X-ray techniques

Within the scope of hard- and soft-matter sciences, x-rays interact with a specimen, and scattered primary or secondary radiation is detected in order to characterize the material. Based on the method of scattering and interaction with the specimen, one classification scheme divides the techniques into the categories of diffraction, spectroscopy, and imaging (Figure 3); however, these processes can overlap and integrate with each other.

Figure 3. Some scattering processes for x-rays, namely (a) diffraction (sketched on a crystal with lattice planes), which is a coherent, elastic process defining a scattering vector Q; (b) spectroscopy, where scattered photons (or particles) change energy (coherent and incoherently); and (c) imaging, here depicted in a radiography setup, where individual rays are attenuated, indicated by the different shaded arrows, projecting the object to a screen. Note: 2θ, scattering angle; k_i, initial state wavevector; k_f, final state wave vector.

Imaging, where an object is placed in a beam and an image is recorded through optical mapping, involving projection as in radiography and in topography^{Reference Baruchel, Bleuet, Bravin, Coan, Lima, Madsen, Ludwig, Pernot and Susini4} or transformation through an optical lens or element is the most intuitive technique. Numerous variations of these basic techniques exist using the lateral coherence of the x-ray beam for phase-contrast imaging, where in an extreme case, an interface or edge between two fully transparent media is mapped by its difference in refractive index. So-called Fresnel diffraction at the media edge is due to the beams slightly deviating from each side of the edges and overlapping in the distance, resulting in interference fringes and thus an image of the edge.^{Reference Wilkins, Gureyev, Gao, Pogany and Stevenson5}

Both spectroscopy and diffraction probe for scattered or secondary photons. In coherent scattering, an x-ray wave can be described by a space-, x, and time-, t, dependent oscillatory function exp(i (kx – ωt)) of wave vector k, wavenumber k = |k|, and angular frequency ω. Both k and ω can potentially change by Q = Δk = k_f – k_i and Δω = ω_f – ω_i, where indices i and f denote initial and final states, respectively. Usually, the distinguishing feature for spectroscopy is Δω ≠ 0, with energy transfer as ΔE = ℏΔω, where ℏ is the reduced Planck constant. In contrast, diffractometry investigates the scattered waves as a function of scattering vector Q, also called the wave vector transfer, and momentum transfer Δp = ℏΔk.

For conventional x-ray diffraction in powders, single crystals, and amorphous substances, Δω = 0, in other words, elastic scattering occurs. In their article in this issue, Simons et al. describe how in modern methods, these regimes of diffraction, spectroscopy, and imaging can be combined and interwoven, such as diffraction-contrast imaging in topographic methods, and particularly in dark-field x-ray microscopy. Both spectroscopic and diffraction methods can be used to scan a sample in order to form a raster map or image, taking advantage of scattered or secondary photons, as applied in fluorescence spectroscopy and reported by Liu and Weng (see their article in this issue), or in white beam Laue microdiffraction, as discussed in the X. Chen et al. article.

In their article, Glazer et al. discuss the application of high-energy x-rays for the study of materials relevant to the realization of modern Li-ion batteries. Such materials are of worldwide interest, employing both synchrotron^{Reference Tanida, Fukuda, Murayama, Orikasa, Arai, Uchimoto, Matsubara, Uruga, Takeshita, Takahashi, Sano, Aoyagi, Watanabe, Nariyama, Ohashi, Yumoto, Koyama, Senba, Takeuchi, Furukawa, Ohata, Matsushita, Ishizawa, Kudo, Kimura, Yamazaki, Tanaka, Bizen, Seike, Goto, Ohno, Takata, Kitamura, Ishikawa, Ohta and Ogumi6} and neutron radiation^{Reference Yonemura, Mori, Kamiyama, Fukunaga, Torii, Nagao, Ishikawa, Onodera, Adipranoto, Arai, Uchimoto and Ogumi7} on dedicated beamlines. Because of the availability of small and brilliant x-ray beams, small specimens can be investigated in tiny volumes under extreme conditions, as reviewed by B. Chen et al. in their article on high-pressure studies. Experimental access to high-pressure (10–100 GPa) and temperature (cryogenic to 5000 K) extreme conditions allows not only for investigation of materials as they occur in the interior of the earth,^{Reference Hemley and Mao8,Reference Mao, Mao, Shu, Fei, Hemley, Meng, Shen, Prakapenka, Campbell, Heinz, Sturhahn and Zhao9} but also for the synthesis of new materials and the study of their fundamental properties. Large-volume multi-anvil pressure cells for specimens of several cubic millimeters have become useful for materials scientists to study microstructure evolution and segregation chemistry during high-pressure thermomechanical processing of engineering-relevant materials,^{Reference Liss, Funakoshi, Dippenaar, Higo, Shiro, Reid, Suzuki, Shobu and Akita10} and are nowadays complemented by an apparatus allowing uniaxial stress components.^{Reference Sano-Furukawa, Hattori, Arima, Yamada, Tabata, Kondo, Nakamura, Kagi and Yagi11}

Applications of synchrotron x-rays in materials research

Principles of two-dimensional x-ray diffraction

In conventional powder x-ray diffraction, intensity is recorded against a single dimension, for example, scattering angle 2θ. This diffraction involves rotational symmetry about the primary beam axis, leading to so-called Debye–Scherrer cones in space. In a typical experimental setup (Figure 4), bundled high-energy x-rays impinge onto a sample volume, while a 2D detector maps these cones to Debye–Scherrer rings at a given distance. The radial intensity distribution of those rings corresponds to a conventional x-ray diffractogram, where the radius is transformed into scattering angles 2θ, or even better, into Q = 2 k sin(θ) = 4π/λ sin(θ), where λ is the x-ray wavelength. In order to increase the intensity, Debye–Scherrer rings are azimuthally integrated if the pattern is isotropic. Such Q-dependent information not only allows extraction of phase changes, but also allows for obtaining microstrain and particle sizes from line broadening. The broadening contributions can be separated by their dependence on scattering transfer Q: since strain ε = –ΔQ/Q, strain broadening increases linearly with Q, while size broadening transforms into reciprocal space by a constant ΔQ ≈ 2π/D for crystallites of coherent size D.

Figure 4. Typical 2D high-energy x-ray diffraction setup: a small beam arriving from the right is scattered by the specimen into Debye–Scherrer cones, which are mapped as diffraction rings on a flat-panel detector. Superimposed to the 2D detector image are four radial sections of the intensity, as further illustrated in Figure 5. The specimen is in a mechanical load frame, heated by halogen lamps; however, a vast variety of sample environments can be designed, such as an in operando battery cell, and reaction chambers. Note: Q, scattering vector; η, azimuthal angle.

Most often, however, strain and particle size are crystallographically anisotropic and also exhibit some distribution, transforming the use of these basic relations into the use of more complicated fitting and modeling procedures.^{Reference Ungár, Gubicza, Ribárik and Borbély32}

Anisotropy may occur in uniaxially loaded specimens and in textured samples,^{Reference Kocks, Tomé and Wenk33} for which such 2D patterns can be sectored^{Reference Liss and Yan31,Reference Liss, Qu, Yan and Reid34} and evaluated along their orientation. In extreme cases, the azimuthal distribution of intensity along the rings is either continuous, stemming from a large number of randomly oriented grains, or shows only a few spots, if any, to be identified as a reflection from a single crystal or crystallite. A small number of reflecting crystallites results in a low number of spots on the rings, and their distribution has been traced by the previously mentioned materials oscilloscope, for instance in plastic-deformation processes at high temperatures (Figure 5).^{Reference Liss and Yan31} The spots are not intrinsically sharp, but are convolved with the beam size. Moreover, they map features of the reflecting grain, which may consist of subgrains with slightly different orientations and stress states.^{Reference Liss, Bartels, Clemens, Bystrzanowski, Stark, Buslaps, Schimansky, Gerling, Scheu and Schreyer35} Mapping of these spots has been developed by some groups,^{Reference Lienert, Li, Hefferan, Lind, Suter, Bernier, Barton, Brandes, Mills, Miller, Jakobsen and Pantleon36} and is now driven by the introduction of magnifying optics in the spot beam path, as described in the Simons et al. article.

Figure 5. 2D in situ data acquisition from a materials oscilloscope. (a) False-color photograph of a glowing titanium aluminide-based alloy specimen (cylinder, 8 mm length and 4 mm diameter) between the jaws of a thermomechanical processor. The thermocouple is shown by the two red lines at the bottom. A sketched incoming beam and a diffraction pattern in the background were added to the illustration.^{Reference Liss30} Diffraction patterns from a zirconium alloy under heating in (b) α phase and (c) (α + β) phase, and (d) during hot plastic compressive flow in the β phase. Radial, Q, and azimuthal, η, coordinates are indicated, as well as an azimuthally integrated powder diffractogram (inset, blue).^{Reference Liss52} Such time-resolved diffractograms not only allow the study of phase evolution with the integrated patterns, but also, deliver information about the grain orientations and relationships expressed by the intensity distribution along the Debye–Scherrer rings, and their evolution with time. Note: Q, wavenumber transfer; η, azimuthal angle; I, intensity; t, time; T, temperature; L, longitudinal direction of compression. Scale markers are given in direct space (8 mm) and reciprocal space (1 Å^–1 cross).

Imaging and spatial mapping

X-ray topography,^{Reference Black and Long37} called dark-field imaging in electron microscopy, is the mapping of a crystal reflection onto a 2D detector and resolving contrasts from various origins. The latter can be crystal distortions, changes in the intensity by increasing the extinction depth, or small-angle grain boundaries by displacing parts of the diffracted beam under an angle such that their imprints can partly overlap or have a gap, resulting in a bright or a dark line, respectively. In parallel to electron backscatter diffraction, orientations of subgrains can be mapped and further evaluated, such as orientation boundaries, and peak width, as described in the Simons et al. article. Here, x-rays have the advantage of much higher intrinsic angular resolution as compared to electron diffraction and are capable of resolving local strain and derivative strain components in the examined material.

Another diffraction-mapping method presented by X. Chen et al. in their article is the application of white beam Laue diffraction as a function of position, as well as rastering the image. In contrast to monochromatic-beam diffraction, as previously explained, a white beam that contains a continuous spectrum impinges a crystal. Then, for a given reciprocal lattice vector length and orientation, a matching wave vector is selected from a large range of wave vectors. Thus, a reflection always exists for any arbitrary orientation, within the half space of Q oriented toward the incident beam and within the limits of the incident spectral distribution. For a single crystal, a multitude of reciprocal lattice vectors (i.e., lattice-plane orientations) results in a set of diffraction spots, from which the orientation of the crystal can be determined. Again, if lattice defects (e.g., dislocations and small-angle grain boundaries) exist, peaks spread out into streaks or distributions, respectively.^{Reference Barabash, Ice, Larson, Pharr, Chung and Yang38,Reference Barabash, Ice, Tamura, Valek, Bravman, Spolenak and Patel39}

In particular, the white beam Laue method has been combined with micro- and nanometer-sized beam diffraction, resolving local structures, and key information has been collected in a book edited by two of the pioneers of this field, Barabash and Ice.^{Reference Barabash and Ice40}

More generally, both white and monochromatic micro- and nanobeam diffraction methods have evolved in various fields of research. Besides the trend of extensive applications in geophysics,^{Reference Chen, Kunz, Tamura and Wenk41} mineralogy, and biomineralogy,^{Reference Zhang, Ma, Chen, Kunz, Tamura, Qiang, Xu and Qi42,Reference Tamura, Gilbert and De Yoreo43} the intensive combination with electron microscopy to explore the nanoscale world^{Reference Yu, Qi, Chen, Mishra, Li and Minor44,Reference Guo, Chen, Oh, Wang, Dejoie, Syed Asif, Warren, Shan, Wu and Minor45} has matured, in conjunction with ongoing improvements in the data-analysis approaches.^{Reference Chen, Dejoie and Wenk46,Reference Li, Wan and Chen47} The article by X. Chen et al. emphasizes some new features and further developments of these techniques, including the significant improvement of spatial resolution at the Taiwan Photon Source, and small-molecule structure refinement by interpreting the monochromatic and polychromatic x-ray diffraction signals from the same crystal.

Besides the discipline of diffraction, spectroscopic methods are widely established at synchrotron sources. In their article, Liu and Weng present an example of the soft x-ray range using absorption spectroscopy. Absorption based on the photoelectric effect is achieved when a bound electron, often inner K or L electrons, is excited by the x-rays, leaving a hole (Figure 6). In this process, the x-ray energy must be sufficient to overcome the binding potential energy of the electron sitting in the atomic shell. When the x-ray energy is scanned upward, higher absorption occurs suddenly in a step pattern at the edge, where the threshold is overcome and the photon energy becomes sufficient to eject the electron. Since, in principle, that same electron could fill the hole again, which is stimulated light emission, the entire process is a coherent resonance phenomenon, where the wave function of the simultaneously bound and freed electron needs to be considered in detail, including its extension to its nearest neighbors.

As the electron wave backscatters toward the hole, the stimulated emission contribution, and thus the whole absorption process, varies in amplitude and yields observable fringes in the absorption spectrum. The electron-wave interference pattern depends sensitively on both electron wavelength (which changes with the x-ray energy) and the local morphology of the electron cloud where the atom sits (i.e., its local crystal structure or other environment), leading to the extended x-ray absorption fine structure, known as EXAFS. In particular, the oxidation state of an ion defines the local environment, namely at the absorbing atom itself, leading to fingerprint-like characteristics at or close to the edge, allowing determination of the oxidation state. The energy of the absorption edges is dictated by the nature of the atoms, covering the very soft and soft x-rays for the lighter elements, hard x-rays for the K-edges of medium elements, and L-edges of heavier elements.^{Reference Thompson, Lindau, Attwood, Liu, Gullikson, Pianetta, Howells, Robinson, Kim, Scofield, Underwood, Kortright, Williams and Winick48}

Figure 6. Schematic for the formation of an x-ray absorption fine structure. Absorption takes place by ejecting a core electron of the central atom from the K or L shell into the conduction band B or C, where it can travel to neighboring atoms and scatter back. The electron amplitude and energy levels depend minutely on the interference of these traveling waves, which depend on energy. Here, band state B has a slightly higher energy level than band state C at the central atom. The scattering process is a superposition of the absorption and stimulated emission of light, and lasts on a femtosecond scale. This process involves many attosecond cycles of the x-ray wave (X), during which a standing electron wave builds up, thus modulating the absorption probability. In quantum mechanics, the process of absorption is not localized at a fixed position, but instead is distributed over many equivalent atoms, giving rise to the interference.

The details and variations of absorption spectroscopy are more deeply explored in Liu and Weng’s article. They present example applications and a study that further explores the chemical bonds at the solid–electrolyte interface in Li-ion batteries, making a thematic link to the diffraction work by Glazer et al. Similarly, the B. Chen et al. article reports on the complementary nature of absorption spectroscopy and diffraction as well as the characterization of materials under high pressure.