**1. Introduction**

Atomic force microscopy (AFM) has been a very useful tool in interrogating the micron-tonano sized structures at both atomic and subnanometer resolution. AFM allows both imaging of surfaces and interactions with surfaces of interest to help researchers explain the crystal lattice structure, and surface chemical and mechanical properties at nano scale. Since the invention of AFM, one has been frequently attracted by AFM images when browsing through many scientific publications in physics, chemistry, materials, geology, and biology (Gan, 2009; Sokolov *et al.*, 1999; Wicks *et al.*, 1994). AFM has been successfully used for imaging solid surfaces with subnanometer resolution for natural materials such as minerals, synthetic materials such as polymers and ceramics, and biological materials such as live organisms. There are also numerous reports of molecular and subnanometer resolution on biological and polymer samples.

Atomic force microscopy (AFM) has been quite successfully used by scientists and researchers in obtaining the atomic resolution images of mineral surfaces. It is quite amazing to see the individual atoms, and their arrangements, that make up the surfaces. In some cases, atoms from the mineral surfaces can be deliberately removed with the AFM so that the internal structure of the surface can be studied.

The key to obtaining atomic-scale imaging is precisely control the interactions between the atoms of the scanning tip and the atoms of the surface being studied. Ideally a single atom of the tip is attracted or repelled by successive atoms of the surface being studied. However, this is a dynamic environment and there can be accidental or deliberate wear of the tip and the surface, so the situation is far from ideal. A number of theoretical and practical studies have added some understanding of this interaction but our understanding is still incomplete (Nagy, 1994). Despite the imperfect knowledge, application of the instrument to mineral studies demonstrates that the AFM works well, often at atomic scale resolution.

It is now well established with some success that AFM can also be used to investigate the crystal lattice structure of mineral surfaces. Atomic resolution has been successfully obtained on graphite (Albrecht & Quate, 1988; Sugawara *et al.*, 1991), molybdenum sulfide (Albrecht & Quate, 1988), boron nitride (Albrecht & Quate, 1987), germanium (Gould *et al.*, 1990), sapphire (Gan *et al.*, 2007), albite (Drake & Hellmann, 1991), calcite (Ohnesorge & Binnig, 1993) and sodium chloride (Meyer & Amer, 1990). The AFM has also been used to

Crystal Lattice Imaging Using Atomic Force Microscopy 3

feedback signals are sent to a signal processing software, which generates a three-

The operating modes of AFM can be divided *into static* (*DC*) *mode* – the probe does not vibrate during imaging, and *dynamic* (*AC*) *mode* – the cantilever is excited to vibrate at or off its resonant frequency. The dynamic mode AFM can be either an amplitude-modulated AFM (AM-AFM) or a frequency-modulated AFM (FM-AFM). Usually, AM-AFM is referred to as intermittent contact mode or tapping mode. The imaging could be conducted by manipulating the repulsive interaction between a probe and the surface, which is referred to as contact mode imaging. When the probe images the surface with an attractive interaction, is usually referred to as non-contact mode. Note that both the DC and AC modes may be operated in contact mode; in most cases, however, DC mode is referred to as contact mode.

The contact mode can be operated in constant force mode or constant height mode, depending on whether the feedback loop is turned on. *Constant force* requires a setpoint that needs to be manually adjusted to compensate for the drift during imaging or to control the tip-surface force. This is done on non-atomically smooth surface. The piezo-drive signal is used for generating the height signal on a topograph. *Constant height* mode is most suitable for scanning atomically smooth surfaces at a fixed setpoint (tip-surface force). The deflection

The intermittent or tapping mode (or AM-AFM) is usually conducted on soft samples, such as loosely attached structure on the surface or even more delicate biological samples such as DNA, cells and micro-organisms. The probe is excited at a setpoint amplitude of cantilever oscillation. The amplitude of the cantilever dampens from full oscillation (non contact) to smaller oscillations when it encounters a structure on the surface (intermittent contact). The change in the amplitude of the probe stores the structural information of the surface, which generates a three-dimensional topograph. A large setpoint amplitude is required in the noncontact region, and a small setpoint amplitude is required in the intermittent contact regime. For example, Gan (Gan, 2009) pointed out that the Magonov group achieved molecular resolution with AM-AFM (Belikov & Magonov, 2006; Klinov & Magonov, 2004) and the Engel group achieved subnanometer resolution on protein

Martin *et al.* (Martin *et al.*, 1987) introduced the concept of non-contact mode (FM-AFM) in 1987 to precisely measure the interaction force between a probe and the surface. During non-contact mode, the probe is excited to oscillate at its resonant frequency. The frequency shift of a probe is monitored, as it encounters a surface structure, which generates surface

of the cantilever is used for generating the height signal on a topograph.

dimensional topograph of the surface.

FM-AFM is usually referred as non-contact mode.

**2.2 Operation modes of AFM** 

**2.2.1 Contact mode** 

**2.2.2 Intermittent or tapping mode** 

samples (Moller *et al.*, 1999).

**2.2.3 Non-contact mode** 

investigate the crystal lattice structure of the tetrahedral layer of clay minerals in 2:1 layer structures, such as muscovite (Drake *et al.*, 1989), illite (Hartman *et al.*, 1990) and montmorillonite (Hartman *et al.*, 1990). Atomic-scale resolution has also been obtained for the basal oxygen atoms of a mixed-layered illite/smectite (Lindgreen *et al.*, 1992), zeolite clinoptilolite (Gould *et al.*, 1990) and hematite (Johnsson *et al.*, 1991).

Wicks *et al.* (Wicks *et al.*, 1992) were probably the first to simultaneously report the surface images of both the tetrahedral and octahedral sheets of lizardite (1:1 layer structure) using AFM, and they identified the surface hydroxyl groups and magnesium atoms in the octahedral sheet. In this way, they identified the two sides of the lizardite clay mineral. The surface images of chlorite (2:1:1-type structure) were also investigated by AFM, and both the tetrahedral sheet and the brucite-like interlayer sheet were observed (Vrdoljak *et al.*, 1994). Recently, Kumai *et al.* (Kumai *et al.*, 1995) examined the kaolinite surface using AFM. They used the "pressed" powder sample preparation technique, and obtained the surface images of both the silica tetrahedral surface and alumina octahedral surface of kaolinite particles.

Despite great success in obtaining atomic resolution, AFM images may be subject to various distortions, such as instrumental noise, drift of the piezo, calibration problem with the piezo, vibrations, thermal fluctuations, artifacts created by the AFM tip, contamination of the mineral or tip surface, and tip induced surface deformations. The initial AFM images are often noisy and suffer from instrumental effects such as image bow due to sample tilt. Some of these problems can be fixed with data processing software by applying appropriate flattening, filter out low frequency noise, and clarify the structural details in an image using two dimensional fast-Fourier transforms (2DFFT). Some of these fixtures will be discussed in the subsequent section of this chapter by following a case study on obtaining crystal lattice images of kaolinite. Similar experimental routine could be applied on obtaining atomic resolution images of any surface of interest.

This chapter summarizes the achievement of AFM to obtain atomic resolution images of mineral surfaces. In particular, a case study for obtaining crystal lattice images on kaolinite surface will be presented. The principles of AFM and its different modes of operation will be introduced. A brief introduction of image acquisition and filtering routines will be discussed followed by tip and surface interaction. This will be followed by different ways to acquire images with atomic resolution. The important issues of reproducibility and artifacts will be discussed. A critical review of literature will be supplemented in each section for obtaining atomic resolution images. Finally, the new challenges for AFM to obtain atomic resolution images on the complex surfaces will be discussed.

## **2. Basic principles and operation modes of AFM**

#### **2.1 Principles of AFM**

An AFM consists of a probe, scanner, controller, and signal processing unit-computer. AFM works by rastering a sharp probe across the surface to obtain a three-dimensional surface topograph. As the probe rasters, it feels the highs and lows of surface topography through complex mechanisms of tip-surface interactions. These signals are sent back via a laser reflected back from the probe surface to a photo-detector. The photo-detector through a feedback control loop, keep the tip at constant height or constant force from the surface. The feedback signals are sent to a signal processing software, which generates a threedimensional topograph of the surface.

#### **2.2 Operation modes of AFM**

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

investigate the crystal lattice structure of the tetrahedral layer of clay minerals in 2:1 layer structures, such as muscovite (Drake *et al.*, 1989), illite (Hartman *et al.*, 1990) and montmorillonite (Hartman *et al.*, 1990). Atomic-scale resolution has also been obtained for the basal oxygen atoms of a mixed-layered illite/smectite (Lindgreen *et al.*, 1992), zeolite

Wicks *et al.* (Wicks *et al.*, 1992) were probably the first to simultaneously report the surface images of both the tetrahedral and octahedral sheets of lizardite (1:1 layer structure) using AFM, and they identified the surface hydroxyl groups and magnesium atoms in the octahedral sheet. In this way, they identified the two sides of the lizardite clay mineral. The surface images of chlorite (2:1:1-type structure) were also investigated by AFM, and both the tetrahedral sheet and the brucite-like interlayer sheet were observed (Vrdoljak *et al.*, 1994). Recently, Kumai *et al.* (Kumai *et al.*, 1995) examined the kaolinite surface using AFM. They used the "pressed" powder sample preparation technique, and obtained the surface images of both the silica tetrahedral surface and alumina octahedral surface of kaolinite particles.

Despite great success in obtaining atomic resolution, AFM images may be subject to various distortions, such as instrumental noise, drift of the piezo, calibration problem with the piezo, vibrations, thermal fluctuations, artifacts created by the AFM tip, contamination of the mineral or tip surface, and tip induced surface deformations. The initial AFM images are often noisy and suffer from instrumental effects such as image bow due to sample tilt. Some of these problems can be fixed with data processing software by applying appropriate flattening, filter out low frequency noise, and clarify the structural details in an image using two dimensional fast-Fourier transforms (2DFFT). Some of these fixtures will be discussed in the subsequent section of this chapter by following a case study on obtaining crystal lattice images of kaolinite. Similar experimental routine could be applied on obtaining

This chapter summarizes the achievement of AFM to obtain atomic resolution images of mineral surfaces. In particular, a case study for obtaining crystal lattice images on kaolinite surface will be presented. The principles of AFM and its different modes of operation will be introduced. A brief introduction of image acquisition and filtering routines will be discussed followed by tip and surface interaction. This will be followed by different ways to acquire images with atomic resolution. The important issues of reproducibility and artifacts will be discussed. A critical review of literature will be supplemented in each section for obtaining atomic resolution images. Finally, the new challenges for AFM to obtain atomic resolution

An AFM consists of a probe, scanner, controller, and signal processing unit-computer. AFM works by rastering a sharp probe across the surface to obtain a three-dimensional surface topograph. As the probe rasters, it feels the highs and lows of surface topography through complex mechanisms of tip-surface interactions. These signals are sent back via a laser reflected back from the probe surface to a photo-detector. The photo-detector through a feedback control loop, keep the tip at constant height or constant force from the surface. The

clinoptilolite (Gould *et al.*, 1990) and hematite (Johnsson *et al.*, 1991).

atomic resolution images of any surface of interest.

images on the complex surfaces will be discussed.

**2.1 Principles of AFM** 

**2. Basic principles and operation modes of AFM** 

The operating modes of AFM can be divided *into static* (*DC*) *mode* – the probe does not vibrate during imaging, and *dynamic* (*AC*) *mode* – the cantilever is excited to vibrate at or off its resonant frequency. The dynamic mode AFM can be either an amplitude-modulated AFM (AM-AFM) or a frequency-modulated AFM (FM-AFM). Usually, AM-AFM is referred to as intermittent contact mode or tapping mode. The imaging could be conducted by manipulating the repulsive interaction between a probe and the surface, which is referred to as contact mode imaging. When the probe images the surface with an attractive interaction, is usually referred to as non-contact mode. Note that both the DC and AC modes may be operated in contact mode; in most cases, however, DC mode is referred to as contact mode. FM-AFM is usually referred as non-contact mode.

#### **2.2.1 Contact mode**

The contact mode can be operated in constant force mode or constant height mode, depending on whether the feedback loop is turned on. *Constant force* requires a setpoint that needs to be manually adjusted to compensate for the drift during imaging or to control the tip-surface force. This is done on non-atomically smooth surface. The piezo-drive signal is used for generating the height signal on a topograph. *Constant height* mode is most suitable for scanning atomically smooth surfaces at a fixed setpoint (tip-surface force). The deflection of the cantilever is used for generating the height signal on a topograph.

#### **2.2.2 Intermittent or tapping mode**

The intermittent or tapping mode (or AM-AFM) is usually conducted on soft samples, such as loosely attached structure on the surface or even more delicate biological samples such as DNA, cells and micro-organisms. The probe is excited at a setpoint amplitude of cantilever oscillation. The amplitude of the cantilever dampens from full oscillation (non contact) to smaller oscillations when it encounters a structure on the surface (intermittent contact). The change in the amplitude of the probe stores the structural information of the surface, which generates a three-dimensional topograph. A large setpoint amplitude is required in the noncontact region, and a small setpoint amplitude is required in the intermittent contact regime. For example, Gan (Gan, 2009) pointed out that the Magonov group achieved molecular resolution with AM-AFM (Belikov & Magonov, 2006; Klinov & Magonov, 2004) and the Engel group achieved subnanometer resolution on protein samples (Moller *et al.*, 1999).

#### **2.2.3 Non-contact mode**

Martin *et al.* (Martin *et al.*, 1987) introduced the concept of non-contact mode (FM-AFM) in 1987 to precisely measure the interaction force between a probe and the surface. During non-contact mode, the probe is excited to oscillate at its resonant frequency. The frequency shift of a probe is monitored, as it encounters a surface structure, which generates surface

Crystal Lattice Imaging Using Atomic Force Microscopy 5

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

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

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

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

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

experiments. They demonstrated that this criticism of 2DFFT is not valid.

refer to Gan (Gan, 2009) for more discussion on probe sizes.

**4. Resolution** 

surface.

**5. Tip-surface interaction** 

in a liquid, and (vi) contamination effects.

topograph. Giessibl (Giessibl, 2000) was able to use an AFM in non-contact mode to obtain atomic resolution images of reactive surfaces such as Si.
