to provide a thermodynamic frame-work on which to base calculations. To this end linerarisedphase diagrams of the alloy system need to be determined.In this study the Fe–C–Mn alloy system is described by areference temperature, (To), a reference solute concentra-tion (Co) in each phase at that temperature, and the slopesof the solvus and solidus, (m) through the reference point.With this information the equilibrium solute concentrationin each phase can be determined for any alloy compositionand domain temperature. This data was generated by thesoftware package ThermoCalc and is shown in Table 2.

The diffusion coefficient of solute in each phase is thenext set of data required, as the microstructure develops asa function of free energy and solute diffusion. This infor-mation is incorporated as a temperature dependent parame-ter in Table 3. Also in this table are data on the interfacialenergies between delta-ferrite grains, austenite grains andthe delta-ferrite/austenite phase. The existence of delta-fer-rite sub-boundaries has been simulated through the use of amisorientation parameter available in the package that en-ables boundaries to be treated as high or low energy. Thesimulation domain settings are shown in Table 4, includingthe number of nodes, the grid size in microns, the numberof grains and sub-grains, the misorientation cutoff point forlow angle boundaries and the mobility/energy pre-factor.

In Fig. 8 simulation domains are reproduced of the twoconditions, without and with sub-boundaries. In this figurethe orientation of each grain has been nominated, andthough there is a crystallographic rationale behind the ab-solute values, in our simulations it is only the relative val-ues that are of importance. Wherever the relative misorien-tation across two adjacent grains of delta-ferrite is less than15°, the grain boundary between them is treated as a lowenergy sub boundary. In the simulation, boundaries that aretreated in this way have an interfacial energy 20% that of astandard grain boundary, a value within the range of valuesexperimentally measured.6) The central delta-ferrite grain inthe Fig. 8(a) is replaced in Fig. 8(b) by 7 grains having orientations between 0 and 10 degrees, therefore forming 7 sub-grains. With respect to the 6 outer grains, the relativemisorientation is always greater than 15 degrees and hence these boundaries are high energy. Where low-energyboundary intersect high energy boundaries, the shape of the

˙ ( )( , )c D k cx t i i iR R

i

n

��

— —Ê

ËÁ

ˆ

¯˜Â f

1

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Table 2. Thermodynamic data.

Table 3. Material data.

Table 4. Phase field model.

Fig. 8. Simulation of delta-ferrite grains without (a) and with (b)sub-boundaries.

triple points are indicative of the mismatch in surface ener-gy, making angles greater than 120 degrees between grainand sub-boundaries.

The modelling package used for our simulations does notaccount for the influence of strain on free energy minimisa-tion, nor enhanced diffusion along interfaces. The first limi-tation is of no consequence when solidification is consid-ered, but in solid-state phase transformations strain plays animportant role in the thermodynamics of phase transition.However, using the arguments of Yin et al.1) regarding thedelta-ferrite to austenite phase transformation, the influenceof strain can be neglected given that the delta-ferrite togamma phase transformation occurs at elevated tempera-ture and hence strain should play only a small role in thetransformation. The inability to account for enhanced diffu-sion along interfaces represents more of a problem in thepresent analysis, given that the transformation is assumedto be diffusion controlled, and in-situ observations haveshown that preferential growth occurs along interfaces.

4.2. Simulation Results

The simulated microstructural development accompany-ing the delta-ferrite to austenite phase transformation ispresented in Fig. 9. Nucleation occurs at the triple point ofthree delta-ferrite grains at time equal to 20 seconds. At t�20.1 s, the austenite has grown preferentially along thegrain boundaries leading to an angular shape, as opposed tocircular if growth was uniform in all directions. The growthof the austenite continues in the next two frames, and attime t�20.3 s preferential growth along sub-boundaries aswell as grain boundaries is observed as pointed regions ofaustenite where boundaries exist. Analysis of the effect ofthe presence of sub-boundaries on the reaction kinetics isbest illustrated with reference to Fig. 10, a graph derived bythe simulation of the fraction austenite formed as a functionof time for two alloys and two boundary conditions. Curvesare shown for Fe–C with and without sub-boundaries, andfor a Fe–C-Mn alloy also with and without sub-boundaries.

In this simulation nucleation has been artificially sup-pressed to impose a large undercooling of 43 K, resulting inrapid transformation kinetics. The growth rate of austenite

in both alloys is higher when sub-boundaries are present.The difference in the reaction kinetics between the Fe–Cand Fe–C–Mn alloys confirms the expected trend with theFe–C–Mn alloy exhibiting slower reaction kinetics, due tothe lower diffusivity of manganese compared to carbon.

In an attempt to compare simulated microstructural de-velopment with experimental observations, two simulationswere made at the experimental cooling rate of 5 K/min. Inthe simulations, two degrees of undercooling were selected,0.5 and 10 K respectively. These results and the experimen-tal measurements are shown in Fig. 11. The simulated mi-crostructural development at an undercooling of 0.5 K pro-ceeded at a rate approximately half that of the experimen-tally measured value. A higher undercooling (say 10 K) willresult in a higher driving force for the transformation andhence, faster transformation are expected. It must be em-phasised that it was not possible to determine the under-cooling in our experimental arrangements and hence this

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Fig. 9. Phase field simulation of delta-ferrite to austenite phasetransition in the presence of sub-boundaries.

Fig. 10. Simulation of fraction austenite formed by the d to g phase transition as a function of time (CR�10 K/min).

value needs to be estimated. It is proposed that at a coolingrate of 5 K/min, the equilibrium undercooling lies some-where between 0.5 and 10 K.

The estimated degree of undercooling is not the only fac-tor that may lead to a disagreement between experimentallymeasured and simulated transformation kinetics. The simu-lation is a two dimensional domain, whereas in reality thesub-boundaries occupy three dimensional space, hence asthe transformation progresses pockets of austenite appearahead of the grain boundary austenite film, as discussedearlier. This leads to a higher observed transformation ratein comparison to the simulation and hence, it can be ex-pected that the experimentally observed transformation ki-netics would be higher than the simulated transformation ofthe same degree of undercooling.

5. Conclusions

The interpretation attached to the mechanism of transfor-mation of delta-ferrite to austenite by Yin et al.1) (the onlyprevious LSCM study into this transformation) has beenquestioned. More specifically, their calculation, based onthe Mullins-Sekerka instability analysis, of the expectedscale of perturbation for the system studied was shown tobe that for the minimum stable wavelength, 120 mm. Thewavelength that is expected to dominate as per Mullins andSekerka3) stability analysis is the fastest growing Fouriercomponent, 213 mm.

On the decomposition of delta-ferrite, newly formedaustenite was observed to grow preferentially along delta-ferrite sub-boundaries. We propose that preferential growthof the newly formed austenite proceeds along sub-bound-

aries in the delta-ferrite phase and not by an unstablegrowth mechanism.

The simulation of the delta-ferrite to austenite phasetransformation incorporating delta-ferrite sub-boundarieshas been established. The modelled transformations reflectin-situ observations of the influence of sub-boundaries onthe kinetics of the delta-ferrite to austenite phase transfor-mation. Preferred growth along sub-boundaries leads to fin-ger-like morphology. Furthermore, the kinetics of the trans-formation are increased by the presence of a sub-boundarynetwork

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323.3) W. W. Mullins and R. F. Sekerka: J. Appl. Phys., 35 (1964), No. 2,

444.4) P. G. Shewmon: Trans. Metall. Soc. AIME, 233 (1965), 736.5) W. Kurz and D. J. Fisher: Fundamentals of Solidification, Trans Tech

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for publication.7) D. J. Phelan: PhD thesis, University of Wollongong, (2002).8) M. Onink, F. D. Tichelaar, C. M. Brakman, E. J. Mittemeijer and S.

van der Zwaag: J. Mater. Sci., 30 (1995), 6223.9) W. Huang and M. Hillert: Metall. Mater. Trans. A, 27A (1996), 480.

10) P. J. Clemm and J. C. Fisher: Acta Metall., 3 (1955), 70.11) H. I. Aaronson: Mater. Forum, 23 (1999), 1.12) I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G. J.

Schmitz and J. L. L. Rezende: Physica D, 94 (1996), 135.13) J. Eiken, M. Apel, B. Böttger, H. J. Diepers, P. Schaffnit, I. Steinbach

and N. Warnken: Proc. Third Int. Alloy Conf. (IAC-3), Estoril,Portugal, (2001).

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Fig. 11. Comparison of simulations and LSCM observations of the kinetics of the delta-ferrite to austenite phase trans-formation, CR�5 K/min.