Effect of Solid–Liquid Interface Morphology on Grain Boundary

Apr 6, 2016 - GBs were exposed to the liquid at the bottom of the groove, and a high impurity concentration at the GB (CGB) was obtained when the area...
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Effect of Solid−Liquid Interface Morphology on Grain Boundary Segregation during Colloidal Polycrystallization Sumeng Hu,* Jun Nozawa,* Suxia Guo, Haruhiko Koizumi, Kozo Fujiwara, and Satoshi Uda Institute for Materials Research (IMR), Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan ABSTRACT: The effect of the solid−liquid interface morphology on grain boundary (GB) segregation during colloidal polycrystallization was investigated by in situ optical observations.The time evolution of the impurity distribution in the liquid in the vicinity of solid−liquid interface was directly observed during crystal growth. Impurities were distributed homogeneously along the direction perpendicular to the growth orientation during the initial stage of the growth and were then gathered in the groove that formed at the solid−liquid interface as crystallization proceeded. GBs were exposed to the liquid at the bottom of the groove, and a high impurity concentration at the GB (CGB) was obtained when the area of the groove was large. The area of the groove changes depending on the crystallographic orientation of neighboring grains across GBs, which results in a difference in the interfacial energies.

I. INTRODUCTION The control of microstructure is important to obtain high functionality of polycrystalline materials because the microstructure in polycrystals directly affects their optical, magnetic, electronic, and mechanical properties.1,2 It is well-known that nucleation and crystal growth are strongly affected by impurities.3−7 Therefore, impurity doping has a significant effect on the microstructure of materials, such as the grain size and grain boundary (GB) morphology. There has been much effort devoted to understanding the mechanism of crystal growth with impurities8 because the control of impurity doping provides good control over the microstructure of crystals. Direct in situ observations of solid−liquid interfaces have been conducted to reveal the detailed partitioning behavior during crystal growth.9−16 For instance, in situ transmission electron microscopy (TEM) analysis of an Al alloy provided visual evidence of Cu segregation at the solid−liquid interface during solidification.9 Among these investigations, it has widely been understood that the microscale solid−liquid interface morphology is strongly related to impurity segregation, such as the cellular growth that develops during unidirectional solidification of alloy crystals10,11 and during the crystallization of multicrystalline silicon (mc-Si).12 It was reported that impurities segregate more at GBs than within grains during solidification of mc-Si, which is possibly explained as due to the peculiar geometry of the solid−liquid interface at the GB. Fujiwara et al. inferred that impurities discharged from the grains are concentrated in a groove that exists at the GB.12 However, there is still no direct experimental evidence on impurity aggregation at such grooves. Although atomic scale in situ observation is one of the most powerful methods to understand various interfacial phenomena,13−16 the high growth temperatures of alloys and silicon make it difficult to employ such a technique. © XXXX American Chemical Society

GBs play a pivotal role in the fabrication of polycrystalline materials. GBs, where atoms are bonded irregularly compared to those in the grains,17 are more chemically reactive than crystal grains, so that impurity atoms preferentially segregate along these boundaries.18 The mechanism of GB segregation during the growth of polycrystalline materials19,20 has been investigated, and the influence of GB segregation on the properties of materials has also been evaluated.2,18,21,22 Although impurity segregation in GBs is generally considered to proceed during heat treatment after crystal growth, Fujiwara et al. and Hu et al. recently proposed that GB segregation probably occurs during solidification.12,23Thus, the detailed mechanism of impurity segregation at GBs, such as the relationship between the solid−liquid morphology and the impurity partitioning in the liquid at the interface, must be determined. Colloidal systems have recently been regarded as a reasonable model to study atomistic phenomena.24,25 The observation of growth in colloidal crystals enables the detailed growth dynamics to be investigated with single-particle resolution in real space and real time with optical microscopy.26,27 Nozawa et al. recently discussed the analogous impurity partitioning between colloidal crystal growth driven by the evaporation of solvent from a solution and unidirectional single crystal growth from a melt.28 The GB dynamics has been intensely investigated to understand the formation mechanisms and behaviors of GBs. Xie et al. reported the GB formation during colloidal crystal growth under the high frequency of alternating electric field (AEF).29 They observed that the Received: January 14, 2016 Revised: March 17, 2016

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existing GB gradually shrank away and finally disappeared with the decrease of AEF frequency that caused the change of interparticle interaction.29,30Yoshizawa et al. have studied the segregation process of highly charged colloidal particles during the grain growth of colloidal crystals, in which the migration of impurities that follow GB movement during grain growth was observed.31 Our former work presented the segregation of impurities at GBs during colloidal polycrystallization,23 in which impurities at a GB are supplied from a diffusion boundary layer that consists of impurity particles rejected from grains. Moreover, we observed that each GB has a groove at the solid−liquid interface. We consider that the slight scattering of impurity concentration in GBs (C GB ) with the same misorientation angle is caused by different morphologies of the solid−liquid interfaces, which results in different CGB values. While many reports have focused on the relationship between impurities and GBs, little research has been conducted on the relationship between the morphology of the solid−liquid interface and the partitioning behavior of impurities during crystal growth. In the present study, we investigate the impurity partitioning at GBs associated with the presence of grooves by in situ optical observations, and we show how the morphology of the solid− liquid interface affects partitioning during colloidal polycrystallization.

Monodisperse polystyrene (PS) particles purchased from Duke Scientific were used in this experiment. PS particles with a diameter of 500 nm served as host particles. In addition, two types of 700 nm diameter PS particles were used as impurities; the same PS as the host and PS dyed with a red fluorescent agent. Red fluorescent PS impurities were used to clearly observe the distribution of impurities. The initial impurity concentration of the dispersions (C0) was 1% for PS impurities (1 impurity particle in 99 constituent particles), while that of red fluorescent PS spheres as impurities was 0.5%. Red fluorescent PS particles were employed for lower concentrations because those fluorescent impurities can be detected to a depth of several particle layers, whereas the other PS impurities can only be detected to one particle layer thickness. All of the experiments were performed under ambient conditions (ca. 25 °C, ca. 30% humidity). In situ observations of colloidal crystallization were performed with an optical microscope equipped with a CCD camera, using an oil immersion lens (N.A. = 1.3 and 100 × magnification). A high-pressure mercury lamp was used for observation of the red fluorescent PS particles.

III. RESULTS AND DISCUSSION Figure 2a shows optical images of growing colloidal polycrystals containing red fluorescent impurities with the distribution of

II. EXPERIMENTAL SECTION The growth method employed here is based on convective selfassembly,32,33 in which the growth of colloidal crystals is driven by the evaporation of solvent from a solution,23 as shown by the schematic illustration of the growth cell in Figure 1. A certain amount of solution Figure 2. Optical microscopic images of growing colloidal polycrystals containing red fluorescent impurities (C0: 0.5%). The white dashed lines indicate the GB, while the white solid lines show the solid−liquid interface. (a) Fluorescence image to show the distribution of impurities during polycrystal growth. (b) Distribution of host particles and fluorescent impurities. The solid−liquid interface appears as a stepped layer structure. Yellow circles indicate solid colloidal particles at the interface.

impurities during growth. Figure 2b shows a higher magnification image to indicate the configuration of particles, where the fluorescence image is superposed on its corresponding reflection image. The close-packed {111} plane of the facecentered cubic (fcc) structure was observed on the observation axis. The distribution of impurities in the solid demonstrates the accumulation of impurities at GBs, more so than in the grains. This segregation of impurities at GBs during colloidal polycrystallization has been previously investigated and discussed,23 where the concentration of impurities at GBs (CGB) was reported to increase with the misorientation angle and the growth rate. The distribution of impurities in the liquid was also investigated by in situ observations. Impurities were observed to prefer accumulating at the groove that formed at the solid− liquid interface where GBs were exposed to the solution. The yellow circles in Figure 2b indicate solid colloidal particles at the interface, and the solid−liquid interface appears as a stepped layer structure where each layer is a close-packed plane. Figure 3 shows a time evolution of the impurity distribution in the liquid during growth revealed by in situ observation. Impurities are distributed homogeneously parallel to the

Figure 1. Schematic illustration of the growth cell for colloidal polycrystals. Red arrows indicate evaporation of the solvent from solution. was filled into a hole at the center of a silicone sheet placed on the top of a glass slide. A small amount of overflowed solution is then trapped in the microscale gap formed between a coverslip and the silicone sheet. Colloidal crystals then grow in this gap. Colloidal particles are transported normal to the solid−liquid interface toward the meniscus, where the edge of the solution is exposed to air, and particles accumulate at the meniscus as evaporation proceeds. When the volume fraction of particles in the solution exceeds approximately 0.49,34 crystallization begins, whereby particles self-assemble into a crystalline structure. One to three layers of crystals were grown with this method. B

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Figure 3. Variation in the distribution of fluorescent impurities with time (t) during crystal growth, with an impurity concentration C0 of 0.5%. (a) The thick yellow lines in the solid indicate the GB, while the white lines indicate the solid−liquid interface. (i) Reflection image and (ii−iv) fluorescence images that show the distribution of impurities at different times.The white dotted line in (iv) indicates the initial position of the solid− liquid interface. (b) Time evolution of the impurity distribution in the liquid along the interface. “0” on the horizontal axis indicates the GB position, which corresponds to the axis shown in (a). The vertical axis indicates the number of impurities in the unit area and the depth axis represents time. (c) Average number of impurities in the unit area of the liquid in the vicinity of grains (blue) around x = 15 μm, and in the groove (red) at x = 0, during polycrystallization.

Figure 4. (a) Groove and groove area development during colloidal polycrystallization (C0: 1%). The white dashed line and white solid line represent the positions of the GB and the solid−liquid interface, respectively. (b−f) Plots of CGB versus misorientation angle and groove area for various growth rates of (b) 14.2, (c) 37.0, (d) 53.8, (d) 85.0, and (e) 117.7 μm/h.

increases, while that in the groove increases significantly, which also supports the accumulation of impurities at the groove. The groove area (Sgr) is defined as Δabc in Figure 4a and is used to investigate the effect of the groove area on GB impurity segregation. It should be noted that the crystallographic orientation and misorientation angle θ are different between two adjacent grains across the GB. These two parameters were determined to evaluate their effects on GB impurity segregation. Plots of CGB versus θ and Sgr for various growth rates are shown in Figures 4b−4f. These figures indicate that CGB increases with the misorientation angle and the growth rate. This dependence of growth rate and misorientation angle on CGB was discussed in ref 23. In addition, CGB increases with Sgr at a certain θ, as shown in the enlarged part of Figure 4f. It was determined that CGB is dependent on Sgr. Next, we discuss the factors that determine the groove area. Figure 5 shows different GBs that were developed during polycrystallization at the same growth rate (53.8 μm/h). The misorientation angle (25 ± 0.3°) is almost the same; however, different groove areas (pink-colored region) of 6.42 and 8.76 μm2 are obtained. We consider that this is due to different energy states of the solid−liquid interface for neighboring grains across the GB.

growth interface at the early growth stage (Figure 3(a)ii), and then they accumulate in the groove as crystallization proceeds (Figures 3(a)iii−3(a)iv). To quantitatively investigate the time evolution of the impurity distribution in the liquid along the interface, the liquid area within distance L from the interface was divided into thin strips with width W, as illustrated in Figure 3(a)i. Here, the unit area (Sunit), i.e., the yellow shaded region (W × L) with an area of 40 μm2 depicted in Figure 3(a)i, is introduced because the area of the strips adjacent to the GB is different from those along the interface of the grain. By counting the number of impurities in each strip, a time evolution profile of the impurity number in the unit area is obtained, as shown in Figure 3b. The x-axis in Figure 3b indicates the positions along the interface, where “0” corresponds to the position of the GB, while the waterfall mapping with different colors along the y-axis shows the impurity distribution at different times. As time elapses, the number of impurities near the “0” area is gradually increased, which indicates that the impurities are accumulating in the groove. Figure 3c shows the time evolution of the average numbers of impurities in the unit area of the liquid in the vicinity of grains (blue) around x = 15 μm, and in the groove (red) at x = 0. These results indicate that the number of impurities at the solid−liquid interface of the grains gradually C

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ΔG = lΔγ − V Δμ

where the surface energy difference for the formation of a groove (Δγ) can be defined as 1 a a b Δγ = −γGB − tan θaγS/L − tan θ bγS/L + γ cos θa groove 1 γb + cos θ b groove (3)

Figure 5. Grooves developed at the GBs between grains. The growth rate was 53.8 μm/h in both (a) and (b). The groove areas of (a) and (b) are different, although the misorientation angles for both GBs are similar. The white dashed lines and white solid lines represent the positions of the GB and the solid−liquid interface, respectively. Orange circles indicate solid colloidal particles at the interface.

According to our observations, there is always a groove at each GB. The decomposition of the solid−liquid interface at the GB into a pair of groove interfaces is energetically preferable; that is, ΔG is negative. Figure 7provides an explanation of how different groove areas are formed with the same misorientation angle, θ. An

The mechanism for the groove formation at the GB and what determines the groove area are discussed next. In an atomic system, the interfacial energy of the solid−liquid interface is determined predominantly by the number of dangling bonds present at the interface, which is dependent on the crystal structure.35 The groove is caused by the difference in the solid− liquid and grain−grain boundary energies.36 In the present experimental system, there is an electrostatic repulsive interaction between colloidal particles.28 Although the surface tension for colloidal crystallization has not yet been clarified, it is similar to an atomic system, so that solid particles at the solid−liquid interface probably induce surface energy from the difference in the particle repulsive interaction energy between solid−solid and solid−liquid. The free energy difference ΔG, which is attributed as the driving force for the formation of the groove, is discussed

Figure 7. Schematic illustration of different groove areas at different GBs with the same misorientation angle. The black lines represent the interfaces between solid and liquid. The blue dashed lines indicate the close-packed plane of each grain.

interface that is not parallel to a close-packed plane often has a stepped structure,35 as shown in Figure 7. The number of dangling bonds at the interface changes as the grain orientation changes with respect to the solid−liquid interface. As a consequence, the interfacial energy is a function of the orientation of the grain to the solid−liquid interface. Suppose two adjacent grains, A and B, with a 30° misorientation angle. The grains shown in Figure 7b are clockwise tilted 15° compared with the grains shown in Figure 7a. The misorientation angle is the same in both Figures 7a and 7b; therefore, the energies of the GBs are also the same as that in a two-dimensional crystal.17,37 However, the interfacial energy of the two grains in Figure 7b is different from those in Figure 7a because the different directions of the grains exposed to the solid−liquid interface result in a different number of dangling bonds. The difference in the interfacial energies of the solid−liquid interfaces results in different groove areas between (a) and (b). In the present observations, grooves were formed for all GBs at the solid−liquid interfaces. The variation of the groove area was dependent on the orientation of the grains with respect to the solid−liquid interface, which resulted in different CGB, even though the growth rate and misorientation angles were the same. Thus, for the impurity partitioning of colloidal polycrystal growth, the orientation of grains to the solid−liquid interface is a dominant factor that determines CGB. The interfacial energy, consisting of surface energy and GB energy, is a parameter that determines the area of a groove even for the systems with repulsive interaction between particles. Similar examples were reported by Xie et al.,29,30 in which GBs moved and disappeared during the annealing process by applying an alternating electric field with various frequencies. The thermodynamic driving force of this process is interfacial

Figure 6. Free energy change attributed as the driving force for the formation of a groove, which is shown by comparison of the surface energy and the bulk energy with and without a groove. (a) Solid− liquid interface at a GB without a groove. (b) GB with a groove (pink region).

(Figure 6). ΔG is expressed as the sum of the surface energy change and the bulk energy change: a b ΔG = −lγGB − l tan θaγS/L − l tan θ bγS/L +

+

l γb − ΔμV cos θ b groove

(2)

l γa cos θa groove (1)

where l is the depth of the groove, θa and θb are the angles between the groove interface and the GB plane for grains A and B, respectively, γaS/L and γbS/L are the surface energies per unit area for grains A and B, respectively, γGB is the energy per unit area of GB, Δμ is the chemical potential difference between the liquid and solid, and V is the volume that corresponds to the groove region (pink-colored region in Figure 6b). Equation 1 can be simplified as D

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(2) Cahn, R. W. The coming of materials science; Pergamon Press: Oxford, 2001. (3) Mendelev, M. I.; Srolovitz, D. J. Impurity Effects on Grain Boundary Migration. Modell. Simul.Mater. Sci. Eng. 2002, 10, R79− R109. (4) Duscher, G.; Chisholm, M. F.; Alber, U.; Rühle, M. Bismuthinduced Embrittlement of Copper Grain Boundaries. Nat. Mater. 2004, 3, 621−626. (5) Kubota, N. Effect of Impurities on the Growth Kinetics of Crystals. Cryst. Res. Technol. 2001, 36, 749−769. (6) Randle, V.; Ralph, B. Interactions of Grain Boundaries with Coherent Precipitates during Grain Growth. Acta Metall. 1986, 34, 891−898. (7) Land, T. A.; Martin, T. L.; Potapenko, S.; Palmore, G. T.; De Yoreo, J. J. Recovery of Surfaces from Impurity Poisoning during Crystal Growth. Nature 1999, 399, 442−445. (8) Tiller, W. A. The science of crystallization: microscopic interfacial phenomena; Cambridge University Press: Cambridge, 1991. (9) Palanisamy, P.; Howe, J. M. In situ observation of Cu segregation and phase nucleation at a solid−liquid interface in an Al alloy. Acta Mater. 2013, 61, 4339−4346. (10) Gotoh, R.; Fujiwara, K.; Yang, X.; Koizumi, H.; Nozawa, J.; Uda, S. Formation mechanism of cellular structures during unidirectional growth of binary semiconductor Si-rich SiGe materials. Appl. Phys. Lett. 2012, 100, 021903. (11) Miller, W.; Rasin, I.; Stock, D. Evolution of cellular structures during Ge1−xSix single-crystal growth by means of a modified phasefield method. Phys. Rev. E 2010, 81, 051604. (12) Fujiwara, K.; Ishii, M.; Maeda, K.; Koizumi, H.; Nozawa, J.; Uda, S. The effect of grain boundary characteristics on the morphology of the crystal/melt interface of multicrystalline silicon. Scr. Mater. 2013, 69, 266−269. (13) Williamson, M. J.; Tromp, R. M.; Vereecken, P. M.; Hull, R.; Ross, F. M. Dynamic microscopy of nanoscale cluster growth at the solid−liquid interface. Nat. Mater. 2003, 2, 532−536. (14) Zheng, H.; Smith, R. K.; Jun, Y.; Kisielowski, C.; Dahmen, U.; Alivisatos, A. P. Observation of Single Colloidal Platinum Nanocrystal Growth Trajectories. Science 2009, 324, 1309−1312. (15) Donnelly, S. E.; Birtcher, R. C.; Allen, C. W.; Morrison, I.; Furuya, K.; Mitsuishi, K.; Dahmen, U. Ordering in a Fluid Inert Gas Confined by Flat Surfaces. Science 2002, 296, 507−510. (16) Eswaramoorthy, S. K.; Howe, J. M.; Muralidharan, G. In Situ Determination of the Nanoscale Chemistry and Behavior of Solid− Liquid Systems. Science 2007, 318, 1437−1440. (17) Callister, W. Materials Science and Engineering: An Introduction, 7th ed.; John Wiley & Sons, Inc.: New York, 2007. (18) Phillips, R. Crystals. Defects and Microstructure: Modeling Across Scales; Cambridge University Press: Cambridge, U.K., 2001. (19) Howe, J. M. Interfaces in Materials; Wiley: New York, 1997. (20) Zykova-Timan, T.; Rozas, R. E.; Horbach, J.; Binder, K. Computer Simulation Studies of Finite-size Broadening of Solid− liquidInterfaces: From Hard Spheres to Nickel. J. Phys.: Condens. Matter 2009, 21, 464102. (21) Hirth, J. P.; Lothe, J. Theory of Dislocations, 2nd ed.; Wiley: NewYork, 1982. (22) Gleiter, H. Nanostructured Materials: Basic Concepts and Microstructure. Acta Mater. 2000, 48, 1−29. (23) Hu, S.; Nozawa, J.; Koizumi, H.; Fujiwara, K.; Uda, S. Grain Boundary Segregation of Impurities During Polycrystalline Colloidal Crystallization. Cryst. Growth Des. 2015, 15, 5685−5692. (24) Herlach, D. M.; Klassen, I.; Wette, P.; Holland-Moritz, D. Colloids as Model Systems for Metals and Alloys: a Case Study of Crystallization. J. Phys.: Condens. Matter 2010, 22, 153101. (25) Ganapathy, R.; Buckley, M.; Gerbode, S.; Cohen, I. DirectMeasurements of Island Growth and Step-Edge Barriers in ColloidalEpitaxy. Science 2010, 327, 445−448. (26) Alsayed, A. M.; Islam, M. F.; Zhang, J.; Collings, P. J.; Yodh, A. G. Premelting at Defects within Bulk Colloidal Crystals. Science 2005, 309, 1207−1210.

energy, and GBs move in the crystals so as to minimize interfacial energy. In our experiment, GBs did not disappear during growth of crystals. This is probably because the higher volume fraction in the crystal hinders the movement of particles. There is a volume fraction gradient in the crystal, and it increases with the distance from solid−liquid interface. GBs near the solid−liquid interface change their positions with time as indicated in our former work,23 where the volume fraction is not high enough to hinder particle movement completely. The difference between interfacial energies, GB energy, and bulk energies leads to the formation of a groove at the solid− liquid interface (where the GB was exposed to the solution), and the groove morphology affects the partitioning of impurities during colloidal polycrystallization. This analysis demonstrates that the control of impurity distribution in materials is embodied by proper control of the morphology of the solid−liquid interface during crystallization. For instance, materials for industrial application such as mc-Si12 and Si-rich SiGe10 are required to be homogeneous in impurity distribution. Our results suggest that the flat shape of the solid−liquid interface is suitable for this requirement. One of the key factors that control the interface shape is the orientation relationship between grains in polycrystal, since the groove size is dependent on the interfacial energy that is predominated by the orientations of grains against the solid− liquid interface. This finding is useful for growing high quality polycrystals containing GBs.

IV. CONCLUSION The time evolution of the impurity distribution in a liquid along an interface during colloidal polycrystallization was investigated by in situ optical observations. The observations revealed that impurities are distributed homogeneously during the initial growth stage and are then gradually accumulated at the solid− liquid interface groove formed at the GB between grains. The impurity concentration of the GB increased with the groove area. For the impurity partitioning of polycrystal colloidal growth, grain orientation was determined to influence the energy state of the solid−liquid interface, which determines the groove area and therefore results in different CGB. The influence of the groove area on grain boundary segregation was experimentally demonstrated. These observations will contribute to the fundamental understanding of grain boundary segregation during polycrystal growth.

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AUTHOR INFORMATION

Corresponding Authors

*Sumeng Hu e-mail: [email protected]. *Jun Nozawa e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by KakenhiGrant-in-Aid (No. 26870047) from the Japan Society for the Promotion of Science (JSPS) and the China Scholarship Council (CSC).

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REFERENCES

(1) Zhang, T. H.; Liu, X. Y. Experimental Modelling of SingleparticleDynamic Processes in Crystallization by Controlled ColloidalAssembly. Chem. Soc. Rev. 2014, 43, 2324−2347. E

DOI: 10.1021/acs.cgd.6b00066 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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(27) Lipowsky, P.; Bowick, M. J.; Meinke, J. H.; Nelson, D. R.; Bausch, A. R. Direct Visualization of Dislocation Dynamics in Grainboundary Scars. Nat. Mater. 2005, 4, 407−411. (28) Nozawa, J.; Uda, S.; Naradate, Y.; Koizumi, H.; Fujiwara, K.; Toyotama, A.; Yamanaka, J. Impurity Partitioning during Colloidal Crystallization. J. Phys. Chem. B 2013, 117, 5289−5295. (29) Xie, R. G.; Liu, X. Y. Controllable Epitaxial Crystallization and Reversible Oriented Patterning of Two-Dimensional Colloidal Crystals. J. Am. Chem. Soc. 2009, 131, 4976−4982. (30) Xie, R. G.; Liu, X. Y. Electrically Directed On-Chip Reversible Patterning of Two-Dimensional Tunable Colloidal Structures. Adv. Funct. Mater. 2008, 18, 802−809. (31) Yoshizawa, K.; Okuzono, T.; Koga, T.; Taniji, T.; Yamanaka, J. Exclusion of Impurity Particles during Grain Growth in Charged Colloidal Crystals. Langmuir 2011, 27, 13420−13427. (32) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Two-dimensional Crystallization. Nature 1993, 361, 26. (33) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Singlecrystal Colloidal Multilayers of Controlled Thickness. Chem. Mater. 1999, 11, 2132−2140. (34) Pusey, P. N.; van Megen, W. Phase Behavior of Concentrated Suspensions of Nearly Hard Colloidal Spheres. Nature 1986, 320, 340−342. (35) Morris, J. W. A Survey of Materials Science: I. Structure;University of California Press: Berkeley, 2007. (36) Dash, J. G.; Hodgkin, V. A.; Wettlaufer, J. S. Dynamics of Faceted Grain Boundary Grooves. J. Stat. Phys. 1999, 95, 1311−1322. (37) Bachurin, D. V.; Weygand, D.; Gumbsch, P. Dislocation−grain boundary interaction in h111i textured thin metal films. Acta Mater. 2010, 58, 5232−5241.

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