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J. Phys. Chem. B 1997, 101, 4260-4264
Simulation of Atomic Force Microscopy Images of Cleaved Mica Surfaces Kazuya Tsujimichi, Hiroyuki Tamura, Akiyasu Hirotani, Momoji Kubo, Masaharu Komiyama,*,† and Akira Miyamoto* Department of Molecular Chemistry and Engineering, Faculty of Engineering, Tohoku UniVersity, Sendai 980-77, Japan ReceiVed: NoVember 13, 1996; In Final Form: March 25, 1997X
Taking into account the Coulomb and exchange forces, atomic force microscopy (AFM) and lateral force microscopy (LFM) simulations were performed for a Si(OH)4 tip and a cleaved mica surface under planer two-dimensional periodic boundary conditions. Imaging of the individual oxygen atoms in hexagonal oxygen rings and/or K+ ions on a cleaved mica surface strongly depended on the tip orientation and the applied force. Experimentally obtained AFM images of cleaved mica surfaces were interpreted in terms of the present simulation results.
1. Introduction Atomic force microscopy (AFM), devised by Binnig, Quate, and Gerber,1 is a powerful tool for real-space imaging of conducting and insulating solid surface structures with atomic resolution. Since the achievement of atomic resolution on insulator surfaces,2 its applications are rapidly expanding into diverse fields such as material science, electrochemistry, and biology. Despite its practical importance and its widespread use, the AFM imaging mechanism is not yet clarified, and there exist certain ambiguities in the interpretations of atomic level AFM images. This ambiguity is caused by several reasons. Firstly, forces exerted by the sample surface atoms on the AFM tip consist of not only one but several components, including electrostatic (Coulomb), dipole, dispersion (van der Waals), and other “chemical” forces such as hydrophobic force. The shapes of respective force curves are expected to differ markedly from each other, and unlike in scanning tunneling microscopy (STM), it is not possible to determine the tip-sample distance experimentally by simply taking an overall force curve. Another source of complexity is that it is not possible to determine experimentally the geometrical arrangement of the apex atoms of an AFM tip. Thus it is sometimes difficult to separate the tip and other artifacts from actual surface properties in AFM, leaving the interpretation of atomic level AFM images and force characteristics often ambiguous and inconclusive. An example of this ambiguity is found in the AFM images of the most frequently observed surface, the cleaved (001) face of muscovite mica, which is commonly used as a standard for AFM instrument calibration. The cleavage plane of muscovite mica consists of two tetrahedral SiO44- (and AlO45-) sheets sandwiching a K+ layer, which balances the negative charge of the tetrahedral sheets. The cleaved (001) plane is shown in Figure 1 with all the K+ ions in place (Figure 1 actually shows the muscovite analog phlogopite, but the atomic arrangement on the (001) surface is almost identical). Here the basal plane oxygen atoms constitute hexagonal rings with a nearest-neighbor oxygen distance of 0.28 nm. Potassium ions are situated at the center of the hexagonal oxygen rings. Upon cleaving, it is not expected to have all the K+ ions on one tetrahedral sheet, not leaving any on the other, since the role of the K+ ions is to balance the negative charges of these tetrahedral sheets. † Department of Chemistry, Yamanashi University, Takeda, Kofu 400, Japan X Abstract published in AdVance ACS Abstracts, May 1, 1997.
S1089-5647(96)03780-7 CCC: $14.00
Figure 1. Top view of the cleaved mica plane used as a model sample surface (a) and its side view (b). Here large black and white circles denote K+ and O2- ions, respectively. Small circles denote Si4+ or Al3+ ions. The rectangle indicated in part a denotes the scanned area that is under two-dimensional periodic boundary conditions. In the rectangle Al3+ ions are indicated by arrows.
Lattice-scale AFM image of muscovite mica was first obtained by Drake et al.4 in water. With an applied force as low as 2 × 10-9 N, they recorded images of (hexagonal) rings arranged on 0.52 nm centers, corresponding to the basal oxygen rings. Similar images have often been obtained under ambient conditions. Recently Yoshida et al.5 obtained two types of muscovite and phlogopite images in carefully performed experiments carried out under pure argon atmosphere with an applied force of ca. 10-9 N: one corresponding to the oxygen rings and the other to the close-packed hexagonal K+ arrangement. It is noted that in any of the above cases no mixed regions having K+ ions on some of the hexagonal oxygen rings have been observed. Routine AFM scans of the muscovite mica commonly produce a close-packed hexagonal array of bright spots with a spacing of 0.52 nm, corresponding to the K+ ion arrangement. Such images may be interpreted as observing the K+ ion array, although it is highly unlikely that all the K+ ions are left only on one side of the cleaved plane. They may also be interpreted as due to having low resolution, and the images are simply reflecting the translational symmetry of the oxygen basal plane. In fact Coleman et al.6 present an image that shows a smooth transition from a ring-resolved structure to a hexagonal closepacked structure. The registry indicates that the bright spots in the hexagonal close-packed region are not situated on the centers of the ring structures but at their rims, indicating that this transition may be caused by a transition to lower resolution, or some other reasons such as data processing. A similar transition is found in Figure 16 in ref 7. © 1997 American Chemical Society
AFM Images of Cleaved Mica Surfaces
J. Phys. Chem. B, Vol. 101, No. 21, 1997 4261 TABLE 1: Potential Parameters Employed for the Present Simulations (after Kawamura15) ion 4+
Si Al3+ O2K+ OH-
Figure 2. (a) Atomic structure of the Si(OH)4 cluster used as a tip, with open and hatched circles denoting OH- and Si4+, respectively. (b-d) Tip orientations, θs (b), θt1 (c), θt2 (d), viewed from the top toward the sample surface.
It has also been pointed out that frictional force between AFM tip and cleaved mica surface plays an important role in AFM imaging.8-10 This would be particularly important when using a position-sensitive photodetector consisting of two semicircles, since in such a system cantilever twist or bend due to frictional force will be convoluted into observed height images.11 On muscovite mica surfaces the frictional force tends to give hexagonal close-packed images.8-10 Thus if frictional force dominates vertical force, hexagonal close-packed images that might appear to have imaged the K+ arrangement would be observed. All those observations lead to one question: where have all the K+ ions gone? And if K+ ions are present on the surface, are there any reasons that we do not see them with AFM? The present paper examines this question through model simulations for the search of possible answers. 2. Method A model AFM system consisting of a Si(OH)4 cluster tip and a topmost cleaved plane of mica was constructed. The model sample surface is shown in Figure 1, with a unit cell enclosed in a rectangle, on which two-dimensional boundary conditions are imposed. The model surface is made of one tetrahedral sheet consisting of SiO44- and AlO45- tetrahedrons as well as K+ ions. The crystal structure of the model sample surface was obtained from X-ray crystallographic data of phlogopite,12 KMg3(OH)2(AlSi3O10), a mica analog of muscovite (KAl2(OH)2AlSi3O10). Their formulas of topmost cleaved planes are the same as each other, which is represented by AlSi3O10, and the structural difference between their topmost cleaved planes is minute. Hence the discussion of simulated AFM images of the cleaved phlogopite plane is also applicable to those of the cleaved muscovite plane. In fact, the experimental AFM images of muscovite and phlogopite cleaved planes are almost identical.5 The Si4+/Al3+ ratio within the constructed tetrahedral sheet is set at 3, with their geometrical distributions following the Loewenstein rule that dictates that Al3+-O2--Al3+ bonds are not permissible in aluminosilicates. The Al3+ positions within the rectangle unit cell are indicated by arrows in Figure 1a. A Si(OH)4 tetrahedron cluster tip, shown in Figure 2a, was employed as a model AFM tip. The choice of this material is based on the fact that the most commonly used AFM cantilevers are made of Si3N4 or Si, both of which, under ambient conditions, are likely to be covered with silicon oxide with its outermost oxygen terminated with hydrogen. The ionic radius of H+ is very small compared to that of O2-, and each OHgroup in the Si(OH)4 cluster tip was taken as one atomic entity here, to decrease the number of atoms in the system for the sake of computational time. The structure of the SiO4 skeleton in this Si(OH)4 cluster tip was adopted from that of quartz, with and O-Si-O angle of 109.5° and a Si-O distance of 0.161 nm.
Z
a/Å
b/Å
4.00 3.00 -2.00 1.00 -1.00
1.012 1.056 1.629 1.595 1.629
0.080 0.080 0.085 0.080 0.085
Three tip orientations, θs, θt1, and θt2, shown in Figure 2bd, were examined. In the figure, tips are seen from the top toward the sample surface: thus θs has a single atom entity at the tip apex, and θt1 and θt2 have a trimer facing the sample surface. In the θt1 orientation one of the trigonal faces is parallel to the scanning direction, x, and in θt2 one of the trigonal faces is perpendicular to it. The whole structure of both the tip and the sample surface was fixed during the calculation, because both materials are considered to be hard enough and do not undergo structural changes during the scanning. For the simulations a recently developed AFM simulator ACCESS (AFM simulation code for calculating and evaluating surface structures)11,13,14 was employed under two-dimensional periodic boundary conditions parallel to the sample surface. The forces acting between the atoms in the tip and those in the sample were calculated by using the differential of the following interatomic potential function.
Φij(rij) )
ZiZje2 ai + aj - rij + f0(bi + bj)exp rij bi + bj
(1)
In eq 1, the first and second terms refer to Coulomb and exchange repulsion, respectively. Here Zi is the atomic charge, e the elementary electric charge, rij the interatomic distance, and f0 a constant. The parameters a and b represent the size and stiffness, respectively. These potential parameters for individual atoms constituting the present model system were adopted from those determined by Kawamura.15 The parameters, listed in Table 1, have successfully reproduced structures of a number of aluminosilicate materials such as cristbalite, quartz, and zeolites. The potential parameters for OH- groups in the Si(OH)4 cluster tip are represented by those for O2- ions, with a Zi value of -1. The sum of Coulomb interactions under two-dimensional periodic boundary conditions was calculated by using Lekner's method.16 Actual calculations for the constant-force image simulation were performed as follows. Using eq 1, the z-component of the force exerted from each of the sample atoms on each atom in the tip is calculated at a certain z-position of the tip, and their sum was taken as the total force on the tip in the z-direction. The z-position of the tip was adjusted by z-position feedback so that the total force on the tip equals a set value (2 or 10 nN), and then the z-position of the tip is recorded (AFM images). The x-component of the force on the tip (LFM images) is also calculated by using eq 1 at the adjusted tip height. This was repeated for each of the tip positions as it scans the surface by steps of 0.455 and 0.453 Å in x and y, respectively, within the area indicated by a rectangle in Figure 1, and the contour maps of the z-position of the tip and the x force component felt by the tip were obtained. Images thus obtained were visualized using an AFM visualization code VITAMIN 95 (visualization tool for atomic force microscopy 1995).14 It is noted that, in the map of the x force component presented in this paper, force toward the +x direction (attractive) is taken as negative and that toward -x as positive. The z-positions of
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the tip are defined as nucleus-nucleus distances between the topmost atomic layer of the sample and the tip apex atomic entity. 3. Results 3.1. Determination of the Vertical Positions of K+ Ions. In the bulk a K+ layer is located at the center of the two tetrahedral silica/alumina sheets, but its position may be relaxed when one tetrahedral sheet is removed by cleaving. In the xyplane it is plausible that the K+ ions are located at the center of the hexagonal oxygen rings on the cleaved plane, considering the Coulomb interaction between the K+ and the O2- ions. The z-coordinate of a K+ ion was determined here by calculating the z force component acting on a K+ ion from the other atoms in the cleaved mica plane. There exist two types of sites in the hexagonal oxygen rings on a cleaved mica plane, one having two AlO45- tetrahedrons in the hexagonal ring (site A) and the other having one (site B). A K+ ion was vertically approached far from the cleaved plane to each site, and the variation of the z force component acting on the approaching K+ ion was calculated as a function of the nucleus-nucleus distance between the K+ ion and the topmost oxygen layer. It was found that the z force component felt by the K+ ion is zero at a distance of 0.359 Å for the site A and 0.369 Å for the site B, indicating that K+ ions are stable at these positions, respectively. Thus in the following calculations K+ ions are fixed at these positions. The small difference between these values for the two sites, namely, 0.010 Å, indicates that the z-positions of the K+ ions are mainly governed by O2- ions consisting of the hexagonal rings of the topmost cleaved mica plane and not very strongly by Si4+ or Al3+ ions present at the center of each tetrahedron constituting the hexagonal rings. Any effects arising from the difference between the positions of K+ ions for each site could not be detected in the present simulations. 3.2. Constant-Force AFM Images: Strongly Repulsive Loading Force (10 nN). Figure 3 shows simulated AFM images for each of the three tip orientations (Figure 3) obtained at a constant repulsive loading force of 10 nN. In the figure large, medium, and small circles indicate K+, O2-, and Si4+ (or Al3+) ions, respectively. With the θs orientation of the tip apex (Figure 3a), the brightest spots appear at the positions of K+ ions. The hexagonal oxygen rings are also seen with weaker contrast. Overall, the θs orientation faithfully reproduces the atomic arrangement of the cleaved mica surface. This result has been expected, since the tip with this orientation has a single atomic entity at its apex, which is an essential condition for having an atomic resolution as numbers of simulations14-19 and experimental observations20 show. With the θt1 orientation (Figure 3b), three bright spots appear centered at the position of a K+ ion. This is a reflection of the tip apex geometry by the K+ ions. A striking feature of this image is that the observed bright spots exactly correspond to the hexagonal arrangement of the basal oxygen rings, although each spot is not located at an actual oxygen position that is indicated by a medium-sized circle in the figure. It is also noted that a weak feature is observed at Si (or Al) positions, while at a basal oxygen location no contrast is visible. With the θt2 orientation (Figure 3c), the atomic arrangement of the tip apex is again reflected in the K+ image. The bright spots form centered hexagons, with the central spots slightly off-axis. With lower resolution the image may be taken as resolving all the basal oxygen atoms and the K+ ions. With this tip orientation no other spots with weaker contrast are apparent.
Figure 3. Simulated constant-force AFM images taken with the applied force of 10 nN for the tip orientations θs (a), θt1 (b), and θt2 (c).
It is again noted that in those constant-force AFM images no essential differences were observed between the SiO44- and AlO45- tetrahedrons, as well as between the K+ ions present on sites A and B. 3.3. Constant-Force AFM Images: Weakly Repulsive Loading Force (2 nN). Similar calculations were performed with a weaker repulsive loading force of 2 nN. Figure 4 shows the simulated results for each of the three tip orientations. Weaker applied force means longer tip-to-sample distances, and our earlier calculations13,14 indicated that this necessarily means the loss of resolution. For the single-atom tip (θs orientation) no resolution loss is observed, and the atom-resolved image is still obtained (Figure 4a). For the trimer tips (θt1 and θt2 orientations) three clear spots observed at the applied force of 10 nN (Figures 3b,c) were blurred into a trigonal spot at the K+ position (Figures 4b,c). Figure 4b may be seen as having a hexagonal ring structure, while Figure 4c may be considered as observing K+ ions. 3.4. Constant-Force LFM Images. Figures 5 and 6 show LFM images (the distribution of the x force component) for
AFM Images of Cleaved Mica Surfaces
Figure 4. Simulated constant-force AFM images taken with the applied force of 2 nN for the tip orientations θs (a), θt1 (b), and θt2 (c).
each of the three tip orientations with a constant repulsive loading force of 10 and 2 nN, respectively. Comparison of the 10 nN AFM and LFM images (Figures 3 and 5, respectively) indicates that the symmetries of the observed images are very similar to each other. For the single-atom tip (θs orientation) the x lateral force (Figure 5a) changes its sign from positive to negative at each oxygen and K+ positions, resolving all the surface atoms. The difference between the AFM (Figure 3a) and LFM is that the contrast of oxygen atoms is weaker than that of K+ ions in the AFM image, while they show almost comparable contrast in the LFM image. Similar observations are made for the θt1 orientation, and the LFM image (Figure 5b) resolves all the atoms observed in the AFM image (Figure 3b), with stronger contrast for the points corresponding to the Si or Al positions. Essentially the same may be said for the applied force of 2 nN (Figures 4 and 6). With the trimer tip orientations the observed LFM images (Figures 5c, 6b,c) could be considered as observing K+ ions or as observing the oxygen basal rings, depending on the data processing conditions.
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Figure 5. Simulated constant-force LFM images taken with the applied force of 10 nN for the tip orientations θs (a), θt1 (b), and θt2 (c).
4. Discussion The present simulation results in interesting observations when it is compared with actual mica AFM images. First, the present simulation indicates that it should be able to resolve all the K+ ions and oxygen atoms on the cleaved surface (cf. Figure 3a), if we have a tip with single atom at its apex. To our knowledge such images have not been reported in the literature, nor have we been able to obtain one in our own AFM observations. This may indicate the difficulty in obtaining and maintaining a single-atom tip in the actual AFM experiments.20 The second and very striking observation is that there exist cases in which images corresponding to the basal oxygen rings are observed, despite the fact that K+ is still present on the surface (cf. Figures 3b,c). Although the appearance of such images seems to depend on the symmetry at the tip apex, the occurrence of such a configuration may be far more likely, considering the difficulty of having a single-atom tip stated above. Loading force apparently has a strong influence on the observed images, by governing the tip-sample distance. The
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Tsujimichi et al. on cantilever movement depends on the cantilever alignment and scan direction,11 it should not be neglected in the interpretations of actual AFM images. A note should also be added here on the effect of much higher loading force. Early ambient mica surface observations are sometimes done with fairly high loading force, on, for instance, the order of micronewtons.8 Under such a high load an AFM tip cannot sustain a single-atom apex and may deform to give an apex consisting of a relatively large number of atoms, as may be indicated by molecular dynamics (MD) simulations.11,21 A surprising result of these simulations with such multiple-atom apexes is that they still produce periodic images that correspond to the sample surface periodicity. The obtained image is not a “true” atomic image, however, since it consists of interferences among the forces felt by an individual apex atom, as exemplified by an appearance of a false atom at a point defect site.14,18 Recent contact-mode AFM observations tend to employ lower applied forces on the order of nanonewtons5,22 in order to avoid damages on both the tip apex and sample surfaces, resulting in well-resolved surface atom images. In summary, we have shown that there exist situations in which K+ ions present on cleaved mica surfaces may not appear in AFM images. The situation depends on the tip apex symmetry, as well as image resolution that may be governed by applied force or tip-sample distance. The importance of taking into account the effect of lateral forces in the interpretation of contact-mode AFM images was pointed out. References and Notes
Figure 6. Simulated constant-force LFM images taken with the applied force of 2 nN for the tip orientations θs (a), θt1 (b), and θt2 (c).
distance in turn governs the resolution, particularly for isotropic potentials.13,14 Thus these images may take various forms depending on the applied force, or tip-sample distance. It should be noted that the absolute value of the force examined in this simulation is not important, since it may strongly depend on the size of the simulated tip.14 Compounded to the problem is the presence of lateral force. The way the lateral force is convoluted in the AFM image depends on the cantilever alignment-scan direction relation.11 Briefly, if we have a cantilever aligned with the scanning direction x, the lateral force either pushes up or pulls down the cantilever, which will be recorded as height variations. In the simulated LFM images shown in Figure 5, calculated lateral forces amount to 7-8 nN full scale, which is almost comparable to the applied force of 10 nN. While the effect of lateral forces
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