To drive free electron laser (FEL)-based, fully coherent, short-wavelength (X-ray) sources and to implement techniques such as laser and plasma acceleration for a future generation of compact electron accelerators requires the most demanding beam parameters: εnr < 1 μm rad, (ΔE/E)<0.1%, Bnr ∼ 1015 A (m rad)−2, τ ≈ ps and peak bunch current Îb ∼ kA. (Such specifications are beyond those at present routinely obtainable. Physics and technology of generating and transporting very high brightness, intense beams are therefore being actively researched and developed worldwide and advancing very fast.) Next generation colliders for particle physics also need a similar source performance and, in addition, high bunch charge, polarized, ribbon-shaped beams.
Preinjector systems (so-called because they are normally only the first part of the injector to the final accelerator) have been developed to approach the above listed specifications, consisting of a high-energy gun and of a number of auxiliary components. A several MeV electron gun is the first component needed to accelerate the source-emitted electrons as fast as possible to relativistic energies to minimize space-charge force effects, scaling like 1/γ2, which tend to blow the beam emittance up. It can be shown, by ideally slicing up the bunch like a loaf, that the emittance at the gun output has a fan-like structure in phase space (Figure 4a) due to space-charge forces being stronger on slices near the bunch center than on tail ones. Each bunch slice thus contributes one of the ribs of the fan, and the rms normalized emittance of the whole fan becomes much larger than that of any individual slice. The fraction of the fan-like blow-up caused by the linear components of the space-charge force can be taken out (compensated) by adding a solenoid at the gun exit followed by a drift space, and by additional accelerating sections and by proper shaping the bunch-charge distribution (should ideally be uniform). How the scheme works is seen in the simulation whose results are presented in Figures 4 and 5. The simulation follows a uniform charge distribution through from cathode to the end of such a space-charge compensated preinjector whose two-Linac sections provide acceleration to 150 MeV.
Figure 4a shows the beam phase-space footprint at the gun output, and its beam-stay-clear equivalent ellipse having four times the area of the fan-like rms distribution. Figures 4b and 4c show how the compensating solenoid and the following drift space reduce the footprint. A further reduction of the rms emittance in the final accelerating sections is shown in Figure 5. The end εn value is essentially due to thermal contributions and to nonlinear space charge force components only.
Peak-normalized brightness values measured at state-of-the-art preinjector installations are shown in Figure 6. Normalized emittances in the 2–4 μm rad range are routinely obtained today at peak bunch currents up to Îb ∼ 50 − 100 A.
To raise the peak bunch current, preinjectors are being developed using the preinjector additional accelerating sections to reduce the bunch length also: energy-chirping of the moderately relativistic (≈5 MeV) bunch produced by the gun and injection into the following accelerator sections far off the RF field crest produces a velocity bunching so that the bunch itself is simultaneously compressed and accelerated. Focusing solenoids are added around the accelerating sections to prevent an emittance blow-up.
Concerning the beam time structure, preinjectors generate bunch trains whose typical configuration is shown in Figure 7: a train of (macro) pulses, each containing a train of short bunches. The macropulse duration TM and repetition frequency, 1/Trep, are usually determined by the allowed average power consumption of the particle source and of the accelerator. Duty factors range from ∼10−5 to ∼10−1. The bunch repetition frequency in the macropulse is a subharmonic of the accelerating field frequency 1/TRF, which also determines the initial bunch duration, τ.
Preinjector high-voltage guns in operation are basically of two types. The first consists of a normal thermionic DC gun followed by a high frequency, standing or traveling wave-accelerating structure. The second (RF gun), simpler and more compact, combines gun and accelerating structure in one by directly embedding the cathode in a standing-wave RF cavity. A≈50–100 MV m−1 peak RF field in the ≈10 cm long cavity provides very fast acceleration to several MeV, thereby minimizing the effect of the defocusing space charge forces. The cathode of either type gun can be either thermionic or a photocathode from which electrons are photoelectrically extracted by illuminating it with a laser beam.
Schematic diagrams of RF gun structures are shown in Figures 8a and 8b, one mounting a thermionic cathode, the other a photocathode.
The main asset of thermionic, metallic cathodes is stability of the emitted current and long lifetime. Drawing from micro-applications technology single crystal, mm-diameter LaB6 cathodes are being proposed to achieve a high current with emittance values at the thermal limit. The required bunch microstructure must be produced by chopping or velocity-bunching their continuous macropulse current.
With photocathodes, the beam microstructure can be directly generated by modulating the drive laser pulse length, shape, spot size, and intensity on a pulse-to-pulse basis. On the other hand, stabilising to percent accuracy, the extracted current, which depends on the pulse-to-pulse stability of the high-power high-repetition rate driving laser, is more difficult. Nevertheless, because they offer much higher extracted current densities than thermionic devices, photocathodes are today’s choice for high-peak current, bright-beam applications.
Photocathode materials such as Cu and Mg, to be illuminated with UV light, can operate in pressures of ∼10−7 hPa, have low, albeit constant, quantum efficiencies (QE) in the 10−3–10−4 range. Alkali (Cs, K, Rb, RbCs) telluride semiconductor devices, illuminated with 4.5 eV UV light, require ultrahigh vacuum (≈10−9 hPa) but have high efficiency and long lifetime: Cs2Te photocathodes have been routinely operated in accelerators with initial QE of ≈10%, gradually dropping to a few percent over many months of useful lifetime.
Negative electron affinity (NEA) photocathodes have the advantage of operating at longer laser wavelengths. Illuminated with polarized light, NEA-GaAs devices can also produce 80–90% polarized beams; they are being developed aiming at ps long, ≈1 nC bunches with εn≈5×10−5 m rad. For acceptable quantum efficiency lifetime though, they must operate in ∼10−11 hPa vacuum, a specification not easy to meet with high-frequency RF guns because of the intrinsic low pumping conductance of the RF structure. Preinjectors equipped with easier-to-evacuate DC guns, low-frequency (larger iris) RF guns or open RF gun structures of the “plane wave transformer” type are therefore also being developed. Other photoemitters such as diamond-based, ferroelectric ceramic, and nanostructured carbon cathodes are also being studied. Parameters of the most commonly used photocathode materials are collected in Table 3.
Table 3. Parameters of various photocathode materials
|Material||Quantum efficiency (QE)||Lifetime||Required vacuum (hPa)||Laser wavelength (nm)|
|Alkali Telluride||0.1||>1 year||10−9||260|
Gun developments include RF devices capable of generating bright, continuous microbunch trains for applications requiring the highest possible average current such as CW operation of superconducting linear accelerators.
New types of preinjectors are also being studied, such as high-brightness devices, promising to directly generate 100 fs, 0.1 nC bunches with peak currents up to ≈103 A, by integrating the gun into the preinjector high-energy accelerating section. A photocathode is mounted only a few mm away from the back wall of a Linac section serving as anode. By generating GV m−1, sub-ps pulses across the mm wide cathode-to-anode gap, photoelectrons are accelerated to several MeV in a few fs and directly injected into the preinjector final acceleration section, so that essentially no space-charge-induced emittance blow-up is expected.
More exotic schemes are being investigated for applications to further future laser–plasma accelerators. As an example, an “all-optical” electron source for a laser-driven plasma wake-field accelerator is claimed to be capable of GV cm−1 electric fields, micrometer spot sizes, femtosecond-long bunches, and GA cm−2 current densities. The scheme foresees a first-drive laser creating a plasma wake by ionizing a confined gas to below its self-trapping threshold (free electrons oscillating around ions). The transverse ponderomotive force of a second (injection) laser pulse, shining orthogonal to the first, then imparts to the plasma electrons an extra kick in the wave direction so as to inject them into the plasma wake-field with the correct phase to be trapped and accelerated.View chapterPurchase book
N.S. Bajaj, R.A. Joshi, in Energy Materials, 2021
188.8.131.52 X-ray diffraction
X-rays are electromagnetic radiation that typical have photon energies in the range of 100–100 keV. For diffraction applications, only short-wavelength X-rays in the range of a few angstroms to 0.1 Å, which means in the range of 1–120 keV energy, are used. Because the wavelength of X-rays is comparable to the size of atoms, they are ideally suited for probing the structural arrangement of atoms and molecules in a wide range of materials. The energetic X-rays can penetrate deep into the materials and provide information about the bulk structure.
X-rays primarily interact with electrons in atoms with which they collide, and some photons from the incident beam are deflected away from the original. If the wavelength of these scattered X-rays does not change, the process is called elastic scattering where only momentum transfer takes place. These diffracted X-rays are measured to extract information about the material, since they carry information about the electron distribution in materials. Diffracted waves from different atoms can interfere with each other and the resultant intensity distribution is strongly modulated by this interaction. If the atoms are arranged in a periodic fashion as in crystals, the diffracted waves will consist of sharp interference maxima with the same symmetry as in the distribution of atoms.
Measuring the diffraction pattern therefore allows us to deduce the distribution of atoms in a material. When certain geometric requirements are met, X-rays scattered from a crystalline solid can constructively interfere, producing a diffracted beam. In 1912, W.L. Bragg gave the relation, which elucidates the condition for constructive interference. The Bragg equation is defined as:(3.1)nλ=2dsinθ
where n denotes the order of diffraction, λ represents the wavelength, d is the interplanar spacing, and θ signifies the scattering angle. The distance between similar atomic planes in a crystal is known as d spacing and is measured in angstroms. The angle of diffraction is called the θ angle and is measured in degrees. For practical reasons, the diffractometer measures an angle twice that of the θ angle [23–25]. A schematic diagram of X-ray diffraction is shown in Fig. 3.2.
The diffraction pattern so obtained acts as a fingerprint of that crystalline substance. Therefore the crystalline phase of a material can also be identified by examining the diffraction pattern. The widths of the diffraction lines are closely related to (1) size, (2) size distribution, (3) defects, and (4) strain in crystals.View chapterPurchase book
Egami Takeshi, Simon J.L. Billinge, in Pergamon Materials Series, 2012
4.3.5 Measurement Geometry and Sample Issues
The RAPDF measurement geometry has been described in detail above. We briefly discuss aspects of some of the other powder diffractometer geometries. Geometries for laboratory sources are discussed in more detail in Klug and Alexander (1974).
Roughly speaking, any powder diffraction measurement carried out to sufficiently high Q can be used for a PDF measurement. One example is the high-resolution powder diffractometer, ID31 at ESRF which has a bank of multiple analyzer crystals (Fitch, 2004). It is mostly used for high-resolution powder diffraction for crystallographic analyses but can also be used to good effect for PDF studies because the beamline can be operated with quite short-wavelength X-rays. No special setup is required, though care should be taken to count for a long time in the high-angle region. The high resolution results in PDFs extending very far in r-space, hundreds of nanometers. The sample geometry in this powder diffractometer is cylindrical (the powders are in capillary tubes). At a synchrotron where the illumination is highly parallel, this is the preferred sample geometry. There is no advantage of having flat samples giving parafocusing of a divergent incident beam. This is also becoming the norm with laboratory X-ray machines that make use of highly efficient graded multilayer mirror optics that both monochromatize and steer the beam. We refer the interested reader to the first edition of this book for a more in-depth discussion of data collection geometries for divergent sources.
As with any powder samples, the particle size should be small (< 40 μm) and uniform. This may be accomplished by careful grinding in a mortar and pestle and sieving the sample through a 400-mesh sieve. It is less relevant for nanoparticulate samples that do not have large coherently scattering grains. It is particularly important to avoid texture, preferential powder orientation, in the sample. This is generally easier when the particle size is smaller but can still be a problem if the powder grains have a particularly oblate or prolate morphology. Oblate samples are generally not a problem in capillaries, but needle-like samples can become significantly orientationally ordered in a capillary if the sample size is too big. Gentle grinding often takes care of the problem, but they could also be measured in the pill-shaped sample geometry described above to mitigate this problem.
Powders in pill form are often supported with thin kapton tape over the surface (Fig. 4.13). This is particularly important if the sample is to be cooled in a vacuum. Samples to be cooled may also be in kapton capillaries. Uncovered powders rarely survive the pump down as air trapped between the grains forces its way out. Differential thermal contraction between the sample holder and the powder itself can also loosen a tightly packed powder. A small amount of grease, or DUCO cement mixed with acetone, can also be mixed with a loose powder to stabilize it if the sample does not have to be recovered in its pristine state after the experiment. The scattering from the stabilizing agent is relatively weak. Traditional techniques of supporting a thin film of powder on a glass slide, widely used, for example, in sample characterization and d-spacing measurements, are unlikely to result in thick or uniform enough samples for the short-wavelength X-rays needed for PDF measurements.
Gwidon W. Stachowiak, … Grazyna B. Stachowiak, in Tribology Series, 2004
Other Methods of Surface Analysis
Most of the techniques discussed so far are unsuitable for the investigation of the crystalline state of the surface material in a wear scar. X-ray diffraction is the technique commonly used in materials research to analyze the crystalline structure of materials. Although this technique is suitable for the analysis of powders including wear debris and thin sections of materials, its applications to the analysis of wear scar surface material are extremely limited. Wear scar material, in most cases, exhibits a very complex structure and pronounced surface topography, which often prevents an accurate data from being collected. A technique, which allows for the analysis of structures of the solids is Extended X-ray Absorption Fine Structure (EXAFS). EXAFS is based on the principle of irradiating the sample material by short wavelength X-rays and measuring the energy spectrum of transmitted X-rays. The energy of the X-rays used is typically about 1 – 2 [GeV] so that a synchrotron is required as the source of X-rays. Analytical data is obtained from changes in X-ray energy when the X-ray photon energy of the impinging radiation is similar to the characteristic X-ray emitted from the sample under examination. A phenomenon known as the ‘absorption edge’ occurs at this point, where imposed X-ray radiation induces a resonant emission of characteristic X-rays. This effect is analogous to shaking a mechanical structure at a frequency close to its resonant frequency. In addition to the primary X-ray response of the absorption edge there are secondary emissions at higher X-ray energies. These higher energy emissions are the source of data for EXAFS. The operating principles of the EXAFS system are shown in Figure 8.36.
Secondary scattering of X-rays between adjacent atoms in a solid generate a superimposed variation in energy of the X-rays after passing through the specimen. Plotting the X-ray energy versus wavelength reveals various peaks. The peaks in X-ray energy spectrum beyond the absorption edge are sensitive to the distances between atoms within a crystalline structure or amorphous entity. This allows EXAFS to provide data about the solid state structure of a specimen. The X-ray spectrum is subjected to Fourier transformation and other analytical techniques, which are too specialised to describe here, before measurements of interatomic distance are obtained. When analysed by EXAFS, amorphous solids reveal one characteristic interatomic distance while crystalline solids show a series of interatomic distances .
EXAFS has been applied in the analysis of surface film formation in a sliding contact lubricated by Zinc Dialkyl Dithiophosphate . Analysis of wear debris, collected from sliding steel surfaces lubricated by Zinc Dialkyl Dithiophosphate (ZnDDP), by EXAFS confirmed that ZnDDP reacts with a steel surface to form an amorphous surface film. An amorphous surface film lacks grain boundaries for rapid diffusion of reacting elements which in this case are zinc, oxygen, sulphur and iron. The amorphous film would therefore not grow as rapidly (by chemical reaction of zinc etc. to form more film material) which would limit corrosive wear. One of the drawbacks of EXAFS is that this is a highly specialised technique requiring access to a synchrotron.
It should be mentioned that in most cases, evidence of either amorphous solid state or ultra-fine crystalline structure can be obtained directly from Transmission Electron Microscope (TEM) analysis.
To provide information of surface films on wear scars, radio-active energy has also been used in some applications. Radio-isotope tracers provide an extremely sensitive means of detecting deposits of specific elements on a surface. For example, in order to detect sulphur deposited in surface films on a wear scar after lubrication by Extreme Pressure additives (E.P. additives), the sulphur isotope S35 can be used . A basic difficulty however with the use of radio-isotope tracers are safety considerations in the laboratory during their use. Radio-isotope tracers can only provide a measure of the quantity of a particular element but unfortunately they do not provide data on the chemical state of an element. For example, the radio-isotope data on sulphur deposited in surface films on a wear scar after lubrication by E.P. additives does not indicate whether the sulphur is physically trapped on the surface as small granules or whether it has reacted to form a metal sulphide film. The limitations of data and severe safety problems have greatly curbed the use of radio-isotope tracers for tribological studies.
Surface films can also be detected by ellipsometry, which employs the measurement of the change in polarization state of light after reflection from a surface under examination. The refractive index and light absorption by any film on a surface can be determined by ellipsometry. Comparing the values of the refractive index and light absorption with external measurement of known material gives a simple form of surface film detection. However, the information available from ellipsometry is limited and has only been applied rarely in tribology [e.g. 94].View chapterPurchase book
Freddy Adams, Carlo Barbante, in Comprehensive Analytical Chemistry, 2015
6.5 Coherence and Imaging
The conventional approach to X-ray imaging relies on X-ray absorption as the sole source of contrast and draws exclusively on ray optics or geometrical optics to describe and interpret image formation. This approach ignores another, potentially more sensitive, source of contrast-phase information. In terms of the complex X-ray refractive index (n = 1 − δ − iβ) this means that the emphasis has been on the imaginary component iβ, with little or no attention paid, until quite recently, to the real component δ. It is with δ that we are primarily concerned when dealing with X-ray phase-contrast imaging.
X-ray beams produced from third-generation SR sources exhibit a high degree of coherence. The coherence results from the small source size σ (in the 50 μm range) combined with a large source-to-sample distance L (in the 100 m range). The transverse coherence length, dc = λL/2σ, is in the 100 μm range. This allows the measurement of ‘phase images’ by propagation, varying the sample-to-detector distance. In principle, this type of imaging provides increased sensitivity on the basis of the phase images by the visualisation of the phase jumps occurring at the edges of a particle or differences in the index of refraction. Phase retrieval approaches provide measurements of the local phase shift, which is proportional to the density variations in the sample.
6.5.1 Phase-Contrast Imaging
It is only over the last years that solutions to the use of coherent radiation for imaging started appearing. By now, Phase-Contrast Imaging (PCI) with X-rays has developed in a number of ways, utilising both synchrotron and laboratory sources. Phase differences can be detected by the various phase-contrast techniques, and there are several alternative approaches to undertake the image-formation process using computational techniques, many of them analogues to optical methods. PCI methods often rely on a relatively large object-to-detector distance to allow wave interference (Fresnel diffraction) to occur and manifest itself as contrast in the image plane. PCI methods are ‘differential’ techniques (depending on the object-to-detector distance used), where the phase contrast achieved depends on a first or second derivative of the phase shift. They allow one to study edge enhancement, e.g. boundaries, cracks, or fibrous structures.
A major class of methods for extracting both phase and absorption information is based on mathematical phase-retrieval techniques. Typically these techniques extract information from holographic or diffraction images of the sample. Alternative approaches are based on Gabor holography. These include synchrotron-based methods using a pinhole or a Fresnel zone plate focus as a secondary source. A simpler method, requiring no additional optics, is in-line PCI, where the wave is allowed to propagate beyond the sample sufficiently for Fresnel diffraction to occur. The in-line phase contrast approach can be used to produce edge-enhanced images of the sample. However, in order to obtain quantitative information about the sample, or to exploit the greater contrast available in the holographic imaging regime, the ability to perform phase retrieval on the images becomes important. Phase retrieval enables the phase shift imposed on the wave by the sample (e.g. in the object plane) to be recovered from the diffracted intensity distribution in the image plane .
Many examples of PCI techniques involve a varying combination of phase and absorption contrast and while both generally decrease with increasing X-ray energy, it is important to note that δ varies as λ2 whereas β varies as λ4 (λ being the X-ray wavelength), in the absence of any elemental absorption edges. Hence, the effects of phase contrast become progressively more dominant, relative to absorption-contrast effects, at shorter X-ray wavelengths.
Several phase-sensitive X-ray imaging methods have been developed in the past years. They can be classified into interferometric methods; techniques using an analyser crystal and free-space propagation methods. These techniques are different in terms of experimental setup, requirements in the illuminating radiation and nature of the detected signal. At the level of fundamental physics, these three modes are associated with direct measurements of the phase change introduced in the incident X-rays passing through the sample.
Phase-contrast X-ray imaging provides substantially enhanced contrast resolution for soft-tissues compared to conventional absorption radiography. Although it is essentially a visualisation technique, not an analytical tool, PCI can be of interest for pinpointing extremely small areas in heterogeneous samples for subsequent chemical imaging. For example, extremely small aerosol-induced lung injuries were observed by PCI .
A particular beamline for tomographic microscopy and coherent radiology experiments (TOMCAT, acronym for Tomographic Microscopy and Coherent rAdiology experimenTs) at the Swiss Light Source is described by Stampanoni et al. . It allows absorption-based tomographic microscopy, propagation-based phase contrast tomographic microscopy and differential phase-contrast tomographic microscopy over the energy range between 8 and 45 keV. The spatial resolution is ca. 1 μm in parallel beam geometry and ca. 200 nm in full-field geometry. The application of high-resolution X-ray phase contrast tomographic imaging with differential phase contrast and phase stepping in the biological and materials science fields is discussed by McDonald et al. . The two methods are complementary to one another: the differential phase contrast method providing higher sensitivity at moderate resolution, while the transfer of intensity approach is better for tomography of small samples at high spatial resolution.
6.5.2 Coherent Diffraction Imaging
In Coherent Diffraction Imaging (CDI), a highly coherent beam of X-rays, electrons or other wavelike particles or photons is incident on an object. CDI is also called lens-less imaging or diffraction microscopy and is the most promising form of high-resolution X-ray imaging. It simply records the intensity of diffraction patterns and reconstructs the image, and is one of the fastest-growing fields in X-ray science. The beam scattered by the object produces a diffraction pattern downstream, which is then collected by a detector. This recorded pattern is then used to reconstruct an image via an iterative feedback algorithm. Progress in diffractive imaging has shown that it is possible to recover the phase of a scattered wave field from its diffraction pattern, as long as the object (or the illumination on the object) is of a finite extent. This phase contrast imaging mode has important applications in improving resolution in electron microscopy, see Chapter 7.
While for X-ray microscopy CDI typically has a rather limited field of view, this problem can be solved by ptychography, a technique in which an extended object is raster scanned by a compact coherent illumination probe. The name ptychography, from the Greek word for fold, derives from this optical configuration; each reciprocal lattice point is convolved with some function, and thus made to interfere with its neighbours. Significant overlap of illumination for adjacent scan points then enables a self-consistent reconstruction from the entirety of collected coherent diffraction patterns . The image shown in Box 3.3 was collected using this technique.
Ptychography builds up an image by means of high-speed detectors, substantial data acquisition and computing power. The images are computed from transmitted X-ray micro-diffraction patterns collected at many positions of an X-ray probe beam as it is scanned across the sample. The real breakthrough of this technique is that the spatial resolution of the computed images is no longer limited by the quality or resolving power of a lens; it is dependent only on the X-ray wavelength and the highest scattering angles recorded in the micro-diffraction patterns. It is now the sample that bends the beam by scattering: the smallest sample line width gives rise to the largest diffracted angles and allows them to be collected by the far-field detector. This information must be decoded by numerical calculations that serve to reverse the propagation of the X-ray wave field that form the object to the far-field detector. Ptychography determines the phases of the diffracted X-rays by using the large redundancy of information encoded in the 3-D data set; a 2-D pattern is recorded for all points of the two transverse dimensions of the probe beam. Because the form of the probe-beam wave field is known, the sample image can be extracted directly, just as in a holographic image reconstruction.
6.5.3 X-ray Holography
X-Ray Fluorescence Holography (XFH) is a method of atomic resolution holography which utilises fluorescing atoms as a wave source or a monitor of the interference field within a crystal sample. The wave source is atoms emitting fluorescent X-rays in a sample. Part of the fluorescent X-rays are scattered by neighbouring atoms and form a hologram with atomic resolution. The interference pattern contains both the phase and the magnitude information of the object wave. Therefore, the original wave front can be reconstructed, giving the 3-D spatial arrangement of the objects.
In hard X-ray holography, the hologram-forming waves are the individual atoms: in principle, atomic-resolution imaging is therefore possible, in practice, 3-D atomic images around a specified element have a range of up to a few nanometres. The technique is expected to be used for medium-range local structural analysis, which cannot be performed by X-ray diffraction or X-ray absorption fine structure analysis .
The difference between CDI and holography is that in the latter case the phase problem is solved with a reference beam that interferes with the beam. The measurement is simple but it is difficult to observe accurately extremely weak holographic signals which are of the order of 10−3 of isotropic fluorescent radiation. Therefore, most of XFH experiments are performed at SR facilities, although laboratory experiments exist.View chapterPurchase book
Victor I. Mikla, Victor V. Mikla, in Medical Imaging Technology, 2014
1.2 The Use of X-Rays for Analysis
X-rays are a form of electromagnetic radiation, as is light (Figure 1.2). Their distinguishing feature is their extremely short wavelength—only about 1/10 000 that of light (or even less). This characteristic is responsible for the ability of X-rays to penetrate materials that usually absorb or reflect ordinary (visible) light.
X-rays exhibit all the properties inherent of light, but in such a different degree as to modify greatly their practical behavior. For example, light is refracted by glass and, consequently, is capable of being focused by a lens in such instruments as cameras, microscopes, telescopes, and spectacles. X-rays are also refracted, but to such a very slight degree that the most refined experiments are required to detect this phenomenon. Hence, it is impractical to focus X-rays. It would be possible to illustrate the other similarities between X-rays and light but, for the most part, the effects produced are so different—especially their penetration—that it seemed preferable to consider X-rays separately from other radiations. Figure 1.2 shows their location in the electromagnetic spectrum.
Their similarities to light led to the tests of established wave optics: polarization, diffraction, reflection, and refraction. Despite limited experimental facilities Roentgen could find no evidence of these. May be, it was additional reason he called them “x” (unknown) rays.
For diffraction applications, only short wavelength X-rays (hard X-rays) in the range of a few Angstroms to 0.1 Å (1−120 keV) are used. Because the wavelength of X-rays is comparable to the size of atoms, they are ideally suited for probing the structural arrangement of atoms and molecules in a wide range of materials. The energetic X-rays can penetrate deep into the materials and provide information about the bulk structure.
The year 2012 marks the 100th anniversary of the discovery of X-ray diffraction (XRD) and its use as a probe of the structure of matter [8–11]. Sixteen years after Rontgen announced in 1895 his discovery of “X” rays that can penetrate the body and photograph its bones, Max von Laue, a professor of physics at the University of Munich in Germany, worked on a theory of the interference of light in plane parallel plates. Laue was Plank’s favorite disciple. His interest covers the whole of physics. If, as some argued, X-rays were not made up of particles but were a form of electromagnetic radiation similar to ordinary (visible) light, and then it should be possible to repeat well-known optical experiments using X-rays instead of beams of ordinary light.
In 1911, Laue suggested to one of his research assistants, Walter Friedrich, and a doctoral student, Paul Knipping, that they try out X-rays on crystals. His reasoning was that X-rays have a wavelength close to the interatomic distances in crystals, and as a result, the crystal should act as a diffraction grating (Figure 1.3). Laue, always the theoretician, did not actually make the necessary experiments. In a single elegant experiment performed by Friedrich and Knipping, Laue had proven the wave-like nature of X-rays and the space–lattice structure of crystals at the same time [8,9]. When he received the Nobel Prize for what the Committee said was his “epoch-making discovery”, Laue gratefully acknowledged Friedrich and Knipping for their roles in the discovery; and for him it went without saying that he shared his prize money with them [10,11]. Einstein hailed Laue’s discovery as one of the most beautiful in the history of physics.
Before the Laue experiment, did anyone dream of tools allowing one to explore the structure of matter on the molecular scale and use this information for deriving structure–property relationships of materials—or for understanding the molecular basis of life? After X-rays had already been used to image the internal anatomy of the human body, with the Laue experiment the internal structure of crystals also became accessible on nanoscale .
Laue’s pioneering work in X-ray crystallography opened the way for two, quite different, developments in physics, both of them of immense importance. First, it confirmed the electromagnetic nature of X-radiation and made it possible to determine the wave length of X-rays with great accuracy. Second, it gave physicists and chemists a new tool for investigating the atomic structure of matter. In the 1950s, it was XRD studies that enabled scientists to reveal the structure of the nucleic acids (DNA and RNA) and to establish the new discipline of molecular biology.
English physicists Sir William Henry Bragg and his son, Sir William Lawrence Bragg, argued that when the X-rays are reflected off two successive planes of atoms in the crystal, they interfere constructively if the difference in the distance traveled is equal to an integral number of wavelengths. Thus, the famous Bragg condition isnλ=2dsinθ
They have developed the above relationship to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (θ) . The variable d is the distance between atomic layers in a crystal, and the variable λ is the wavelength of the incident X-ray beam; n is an integer. This observation is an example of X-ray wave interference, commonly known as XRD, and was direct evidence for the periodic atomic structure of crystals. By 1913, just a year after they had pioneered the method, crystal analysis with X-rays had become a standard method. The results gave insight into the structure of crystals. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond (Figure 1.4) [2,11–13].
Bragg’s law describes the mechanism by which XRD occurs and was an extremely important discovery—it formed the basis for what is now known as crystallography (Figure 1.5).
X-rays primarily interact with electrons in atoms. When X-ray photons collide with electrons, some photons from the incident beam will be deflected away from the direction where they originally travel. If the wavelength of these scattered X-rays did not change (this means that X-ray photons did not lose any energy), the process is called elastic scattering in that only momentum has been transferred in the scattering process. These are the X-rays that one measure in diffraction experiments, as the scattered X-rays carry information about the electron distribution in materials. On the other hand, in the inelastic scattering process, X-rays transfer some of their energy to the electrons and the scattered X-rays will have different wavelength than the incident X-rays.
Diffracted waves from different atoms can interfere with each other and the resultant intensity distribution is strongly modulated by this interaction. If the atoms are arranged in a periodic fashion, as in crystals, the diffracted waves will consist of sharp interference peaks with the same symmetry as in the distribution of atoms. Measuring the diffraction pattern therefore allows us to deduce the distribution of atoms in a material. The peaks in an XRD pattern are directly related to the atomic distances.
In the same year, Moseley showed the wavelengths were not only characteristic of the element the target was made of, but also they had the same sequence as the atomic numbers. This allowed atomic numbers to be determined unambiguously for the first time.
X-ray crystallography is a standard technique for solving crystal structures. Its basic theory was developed soon after X-rays were first discovered more than a century ago. Over the years that follow it has gone continual development in data collection, instrumentation, and data reduction methods. In recent years, the advent of synchrotron radiation sources, area detector-based data collection instruments, and high-speed computers has dramatically enhanced the efficiency of crystallographic structural determination. Synchrotron radiation is emitted by electrons or positrons traveling at near light speed in a circular storage ring. These powerful sources, which are thousands to millions of times more intense than laboratory X-ray tubes, have become indispensable tools for a wide range of structural investigations and brought advances in numerous fields of science and technology .
Today X-ray crystallography is widely used in materials and biological research.
In X-ray crystallography, integrated intensities of the diffraction peaks are used to reconstruct the electron density map within the unit cell in the crystal. To achieve high accuracy in the reconstruction, which is done by Fourier transforming the diffraction intensities with appropriate phase assignment, a high degree of completeness as well as redundancy in diffraction data is necessary, meaning that all possible reflections are measured multiple times to reduce systematic and statistical error. The most efficient way to do this is by using an area detector. The latter can collect diffraction data in a large solid angle.
The most common use of powder (polycrystalline) diffraction is chemical analysis. This can include phase identification, investigation of high (low) temperature phases, solid solutions, and determinations of unit cell parameters of new materials. The crystalline inclusions in inorganic and organic polymers give sharp narrow diffraction peaks and the amorphous component gives a very broad peak (halo). The ratio between these intensities can be used to calculate the amount of crystallinity in the material.
Nowadays, XRD allows a range of determinations to be made including phase identification of crystalline materials, phase quantification, glass content, and quality control methods, to say about few.
Soon after it was also established that secondary fluorescent X-rays were excited in any material irradiated with beams of primary X-rays. This started investigation into the possibilities of fluorescent X-ray spectroscopy as a means of qualitative and quantitative elemental analysis.View chapterPurchase book
Yousef A. Eltbaakh, … M.I. Fadhel, in Renewable and Sustainable Energy Reviews, 2011
2 Measuring broadband solar irradiance
Broadband instruments measure the combined solar intensity (irradiance) at all wavelengths (Pecht ). The instrument must be uniformly sensitive to all wavelengths from the very energetic and short wavelength X-rays to the very longest infrared wavelength (Calisesi et al. ). The most commonly used instruments to measure solar radiation today are based on either the thermoelectric or the photoelectric effects. The thermoelectric effect is achieved using thermopile that comprises collections of thermo couples, which consist of dissimilar metals mechanically joined together (Ghassemi ). The photoelectric effect is simpler and has instantaneous response and good overall stability. Among the photoelectric devices, photovoltaic instruments (PV) are most numerous in the field of solar radiation measurement. A photovoltaic device is made of a semiconducting material such as silicon (Igbal ). Instruments used to measure the transmission of sunlight through earth’s atmosphere fall two general categories (Ghassemi ):1.
Pyrheliometers: these are instruments that measure direct radiation. Instruments measuring direct radiation usually include radiation coming out to an angle of about 3° away from the sun’s disk. The sensor is a temperature-compensated thermopile placed at the bottom of a blackened collimator tube that limits the angular acceptance of solar radiation to about 5–6° (total). The instrument is oriented such that the direct radiation from the sun is parallel to the axis of the collimator tube.2.
Pyranometers: these are instruments that measure global and diffuse radiation. They have a shading disk to prevent direct solar radiation from reaching the sensor. The measurement for diffuse radiation involves correcting for the portion of the radiation shielded from the sensor by the shading disk. The sensor is a thermopile with alternate blackened junctions heated by the sun. The unheated junctions are near ambient temperature, which may be ensured by putting the unheated junctions in thermal contact with a white surface, heating by the sun is accomplished by placing the junctions in contact with a black surface (with high thermal conductivity) or by placing a black coating on the junctions. The instrument is installed in a level position, the sensor facing up towards the sky. Less expensive pyranometers may use a photovoltaic sensor to measure solar radiation (Pecht ).
2.1 Total broadband solar irradiance measurement
Lam and Li  measured both hourly horizontal global and diffuse solar components at City Polytechnic of Hong Kong during the 3-year period from 1991 to 1993 by using two pyranometers (CM11), manufactured by Kipp and Zonen. The diffuse radiation pyranometer was fitted with shadow-ring (CM121) to shade the thermopile from the direct sun. The pyranometers connected to an integrator (CM12) to calculate radiation over selected periods. A Pascal program had been written to capture the data from the integrator and store the data on a micro-computer. The monthly average of daily global, diffuse and direct solar radiations on a horizontal surface are shown in Fig. 1. The results showed that the annual average of global, diffuse and direct radiation were 13.4, 6.8 and 6.6 MJ m−2 d−1 respectively. Solar radiation during the day lends to be more evenly distribution in summer than in winter, and the maximum hourly value occurred at solar noon for both global and diffuse radiation.
Jacovides et al.  used several measured wavebands, 300–630 nm, 300–710 nm and 300–2800 nm which was measured using the Linke–Feussner pyrheliometric in Athens, Greece for the period 1954–1990 to study the effects of aerosol on the direct beam spectral solar irradiance distribution through effective optical depths. The observations were made at the National Observatory of Athens (NOA: latitude = 37°58′, longitude = 23°43′E, height above sea level = 107 m), at 11:20 and 14:20, Local Standard Time (LST is 2 h ahead of UTC) were used whenever clouds did not obscure the sun. Approximately seven thousand observations of direct solar spectra (300–710 nm) were taken under clear sky conditions defined to be less than 1/8 cloud cover with no clouds near the sun disk. Effective optical depths in the wavebands 300–630 nm, 300–710 nm and 300–2800 nm were calculated using Eqs. (1)–(3) respectively(1)τt=[ln It*−ln It]m
where It*=IΔλ* and It = IΔλ are the direct beam irradiances for an aerosol free and a real atmosphere, respectively, for the whole spectrum 300–2800 nm.(2)τt=[ln Ir*−ln Ir]m
where Ir*=I(300−630 nm)* and Ir = I(300−630 nm) are the corresponding direct beam irradiances for the finite waveband 300–630 nm.(3)τv=[ln Iv*−ln Iv]m
where Iv*=I(300−710 nm)* and Iv=I(300−710 nm) are the corresponding direct beam irradiances for the finite waveband.
Fig. 2 shows the variation in mean monthly values of effective optical depths τr, τv and τt and their standard deviations (SD) for the Athens Basin.
The relationships between τr and τv, and τt and τv were found to be linear.2
Both spectrally resolved optical depths τr and τv increase from 1954 until approximately 1975 and thereafter decrease gradually. τt optical depth increases during the period 1954–1977 and from 1985 decreases slightly towards the end of the period. During the early period 1954–1961 and during 1985–1990 the mean monthly values of both spectrally resolved optical depths coincide.3
The results showed that there may be a considerable depletion of direct beam solar irradiance because of the effective attenuation by atmospheric aerosol. In addition, the spectral distribution of direct irradiance in the visible waveband may also be significantly altered as attenuation by scattering increases markedly towards shorter.4
The effect of increasing aerosol concentrations on the visible band in the direct solar beam was investigated indirectly through the spectrally resolved optical depth τv. It was shown that the direct solar beam in the waveband 300–700 nm was markedly depleted.
Singh et al.  measured the global solar radiation on a horizontal surface at Lucknow (latitude 26.75°N, longitude: 80.50°E, altitude 120 m above sea level), Uttar Pradesh, India from April 1991 to March 1992 by using a precision pyranometer (calibration constant: 5.5 mV cal−1 cm−2 min−1). A potentiometric chart (0–10 mV, a chart width of 120 mm and a normal chart speed of 20 mm h−1) recorder used to record the output of the pyranometer. These data had been analysed to develop new regression constants for estimating the hourly global solar radiation on a horizontal surface, which is based on the solar model proposed by Al-Sadah et al. Verification of the present constants was made by comparing the estimated ratios of hourly to daily global radiation (I/H) with the measured values. The estimated values of the monthly mean ratios (r/R), along with the measured values, as a function of the local time t for all the months of the year were plotted. Two samples have been chosen to be presented in this review (see Fig. 3). The results showed that the hourly global solar radiation on a horizontal surface can be satisfactorily estimated for the plane areas of Uttar Pradesh, India by using the new regression constants.
Souza et al.  used a Kipp and Zonen pyranometer, model CM5, to measure global solar radiation over the area of Maceió (9°40′S, 35°42′W, 127 m), located in Northeastern state of Alagoas, Brazil, during the period of January 1997–December 1999. The instrument connected to a data acquisition system, Microllogger 21XL Campbell Scientific Inc. which was programmed to yield information every 10 s and store averages value every 5 min. On cloudy days (Ktd≤0.03) during the dry season and rainy period (Fig. 4a and b) they were observed. The results showed that the maximum value of the hourly global solar radiation in the dry (September–February) and rainy (March–August) seasons were 3.18 and 2.5 MJ m−2, respectively.
Islam et al.  measured the global solar radiation at the Petroleum Institute of the capital city of the UAE, Abu Dhabi (24.43°N, 54.45°E) for one complete year 2007 with Middleton Solar EQ08-E First Class pyranometer; its calibration accuracy is ±3%, its short wave sensitivity is 1.00 mV W−1 m−2 and its response time (95%) is 11.7 s to get a better view of the solar energy potential in Abu Dhabi. Fig. 5 describes the daily average and daily maximum global solar radiation for the whole year of 2007. Daily average solar radiation data showed that average values were higher in the summer from April to August and were comparatively lower in winter. The highest daily average solar radiation value of 369 W m−2 was measured on May 3, whereas the daily maximum global radiation of 1041 W m−2 was recorded on February 8. Average daily energy throughout the year 2007 was 18.48 MJ m−2 day−1.
Islam et al.  measured the direct solar radiation at the Petroleum Institute of the capital city of the UAE, Abu Dhabi (24.43°N, 54.45°E) with Middleton Solar DN5-E pyroheliometer in 2007 for a complete year. The instrument was set 15 m from the ground level and recorded the direct solar radiation each 1 min. Daily and monthly of direct solar radiation were calculated from the one-minute average recorded by a Middleton Solar DN5-E pyranometer. Fig. 6 displays daily averages and daily peaks of direct beam solar radiation throughout the year. The results shows that the daily 1-min average maximum radiation of 937 W m−2 was recorded on February 20 whereas the highest daily average direct solar radiation value of 730 W m−2 was recorded on March 30, 2007.
2.2 Ultraviolet broadband solar irradiance measurement
Ogunjobi and Kim  made a series of measurements included ultraviolet UVB (280–320 nm), UVA (320–400 nm), broadband global (HG), and diffuse (HD) horizontal solar radiation continuously recorded from June 1998 to August 2001 at the Department of Environmental Science Building, Kwangju Institute of Science and Technology (lat. 35°10′N, long, 126°53′E, altitude 90 m asl), South Korea. The Kipp and Zonen model CM-11 pyranometers used to measure global solar irradiance and a second Kipp and Zonen model CM11, with a polar axis shadow band used to measure solar diffuse irradiance. The shadow band of the instrument blocks a strip of sky with a 3.3° umbral angle. The UV-S-B-T and UV-S-A-T pyranometers from Scintec were used to measure total irradiance from 280 to 320 nm and from 320 to 400 nm, respectively. The manufacturer indicates an accuracy of 10% for observation made for zenith angles between 0 and 50°, 6% between 50° and 60°, and 8% between 60j and 70°. The UVA and UVB radiometers present a cosine effect that is better than 5% for 0–60° zenith angles. Results from statistical analysis indicated that the minimum values were not representative of the total UV irradiation (HUVT) characteristics in Kwangju and, as such, they must be treated as being atypical. However, it may be concluded that the maximum values varying between 65.4 and 158.9 kJ m−2 can be considered as being representative of the hourly HUVT radiation at Kwangju. The monthly average hourly ratio of HUVT to HG varies from 7.0% to 9.4%. The highest value of HUVT accumulated throughout the year was observed in August, while the minimum was in January.
Jacovides et al.  measured the hourly global UV (GUV) (UVB and UVA), global (Gh) and diffuse (Gd) solar irradiances at the semi-urban Athalassa site, Cyprus (35°15′N, 33°40′E, 165 m above MSL) in the eastern Mediterranean basin, during an ongoing joint research campaign (1 January–31 December 2004) between the University of Athens (Laboratory of Meteorology) and the Meteorological Service of Cyprus, to determine the ratio of solar global UV to solar global irradiation (GUV/Gh) and its dependence on various atmospheric conditions. Solar global irradiance (305–2800 nm) was measured using the Kipp & Zonen model CM11 pyranometer (Delft, The Netherlands); a second Kipp & Zonen model CM11 with a polar axis shadow-band was used to measure the diffuse component. Solar global UVB and UVA components were measured with Skye High-Output Sensors (SKU-430 and 420, respectively, Skye, Powys, UK). Both instruments used a photovoltaic sensor in combination with special filters to detect the wavelengths they are designed for. The Skye sensors are calibrated in accordance with UK national standards via the National Physical Laboratory (NPL). Fig. 7 shows the daily variability of both radiant fluxes, Gh and Guv, for the period of measurements.
The results showed that the percentage ratio Guv/Gh ranges from 3.9570.29% in September to 2.9270.42% in August for hourly values, while for daily values, the ratio varies between 3.6870.1% in September and 2.8570.32% in August, with annual mean value of 3.1970.17% for daily ratios and up to 3.3370.21% for hourly values. The hourly and daily values of both radiant fluxes are highly correlated with a general linear relationship of the form Guv = αGh between the measured values providing coefficients of determination R2 always greater than 0.91 for hourly and 0.88 for daily fittings.View article
A review of polymethyl methacrylate (PMMA) as a versatile lithographic resist – With emphasis on UV exposure
Faiz Rahman, … Savas Kaya, in Microelectronic Engineering, 2020
3.2 Positive tone lithography using X-rays
PMMA is also widely used as a positive tone X-ray resist. Even way back in 1980, Flanders reported the replication of 175-Å lines and spaces in PMMA using X-ray lithography . Later, during the 1999–2002 period, Cerrina and Ade published detailed studies of PMMA and other organic materials as resists for X-ray lithography [55,56]. Another very useful survey, that also covers electron beam resists, has been provided by Schnabel and Sotobayashi . At such short wavelengths, X-ray photons behave very much like accelerated electrons and thus X-ray lithography, except for the exposure source, works mechanistically very much like conventional electron beam lithography. However, the major difference is that whereas electron beam lithography is serial (line-by-line exposure), X-ray lithography is a parallel patterning process. This makes X-ray lithography of particular interest for ultra-small structure definition in the industry. The main challenge in carrying out X-ray lithography (other than having access to a suitable X-ray source) is having the right mask. X-ray lithography masks are significantly more challenging to make when compared with UV and DUV masks. Thus, a great deal of effort in X-ray lithography goes into making suitable masks which are generally made from thin suspended silicon nitride membranes overlaid with either gold or multilayer metal films of silicon and molybdenum; acting as X-ray blockers. Gold is generally preferred because due to its high atomic weight it provides good X-ray blocking. Molybdenum/silicon multilayers are used for reflective X-ray masks because they act as efficient Bragg mirrors at X-ray wavelengths. Good descriptive coverage in this area has been provided by Malek et al. They have described the requirements for deep x-ray lithography (DXRL) masks and also a cost-effective mask fabrication process. Furthermore, their review includes a summary of tabulated properties for materials used in the fabrication of DXRL masks . Klein et al. have also described X-ray mask making techniques and their performance metrics with good detail . X-ray sources, masks and PMMA as a resist for X-ray lithography are also particularly well described by Christenson and Guckel . Their work was mainly carried out at the 2.5 GeV National Synchrotron Light Source (NSLS) storage ring at Brookhaven National Laboratory.
The PMMA used in X-ray lithography is, generally, developed by the same developer as is used for electron beam lithography i.e. a mixture of MIBK and IPA. Some alternative developer schemes have been described by Malik and Yajamanyam . Their studies of the development characteristics of PMMA under X-ray exposure included the influence of various parameters, such as resist thickness, pre-exposure thermal treatment), exposure conditions (x-ray incident energy, dose at the bottom of the resist, rate of dose deposition, distribution of dose inside the resist), development conditions (temperature, megasonic-assistance, length of cycle into developer and rinse baths), post-exposure treatments (storage, thermal treatment), etc. The study also focused on the surface finish of the parts corresponding to different exposure and development conditions.
Beyond conventional X-ray lithography, there have also been other innovations in this field. Sugiyama et al., for instance, have described X-ray exposure on a moving resist . They employed X-rays from a Synchrotron source to expose a moving resist + substrate system. The resulting time-variable exposure was used to fabricate micro-lens and micro-needle arrays with sloped side-walls and curved surfaces, respectively. They named their technique plain-pattern to cross-section transfer (PCT) technique. X-ray lithography-based Micro-needle arrays have also been fabricated by Moon and Lee using inclined X-ray exposure .