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Acta Materialia 68 (2014) 159–168

Time-resolved X-ray diffraction studies of solidificationmicrostructure evolution in welding

W.U. Mirihanage a,⇑, M. Di Michiel b,A. Reiten a, L. Arnberg c, H.B. Dong d, R.H. Mathiesen a

a Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norwayb European Synchrotron Radiation Facility, 38000 Grenoble, France

c Department of Materials Science and Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norwayd Department of Engineering, University of Leicester, Leicester LE1 7RH, UK

Received 3 December 2013; received in revised form 15 January 2014; accepted 17 January 2014Available online 20 February 2014

Abstract

High-brilliance and high-energy polychromatic X-ray diffraction (XRD) has been used for time-resolved studies of rapid solidificationmicrostructure evolution in situ during simulated spot welding in austenitic steels. Weld pools of 5.0 mm diameter and 0.6–1.5 mm depthwere formed at the steel plate surfaces by radiation heating from halogen lamps. Solidification was initiated by powering off the lamps,and completed within 1.5 s while measuring diffraction from the solidifying grains of the pool at a 1 kHz frame rate. The data containtime-resolved information on individual grain growth and overall solid fraction evolution, and furthermore reveal prominent individualand collective motion of grains during early stages of solidification, presumably caused by convective currents in the pool. Ultrafast poly-chromatic high-energy XRD is novel in studies of microstructure evolution during welding. The experimental technique could quite read-ily be used for similar studies in real welding.� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Solidification; Welding; Dendrite re-orientation; In situ X-ray diffraction

1. Introduction

In fusion welding, metals coalesce via extremely rapidsolidification where liquid! solid phase transformationscontrolled by mass and heat transport occur under condi-tions far from equilibrium. The transport conditions aredecisive to the microstructure pattern formation and mor-phological evolution of the advancing solidification fronts,as well as to chemical segregation that may develop in theweld pool. As a result, the final microstructure andmechanical properties of the weld, especially in criticalregions where the terminal solidification fronts meet and

http://dx.doi.org/10.1016/j.actamat.2014.01.040

1359-6454/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights r

⇑ Corresponding author.E-mail address: wajira.mirihanage@ntnu.no (W.U. Mirihanage).

weld failures often occur, will be dictated by the fulldynamic history of the growth processes. In mostapproaches to welding, the weld fusion zone (FZ) is consid-ered as a mini-casting and its solidification behaviour ishandled by extrapolation of simulation models developedfor solidification processes [1,2] at cooling rates that couldbe orders of magnitude lower than those that apply to realwelds [3–6]. Improvements in computational capabilitieshave allowed for numerical simulations of variousadvanced solidification processes and are often guided byor verified via in situ experiments [1,2].

Experimental studies have also been reported for weldsolidification [7–9] or welding-related solid-state transfor-mations [10,11], employing X-ray diffraction (XRD) tech-niques. However, the high cooling rates, corresponding

eserved.

160 W.U. Mirihanage et al. / Acta Materialia 68 (2014) 159–168

rapidness and complexity of welding processes have madedirect in situ experimental studies of the solidification partof the process extremely demanding. In a recent paper,Yonemura et al. [9] report an in situ XRD study of micro-structure evolution in arc welds, but mainly with a focus onpost-solidification transformations. Nevertheless, the first2 s or so of observations are associated with the actualsolidification part of the process. Yet, besides a few rathervague assumptions, the observations corresponding tosolidification are not analysed in any greater detail to yieldresults on individual grain growth. The data are alsoconcerned with features, such as prominent diffuse X-rayscattering, which are not fully accounted for. Thus, solidi-fication dynamics or individual grain growth in actualmetallic welds has not yet been studied in any detail.

The present work provides novel time-resolved data onindividual dendrite evolution during spot welding of anaustenitic steel, studied in situ by polychromatic synchro-tron ultrafast XRD.

2. Experimental

Samples were cut from 2 mm thick rolled and annealedFe–Cr–17.3% Ni–11.1% Mo–2.1% C < 0.1% austeniticsteel plates into 30 mm � 20 mm rectangular pieces.

The primary heat source employed to simulate a realspot-welding process comprised seven 1 kW halogen lampsequipped with elliptical reflectors, each yielding a circularfocal spot �4 mm in diameter. The lamps were mountedin a custom-built rig that allowed for individual adjust-ments to superpose all lamps into a common focal spotat the centre of the sample surface with closely circularcross-sections �5.0 ± 0.5 mm diameter, at a controlledposition from one sample to the other to a precision±1.0 mm. The sample was placed on top of a boron nitrideplate heated from below by a resistance heater, allowing forcooling rates to be adjusted during pool freezing. A con-trolled argon flow could be brought in at the sample sur-face just adjacent to the weld spot to reduce oxidationrates at the pool surface. Weld pool depths varied between0.6 and 1.5 mm, depending on the setting temperature ofthe resistive heater and on the Ar flow rate. During eachin situ welding experiment, the resistive heater was keptat a constant temperature and the Ar flow set at a fixedrate, before switching on the halogen lamps to full power.Typically melting initiated after a few seconds, followed bystabilization of a molten pool within 1–3 s. As soon ascomplete melting in the part of the pool illuminated bythe incident X-ray beam was verified, pool freezing was ini-tiated by powering off the halogen heaters (the power-offtime is referred to as t = 0 s hereafter). Typically, theobserved region of the weld pool re-solidified completelywithin 1.0–1.5 s.

The experiments were carried out at the ID15Abeamline at the European Synchrotron Radiation Facility.For each welding experiment, a sample was placed on topof the resistive heater with the surface normal tilted

0.035 rad towards the incident beam (see Figs. 1 and 2).The incident X-rays were polychromatic, i.e. a white beamas delivered at the beam line by the U22 undulator, withphoton energies in the range 50–150 keV, and defined byapertures upstream of the sample to a cross-section of1 � 0.1 mm2 (H � V). The incident beam was positionedconcentric to the pool surface centre, and with the sampletilt and the incident beam geometry, the region monitoredthroughout the experiments corresponded to a 1 mm wideregion stretching diametrically across the pool surface, withmaximum penetration into the pool of �140 lm towardsthe exit beam side (see Fig. 2). Due to the low sample tiltangle with respect to the incident beam and the angularcoverage of the detector, only X-ray photons diffracted atangles <�0.15 rad relative to the sample surface are regis-tered in the two-dimensional (2-D) detector. In a typicalspot weld, columnar grains grow towards the centre ofthe weld from the FZ periphery, opposite to the heat flow.For the experiments present here, the X-ray beam width issmall compared to weld pool diameter, and accordingly,columnar grains under X-ray illumination would beexpected to grow nearly parallel or anti-parallel to thebeam direction in the surface-near regions of the weld, asindicated schematically in Fig. 2.

During experiments, temperature was monitored by athermocouple placed inside the boron nitride plate on topof the resistance wires. XRD was collected in reflectiongeometry in one quadrant of the upper hemisphere in theforward scattering direction, and at a distance,d = 920 mm from the sample, spanning an angular range2h 2 ½0:06; 0:3� rad. Diffraction data were collected with aPCO.dimax� complementary metal oxide semiconductor(CMOS) equipped with an image intensifier, The CMOSspans a 2016 � 2016 pixel array, and was read at a1.0 kHz frame rate. In total, 24 XRD data sequences werecollected in situ during simulated spot welding.

3. Polychromatic XRD and data processing

The diffraction condition with polychromatic X-rays isbest illustrated in reciprocal space. In the monochromaticcase, reciprocal space illustration of the diffraction condi-tion is by the so-called Ewald sphere construction [12].By selecting an arbitrary reciprocal lattice point as the ori-gin, and letting the incident wave vector, k0, terminate atthis lattice point, the diffraction condition is constructedby drawing an Ewald sphere with radius |k0| about the posi-tion from which k0 originates. Any other reciprocal latticepoints, with reciprocal lattice vector h relative to the origin,are said to be in diffraction condition if they intersect withthe surface of the sphere, with a diffracted wave propagat-ing along kh, as can be seen in Fig. 3A. Rotation of thecrystal is equivalent to a rotation of the reciprocal latticeabout the origin relative to a fixed sphere, and bringsnew reciprocal lattice points into diffracting position, asshown in Fig. 3b. If the material is polycrystalline (or mul-tiphase), there will simply be one set of reciprocal lattice

Fig. 1. Sketch of the experimental setup.

Fig. 2. Weld pool and X-ray beam geometry (not scaled). (a) Schematic cross-section view: the X-ray beam height is 0.1 mm and maximum penetrationdepth into the weld pool from the sample surface is �0.14 mm. (b) Schematic plan view of growth directions in a weld pool; columnar grains grow mostlyparallel to the beam direction as beam width is small compared to weld pool diameter.

Fig. 3. Schematic 2-D projections of Ewald spheres for (a) single-crystal and monochromatic beam, (b) the same single crystal as in (a) with a slightrotation and (c) single crystal and polychromatic beam. Lattice points that satisfy the diffraction condition are coloured in blue. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version of this article.)

W.U. Mirihanage et al. / Acta Materialia 68 (2014) 159–168 161

points associated with each crystallite (or phase), all withcoinciding origins where k0 terminates.

The polychromatic situation is quite readily illustratedby imagining a series of Ewald spheres, one for each dis-crete wavelength component. If the X-ray source is contin-uous over a range of X-ray photon energies, it suffices to

draw the Ewald spheres corresponding to maximum andminimum photon energies, as shown in Fig. 3c. Now, everyreciprocal lattice point which falls inside the volumespanned between the delimiting upper and lower energyspheres is in diffraction condition for some given wave-length component of the source spectrum.

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There may be several aspects that distinguish a typicalmonochromatic X-ray diffraction experiment from a poly-chromatic one, but here the focus will be only on the pointsmost crucial to this particular study. In order to resolveindividual grain growth dynamics taking place in a weldpool during freezing, it is necessary to track and monitora set of reflections as a function of time throughout theexperiment. For the monochromatic case this may be extre-mely difficult or even impossible, as the diffraction condi-tion by intersection of the lattice node with a discretestationary surface is highly sensitive to any changes inthe reciprocal lattice during the process, such as might becaused by e.g. grain rotation or thermal contraction ofthe crystal lattice. Thus, in the monochromatic situationindividual reflections may only be followed through a fewtime frames, and as a result the experiment would fail tobring about through-process information on the dynamicsand kinetics of individual grains. In the polychromaticcase, however, tracking of specific reflections is robusttowards changes in the reciprocal lattice as long as the lat-tice node remains inside the diffraction volume. Thus,extraction of through-process data for individual grains ispossible and robust towards dynamic effects like crystalre-orientation, thermal contraction, lattice parameterchanges by stresses, solid solutions, etc. On the other hand,indexing of reflections becomes more cumbersome in thepolychromatic case compared to a monochromatic one,in particular when the sample is polycrystalline.

As mentioned above, XRD data were collected frame byframe at a fixed rate of 1.0 kHz. Each frame comprises a setof raw pixel intensities that must undergo a few processingsteps to arrive at useful quantities. Background intensitycaused by diffuse scattering from air or the liquid metalwas assessed from frames captured with the weld pool com-pletely molten, and found to be weak and fairly constantacross the solid angle covered by the detector. Accordingly,corrections could be performed simply by subtracting themean background intensity value Jbck from all pixels toarrive at a set of net pixel intensities for each frame. Afterbackground intensity subtraction, separable diffractionpeaks emerged as islands of interconnected pixels withnet intensities Jnet(rh,wh ,t), delimited by the Jnet(rh,wh,t) > 2r(Jbck) boundary, with t as the time stamp of theframe, r(Jbck) the standard deviation of pixel intensitiescalculated from the background frames and rh and wh rep-resenting radial and asimuthal polar coordinates in thedetector plane, respectively. The situation of having netintensities superimposed on a flat background is favourablefor data processing since it allows morphological renderingof diffraction peaks by a simple Jnet > 2r(Jbck) 2-D thresh-old masking of the background-corrected data. Due tohigh X-ray energies involved and small angular range cov-ered, relative corrections for beam polarization and X-rayabsorption is reasonably uniform and modest for all dataand may be neglected. The scattering power itself alsoincludes X-ray-energy-dependent terms and can be shownto scale with k�3 J0(k), where k = |k0| = |kh| = 1/k is the

wave vector magnitude, k the X-ray wavelength and J0(k)the photon-energy-specific power density of the incidentbeam at the sample position. A prominent dynamic featureof the experiment(s) was substantial grain motions,observed as angular motions of the diffraction peaks, inparticular during the earlier stages of freezing. These madeit necessary to track and follow reflections along theirangular trajectories, requiring corrections to be made as areciprocal lattice node move and the X-ray energy at whichit diffracts is shifted. The ID15 U22 undulator source deliv-ers a J0(k) which varies by orders of magnitude over the rel-evant energy range. This needs to be corrected for, andmay not be entirely straightforward, since it requiresknowledge of the exact length of the reciprocal lattice vec-tor and its orientation at any time to precisely assign thecorrect diffracting position and X-ray energy. The angularrotations encountered here were three to four orders ofmagnitude larger than those that would result from ther-mal contraction [13,14], stresses or any other change ofthe lattice parameter, and could accordingly be ascribedmainly to rigid body rotation of the reciprocal lattice.Therefore, neglecting to a first approximation changes ofthe lattice parameters during grain growth, the intensitydata may be corrected under the constraint of |h| = con-stant, for which it becomes possible to determine the exactdiffraction geometry kh(t), and thereby also J0(k(t)) = J0(t)uniquely for any spot in every frame. After corrections,every frame consists of a set of scaled pixel intensities,Jsc(rh,wh, t) = k(t)3Jnet(rh,wh, t)/J0(t).

After scaling the next processing step is intensity inte-gration for individual diffraction peaks or reflections. LetIh(t) denote the integrated intensity associated with reflec-tion h. Ih(t) is computed directly from the scaled pixelintensities of the corrected images as

IhðtÞ ¼X

r;w

J scðw; r; tÞ ð1Þ

where the sum is taken over all interconnected pixels insidethe Jnet > 2r(Jbck,sc) bounded region. Another useful quan-tity to track in order to analyse lattice parameter changesor rotation of the grain is the peak centre of mass(c.o.m.) {rh(t),wh(t)}, given by

rhðtÞ ¼P

w;rJ scðr;w; tÞrIhðtÞ

ð2Þ

whðtÞ ¼P

w;rJ scðr;w; tÞwIhðtÞ

ð3Þ

where the sums are taken over every pixel {W, r} inside the2r(Jbck,sc) bounded regions. It was also found convenientto keep track of the time evolution of the peak area, repre-sented by the peak full widths, {rr(t),rW(t)}, along the ra-dial rh(t) (Eq. (2)) and asimuth wh(t) directions (Eq. (3)),respectively.

It follows from the theory of kinematical diffraction thatIh from a single grain volume bathed in the incident beamcan be expressed as [12]

W.U. Mirihanage et al. / Acta Materialia 68 (2014) 159–168 163

Ih ¼ V �2c KhjFhj2 � V g ð4Þ

where Vc is the volume of the unit cell and Vg the X-rayilluminated grain volume. Kh is a factor that collects reflec-tion-dependent experimental corrections and universalphysical constants, and the former may be neglected hereas all required corrections have been done on the pixelintensities. Finally, |Fh| is the amplitude of the structurefactor. As long as crystal growth is analysed on a relativescale, and under the assumption that the effect of thermalcontraction can be neglected, the time evolution of thecrystal volume can be expressed in terms of a relativefraction:

fgðtÞ ¼V gðtÞV 1

¼ IhðtÞI1

ð5Þ

where V1 and I1 represent the final X-ray illuminatedgrain volume and the corresponding intensity scattered indirection kh at sequence termination when the weld poolis completely solidified.

4. Results and discussion

The 24 sequences collected for the weld simulations werefound to be quite similar in a statistical sense in terms ofgrain motion, individual and overall grain growth. Typi-cally, the first diffraction spots appeared at aboutt � 100 ms relative to power-down of the primary heatsource at t = 0. Most diffraction spots start to appearwithin t � 100–400 ms, although in some sequences a fewnew spots are found to appear in the images at later times.The geometry of the experiment does not allow us to con-clude directly from the X-ray images whether the spots thatappear correspond to nucleation events or to situationswhere crystals grow from the outside and into the X-rayilluminated region. Yet, from post-experimental metallog-raphy on some of the weld pools, as shown in Fig. 4, it

Fig. 4. Typical experimental weld cross-section micrographs sectionedalong the beam direction. (a) Full weld cross-section from a post-experimental sample. (b) Half-cross section detailing an experimental weldpool. A depleted centre zone (i) and a significant bulging at the weld poolperiphery (ii) is observed in the post-solidified samples.

seems likely that the grains form predominantly at themelt–solid interface at t � 0 and grow into the X-ray illu-minated region, as illustrated schematically in Fig. 2,within the first 300–400 ms or so. Post-experimental metal-lography shows evidence of substantial convection alsobeing present in the pool, with a depletion at the weld cen-tre and a protruded ring on top of the original sample sur-face extending outwards from the periphery of the originalmelt interface.

In the early stages of pool freezing, t < 400 ms, individ-ual diffraction spots move along closely fixed trajectorieswith quite substantial angular velocities xr ¼ duh

dt ; xw ¼dwhdt , where ur = tan�1(rh/d). Fig. 5 shows uh(t) and wh(t)

evolution for 10 representative grains, selected from twodifferent welding sequences. The first peaks that appearedbefore t < 250 ms showed very high x, typically>�1 rad s–1, and disappeared from the angular field ofview covered by the detector within some tens of millisec-onds or less. Around t � 250 ms, the angular motionreduced by at least one order of magnitude, however themotion still remained prominent for most peaks. Ataround t � 700 ms and later, angular motion reduced torates <0.001 rad s–1, which is proximetrically consistentwith thermal contraction at 200–400 K s–1 cooling rate.Accordingly, angular motions at t < 700 ms are assumedto relate exclusively to re-orientation/rotation of the dif-fracting grains.

Generally, spots appearing before t < 250 ms pop upsomewhere inside the 2-D detector area, move some dis-tance across the field of view and then disappear suddenly,well before reaching the edges of the detector. Togetherwith the post-welding metallography, this supports a con-clusion that the initial spots originate from free crystalsthat eventually move completely out of the X-ray illumi-nated region. We cannot firmly conclude whether theseare fragments that detach from a columnar growth frontor equiaxed dendrites that form in the melt. Their suddenappearance may indicate that the free grains form predom-inantly outside the X-ray illuminated region. As seen inFig. 4, a particular region with equiaxed dendrites fairlyclose to the original edge of the melt pool coincide withthe area where grains would enter into the incident X-raybeam. The peaks that start to appear at t > 250 ms areclearly distinguishable from the initial free crystals not onlyby their maximum angular velocities, but also by remainingwithin the X-ray illuminated volume throughout theexperiment.

The archetype grain re-orientation/rotation dynamicsare further illustrated in Fig. 6, and arrangement of theobservations in this manner allowed individual crystals tobe ascribed into: (i) ultrafast moving free crystals (f)appearing at t < 250 ms (typical example are illustratedby f1, f2 and f3) and (ii) columnar crystals (c), appearingat t > 250 ms (typical examples are illustrated by c1, c2and c3). It can be seen that c-crystals show reduced motionat early stages, within one order of magnitude slower thanthose of the f-crystals at the same time. Crystals of the

Fig. 5. Observed uh(t) and wh(t) evolution. (a and b) Evolution in the first 500 ms of solidification from two experiments, referred here as a and b,respectively. (c) Time evolution of uh(t) and wh(t) from experiment a, for complete solidification time 1500 ms. f1, f2 denote two peaks from each sequencerepresentative of the free grain motion, while c1, c2 and c3 denote three peaks representative of the columnar grains.

Fig. 6. Time evolution of angular velocities, including standard errors, for six re-orienting crystals. A logarithmic scale is used for better illustration of thevelocity range accounted for during grain motion. Velocities are binned every 5 ms to enhance data readability.

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f-category show consistent and very high angular peakvelocities before disappearing from the illuminated regionwithin �80–150 ms. Assuming equiaxed grain sizes as thosefound in the post solidified metallographic samples and thediffraction peak motion rates, we accounted for metricrotation velocities at the free-crystal periphery up to�5 mm s–1. Motion of c-type crystals reduces exponentiallyuntil t � 450 ms, where an abrupt decelerating transient by2.5–3 orders of magnitude to more or less fixed orientationsoccurs. After this transient, the crystals remain stationarywith respect to diffracting positions within the limits thatcould be ascribed to thermal contraction effects.

For each sequence, the time evolution of a set of individ-ual c-type grain volume fractions, fg(t), was extracted asoutlined in Section 3 (see Eq. (5)). Typical growth curvesare presented in Fig. 7, by data selected from two

sequences. Note that no smoothing has been carried outwith the fg(t) data, such that the curve smoothness encoun-tered serves to underline high quality in terms of diffractionsignal statistics, as well as soundness in the correctionscheme applied. These crystals would continue to growwithin the X-ray illuminated region throughout theremaining pool freezing time, as illustrated for the casesc1 and c2 in Fig. 7a, as well as for all four c-crystals inFig. 7b. c3 in Fig. 7a grows in a direction at a much higherangle to the incident beam and therefore relatively rapidlyextends outside the X-ray illuminated region. c4 in Fig. 7ais a late arriver, assumed to grow semi-parallel to the sur-face plane, but directed at a higher angle with respect to k0.

The hypothesis of convection-driven crystal motion atearly stages is further supported by observations for thec-type crystals. c-Crystals that can be tracked throughout

Fig. 7. Volume fraction evolution, fg(t) of eight selected solidifying crystals and overall solid fraction, favg(t) of the weld pool, taken from tworepresentative welding sequences, a and b. Note that the error bars fall within range covered by the data point markers.

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the full pool freezing experiment are grains that grow withtheir columnar tip directions at relatively modest angles tok0. In each experiment, the simultaneous appearance ofsome of the diffraction peaks allowed us to identify possiblereflection pairs or triplets, likely to belong to the samecolumnar crystal. If one assumes h100i as the preferredtip-growth direction for austenitic steel dendrites [6,9], itallowed peak-pairs or triplets from classes [002], [020]and [02 2] to be indexed, corresponding to h100i columnarcrystals growing at angles <�0.2 rad to k0. As the grainsdetected and tracked have similar orientations, and aresomewhat constrained in motion by being semi-parallelto nearby primary branches, the associated diffraction spotmotions follow along relatively straight lines in reciprocalspace. To understand more of the nature of this motion,one has to consider several possibilities. If the motionresults in a shift of rh(t) and/or wh(t), it would correspondto re-orientation of the whole crystal, i.e. rigid body rota-tion. This would be consistent with tilting of the wholecolumnar branch, probably by bending at its attaching rootto the original solid [15]. If the motion results in an increasein the profile width along the same direction as xr + xW, itwould relate to local re-orientation along the branch, i.e.peak-broadening effects associated with lattice strain. Thiswould be observed if the liquid–solid momentum transfercaused the dendrites to bend along the primary stalk. It

Fig. 8. Time evolution of rr(t) for the grains shown in Fig. 7. rr(t) has been convalues, Max(rr(t)). rr values are binned every 5 ms to enhance data readabilit

is, however, necessary to keep in mind that peak broaden-ing may also result from other phenomena, such as crystalgrowth, as the diffraction spot area is basically a projectionalong kh of the diffracting grain. Fig. 8 presents the timeevolution of the peak widths, rr in the radial direction(along rh) for the intensity–grain volume curves presentedin Fig. 7. It was found that the change in peak area wasmore or less entirely directed along rh, with the increasealong Wh being very modest or even negligible.

Thus, to distinguish these two possible sources it is con-venient to compute the average time correlations, q(rr(t),x(t)), between peak broadening rr(t), and the correspond-ing crystal fraction, x(t) = fg(t), and crystal rotation,x(t) = x(t), respectively. The results, as extracted from 36crystals taken from three sequences, yield correlationq(r(t), fg(t)) = 0.79 (+0.12/–0.09), whereas q(rr(t), xr(t)) =0.37 (+0.14/–0.16). Thus, peak-broadening effects arerather strongly correlated with growth, and hence the pre-dominant rotation for c-crystals seems to be tilting, i.e.rigid body motion of the primary stalks by bending at theirattaching roots [15]. Liquid–solid momentum transfer fromconvection implies that the columnar dendrites tend tomove with the shear flow direction at the solidificationfront. It should be noted that the neck (base) of rapidlygrowing dendrites are generally observed to be much nar-rower than the primary dendrite trunk. Furthermore, as

verted to non-dimensional quantities by normalization with the maximumy in the figure.

Fig. 9. Statistics for the maximum dendrite tip-tilting velocities estimatedfor 36 different columnar crystals analysed in three separate weldingsequences. Crystals that appear after t � 700 ms, when motion terminates,have been excluded from the data.

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the temperature approaches the melting point, the elasticmoduli of c-iron, as with many other metals, is expectedto reduce drastically [16]; which may also be supportedby rather crude extrapolation from low temperature data[17]. The presence of shear flow also means that solute-enriched liquid ahead of the tips is constantly taken away,at least in the early stages of growth, which again shouldhave a prominent effect on the growth rates.

Compared to the previous experimental attempts onin situ characterization of phase transformations in weld-ing by XRD [7–11], the main technical difference of the cur-rent experiment is the use of polychromatic X-rays. Eventhough data processing is more cumbersome for the latter,it is pivotal for successful intensity integration and peakposition tracking during solidification if grains arere-orienting in consequence of the processes involved. Infact, it would not have been possible to track individualgrain growth or grain rotation, as evident here, in solidify-ing weld pools by monochromatic X-rays. Even thoughYonemura et al. [9] in their monochromatic X-ray studymainly report on transformations that take place aftersolidification, they also briefly report observations of“mist-like” data in the very first few frames that areascribed to solidification. Given that the frame ratesreported are in the range 10–100 Hz, it is reasonable toassume, the rate is inadequate to capture grain growth ina truly time resolved manner during the actual weld poolfreezing stage. At least if the pool solidified completelywithin 1–2 s, like in the current study, which also compareswell to typical pool solidification times reported in litera-ture [4–6]. It therefore seems tempting to suggest that theobservations of Yonemura et al. of diffuse scattering duringsolidification, at least in part, can be ascribed to time blur-ring during single frame exposure by crystals rotating inand out of the diffraction condition. Accordingly, the cur-rent study may be the first to report on real individual time-resolved crystal growth and solidification related dynamicsin freezing weld pools. Columnar grain orientations seen inthe weld cross-section micrographs in Fig. 4 support theassumption that the heat flow is closely radically symmetricfrom the weld centre spot. A simple linear extrapolation toapproximate the cooling rate at the initiation of solidifica-tion in the pool was carried out from cooling ratesextracted from thermal contraction of the lattice att > 750 ms, i.e. after columnar grain motion has come toa complete stop. The cooling rates extrapolated linearlyin time to t = 0 s are in excess of 1000 K s–1, and reason-ably close to the cooling rates associated with similar sizewelds [18]. Further comparison to Elmer et al. [18], sug-gests that the average thermal gradient across the FZ cen-tre to the periphery could be �200 K mm–1. In futureextensions of the method presented, further efforts shouldbe made to extract spatiotemporal data on the temperaturefield in the pool.

Even though our XRD data analysis suggests consider-able convective effects in the weld pool, the primaryheating employed in the experiments did not involve any

electromagnetic arc or plasma as common to many realfusion welding processes. Accordingly, flow is presumedto be driven mainly by a combination of high cooling ratesand the surface tension/chemistry of the molten pool, inline with computational studies found in the literature[5,6], where considerable flow velocities are predicted, evenin the absence of any arc pressure or Lorentz forces. Themaximum possible flow velocity in the melt pool calculatedfor the experimental conditions via an analytical relation-ship [4] is over 400 mm s–1. Weld-centre depletions andedge-region protrusions found in the welded samples alsoconfirm the presence of a relatively strong convectionwhich drives melt from the centre and out of the weld pool.The detected crystal motion, which is most prominent atearly stages, is believed to be caused mainly by liquid–solidmomentum transfer and related back to convection as thedriving force. Correlating the grain motion and cessationof it with the grain growth; as shown in Fig. 7, it is readilyseen that the overall solid volume fraction, favg, and indi-vidual crystal volume fractions, fg, at the same time are�0.4, which could support the conclusion that at this timethe solid fraction in the illuminated pool region reaches avalue where there is simply not enough bulk liquid left touphold appreciable convection.

For quantitative comparison of columnar growth withconvection-driven tilting, approximate time-dependentcrystal length evolution, l(t), can be extracted via a para-bolic envelope fitting to fg(t) and the average columnardendrite length, as measured from the solidified samplemicrographs. The resulting tip growth velocities, dl(t)/dtare found to exceed 4 mm s–1, and on average, the colum-nar grains peak at growth velocities of 2.4 mm s–1. At theemergence of the fg(t) curves in Fig. 7, the very initial tran-sients [19] in tip growth rates are missing. However, we cananticipate that c-dendrites may set out to grow at theregions outside the X-ray illuminated volume, mostly atthe boundaries of the weld pool and initial transients inthese regions are not illuminated by our incident X-rays.From l(t) it is also possible to calculate metric tilting veloc-ities, l(t) xr(t), for the columnar tips. Fig. 9 presents themaximum values for tip-tilting velocities, which have beenextracted for 36 columnar grains from three spot-welding

Fig. 10. (a–d) Evolution of growth and tilting for four representative c-type crystals. All four crystals grew with their major component || to the incident X-ray beam direction, k0. Average growth velocities are binned every 5 ms.

W.U. Mirihanage et al. / Acta Materialia 68 (2014) 159–168 167

sequences. The data reveal a distribution where �80% ofthe crystals have maximum tip-tilting velocities ofP0.5 mm s–1.

Experimental evidence of strong crystal rotations andtilting from the root is novel to the case of welding or similarrapid solidification processing, and apparently not incorpo-rated in any simulation models, although its presence inprinciple could be rationalized hypothetically, as it is well-recognised that many real welding processes are concernedwith very strong convection currents [4–6]. When growthand tilting are compared, especially at the initial stage ofcolumnar growth, i.e. �250 ms < t < �450 ms, the colum-nar crystal growth velocities and the tilting velocities arefound to be of the same order of magnitude, as illustratedin Fig. 10.

Thus, it seems reasonable to assume that solute pile-upahead of the columnar front is effectively removed by con-vection, and in addition the columnar tips are moving, suchthat growth at this stage should be rather heavilyinfluenced by the present hydrodynamics. Therefore, it isquestionable to what extent growth models developed formore conventional solidification problems could be extrap-olated to account properly for the situations that apply torapid solidification during early to intermediate stages inweld processing. The experimental findings presented hereserve to underline the role of melt flow both on crystalgrowth and on crystal motion, and may serve to stress thatthese effects should be taken more thoroughly into accountin future simulation models for weld solidification. Thereasons for not incorporating crystal motion into thecurrent weld solidification simulation schemes may be acomplete lack of relevant experimental benchmark data.Owing to the early stages at which tilting take place, littleevidence from post-experimental characterization couldbe anticipated.

5. Summary

In situ time-resolved studies of evolving microstructuresin steel alloy weld solidification were carried out usingultrafast polychromatic X-ray diffraction. Data analysishas brought quantitative insight to individual and overallcrystal growth rates in solidifying welds. The study hasshown that substantial crystal rotation, tilting and motionare present, especially in the earlier stages of solidification,and are likely to have a strong influence on the transientbehaviour of growing crystals in welds. Furthermore, theexperimental method and analysis developed within thisstudy could be quite readily adapted to other in situ studiesof welding or other rapid phase transformations in materi-als science.

Acknowledgements

The European Synchrotron Radiation Facility isacknowledged for granting beamtime to the experimentsunder code MA1358. The research leading to these resultshas received funding from the European Community’sSeventh Framework Programme under Grant AgreementNo. 229108.

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