Journal of Crystal Growth 354 (2012) 174–180

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Journal of Crystal Growth

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The effect of non-equilibrium d/g transition on the formation of metastable‘‘dendrite core’’ in undercooled Fe–Cu alloy

Z. Chen a,b,n, F. Liu b, X.Q. Yang a, N. Liu c, C.J. Shen a

a School of Materials Science and Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221008, PR Chinab State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR Chinac School of Metallurgy and Materials, Jiangsu University of Science and Technology, Zhangjiagang, Jiangsu 215600, PR China

a r t i c l e i n f o

Article history:

Received 3 November 2011

Received in revised form

5 May 2012

Accepted 8 May 2012

Communicated by M. Rettenmayrin the incomplete transition of the primary d dendrite to g phase. In combination with the JMA solid-

Available online 16 May 2012

Keywords:

A1. Crystal structure

A1. Solidification

A2. Growth from melt

B1. Alloys

48/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.jcrysgro.2012.05.011

esponding author at: China University of Mi

rial Science and Engineering, Xuzhou, Jiangsu

6 0516 83897715; fax: þ86 0516 83591870.

ail address: chenzheng1218@163.com (Z. Che

a b s t r a c t

The effect of non-equilibrium d/g transition on the formation of metastable ‘‘dendrite core’’ in

undercooled Fe–Cu alloy was studied. Three kinds of solidified paths were adopted following

recalescence, i.e., quenching at recalescence moment, quenching after recalescence plateau and natural

cooling. In comparison of the three paths, it was evidenced that the metastable ‘‘dendrite core’’ resulted

state transition kinetic theory, the formation of ‘‘dendrite core’’ was dominated by volume diffusion

controlled-d/g transition. Two typical morphologies, i.e., small granules and dendrite trucks in

‘‘dendrite cores’’, have been detected. It may be attributed to the volume fraction of d/g transition.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

The solidification of undercooled melts is of great interest withrespect to microstructure evolution and phase selection, since itdetermines the microstructure development through nucleationand crystal growth [1]. Moreover, the non-equilibrium solidifica-tion of undercooled metallic melts offers the opportunity forimprovement of the alloy parameters by grain refinement or theformation of novel microstructures and metastable phases [2–4].Recently, much interest has been focused on the metastable phase(such as ‘‘metastable dendrite core’’) formation in undercooledFe-based melts [4,5].

In some undercooled Fe-based alloys (e.g. Fe–Cr–Ni [6], Fe–Co[7,8], Fe–Ni [9], Fe–Cu), black dots are often observed if under-cooling DT exceeds a critical value. We term the dots ‘‘dendritecores’’ as suggested by Koseki and Flemings [10], who founddispersed dots embedded in some grains in undercooled Fe–Cr–Nialloys. After that, the role of melt undercooling on the formationof metastable ‘‘dendrite core’’ was extensively investigated.Koseki and Flemings [10] believed that these particles werea metastable phase and nucleated primarily from the melts.Willnecker et al. [11] found that the formation of metastable

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ning and Technology, School

221008, PR China.

n).

‘‘dendrite core’’ was determined by phase competition betweenthe body-centered cubic d phase (bcc) and the equilibrium face-centered cubic g phase (fcc). So far, two strategies have beendevised to describe the formation mechanism of ‘‘dendrite core’’,i.e., remelting of primary d dendrite or incomplete d/g transition.The strategy of ‘‘remelting’’ [8] considers that the high tempera-ture d phase solidified as the primary phase and was remelteddue to the recalescence effect, and then transformation from g tostable a phase occurred. Since the a phase transformed fromprimary d dendrite was different from the matrix, and looked likeblack dots, it was called ‘‘dendrite core’’. Another strategy con-siders that the incomplete transition from the high temperature dphase to the g phase [4,5] led to the remaining metastable‘‘dendrite core’’ at room temperature.

Recently, the ‘‘dendrite core’’ was observed in the as-solidifiedmicrostructures of undercooled Fe–Cu immiscible alloy. Accord-ingly, whether remelting or solid-state transition of d phase orother possible mechanism is responsible for the formation of such‘‘dendrite cores’’ was still in doubt. With reference to the Fe–Cuphase diagram as shown in Fig. 1, we aim to investigate theforming mechanism of the ‘‘dendrite cores’’ in Fe–4 at% Cu alloy.

2. Experimental procedure

Two kinds of experiments were adopted, i.e., highly under-cooled experiment performed by fluxing and cyclic superheating

Fig. 1. Equilibrium phase diagram of Fe–Cu alloy above 600 1C.

Fig. 2. Typical temperature–time curves of Fe–Cu samples. Three kinds of solidified stages were adopted, i.e., a) natural cooling, b) rapid quenching after recalescence

plateau and c) rapid quenching at recalescence moment.

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180 175

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180176

technique and rapid quenching experiment at the recalescencemoment and after the recalescence plateau.

The alloy samples were undercooled by fluxing and the cyclicsuperheating technique. High purity (better than 99.95 wt%)elements Fe and Cu were alloyed in situ to form 5 g samples.Bulks with a composition of Fe–4 at% Cu were prepared in quartztubes in a high frequency apparatus under the protection of B2O3

glass slag, to denucleate the alloy by reaction, adsorption, andpassivation of the foreign catalytic sites. Each sample was melted,superheated and solidified several times, in order to obtain ahigh DT.

After the high frequency power source was turned off, thealloy sample was cooled spontaneously, while the thermal beha-vior was monitored by an infrared pyrometer (see Fig. 2). Thesamples were rapidly quenched into Ga–In–Sn alloy with coolingrates of about 1000 K/s at the recalescence moment (Fig. 2c) andafter the recalescence plateau (Fig. 2b). The rapid quenchingpoints have been shown in the temperature–time curves inFig. 2 By comparison of the three kinds of microstructures(quenching at recalescence moment, quenching after recalescenceplateau and natural cooling), the forming mechanism of ‘‘dendritecore’’ was investigated.

Fig. 3. Microstructure of the samples (after recalescence): (a) solidificationþna

(c) solidificationþrapid quenching after recalescence plateau at DT¼35 K; (d) solidifi

tionþrapid quenching at recalescence moment at DT¼45 K; and (f) solidificationþrap

Each sample was polished, and then etched with 2 wt%nitric acid solution diluted with alcohol. The microstructure wasobserved using a PMG3 Olympus optical microscope and VEGA IIXMH scanning electron microscopy (SEM). Phase and compositionwere identified using the energy dispersive mode (EDS) and aPanalytical X’pert Pro type X-ray diffractometer (XRD). The imageof small dark spots in the grains was observed using EM-200CKtransmission electron microscopy (TEM).

3. Experimental results

According to Fig. 2, three kinds of processes, i.e., quenching atrecalescence moment, quenching after recalescence plateau andnatural cooling were investigated. The naturally solidified micro-structures (Fig. 2a) of Fe–4 at% Cu alloy melt subjected to differentDT are shown in Fig. 3. For DT¼30 K, a dendritic pattern wasformed (Fig. 3a). For DT¼190 K, the dendritic pattern was sub-stituted by coarse grains with some small dark spots (Fig. 3b).Analogous to the naturally solidified samples, the rapidlyquenched samples after recalescence plateau (Fig. 2b) formed adendritic pattern (Fig. 3c) at DT¼35 K and coarse grains with

tural cooling at DT¼30 K; (b) solidificationþnatural cooling at DT¼190 K;

cationþrapid quenching after recalescence plateau at DT¼196 K; (e) solidifica-

id quenching at recalescence moment and DT¼192 K (see Fig. 2).

Fig. 5. XRD spectrums of the as-solidified Fe–4 at% Cu alloy (solidificationþrapid

quenching after recalescence plateau at DT¼196 K).

Fig. 4. Morphologies of the dark spots (solidificationþrapid quenching after

recalescence plateau at DT¼196 K).

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180 177

abundant dark spots at DT¼196 K (Fig. 3d). As for samples withrapid quenching at the recalescence moment (Fig. 2c), the as-solidified microstructures subjected to different DT are shown inFig. 4e and f. Analogous to Fig. 4a and c, a typical dendriticstructure was formed (Fig. 4e), in combination with remainingliquid from the rapidly quenched experiment at DT¼40 K. Com-pared to Fig. 4b and d, the dark spots were not observed in thequenched sample but it presented the refined equiaxed morphol-ogies at DT¼192 K (Fig. 4f).

Although rapid quenching at the recalescence moment couldinhibit the dark spots, the spots were still obtained in the sampleswithout rapid quenching and rapid quenching after recalescenceplateau as compatible with the phenomenon observed in Fe–Ni[9,12] and Fe–Co peritectic alloys [4,8]. Analogously, the dark spotwas defined as ‘‘dendrite core’’ here. Through SEM analysis theshape of ‘‘dendrite core’’ at high magnification was spherical or

vermicular (Fig. 4). In terms of the XRD analyses, it was found thatthe as-solidified microstructures belonged to bcc lattice structure,as shown in Fig. 5.

Because both martensite and a-ferrite possessed bcc structure,TEM was carried out to further clarify the detailed phase con-stitutions of the as-solidified microstructures. The results indi-cated that the as-solidified microstructures exhibited lathymartensite and a few a ferrite spots (Figs. 6 and 7). Moreover,at least two micro-morphologies were found in ‘‘dendrite core’’ byTEM analysis, i.e., small granules and fragments of dendrite. Onthis basis, the forming mechanism of ‘‘dendrite core’’ in under-cooled Fe–Cu alloy was discussed.

4. Discussion

In the equilibrium Fe–Cu phase diagram [13], the Fe–4 at% Cualloy experiences at least three phase transitions, i.e., L-d-g-a–FeþCu. After high DT, the d phase was normally solidified asthe primary phase in recalescence, owing to its lower interfaceenergy than that of the g phase [14]. If the recalescence tempera-ture rises to the liquidus temperature, the formed d phase willbecome unstable and has a tendency to either remelt or transformto g phase by solid-state transition. On this basis, three possiblepathways for the overall phase transition of the d phase in theundercooled Fe–4 at% Cu can be illustrated schematically as inFig. 8. After high DT, the d phase was initially formed inrecalescence, and then partially remelted into liquid or trans-formed to g phase. After solidification, the g phase transformed tothe martensite phase, which has been detected by TEM, as shownin Fig. 6, and the remaining primary d phase transforms to a-Fe,i.e., metastable ‘‘dendrite cores’’ (Fig. 4).

In comparison of the three rapid quenching paths, i.e., quench-ing at recalescence moment, quenching after recalescence plateauand natural cooling, it is evidenced that neither quenching afterthe recalescence plateau nor natural cooling could inhibit produc-tion of ‘‘dendrite cores’’ (Fig. 3a–d), whereas rapid quenching atthe recalescence moment could inhibit the formation of ‘‘dendritecores’’ (Fig. 3e and f). The quenching after recalescence plateauonly inhibited the eutectoid transition of g phase, but did notinfluence the d/g transition at higher temperature. As for naturalcooling and quenching after the recalescence plateau, the samplewas cooled spontaneously with the d/g transition at the samecooling rate of about 20 K/s. Only rapid quenching into Ga–In–Snalloy at the recalescence moment with cooling rate of about1000 K/s greatly influenced the d/g transition, and finally inhib-ited the production of metastable ‘‘dendrite cores’’. It can beproved that the ‘‘dendrite cores’’ formed in the d/g transitionprocess. The ‘‘dendrite cores’’ were the products of the untrans-formed d phase during d/g transition at room temperature.Therefore, the mechanism of non-equilibrium d/g transition inundercooled Fe–Cu alloy was studied as follows.

After rapid recalescence, the d/g transition, in the as-formed dphase of Fe–4 at% Cu alloy, can proceed by the following twomodes: (I) volume diffusion-controlled transition, where long-range compositional change by volume diffusion takes place[15,16] and (II) interface controlled massive transition, which, incontrast with volume diffusion-controlled transition, proceedsvery rapidly, in the absence of compositional change [16].Based on the classical JMA kinetics [15,16], the TTT diagram canbe used to describe the kinetics of d/g solid-state transition ofundercooled Fe–Cu alloy. Detailed procedure is available inAppendix A. As shown in Fig. 9, the d/g transition will occurthrough the mode of diffusion-controlled transition, of quenchingthe samples after recalescence plateau or without quenching, i.e.,keeping natural cooling in d/g transition process with a cooling

Fig. 6. TEM bright field images of the as-solidified microstructure rapid quenching after recalescence plateau at DT¼196 K. The morphologies of small particle in ‘‘dendrite

cores’’ and martensite are observed, and concentrations of a ferrite particle and martensite matrix are shown.

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180178

rate of about 20 K/s. Since the diffusion-controlled d/g transitioncould not proceed completely upon further cooling, the meta-stable ‘‘dendrite cores’’ remained in the final microstructures(Figs. 3 and 4). On the other hand, the d/g transition occurredthrough the mode of massive transition for rapid quenchinginto Ga–In–Sn bath at the recalescence moment with acooling rate of about 1000 K/s (Fig. 2c). Upon massive transition,the bulk chemical compositions of the product and the parentphases remained invariable and the metastable phase wassuppressed.

This mode was further proved by EDS analysis of Cu concen-tration. The measurement results on metastable ‘‘dendrite cores’’and matrix martensite of Fe–4 at% Cu alloy are shown in Fig. 6. Itis demonstrated that the ‘‘dendrite cores’’ are significantly poor inCu (3.2 at%), the concentration of which is lower than the matrixconcentration (4.1 at%). The obvious distinction between ‘‘den-drite cores’’ and martensite excluded the massive transitionmechanism and confirmed that d/g transition occurred throughthe mode of diffusion-controlled transition.

Moreover, as shown in Figs. 6 and 7, two typical morphologiesin ‘‘dendrite cores’’ have been detected. Fig. 6 shows the typicalmorphologies of fragments of dendrite by TEM, which has beendetected by Li et al. [8] in undercooled Fe–Co alloys. Li et al. [8]found that the metastable ‘‘dendrite cores’’ were the fragments ofthe primary dendrite which were isolated in the remaining liquidafter recalescence through the detection of interface of mismatchbetween the bcc phase and the fcc phase boundary. However, theobvious interface between the two phases was not observed inthe present work (Figs. 6 and 7). According to Schwarz’s model[17], the trunk radius Rtrunk, as a function of DT, is proportional tothe dendrite tip radius Rtip with Rtrunk/Rtip of 20. Applying anextended non-equilibrium dendrite growth theory consideringnon-linear liquidus and solidus [2], Rtip can be calculated, and inturn, Rtrunk, as shown in Fig. 10.Detailed calculation and para-meters about Rtip can be found in Refs. [18,19]. It is shown that

the size of dendrite trunk is in the range of Rtip and Rtrunk, asshown in Fig. 10. The size of trunk in the present observation waslarger than Rtip since the growth of the dendrite should be takeninto consideration rather than the dendrite tip remelted asfragments. However, the size was smaller than the estimationsof Rtrunk, which may be caused by the rapid cooling that inhibitedthe further coarsening of remelted fragments. Based on the aboveanalysis, the dendrite trunk in ‘‘dendrite cores’’ was still theremainder of d/g transition. When volume fraction of d/g transi-tion, X, was at a low value, a great mass of primary d dendritetrunks remained. On the other hand, once X was large, most of thedendrite trunks were transformed to the g phase, and the lessresidual d dendrite was presented as small granules, as shown inFig. 7. An analogous structure has been detected by Chen et al. [5]and Liu et al. [20].

Therefore the metastable ‘‘dendrite cores’’ of a ferrite were theproducts of the untransformed d phase during d/g transition. Theformation of ‘‘dendrite core’’ was dominated by volume diffusion-controlled transition of d dendrite. Furthermore, the micro-morphologies in ‘‘dendrite cores’’ were influenced by the fractionof phase transition, X.

5. Conclusions

The effect of non-equilibrium transition on the formation ofmetastable ‘‘dendrite core’’ in undercooled Fe–Cu alloy wasstudied. Three rapid quenching paths were adopted followingrecalescence, i.e., quenching at recalescence moment, quenchingafter recalescence plateau and natural cooling. The main conclu-sions of this analysis can be summarized as follows.

1.

In comparison of the three stages, it was evidenced thatthe metastable ‘‘dendrite core’’ resulted in the incompletetransition from the primary d dendrite to g phase.

Fig. 8. Schematic diagram of three possible solidification and solid-state transi-

tion pathways of d phase for highly undercooled specimens.

Fig. 9. TTT diagram of d/g solid-state transition in the as-formed non-equilibrium

microstructure of Fe-4at% Cu alloy after rapid recalescence subjected to rapid

quenching after recalescence plateau (with cooling rates of about 20 K/s) and

rapid quenching at recalescence moment (with cooling rates of about 1000 K/s).

Fig. 10. Trunk radius R(DT) and dendrite tip radius Rtip as a function of DT. It is

shown that the size of dendrite trunk is in the range of Rtip and Rtrunk.

Table 1Parameters of Fe-4 at% Cu alloy used in the calculations of

JMK kinetic.

Parameters Values

sd/g (J/m2) 0.4

f(y) 0.1113

Ga (kJ/mol) 252

QN (kJ/mol) 126

DSd/g (J/mol K) 0.6

Ttr 1750

Fig. 7. TEM bright field images of the as-solidified microstructure rapid quenching

after recalescence plateau at DT¼196 K. The morphologies of dendrite trunk and

martensite matrix are shown.

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180 179

2.

In combination with the JMA solid-state transition kinetictheory, it was evidenced that the formation of ‘‘dendrite core’’was dominated by the mode of volume diffusion controlled-transition.

3.

Two typical morphologies i.e., small particles and dendritetrucks, in ‘‘dendrite cores’’ have been detected. It may beattributed to the volume fraction of d/g transition, X. Large

X corresponded to small granules and small X corresponded todendrite trucks.

Acknowledgments

The authors are grateful to the Natural Science Foundation ofChina (Grant No. 51101169), the Fundamental Research Funds forthe Central Universities (2010QNA06), the fund of the State Key

Z. Chen et al. / Journal of Crystal Growth 354 (2012) 174–180180

Laboratory of Solidification Processing in NWPU (SKLSP201119),the Natural Science Foundation of the Education Department ofJiangsu province (09KJB430004) and China National Funds forDistinguished Young Scientists (51125002). The authors are alsothanks to Project Funded by the Priority Academic ProgramDevelopment of Jiangsu Higher Education Institutions (PAPD).

Appendix A. TTT diagram for d/c solid-state transition

TTT (temperature–time–transition) diagram can be used todescribe the kinetics of d/g solid-state transition of undercooledFe–Cu alloy. The volume fraction during phase transition, X, attime t, can be expressed as [15]

X ¼ 1�exp �g

Z t

0ISS

Z t

tu dt

� �d=m

dt !

ðA1Þ

where ISS is the steady state nucleation rate, u the growth rate,g the particle-geometry factor, m the growth mode parameter(m¼1 for interface-controlled growth; m¼2 for volume diffusion-controlled growth) and d the dimensionality of the growth(d¼1, 2, 3). According to the classical nucleation theory, ISS isgiven as [16]

ISS ¼ I0 exp �Ga

kBT

� �exp �

DGn

kBT

� �ðA2Þ

where I0 is a constant (E1041) [16], Ga is the activated energy fordiffusion, DGn (¼16ps3f(y)/(3DGV

2)) the critical nucleation workwith DGV (¼DSd-g DTtr) the free energy difference betweend phase and g phase, kB and T are the Boltzmann constant andtemperature, respectively. s is the interfacial energy, DSd-g theentropy change during phase transition, DTtr the undercoolingprior to phase transition, and f(y) the catalytic factor whichdepends on the wetting angle y.

For diffusion-controlled transition, the crystal growth velocityu can be expressed as

u¼D=ð2ðDtÞ1=2Þ ðA3Þ

where D (¼D0 exp(–Ga/kBT)) is the diffusion coefficient. Formassive transition, u is determined as

u¼ u0 exp �Q

RT

� �1�exp

DGV

RT

� �� �ðA4Þ

where u0 is the pre-exponential factor for growth which can beestimated as about 106 m/s, and Q the activation energy for

the transfer of atoms through the parent phase/new phaseinterface.

Assuming mass fraction X¼10�3, the TTT diagram can beplotted for the corresponding d/g solid-state transition usingEqs. (A1)–(A4) and parameters in Table 1 according to Refs. [21–25],as shown in Fig. 9.

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