Directional grain growth from anisotropic kineticroughening of grain boundaries in shearedcolloidal crystalsShreyas Gokhalea,1, K. Hima Nagamanasab,1, V. Santhoshc, A. K. Sooda,c, and Rajesh Ganapathyc,2

aDepartment of Physics, Indian Institute of Science, Bangalore 560012, India; bChemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for AdvancedScientific Research, Bangalore 560064, India; and cInternational Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research,Bangalore 560064, India

Edited by James A. Warren, National Institute of Standards and Technology, Gaithersburg, MD, and accepted by the Editorial Board October 25, 2012(received for review June 19, 2012)

The fabrication of functional materials via grain growth engineer-ing implicitly relies on altering the mobilities of grain boundaries(GBs) by applying external fields. Although computer simulationshave alluded to kinetic roughening as a potential mechanism formodifying GB mobilities, its implications for grain growth haveremained largely unexplored owing to difficulties in bridging thewidely separated length and time scales. Here, by imaging GBparticle dynamics as well as grain network evolution under shear,we present direct evidence for kinetic roughening of GBs andunravel its connection to grain growth in driven colloidal poly-crystals. The capillary fluctuation method allows us to quantita-tively extract shear-dependent effectivemobilities. Remarkably, ourexperiments reveal that for sufficiently large strains, GBs withnormals parallel to shear undergo preferential kinetic roughening,resulting in anisotropic enhancement of effective mobilities andhence directional grain growth. Single-particle level analysis showsthat the mobility anisotropy emerges from strain-induced direc-tional enhancement of activated particle hops normal to the GBplane. We expect our results to influence materials fabricationstrategies for atomic and block copolymeric polycrystals as well.

colloids | grain boundary migration | anisotropic grain growth

The motion and rearrangement of grain boundaries (GBs) iscentral to our understanding of recrystallization (1), grain

growth and its stagnation (2), and superplasticity (3) in a broadclass of polycrystallinematerials includingmetals (4), ceramics (5),colloidal crystals (6), and block copolymers (7, 8). Polycrystals arepervasive as engineering materials and elucidating mechanismsthat determine the structure and dynamics of theirGBs continue tobe a central goal of materials research (9). Advances in computersimulation methods (2, 10, 11) and experiments (12, 13) haveprovided substantial insights into the microscopic origins of thesemechanisms. In conventional materials, nevertheless, establishinga direct link between the dynamics at the single/few atom lengthscale and the collective behavior of the many thousands of atomsthat constitute GBs and grains poses a serious challenge (14).A bridging of length scales is vital for grain growth studies. The

key parameter in grain growth and its stagnation is the mobility ofGBs, which is determined by their roughness (2, 15). Althoughtransmission electron microscopy (TEM) is well-suited for graingrowth measurements, no technique exists that can nonintrusivelyquantify the atomic scale roughness of buried GBs (14). Theseexperimental shortcomings are compounded in driven polycrystals,which assume practical significance in the fabrication of functionalmaterials via grain growth engineering (2, 7). Driven GBs (16) arethought to kinetically roughen (17), which may result in signifi-cantly enhanced mobilities (15) and influence grain growth. Fur-ther, in nanocrystalline materials, which often possess superiormechanical properties compared with their coarse-grained coun-terparts (18), kinetic roughening is expected to have a profoundimpact on mechanical behavior (16). Despite its technological

relevance, the implications of kinetic roughening for GB mobilityand grain growth remain poorly understood. Although moleculardynamics simulations canmodel atomistic phenomena realistically,they often are limited to small system sizes (19) and short timescales (11), which may influence measurements of GB roughness(15) and predictions of grain growth laws (2, 20). Kinetic MonteCarlo simulations (21) and phase field models (22) are insensitiveto microscopic details. Thus, there is a need for a complementarymultiscale approach that can probe kinetic roughening and its linkto grain growth in driven polycrystals.In this work, we combined techniques in colloid science to in-

vestigate the dynamics of GBs in sheared 3D colloidal crystals overlength scales spanning from the single-particle level to that of theGB network. Our single-particle resolution experiments revealthat for large oscillatory strains, boundaries with normals orientedparallel to shear are preferentially kinetically roughened. We findthat the equilibrium capillary fluctuation method (CFM) allows usto extract effective mobilities, even under shear. Analysis of dy-namics at the single-particle level reveals that strain-induced an-isotropy in particle displacements is manifested as a preferentialenhancement of the effective mobilities. Most strikingly, by im-aging the GB network under shear, we show that this shear-in-duced anisotropy in the mobility leads to directional grain growth.Because colloid models are valuable analogs of atomic systems(23–27), insights gained from the present studies should be rele-vant for atomic and block copolymeric polycrystals as well.Our system consisted of thermo-responsive size-tunable poly

(N-isopropylacrylamide) (PNIPAm) colloids tagged with the fluo-rophore rhodamine 6G for confocal imaging (Materials and Meth-ods). We adjusted the suspension volume fractions ϕ such that at311 K, where the particle diameter σ = 0:60 μm, ϕ< 50%, and theequilibrium phase is a liquid. Annealing the samples to 296 K led toparticle swelling, with σ = 0:95 μm, resulting in a ϕ∼ 70%, and thesuspension crystallized into a polycrystalline state. A particularadvantage of PNIPAm colloids is that they allow us to control thegrain size systematically by altering the annealing rate (SI Text andFig. S1). To mimic the nanocrystalline regime in which GB-mediated response is predominant (12, 18) and grain sizes typ-ically are 50–200 atom diameters across, we aimed for averagegrain sizes of the order of 100 colloid diameters. We restricted

Author contributions: S.G., K.H.N., A.K.S., and R.G. designed research; V.S. and R.G.designed the confocal rheometer; S.G. and K.H.N. performed research; V.S. and R.G.contributed new reagents/analytic tools; S.G. and K.H.N. analyzed data; and S.G., K.H.N.,A.K.S., and R.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. J.A.W. is a guest editor invited by the EditorialBoard.1S.G. and K.H.N. contributed equally to this work.2To whom correspondence should be addressed. E-mail: rajeshg@jncasr.ac.in.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1210456109/-/DCSupplemental.

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our attention to high-angle grain boundaries (HAGBs) formedwhen adjacent grains that straddle the boundary have a mis-orientation angleΘ> 128. Geometrically, GBs can be described bya planar array of misfit dislocations (28). In HAGBs, the density ofgeometrically necessary dislocations is large and the dislocationcores overlap, leading to a continuous disordered interface.

Results and DiscussionUsing our confocal rheometer, we simultaneously imaged thereal-space particle-level microstructure of colloidal polycrystalssubjected to a controlled shear deformation (Materials andMethods, SI Text, and Fig. S2). Samples were loaded in a custom-designed temperature-controlled parallel-plate shear cell witha typical plate separation of g= 45 μm, corresponding to roughly60 crystalline layers. Thermal annealing of the colloidal suspen-sion at a rate of 0.125 K/min yielded the desired grain size withthe ½1; 1; 1� crystal planes parallel to the walls of our shear cell;therefore, our studies are confined to pure tilt boundaries. Theplane pqrs in Fig. 1A shows a snapshot of an HAGB. We quantifythe dynamics of the GB interface (SI Text) by the height functionhðx; tÞ, which is the 1D string formed by the intersection of the

GB plane n with the imaging plane pqrs (thick white line in Fig.1A). The image plane pqrs typically is 8–10 layers above thebottom plate to avoid wall effects. To investigate shear-inducedanisotropic effects, experiments consisted of studying the dy-namics of hðx; tÞ at different oscillatory shear strains, γ, for twoGB configurations: n k v (denoted by GBk) and n k ∇× v(denoted by GB⊥), where v is the velocity (Movie S1).γ= γosinðωtÞ was changed in our experiments by keeping the os-cillation frequency fixed at ω = 1 rad/s and changing the strainamplitude γo. The values of γo quoted here have been correctedto incorporate the effect of wall slip (SI Text and Fig. S3). GBproperties sensitively depend on Θ (4, 27, 28), and hence we fo-cused on HAGBs within a narrow range of Θs, 198<Θ< 218, tofacilitate quantitative comparison of results from experiments onGBk and GB⊥.

Kinetic Roughening of GBs. To characterize the roughness of theinterface, we quantify a related parameter: the interface width, w,defined as the root-mean-squared (rms) fluctuations of hðx; tÞ (29).In Fig. 1 B–E, we plot the normalized histograms of height fluc-tuations PðΔhÞ for increasing γo. Here,Δhðx; tÞ= hðx; tÞ− hhðx; tÞit.For all γo, PðΔhÞ is gaussian for GBk (solid curves) and GB⊥(dashed curves), allowing us to estimate w (shown by circles) di-rectly from the fits (Fig. 1C–E). For γo ≤ 2%,wk ≈w⊥ (Fig. 1B andC). Remarkably, we find that for γo ≥ 8:3%, GBk undergoespreferential kinetic roughening with wk >w⊥ (Fig. 1 D and E).Earlier studies addressed equilibrium roughening of HAGBs, inthe context of faceting–defaceting transition (30), and kineticroughening of ΣGBs (16). An important finding from the presentstudy is that general nonfaceted HAGBs also undergo kineticroughening (15). Further, the migration mechanism of GBs isexpected to change from a step-type motion to a continuousmotion across the roughening transition. In Fig. S4, we plot theGB center-of-mass, defined as hhðx; tÞix, with t. Although it isdifficult to estimate the roughening transition temperature for ourHAGBs, we indeed find that the motion of GBs at zero-shear andGB⊥ at γo = 8:3% is stepped and that of the kinetically roughenedGBk (γo = 8:3%) is continuous (Fig. S4).

Shear-Induced Anisotropy in GB Mobility. Having quantified theroughness of GBs, we next focused on determining their mobility,M, which relates the migration velocity of the boundary vGB =MFto the driving force F (4). The net driving force acting ona boundary is composed of two parts, F =Γκ+Pext, where the firstterm is due to intrinsic boundary curvature, κ, and the second termis from externally imposed stresses. Here, Γ is the GB stiffness(31). To calculate M, we first determined Γ using the CFM (32–34). In the present studies, a 1D section of the 2D GB interface isconsidered, which is not unreasonable as recent experiments haveshown that Γ for an equilibrium crystal–melt interface obtained byignoring the third dimension completely is in good agreement withthat obtained from 3D computer simulations (35). The equilib-rium roughness of an interface is a tradeoff between the interfacialfree energy, which isminimum for a smooth interface, and thermalenergy. In CFM, thermally excited capillary fluctuations of theinterface are decomposed into normal modes and the amplitudeof the modes decays as hjAðkÞj2i= kBT

LΓk2. Here, kBT is the thermalenergy, k is the wavevector, and L is the interface length. AlbeitCFM is an equilibrium statistical mechanics approach, studies ona driven colloidal liquid–gas interface have shown that shearleaves the k dependence of hjAðkÞj2i unchanged, which allows thedefinition of an effective shear-dependent stiffness, even when thesystem is out of equilibrium (36).We perform a Fourier decomposition of Δhðx; tÞ (SI Text and

Fig. S5) and plot LhjAðkÞj2ik2 vs. k for GBk (solid circles) andGB⊥ (hollow circles) for increasing γo (Fig. 2 A–C). In closeparallel with the sheared colloidal liquid–gas interface (36), theequilibrium CFM analysis is valid for driven solid–solid interfaces

Θ = 19°Θ = 19°

∇ x x v

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Fig. 1. Kinetic roughening of HAGBs. (A) Schematic of the shear geometry.The planes a′b′c′d′ and e′f ′g′h′ form the top and bottom plates of our shearcell. The imaging plane pqrs shows two crystallites with Θ= 198. The GB planeis the shaded region denoted by normal n. This figure corresponds to theconfiguration n k v. (B–E) Probability distribution of height fluctuationsPðΔhÞ for increasing γo: (B) γo = 0%, (C) γo = 2%, (D) γo = 8:3%, and (E)γo = 18:3%. In C–E, solid curves and dashed curves are gaussian fits to histo-grams that correspond to GBjj and GB⊥, respectively. The circles correspond tow, and the width of the gray-shaded region corresponds to thew for γo = 0%.

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as well (Fig. S6). We find that LhjAðkÞj2ik2 is nearly a constant kBTΓover a decade in k, for both boundary configurations and for allγo. Notably, we find that Γ, obtained by averaging LhjAðkÞj2ik2over the shaded region (Fig. 2 A–C), is preferentially loweredfor GBk (solid circles) compared with GB⊥ (hollow circles) forγo ≥ 8:3% (Fig. 2D and Fig. S5A). An anisotropic lowering of Γ forGBk vs. GB⊥ is a result of anisotropic enhancement in the interfaceroughness and is consistent with Fig. 1C–E. It is important to notethat in ref. 36 Γ depends on the shear rate _γ, whereas for HAGBswe find that Γ depends strongly on γo (SI Text and Fig. S7).For capillary fluctuations that decay as hAðk; 0ÞA* ðk; tÞi=

hjAðkÞj2ie−MΓk2t, the dynamic correlation function gdðτÞ=hΔhðx; tÞΔhðx; t + τÞix;t = kBTξ

Γ erfc�

ðΓMtÞ12ξ

�(SI Text, Fig. S8, and

Fig. S9 A–C) yields the product MΓ (37). Here, ξ is the lateralcorrelation length (38) obtained from exponential fits to the height–height correlation function ghðδxÞ= hΔhðx; tÞΔhðx + δx; tÞix;t (Fig.S9D and E) and erfcðtÞ is the complementary error function. Fig. S9A–C shows gdðτÞ for GBk (solid circles) and GB⊥ (hollow circles) forincreasing γo. Plugging in the value of Γ (Fig. 2D), obtained earlier,into the complementary error function fits of the data (black lines inFig. S9A–C) yields an effective shear-dependentmobilityM.We findthat the increase inMwith γo for the kinetically roughened boundary,GBk (Fig. 2E, solid circles), is more rapid compared with GB⊥ (Fig.2E, hollow circles) and is almost an order of magnitude larger atγo = 18:3% (Fig. S5B). It generally is believed that kinetic rougheningalters GB mobilities and dictates microstructure evolution in drivenpolycrystals. However, even in the zero-driving force limit, a connec-tion between roughness and mobility has been shown only in com-puter simulations (15) and its extension to nonzero driving forces hasnot been explored. By integrating fast confocal microscopy withrheology, we have shown that the shear-induced anisotropy in M isa direct consequence of preferential kinetic roughening.Will shear-induced anisotropy in mobility, Mk >M⊥, lead to

directional grain growth? To answer this question, we take a closerlook at themobility relation v=MΓκ+MPext (31). Focusing on thesecond term, one would naively expect that an anisotropy in Mimplies an anisotropy in v. Although it is difficult to characterizePext acting on GBs in a driven polycrystal (2), it chiefly consists ofcontributions from the applied bulk stress and its coupling to theelastic anisotropy in adjacent grains (39). In our experiments, weexpect the driving force due to bulk stress to be zero because of the

oscillatory nature of the applied strain. Further, the driving forcedue to elastic anisotropy becomes significant only for grain sizeslarger than about 1 μm (∼3,000σ) in atomic systems (39), which ismuch larger than the grain sizes used in our experiments (∼100σ).It therefore is likely that in our experiments, Pext = 0 and hencev=MΓκ. We note that with increasing γo, M increases (Fig. 2E)whereas Γ is found to decrease (Fig. 2D) for both GBk and GB⊥.Thus, in the approximation Pext = 0, we expect an anisotropy in GBmotion and grain growth only if the reducedmobility,M* = MΓ, isitself anisotropic. Remarkably enough, Fig. 2F shows that aniso-tropic kinetic roughening indeed results in anisotropic-reducedmobilities with Mp

k >Mp⊥ at large γo. Although we considered a

narrow range of Θs to allow comparison across the two GB con-figurations, given that HAGBs exhibit qualitatively similar dy-namics over a broad range ofΘs (27, 40), we expect the anisotropyin M and M* to be a generic feature of these boundaries.

Directional Grain Growth Under Shear. Even as our single-particleresolution measurements revealed a shear-induced anisotropy inbothM andM*, to link this to grain growth it is necessary to probeGBdynamics under shear at the grain network length scale. To thisend, we performed Bragg diffraction microscopy (BDM), which isthe analog of TEM for colloidal crystals (41), simultaneously withrheometry (Materials and Methods, SI Text, and Fig. S2B). Here,the colloidal crystal sample, confined between the shear plates, isilluminated by a white-light source and a detector is placed at thefirst Bragg diffracted spot. A perfect single crystal would result inuniform intensity at the detector. For a polycrystal, however, theBragg condition is met only by crystallites of a particular orienta-tion, resulting in a diffraction contrast image. We note here thatBDM does not yield an orientation map of the polycrystal butallows us to distinguish between low-angle GBs, which appear asarrays of discrete spots corresponding to dislocation cores, andHAGBs, which appear as continuous curves (42). A typical BDMsnapshot of the colloidal polycrystal is shown in Fig. 3A, with GBksshown by solid lines and GB⊥s shown by dashed lines. Fig. 3 B andC shows hhðx; tÞix vs. t for γo = 3:9%. In complete concord withresults thus far, anisotropy in M and M* indeed results in aniso-tropic grain growth with vk > v⊥ on an average (Movie S2; see alsoSI Text, Fig. S10, and Movie S3). As a consistency check, we esti-mated the expectedGB velocity by plugging in the value ofM* andassuming κ= 1

d, where d is the average grain radius, which is ∼100

ο ο ο

A B C

D E F

γ = 2% γ = 8.3% γ = 18.3%

Fig. 2. Shear-induced anisotropy in GB mobility. LhjAðkÞj2ik2 vs. k for (A) γo = 2%, (B) γo = 8:3%, and (C) γo = 18:3% for GBjj (●) and GB⊥ (○). (D) Stiffness Γ asa function of γo obtained from A–C by averaging LhjAðkÞj2ik2 over the shaded region. (E) Mobility M and (F) reduced mobility M*=MΓ as a function of γo forGBjj (●) and GB⊥ (○). In D–F, (□) corresponds to γo = 0%.

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μm. The calculated GB velocity is in close agreement with thoseobtained from BDM measurements.

Microscopic Origins of Directional Grain Growth. Our observationscannot be rationalized within the theoretical framework of shear-coupled GB migration because our HAGBs possess no identifi-able structural units, the resolved shear stress has no componentin the glide plane of boundary dislocations (43–45), and the cap-illary fluctuation spectrum decays as 1

k2 (46). Instead, we chose toexploit the analogy between HAGBs and glass-forming liquids(27, 40). ForHAGBs, the rate-controlling events formigration aresingle-atom hops across the boundary plane (47, 48) and thecharacteristic time associated with these hops is the cage-breaking

time t*. We extracted t* from the inflection point in the mean firstpassage time τðrÞ (48), defined as the average time taken bya particle to traverse a distance r for the first time. We find that t*for γo= 2% is greater than t* for γo= 8.3% for both GBk andGB⊥(Fig. 4 A), implying that the activation barrier for cage breaking islowered at a higher γo (SI Text and Fig. S11). This lowering ofactivation barriers is reminiscent of the strain-induced de-formation of the potential energy landscape of sheared glasses(49). For a migrating boundary, the self-part of the van Hovecorrelation function Gsðr;ΔtÞ for Δt≥ t* develops a character-istic peak at an intermediate distance r with rcage < r< σ. Here,rcage corresponds to the cage size. However,Gsðr;ΔtÞ (Fig. 4B andC) do not exhibit peaks between rcage and σ for both GBk andGB⊥

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Fig. 3. Directional grain growth under shear. (A) Snapshot of a colloidal polycrystal obtained using BDM. The white arrow labeled v shows the shear velocitydirection. The curves highlight GBs for which migration velocities were measured. Solid curves indicate GBjjs and the dashed curves indicate GB⊥s. The arrowspoint along the direction of GB motion, and their length is proportional to the GB migration velocity vGB. (B) hhðx; tÞix vs. t for GBjjs. (C) hhðx; tÞix vs. t for GB⊥s.The lines are least-squares fits to the data. The numbers shown adjacent to the GB center-of-mass profiles vs. time in B and C correspond to those in A.Boundary 4 was used as a reference for the drift correction for GBjjs and GB⊥s.

B C

D E

A

Fig. 4. Single-particle dynamics at GBs. (A) Mean first passage time τðrÞ for GBjj [γo =2% (■), γo = 8:3% (●)] and GB⊥ [γo =2% (□), γo = 8:3% (○)]. The dashedcurves are Hill function fits used to extract the inflection point t*, shown as solid lines for GBjj and dashed lines for GB⊥. (B and C) Self part of the van Hovecorrelation function Gsðr;ΔtÞ for γo = 8:3% for GBjj (B) and GB⊥ (C) at Δt = 0:5t*, t*, and 2t*. (D and E) Angular distribution of displacements contributing tothe nearest-neighbor peak of Gsðr;ΔtÞ for γo = 8:3% over Δt = t* for GBjj (D) and GB⊥ (E). In D and E, the solid arrow denotes the shear direction and thedashed arrow denotes the GB normal. About 50% of particle hops happen within a 40° window centered on the shear direction for both GBjj and GB⊥.

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even for Δt> t*, in striking resemblance to observations on sta-tionaryGBs (48). This is not entirely surprising given that over theduration of our confocal rheology experiments (420 s), the netdisplacement of hhðx; tÞix is only about 0:5σ, even for GBjj. Fur-ther, although displacements in all directions contribute to thepeak at r= σ in Gsðr;ΔtÞ (Fig. 4 B and C), hops normal to the GBplane are the ones that primarily influence boundary mobility. Todetermine whether shear biases activated hops, we plot the an-gular distribution of displacements contributing to the peak inGsðr= σ;Δt= t*Þ for GBk and GB⊥. For γo = 2%, the displace-ments are more isotropically distributed (Fig. S12) compared withγo = 8:3% for which we find a significant enhancement along theshear direction for both GBk and GB⊥ (Fig. 4 D and E). For GBk,these shear-enhanced hops are normal to the boundary plane andtherefore lead to a preferential increase in hjAðkÞj2i (Fig. S6) andM (Fig. 2E). Collectively, our observations show that strainenhances HAGB interface fluctuations without contributing toa bulk driving force for migration, consistent with our earlier as-sumption of Pext = 0, and is therefore analogous to temperature.As expected, similar to the variation ofM and Γ with temperature(50), the dependence of M on γo is much stronger than that of Γ(Fig. 2). Not only does this rationalize the success of the CFMin extracting Γ and M for sheared HAGBs, but it also accountsfor the anisotropic enhancement in M* and therefore directionalgrain growth.

ConclusionsBy bringing together experimental techniques in colloid science,we have bridged vastly disparate length and time scales to unravelthe microscopic underpinnings of grain growth in sheared poly-crystals. We have shown conclusively that preferential kineticroughening (Fig. 1 C–E) and the resulting anisotropy in effectivemobilities (Fig. 2E) ultimately lead to directional grain growth(Fig. 3). We find that strain enhances only the amplitudes ofcapillary fluctuation modes (Fig. 2 A–C) but leaves the fluctua-tion spectrum itself qualitatively unchanged (Fig. S6). Thisstrongly suggests that the paradigm of shear as an effectivetemperature, routinely adopted to describe driven glasses (51), isgermane even to theHAGB interfaces investigated here (27).Weobserve that the strain-induced lowering of activation barriersand the concomitant anisotropic enhancement of particle dis-placements satisfactorily explain the observed anisotropy in GBmobility (Fig. 4). Owing to the close similarity in the physics ofGBs across diverse systems (4, 8, 27, 37), we expect our results canbe extended to atomic and block copolymeric polycrystals as well.Further, by combining the temperature-tunability of PNIPAm

colloids with template-directed growth (25, 41), in principle itshould be possible to design bicrystals and polycrystals of con-trolled grain crystallography and size and investigate their re-sponse to shear deformation. More importantly, our experimentsexemplify a multiscale approach that can be applied readily toelucidate fundamental as well as technologically relevant phe-nomena, such as grain rotation and coalescence, GB sliding, andtexture evolution in driven polycrystals.

Materials and MethodsPNIPAm colloids of diameter 950 nm (polydispersity <5%) were synthesizedby the standard emulsion polymerization route. All the chemicals used werepurchased from Sigma-Aldrich and had a purity in excess of 98%. Particleswere purified using the method described in ref. 27. The purified sampleswere concentrated to yield ϕ∼ 70% at 296 K.

Confocal Rheology. To facilitate confocal imaging under shear, we integrateda fast confocal microscope (Visitech VT-Eye) with a commercial rheometer(MCR-301, Anton Paar) mounted on a homemade mechanical stage (SI Textand Fig. S1A). Samples were imaged using a Leica objective (Plan Apo-chromat 100× N.A. 1.4, oil immersion) and a laser excitation centered at 514nm. The field of view was a 54 × 54-μm slice containing ∼3,200 particles.Images were captured at 10 frames per second (fps) for γo = 2% and 8.3%and 26 fps for γo = 18.3%. The temperature was maintained at 296 K for allexperiments. Standard codes were used for particle tracking (52), and sub-sequent analysis was performed using algorithms developed independently.The particle-tracking resolution as calculated from the micrometer to pixelratio is 0.07 μm.

BDM Under Shear. For grain growthmeasurements under shear, we integratedBDM with rheometry (SI Text). The sample was illuminated by a white lightLED source incident at an angle θ = 56˚ (see Fig. S1B for a schematic). A low-magnification Leica objective (Plan Apochromat 10× N.A. 0.4, dry) was usedto image the GB network. The temperature was maintained at 296 K, and anoscillatory strain of frequency ω = 1 rad/s and amplitude γo = 3.9% was ap-plied to the sample. The 0.915 × 0.680-mm field of view contained ∼25 grains.Images were captured at 1 fps for 4 hours, and GB profiles were trackedmanually at periodic intervals to generate their center-of-mass time series. Tosubtract drift contributions from the GB motion, a flat immobile boundarywas used as a reference.

ACKNOWLEDGMENTS. The authors thank Jack Douglas and Vikram Desh-pande for useful discussions. The authors also thank the anonymousreviewers for their valuable suggestions. S.G. thanks the Council forScientific and Industrial Research (CSIR) India for a Shyama PrasadMukherjee Fellowship, K.H.N. thanks CSIR India for a Senior ResearchFellowship, A.K.S. thanks CSIR India for a Bhatnagar Fellowship, and R.G.thanks the International Centre for Materials Science and the JawaharlalNehru Centre for Advanced Scientific Research for financial support.

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