Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Screw Dislocation Generation by Inclusions in Molecular Crystals Xiaodi Zhong, Alexander G. Shtukenberg, Theodore Hueckel, Bart Kahr,* and Michael D. Ward* Department of Chemistry and the Molecular Design Institute, New York University, 100 Washington Square East, New York, New York 10003-6688, United States S Supporting Information *
ABSTRACT: Dislocations in crystals affect material properties and are essential for crystal growth near equilibrium, yet their genesis in the absence of external or internal stresses is unresolved. X-ray topography has revealed microscopic inclusions as dislocation sources, but the real-time creation of a dislocation by a particulate inclusion has not been reported. In situ atomic force microscopy (AFM) was used herein to visualize dislocation generation in an L-cystine crystal by a cube-like hematite particle embedded in, and slightly inclined with respect to, the L-cystine {0001} surface. The particle produced two pairs of heterochiral screw dislocations with opposing Burgers vectors. After overgrowth of the particle, dissolution in undersaturated solutions revealed the dislocations once again until the detachment of the particle exposed a flat basal plane devoid of dislocations, thereby corroborating the essential role of the particle. Hematite particles with their flat faces parallel or at high angle to the surface, as well as spherical poly(styrene) particles, did not produce dislocations, suggesting that shape and orientation of the particle with respect to the step train advancing across the growing crystal surface are critical features for dislocation generation.
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regeneration of crystal surfaces,18,25 coalescence of islands in Volmer−Weber and Stranski−Krastanov growth modes,26 healing of scratches,21 fusion of dendrite branches,27,28 growth at reentrant angles in thin lamellae,29 and collision of thin layers on the crystal surface.30,31 X-ray diffraction topographs32−35 have suggested a role for inclusions as dislocation sources,20−24 but this method suffers from poor spatial resolution, and in situ measurements are challenging. Moreover, the correlation of inclusions and dislocations does not reveal causation.36 An optical microscopy study revealed dislocation creation in βmethylnaphthalene by the capture of “extremely fine graphite” particles,19 but determination of the particle characteristics and the geometric considerations for dislocation generation could not be obtained optically. Although the origin of dislocations has long been attributed to adventitious particles of unknown composition, size, and shape, little is known about these factors, nor has direct visual evidence of the genesis of a screw dislocation been reported. There are innumerable particles in ambient environments, and it is reasonable to suggest that a select few particles have the characteristics required for dislocation creation as the number of particles surely outnumbers the number of dislocations. In the absence of a predictive model, we presumed that (i) the creation of screw dislocations would be more likely for particles having dimensions comparable to the length scale of the micromorphology of the growing crystal face, and (ii) the formation of dislocations rather than direct overgrowth would be more likely for hard particles that oppose the crystallization
INTRODUCTION Unlike chemical reactions in homogeneous media, the development of a crystal requires nucleation, the generation of emergent structures that actuate growth at low supersaturation, and then stepwise unit cell-level assembly, a sequence that occurs across various time and length scales. The understanding of crystal growth from solution has advanced spectacularly with the rise of real-time in situ atomic force microscopy (AFM),1−6 which has enabled direct visualization of active growth hillocks emerging from screw dislocations that are necessary for creating step fronts for solute attachment and growth. Moreover, AFM can provide kinetic data, in the form of step velocities, which can establish activation parameters associated with step advancement across crystal faces. These investigations, however, have not yet revealed the initial stage of growth spiral formationthe creation of a screw dislocationthat is essential for crystal growth near equilibrium.7,8 Understanding the genesis of dislocations is a crucial first step toward controlling their formation, which can be critical for regulating mechanical properties, particularly plastic deformation,9−11 and minimizing defects for high-performance electrical12,13 and optical properties.14,15 Dislocations can be generated both during and after crystal growth as a consequence of thermal and mechanical stresses.16 These stresses are thought to be prevalent at high homologous temperatures, but many crystals are grown at low homologous temperatures at which thermal stress and dislocation mobility are minimal. This conflict led to the concept of “growth dislocations”, whereby dislocations formed through a mismatch of growth layers on the crystal surface.17,18 Growth dislocations can be produced during the overgrowth of inclusions,19−24 © XXXX American Chemical Society
Received: September 12, 2017 Revised: November 27, 2017
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DOI: 10.1021/acs.cgd.7b01292 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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to search for the particles and to record their incorporation and growth of the L-cystine crystal surface. Dissolution experiments were conducted by injecting undersaturated solution of L-cystine (0.3 mM) into the cell. The AFM images were analyzed using the software package Gwyddion.42
pressure. Herein, we report direct visualization, by real-time in situ AFM, of dislocation generation by layer mismatch induced by a well-defined cube-like hematite particle embedded in the {0001} surface of an L-cystine crystal, supporting a mechanism proposed previously17 and observed directly at the nanoscale.
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RESULTS AND DISCUSSION Solution grown L-cystine crystals were chosen as a model system to study generation of dislocations from foreign particles. L-Cystine (P6122 space group; a = 0.5422 nm, c = 5.6275 nm)43 crystallizes as thin hexagonal plates (Figure 1A)
EXPERIMENTAL SECTION
Crystallization of Hexagonal L-Cystine Crystals. Hexagonal Lcystine was crystallized from aqueous supersaturated solutions at pH = 6.3 (C = 3 mM; C/Ceq ≈ 4.3; Ceq = 0.7 mM at pH 7, 25 °C, as reported previously37−39). Specifically, 0.072 g of L-cystine (SigmaAldrich) was added to 100 mL of deionized water, and then the mixture was heated under reflux at 100 °C for 20 min with stirring until L-cystine dissolved completely. The solution was then cooled slowly to room temperature under constant stirring and stored in a sealed glass container at room temperature in a quiescent environment for 72 h, after which single crystals were collected by vacuum filtration (Whatman grade 1 filters, 11-μm pores) and dried in air. Synthesis of Cube-like Hematite Particles. Hematite particles were prepared via the gel−sol method previously described by Sugimoto,40,41 whereby the addition of 100 mL of 5.4 M NaOH (Sigma-Aldrich) into 100 mL of 2 M FeCl3·6H2O (Sigma-Aldrich) caused the formation of a gel in which cube-shaped hematite particles nucleated and grew. The gel was aged in an oven at 100 °C for up to 3 days until the particles reached their final size of approximately 100− 650 nm. Shorter aging time yielded smaller, more polydisperse particles. The final product was isolated by repeated sedimentation and suspension cycles in deionized water. Synthesis of Polystyrene Particles. Polystyrene particles, approximately 1 μm in diameter, were prepared by surfactant-free emulsion polymerization using potassium persulfate (KPS, SigmaAldrich) as a radical initiator. In a typical synthesis, 50 mL of styrene monomer (99% from Sigma-Aldrich) was added to a 1 L three-neck round-bottom flask containing 500 mL of an aqueous solution containing 17 mM NaCl (Sigma-Aldrich). Under a nitrogen atmosphere, the mixture was emulsified by mechanical stirring at 330 rpm, after which 0.5 g of KPS initiator was added and the temperature was increased to 70 °C. After 16 h the mixture was allowed to cool to room temperature, and the particles were washed in deionized water via multiple sedimentation and resuspension cycles. Larger particles (1.8 μm in diameter) were obtained by seeded growth, wherein the procedure above was repeated in the presence of 1-μm polystyrene seeds suspended in the reaction mixture. AFM Measurements. L-Cystine crystals, prepared by the procedure described above, were mounted on an AFM specimen disk coated with partially cured Norland optical adhesive (type 81) by exposure to UV light (model EA-106, Spectroline, Spectronics Corporation, λ = 365 nm) for 50 s. The optical adhesive then was cured completely under UV exposure for another 10 min to firmly attach the crystals to the disk. Most of the crystals mounted in this manner had their {0001} faces parallel with the specimen disk, enabling image acquisition on these faces. The mounted L-cystine crystals were etched slightly by immersion in deionized water for 1 min to remove any impurities present on the crystal surfaces. Real-time in situ AFM was performed with a Bruker Multimode AFM using a Bruker MTFML-V2 cell designed for operation in fluids. All measurements were performed in contact mode with the cantilever in constant deflection using Bruker DNP-10 Si3N4 tips on silicon nitride cantilevers with a spring constant of 0.12 N/m (triangular tip B, 205 μm length, 40 μm width). The mounted crystals were grown for 20 min prior to measurements in order to regenerate the crystal surface by continually flowing the supersaturated solution (2 mM or 0.072 g of L-cystine in 150 mL of deionized water) through the fluid cell at a rate of 20 mL/h using a syringe pump (model R-100E, Razel Scientific Instruments). A suspension of foreign particles in 2 mM Lcystine solution was injected into the fluid cell and allowed to stand without scanning for 10 min. An aqueous solution supersaturated with L-cystine (2 mM) then was continuously injected into the fluid cell at a rate of 20 mL/h. Contact mode AFM measurements were performed
Figure 1. (A) Scanning electron micrograph of a typical hexagonal Lcystine crystal. (B) AFM deflection error image of a growth hillock on the {0001} face of an L-cystine crystal captured in situ and in real-time in aqueous solution supersaturated in L-cystine (C = 2 mM) using contact mode with constant cantilever deflection. (C) Scanning electron micrograph of cube-like, hematite particles.
with large basal {0001} faces bounded by six {1010̅ } faces. Screw dislocations emerge on the {0001} crystal surface, creating continually growing spirals that form well-defined growth hillocks and serve as step sources. In aqueous solutions supersaturated in L-cystine (C = 2 mM; equilibrium solubility Ceq = 0.7 mM),37−39 {0001} faces grow via a dislocation spiral mechanism (Movie S1).44−47 Figure 1B displays a representative growth hillock defined by six major {101̅0} steps, each with a height of 5.6 nm equivalent to the length of the c-axis. Each major step is a bunch of six minor steps, each minor step corresponding to the height of one L-cystine molecule (ca. 0.9 nm; c/6). Dislocation generation was investigated using microscopic, near-isometric, hematite rhombohedra that have been described as “pseudocubic”40,41,48 (Figure 1C), with sizes ranging from 100 to 650 nm (Table S1). A mixture of particles with different sizes (100−650 nm) was introduced to an AFM liquid cell containing surface-anchored L-cystine crystals in a supersaturated solution (2 mM). In the example illustrated in Figure 2, a hematite particle adhered to a {0001} face of an L-cystine crystal and became partially embedded (Figure 2A). The particle was far from any screw dislocation core in the crystal, and it was inclined slightly with respect to steps on {0001} Lcystine surfaces (Figure 2B,C). The side at the lower end of the step train was 11 nm (ca. 2c) lower than the other (Figure S1). Initially, the upper end of the particle protruded 40 nm above the crystal surface, and steps from the remote dislocation advanced around both sides of the particle, eventually rejoining to form defect-free steps that continued to advance beyond the particle. As the steps successively grew around the particle, the height difference between the particle surface and the surrounding crystal decreased (Figure 2B, Movie S2). The Lcystine layers eventually reached the height of the lower end of the particle (Figure 2D), continuing to advance upward along the inclined particle surface until the lower and higher terraces merged and covered the particle. The L-cystine layer above the B
DOI: 10.1021/acs.cgd.7b01292 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Figure 2. (A−F) AFM deflection error images acquired during realtime in situ growth of the L-cystine {0001} face in supersaturated solution (C = 2 mM) at a region where an anchored hematite particle was located. The images illustrate consecutive stages of overgrowth of the hematite particle (elapsed time: A = 0; B = 250; C = 340; D = 530; E = 730; F = 1750 s). The positions of the four screw dislocations are highlighted in panel F. The bent layer mentioned above is evident from the arc in the deflection image between the blue and red circles. (G−I) AFM images of the same region during dissolution in undersaturated solution (C = 0.3 mM; G = 3620; H = 5130; I = 5240 s). (G) Four etch pits are revealed at 3620 s, each derived from one of the four dislocations, above the submerged hematite particle. (H, I) The crystal surface after detachment of the hematite particle during dissolution at 5130 and 5240 s, revealing the absence of the etch pits and spirals. These images demonstrate that the dislocations did not exist prior to particle attachment to the crystal surface. All images were acquired in contact mode with constant cantilever deflection. Readers should note that deflection error images can create a perception that pits are mounds, and vice versa. Scale bars = 250 nm.
Figure 3. (A, B) AFM deflection error images of the region on the Lcystine {0001} face after the hematite particle in Figure 2 was overgrown. The handedness of the screw dislocations, labeled d1 − d4, is denoted by circular arrows. (C, D) Height images corresponding to panels A and B, respectively, illustrating the paths used for tracing the height profiles. (E) Three-dimensional AFM image corresponding to (B) depicting the opposite direction of Burgers vectors of each pair of dislocations by vertical arrows. (F) Height profiles along paths illustrated in panels (C and D). The magnitude of Burgers vector of dislocation 3 is ca. 5.6 nm. The full circle enclosed the area of the four dislocations has no height mismatch. The image area in panels A−D is 1 μm × 1 μm.
tilted hematite subsurface emerged as a bent layer (Figure 2E,F), indicative of a discontinuity that signals the genesis of the dislocations. Two pairs of heterochiral screw dislocations were observed following the overgrowth of the hematite particle (Figure 2F, Movies S3A, S3B, S3C), with Burgers vectors characterized by Burgers circuits constructed from height images (Figures 3C,D and S2). The distance between the two dislocations in each heterochiral pair was 240 nm, and the distance between the two heterochiral pairs was 180 nm. The generation of these dislocations by the hematite particle was confirmed by dissolution of the L-cystine surface in undersaturated (0.3 mM) L-cystine solution immediately after overgrowth while imaging over the same region (Movies S4A, S4B, S4C). These images revealed etch pits around each of the screw dislocations, signaling fast dissolution at the dislocation cores (Figure 2G). After further dissolution of the crystal, the hematite particle was exposed and then swept away by the AFM probe, and the four etch pits were no longer evident. The bottom of the cavity, flat and devoid of dislocations, continued to expand (Figure 2H,I). This is unlike dissolution of single native dislocation cores in Lcystine, in which the etch pit surface exhibited the familiar spiral
arms rather than a flat basal plane.49 These observations corroborate the exclusive role of the hematite particle in dislocation generation. Moreover, we have never observed the creation of dislocations−single or pairs−in numerous prior investigations of L-cystine growth.44−47 The Burgers vectors associated with each of the four dislocations in the quadruplet, determined from deflection and height images, were b = ± [0001], with two right-handed and two left-handed screw dislocations (Figure 3). Each pair of screw dislocations consisted of two dislocations with opposite Burgers vectors and handedness (Figure 3B,E). Therefore, the total Burgers vector is zero (b1 + b2 + b3 + b4 = 0), and a circuit around the periphery of the region enclosing all four dislocations (Figure 3D,F) is characterized by zero net displacement in the [0001] direction. Figure 4 schematically illustrates the generation of the dislocation quadruplet by a captured cube-like particle (depicted as gray) that is slightly larger than the step spacing, similar to the AFM image in Figure 2A (particle size ≈ 330 nm; step spacing ≈ 300 nm). The embedded particle was inclined C
DOI: 10.1021/acs.cgd.7b01292 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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to depend strongly on growth rates,19 which also may be a factor in the frequency of dislocation generation but was not examined here. We have observed incorporation of 37 particles of various shapes and sizes on L-cystine {0001} faces. Spherical polystyrene particles, or hematite particles with a face strictly parallel to the {0001} surface or with a body diagonal perpendicular to the {0001} surface, did not generate dislocations (Figures 5, S3, and Movies S5, S6A, S6B, S7).
Figure 4. (A−J) Dislocation generation by an inclined cube-like particle, forming two confined Frank−Read sources during growth. Steps originated from a pre-existing growth hillock advanced from left to right and are denoted with numbers corresponding to their order of appearance as they approach the particle. The four dislocations are flagged by vertical lines with colors corresponding to Figures 2 and 3.
with respect to the {0001} plane, with the upper side 11 nm higher than the lower side, roughly equivalent to the height of two bunched steps (5.6 nm each). The opposite sides of the embedded particle intersected the two terraces at the same height. Steps originating from a growth hillock outside the frame of the image (or in this case, the schematic) swept continually from left to right, navigated around the corners of the particle, and then grew inward around this intersection, resembling a Frank−Read source (i.e., a pair of heterochiral dislocations), but one confined within the step width (Figure 4B). This confined Frank−Read source resulted in growth upward on the surface of the inclined particle, eventually bending inward (Figure 4C). The process repeated where the particle intersects the crystal layer near Step 2 (Figure 4D,E), generating a second confined Frank−Read source. The steps originating from the four dislocations eventually merged into a single terrace as expected for Frank−Read sources owing to the annihilation of opposing Burgers vectors (Figure 4F). This new terrace was not planar as it bridged three steps, which along with others generated from a distant native hillock advance across the quadruplet (Figure 4G−J). Although the generation of dislocations in L-cystine via overgrowth of foreign particles was limited here to a singular example, natural and laboratory-grown crystals encounter many particles with a wide range of shapes and sizes, such that a select few may be sufficient for dislocation formation. Moreover, dislocation generation by particle inclusions has been reported
Figure 5. AFM deflection error images acquired during real-time in situ AFM imaging of overgrowth of L-cystine {0001} face over three different particles without generating dislocations: (A1−A4) a 135 nm hematite particle with a face parallel to {0001}; (B1−B4) a 650 nm hematite particle with a body diagonal perpendicular to {0001}; (C1− C4) a 1.98 μm spherical polystyrene particle. These images were acquired in deflection mode and are displayed here as deflection error images because the surface features and the embedded particle are more clearly evident than in standard height images. The heights of the steps correspond to a single unit cell length along the c-axis (5.6 nm). All scale bars correspond to 400 nm.
This argues that particle shape, orientation, and size, relative to step spacing, are critical for dislocation generation. That is, dislocation generation appears to be favored if the particle is inclined slightly and spans a distance that is roughly equivalent to the step spacing. In this way, the overgrown crystalline layers can bend to conform to the stepped surface, thereby accommodating a vertical displacement. Notably, images in Figure 5 acquired before the particles were overgrown reveal a disturbance that generates symmetry related steps pinned by the particle. These steps advance to close the gap when they reach a critical length, which is comparable to the particle diameter. D
DOI: 10.1021/acs.cgd.7b01292 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Notes
In contrast, if the particle surface is parallel to the crystal surface, as observed for three embedded hematite particles with diameters ranging from 100 to 140 nm (Figure 5A, S3, Movie S5, Table S1), the height displacement required for screw dislocation creation cannot be achieved. Particles inclined at large angles, observed for four hematite particles with diameters ranging from 150−650 nm (Figure 5B, S3, Movie S6A, S6B, Table S1), impeded the advancement of steps until the particle was overgrown. Overgrowth was observed for 30 spherical polystyrene particles, 26 with diameters of 1 μm and 4 with diameters of 1.8 μm (Figure 5C, S3, Movie S7, Table S1). This result is consistent with the absence of active growth hillocks in potassium acid phthalate crystals that incorporated spherical fluorescent polystyrene particles.36 Moreover, dislocation generation is more likely for particle inclusions with a larger modulus than that of the crystal matrix, as this would favor perturbation of the growth layers rather than deformation of the particle. Deformations of soft particles incorporated by hard crystals, specifically, micelles in calcite50 and petroleum droplets in KNO3 crystals,51 have been reported. Although the role of the particle size needs to be explored further, it is reasonable to suggest that the particle size needs to be larger than the diameter of the critical nucleus for advancement of the growth layers between the heterochiral dislocations of a given pair.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported primarily by the NYU MRSEC Program of the National Science Foundation (NSF) under Award Number DMR-1420073. The authors are grateful to S. Sacanna for helpful discussions.
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CONCLUSION The origin of dislocations has customarily relied on postmortem analyses rather than real-time observations that, as demonstrated here, provide some key insights into the particle characteristics and geometric considerations for dislocation generation, such as the necessity of an inclined particle spanning a terrace between two steps on a well-defined crystal surface. The hematite particle created two heterochiral dislocation pairs that behave as Frank−Read sources, which continually spin out new growth layers. Although Frank−Read sources are well documented, the example described here reveals a possible mechanism for their creation that may be quite general, requiring only inclusion of a foreign particle.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b01292. Figure S1−S3, AFM images and data, additional schematics of particle overgrowth; Table S1 describing characteristics of particles embedded in L-cystine crystals (PDF) Movies S1−S7 of real-time in situ crystal growth using AFM: Movie S1 (AVI1), Movie S2 (AVI2), Movie S3 (AVI3, AVI4, AVI5), Movie S4 (AVI6, AVI7, AVI8), Movie S5 (AVI9), Movie S6 (AVI10, AVI11), Movie S7 (AVI12)
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AUTHOR INFORMATION
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*(B.K.) E-mail:
[email protected]. *(M.D.W.) E-mail:
[email protected]. ORCID
Alexander G. Shtukenberg: 0000-0002-5590-4758 Bart Kahr: 0000-0002-7005-4464 Michael D. Ward: 0000-0002-2090-781X E
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