17.4.1 Buoyancy

Thermogravimetric kinetic measurement will be perturbed, and errors introduced in all cases where buoyancy varies with time. To illustrate this, consider a solid of volume V immersed at temperature T in a perfect gas mixture of mean molar mass M at a pressure P. The effect of buoyancy can then be described by

17.1

where g is the acceleration due to gravity and α the ratio T°/P°V° of the temperature, pressure, and molar volume of gases under normal conditions. This relation first shows that buoyancy depends on temperature so that temperature variations during the experiment lead to apparent mass changes, but these are easy to calculate. As example, consider a typical rectangular sample with dimensions 20 × 10 × 2 mm³ placed in oxygen. Heating this sample from room temperature to 1000 °C will lead to an apparent increase in mass of approximately 0.5 mg. It can be ascertained that, to achieve maximum balance sensitivity under nominally isothermal measurements, care must be taken to ensure a high standard of temperature control of the furnace. For example, with temperature variations of ±3 °C near 300 °C, the apparent mass variations are of the order of ±2 µg; at higher temperatures, the error in the determination of mass is less, e.g. ±0.3 µg at 1000 °C, because of the lower gas density. Buoyancy force variations with the increase of sample volume during oxidation can also be calculated but are generally negligible compared with the accuracy of the thermobalances.

17.4.2 Convection Currents

Convection currents result from the effect of gravity on temperature‐induced differences in the specific mass of gas at different locations within the reaction vessel. They become noticeable for pressures greater than 100–200 mbar and are manifested by convection loops that can perturb the thermogravimetric measurements.

In open static reaction vessels, the convection loops curl outside the reaction vessel, and the well‐known chimney effect is observed (Figure 17.6a). Such a configuration has to be avoided, or one end of the reaction vessel has to be plugged.

In closed static reaction vessels, convection may occur due to radial temperature gradients, as shown schematically in Figure 17.6b where the sample is envisaged to have a temperature slightly lower than that of the vessel wall. The convection loops in this case lead to an apparent mass increase. Near the top of the furnace, where strong radial and longitudinal gradients are present, convection phenomena are present. Such a region (20 cm above the furnace) is subject to turbulence that may be minimized by the use of thin suspension wires having no geometrical irregularities such as asperities or suspension hooks.

A semiquantitative assessment of the importance of these natural thermal gravity convection currents can be obtained through the use of the Rayleigh number, Ra. This dimensionless number is defined as

17.2

where g is the acceleration due to gravity, β the coefficient of thermal expansion of the gas (for a perfect gas: β = 1/T), C_p the thermal capacity of the gas at constant pressure, ρ the density of the gas, b the length of the non‐isothermal zone, ΔT the temperature difference, η the dynamic viscosity of the gas, and K the thermal conductivity of the gas.

For low values of the Rayleigh number (Ra < 40 000), natural thermal gravity convection may be neglected. For higher values, convection loops may perturb thermogravimetric measurements, sometimes creating very strong movements of the sample suspension system and leading to a drastic decrease in accuracy.

In dynamic reaction vessels, the imposed gas flow leads to forced convection whose effects are generally greater than those due to natural convection. The flow behavior within the vessel can then be described by the Reynolds number (Re). This dimensionless number is defined as

17.3

where ρ is the density of the gas, u the linear velocity of the gas, L the characteristic length of the system, and η the dynamic viscosity of the gas, calculated using the following equation:

17.4

where k is the Boltzmann’s constant, m the mass of one gas molecule, T the absolute temperature of the reaction vessel, and σ the mean collisional cross section of a molecule (σ = 4πr², where r is the molecule radius).

This approach, though necessarily simple, provides insights into the factors that affect the accuracy of the experimental values obtained in thermogravimetric tests. It should be noted that the values given for the Rayleigh and Reynolds numbers have to be considered as an order‐of‐magnitude guide only. For example, a gas flow with a Reynolds number of 2000 may be turbulent in a tube of high internal roughness but perfectly laminar in a smooth silica tube.

17.4.3 Thermomolecular Fluxes

In contrast to convection forces, which are active at moderate and high gas pressures, thermomolecular fluxes appear at low pressures in the domain where the gas may be considered as a Knudsen gas. The term Knudsen gas describes a situation where molecules do not collide with each other but only with the vessel wall. Such behavior occurs for values greater than 1 of the dimensionless Knudsen number (Kn):

17.5

where λ is the mean free path of molecules and d is a characteristic distance, e.g. the tube radius for a cylindrical reaction vessel.

In this Knudsen domain, gas pressure relates to temperature according to

17.6

Consider a cylindrical sample immersed in a Knudsen gas and submitted to a temperature difference T₂ − T₁ applied across a horizontal plane whose trace is XY in Figure 17.7. This sample is then submitted to two resulting Knudsen forces:

• A resulting normal Knudsen force, F_n, acting on the horizontal circular section (Figure 17.7a).
  
• A resulting tangential Knudsen force, F_t, acting on the vertical surfaces of the cylindrical sample (Figure 17.7b).

The resulting force F_n arises from the difference in the pressure forces on the two circular bases of the cylinder (Figure 17.7a):

17.7

The resulting tangential force is due to the difference in the momentum of the molecules hitting the vertical surface of the sample and arriving from the upper (hot) or the lower (cold) part of the reaction vessel (Figure 17.7b). Such a force was forecasted by Maxwell (1973). It can be expressed by

17.8

In the intermediate domain, defined by a Knudsen number between 1 and 10⁻⁵, normal and tangential forces are the result of a gas flux generated according to the exchange of momentum between molecules. The calculation of these forces is complex, but it can be shown that they increase with pressure and pass through a maximum before they decrease. This decrease results from the modification of gas properties and the appearance of a regime where the pressure in a closed isothermal vessel has a unique value.

Table 17.2 describes the different gas flow phenomena that may perturb thermogravimetric measurements and identifies the domains where they are active.

In order to limit all the perturbations described above, a symmetrical furnace setup is particularly efficient. In order to optimize performance, both furnaces are operated as nearly as possible at the same temperature and with the same temperature gradients.

Setaram, for example, supplies accurate thermobalances of this type of symmetrical furnaces.

17.6.1 X‐Ray Diffraction

The average bulk structure of many materials can be readily revealed using XRD. The technique provides a measure of the amount of ordered material present and can be used to give an indication of the size of the crystallites that make up the ordered structure.

The samples are usually prepared either as powders in capillaries or spread on a flat sample holder. The XRD pattern is recorded either on film or with a diffractometer. Figure 17.9 shows the arrangement of a powder diffractometer.

The resulting pattern is the amount of scattering over a range of scattering angles, θ, and can be analyzed in terms of diffraction peaks, their positions, and their widths. For the most accurate work, a standard (usually a crystalline salt) is added to the powder to provide internal calibration of the peak positions and widths, thereby allowing any instrumental factors to be taken into account.

Although the main scattering derives from the ordered material present, some indication of the amount of disorder can be obtained by the background scatter. Similarly, the broadening of the diffraction peaks allows an estimation of the mean particle size to be made. Line broadening arises from both the strain or defects in the lattice and the finite crystal size. Assuming that the defects in the lattice reduce the extent of order, an effective crystallite size, t, can be estimated from the amount of broadening, β, using the Scherrer equation

17.9

where λ is the wavelength, θ is the scattering angle, and the value of κ (∼1) depends upon the shape of the crystallite, e.g. κ has the values of 0.9 for L_c and 1.84 for L_a.

β is the amount of broadening due to the sample, and the observed broadening, B, usually needs to be corrected for the instrumental broadening, b, using relationships such as

17.10

The measuring of line broadening is illustrated in Figure 17.10.

The parameters usually quoted from XRD experiments are

• d₍₀₀₂₎ interlayer spacing, L_c stack height, and L_a stack width.

These give some indication of the degree of crystallization of the material. One specialized area of diffraction is that of fiber diffraction. Both normal and small‐angle scattering patterns are used for this investigation. Materials with large surface area can also be successfully investigated by a combination of small (low) and normal (high) angle scattering. Small‐angle scattering has also been used to give some indication of pore structure.

17.6.2 Low‐Energy Electron Diffraction

Scattering of electrons from solid surfaces is one of the paradigms of quantum physics. The pioneering experiments of Davisson and Germer, in 1928, confirmed the Broglie’s concept of the wave nature of particles (de Broglie 1925), a concept at the very heart of quantum mechanics (wave–particle dualism). Already in these early works, they recognized the potential of LEED as a tool for the determination of surface structures and applied it to gas adsorbate layers on Ni(111) (Davisson and Germer 1928a,b). This success was only possible due to two important properties of LEED: surface sensitivity and interference.

In fact, an alternation of the electron beam intensity with sample thickness was observed by Davisson and Germer (1928a,b). Electrons in an LEED experiment have a typical kinetic energy in the range of 20–500 eV.

Experiments with energies below this range are called very low‐energy electron diffraction (VLEED), and those with higher energies medium‐energy electron diffraction (MEED). At even higher energies, one uses grazing electron incidence and emission to obtain surface sensitivity, that is, RHEED. Due to the interaction of the incoming electron with the electrons in the sample, the former penetrates into the solid only a few angstroms. Typical penetration lengths taken from the “universal curve” (Figure 17.11) range from 5 to 10 Å (Rundgren 1999). Therefore, LEED spectra usually carry less information about the geometrical structure of the volume of the solid, i.e. the bulk, than of the solid’s surface region.

Concerning interference, de Broglie showed that a particle with momentum p can be associated with a wave with wavelength 2π/p (p = |p|). For example, an electron in vacuum can be described by a plane wave:

17.11

with wavenumber k = 2π/λ and energy E = ω = k²/2. de Broglie’s picture of electrons as waves and the interpretation of Davisson–Germer LEED experiments lead to the question: Are electrons waves? (Davisson 1928). Comparison was made to X‐ray scattering in view of the determination of structural information, and Davisson came to the conclusion that if X‐rays are waves, then electrons are, too. However, he/she admitted that the picture of electrons as particles is better suited for the explanation of the Compton effect or the photoelectric effect.

The schematic setup of a LEED experiment is shown in Figure 17.12. A monoenergetic beam of electrons with kinetic energy E impinges on the sample. The reflected electron beams are detected and analyzed with respect to their direction and energy. Usually, one detects only elastically reflected electrons (for which the energy is conserved) and uses incidence normal to the surface. Therefore, a set of LEED spectra – or I(E) curves – represents the current I of each reflected beam versus the initial energy E. Note that the reflected intensities are roughly as large as 1/1000 of the incoming intensity.

In the wave picture of electrons, the LEED experiment can be regarded as follows. An incoming plane wave, the incident beam, is scattered at each site, and the outgoing plane waves, the outgoing beams, are measured. Both amplitude and phases of each outgoing wave are determined by the scattering properties and the position of each scatterer. For example, a change in the position of a scatterer will change the wave pattern in the solid and, therefore, will affect both amplitudes and phases of the outgoing waves. Because the LEED current of a beam is given by the wave amplitude, it carries information on both positions and scattering properties of the sites. This mechanism can be used, for instance, to obtain images of the geometrical structure in configuration space by LEED holography (Heinz et al. 2000).

Although LEED is sensitive to the outermost region of the sample, it is capable of detecting fingerprints of the electronic states of the film–substrate system. As mentioned previously, the LEED intensities depend on the electronic structure of the sample above the vacuum level and, therefore, contain information of the electronic structure of the entire film. In particular, quantized states that are confined to the film have a pronounced effect on the LEED spectra.

It took considerable time to develop theories that include multiple scattering of the LEED electron (Kambe 1967), which obviously is necessary for a proper description of LEED spectra. Textbooks that are introduced to the field and present computer codes for the calculation of I(E) spectra were written by Pendry (1974) as well as van Hove et al. (1986). Van Hove and Tong also provide review articles (1979).

Additional information can be obtained if one uses a spin‐polarized beam of incoming electrons, that is, spin‐polarized low‐energy electron diffraction (SPLEED), and uses a spin‐sensitive detector, for example, a Mott detector or a SPLEED detector. Interestingly, the latter exploits the LEED mechanism itself for a spin resolution in the experiment. Pioneering works were carried out by Feder (1985) and by Kirschner and Feder (1979) on the experimental side.

17.6.3 Reflection High‐Energy Electron Diffraction

The short history of RHEED study of oxides is relatively recent, and good general introductions to this matter date from Lagally (1985) and Lagally and Savage (1993); there one can find a clear explanation of the electron diffraction, reciprocal‐space representation, reflection from imperfect surfaces, and so on.

RHEED patterns result from and contain detailed information on the crystalline properties of surfaces. In the field of oxide thin films, RHEED analysis is currently used mainly for qualitative information, simply to watch diffraction problems and to note their evolution in time. Even this can be quite useful and can reveal atomic scale information on how a sample is growing with reference to phenomenology developed by experience. As discussed below, it is possible to distinguish a flat two‐dimensional (2D) surface from one having (usually unwanted) 3D nanoparticles. For the time being, we consider the former case.

At least in principle, the diagnostic value of RHEED monitoring could be substantially increased if it were supplemented by a quantitative analysis of the entire RHEED pattern. Ultimately, one could envision a numerical routine that solves the inverse problem in real time, that is, computes the real‐space atomic arrangement on the surface that corresponds to a given RHEED image.

In Figure 17.13, a schematic of a typical calculation and of an experimental RHEED setup is shown. The electron beam (E) impinges onto the film surface (F) at a nearly grazing angle (θ) and is reflected (E′) onto the screen (S).

The electron beam is coherent over several thousand angstroms and is nearly monoenergetic; in our case, the electron energy is typically ≈8.5–10.0 keV. The film surface is approximated as a perfect but finite rectangular N × M array of atoms with the lattice periods a and b, respectively.

Since typically a ≈ b ≈ 4 Å > λ_e ≈ 0.15 Å, the electrons are strongly diffracted, and one expects to see multiple interference maxima on the screen. In this case, the refinement procedure provides an estimate of the size of in‐plane crystallographic coherence, that is, an estimate of the numbers N and M.

To calculate the diffraction pattern, the scattering contributions from all of the atoms are summed. The resulting intensity distribution on the screen is given by

17.12

where

17.13

and

17.14

where E and m are the electron energy and mass and r = (ia)e_x + (ja)e_z, R_a, X_ae_x + Y_ae_y + Z_ae_z and R = Xe_x + Ye_y + Ze_z are the positions of the (i, j)th atom in the plaquette, the electron source, and the screen pixel, respectively.

When the atoms are not all identical, their contributions are weighted by the respective form factors, S_ij (not shown in Eq. 17.13).

As the first step to aid the reader’s intuition, in Figure 17.13 we show the calculated RHEED patterns for three ideal but finite atomic lattices, 10 × 10, 10 × 100, and 10 × 1000 unit cells, respectively, with a = b = 4 Å. These three cases correspond to different degrees of crystallographic coherence in the direction that the electron beam is propagating. Here we have taken Z_a = Z = 1 000 000 Å, ensuring that we are in the far‐field regime. We set Y_a = 0, which is equivalent to setting the azimuthal angle of the sample crystal to zero; the beam is almost parallel to the <100> film direction, except for the out‐of‐plane tilt by θ = 0.5°. It can be seen from Figure 17.14 that as the long‐range order along the beam direction is increased, the streaks get shorter and eventually evolve into a spot – the specular reflection image of the incoming electron beam. Note that a substantial domain of local flatness is required to obtain coherent scattering into a specularly reflected spot.

The presence of the specular spot is suggestive of essentially perfect crystalline order extending over thousands of unit cells. On the other hand, when they appear as streaks, this shows evidence for the presence of terracing and other surface irregularities. Hence, some amount of surface roughness or disorder typically transforms interference spots into streaks.

In Figure 17.15 we show the calculated RHEED pattern for the same 10 × 10 lattice model as in Figure 17.13a but with Y_a = 200 000 Å; this corresponds to the azimuthal rotation of the sample by arctan(0.2) = 11.3°. As the crystal is rotated around the (001) axis, the pattern apparently changes. Reversing the argument, one can infer the crystal orientation from the shape of the RHEED pattern. In practice, one simply rotates the substrate azimuthal orientation and brings it to a desired “low‐index” orientation for analysis during growth.

In recent years, there has been a surge of interest in deposition of high‐quality (i.e. single‐crystal) films of complex oxides such as cuprate superconductors or perovskite ferroelectrics. The RHEED method is currently one of the important techniques for in situ real‐time analysis of the growing surface of such films.

Here, we have reviewed some basic issues specific to RHEED monitoring of deposition of complex oxides.

The RHEED analysis can be made quantitative. This is being done by performing some numerical simulations and comparing the calculated RHEED patterns with the experimentally observed ones. In the future, it could be expected that real‐time RHEED analysis can and will be further improved. For example, it could be expected that intelligent programs will be developed, including pattern recognition capability based on a built‐in library of RHEED images, to aid the grower and ultimately even to control the growth.

17.6.4 Neutron Scattering

A neutron is an uncharged (electrically neutral) subatomic particle with mass m = 1.675 × 10⁻²⁷ kg (1839 times that of the electron), spin 1/2, and magnetic moment −1.913 nuclear magnetrons. Neutrons are stable when bound in an atomic nucleus while having a mean lifetime of approximately 1000 seconds as a free particle. The neutron and the proton form nearly the entire mass of atomic nuclei, so they are both called nucleons. Neutrons are classified according to their wavelength and energy as “epithermal” for short wavelengths (λ ∼ 0.1 Å) and “thermal” and “cold” for long wavelengths (λ ∼ 10 Å). The desired range of λ is obtained by moderation of the neutrons during their production, either in reactions or spallation sources.

Neutrons interact with matter through strong, weak, electromagnetic, and gravitational interactions. However, it is their interactions via two of these forces – the short‐range strong nuclear force and their magnitude moments – that make neutron scattering such a unique probe for condensed matter research. The most important advantages of neutrons over other forms of radiation in the study of structure and dynamics on a microscopic level are summarized below:

• Neutrons are uncharged, which allows them to penetrate the bulk of materials. They interact via the short‐range strong nuclear force with the nuclei of the material under investigation.
  
• The neutron has a magnetic moment that couples to spatial variations of magnetization on the atomic scale. They are therefore ideally suited to the study of magnetic structures and the fluctuations and excitations of spin systems.

The energy and wavelength of neutrons may be matched, often simultaneously, to the energy and length scales appropriate for the structure and excitations in condensed matter. The wavelength, λ, is dependent on the neutron velocity following the de Broglie relation

17.15

where h is Planck’s constant (6.636 × 10⁻³⁴ J s) and v the particle velocity. The associated kinetic energy is

17.16

Because their energy and wavelength depend on their velocity, it is possible to select a specific neutron wavelength by the time‐of‐flight (TOF) technique. Neutrons do not significantly perturb the system under investigation, so the results of neutron scattering experiments can be clearly interpreted. Neutrons are nondestructive, even to delicate biological materials. The high‐penetrating power of neutrons allows probing the bulk of materials and facilitates the use of complex sample environment equipment (e.g. for creating extremes of pressure, temperature, shear, and magnetic fields). Neutrons scatter from materials by interacting with the nucleus of an atom rather than the electron cloud. This means that the scattering power (cross section) of an atom is not strongly related with its atomic number, unlike X‐rays and electrons where the scattering power increases in proportion to the atomic number. Therefore, with neutrons, light atoms such as hydrogen (deuterium) can be distinguished in the presence of heavier ones. Similarly, neighboring elements in the periodic table generally have substantially different scattering cross sections and so can be distinguished. The nuclear dependence of scattering also allows isotopes of the same element to have substantially different scattering lengths for neutrons. Hence, isotopic substitution can be used to label different parts of the molecules making up a material.

Neutron beams may be produced in two general ways: by nuclear fission in reactor‐based neutron sources or by spallation in accelerator‐based neutron sources. The two world’s most intense neutron sources are the Institut Laue–Langevin (ILL) in Grenoble, France (ILL World Wide Web), and the ISIS facility at the Rutherford Appleton Laboratory in Didcot, UK (ISIS World Wide Web).

Neutrons have traditionally been produced by fission in nuclear reactors optimized for high neutron brightness. In this process, thermal neutrons are adsorbed by uranium‐235 nuclei, which split into fission fragments and evaporate a very high‐energy (megaelectron volts) constant neutron flux (hence the term “steady‐state” or “continuous” source). After the high‐energy (megaelectron volts) neutrons have been thermalized to megaelectron volt energies in the surrounding moderator, beams are emitted with a broad band of wavelengths. The energy distribution of the neutrons can be shifted to higher energy (shorter wavelength) by allowing them to come into thermal equilibrium with a “hot source” (at the ILL this is a self‐heating graphite block at 2400 K) or to lower energies with a “cold source” such as liquid deuterium at 25 K (Finney and Steigenberger 1997). The resulting Maxwell distributions of energies have the characteristic temperatures of the moderators (Figure 17.16a). Wavelength section is generally achieved by Bragg scattering from a crystal monochromator or by velocity selection through a mechanical chopper. In this way, high‐quality, high‐flux neutron beams with a narrow wavelength distribution are made available for scattering experiments. One of the most powerful of the reactor neutron sources in the world is the 58 MW HFR (high‐flux reactor) at the ILL.

In accelerator sources, neutrons are released by bombarding a heavy metal target (e.g. U, Ta, W), with high‐energy particles (e.g. H⁺) from a high‐power accelerator – a process known as spallation. The methods of particle acceleration tend to produce short intense bursts of high‐energy protons and hence pulses of neutrons. Spallation releases much less heat per useful neutron than fission (typically 30 MeV per neutron, compared with 190 MeV in fission). The low heat dissipation means that pulsed sources can deliver high neutron brightness – exceeding that of the most advanced steady‐state sources – with significantly less heat generation in the target. As said above, one of the most powerful spallation neutron sources in the world is the ISIS facility that is based around a 200 µA, 800 MeV, proton synchrotron operating at 50 Hz, and a tantalum (Ta) target that releases approximately 12 neutrons for every incident proton.

At ISIS, the production of particles energetic enough to result in efficient spallation involves three stages:

1. Production of H⁻ ions (proton with two electrons) from hydrogen gas and acceleration in a pre‐injector column to reach an energy of 665 keV.
   
2. Acceleration of the H⁻ ions to 70 MeV in the linear accelerator (Linac) that consists of four accelerating tanks.
   
3. Final acceleration in the synchrotron – a circular accelerator 52 m in diameter that accelerates 2.8 × 10¹³ protons per pulse to 800 MeV. As they enter the synchrotron, the H⁻ ions pass through a very thin (0.3 µm) alumina foil so that both electrons from each H⁻ ion are removed to produce a proton beam. After traveling around the synchrotron (approximately 10 000 revolutions), with acceleration on each revolution from electromagnetic fields, the proton beam of 800 MeV is kicked out of the synchrotron toward the neutron production target. The entire acceleration process is repeated 50 times a second.

Collision between the proton beam and the target atom nuclei generates neutrons in large quantities and of very high energies. As in fission, they must be slowed by passage through moderating materials so that they have the right energy (wavelength) to be useful for scientific investigations. This is achieved by hydrogenous moderators around the target. These exploit the large inelastic scattering cross section of hydrogen to slow down the neutrons passing through by repeated collisions with the hydrogen nuclei. The moderator temperature determines the spectral distributions of neutrons produced, and this can be tailored for different types of experiments (Figure 17.16b). The moderators at ISIS are ambient temperature water (316 K, H₂O), liquid methane (100 K, CH₄), and liquid hydrogen (20 K, H₂).

The characteristics of the neutrons produced by a pulsed source are therefore significantly different from those produced at a reactor (Figure 17.16c). The time‐averaged flux (in neutrons per second per unit area) of even the most powerful pulsed source is low in comparison with reactor sources. However, the judicious use of TOF techniques that exploit the high brightness in the pulse can compensate for this. Using TOF techniques on the white neutron beam gives a direct determination of the energy and wavelength of each neutron.

Scattering events arise from radiation–matter interactions and produce interference patterns that give information about spatial and/or temporal correlations within the sample. Different modes of scattering may be produced: elastic or inelastic but also coherent or incoherent. Coherent scattering from ordered nuclei produces patterns of constructive and destructive interference that contain structural information, while incoherent scattering results from random events and can provide dynamic information. In small‐angle neutron scattering (SANS) (Bacon 1977), only coherent elastic scattering is considered, and incoherent scattering, which appears as a background, can be easily measured and subtracted from the total scattering. To further explain, coherent scattering is “in phase” and thus can contribute to small‐angle scattering; incoherent scattering is isotropic and in a small‐range experiment and thus contributes to the background signal and degrades signal to noise.

Neutrons interact with the atomic nucleus via strong nuclear forces operating at very short range (∼10⁻¹⁵ m), i.e. much smaller than the incident neutron wavelength (∼10⁻¹⁰ m). Therefore, each nucleus acts as a point scatterer to the incident neutron beam, which may be considered as a plane wave. The strength of interaction of free neutrons with the bound nucleus can be quantified by the scattering length, b, of the atom, which is isotope dependent. In practice, the mean coherent neutron scattering length density, ρ_coh, abbreviated as ρ, is a more appropriate parameter to quantify the scattering efficiency of different components in a system. As such, ρ represents the scattering length per unit volume of substance and is the sum over all atomic contributions in the molecular volume V_m:

17.17

where b_{i, coh} is the coherent scattering length of the ith atom in the molecule of mass density D and molecular weight Mw. N_a is Avogadro’s constant. Some useful scattering lengths are given in Table 17.7, and scattering length density for selected molecules in Table 17.8 (King 1997). The difference in b values for hydrogen and deuterium is significant, and this is exploited in the contrast variation technique to allow different regions of molecular assemblies to be examined; i.e. one can “see” proton‐containing hydrocarbon‐type material dissolved in heavy water, D₂O.

In neutron scattering experiments, the intensity I is measured as a function of a scattering angle, θ, which in the case of SANS is usually less than 10°.

For coherent elastic scattering, the incident wave vector of magnitude 2π/λ, |k_o| = |k_s| = 2πn/λ, where n is the refractive index of the medium, which for neutron is ∼1, and K_s is the scattered wave vector, so the amplitude of the scattered vector, |Q|, can be obtained by geometry as

17.18

The magnitude Q has dimensions of reciprocal length and units are commonly Å⁻¹; large structures scatter to low Q (and angle) and small structures at higher Q values.

Radiation detectors do not measure amplitudes as they are not sensitive to phase shift, but instead the intensity I_sc of the scattering (or power flux), which is the squared modulus of the amplitude

17.19

For an ensemble of n_p identical particles, Eq. 17.19 becomes (Dickinson 1995)

17.20

where the ensemble averages are over all orientations, o, and shapes, s.

Therefore, there is a convenient relationship (Eq. 17.18) between the two instrumental variables, θ and λ, and the reciprocal distance, Q, that is related with the positional correlations r between point scattering nuclei in the sample under investigation. These parameters are related with the scattering intensity I(Q) (Eq. 17.20) that is the measured parameter in an SANS experiment and contains information on intraparticle and interparticle structure.

17.7.1 Scanning Electron Microscopy

SEM was a central part in a work for surface image and analysis. The SEM operates by scanning the surface with a beam of electrons, which are generated by an electron gun and focused with magnetic lenses down to a diameter of about 10 Å when hitting the specimen. The electrons interact with atoms at the surface, leading to emission of new electrons. These emitted electrons are collected and counted with a detector. SEM can be used in a mode detecting either secondary electrons (SEs) or backscattered electrons (BSE). SEs can escape only from a shallow region and offer the best image of surface topography. BSEs undergo a number of collisions before eventually scattering back out of the surface. They are generated from a larger region than SEs and provide information about specimen composition since heavier elements generate more BSEs and thus a brighter image.

The quality and resolution of SEM images are function of three major parameters: (i) instrument performance, (ii) selection of imaging parameters (e.g. operational control), and (iii) nature of the specimen. All three aspects operate concurrently, and neither of them should be or can be ignored or overemphasized.

One of the most surprising aspects of SEM is the apparent ease with which SEM images of 3D objects can be interpreted by any observer with no prior knowledge of the instrument. This is somewhat surprising in view of the unusual way in which image is formed, which seems to differ greatly from normal human experience with images formed by light and viewed by the eye.

The main components of a typical SEM are electron column, scanning system, detector(s), display, vacuum system, and electronic controls (Figure 17.17).

The electron column of the SEM consists of an electron gun and two or more electromagnetic lenses operating in vacuum. The electron gun generates free electrons and accelerates these electrons to energies in the range of 1–40 keV in the SEM. The purpose of the electron lenses is to create a small, focused electron probe on the specimen. Most SEMs can generate an electron beam at the specimen surface with spot size less than 10 nm in diameter while still carrying sufficient current to form acceptable image. Typically, the electron beam is defined by probe diameter (d) in the range of 1 nm to 1 µm, probe current (i_b) – picoamperes to microamperes, and probe convergence (α) – 10⁻⁴–10⁻² rad.

In order to produce images, the electron beam is focused into a fine probe, which is scanned across the surface of the specimen with the help of scanning coils (Figure 17.17). Each point on the specimen that is struck by the accelerated electrons emits signal in the form of electromagnetic radiation. Selected portions of this radiation, usually SEs and/or BSEs, are collected by a detector, and the resulting signal is amplified and displayed on a TV screen or computer monitor. The resulting image is generally straightforward to interpret, at least for topographic imaging of objects at low magnifications.

The electron beam interacts with the specimen to a depth of approximately 1 µm. Complex interactions of the beam electrons with the atoms of the specimen produce a wide variety of radiation. The need of understanding of the process of image formation for reliable interpretation of images arises in special situations and mostly in the case of high‐magnification imaging. In such case, knowledge of electron optics, beam–specimen interactions, detection, and visualization processes is necessary for successful use of the SEM power.

The purpose of the electron lenses is to produce a convergent electron beam with desired crossover diameter. The lenses are metal cylinders with cylindrical hole, which operate in vacuum. Inside the lenses, magnetic field is generated, which in turn is varied to focus or defocus the electron beam passing through the hole of the lens.

The general approach in SEM is to minimize the probe diameter and maximize the probe current. The minimum probe diameter depends on the spherical aberration of the SEM electron optics, the gun source size, the electron optical brightness, and the accelerating voltage.

The probe size, which directly affects resolution, can be decreased by increasing the brightness. The electron optical brightness β is a parameter that is function of the electron gun performance and design. For all types of electron guns, brightness increases linearly with accelerating voltage, so every electron source is 10 times as bright at 10 kV as it is at 1 kV. Decreasing the wavelength and the spherical aberration also decreases the probe size.

The interaction volume of the primary beam electrons and the sampling volume of the emitted secondary radiation are important both in the interpretation of SEM images and in the proper application of quantitative X‐ray microanalysis. The image details and resolution in the SEM are determined not by the size of the electron probe by itself but rather by the size and characteristics of the interaction volume.

When the accelerated beam electrons strike a specimen, they penetrate inside it to depths of about 1 µm and interact both elastically and inelastically with the solid, forming a limiting interaction volume from which various types of radiation emerge, including BSE, SE, characteristic and bremsstrahlung X‐rays, and cathodoluminescence in some materials.

The combined effect of elastic and inelastic scattering controls the penetration of the electron beam into the solid. The resulting region over which the incident electrons interact with the sample is known as interaction volume. The interaction volume has several important characteristics that determine the nature of imaging in the SEM.

The energy deposition rate varies rapidly throughout the interaction volume, being greatest near the beam impact point. The interaction volume has a distinct shape (Figure 17.18). For low‐atomic‐number target, it has distinct pear shape. For intermediate and high‐atomic‐number materials, the shape is in the form of hemisphere.

The interaction volume increases with increasing incident beam energy and decreases with increasing average atomic number of the specimen. For SEs, the sampling depth is from 10 to 100 nm, and diameter equals the diameter of the area emitting BSEs. BSE are emitted from much larger depths compared with SE.

Ultimately, the resolution in the SEM is controlled by the size of the interaction volume.

Since the SEM is operated under high vacuum, the specimen that can be studied must be compatible with high vacuum (∼10⁻⁵ mbar). This means that liquids and materials containing water and other volatile components cannot be studied directly. Also, fine powder samples need to be fixed firmly to a specimen holder substrate so that they will not contaminate the SEM specimen chamber.

Nonconductive materials need to be attached to a conductive specimen holder and coated with a thin conductive film by sputtering or evaporation. Typical coating materials are Au, Pt, Pd, their alloys, and carbon.

There are special types of SEM instruments such as variable pressure scanning electron microscopy (VP‐SEM) and environmental scanning electron microscopy (ESEM) that can operate at higher specimen chamber pressures, thus allowing for nonconductive materials (VP‐SEM) or even wet specimens to be studied (ESEM). SEM can also be combined with a number of different techniques for chemical analysis, the most common being energy‐dispersive spectroscopy (EDS). When the electron beam interacts with the surface, X‐ray photons are generated. The energy of radiating photons corresponds to a transition energy that is characteristic for each element. Figure 17.17 illustrates the interaction volume from which electrons and X‐rays are generated. With wavelength‐dispersive X‐ray spectroscopy (WDS), the radiated photons are diffracted by a crystal, and only X‐rays with a specific wavelength will fall onto the detector. WDS analysis is more accurate but also more time consuming than EDS analysis and used in particular for analyses of light elements or separating overlaps in the EDS spectra.

Carbon surfaces that have been polished for optical microscopy show very few features in a SEM examination (no topography). However, etching the surface either chemically (with chromic acid) or by ion bombardment reveals a wealth of detail that can be related to the optical texture of the sample. A specialized application of this is the “same area” technique where a specific part of a polished surface that has been identified and characterized optically is reexamined by SEM following etching. Figures 17.19 and 17.20 show micrographs illustrating this technique.

SEM is an excellent method for monitoring the changes in topography following various treatments, such as gasification, heat treatment, etc. Figures 17.21 and 17.22 are micrographs of metallurgical (blast furnace) coke before and after reaction with carbon dioxide.

17.7.2 Transmission Electron Microscopy

TEM provides a means of obtaining high‐resolution images of diverse materials. Figure 17.23 includes an outline of the general arrangement of a TEM. Electrons are generated in the same way as in SEM, using a tungsten filament, and focused by a condenser lens system. The electrons strike the thin‐film specimen and may undergo any of several interactions with the specimen. One of these interactions, diffraction of the electrons by the periodic array of atomic planes in the specimen, ultimately produces the contrast that most commonly enables observation of structural details in crystalline material. The electrons that pass through the thin crystal without being diffracted are referred to as transmitted electrons.

Downstream of the specimen are several post‐specimen lenses that include the lower half of the objective lens, a magnifying lens, an intermediate lens, and a projection lens. The series of post‐specimen lenses is referred to as an image formation system. After passing through the image formation system, the electrons form an image either on a fluorescent screen or on a photographic film. The theoretical resolution in a TEM image approaches the wavelength of the incident electrons, although this is generally not attained due to a spherical and chromatic aberration and aperture diffraction. Typical line‐to‐line resolution in TEM is around 1.5 Å.

The conventional TEM is thus capable of simple imaging of the specimen and generation of SADP. Images formed using transmitted electrons are known as bright‐field (BF) images, while those due to specific (hkl) planes are known as dark‐field (DF) images. An EDX system can be attached to a TEM to determine the elemental composition of various phases.

The techniques of TEM can be divided into three areas: conventional transmission electron microscopy (CTEM), analytical transmission electron microscopy (AEM), and HREM.

CTEM techniques include BF imaging, DF imaging, and selected area electron diffraction (SAD). These methods can be used to identify reaction products and to characterize the microstructure of the scale and the metal/scale interface. Defects, such as dislocations, voids, and microcracks, which play an important role on the growth and adhesion of the scale, can also be detected. With electron diffraction techniques, it is possible to determine the crystal structure and the relative orientation relationship between the metal and the scale.

The second area is AEM. The distribution of impurities and dopants as well as chemical profiles and compositional gradients can be determined with AEM techniques. AEM techniques include energy‐dispersive X‐ray spectroscopy (EDS) and EELS. A review and comparison between EDS and EELS was presented by Müllejans and Bruley (1993). The highest spatial resolution (0.4 nm) and smallest probe size (<1 nm) can be reached if these analytical methods are combined with a dedicated STEM, such as a VG HB501 STEM.

EELS can provide information about the chemical bonding at interfaces. For example, the oxidation states of metals can be investigated as has been demonstrated for Nb/α‐Al₂O₃ interfaces (Bruley et al. 1994). It is possible by analyzing the energy‐loss‐near‐edge structure (ELNES) of EELS spectra to determine the coordination and distance of atoms at interfaces. A line scan across the interface can provide information about the chemical width of the interfacial region.

The third area of TEM is HREM. Using HREM, the crystal lattice can be imaged, and the atomistic structure of materials can be investigated. The point‐to‐point resolution (Spence 1988) of conventional HREM instruments (400 kV) is about 1.7 Å (0.17 nm). However, a new generation of HREM instruments operates at 1250 kV with a point‐to‐point resolution of 1 Å (0.10 nm). With this resolution, the structure of many different interfaces and defects in materials can be investigated.

However, HREM can only be applied if special conditions are fulfilled. The thickness of the TEM sample has to be smaller than 10 nm. This means that very high quality of sample preparation is required. Lattice images of heterophase boundaries or grain boundaries are only possible if both crystals adjacent to the interface are oriented parallel to low‐index Laue zones. The interface itself has to be parallel to the incoming electron beam, since small tilts away can change the lattice image and make interpretation difficult.

The interpretation of HREM micrographs is not possible on a naïve basis owing to phase shifts introduced by lens aberrations, defocus values, sample composition, and thickness. Therefore, computer calculations are necessary to simulate images of model structures of crystals and defects (e.g. interfaces) for comparison with experimental images (Spence 1988).

The preparation techniques of TEM are quite difficult. It is necessary to obtain a very thin section of the carbon, less than 100 nm, of a uniform thickness. Specimen breakage can often give good results, but this should be treated with caution as it can lead to random variations in thickness that cannot be fully interpreted in terms of the image produced. A more controlled method of producing suitable material is by cutting a thin section of a microtome and further thinning the center portion by ion bombardment. The uniform thickness is important because, in these investigations, it is the variation in the amount of material through which the electron beam passes that provides the image contrast, and fringe imaging can be an artifact of a tapered sample. When the conditions are correctly established, high‐resolution TEM can provide direct imaging of the layer planes in carbon materials, reveal the complexity of the most regular structures, and show the ordering present down to the nanometer level.

In the following paragraphs (see Figure 17.24), a standard method for TEM cross‐sectional preparation will be explained (Strecker et al. 1993). After characterization of the specimen surface with optical microscopy and SEM, two pieces of the metal carrying the corrosion scale are glued together as a sandwich (Figure 17.24a). The sandwich is glued within a brass tube, with an outer diameter of 3 mm (Figure 17.24b,c). Thin disks are cut from this tube and ground with SiC paper to a thickness of about 200 µm (Figure 17.24d). The disks are dimpled from both sides with a 3 µm diamond, resulting in a residual thickness of 10 µm.

The final step in thinning is ion milling. The samples are ion thinned with a low angle of incidence (4°) from both sides with a BalTec ion mill. This method produces cross‐sectional samples with high efficiency (80%). The details of the preparation method will differ between different systems in order to obtain the optimal sample.

Although the effort for TEM sample preparations of the relevant systems is very high, TEM yields important information in the investigation of high temperature corrosion, as has been demonstrated with oxidation studies of Ni (Sawhill and Hobbs 1984), Fe and FeCrNi (Newcomb and Stobbs 1985), NiAl (Doychak and Rühle 1989), Ni₃Al (Bobeth et al. 1994; Schumann and Rühle 1994), and on thin oxide films, and the cross section of the scales for identification of various phases.

17.7.3 High‐Resolution Transmission Electron Microscopy

HRTEM is the ultimate tool in imaging defects. In favorable cases, it shows directly a 2D projection of the crystal with defects and all. Of course, this only makes sense if 2D projection is down to some low‐index direction, so atoms are exactly on top of each other. Accordingly, HRTEM is easy to grasp: consider a very thin slice of crystal that has been tilted so that low‐index direction is exactly perpendicular to the electron beam. All lattice planes almost parallel to the electron, enough to the Braggs position, will diffract the primary beam. The diffraction pattern is the Fourier transform of the periodic potential for the electron in two dimensions. In the objective lens, all diffracted beams and the primary beam are their interference, which provides a back‐transformation and leads to an enlarged picture of the periodic potential. This picture is magnified by the following electron optical system and finally seen on the screen at magnifications of typically 10⁶. The practice of HRTEM, however, is more difficult than the simple theory. Even so, significant work is now being conducted to analyze the cross sections of the scales to obtain information such as porosity voids and interface morphology between the metal substrate and oxide, as well as between the various oxide layers in a more complex sample. Figures 17.25 and 17.26 show two examples of the resolution layer planes in both highly ordered and less ordered materials obtained by HRTEM.

17.7.4 Low‐Energy Electron Microscopy

LEEM is a branch of microscopy involving low‐energy elastically BSEs for imaging of solid body surfaces.

LEEM was invented by Ernst Bauer in the early 1960s and has been widely used in surface research since the 1980s. In a microscope, primary low‐energy (up to 100 eV) electrons are emitted onto a subject surface, and the electrons reflected from the surface are focused to create a magnified image of the surface. This type of microscope has a spatial resolution of as much as several dozen nanometers. Image contrast depends on the variations of a surface’s ability to reflect slow electrons due to differences in crystal orientation, surface reconstruction, or coverage. While microscopic images may be generated very quickly, LEEM is often used to examine dynamic processes occurring on different surfaces, including the growth of thin films, etching, adsorption, and phase transitions in real time. In illustration thereof, Figure 17.27 shows a microscopic image of the surface of Si(111) during phase transition from reconstruction 7 × 7 to reconstruction 1 × 1 occurring in an environment with temperature 860 °C (Tromp 2000).

A layout of the Elmitec LEEM system is shown in Figure 17.28. This instrument is capable of BF and DF imaging with 10 nm resolution, selected area low‐energy electron diffraction (μLEED), and spectroscopic low‐energy electron reflectivity (LEER) measurements. This is primarily used for characterizing epitaxial films of 2D materials, in which case the spatial and crystal orientation of the grains is determined (from imaging of the μLEED), along with the number of 2D layers in each grain (from LEER measurements).

The operation of this instrument is easy to grasp: electrons are produced in an electron gun containing a thermionic LaB₆ emitter, which is biased at typically −20 keV. Once the electron beam has left the emitter, it is accelerated to high energy by a grounded extractor into the illumination column, after which the beam is deflected toward the sample surface by a magnetic deflector. Passing through the grounded objective lens, the beam is rapidly decelerated to low energy due to the large potential difference between the objective and the sample, which is also close to −20 keV. A potential difference, V_s (start voltage or sample voltage), can be applied between the sample surface and the gun filament to alter the incident electron energy. Typically, incident energies of 0–50 eV are employed. The electrons are then reflected, or diffracted, from the sample surface. They pass through the magnetic deflector again and then are imaged (either as a diffraction pattern or as a real‐space image) on the micro‐channel plate. A contrast aperture is used to select particular diffraction spots for imaging. BF images are formed using the reflected (0, 0) spot, whereas DF images are formed using other, specifically selected, diffraction spots. Due to their low energies, the only electrons to leave the surface are those that originate from the top few atomic layers of the sample. Hence, LEEM is a very surface‐sensitive technique.

LEEM has developed into one of the premier techniques for in situ studies of surface dynamical processes, such as epitaxial growth, phase transitions, chemisorption, and strain relaxation phenomena. Over the last few years, new LEEM instruments have been designed and constructed, aimed at improved resolution, improved diffraction capabilities, and greater ease of operation compared with present instruments (Bauer 1998).

17.8.1 Extended X‐Ray Absorption Fine Structure

The origins of extended X‐ray absorption fine structure (EXAFS) are attributed to Kossel and Kronig more than 85 years ago. The X‐ray absorption of a material will in general display several sudden upward jumps (termed K, L edges) as the X‐ray photon energy is increased, corresponding to specific electron excitations in the constituent elements of the material. Closer examination of the high‐energy side of these edges (i.e. some hundreds of electron volts above the edge) reveals small oscillations in absorption, which are the fine structure referred to in EXAFS. These oscillations arise from small energy fluctuations associated with interference effects between an outgoing electron wave from the excited atom and that fraction that is scattered back by the surrounding atoms (Figure 17.29). Thus, they carry information about the local environment of an excited atom/ion. An appropriately weighted Fourier transform of these EXAFS spectra will produce a radial distribution plot, that is, a plot of the surrounding atomic density versus distance from the excited atoms.

The key feature of EXAFS is that each absorption edge is specific of a given atom type in the material, so that each EXAFS spectrum yields an individual atom type’s view of its local environment. The technique does not require that the material be crystalline: indeed it can be amorphous or liquid. This contrasts sharply with conventional crystallography that seeks diffraction patterns from crystalline material, the diffraction patterns themselves being complex superpositions of scattering from all the constituent atomic/electron density. Considerable crystallographic skill is required to disentangle the diffraction contributions from each atom in order to produce a 3D structural map of the material. EXAFS can directly probe the structure of each atom type, though this structural information extends only to the nearer coordination shells around the given atom.

Not surprisingly, being such a direct and versatile technique, EXAFS has become an increasingly popular technique in all walks of materials science. In particular, catalytic processes can be studied where specific atomic interactions are implicated and also amorphous/glassy materials where crystallography can give only limited structural information. Although EXAFS spectra can in principle be collected using the weak bremsstrahlung (white) X‐ray yield from laboratory sources, the synchrotron, with its intense and continuous energy X‐ray spectrum, is ideal for EXAFS. Practical collection times (minutes to hours) are therefore many orders of magnitude faster than laboratory measurements (days to weeks). The case for synchrotron EXAFS is now so strong in academic and industrial materials research programs that dedicated synchrotrons devote a sizeable fraction of their resources to EXAFS instrumentation.

EXAFS has evolved into many forms of measurement. A number of acronyms sprung up to describe the more popular versions of its use (Table 17.9).

The use of EXAFS for studies on catalysis has largely been mentioned. An exciting development in this pursuit is the marrying of EXAFS data with diffraction data. One example involves nickel‐exchanged zeolite Y that is used for converting three acetylene molecules into one benzene molecule. By making in situ EXAFS and powder diffraction measurements in controlled environments, it has been possible to study the complex structural changes involved: during dehydration, some nickel cations move from the super cage into the smaller cages, while others remain attached to the walls of the super cage; further movement of the cations occurs during catalytic activity.

Glasses, unlike crystalline zeolites, do not display long‐range order. Conventional X‐ray/neutron scattering can give short‐range structural information, but this is averaged over all atom types, and special techniques (anomalous absorption for X‐rays, isotopic substitution for neutrons) are required to apportion scattering to individual atom types. EXAFS has proved to be a more discriminating probe of local structure in glasses.

The differing environments of silicon, sodium, and calcium in soda lime–silica glass are readily obtained from the K‐edge EXAFS spectra, Figure 17.30 (Greaves 1990): silicon is tetrahedrally coordinated with oxygen at 1.61 Å, sodium is sixfold coordinated with a short bond of 2.3 Å, while calcium is similarly octahedrally coordinated but with a longer oxygen distance of 2.5 Å. These EXAFS data are consistent with a modified random network model of the glass containing channels of mobile cations ionically bonded in non‐bridging oxygens. This model is also consistent with the known bulk properties such as the reported emission of sodium on fracture, which appears to occur along these cation channels.

17.8.2 Photoemission

Photoemission is a low‐energy technique exploited by surface science. It uses X‐ray photons in the low 100 eV energy range (i.e. wavelengths ∼100 Å). For example, photoemission spectra from an aluminum (111) surface, before and after exposure to oxygen gas at ∼2 × 10⁻⁷ torr, record the very early stages of aluminum oxidation (McConville et al. 1987). The chemical shifts of the photoemission peaks can be interpreted in terms of various proposed models. One possibility is that at low coverage, the oxygen chemisorbs onto the aluminum surface in three different states. This is identified by three peak shifts corresponding to aluminum atoms bonded to one, two, or three chemisorbed oxygen atoms. At higher exposures, the oxygen may diffuse to form a complete oxide‐like underlayer beneath the surface.

Although surface science is an expensive and time‐consuming discipline, it addresses fundamental problems in materials science, involving the structure and composition of surfaces. These influence important technologies such as semiconductor growth, surface catalysis, and corrosion protection.

17.8.3 Auger and X‐Ray Photoelectron Spectroscopy

These processes, described in detail elsewhere (Haugsrud 2003), are schematically illustrated in Figure 17.31. In both techniques, a surface atom is ionized by removal of an inner‐shell electron. In XPS or ESCA, this is achieved by bombarding the surface with photons with energies between 1 and 2 keV. The resulting photoelectron has an energy given by

17.21

The energy of the photoelectron is measured using a concentric hemispherical analyzer. Typically the energy can be measured to an accuracy of ±0.1 eV. Knowing the energy of the incident photon, the binding energy of the electron in the atom can be determined. In addition, changes in binding energy that occur when elements combine together can be detected, and the chemical state of the atom identified.

In AES, ionization is produced by bombarding the surface with electrons with energies from 2 to 15 keV. When an electron is ejected from an inner shell (K shell) of an atom, the resultant vacancy is soon filled by an electron from one of the outer shells (L). This releases energy, which may be transferred to another outer electron (L shell), which is ejected. The energy of the Auger electron is given by

17.22

The energy of the Auger electron is measured by either hemispherical or cylindrical analyzers. The former has better energy resolution and hence gives chemical state information, while the latter has a higher transmission function and is useful for kinetic studies.

XPS has the advantage that it can give reliable chemical state information but has limited spatial resolution, while AES has excellent spatial resolution (10 nm) but limited chemical state.

Concerning the oxide characterization, it is important to identify the initial stages and corresponding thin films that form initially. In this respect, both XPS and AES are useful.

Figure 17.32 shows the oxygen 1s peak during the initial stages of exposure of nickel to oxygen at room temperature and then the effect of heating on this oxide (Allen et al. 1979). Initially undissociated oxygen is detected (stage 1), which then dissociates forming a layer of dissociated and undissociated oxygen on the top of the nickel metal (stage 2). Oxygen then diffuses into the nickel (stage 3) that may be slow at room temperature, but as the temperature is increased, the speed of the reaction increases. By determining the temperature at which this diffusion occurs from the O 1s peak shift, the activation energy can be determined.

In binary and ternary alloys, the oxide that first forms is determined by the temperature and rate of arrival of the gas atoms. Figure 17.33 shows spectra from stainless steel exposed to low oxygen pressure at room temperature and 873 K. At room temperature, the initial oxide is an iron‐rich spinel of the form Fe₃O₄, but, at high temperature and low gas pressure, the chromium‐rich rhombohedral oxide Cr₂O₃ is able to form.

Elements present in the bulk in very small quantities can have a dramatic effect on the initial oxidation. Sulfur is present in austenitic steels at a level of approximately 200 ppm. At temperatures of 500 °C and above, the sulfur diffuses to the surface where it reacts with the impinging gas atoms to form SO₂ that is released into the environment (Wild 1977). Figure 17.34 shows the surface composition of a stainless steel, determined using AES, as a function of time exposed to 10⁻⁵ Pa oxygen at 873 K. Initially the surface has a high concentration of sulfur present, but this is gradually reduced by reaction with oxygen. It is only when the sulfur has been effectively removed from the bulk that the surface oxide can form. It then does this by forming the rhombohedral Cr₂O₃, but almost immediately manganese is incorporated into this oxide forming the spinel oxide MnCr₂O₄.

The surface layer to be analyzed by depth profiling using AES or XPS may be divided into different groups according to their thickness:

1. Very thin layers of 1–5 nm thickness may be analyzed by angle resolution AES or XPS measurements.
   
2. An ion sputtering may be used for layer thickness of 3–100 nm.
   
3. For 100–2000 nm thick layers, depth profiling, lapping, or ball cratering may be applied.
   
4. For layer thicknesses >2 mm, lapping or ball cratering is recommended.

Further information on the oxidation process during oxidation can also be obtained by AES and XPS. Complete characterization of oxides and other products can be obtained by these surface analytical techniques combined with other specialized techniques (Birks et al. 2006; Khanna 2004; Levitin 2005; Schütze 1997; Tempest and Wild 1988).

17.8.4 Rutherford Backscattering

In RBS, the specimen to be analyzed is bombarded by a beam of α‐particles with energy of approximately 0.9–3 MeV. The energy of the backscattered particles depends on the atomic number of the atom at which the particle is scattered and the distance of this atom from the specimen surface. Therefore, RBS is a nondestructive depth profiling method that is element and depth sensitive. Although a standard is needed to calibrate the experimental setup, RBS can be more or less considered as a nondestructive, absolute method (Quadakkers et al. 1992).

The quantitative depth information requires an iterative fitting procedure. In most laboratories, the program RUMP is being used. The information depth is c. 0.5–2 µm depending on the primary energy. The depth resolution is typically 10–30 nm and, in most cases, will therefore be determined by the irregularities of the oxide scale. A major requirement for the successful application of RBS is that the surfaces of the specimens have to be flat. An important limitation in using RBS is the overlapping of signals (Quadakkers et al. 1992). Figure 17.35 shows RBS spectra of an alumina scale on an yttria‐containing FeCrAl alloy. The measured intensity at the high‐energy edge of Fe unequivocally reveals the presence of a low concentration of this element at the alumina surface. The yield at slightly lower energies, however, might be caused by the presence of Fe in greater depth and/or Cr and/or Ti at the surface. Therefore, reliable in‐depth information on the elements Fe, Cr, and Ti cannot be derived. The situation is different if a high Z element like Y is incorporated in the scale. Only then, quantitative in‐depth concentration of this element, in this case up to around 0.3 µm, can be obtained. Because of the mentioned significant limitations, RBS cannot be considered as a suitable technique for standard depth profiling of corrosion scales. The method can sometimes be advantageous if heavy elements are to be analyzed in a light matrix. For analysis of light elements in a heavy matrix, NRA can, in some cases, be suitable.

17.8.5 Secondary Ion Mass Spectrometry

In SIMS, the specimen to be analyzed is bombarded by a beam of ions of energy 3–12 keV. The particles that are eroded from the surface by the bombardment leave the surface in the form of neutrals or ions (Rudenauer and Werner 1987). Analysis of the secondary ions by a mass spectrometer allows a chemical analysis of the specimen (corrosion scale) laterally and as a function of sputtering time, i.e. eroded depth (depth profiling by dynamic SIMS).

SIMS is a suitable method for the depth profiling of laterally uniform scales of 50 nm to 10 µm thickness. For thinner scales, AES/XPS might be more suitable, whereas for thicker scales conventional or tapered cross sections should be used. With modern ion sources, scales of up to several micrometers thickness can be analyzed within one hour. Compared with other surface analysis methods, SIMS is very suitable to measure trace elements because it can theoretically detect all elements and their isotopes, most of them down to concentrations in the ppb range; however the sensitivity differs for the various elements, and, in practice, nitrogen, for example, appears to be difficult to measure.

The analysis of oxide scales can be hampered by the fact that the sputtering process induces charging of the specimen surface. Charging affects the primary ion beam and, more important, alters the part of the energy distribution contributing to the detected signal. For thin films this can be overcome by a gold coating (10–20 nm) of the specimen, but, in most cases, especially for thicker scales, charge neutralization by electron bombardment of the specimen is required.

Studies reported by Benninghoven et al. (1991) have shown that the matrix effect can strongly be reduced by using MCs⁺‐SIMS. In this technique, the oxidized specimen is bombarded by Cs⁺ ions, whereas the positive molecule cluster ions of the elements (M) with Cs are being analyzed. Although the mechanisms of the molecule formation at the specimen surface are not yet completely understood, a number of recent studies seem to confirm the suitability of this technique for quantitative scale analysis, provided that the impact angle is larger than about 65° (depending on material and sputter yield). Figure 17.36 shows an example of the reduced matrix effect during analysis of an alumina scale formed on an FeCrAl alloy. It can be seen that a good approximation of the real concentration profiles is obtained by using relative sensitivity factors (RSFs) for the various elements (same RSFs for oxide and alloy) that lie in the same order of magnitude, in contrast to conventional SIMS, where the sensitivity factors for the various elements can differ by several orders of magnitude. Figure 17.36 illustrates that MCs⁺‐SIMS is capable of measuring concentrations as high as 60 at.% and as low as 0.01% simultaneously in one depth profile. If the RSFs are constant throughout the depth profiling, they provide the possibility to derive the relative sputter yields during the depth profile. Combined with an absolute measurement of the crater depth, a depth scale can then be derived. Further studies are necessary to prove the suitability of the MCs⁺‐SIMS technique.

If the oxide scale composition is not laterally homogeneous, depth profiles can only give limited information of the real element distribution in the scale because they give an average value over the analyzed area. In such cases, the good lateral resolution that is achieved by SIMS imaging can be used for scale characterization. The achievable lateral resolution depends on a number of experimental factors.

In imaging, even by using the MCs⁺‐SIMS technique, the matrix effect can make the mapping result difficult to interpret, because differences in sputter rates and/or ion yields of different phases in the oxide scale can indicate different concentrations of the various elements that, in reality, do not exist. Therefore, in multiphase scales, the intensities at every measured pixel of the image should be corrected to account for the differences in sputter rate and ion yield for obtaining the real element distribution. This obviously requires significant computer capacity; however, in using MCs⁺‐SIMS, promising results have been obtained.

The big advantage of the technique is its high sensitivity for most elements in many materials including insulating compounds. The profiling mode must be used with care due to the poorly defined relation between sputtering time and depth, particularly in nonhomogeneous materials such as oxidized metals.

An example of SIMS profiling is also given in Figure 17.37 for the case of the oxidation in oxygen of the binary nitride Ti_xAl_1−xN obtained by chemical vapor deposition.

The figure shows that alumina, Al₂O₃, is located at the external part of the oxidized scale, whereas the internal part consists of a mixture of alumina and titania, Al₂O₃ + TiO₂.

17.8.6 Ion Scattering Spectroscopy

Using ion beams of much lower energies (0.2–2 keV), produced by low‐cost and easy to use ion guns, may generate the same analytical information as RBS but limited to surface atoms. The physical phenomenon is not changed, and the expression of the kinematic factor describing the backscattering yield is always given by Eq. 17.23:

17.23

where μ is the ratio m/M of the masses of the incident ion and of the target atom and θ is the angle at which the backscattering ions are collected. The technique is here called ion scattering spectroscopy, and this is mainly a surface analysis technique comparable with the electron spectroscopes described above. However, it is possible to obtain depth information by sputtering inward from the specimen surface. The lifetime t_m of the surface monolayer of the solid under ion sputtering is given by

17.24

where C_s is the surface concentration of the solid (atoms m⁻²), F_B is the ion flux of the beam (ion m⁻² s⁻¹), and S is the sputtering yield (number of sputtered atoms/number of incident ions). The first two of these parameters are easy to measure and control, but the third is more difficult to evaluate. The sputtering yield is dependent not only on the nature, energy, and the angle of incidence of the sputtering ions but also on the nature, crystalline orientation, and properties of the bombarded surface. For example, using Ar⁺ ions of 1 keV to bombard pure polycrystalline aluminum at 60° incident angle gives a sputtering yield of about 2. Using a value of 1 × 10¹⁹ atoms m⁻² for C_s, a monolayer removal time of one second (t_m = 1) needs a beam flux of 5 × 10¹⁸ ions m⁻² s⁻¹, corresponding to an ion current of monocharged species of 0.8 A m⁻². Modern ion guns cover a large range of currents from 10⁻⁵ to 10 A m⁻² so that an experimentally convenient choice of sputtering rate can usually be obtained.

17.8.7 Low‐Energy Electron Loss Spectroscopy

Low‐energy electron loss spectroscopy (LEELS) is a surface analysis technique that provides quantitative information about physicochemical properties of materials from their nano‐size near‐surface region. It is well known that physical phenomena such as secondary electron emission (SEE) can be used to investigate the near‐surface area of a solid to obtain information on its crystal structure, elemental composition, and electronic configuration of its atoms (Luth 1993). Figure 17.38 shows the energy distribution of reflected SEE from a surface irradiated by an electron beam of primary energy E₀. Four ranges in N(E) can be observed that are due to interactions between elastic and inelastic scattering together with SEE.

Region II is due mainly to electrons that have lost some of their energy by inelastic scattering; directly by the elastic peak, one finds electrons that have suffered discrete energy losses from the excitation of inter‐ and intraband electronic transitions, surface and bulk plasmons, hybrid modes of plasmons, and ionization losses (ionization spectroscopy). That range is usually 30–100 eV. Usually, the losses related to surface and bulk plasmon excitations are most intensive lines in the electron energy loss spectrum. The spectra of plasma oscillations are potential data carriers about composition and chemical state of elements on the surface of solid and in the adsorbed layers. The energy losses are called as characteristic losses because they do not depend on the primary electron energy E₀ and its value is individual for the chemical element and compound. Region II is called as electron energy loss spectroscopy. At energy E₀ < 1000 eV, it can be called as LEELS. On Figure 17.39 really LEELS spectra are shown with interpretation of losses for the Co–Cr–Mo alloy surface that was measured at the primary electron beam energy E₀ = 350 eV in dN/dE mode (Vasylyev et al. 2008).

LEELS, with its variants ionization spectroscopy and surface and bulk plasmon excitations (these are potential data carriers about composition and chemical state of elements on the surface and bulk of solid and in the adsorbed layers), is based on the measurement of the energy spectra of electrons, which have lost a particular portion of the energy ΔE_β for the excitation of electronic transitions that are typical for a given kind of atom β. The position of an intensity line (IL) in the spectrum with respect to the primary electron energy E₀ is determined by the binding energy of electrons in the ground state and by the distribution of the density of empty states, but it does not depend on the value of E₀, on the work function, or on the value of the surface charge.

The calculation of the contribution to the intensity of an IL by the electrons having lost an amount of energy ΔE_β at the depth Z from the sample surface by the ionization of the core states of the atoms β is simple when a traditional experimental configuration is used (an incident beam of the primary electrons is directed perpendicularly to the sample surface (θ₀ = 0), and the SE are registered at the angle θ with respect to the normal). In this case, calculations within the framework of a two‐stage model allow us to obtain the following expression for the intensity of an IL (Vasylyev et al. 2006):

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where K is an instrumental factor, σ_β is the ionization cross section of the core level, n_β(Z) is the concentration of atoms at depth Z from surface, and is the elastic scattering factor of electrons. Λ_β is the effective free path of electrons in a sample with respect to inelastic collisions, which is determined by the equation

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For the Pt–Me (Me: Fe, Co, Ni, Cu) alloys (Seah and Dench 1979)

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An effective probing depth in IS amounts to ∼3Λβ because the SE created in the near‐surface region of this thickness contribute with 95% to the total intensity of an IL. An increase in the effective probing depth upon increasing the energy E₀ also results in an increased contribution from the deeper layers of the concentration profile into the IL intensity. This enables us to carry out a layer‐by‐layer reconstruction of the concentration profiles of the elements using the energy dependencies of the IL.

In summary, LEELS with energy ionization losses allows investigation of the layer‐by‐layer concentration profile for the single‐crystal alloys with monolayer resolution, element distribution on the depth for the polycrystalline alloys, and study of kinetics of surface processes at thermo‐induced treatment or after ion irradiation of the surface.

Plasmon excitations are very sensitive to structural and chemical state of surface and bulk and can be used for the study of electronic states of free electrons in the near‐surface region and influence of different kinetic processes on changing of electronic structure of materials.

Accordingly, LEELS with plasmon excitations can also define a surface–bulk interface with different physicochemical properties as compared with the bulk material. These results have good correlation with data of surface composition on depth that are obtained by ISS and AES.

17.9.1 Scanning Tunneling Microscopy

Classically, an object hitting an impenetrable barrier will not pass through. In contrast, objects with a very small mass, such as the electron, have wavelike characteristics that allow such an event, referred to as tunneling.

Electrons behave as beams of energy, and, in the presence of a potential U(z), assuming 1‐dimensional case, the energy levels Ψ_n(z) of the electrons are given by solutions of Schrödinger’s equation:

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where h is the reduced Planck’s constant, z is the position, and m is the mass of an electron.

Inside a barrier, E < U(z) so the wave functions that satisfy this are decaying waves. Knowing the wave function allows one to calculate the probability density for that electron to be found at some location. In the case of tunneling, the tip and sample wave functions overlap such that when under a bias, there is some finite probability to find the electron in the barrier region and even on the other side of the barrier (Chen 1993).

When a small bias V is applied to the system, only electronic states very near the Fermi level, within eV (a product of electron charge and voltage, not to be confused here with electron volt unit), are excited. These excited electrons can tunnel across the barrier. In other words, tunneling occurs mainly with electrons of energies near the Fermi level. However, tunneling does not require that there be an empty level of the same energy as the electron for the electron to tunnel into on the other side of the barrier. It is because of this restriction that the tunneling current can be related to the density if available or filled states in the sample. The current due to an applied voltage V (assume tunneling occurs sample to tip) depends on two factors: (i) the number of electrons between E_f and eV in the sample and (ii) the number among them that have corresponding free states to tunnel into on the other side of the barrier at the tip. The higher the density of available states, the greater the tunneling current. When V is positive, electrons in the tip tunnel into empty states in the sample; for a negative bias, electrons tunnel out of occupied states in the sample into the tip (Chen 1993).

One can sum the probability over energies between E_f–eV and E_f to get the number of states available in this energy range per unit volume, thereby finding the local density of states (LDOS) near the Fermi level. Now, using Fermi’s golden rule, which gives the rate for electron transfer across the barrier, it is possible to obtain the full tunneling current and consequently the Fermi distribution function that described the filling of electron levels at a given temperature.

A scanning tunneling microscope (STM) is an instrument for imaging surfaces at the atomic level, with a 0.1 nm lateral resolution and 0.01 nm (10 pm) depth resolution. It is based on the concepts of quantum tunneling reported above and can be used not only in ultrahigh vacuum (UHV) but also in air, water, and various other liquid or gas ambients and at temperatures ranging from near‐zero kelvin to over 1000 °C.

The components of an STM include a scanning tip, a piezoelectric controlled height and an x, y scanner, coarse sample‐to‐tip control, vibration isolation system, and computer (Oura et al. 2003).

The resolution of an image is limited by the radius of curvature of the scanning tip of the STM. Additionally, image artifacts can occur if the tip has two tips at the end rather than a single atom; this leads to “double‐tip imaging,” a situation in which both tips contribute to the tunneling. Therefore, it has been essential to develop processes for consistently obtaining sharp, usable tips. Recently, carbon nanotubes have been used in this instance (Lapshin 2007).

The tip is often made of tungsten or platinum–iridium, though gold is also used. Tungsten tips are usually made by electrochemical etching, and platinum–iridium tips by mechanical shearing (Bai 1999). Maintaining the tip position with respect to the sample, scanning the sample, and acquiring the data are computer controlled. The computer may also be used for enhancing the image with the help of image processing, as well as performing quantitative measurements (Lapshin 2007).

17.9.2 Atomic Force Microscopy

AFM or scanning force microscopy (SFM) is a type of scanning probe microscopy (SPM) with demonstrated resolution in the order of fractions of a nanometer or more than 1000 times better than the optical diffraction limit. The technique allows force measurement manipulation and acquisition of topographical images.

In force measurement, AFMs can be used to measure the forces between the probe and the sample as a function of their mutual separation. This can be applied to perform force spectroscopy.

For imaging, the reaction of the probe to the forces that the sample imposes on it can be used to form an image of the 3D shape (topography) of a sample surface at a high resolution. This is achieved by raster scanning the position of the sample with respect to the tip and recording the height of the probe that corresponds to a constant probe–sample interaction. The surface topography is commonly displayed as a pseudocolor plot.

In manipulation, the forces between tip and sample can also be used to change the properties of the sample in a controlled way. Examples of this include atomic manipulation, scanning probe lithography, and local stimulation of cells.

An AFM typically consists of a small cantilever, a piezoelectric element, a tip or probe, a detector of deflection, and motion of the cantilever, the sample, an x, y, z drive, and the sample stage (Butt et al. 2005).

According to this configuration, the interaction between tip and sample, which can be an atomic scale phenomenon, is transduced into changes of the motion of cantilever that is a macroscale phenomenon. Several different aspects of the cantilever motion can be used to quantify the interaction between the tip and sample, most commonly the value of the deflection, the amplitude of an imposed oscillation of the cantilever, or the shift in resonance frequency of the cantilever (tip contact or static mode of motion, tip tapping or intermittent contact mode of motion and of the detection mechanism or noncontact mode of motion).

Various methods of detection can be used, e.g. interferometry, optical levers, the piezoresistive method, the piezoelectric method, and STM‐based detectors (beam deflection measurement, capacitive detection, laser doppler vibrometry, etc.).

The AFM signals, such as sample height or cantilever deflection, are recorded on a computer during the x–y scan. They are plotted in a pseudocolor image, in which each pixel represents an x–y position on the sample and the color represents the recorded signal.

Noncontact mode AFM does not suffer from tip or sample degradation effects that are sometimes observed after taking numerous scans with contact AFM. This makes noncontact AFM preferable to contact AFM for measuring soft samples, e.g. biological samples and organic thin film. In the case of rigid samples, contact and noncontact images may look the same. However, if a few monolayers of adsorbed fluid are lying on the surface of a rigid sample, the images may look quite different. An AFM operating in contact mode will penetrate the liquid layer to image both the liquid and surface.

AFM has several advantages over the SEM. Unlike the electron microscope, which provides a 2D image of a sample, the AFM provides a 3D surface profile. In addition, samples viewed by AFM do not require any special treatments (such as metal/carbon coatings) that would irreversibly change or damage the sample and do not typically suffer from charging artifacts in the final image. While an electron microscope needs an expensive vacuum environment for proper operation, most AFM modes can work perfectly well in ambient air or even in a liquid environment. This makes it possible to study biological macromolecules and even living organisms. In principle, AFM can provide higher resolution than SEM. It has been shown to give true atomic resolution in UHV and, more recently, in liquid environments. High‐resolution AFM is comparable in resolution with scanning tunneling microscopy and TEM. AFM can also be combined with a variety of optical microscopy techniques such as fluorescent microscopy, further expanding its applicability. Combined AFM–optical instruments have been applied primarily in the biological sciences but have also found a niche in some materials applications, especially those involving photovoltaic research (Geisse, 2009).

Table 17.10 summarizes the functions of STM and AFM, thus clarifying the advantageous characteristics of these microscopy surface techniques. But it should be noticed that disadvantages also exist. For example, a disadvantage of AFM compared with SEM is the single scan image size; the scanning speed of an AFM is also by far slower than the scanning speed of a SEM. AFM images can also be affected by nonlinearity, hysteresis, and creep of the piezoelectric material and cross talk between the x, y, z axes that may require software enhancement and filtering (Lapshin, 1995, 2007).

17.9.3 Surface Force Apparatus

The SFA (Israelachvili and Adams 1978) was the pioneer scientific instrument to measure nanoscale forces. It was originally designed to study colloidal interactions, including steric, electrostatic, van der Waals, and solvation forces, and, today, it can also be used to monitor the assembly of biomolecules in real time.

The SFA technique stems from right after World War II as David Tabor was studying frictional interactions between surfaces in the Cavendish laboratory. He/she had an industrial contract aimed at developing improved windscreen wipers, which led him to modelize the interactions between rubber and glass in water. Using hemispherical rubber samples pressed against a flat glass surface, his/her team could follow the interaction by interferometry. When the rubber/glass interaction experiments were performed in air, contact was immediately established, and the rubber hemisphere became flattened over some area even under zero (compression) force. Under negative (pulling) force, and up to the onset of separation, the contact area remained nonzero, suggesting that attractive forces were operating between these two solid surfaces. This observation led his/her team to develop the Johnson–Kendall–Roberts (JKR) theory (Johnson et al. 1971) for the adhesion between two solid bodies, which predicts that the pull‐off force F to separate a deformable sphere of radius R from a plane is equal to

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