**6. General tips to achieve atomic resolution**

Atomic resolution images can be obtained by controlling tip-surface interactions as discussed above. In addition to tip-surface interactions, the following suggestions can be made to achieve atomic resolution:


#### **7. Artifacts and reproducibility**

The topographs obtained by AFM should be reproducible and represent the real surface structure of the sample. Artifacts at the atomic scale are topographic features by which uncertainties and errors enter the surface structure determination. There are numerous

properties of the materials and the medium, and the tip geometry. In most cases, vdW forces are attractive between tip and surface of interest. The capillary force arises when tip approaches the surface in air. The water molecules on the surface forms a bridge with the tip and an increased force must be applied in order to detach the tip from the surface. This increased force is called the capillary force, and depends on the surface properties, humidity, temperature and geometry of the tip. The capillary force is usually more longranged than the van der Wall force under moderate humidity conditions. Short-range forces become important when the tip-surface distance is less than 1 nm. Short-range force may originate from Born repulsion, chemical bonding, and electrostatic and vdW interactions between atoms. The electrical double layer force arises when two surfaces approach each other in solution. The surfaces develop charges either by protonation/de-protonation, adsorption, and specific chemical interaction, which attracts counterions and co-ions from solution. Lastly, contaminants, particularly organic materials adheres either to surface or tip, even in trace amounts, can significantly affect the tip-surface interaction. Therefore, a clean tip and surface are highly desirable prior to and throughout the experiments. This is a brief review of tip-surface interactions, and readers are advised to review classic textbooks (Butt

In order to achieve atomic resolution image, the external load on the tip must counteract the tip-surface interactions discussed above. The external load is a function of spring constant of the tip and its bending. It is highly desirable to keep the tip load as low as possible to

Atomic resolution images can be obtained by controlling tip-surface interactions as discussed above. In addition to tip-surface interactions, the following suggestions can be

 Use sharper tips. Weih *et al.* (Weihs *et al.*, 1991) showed by calculations that the lateral resolution increased by a factor of 4 by reducing the tip radius from 200 to 20 nm. The sharper tip also reduces the adhesion force between a tip and the surface, which also

 Use stiffer tips. The elastic modulus could be increased by using a stiffer tip to achieve a smaller contact area between a tip and the surface. The smaller contact area between a tip and the surface is desired so as to realize only few atoms in contact. Ideally, a single atom of the tip should interact with each surface atom to obtain atomic resolution. Reduce tip load. By applying the cantilever bending force, the contact area between a

Reduce adhesion. The work of adhesion can be minimized by immersing the tip and

The topographs obtained by AFM should be reproducible and represent the real surface structure of the sample. Artifacts at the atomic scale are topographic features by which uncertainties and errors enter the surface structure determination. There are numerous

tip and the surface could be reduced by lowering the tip load.

*et al.*, 2003; Israelachvili, 1985; Masliyah & Bhattacharjee, 2006).

**6. General tips to achieve atomic resolution** 

produce high resolution image.

made to achieve atomic resolution:

decrease the tip load.

sample in liquid.

**7. Artifacts and reproducibility** 

types of AFM artifacts, including missing atoms/molecules/vacancies, ghost atoms, and fuzzy steps etc. Most artifacts are caused by multiple-tip surface contacts and high tip loads. Ideally, a single atom tip interacts with the surface to obtain atomically resolved topographs. In reality, however, the structure, geometry, and surface chemistry of the AFM tips are usually poorly defined. During imaging, the AFM tip may get deformed and cause multiple point contacts. It is therefore highly desirable to monitor the structural and chemical modification of the tip before and after experiments. Equally, the low tip load is desirable for achieving high resolution atomic images. Ohnesorge and Binnig (Ohnesorge & Binnig, 1993) have demonstrated the dramatic change in topograph by carefully controlling the tipsurface interaction. Sokolov and Henderson (Sokolov & Henderson, 2000) also showed that an increased tip load destroys the atomically resolved images determined from the vertical force contrast and only improves lattice resolution images determined from the friction forces. Cleveland *et al.* (Cleveland *et al.*, 1995) also showed through atomic imaging of calcite and mica surfaces in water, that surface atoms could only be unambiguously identified when the tip load was attractive. It is thus highly recommended that one be cautious in interpreting AFM images before systematic studies of the tip load effect are carried out.

The AFM images should show the real surface structure and be reproducible. The surface structure should remain unchanged with varying probes, scanning directions, different location on the same surface, different sample of same material, tip-surface forces, and even different instruments and techniques if possible.

Finally, more confidence in the recorded AFM topographs will be gained if the same surface can be analyzed with other techniques such as STM, high resolution transmission electron microscopy, x-ray crystallography etc. Electron microscopy requires complex surface preparation procedures, but they are free from artifacts introduced in AFM images. These alternative techniques may compliment AFM in obtaining and verifying the atomic images.

## **8. Case study: Crystal lattice imaging of silica face and alumina face of kaolinite**

Kaolinite naturally exists as pseudo-hexagonal, platy-shaped, thin particles generally having a size of less than one micron extending down to 100 nm. The crystallographic structure of kaolinite suggests that there should be two types of surface faces defined by the 001 and the 001 basal planes. In this way, one face should be described by a silica tetrahedral surface and the other face should be described by an aluminum hydroxide (alumina) octahedral surface as shown in figure 1. The objective of this case study is to demonstrate the bi-layer structure of kaolinite – a silica tetrahedral layer and an alumina octahedral layer, through atomic resolution obtained using AFM.

#### **8.1 Materials and methods**

#### **8.1.1 Sample preparation**

A clean English kaolin (Imerys Inc., UK) was obtained from the St. Austell area in Cornwall, UK. The sample was cleaned with water and elutriation was used to achieve classification at a size of less than 2 µm. No other chemical treatment was done. Further details about the kaolinite extraction and preparation are given in the literature (Bidwell *et al.*, 1970).

Crystal Lattice Imaging Using Atomic Force Microscopy 9

The kaolinite suspension (1000 ppm) was prepared in high purity Milli-Q water (Millipore Inc.) with a resistivity of 18.2 MΩ-cm. The pH was adjusted to 5.5 using 0.1 M HCl or 0.1 M

Two substrates – a mica disc (ProSciTech, Queensland, Australia) and a fused alumina substrate (Red Optronics, Mountain View, CA), were used to order the kaolinite particles (Gupta & Miller, 2010). The kaolinite particle suspension (1000 ppm) was sonicated for 2 minutes, and about 10 µl of the suspension was air-dried overnight on a freshly cleaved mica substrate under a petri-dish cover in a laminar-flow fume hood. In this way, the kaolinite particles attach to the mica substrate with the alumina face down exposing the silica face of kaolinite, as shown from previous surface force measurements (Gupta & Miller, 2010), i.e., the positively charged alumina face of kaolinite is attached to the negatively

The fused alumina substrate was cleaned using piranha solution (a mixture of sulfuric acid and hydrogen peroxide in a ratio of 3:1) at 1200C for 15 minutes, followed by rinsing with copious amounts of Milli-Q water, and finally blown dry with ultra high purity N2 gas. A 10 µl kaolinite suspension was applied to the alumina substrate and dried in the same manner as the mica. It was found that the alumina face of kaolinite was exposed on the fused alumina substrate based on previous surface force measurements (Gupta & Miller, 2010), i.e., the negatively charged silica face of kaolinite is attached to the positively charged fused-

The samples were prepared the night before AFM analysis and stored in a desiccator until their use. Just prior to the AFM experiments, the substrates were sonicated for a minute in Milli-Q water to remove loosely adhered kaolinite particles, washed with Milli-Q water, and gently blown with N2 gas before AFM investigation. All substrates were attached to a

A Nanoscope AFM with Nanoscope IV controller (Veeco Instruments Inc., Santa Barbara, CA) was used with an E-type scanner. Triangular beam silicon nitride (Si3N4) cantilevers (Veeco Instruments Inc., Santa Barbara, CA), having pyramid-shaped tips with spring constants of about 0.58 N/m, were used. The cantilevers were cleaned using acetone, ethanol, water in that order, and gently dried with ultra high purity N2 gas. The cantilevers were subsequently cleaned in a UV chamber for 30 minutes prior to use. The substrates were loaded on AFM equipped with a fluid cell. The contact mode imaging was done in Milli-Q water. The AFM instrument was kept in an acoustic and vibration isolation chamber. The imaging was commenced 30 minutes after sample loading to allow the thermal vibration of the cantilever to equilibrate in the fluid cell. First, an image of the particles was obtained at a scan rate of 1 Hz and scan area of 1 µm. Subsequently, the atomic resolution imaging was completed using the zoom-in and offset feature of the Nanoscope vs. 5.31R1 software (Veeco Instruments Inc., Santa Barbara, CA) to scan an area of 12 nm on the particle surface. The atomic imaging was obtained at a scan rate of 30 Hz at scan angle of 800–900 with very low

KOH solutions.

**8.1.2 Substrate preparation** 

charged mica substrate.

alumina substrate.

standard sample puck using double-sided tape.

**8.1.3 Atomic Force Microscopy** 

Fig. 1. Side view (A) and Top view (B) of kaolinite (001) surface structure. The silica tetrahedra (red: oxygen, blue: silicon) and alumina octahedra (yellow: aluminum, green: hydroxyl) bilayers thought to be bound together via hydrogen bonding are illustrated in (A).

The kaolinite suspension (1000 ppm) was prepared in high purity Milli-Q water (Millipore Inc.) with a resistivity of 18.2 MΩ-cm. The pH was adjusted to 5.5 using 0.1 M HCl or 0.1 M KOH solutions.

#### **8.1.2 Substrate preparation**

8 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

Fig. 1. Side view (A) and Top view (B) of kaolinite (001) surface structure. The silica tetrahedra (red: oxygen, blue: silicon) and alumina octahedra (yellow: aluminum, green: hydroxyl) bilayers thought to be bound together via hydrogen bonding are illustrated in (A).

**A**

**B**

Two substrates – a mica disc (ProSciTech, Queensland, Australia) and a fused alumina substrate (Red Optronics, Mountain View, CA), were used to order the kaolinite particles (Gupta & Miller, 2010). The kaolinite particle suspension (1000 ppm) was sonicated for 2 minutes, and about 10 µl of the suspension was air-dried overnight on a freshly cleaved mica substrate under a petri-dish cover in a laminar-flow fume hood. In this way, the kaolinite particles attach to the mica substrate with the alumina face down exposing the silica face of kaolinite, as shown from previous surface force measurements (Gupta & Miller, 2010), i.e., the positively charged alumina face of kaolinite is attached to the negatively charged mica substrate.

The fused alumina substrate was cleaned using piranha solution (a mixture of sulfuric acid and hydrogen peroxide in a ratio of 3:1) at 1200C for 15 minutes, followed by rinsing with copious amounts of Milli-Q water, and finally blown dry with ultra high purity N2 gas. A 10 µl kaolinite suspension was applied to the alumina substrate and dried in the same manner as the mica. It was found that the alumina face of kaolinite was exposed on the fused alumina substrate based on previous surface force measurements (Gupta & Miller, 2010), i.e., the negatively charged silica face of kaolinite is attached to the positively charged fusedalumina substrate.

The samples were prepared the night before AFM analysis and stored in a desiccator until their use. Just prior to the AFM experiments, the substrates were sonicated for a minute in Milli-Q water to remove loosely adhered kaolinite particles, washed with Milli-Q water, and gently blown with N2 gas before AFM investigation. All substrates were attached to a standard sample puck using double-sided tape.

#### **8.1.3 Atomic Force Microscopy**

A Nanoscope AFM with Nanoscope IV controller (Veeco Instruments Inc., Santa Barbara, CA) was used with an E-type scanner. Triangular beam silicon nitride (Si3N4) cantilevers (Veeco Instruments Inc., Santa Barbara, CA), having pyramid-shaped tips with spring constants of about 0.58 N/m, were used. The cantilevers were cleaned using acetone, ethanol, water in that order, and gently dried with ultra high purity N2 gas. The cantilevers were subsequently cleaned in a UV chamber for 30 minutes prior to use. The substrates were loaded on AFM equipped with a fluid cell. The contact mode imaging was done in Milli-Q water. The AFM instrument was kept in an acoustic and vibration isolation chamber. The imaging was commenced 30 minutes after sample loading to allow the thermal vibration of the cantilever to equilibrate in the fluid cell. First, an image of the particles was obtained at a scan rate of 1 Hz and scan area of 1 µm. Subsequently, the atomic resolution imaging was completed using the zoom-in and offset feature of the Nanoscope vs. 5.31R1 software (Veeco Instruments Inc., Santa Barbara, CA) to scan an area of 12 nm on the particle surface. The atomic imaging was obtained at a scan rate of 30 Hz at scan angle of 800–900 with very low

Crystal Lattice Imaging Using Atomic Force Microscopy 11

Fig. 2. Crystal lattice imaging of mica substrate showing (A) Flattened height image, (B) FFT spectra, (C) FFT transformed flattened height image, and (D) Zoomed-in image of (C) of scan area of 36 nm2. The six light spots in (D) show the hexagonal ring of oxygen atoms

substrates (compare Figure 8.2D, Figure 8.4D, and Figure 8.5D). The image shown in Figure 8.5D is similar to the octahedral sheet of lizardite (Wicks *et al.*, 1992), the internal octahedral sheets of micas and chlorite (Wicks *et al.*, 1993), and the brucite-like layers of hydrotalcite (Cai *et al.*, 1994). The octahedral sheet of kaolinite consists of a plane of hydroxyls on the surface. The average hydroxyl-hydroxyl distance of the octahedral sheet is 0.36 ± 0.04 nm which is in reasonable agreement with the literature value of 0.29 nm (Wyckoff, 1968). For a kaolinite pellet, Kumai *et al.* (Kumai *et al.*, 1995) observed the distance between the hydroxyl

around the dark spots representing a hole. Adapted from (Gupta *et al.*, 2010).

**A B**

**C D**

atoms as 0.33 nm.

integral and proportional gain (0.06). The online filters (low pass and high pass) were turned off during the online crystal lattice imaging.

During offline image processing, flattening and low pass filtering were applied to obtain clear images using Nanoscope vs. 5.31R1 software. The images were further Fourier-filtered (2D FFT) to obtain the crystal lattice images using SPIP software (Image Metrology A/S, Denmark).

#### **8.2 Results and discussion**

In order to obtain the crystal lattice imaging of the silica face and alumina face of kaolinite, the scanner was first calibrated using a mica substrate. Figure 8.2 presents the crystal lattice imaging of mica, which shows the height image, fast-Fourier transform (FFT) spectra and the FFT transformed height image. In order to make sure that the image is real, the imaging was acquired from other locations on the mica substrate and also with varying scan size and scan angle. The repeated pattern of dark and light spots was reproducible and the dark spots observed were scaled appropriately with the scan size and angle. The images showed some drift in both x and y direction during imaging. The dark spots in Figures 8.2C and 8.2D correspond to a hole surrounded by the hexagonal lattice of oxygen atoms. The light spots are attributed to the three-surface oxygen atoms forming a SiO4 tetrahedron or pairs of SiO4 tetrahedra forming a hexagonal ring-like network. Similar images were reported for the 1:1 type clay mineral, lizardite (Wicks *et al.*, 1992) and other 2:1 type clay minerals (Drake *et al.*, 1989; Hartman *et al.*, 1990; Sharp *et al.*, 1993) from AFM observations on a single crystal. The fast-Fourier transform showed the intensity peaks of oxygen atoms arranged in a hexagonal ring network (see Figure 8.2B). The crystal lattice spacing between neighboring oxygen atoms was calculated as 0.51 ± 0.08 nm, from the average of 10 neighboring atoms. This is in very good agreement with the literature value of 0.519 nm (Wicks *et al.*, 1993).

Figure 8.3 shows an image of a kaolinite particle on a mica substrate. The image shows the platy nature and the pseudo-hexagonal shape of the kaolinite particle. The scanning was sequentially zoomed on the particle. Figure 8.4 shows the crystal lattice imaging of the silica face of a kaolinite particle on the mica substrate. The flattening and low pass filtering was applied to the height image in an offline mode (see Figure 8.4B). The FFT spectra showed the similar intensity of peaks of oxygen atoms arranged in a hexagonal ring network as observed for the mica substrate. As expected, the silica face of kaolinite showed the similar hexagonal ring-like network of oxygen atoms as observed on the mica substrate (compare Figure 8.2D and Figure 8.4D). Note that the scan scale for the image of the silica face of kaolinite was twice that used for the mica substrate (12 nm vs. 6 nm), which shows the reproducibility of the crystal lattice images obtained on different substrates. The crystal lattice spacing between neighboring oxygen atoms was calculated as 0.50 ± 0.04 nm, from the average of 10 neighboring atoms. This lattice spacing is in good agreement with 0.53 nm as reported in the literature (Kumai *et al.*, 1995).

The crystal lattice imaging of the alumina face of kaolinite on a fused alumina substrate is shown in Figure 8.5. The FFT spectra shows the intensity peaks of the hydroxyl atoms forming a hexagonal ring network similar to that obtained on the silica face of kaolinite (see Figure 8.5C). Notice that the hexagonal ring of hydroxyls shows the inner hydroxyl in the center of the ring instead of a hole as observed for the silica face of kaolinite and mica

integral and proportional gain (0.06). The online filters (low pass and high pass) were turned

During offline image processing, flattening and low pass filtering were applied to obtain clear images using Nanoscope vs. 5.31R1 software. The images were further Fourier-filtered (2D FFT) to obtain the crystal lattice images using SPIP software (Image Metrology A/S,

In order to obtain the crystal lattice imaging of the silica face and alumina face of kaolinite, the scanner was first calibrated using a mica substrate. Figure 8.2 presents the crystal lattice imaging of mica, which shows the height image, fast-Fourier transform (FFT) spectra and the FFT transformed height image. In order to make sure that the image is real, the imaging was acquired from other locations on the mica substrate and also with varying scan size and scan angle. The repeated pattern of dark and light spots was reproducible and the dark spots observed were scaled appropriately with the scan size and angle. The images showed some drift in both x and y direction during imaging. The dark spots in Figures 8.2C and 8.2D correspond to a hole surrounded by the hexagonal lattice of oxygen atoms. The light spots are attributed to the three-surface oxygen atoms forming a SiO4 tetrahedron or pairs of SiO4 tetrahedra forming a hexagonal ring-like network. Similar images were reported for the 1:1 type clay mineral, lizardite (Wicks *et al.*, 1992) and other 2:1 type clay minerals (Drake *et al.*, 1989; Hartman *et al.*, 1990; Sharp *et al.*, 1993) from AFM observations on a single crystal. The fast-Fourier transform showed the intensity peaks of oxygen atoms arranged in a hexagonal ring network (see Figure 8.2B). The crystal lattice spacing between neighboring oxygen atoms was calculated as 0.51 ± 0.08 nm, from the average of 10 neighboring atoms. This is in very good agreement with the literature value of 0.519 nm (Wicks *et al.*, 1993).

Figure 8.3 shows an image of a kaolinite particle on a mica substrate. The image shows the platy nature and the pseudo-hexagonal shape of the kaolinite particle. The scanning was sequentially zoomed on the particle. Figure 8.4 shows the crystal lattice imaging of the silica face of a kaolinite particle on the mica substrate. The flattening and low pass filtering was applied to the height image in an offline mode (see Figure 8.4B). The FFT spectra showed the similar intensity of peaks of oxygen atoms arranged in a hexagonal ring network as observed for the mica substrate. As expected, the silica face of kaolinite showed the similar hexagonal ring-like network of oxygen atoms as observed on the mica substrate (compare Figure 8.2D and Figure 8.4D). Note that the scan scale for the image of the silica face of kaolinite was twice that used for the mica substrate (12 nm vs. 6 nm), which shows the reproducibility of the crystal lattice images obtained on different substrates. The crystal lattice spacing between neighboring oxygen atoms was calculated as 0.50 ± 0.04 nm, from the average of 10 neighboring atoms. This lattice spacing is in good agreement with 0.53 nm

The crystal lattice imaging of the alumina face of kaolinite on a fused alumina substrate is shown in Figure 8.5. The FFT spectra shows the intensity peaks of the hydroxyl atoms forming a hexagonal ring network similar to that obtained on the silica face of kaolinite (see Figure 8.5C). Notice that the hexagonal ring of hydroxyls shows the inner hydroxyl in the center of the ring instead of a hole as observed for the silica face of kaolinite and mica

off during the online crystal lattice imaging.

as reported in the literature (Kumai *et al.*, 1995).

Denmark).

**8.2 Results and discussion** 

Fig. 2. Crystal lattice imaging of mica substrate showing (A) Flattened height image, (B) FFT spectra, (C) FFT transformed flattened height image, and (D) Zoomed-in image of (C) of scan area of 36 nm2. The six light spots in (D) show the hexagonal ring of oxygen atoms around the dark spots representing a hole. Adapted from (Gupta *et al.*, 2010).

substrates (compare Figure 8.2D, Figure 8.4D, and Figure 8.5D). The image shown in Figure 8.5D is similar to the octahedral sheet of lizardite (Wicks *et al.*, 1992), the internal octahedral sheets of micas and chlorite (Wicks *et al.*, 1993), and the brucite-like layers of hydrotalcite (Cai *et al.*, 1994). The octahedral sheet of kaolinite consists of a plane of hydroxyls on the surface. The average hydroxyl-hydroxyl distance of the octahedral sheet is 0.36 ± 0.04 nm which is in reasonable agreement with the literature value of 0.29 nm (Wyckoff, 1968). For a kaolinite pellet, Kumai *et al.* (Kumai *et al.*, 1995) observed the distance between the hydroxyl atoms as 0.33 nm.

Crystal Lattice Imaging Using Atomic Force Microscopy 13

Fig. 4. Crystal lattice imaging of the silica face of kaolinite showing (A) Theoretical atomic lattice structure, (B) Flattened-low pass filtered height image, (C) FFT spectra, and (D) FFT transformed flattened-low pass filtered height image of scan size 36 nm2. The six black circles in (D) show the hexagonal ring of oxygen atoms around the dark spots representing a

**A B**

**C D**

hole. Adapted from (Gupta *et al.*, 2010).

Fig. 3. (A) Topography, and (B) Deflection images of kaolinite particle on the mica substrate. Adapted from (Gupta *et al.*, 2010).

Fig. 3. (A) Topography, and (B) Deflection images of kaolinite particle on the mica substrate.

**A**

**B**

Adapted from (Gupta *et al.*, 2010).

Fig. 4. Crystal lattice imaging of the silica face of kaolinite showing (A) Theoretical atomic lattice structure, (B) Flattened-low pass filtered height image, (C) FFT spectra, and (D) FFT transformed flattened-low pass filtered height image of scan size 36 nm2. The six black circles in (D) show the hexagonal ring of oxygen atoms around the dark spots representing a hole. Adapted from (Gupta *et al.*, 2010).

Crystal Lattice Imaging Using Atomic Force Microscopy 15

Looking ahead, we must face several challenges to produce fast and reproducible atomic resolution images. One should be skeptical of high resolution topographs, and do diligent work in reporting data. The image acquisition procedures and filtering routines discussed in this chapter should be applied judiciously. One should be aware of artifacts introduced during real-time image acquisition or post processing should be dealt with cautiously, and must be reported. Probes play a key role in realizing high resolution topographs. The benefits of sharper tips are numerous, such as smaller contact area and reduced long range forces. Most conventional tips are made from silicon nitride and silicon. Polymers or diamond tips have also used in some applications (Beuret *et al.*, 2000). Recent developments in producing nano-tips through whiskers or carbon fiber may find potential application in

Recent developments on cantilever dynamic studies (Holscher *et al.*, 2006; Strus *et al.*, 2005) and new experimental techniques, such as Q-control (Ebeling *et al.*, 2006; Okajima *et al.*, 2003) and higher order vibration imaging (Martinez *et al.*, 2006) will very likely make AFM a powerful tool for high resolution characterization in the future. Despite recent developments in AFM instrumentation for precise control of tip movement, it is still highly desirable to confirm the reliability of AFM topographs with complimentary techniques such as transmission electron microscopy (Matsko, 2007). We can conclude that AFM is a

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Fig. 5. Crystal lattice imaging of the alumina face of kaolinite showing (A) Theoretical atomic lattice structure, (B) Flattened-low pass filtered height image, (C) FFT spectra, and (D) FFT transformed flattened-low pass filtered height image of (B). The seven black circles in (D) show the hexagonal ring of hydroxyl atoms with a central inner hydroxyl atom. Adapted from (Gupta *et al.*, 2010).
