Dynamical Processes of Interstitial Diffusion in a Two-Dimensional Colloidal Crystal

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X.S.L. The and and S.-C.K. A.P., and data; S.-C.K., analyzed research; X.S.L. paper. and designed L.Y., S.-C.K., X.S.L. research; and formed A.P. contributions: Author of made crystals colloidal 2D in a performed was experiment Our Results can One defect–lattice and from determined. interactions. defect emerge can point are behavior a nonequilibrium of lattice how see dynamics the equilibrium the in visualize directly diffuses inter- colloidal an defect fast 2D how stitial a determine that in origins diffusion microscopic The during crystal. defects interstitial in tuations defects point result, of a type this elusive. As of remain (16). processes dynamical techniques the atomic indirect of in details on the defects based point mostly of are studies solids Previous (15). crystals heated h xeietlstpcnb on nrf 17. ref. in found be can setup sepa- experimental constant disk) the lattice thick with a crystal and colloidal coverslip Two thin by potential. 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Fig. 1. (A and B) Video images of an isolated (A) mono- and (B) diinterstitial in a 2D colloidal crystal. Red and blue dots indicate 5- and 7-coordinate disclinations. The 5 × 5 diamond region contains nine particles in a perfect lattice but 10 particles when it encloses the core of a monointerstitial. The 4 × 6 diamond has 10 particles when it contains the core of a diinterstitial. (C and D) Delaunay triangulation diagrams of corresponding images in A and B.(C and D, Insets) The Burgers vectors are deﬁned as the displacement between disclinations, from low to high coordinations.

An optical tweezers system with an Ar + laser (Coherent time, it is a monointerstitial; with less frequency we also find two INNOVA 90; λ = 514 nm) was constructed on an inverted micro- extra particles in that region, a diinterstitial, the main subject of scope (Zeiss Axiovert 135) with a 100× objective (Zeiss Plan this study. Neofluar; N.A. = 1.3, oil immersion). We used rotatable mirrors Direct video imaging of the real-time behavior of the inter- to control the position of the beam so that we can capture a par- stitial diffusion provides unprecedented insights into the micro- ticle and move it across the field of view (∼50 µm × 50µm). The scopic processes of defect dynamics. Fig. 1 shows two represen- real-time images were recorded as videos at a rate of 30 frames tative captured video images and their corresponding Delaunay per second using a monochrome charge-coupled device (CCD) diagrams. The point defects and their configurations are identi- camera (Sony SSC-M370) and a Sony SVO-9500MD recorder. fied by counting the number of particles inside the dashed line The CCD images were captured by a frame grabber (NI-1409) loops. Clearly, by simple counting, one can see a single inter- and analyzed using a particle-tracking algorithm (18). stitial in Fig. 1A and two interstitials in Fig. 1B. This example In our 2D colloid experiment, initially we used optical tweez- shows diinterstitials directly observed in a real experiment. Red ers as a tool for removing impurity particles; mostly two particles dots indicate 5 or fewer coordinate particles and blue dots indi- stuck together irreversibly (by van der Waals force). In the pro- cate 7 or more coordinate particles. Interstitial configurations cess, we discovered that we can drag a “good” particle off its can be viewed as a combination of several bound pairs of 5, 7 lattice site to create a vacancy (17). Furthermore, we found that coordinated disclinations. Being topologically neutral, a point by dragging the particle along one of the three crystalline axes, defect should have no net Burgers vector. The Burgers vectors we can cause a row of several particles to displace, resulting in ~nij (pointing from red dot to blue dot in Fig. 1, Insets) indeed interstitials forming at the other end of the row. Most of the add up to zero in each configuration (7).

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18 Fig. 3. Trajectories of mono- and diinterstitial defects. (A) Monoin- terstitial trajectory for ∼30 s. (B) Diinterstitial trajectories for ∼10 s. The yellow lines show a triangulation diagram, superimposed on the trajectories a few seconds after the interstitial diffused away 16 from the ﬁeld of view. Blue circle is starting point of trace and black 36 38 40 42 44 46 dots are centers of interstitial.

Following the standard Delaunay triangulation method (18), observed in Fig. 2 A–F for monointerstitials and in Fig. 2 G–L we first calculate the coordinates of each particle from each for diinterstitials; the notation is adopted from refs. 19 and 20. snapshot, as shown in Fig. 2. Distinct defect configurations are The position of a point defect is defined as the center-of-mass

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5 Fig. 4. Time dependence of mean-square displacement: mono- and diinterstitial. The mean- square displacement as a function of δt was cal- Mean square displacement ( 0 culated from ∼6-s trajectories. Red and blue lines are linear ﬁts for mono- and diinterstitials, respec- 0.0 0.5 1.0 1.5 2.0 2.5 tively, and ﬁts are for δt values of 1 ∼ 3 s. Most diinterstitials move out of the 2D sample region Time (sec) quickly.

4 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1918097117 Kim et al. Downloaded by guest on September 23, 2021 Downloaded by guest on September 23, 2021 i tal. et Kim s. 8 over aver- and lags time different with displacements square the direction. its diinterstitial the while 3B lattice, Fig. triangular in 2D a in randomly moves h atc ofiuainfo eunilvdofaefloigta in that following frame video sequential a from configuration lattice The (B) dislocations. (Inset edge “o.” indicate lines red The tions. 5. Fig. described are tracked are movements proce- defect in The the diffusion. in which in diinterstitials by differently and dures behave mono- crystals that is colloidal observation field 2D the first from The away view. colloidal moved interstitial of The the after lattice. obtained colloidal is lattice underlying 3, the Fig. in on shown as superimposed interstitials the of trajectories green time-elapsed the a within disclinations coordinated 2). 7 (Fig. 5, loop all from position CD AB rmtetaetre fmlil nesiil,w calculated we interstitials, multiple of trajectories the From osuytedfuindnmc ftedfcs econstructed we defects, the of dynamics diffusion the study To R (µm) 3 Fig. S1. Fig. Appendix, SI 0 1 2 3 eanytinuaindarmo oonesiilwt h etrmre sa x n h / disclina- 5/7 the and “x” an as marked center the with monointerstitial a of diagram triangulation Delaunay (A) diffusion. interstitial of Dynamics 02468 h ipaeetvector displacement The ) ifssaogacranltieai n edmchanges seldom and axis lattice certain a along diffuses mono-interstitial ie(sec) Time ~ A R fteitrtta sdfie rmxt .(C o. to x from defined is interstitial the of hw htamonointerstitial a that shows tn fmnitrttasi infiatylre hnta of that than larger significantly con- is diffusion monointerstitials that the Surprisingly, than of (21). larger stant divacancies indeed and is monointerstitials of of constant view diffusion microscopic the the in the disclinations of of out by mean- one explained disappears window. the because be quickly sampling and can diinterstitial enough diinterstitial line of the linear lack of con- between confirm- displacement diffusion discrepancy square 4, are The minor fitting, Fig. linear The walkers. the in from random obtained diinterstitials 10.95 these as are and that which behavior stants, found mono- time their We on both ing dependence type. for linear interstitial lag show each displacements for mean-square them aged speitdi ueia aclto 2) efudthat found we (20), calculation numerical a in predicted As

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Fig. 6. (A and B) Plot of (A) 5- and (B) 7-disclination positions over 8 s, colored by each conﬁguration and centered about the monointerstitial defect core. (C and D) Same plot of particle positions of (C) 5- and (D) 7-coordinate disclinations overlapped on top of the centered defect core of the diinterstitial during 8 s.

diinterstitials. The difference here is much more pronounced For thermally activated processes, the residence time in a par- than the difference between the mono- and divacancies. Note ticular configuration contains the information regarding attempt that the experimental conditions used for the vacancy diffusion rate and activation barrier (23). We estimated the residence study previously (17) were the same as those used in this paper. time of the interstitials to be approximately τmono = 0.04 s for In a 2D colloidal crystal, the grab and release of a colloid particle monointerstitials and τdi = 0.02 s for diinterstitials. (The proce- by the optical tweezers generates the interstitials and vacancies dure is described in SI Appendix, Fig. S2; for more details, see simultaneously. If they are within a few lattice constants, they ref. 24.) recombine and disappear, as described in the previous paper Fig. 5 provides additional insight into the thermally activated (22). But if they are created at more than ∼10 lattice constants dynamics of interstitial diffusion. The fluctuations of the hop- apart, they behave independently and diffuse out of the field of ping distance are shown as a function of time for both mono- and view individually. (The actual 2D region of the colloidal crystal is diinterstitials. Here, we define the center of the interstitial as the approximately five times the field of view.) average position of all fivefold and sevenfold disclinations. The

6 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1918097117 Kim et al. Downloaded by guest on September 23, 2021 Downloaded by guest on September 23, 2021 1 .Fe,D .Nlo,D .Fse,Itrttas aace,adsproi re nvortex in order supersolid and vacancies, Interstitials, Fisher, S. D. Nelson, R. D. Frey, E. 11. 2 .S e nenlfito nteitrtta oi ouin fCadOi tantalum. in O and C of solutions solid interstitial the in friction Internal Ke, S. T. 12. C L. DaSilva, L. 10. 4 .H tligr .A ee,Pitdfcsi c rsas tutrs rniinkinetics, transition Structures, crystals: bcc in defects Point Weber, A. T. Stillinger, H. coefficients. F. diffusion 14. atomic Interstitial Zener, C. Wert, C. 13. 5 .V rnt,Itrttac oe o odne atrsae fface-centered-cubic of states matter condensed for model Interstitialcy Granato, V. A. 15. ie ne h aecniin tmeaue oi tegh.As strength). ionic lat- (temperature, same conditions the same in the are under they tice, not preserve though is even locally behavior diinterstitials equilibrium for fluctuations preserved this when However, (25). only (disclina- balance possible defects detailed that is topological symmetry This the by tions). the broken restore over spontaneously order fluctuations was this thermal restore transi- Namely, a cause configurations, time. at which different order fluctuations, between Thermal orientational tions time. the in destroy instant locally given interstitial similar an a with exhibit disclinations sevenfold of behavior. distributions the ftedslnto oain ntefu ifrn configurations different distribution four the the in We in symmetry 2. I locations sixfold Fig. disclination striking in the a configuration of is each of there by coordi- out top that grouped on sevenfold find diffuses core plotted and it defect and five- the shifted (before are of of s interstitials locations 8 of we The disclinations to of view). nated 6, relative period of Fig. a positions field In over disclinations the origin. core sevenfold physical defect and the deeper five- a the anal- missed these plot have However, may (21). diffusion yses defect individual studying diffuse diinterstitials walker. result, random a quasi–one-dimensional As a in behavior. as this displacements confirms core S3 diinterstitial Fig. and a distribution is angular mono- observed The of detailed have diinterstitials. for we A effect what direction. memory that strong previous conclusion the a config- to between of fluctuations leads the memory urations of S3 ) a Fig. Appendix, has (SI it analysis direc- two process if or hopping one as only the tions has diinterstitial of the However, directions diverse. the are monointerstitial the For 4. Fig. to in contrary the result monointerstitials, expect the than would faster one diffuse stochastic, to purely diinterstitials are observa- processes this in the With if distance. shown tion, hopping as smaller and frames, time residence sequential two 5 from Fig. positions center the vector displacement i tal. et Kim .E okye .Esr nreiso on eet ntetodmninlWigner two-dimensional the in defects point of Energetics Elser, visualization V. Direct Bausch, Cockayne, R. A. E. Nelson, R. 9. D. Meinke, H. defects J. Bowick, point J. of M. Lipowsky, energetics P. and 8. configurations Equilibrium Ling, in S. crystals X. colloidal Pertsinidis, paramagnetic A. of melting 7. Two-stage Maret, G. Lenke, R. Zahn, dimensions. K. two in 6. gas Coulomb vector the and melting. Melting Young, two-dimensional P. A. of 5. Theory Nelson, two- R. D. in transitions Halperin, phase B. and metastability 4. Ordering, Thouless, J. D. Kosterlitz, M. one- J. in antiferromagnetism 3. or ferromagnetism of Absence Wagner, H. Mermin, D. N. 2. Anderson, W. P. 1. 2 , h ipeitrrtto sta h iciain associated disclinations the that is interpretation simple The h bv nlssaebsdo h tnadpoeue of procedures standard the on based are analyses above The 3. Fig. in found be can mystery this to solution the of hint A crystals. crystals. colloidal two-dimensional in defects point crystal. scars. grain-boundary in dynamics dislocation of crystals. colloidal two-dimensional in dimensions. two (1979). 1855–1866 (1978). 121–124 systems. dimensional models. Heisenberg isotropic two-dimensional or 2. chap. Rev. n etn implications. melting and (1949). metals. I 3 , –5(1948). 9–15 74, I A hs e.B Rev. Phys. hs e.Lett. Rev. Phys. 4 hs e.B Rev. Phys. and , and nio .D .Csa .Oier,Fraineeg n neato of interaction and energy Formation Oliveira, O. Costa, F. D. L. andido, ˆ ai oin fCnesdMte Physics Matter Condensed of Notions Basic hs e.Lett. Rev. Phys. I h oonesiil edt aelonger have to tend monointerstitials The B. 2d 2–2 (1991). 623–629 43, 7394 (1994). 9723–9745 49, .Py.CSldSaePhys. State Solid C Phys. J. 7–7 (1992). 974–977 68, nFg 6B, Fig. In 6A. Fig. in monointerstitials of R ~ .Ce.Phys. Chem. J. sdfie stedslcmn between displacement the as defined is 7122 (1999). 2721–2724 82, hs e.Lett. Rev. Phys. 0550 (1984). 5095–5103 81, 1110 (1973). 1181–1203 6, a.Mater. Nat. hs e.Lett. Rev. Phys. hs e.B Rev. Phys. 933(2001). 098303 87, hs Rev. Phys. AdsnWse,1984), (Addison-Wesley, 0–1 (2005). 407–411 4, 341(2007). 035441 76, hs e.Lett. Rev. Phys. 13(1966). 1133 17, IAppendix, SI hs e.B Rev. Phys. 1169–1175 8, Phys. 19, 41, 4 .Km Tasoto hre olisadDAi ircanl, hD thesis, Ph.D. microchannels,” in Kampen, DNA van and G. N. colloids 25. charged of “Transport Kim, S. Kramers. after 24. years Fifty theory: Reaction-rate Borkovec, M. Talker, P. Hanggi, P. 23. 6 .Paii esr ftevoaino h ealdblneciein possible A criterion: balance detailed the of violation the of Measure Platini, T. 26. micromechan- a as tweezers colloidal “Optical Ling, two-dimensional S. X. in Pertsinidis, A. defects Huang, S. point Yu, L. of Kim, S. Diffusion 22. Ling, in S. X. strings Pertsinidis, interstitial A. and 21. vacancy of Lib mechanics Statistical A. 20. Nelson, R. D. studies. colloidal Jain, for microscopy S. video digital 19. of Methods and Grier, one- G. D. of Crocker, studies C. micromechanics J. and 18. microscopy Video Ling, S. X. Pertsinidis, A. 17. metals. of properties thermophysical and vacancies Equilibrium Kraftmakher, Y. 16. 9 .Rihad,C .OsnRihad,Dpnigadnnqiiru yai phases dynamic nonequilibrium and crystals. Depinning Reichhardt, colloidal Olson of J. melting C. local Reichhardt, C. driven and thinning particle 29. Shear a Bechinger, for C. drag Dullens, and A. P. melting R. Local 28. Reichhardt, Olson J. C. Reichhardt, C. 27. onainDvso fMtrasRsac DR rn 1005705. Grant (DMR) Research Materials of Division Foundation ACKNOWLEDGMENTS. SVO-9500MD Sony request. a upon using available tapes are VHS recorder, in on provided recorded are data, video 3 Fig. for mat The of Availability. areas 28). Data many (27, for crystal interest par- of colloidal (29). large be physics 2D should condensed-matter a a here when presented through phenomenon results rem- dragged melting is is local diinterstitial ticle the a the of that surrounding note iniscent create to structure to interesting way is local feasible It a disordered defects. be such may using it melting that studying local suggest to for we seem time, system that in the diinterstitials model persist by Given created a (26). distortions as systems local significant nondriven serve in may dynamics it nonequilibrium as more deserves studies configurations It striking. fluctuating future particularly the is break- in diffusion diinterstitial balance apparent of detailed The local respectively. can of diinterstitials, down we dynamics and Thus, nonequilibrium mono- defect. and rela- of the equilibrium fluctuations of the equilibrium position visualize configurational the directly center-of-mass the the ascertain at to to tive looking method by simple dynamics a quasi–one-dimensional. random developed is effect. 2D diffusion We memory as diinterstitial strong diffuse while to a walkers, found have were diinterstitials monointerstitials the Namely, configurations, that between found By transitions we larger. microscopic significantly is the diffu- monointerstitial the examining the that discovered of and coefficient coefficients diinterstitials sion diffusion in and the dynamics mono- determined both diffusion We for interstitial crystal. of colloidal 2D study a detailed a report We long a for Discussion it observe and diinterstitial the trap period. to able same 6 were In Fig. the we period. in whether long patterns conclude a symmetry cannot sixfold for we configuration experiment, symmetric present our twofold a in live 6 Fig. in shown rw nvriy rvdne I(2012). RI Providence, University, Brown Phys. Mod. ento fa“itne rmequilibrium. from “distance” a of definition 1992). in crystals” colloidal 2D VIII in Micromanipulation defects studying for tool ical crystals. crystals. colloidal dimensional crystals. columnar hexagonal Sci. Interface Colloid crystals. colloidal two-dimensional Rep. fpril sebisdie vrrno n ree usrts review. A substrates: ordered and random over Phys. Prog. driven assemblies particle of Lett. Rev. Phys. crystal. colloidal a through 918(1998). 79–188 299, l .Rihad,C .OsnRihad,Pitdfc yaisi two- in dynamics Point-defect Reichhardt, Olson J. C. Reichhardt, C. al, ´ Nature 5–4 (1990). 251–342 62, 251(2017). 026501 80, 331(2011). 138301 107, 4–5 (2001). 147–150 413, C tcatcPoessi hsc n Chemistry and Physics in Processes Stochastic h orsodn ie lsi PGfor- MPEG in files video corresponding The 9–1 (1996). 298–310 179, and 07X 011/2871 (2011). 10.1117/12.897416 80970X, , hswr a upre yteNtoa Science National the by supported was work This hs e.Lett. Rev. Phys. tapasta inesiilsesto seems diinterstitial a that appears it D, hs e.E Rev. Phys. hs e.E Rev. Phys. e .Phys. J. New h original The S2. and S1 Movies 5911 (2000). 1599–1615 61, 143(2007). 011403 75, 031(2004). 108301 92, hs e.B Rev. Phys. A 3(2005). 33 7, and NSLts Articles Latest PNAS B pia rpigadOptical and Trapping Optical 119(2011). 011119 83, a ercvrdif recovered be can Esve Science, (Elsevier | f7 of 7 Phys. Rep. Rev. J.

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