**3. Image acquisition and filtering**

The quality of the raw data is of primary importance in obtaining high resolution AFM images. A good quality raw image must be obtained without the use of online filters. Special attention should be taken in order to determine if an image is of good quality for a particular sample and whether the image is real or not. This is done by varying scan direction and speed, varying instrumental gains and contact force, changing sample locations, retracting and extending the tip, and collecting multiple set of data from different sample and using different tips. Other factors such as varying color contrast/offset, z-height range, and checking for periodicity, by looking at the screen close up and from a distance, are important.

Once a good raw image has been obtained, some filtering can be applied to enhance the features seen in the image, and to distinguish between instrumental artifacts and real features. A filtered image should always be compared to the unfiltered image as a cross check to ensure that artifacts have not been introduced as a result of filtering.

A variety of data processing programs are available to filter images. These will vary from instrument to instrument and are explicitly described in the user's manual. Some of the commonly followed filter routines are described below.

#### **3.1 Flattening**

Flattening subtracts the average value of the height of each scan line from each point in the scan line and reduces the effect of image bow and vibration in the *Y* direction. This could be applied automatically during real time imaging or manually after the image is captured. At times, a plane is fitted to the captured image. Plane fit calculates a best fit second order polynomial plane, and subtracts it from the image. Usually this is applied once in *X*  direction and once in *Y* direction

#### **3.2 Low pass / high pass filters**

Lowpass filtering replaces each data point in the image with a weighted average of the 3 x 3 cell of points surrounding and including the point. It may be applied a number of times. This removes the high frequency noise, but it also reduces image resolution by "defocusing" the periodic features observed in the raw data. Highpass filtering on the other hand replaces each data point with a weighted difference between the data point and each of its eight neighbors. This routine is particularly good for enhancing height differences within an image.

#### **3.3 2-Dimensional Fast Fourier Transforms (2DFFT)**

This is the most useful filtering routine which can greatly improve images. This technique converts the image to the frequency domain by calculating the 2-dimensional power spectrum or 2DFFT. The 2DFFT of the image may then be filtered and an inverse transform performed on the filtered data to produce a new image. This routine should be practiced with care by resizing the image to the maximum pixel dimensions, prior to the application of the 2DFFT, and then varying color contrast/offset of the power spectrum image. Some criticism of this technique by AFM users were reported as (1) 2DFFT may introduce the features which are not present in the initial image, and (2) use of a 2DFFT smears the atomic positions so that the resolution of individual atom is not obtained. In first case, it's possible to introduce the artifacts after 2DFFT processing, and it's a matter of experience and competence in selecting or rejecting the right periodicities to obtain an image. In contradiction to the second criticism, Wicks *et al.* (Wicks *et al.*, 1994) successfully reported two different atomic–repeat units of lizardite in a single image during a high tracking force experiments. They demonstrated that this criticism of 2DFFT is not valid.

## **4. Resolution**

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

topograph. Giessibl (Giessibl, 2000) was able to use an AFM in non-contact mode to obtain

The quality of the raw data is of primary importance in obtaining high resolution AFM images. A good quality raw image must be obtained without the use of online filters. Special attention should be taken in order to determine if an image is of good quality for a particular sample and whether the image is real or not. This is done by varying scan direction and speed, varying instrumental gains and contact force, changing sample locations, retracting and extending the tip, and collecting multiple set of data from different sample and using different tips. Other factors such as varying color contrast/offset, z-height range, and checking for periodicity, by looking at the screen close up and from a distance,

Once a good raw image has been obtained, some filtering can be applied to enhance the features seen in the image, and to distinguish between instrumental artifacts and real features. A filtered image should always be compared to the unfiltered image as a cross

A variety of data processing programs are available to filter images. These will vary from instrument to instrument and are explicitly described in the user's manual. Some of the

Flattening subtracts the average value of the height of each scan line from each point in the scan line and reduces the effect of image bow and vibration in the *Y* direction. This could be applied automatically during real time imaging or manually after the image is captured. At times, a plane is fitted to the captured image. Plane fit calculates a best fit second order polynomial plane, and subtracts it from the image. Usually this is applied once in *X* 

Lowpass filtering replaces each data point in the image with a weighted average of the 3 x 3 cell of points surrounding and including the point. It may be applied a number of times. This removes the high frequency noise, but it also reduces image resolution by "defocusing" the periodic features observed in the raw data. Highpass filtering on the other hand replaces each data point with a weighted difference between the data point and each of its eight neighbors. This routine is particularly good for enhancing height differences within an

This is the most useful filtering routine which can greatly improve images. This technique converts the image to the frequency domain by calculating the 2-dimensional power spectrum or 2DFFT. The 2DFFT of the image may then be filtered and an inverse transform

check to ensure that artifacts have not been introduced as a result of filtering.

atomic resolution images of reactive surfaces such as Si.

commonly followed filter routines are described below.

**3.3 2-Dimensional Fast Fourier Transforms (2DFFT)** 

**3. Image acquisition and filtering** 

are important.

**3.1 Flattening** 

image.

direction and once in *Y* direction

**3.2 Low pass / high pass filters** 

AFM is a computer-controlled local probe technique which makes it difficult to give a straightforward definition of resolution. The AFM vertical resolution is mainly limited by thermal noise of the deflection detection system. Most commercial AFM instruments can reach a vertical resolution as low as 0.01 nm for more rigid cantilevers. The lateral resolution of AFM is defined as the minimum detectable distance between two sharp spikes of different heights. A sharp tip is critical for achieving high resolution images. Readers may refer to Gan (Gan, 2009) for more discussion on probe sizes.

Despite great success by researchers in obtaining atomic resolution images, AFM is looked at with doubt as compared to scanning tunneling microscopy. These doubts about resolution have been dispersed. For example, Ohnesorge and Binnig (Ohnesorge & Binnig, 1993) obtained images of the oxygen atoms standing out from the cleavage plane of calcite surface in water. Similarly, Wicks *et al.* (Wicks *et al.*, 1993) used high tracking force to strip away the oxygen and silicon of the tetrahedral sheet to image the interior O, OH plane of lizardite at atomic resolution. Recently, Gupta *et al.* (Gupta *et al.*, 2010) showed high resolution images of silica tetrahedral layer and alumina octahedral layer of kaolinite surface.

#### **5. Tip-surface interaction**

Tip-surface forces are of paramount importance for achieving high resolution AFM images. They can be described based on (i) continuum mechanics, (ii) the long range van der Waals force, (iii) the capillary force, (iv) the short range forces, (v) the electrical double layer force in a liquid, and (vi) contamination effects.

A continuum model treats the materials of the tip and sample as continuum solids. Various continuum models such the Hertz model, the JKR model, the MD model, and the Schwarz model consider mechanical deformation or surface energy alone or both. At high applied force, the tip and the substrate may deform inelastically. One should thus be cautious in using continuum models to predict tip-surface interactions. The van der Waals (vdW) force between macroscopic objects is due to the dispersion interactions of a large number of atoms between two objects interacting across a medium. The strength of the vdW force is measured with the Hamaker constant. The macroscopic vdW force is determined by the

Crystal Lattice Imaging Using Atomic Force Microscopy 7

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

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.

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

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).

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

different instruments and techniques if possible.

**kaolinite** 

resolution obtained using AFM.

**8.1 Materials and methods 8.1.1 Sample preparation** 

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

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 produce high resolution image.
