Dynamical Processes of Interstitial Diffusion in a Two-Dimensional Colloidal Crystal
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Dynamical processes of interstitial diffusion in a two-dimensional colloidal crystal Sung-Cheol Kima,1 , Lichao Yua,2, Alexandros Pertsinidisa,3, and Xinsheng Sean Linga,4 aDepartment of Physics, Brown University, Providence, RI 02912 Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved April 20, 2020 (received for review October 16, 2019) In two-dimensional (2D) solids, point defects, i.e., vacancies and heated crystals (15). Previous studies of point defects in atomic interstitials, are bound states of topological defects of edge dislo- solids are mostly based on indirect techniques (16). As a result, cations and disclinations. They are expected to play an important the details of the dynamical processes of this type of point defects role in the thermodynamics of the system. Yet very little is remain elusive. known about the detailed dynamical processes of these defects. Here we report a direct video imaging study of the local ﬂuc- Two-dimensional colloidal crystals of submicrometer microspheres tuations in interstitial defects during diffusion in a 2D colloidal provide a convenient model solid system in which the microscopic crystal. The microscopic origins that determine how fast an inter- dynamics of these defects can be studied in real time using video stitial defect diffuses in the lattice are determined. One can microscopy. Here we report a study of the dynamical processes directly visualize the equilibrium dynamics of a point defect and of interstitials in a 2D colloidal crystal. The diffusion constants see how nonequilibrium behavior can emerge from defect–lattice of both mono- and diinterstitials are measured and found to interactions. be signiﬁcantly larger than those of vacancies. Diinterstitials are clearly slower than monointerstitials. We found that, by plotting Results the accumulative positions of ﬁve- and sevenfold disclinations Our experiment was performed in 2D colloidal crystals made of relative to the center-of-mass position of the defect, a sixfold sym- a ∼1% aqueous suspension of 0:36 µm diameter polystyrene- metric pattern emerges for monointerstitials. This is indicative of sulfate microspheres (Duke Scientiﬁc No. 5036). The aque- an equilibrium behavior that satisﬁes local detailed balance that ous solution was thoroughly deionized to achieve an estimated the lattice remains elastic and can be thermally excited between −1 Debye screening length κ ≈ 390 nm, at room temperature APPLIED PHYSICAL SCIENCES lattice conﬁgurations reversibly. However, for diinterstitials the (22 ◦C). The colloidal spheres, being negatively charged, form sixfold symmetry is not observed in the same time window, and a crystal due to the repulsive screened Coulomb potential. Two the local lattice distortions are too severe to recover quickly. This fused silica substrates (a thin coverslip and a thick disk) sepa- observation suggests a possible route to creating local melting of rated by ∼2 µm conﬁned the suspension to form a single-layer a lattice (similarly one can create local melting by creating diva- colloidal crystal with lattice constant a ≈ 1:1 µm. The details of cancies). This work opens up an avenue for microscopic studies of the experimental setup can be found in ref. 17. the dynamics of melting in colloidal model systems. 2D colloidal crystal j interstitial defects j diffusion j detailed balance Signiﬁcance rystallization is a spontaneous symmetry-breaking process Defects in crystalline materials are of broad and fundamental Cduring which the many-body system acquires the emer- interest. In condensed-matter physics, defect dynamics con- gent properties of shear rigidity and long-range order (1). In tain essential information about the microscopic processes of two dimensions at ﬁnite temperatures, true long-range order crystal formation and melting. Two-dimensional melting (2D) is absent due to the accumulative effects of long-wavelength is widely accepted to be mediated by the proliferation of phonons (2). Nevertheless, the orientational (or topological) edge dislocations. In 2D crystals, vacancies and interstitials order survives. The melting of a two-dimensional (2D) crys- are, in fact, bound pairs of edge dislocations and disclina- tal can be either ﬁrst order or continuous via the well- tions. They are expected to play critical roles in 2D melting. We known mechanism of defect unbinding proposed by Kosterlitz demonstrated signiﬁcant progress in quantifying the dynam- and Thouless (3), Halperin and Nelson (4), and Young ical processes of interstitials. We also propose a simple yet (5). In well-controlled experiments, it is apparent that the powerful method in visualizing the time-averaged conﬁgura- Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) mecha- tions of the defects, providing a direct tool to assess whether nism of melting has been conﬁrmed (6). However, in real mate- the detailed balance is obeyed or violated in the ﬂuctuating rials, defects are always present, and their roles in the melting processes in a lattice. transition are less understood. There are growing interests in recent years in the dynamics of various kinds of defects in 2D Author contributions: A.P. and X.S.L. designed research; S.-C.K., A.P., and X.S.L. per- colloidal crystals (7, 8) and how they may change the physics of formed research; S.-C.K., L.Y., and X.S.L. analyzed data; and S.-C.K. and X.S.L. wrote the 2D melting. paper. y In two dimensions, point defects, vacancies, and interstitials The authors declare no competing interest.y are nontrivial as they are composites of topological defects, edge This article is a PNAS Direct Submission.y dislocations, and disclinations (9–11). Thus it is expected that Published under the PNAS license.y they will play important roles in the melting processes. Near 1IBM T. J. Watson Research Center, Yorktown Heights, NY 10598.y melting, vacancies will be essentially indistinguishable from ther- 2 Google LLC, Cambridge, MA 02142.y mally excited dislocation pairs (7). The physics of interstitials are 3Structural Biology Program, Memorial Sloan Kettering Cancer Center, New York, NY less clear. In fact, interstitials have long been of importance to 10065.y the study of solids, e.g., in the understanding of acoustic absorp- 4 To whom correspondence may be addressed. Email: Xinsheng [email protected] tion in metals (12, 13) and for understanding the properties of This article contains supporting information online at https://www.pnas.org/lookup/suppl/ crystalline solids near melting (14). There have been suggestions doi:10.1073/pnas.1918097117/-/DCSupplemental.y that interstitials may play a critical role in the melting of super- www.pnas.org/cgi/doi/10.1073/pnas.1918097117 PNAS Latest Articles j 1 of 7 Downloaded by guest on September 23, 2021 AB 1 μm 1 μm CD 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). 2 of 7 j www.pnas.org/cgi/doi/10.1073/pnas.1918097117 Kim et al. Downloaded by guest on September 23, 2021 A B C SI I2 I2d DFE I2a I3 I4 PHYSICAL APPLIED SCIENCES G H I SDI DI2d,a DI2d,b J K L DI2a DI3d DI4d Fig.