Optics, Optical Methods, and Microscopy

Propagation of light is described as the simple harmonic motion of transverse waves. Combining waves that propagate on orthogonal planes give rise to linear, elliptical, or spherical polarization, depending on their amplitudes and phase differences. Classical experiments of Huygens and Young demonstrated the principle of optical interference and diffraction. Generalization of Fraunhofer diffraction to scattering by a three-dimensional arrangement of atoms in crystals forms the basis of diffraction methods. Fresnel diffraction finds application in the design of zone plates for X-ray microscopy. Optical microscopy, with resolution given by the Rayleigh criterion to be approximately half the wavelength, works best when tailored to the optimal characteristics of the human eye (λ = 550 nm). Lenses suffer from spherical and chromatic aberrations, and astigmatism. Optical microscopes operate in bright-field, oblique, and dark-field imaging conditions, produce interference contrast, and can image with polarized light. Variants include confocal scanning optical microscopy (CSOM). Metallography, widely used to characterize microstructures, requires polished or chemically etched surfaces to provide optimal contrast. Finally, the polarization state of light reflected from the surface of a specimen is utilized in ellipsometry to obtain details of the optical properties and thickness of thin film materials.

X-Ray Diffraction

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

Crystallography and Diffraction

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

Scanning Probe Microscopy

Scanning probe microscopy (SPM) scans a fine tip close to a surface and measures the tunneling current (STM) or force (SFM), based on many possible tip-surface interactions. STM provides atomic resolution imaging, or the local electronic structure (spectroscopy) as a function of bias voltage, and is also used to manipulate adsorbed atoms on a clean surface. STM operates in two modes— constant current or height—and requires a conducting specimen. SFM uses a cantilever (force sensor) to measure short range (< 1 nm) chemical, and a variety of long-range (< 100 nm) forces, depending on the tip and the specimen; a conducting specimen is not required. In static mode, the tip height is controlled to maintain a constant force, and measure surface topography. In dynamic mode, changes in the vibrational properties of the cantilever are measured using frequency, amplitude, or phase modulation as feedback to control the tip-surface distance and form the image. Dynamic imaging includes contact and non-contact modes, but intermittent contact or tapping mode is common. SPMs measure properties (optical, acoustic, conductance, electrochemical, capacitance, thermal, magnetic, etc.) using appropriate tips, and find applications in the physical and life sciences. They are also used for nanoscale lithography.

Probes: Sources and Their Interactions with Matter

Probes are generated using laboratory sources, or in large user facilities. Photon sources include incandescence and plasma discharge lamps. Electron beams are generated using thermionic or field-emission sources. RF plasma sources generate ions that are accelerated and used for scattering experiments. Specimens should be probed first with light, as it causes the least damage. Electron interaction with matter causes beam broadening, atomic displacements, sputtering, or radiolysis leading to mass loss and local contamination. Neutrons are heavier than electrons, penetrate more deeply in materials, and require more sample for analysis. Protons (positive charge, heavier than electrons) go a longer way in the specimen without significant broadening. Ions in solids undergo kinematic collisions with conservation of energy and momentum; they also lose energy continuously as they propagate. In the back-scattering geometry, they form important methods of Rutherford backscattering spectroscopy (RBS) and low-energy ion scattering spectroscopy (LEISS). Medium energy ions generate secondary ions by sputtering that can be analyzed by mass spectrometers to determine specimen composition (SIMS). Alternatively, its composition is analyzed (ICP-MS), by creating an aqueous dispersion and converting it to a plasma. Finally, interaction of high-energy ions with core electrons can lead to inner shell ionization and characteristic X-ray emission (PIXE).

Atomic Structure and Spectra

We review the structure of atoms to describe allowed intra-atomic electronic transitions following dipole selection rules. Inner shell ionization is followed by characteristic X-ray emission or non-radiative de-excitation processes leading to Auger electrons that involve three atomic levels. Photon incidence also results in characteristic photoelectron emission, reflecting the energy distribution of the electrons in the solid. We present details of laboratory and synchrotron sources of X-rays, and discuss their detection by wavelength or energy-dispersive spectrometers, as well as microanalysis with X-ray (XRF), or electron (EPMA) incidence. Characteristic X-ray intensities are quantified in terms of composition using corrections for atomic number (Z), absorption (A), and fluorescence (F). Electron detectors use electrostatic or magnetic dispersing fields; two common designs are electrostatic hemispheric or mirror analyzers. Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS), used for surface analysis, require ultra-high vacuum. AES is a weak signal, best resolved in a derivative spectrum, shows sensitivity to the chemical state and the atomic environment, provides a spatially-resolved signal for composition mapping, and can be quantified for chemical analysis using sensitivity factors. Finally, we introduce the basics of XPS, a photon-in, electron-out technique, discussed further in §3.

Bonding and Spectra of Molecules and Solids

The electronic structure of molecules includes electronic (2-10 eV, UV-Vis absorption), vibrational (10-2 - 2 eV, infrared spectroscopy & Raman scattering), and rotational (10–5 – 10–3 eV, microwave spectroscopy) energy levels that are probed by appropriate spectroscopy methods. Light, incident on a molecule or molecular solid, is either absorbed (IR, single photon, non-zero derivative of dipole moment), or elastically (Rayleigh) or inelastically (Raman, two-photon, non-zero derivative of the polarizability) scattered. Fourier transform infrared (FTIR) spectroscopy finds much use in materials characterization, including in studying the curing of polymer composites now incorporated in aircraft structures. When atoms form solids their electronic structure, particularly the energy levels of the outer electrons involved in the bonding, are significantly altered. Both occupied and unoccupied levels in solids are probed. Photoemission spectroscopy (PES) with X-rays (XPS) or ultraviolet light (UPS) incidence, and inverse PES probe occupied and unoccupied energy levels of surfaces, respectively. X-ray absorption spectroscopy (XAS) complements XPS, and probes unoccupied energy levels of solids. X-ray absorption near-edge structure (XANES) provides information on the final density of unoccupied states, the transition probabilities, and many body effects. Extended X-ray absorption fine structure (EXAFS) provides element-specific nearest neighbor distances and their coordination number.

Diffraction of Electrons and Neutrons

Electron scattering, significantly stronger than that for X-rays, is sensitive to surfaces and small volumes of materials. Low-energy electron diffraction (LEED) provides information on surface reconstruction and the arrangement of adsorbed atoms. Reflection high energy electron diffraction (RHEED) probes surface crystallography, and monitors, in situ, mechanisms of thin film growth. Transmission electron diffraction reveals a planar cross-section of the reciprocal lattice, where intensities are products of the structure and lattice amplitude factors determined by the overall shape of the specimen. The amplitude of any diffracted beam at the exit surface oscillates with thickness (fringes) and the excitation error (bend contours). Selected area diffraction produce spot or ring patterns, where low-index zone-axis orientations reflect the symmetry of the crystal, and double-diffraction shows positive intensities even for reflections forbidden by extinction rules. Kikuchi lines appear as pairs of dark and bright lines, and help in tilting the specimen. A focused probe produces convergent beam electron diffraction (CBED), useful for symmetry analysis at nanoscale resolution. Neutrons interact with the nucleus and the magnetic moment of the atom via the spin of the neutron; the latter finds particular use in studies of magnetic order. The atomic scattering factor for neutrons shows negligible angular dependence.

Introduction to Materials Characterization, Analysis, and Metrology

Tailoring microstructures is central to materials development for any technological application. Microstructure includes information on the atomic, mesoscopic, and microscopic length scales, and its tailoring is enabled by characterization, which relates synthesis and processing of materials to their structure, properties, and performance. Typically, probe and signal radiations are used to characterize a specimen and their interactions may be elastic or inelastic, and coherent or incoherent. Probes are based on the electromagnetic spectrum, and their characteristics (e.g. energy, wavelength, momentum, polarization) define their interaction with matter, and determine the nature, scope, and details of any characterization method. Probes or signals, can also be electrons, ions, or neutrons. Characterization techniques are classified as spectroscopy, diffraction and scattering, and imaging and microscopy. Principal features of the materials, i.e. details of their electronic structure, including atomic mass, their crystallography, composition, phase, and morphology contribute to the observable signals. Criteria for technique selection also include penetration depth and mean free path, resolution, detection limits, potential damage to the specimen, and specimen preparation requirements; our goal is to maximize information while minimizing damage. Characterization methods find wide use across many disciplines including engineering, scinces, and art conservation.

Summary Tables

The three tables that follow provide an easily accessible comparative summary of the key points and features of the major characterization methods discussed in the text. The techniques are classified into three broad groups/methods: spectroscopy/chemical, diffraction/scattering, and imaging. For each technique, a concise description of the method and its use is followed, in bullet form, by its salient details and other characteristics, such as resolution, sensitivity etc., as well as specimen requirements that determine its practice. A general estimate of cost and space requirements is also included, but needless to say, this is only a snapshot for comparison and is definitely subject to change with time.