Dislocation-Driven Nanowire Growth and Eshelby Twist

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Science  23 May 2008:
Vol. 320, Issue 5879, pp. 1060-1063
DOI: 10.1126/science.1157131


Hierarchical nanostructures of lead sulfide nanowires resembling pine trees were synthesized by chemical vapor deposition. Structural characterization revealed a screwlike dislocation in the nanowire trunks with helically rotating epitaxial branch nanowires. It is suggested that the screw component of an axial dislocation provides the self-perpetuating steps to enable one-dimensional crystal growth, in contrast to mechanisms that require metal catalysts. The rotating trunks and branches are the consequence of the Eshelby twist of screw dislocations with a dislocation Burgers vector along the 〈110〉 directions having an estimated magnitude of 6 ± 2 angstroms for the screw component. The results confirm the Eshelby theory of dislocations, and the proposed nanowire growth mechanism could be general to many materials.

In the burgeoning field of nanoscience, a major ambition is to synthesize nanoscale building blocks of arbitrary dimensions, morphologies, and materials of increasing complexity. One-dimensional (1D) nanowire materials, in particular, have already found many applications in nanoelectronics, nanophotonics, and biotechnology (1, 2). To break the symmetry of bulk crystals and enable the anisotropic 1D crystal growth of inorganic nanowires, the well-known vapor-liquid-solid (VLS) growth method uses metal nanoparticles that form low–melting point eutectic alloys with the targeted materials to serve as the catalytic seeds for 1D anisotropic growth (3, 4). Except for direct vapor-solid growth (5), most nanowire-formation mechanisms, including solution-liquid-solid growth (SLS) (6) and variants of VLS such as vapor-solid-solid growth (7), require the use of catalytic nanoparticles, either added intentionally or generated in situ, to enable the 1D anisotropic crystal growth. “Treelike” or hyperbranched nanostructures have also been reported, but they all rely on multiple applications of metal catalysts with subsequent VLS (8, 9) or SLS (10) growth steps.

We suggest a nanowire growth mechanism that does not depend on catalysts but instead is driven by an axial screwlike dislocation along the length of the nanowire. It results in hierarchical lead sulfide (PbS) nanostructures of pine tree morphology when combined with a slower in situ VLS branching nanowire growth. The geometrical features of the resulting structures can be quantitatively understood with the simple elasticity theory of dislocations.

The nanostructures of PbS are synthesized via chemical vapor deposition with PbCl2 and elemental sulfur as precursors under argon flow with a co-flow of H2 at atmospheric pressure and with temperatures between 600° and 650°C (11). Typical synthesis conditions involve reactions at 600°C for 15 min under 150 standard cubic centimeters per minute (sccm) of argon flow and 900 torr pressure with the hydrogen flow at 1.8 sccm for the first 1 min and 1.0 sccm for the remaining 14 min. Even though the synthetic procedure is similar to that for the hyperbranched PbS nanowires (see examples in figs. S2 and S3) (12), the nanowire growth appears to be driven by different mechanisms. The key difference between the growth of pine trees and the growth of hyperbranched nanowires (12) and other previously reported PbQ (Q is S, Se, or Te) nanowire growth (13, 14) is the hydrogen flow profile. The optimized reactions (11) reproducibly yield many intricate treelike PbS nanowire structures over large areas (1 to 2 cm2) on the growth substrate, as revealed by scanning electron microscopy (SEM) (Fig. 1 and fig. S1; also see fig. S4 for phase identification). These trees have trunks that are up to hundreds of micrometers in length and branches that are commonly tens of micrometers long. Individual wires grow consistently along the 〈100〉 crystallographic directions and their diameters range from 40 to 350 nm. Closer examination of these nanostructures, particularly those with less dense branching (Fig. 1, D to F), reveals that each tree has four sets of epitaxial branches that are perpendicular to the trunk and the neighboring branches and rotate around the trunk in a helical staircase fashion. The pitch of the rotations ranges from 16 to 220 μm and can vary down the length of a single tree. Right- or left-handed rotating trees have roughly equal probability of occurrence (measured ratio: 107:126) (11). The rotating branches become progressively shorter from the base to the tip of the trees, resulting in conelike envelopes that enforce the tree morphology. The combination of the helical rotation and the regular length progression of the evenly spaced branches leads to beautiful curves formed by the branch tips, which are further accented when the tips are decorated with PbS cubes in some syntheses (see an example in the inset of Fig. 1G). These trees can grow both upward from the growth substrate and horizontally to the substrate from some nucleation clusters, creating a dense copse of freestanding nanowire trees, which often resembles a forest when viewed from the side of the growth substrates (Fig. 1C). Within a common cluster, the trees occasionally grow epitaxially as evidenced by the perpendicular or parallel orientations between the trees (Fig. 1B). Tree structures sometimes coexist with or grow off from hyperbranched nanowire clusters (Fig. 1E and fig. S2). Occasionally, multiple levels of “tree-on-tree” morphology can be observed (Fig. 1G).

Fig. 1.

SEM micrographs of PbS pine tree nanowires. (A) Overview of dense forest of many nanowire trees. (B) Tree clusters showing epitaxial growth along 〈100〉 directions. (C) Side view of growth substrate showing forest growth. (D to F) High-magnification views of trees highlighting the twisting (Eshelby twist) of the central trunk and helical rotating branches, with (E) further illustrating branch epitaxy on the tree trunk and (F) showing a tree with fewer branches. (G) An example of “tree-on-tree” morphology that can be occasionally observed. (Inset) A magnified view of the tips of nanowires after synthesis highlighting the cubes that sometimes decorate the tips. The inset scale bar is 200 nm. The images are false colored.

Further scrutiny of the distinct morphology and large length difference between the trunks and branches of these pine tree nanowires suggests that the trunks grow faster than the branches. It was previously suggested that hyperbranched PbS nanowires are grown via a self-catalyzed VLS mechanism: Lead itself serves as the eutectic catalyst and is consumed or evaporated during growth (15), thereby limiting the length of wire growth (12, 13). Although no lead catalyst caps were observed at the tips of either the trunk or branch nanowires after growth, a similar length limit was sometimes also observed for the tree branches (fig. S5), suggesting that the branch growth is likely VLS driven. Successive generations of hyperbranched nanowires (12, 13) grow at a similar rate and lead to more isotropic “cubic” morphology (figs. S2 and S3). In contrast, the pine trees have steep cone angles that do not change over the duration of growth for a given tree, suggesting that the trunk nanowires grow much faster than the branches in the tree structures. The cone angles of the outer envelopes of the trees are dictated by the relative ratios between the fastest growth rates of the trunks and branches and do not depend on the actual length and possible delays in nucleation events. To quantitatively represent the growth rate difference between the trunks and branches, the cotangent of the cone angle (θ) of 80 tree envelopes is measured and ranges from 4 to about 10 (Fig. 2A). This distinct morphology and growth rate difference contrasts with the hyperbranched nanowires under similar reaction conditions, suggesting a different growth process for the trunks of pine tree nanowires.

Fig. 2.

Distinctive difference in the growth rates of trunk and branch nanowires and the proposed dislocation-driven nanowire growth in the trunk of tree structures. (A) Approximate relative ratios of growth rates between trunk and branch nanowires that are calculated as cotangents of the cone angles (θ as illustrated in the inset) of the outer envelopes of 80 individual trees. (B) Dramatized scheme of the magnified tip of a tree structure highlighting the combined faster dislocation-driven trunk nanowire growth and slower VLS-driven branched nanowire growth. (C) A simplified scheme illustrating that the self-perpetuating steps of a screw dislocation spiral at the tip of a trunk can enable 1D crystal growth of nanowires.

We propose that the growth of the trunk nanowires is driven by the screw dislocation component of an axial dislocation along the length of the nanowire, providing a continuous growth front for 1D crystal growth. The self-perpetuating steps of a screw dislocation provide facile spiral growth fronts when the supersaturation is lower than what is required for crystal growth on perfect crystal facets, and this is known as Frank's mechanism for crystal growth (16, 17). When the supersaturation is low, only fast crystal growth at the self-perpetuating steps of a screw dislocation spiral is possible, whereas growth on the crystalline side walls is suppressed (Fig. 2C). This breaks down the symmetry and drives the 1D anisotropic crystal growth without catalysts. This dislocation-driven growth was proposed in the 1950s by Sears to explain the formation of micrometer-diameter metal “whiskers” (18, 19), which predates the VLS whisker growth. However, starting from the original Wagner and Ellis VLS work (4, 20), much effort has been undertaken to rule out crystal dislocations as the driving force for the 1D anisotropic growth. Since then, little has been mentioned about the role of dislocation defects in whiskers (1, 21) (and now nanowires).

We confirm the presence of screw dislocations in the trunks of these tree structures using diffraction contrast transmission electron microscopy (TEM) under the strong two-beam conditions (22). Diffraction contrast TEM is a powerful technique to image dislocations in crystals that relies on additional electron diffraction due to the bending of atomic planes near the dislocation core. If an image is reconstructed from specific reciprocal space diffraction spots (g) that are selected by a physical aperture, these additional diffracted electrons create a visible contrast around the dislocation. However, certain diffraction spots (g) with specific orientations to the Burgers vector of the dislocation (b) produce no dislocation contrast—the “invisibility criterion” (11). TEM sample preparation proved to be difficult due to the need to preserve the tree morphology during transfer, while also avoiding trees with too many branches that would obstruct the view and prevent the observation of a dislocation. After experimenting with many different transfer methods, we found micromanipulation to be the only technique that allows the effective transfer of individual trees onto TEM grids while preserving their complex and fragile morphology (fig. S6 and movie S1) (11). Great care was taken to avoid excessive mechanical force, which can result in the dislocation being worked out along the slip planes. In trees that clearly preserve the twisting structures under microscope observation (such as in Fig. 3E), dark lines running the entire length of tree trunks representing high dislocation contrast were observed under TEM. This is shown for g = (220) in Fig. 3A along the Embedded Image zone axis, in Fig. 3F along the Embedded Image zone axis, and in fig. S7 with a more complete mapping. However, no dislocations were observed in the branches of any tree investigated. No dislocations were observed in hyperbranched nanowires (fig. S9), with more than 20 samples having been examined. These observations are consistent with the suggestion that the nanowire trunks in the trees are driven by dislocation, whereas the branches of the trees (and the hyperbranched nanowires) grow via a slower VLS process (Fig. 2B).

Fig. 3.

Diffraction contrast TEM imaging of the dislocation in the tree trunk. (A to C) TEM images along the Embedded Image zone axis under the strong two-beam conditions. (A) represents strong diffraction contrast, and (C) represents invisibility conditions as highlighted in the zone axis pattern (ZAP) (B). (D) Schematic superposition of real and reciprocal space of a dislocation-containing nanowire along the [001] zone axis illustrating the Burgers vector relationship. Because the line dislocation vector u is [100], directions of screw and edge character Burgers vectors, bscrew and bedge, are known. As the Burgers vector is determined to be b110, the high-contrast results at g1 are due to the g1||b relationship and the perpendicular g0-beam results in the invisibility criterion. (E) Low-magnification TEM image showing the tree and area analyzed. (F) to (H) display Embedded Image zone axis TEM under the strong two-beam conditions. (F) represents g||b conditions, (H) represents invisibility conditions as highlighted in the zone axis diagram (G).

We have determined the dislocation Burgers vector (b) to be along the [110] direction. This detailed diffraction contrast TEM analysis requires finding two noncollinear diffraction spots (g beams) in reciprocal space that satisfy the invisibility criterion. The dislocation Burgers vector is along the direction of the cross product of these two g vectors. The tree structure shown in Fig. 3E has been analyzed under the strong two-beam conditions, as illustrated schematically in Fig. 3D. The same segment of this tree was tilted to the Embedded Image zone axis (Fig. 3, A to C) and the Embedded Image zone axis (Fig. 3, F to H), respectively. The image with the (220) diffraction spot (Fig. 3A) shows high dislocation contrast (corresponding to the g||b contrast maximum), while the dislocation meets the invisibility criterion under the perpendicular Embedded Image spot (Fig. 1C). Similarly, along the Embedded Image zone axis, the (220) diffraction spot shows high contrast (Fig. 3F) while the perpendicular Embedded Image the spot (Fig. 3H) meets the invisibility criterion. Therefore, taking the cross product of the Embedded Image and Embedded Image vectors shows that the Burgers vector is along the [110] direction. Electron diffraction patterns of the area analyzed are shown in fig. S8. It is known that the Burgers vector of the most stable dislocations in rock salt (face-centered cubic) crystals is along 〈110〉, and this has been previously observed in bulk PbS crystals (23, 24). Because the dislocation line direction (u) is along the [100] nanowire growth direction, the [110] Burgers vector represents a mixed dislocation: a screw dislocation component along the [100] (or Embedded Image) direction mostly responsible for driving the nanowire growth, and an edge dislocation component along the [010] (or Embedded Image) direction, whose role in promoting crystal growth (25) is not clear but cannot be ruled out completely at present.

What, then, is the reason for the helical rotation of branches on the screw dislocation-driven nanowire trunks? All dislocations create strain (and hence stress) within the otherwise perfect crystalline lattice. Using elasticity theory, Eshelby has shown that in a finite cylindrical rod containing an axial screw dislocation at the center, the stress field created by the dislocation exerts a torque at the free ends of the rod, resulting in a twist of the rod along the axial direction (Fig. 4A) (23, 26). This “Eshelby twist” is mathematically expressed as: Embedded Image(1) where α is the twist of the lattice in radians per unit length, R is the radius of the cylinder, and b is the magnitude of the screw component of the Burgers vector (27). Attempts to observe the Eshelby twist in micrometer-scale whiskers were made in the late 1950s, but the results were often inconclusive (28, 29). The Eshelby twist is readily observed in the tree nanowires because the 1/R2 dependence makes the twist much more pronounced at the nanoscale compared to the micrometer-sized whiskers, and because the overgrowth of epitaxial branching nanowires allows easy visualization of the twist. This allows a direct measurement of Eshelby twists and a simple estimate of the magnitude of the Burgers vector screw component.

Fig. 4.

Analysis of the Eshelby twists in tree nanostructures. (A) Schematic representation of the forces and resulting crystal displacement due to a screw dislocation. (B) SEM images of a tree illustrating the measurement of twist (a quarter of the pitch measured) and the measurement of diameter (inset), which was converted to radius for calculation. (C) Scatterplot of twists measured from 247 spots on 90 individual trees against their inversed cross-sectional areas [(πR2)–1]. The red line is a least-squares fit through the data whose slope (6 Å) is the magnitude of the screw component of the Burgers vector. (D) Histogram of the calculated Burgers vectors for each data point shown in (C) with a Gaussian fit to the data. The Gaussian peak is centered at 6 Å with a standard deviation of 2 Å.

As illustrated in Fig. 4B, SEM images can be examined to determine both the radius of a trunk nanowire and also its twist by tracking the periodic repeat of the branches (a quarter of the pitch is actually measured because of the four orthogonal epitaxial branches). The Eshelby twists (α) as a function of the inverse cross-sectional areas [(πR2)–1] of the nanowires were measured at 247 points on 90 individual trees from 16 synthetic batches (Fig. 4C). To extract the magnitude of the Burgers vector, a line can be fit to the data as plotted, with the slope representing b from Eq. 1 above. This can be more directly seen in a histogram of the calculated Burgers vectors (Fig. 4D). A Gaussian fit to these data yields the average magnitude of the screw component of the Burgers vector b = 6 ±2 Å. Because the Burgers vector direction is confirmed to be [110] by TEM, a 6 Å screw component of the Burgers vector (the projection of b onto the dislocation line u [100]) is approximately equal to the lattice constant of PbS, a = 5.94 Å. It is known that smallest b allowable is the shortest lattice translation vector in a material (23), which in the case of rock salt crystals is ½〈110〉, whose screw component is ½〈100〉 (half the lattice constant a). Given various sources of errors in this estimate (27), it is satisfying to see that no data were observed substantially below the theoretical minimal vector, and the average estimated b value of twice the minimal theoretical length is reasonable. Additionally, theory predicts that left-handed dislocation spirals lead to right-handed Eshelby twists and vice versa (23, 26); therefore, the equal probability of twist handedness implies equal probability of Burgers vector sense (sign).

The observation of Eshelby twist in these pine tree nanowires is a clear demonstration and validation of Eshelby's theory on dislocations. The results also provide evidence for a catalyst-free nanowire growth mechanism driven by axial screw dislocations and imply that VLS and screw dislocation-driven nanowire growth can coexist. Because of the distinct morphology difference from the hyperbranched nanowires, it is unlikely that the dislocation is a result of cool-down or other postgrowth perturbation. Although some general discussions on the origins of dislocations exist (23, 30), an experimentally observed mechanistic understanding is currently lacking. We suggest that this dislocation-driven nanowire growth mechanism proposed for PbS trees is likely general to and is underappreciated in the synthesis of 1D nanostructures, particularly in cases where the growth mechanism is inconclusively explained and especially when free of catalysts. Besides the analogous PbSe for which we have found preliminary evidence of similar growth phenomena, the dislocation-driven nanowire growth mechanism is likely to occur in materials that are prone to have screw dislocations, such as SiC, GaN, ZnO, and CdS, both in vapor-phase growth and in solution-phase synthesis. However, we caution that postgrowth mechanical perturbation could work the dislocation out of the nanowires, and one might not be able to observe dislocations in the final nanowire products if samples are not handled properly.

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