REPORTS iral is possible, whereas growth on the cry ws the effective transfer of individual trees onto the dislocation meets the invisibility criterion lline side walls is suppressed(Fig. 2C). This grids while preserving their complex and under the perpendicular(228)spot(Fig. I breaks down the symmetry and drives the ID ile morphology (fig. S6 and movie SI)(In). Similarly, along the [111 zone axis, the(220) anisotropic crystal growth without catalysts. This Great care was taken to avoid excessive me- diffraction spot shows high contrast(Fig. 3F) dislocation-driven growth was proposed in the chanical force, which can result in the dislocation while the perpendicular(224) spot(Fig. 3H) 1950s by Sears to explain the formation of being worked out along the slip planes In trees meets the invisibility criterion. Therefore, taking micrometer-diameter metal"whiskers"(18, 19), that clearly preserve the twisting structures under the cross product of the(228)and(224)vectors which predates the VLS whisker growth. How- microscope observation(such as in Fig. 3E), shows that the Burgers vector is along the [1 ever, starting from the original Wagner and Ellis dark lines running the entire length of tree trunks direction. Electron diffraction patterns of the area VLS work(4, 20), much effort has been under- representing high dislocation contrast were ob. analyzed are shown in fig. S8. It is known that taken to rule out crystal dislocations as the served under TEM. This is shown for g=(220) the Burgers vector of the most stable dis- driving force for the ID anisotropic growth. in Fig 3A along the 221] zone axis, in Fig. 3F locations in rock salt( face-centered cubic)crys- Since then, little has been mentioned about the along the [111 zone axis, and in fig. S7 with a tals is along(110), and this has been previously ole of dislocation defects in whiskers (1, 21) more complete mapping. However, no disloca- observed in bulk Pbs crystals(23, 24). Because (and now nanowires ons were observed in the branches of any tree the dislocation line direction (u) is along the We confirm the presence of screw disloc- investigated. No dislocations were observed in [100 nanowire growth direction, the [1101 tions in the trunks of these tree structures using hyperbranched nanowires (fig. S9), with more Burgers vector represents a mixed dislocation diffraction contrast transmission electron micros- than 20 samples having been examined. These a screw dislocation component along the [100] copy(TEM) under the strong two-beam condi- observations are consistent with the suggestion (or 100) direction mostly responsible for driv- tions(22). Diffraction contrast TEM is a powerful that the nanowire trunks in the trees are driven ing the nanowire growth, and an edge dis- technique to image dislocations in crystals that by dislocation, whereas the branches of the trees location component along the [o10](or [010) relies on additional electron diffraction due to (and the hyperbranched nanowires) grow via a direction, whose role in promoting crystal growth the bending of atomic planes near the disloc- slower Vls process(Fig 2B) (25) is not clear but cannot be ruled out com- We have determined the dislocation Burgers pletely at presen ific reciprocal space diffraction spots(g) that vector(b) to be along the [110] direction. This What, then, is the reason for the helical rota are selected by a physical aperture, these addi- detailed diffraction contrast TEM analysis re- tion of branches on the screw dislocation-driven tional diffracted electrons create a visible con- quires finding two noncollinear diffraction spots nanowire trunks? All dislocations create strain trast around the dislocation. However, certain (g beams) in reciprocal space that satisfy the (and hence stress) within the otherwise perfect diffraction spots(g) with specific orientations invisibility criterion. The dislocation Burgers vec- crystalline lattice. Using elasticity theory, Eshelby to the Burgers vector of the dislocation (b) tor is along the direction of the cross product of has shown that in a finite cylindrical rod con- produce no dislocation contrast--the"invisi- these two g vectors. The tree structure shown in taining an axial screw dislocation at the center, bility criterion"(11). TEM sample preparation Fig. 3E has been analyzed under the strong two. the stress field created by the dislocation exert proved to be difficult due to the need to pre- beam conditions, as illustrated schematically in torque at the free ends of the rod, resulting in a serve the tree morphology during transfer, while Fig. 3D. The same segment of this tree was twist of the rod along the axial direction(Fig 4A) also avoiding trees with too many branches that tilted to the[] zone axis(Fig. 3, A to C)and (23, 26). This"Eshelby twist " is mathematically would obstruct the view and prevent the obser- the [111] zone axis(Fig 3, F to H), respectively pressed as vation of a dislocation. After experimenting with The image with the (220)diffraction spot many different transfer methods, we found micro(Fig. 3A)shows high dislocation contrast(cor anipulation to be the only technique that al- responding to the g b contrast maximum), while Fig. 4. Analysis of the where a is the twist of the lattice in radians pe Eshelby twists in tree unit length, R is the radius of the cylinder, and b nanostructures. (A)Sche- matic representation of aS the magnitude of the screw component of the Burgers vector(27). Attempts to observe the the forces and resulting Eshelby twist in micrometer-scale whiskers were crystal displacement due made in the late 1950s. but the results were often a screw dislocation. (B) inconclusive(28, 29). The Eshelby twist is read SEM images of a tree il- xI ily observed in the tree nanowires because the lustrating the measure- 1/R dependence makes the twist much more ment of twist (a quarte pronounced at the nanoscale compared to the of the pitch measured and the measurement of c micrometer-sized whiskers. and because the over- diameter (inset), which growth of epitaxial branching na was converted to radius =o easy visualization of the twist. This allows a di for calculation. (C) Scat- I rect measurement of Eshelby twists and a simple plot of twists measured estimate of the magnitude of the burgers vector from 247 spots on 90 individual trees agains As illustrated in Fig 4B, SEM imag be their inversed cross xamined to determine both the radius of a trunk ctional areas [GR-1 nanowire and also its twist by tracking the The red line is a least- 0408 wares fit through the A(rR)(um) periodic repeat of the branches(a Burgers vector(nm) pitch is actually measured because of the four se slope(6 A) is the magnitude of the screw component of the Burgers vector. (D)Histogram of the orthogonal epitaxial branches). The Eshelby ed Burgers vectors for each data point shown in(O with a Gaussian fit to the data. The Gaussian peak is twists (a)as a function of the inverse cross at 6 A with a standard deviation of 2a sectional areas [(R] of the nanowires wer 1062 23mAy2008Vol320ScieNcewww.sciencemag.orgspiral is possible, whereas growth on the crys￾talline 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. How￾ever, starting from the original Wagner and Ellis VLS work (4, 20), much effort has been under￾taken 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 disloca￾tions in the trunks of these tree structures using diffraction contrast transmission electron micros￾copy (TEM) under the strong two-beam condi￾tions (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 disloca￾tion core. If an image is reconstructed from spe￾cific reciprocal space diffraction spots (g) that are selected by a physical aperture, these addi￾tional diffracted electrons create a visible con￾trast around the dislocation. However, certain diffraction spots (g) with specific orientations to the Burgers vector of the dislocation (b) produce no dislocation contrast—the “invisi￾bility criterion” (11). TEM sample preparation proved to be difficult due to the need to pre￾serve the tree morphology during transfer, while also avoiding trees with too many branches that would obstruct the view and prevent the obser￾vation of a dislocation. After experimenting with many different transfer methods, we found micro￾manipulation to be the only technique that al￾lows 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 me￾chanical 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 ob￾served under TEM. This is shown for g = (220) in Fig. 3A along the ½221
zone axis, in Fig. 3F along the ½111
zone axis, and in fig. S7 with a more complete mapping. However, no disloca￾tions 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). We have determined the dislocation Burgers vector (b) to be along the [110] direction. This detailed diffraction contrast TEM analysis re￾quires finding two noncollinear diffraction spots (g beams) in reciprocal space that satisfy the invisibility criterion. The dislocation Burgers vec￾tor 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 ½221
zone axis (Fig. 3, A to C) and the ½111
zone axis (Fig. 3, F to H), respectively. The image with the (220) diffraction spot (Fig. 3A) shows high dislocation contrast (cor￾responding to the g||b contrast maximum), while the dislocation meets the invisibility criterion under the perpendicular ð228Þ spot (Fig. 1C). Similarly, along the ½111
zone axis, the (220) diffraction spot shows high contrast (Fig. 3F) while the perpendicular ð224Þ spot (Fig. 3H) meets the invisibility criterion. Therefore, taking the cross product of the ð228Þ and ð224Þ 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 dis￾locations in rock salt (face-centered cubic) crys￾tals 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 ½100
) direction mostly responsible for driv￾ing the nanowire growth, and an edge dis￾location component along the [010] (or ½010
) direction, whose role in promoting crystal growth (25) is not clear but cannot be ruled out com￾pletely at present. What, then, is the reason for the helical rota￾tion 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 con￾taining 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: a ¼ b pR2 ð1Þ where a 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 read￾ily 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 over￾growth of epitaxial branching nanowires allows easy visualization of the twist. This allows a di￾rect measurement of Eshelby twists and a simple estimate of the magnitude of the Burgers vector screw component. 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 (a) as a function of the inverse cross￾sectional areas [(pR2 ) −1 ] of the nanowires were Fig. 4. Analysis of the Eshelby twists in tree nanostructures. (A) Sche￾matic representation of the forces and resulting crystal displacement due to a screw dislocation. (B) SEM images of a tree il￾lustrating the measure￾ment of twist (a quarter of the pitch measured) and the measurement of diameter (inset), which was converted to radius for calculation. (C) Scat￾terplot of twists measured from 247 spots on 90 individual trees against their inversed cross￾sectional areas [(pR2 ) −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. 10 µm 500 nm A B 25 20 15 10 5 Count 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Burgers vector (nm) R b unit length 0.4 D 0.3 0.2 0.1 0.0 Twist (rad/µm) 100 200 300 400 500 600 1/(πR2 ) (µm-2) C α 1062 23 MAY 2008 VOL 320 SCIENCE www.sciencemag.org REPORTS