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Atom Movement on a Dislocated Surface Grazyna Antczak* and Przemyslaw Jo´z´wik Materials Research Laboratory, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801 and Institute of Experimental Physics, UniVersity of Wroclaw, Poland ReceiVed July 7, 2008. ReVised Manuscript ReceiVed August 12, 2008 The standard picture of growth at a screw dislocation assumes that the movement of adatoms on a dislocation loop is the same as on an ideal plane. We have examined this proposition by investigating the movement of a single tungsten adatom on a W(110) plane intersected by a screw dislocation. Surprisingly enough, adatom movement was entirely different than on a normal (110) plane: the overall diffusivity was higher, and the mobility varied with the location of the adatom relative to the dislocation core. This study demonstrates that surface transport is strongly affected in the vicinity of dislocations.
Dislocations at the surface influence a number of properties of technically important materials, such as plasticity and other mechanical properties as well as their growth.1,2 Despite that, growth at a screw dislocation has never been looked at with atomic resolution, and details of the atomic events are unknown. We have now used field ion microscopy3 to atomically resolve edge atoms of the dislocation loop as well as the position of an adatom deposited on the dislocated surface. During the process of crystal growth, a dislocated surface, shown schematically in Figure 1a, is bombarded with metal atoms from the gas phase. The condensed atoms diffuse over the surface until they reach a lattice step, where they can incorporate into the crystal, forming a growth spiral. A great deal is now known about atom diffusion on metal surfaces as well as about transitions over plane edges and incorporation.4 The standard assumption5 made in crystal growth is that diffusion occurs at the same rate on a dislocated surface as on an unimpaired one, so it should be a straightforward matter to estimate the overall rate of incorporation. However, this process has never been examined in atomic detail, even though both the scanning tunneling microscope (STM) and the field ion microscope (FIM) have a resolution adequate for visualizing adatoms, and dislocations were extensively studied by the latter technique.6 Recently, however, we have had the opportunity to carry out such an examination in the FIM, at a pressure below 10-10 Torr before measurements, and have uncovered quite unexpected resultssdiffusion occurs in a remarkably different fashion from normal atomic behavior. A tungsten (110) surface on a well-annealed tip was first prepared with a screw dislocation emanating from it, as shown in Figure 1b. By field evaporation3 at ∼20 K, it was possible to take individual atoms from the dislocation step, and this process was continued until four layers had been removed. Field evaporation allows us to map the position of edges in three dimensions, and it is clear that the edges form a spiral going into the bulk. The surface formed after evaporation, shown in Figure * Corresponding author. E-mail:
[email protected]. (1) Burton, W. K.; Cabrera, N.; Frank, F. C. Phil. Trans. R. Soc., Sect. A 1951, 243, 299–358. (2) Frank, F. C. AdV. Phys. 1952, 1, 91–109. (3) Mu¨ller, E. W.; Tsong, T. T. Field Ion Microscopy; Principles and Applications; American Elsevier: New York, 1969. (4) Antczak, G.; Ehrlich, G. Surf. Sci. Rep. 2007, 62, 39–61. (5) Mutaftschiev, B. The Atomistic Nature of Crystal Growth; Springer-Verlag: Berlin, 2001. (6) Bowkett, K. M.; Smith, D. A. Field Ion Microscopy; North-Holland: Amsterdam, 1970.
1c, can be superposed nicely on the original one in Figure 1b; the shape of the spiral is conserved, and the core of the dislocation therefore intersects the (110) plane at a right angle.7 No edge component was detected during this process. The radius of the central dislocation loop is ∼14 atomic spacings (around 38 Å), so our measurements were made relatively close to the dislocation core. On the basis of the conservation of shape of the spiral during the evaporation process and the superposition of the edge atoms before and after evaporating four layers of the dislocated surface, as well as on the map of places the adatom visits, we conclude that the position of the dislocation core is somewhere in the center of the dislocation loop, marked by a star in Figure 2. However, the exact location of the core is impossible to specify. Lack of change in the shape and absence of a visible edge component in the FIM image suggest that the Burgers vector for this dislocation is perpendicular to the surface. A single tungsten atom was deposited on the dislocated surface at ∼20 K, and its locations were observed in 290 measurements after 10 s diffusion intervals at 340 K; these are shown in Figure 2. The mean square displacement along the [001] and [11j0] directions as well as the diffusivity obtained in these measurements are presented in Table 1 together with data for movement on the defect-free surface. The mean square displacement is correlated with the diffusivity according to
〈∆x2 〉 ) 2Dt
(1)
It is clear from Figure 2 that the adatom does not visit sites close to the steps, so edge corrections are not required for this study. Also, measurements on the dislocated surface were done on exactly the same time tip as measurements for the defect-free surface, which lowers the uncertainty in the temperature to that of the temperature controller, which amounts to 0.5 K for our system.8 From studies of tungsten adatoms on a normal W(110) plane, on the very the same tip, we expect that at this temperature the diffusivity along the [001] direction should be 0.169 ( 0.008 (a/2)2 per second,9 where a is the lattice constant and the diffusivity will not depend on the position of the adatom on the surface. However, for the atom on the dislocated surface, the diffusivity along [001] was much higher and amounted to 0.229 ( 0.027 (7) Antczak, G. http://users.mrl.uiuc.edu/antczak/dislocation.avi, http://users. mrl.uiuc.edu/antczak/dislocation.wmv 2008. (8) Wang, S. C.; Ehrlich, G. Surf. Sci. 1988, 206, 451–474. (9) Antczak, G.; Ehrlich, G. Phys. ReV. Lett. 2004, 92, 166105–1-4.
10.1021/la802036z CCC: $40.75 2008 American Chemical Society Published on Web 08/22/2008
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Figure 1. (a) Schematic of end of a tip intercepted by a screw dislocation; 1, 2, 3, and 4 indicate the number of each layer counted from the top. (b) Field ion image of a screw dislocation at 20 K before field evaporation; numbers are correlated with the numbers on the schematic. (c) Field ion image after field evaporation of four layers. Positions of edge atoms in b and c are superposed, proving that the core is at a right angle and is not an artifact. Table 1. Diffusivity of Adatom at 340 K on W(110) Intersected by Screw Dislocation and on a Defect-Free W(110) Plane
type of surface
region analyzed
defect-free plane whole plane screw dislocation all data screw dislocation outer region inner region screw dislocation upper ramp lower ramp screw dislocation outer upper region outer lower region inner upper region inner lower region
mean square diffusivity mean square displacement in Dy in The displacement in time number of diffusivity Dx [110] direction observations interval the [001] direction the [110] direction in the [001] 〈∆x2〉 in (a/2)2 t(s) N 〈∆y2〉 in (a√2/2)2 direction in (a/2)2 s-1 in (a√2/2)2 s-1 1200 290 140 135 123 167 68 72 42 91
4 10 10 10 10 10 10 10 10 10
1.353 ( 0.065 4.583 ( 0.531 6.500 ( 1.003 2.556 ( 0.357 2.081 ( 0.378 6.425 ( 0.852 2.162 ( 0.531 10.597 ( 1.758 1.048 ( 0.202 3.220 ( 0.507
(a/2)2 per second. A similar relation was observed for the [11j0] direction, only with a slightly smaller difference; the diffusivity was 0.223 ( 0.024 [a(21/2)/2]2 on the dislocated surface, whereas on the defect-free surface the value was 0.188 ( 0.010 [a(21/2)/2]2. The different uncertainties of the diffusivity for the dislocated and defect-free surfaces reflect the different number of measurements in the two experiments. However, the diffusivities are not comparable within their uncertainties, suggesting that diffusion clearly varied with position. Further analysis confirmed this conclusion, showing huge differences in diffusivity in different regions of the dislocated surface. The second point of interest here is that after these position measurements the adatom disappeared from sight. Its last observed position, indicated in Figure 2 by a small square, was far from any obvious descending edges. In previous FIM studies of tungsten atoms on W(110), the loss of diffusing atoms occurred only occasionally and then quite close to the plane edges where the electric field at constant applied voltage rises. One possibility in the present case is that the adatom diffused over the surface and attached itself to the lattice step close to the dislocation core, which we do not see but should be nearby. Here we note that adatoms a couple of spacings from an ascending step on a normal plane almost immediately attach to it.10 We also emphasize that the grid lines in Figure 2a, connecting binding sites observed for the adatom and indicating the [11j1] direction on the dislocated surface, are not parallel to each othersthose on the right side are tilted to around 5° with respect to those on the left. Such a shift is probably associated with a change in interatomic distances near the dislocation due to strain. Instead, lines along the [11j1] direction, shown Figure 2b, are almost parallel to each other, and (10) Wang, S. C.; Ehrlich, G. Phys. ReV. Lett. 1993, 70, 41–44.
1.503 ( 0.079 4.459 ( 0.483 6.071 ( 0.864 2.763 ( 0.476 1.659 ( 0.236 6.521 ( 0.785 1.397 ( 0.235 10.486 ( 1.492 0.952 ( 0.190 3.440 ( 0.670
0.169 ( 0.008 0.229 ( 0.027 0.325 ( 0.051 0.128 ( 0.018 0.104 ( 0.019 0.321 ( 0.043 0.108 ( 0.027 0.530 ( 0.088 0.052 ( 0.010 0.161 ( 0.026
0.188 ( 0.010 0.223 ( 0.024 0.304 ( 0.044 0.138 ( 0.024 0.083 ( 0.012 0.326 ( 0.039 0.070 ( 0.012 0.524 ( 0.075 0.048 ( 0.010 0.172 ( 0.034
lines from the upper ramp almost agree with lines from the lower ramp. If any such shift exists, then it is very small and much less pronounced than in the [11j1] direction. It is known that on a defect-free surface the easiest path for adatom movement is in the 〈111〉 directions and both 〈111〉 directions existing on the bcc(110) surface are equally probable.9 That is no longer true on the dislocated surface. The mean square displacement of an adatom in the [11j1] direction amounted to 4.00 ( 0.49 [a(3)1/2/2]2 whereas in the [11j1] direction it was only 0.93 ( 0.12 [a(3)1/2/2]2, which is roughly one-fourth. The lines in Figure 2a indicate the easy path created for the adatom along the [11j1] direction. This anisotropic movement on a dislocated surface is of course not reflected in the diffusivity along the [001] and [11j0] directions, shown in Table 1; movement in the [11j1] direction equally influences both the [001] and the [11j0]. It is also interesting that the adatom is not seen in the central part of the plane, where the dislocation emerges. More surprising still are the details of the diffusion behavior; displacements occur quite differently on different parts of the dislocated surface, whereas on an ordinary plane there is little difference between excursions in different regions. For three sets of 100 observations in various parts of a flat W(110) on the same tip after movement at 340 K, the diffusivities in the [001] direction were measured to be 0.206 ( 0.030, 0.175 ( 0.030, and 0.168 ( 0.021 (a/2)2 per second; they are the same within the small statistical error that accounts for the lower number of observations. That is not true on the dislocated surface. We separate movements of the adatom on the right side of the dislocation loop (lower ramp) from those on the left side (higher ramp), as shown in Figure 3a. From the data in Table 1, it is clear that movement on the lower ramp is ∼3 times faster than
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Figure 2. Map of adsorption sites visited by adatom in movement at 340 K during a time interval of 10 s. The map clearly shows the regions that the adatom avoids: ∼2 atomic spaces from the descending edge as well as close to the core. (a) Grids associated with the [11j1] direction at the right are tilted with respect to the left part of the diagram. (b) Grids associated with the [1j11] direction are linear, and the lines on the right side of the diagram match the ones on the left. ([) Dislocation’s edge atoms, (b) places visited by an adatom, (gray circle) starting point, (gray triangle) place where adatom disappeared, (/) expected position of the core.
movement on the upper ramp. When we divide the area of the central loop between inner (closer to the dislocation core) and outer regions (closer to the edges), illustrated in Figure 3b, there can be no doubt that in the outer regions the adatom is moving faster than in the inner region. Additionally, in the inner region movement is slower than on a defect-free surface, whereas in the outer region movement is faster. Because these observations were quite unexpected, we decided to separate movement on the lower ramp from that on the upper ramp and divided the area of both ramps between inner and outer regions. After this separation, the differences in diffusivity are even more pronounced: on the outer lower ramp, movement is much faster, by a factor of roughly 5, than on the upper inner ramp. Atom motion
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Figure 3. Schematics of different regions on the central loop of the screw dislocation. (a) Upper and lower ramps. (b) Inner region, up to ∼6 atomic spaces from the core of the dislocation. Outer region, roughly 6 to 12 atomic spaces from the core of the dislocation.
in the outer lower ramp occurs ∼3 times as fast as on a good (110) plane, whereas on the inner upper it is one-third less than the normal diffusivity. The value in the inner lower region is quite close to that for movement on a flat plane. More than that, the adatom does not like to incorporate into the outer descending lattice step; it always stays roughly 2 spaces away. Again, this is quite different from the behavior on a normal plane, where atoms are reflected by the step edge barrier but get very close to the edge.11 The atom is also not seen in the region relatively close to the emerging step. It is important to note that after removing the dislocation by field evaporation the diffusivity on the newly developed flat plane came back to entirely normal behavior. We believe that the phenomena reported here will be observed on other dislocations as well. So far, however, it is the first direct measurement of adatom motion on a dislocation loop, giving the (11) Oh, S.-M.; Kyuno, K.; Wang, S. C.; Ehrlich, G. Phys. ReV. B 2003, 67, 075413–1-7.
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first indication of strange adatom behavior close to a dislocation core. It is natural to rationalize these unusual observations of the diffusivity in terms of the strain field associated with creation of the dislocation. It is well documented experimentally as well as theoretically that diffusion depends on the strain at the surface: the barrier is reduced by compressive strain at the surface and increased by tensile strain.12-14 Our observation would suggest that strain changes with distance from the core, from tensile to compressive, with stronger tensile strain in the inner region of the upper ramp and stronger compressive strain in the outer region of the lower part. Unfortunately, the exact strain field close to the core is not available for comparison. We have a clear indication of the strain parallel to the surface as a result of lateral changes in the positions of surface atoms. This strain seems to depend on the distance from the core, causing rotation of the 〈111〉 lines, but we also cannot rule out the presence of strain perpendicular to the surface because this might be responsible for the difference in diffusion between the lower and upper ramps of the dislocation loop. Of course this explanation, based only on the effect of strain on diffusivity, might not account for all factors influencing adatom movement. Normal elastic theory15 does not adequately account for observations close to the core. The well-known predictions are
that the only shear strain is εθz ) b/(4πr), where b is the magnitude of the Burgers vector and r is the distance from the dislocation core, so that the strain decreases on moving away from the core and diffusion should become close to normal. Of course at large enough distances the normal value should again be attained. However, exactly the opposite is observed at distances of up to 14 atomic spaces (∼38 Å). Though we do not yet know how the different phenomena described here come about, it is clear that diffusion does not take place on the dislocated surface in the same way as on an ideal plane and that on the lower ramp of the dislocation spiral diffusion occurs much more rapidly than elsewhere. Detailed calculations on the atomistic level are evidently needed here. The dislocation introduces distortions into the surface, which appear to have a huge effect on the movement and incorporation process on the atomic scale, and these will have to be taken into account in investigating the rate of crystal growth and the thermal evolution of spirals.
(12) Brune, H.; Bromann, K.; Roder, H.; Kern, K.; Jacobsen, J.; Stoltze, P.; Jacobsen, K.; Norskov, J. Phys. ReV. B 1995, 52, R14380–14383. (13) Ratsch, C.; Seitsonen, A. P.; Scheffler, M. Phys. ReV. B 1997, 55, 6750– 6753. (14) Yu, B. D.; Scheffler, M. Phys. ReV. B 1997, 56, R15569–15572.
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Acknowledgment. We are indebted to the Petroleum Research Fund, administered by the ACS under grant ACS PRF 44985AC5, for the support of this study. We thank G. Ehrlich, T. C. Chiang, and R. Chambers for discussions and critical reading of the manuscript.
(15) Hull, D.; Bacon, D. J. Introduction to Dislocations; Butterworth Heinemann: Oxford, U. K., 2001.
