Chapter 6 Properties, Sources, and Detection of Radiation

In the preceding five chapters, we introduced basic concepts of symmetry, and discussed the structure of crystals in terms of three-dimensional periodic arrays of atoms and/or molecules, sometimes perturbed by various modulation functions. In doing so, we implicitly assumed that this is indeed the reality. Now it is time to think about the problem from a different point of view: how atoms or molecules can be observed – either directly or indirectly – and thus, how is it possible to determine the crystal structure of a material and verify the concepts of crystallographic symmetry.

To begin answering this question, consider the following mental experiment: imagine yourself in a dark room next to this book. Since human eyes are sensitive to visible light, you will not be able to see the book, nor will you be able to read these words in total darkness (Fig. 6.1, left). Only when you turn on the light, does the book become visible, and the information stored here becomes accessible (Fig. 6.1, right). The fundamental outcome of our experiment is that the book and its content can be observed by means of a visible light after it has been scattered by the object (the book), detected by the eyes.

In general, a source of rays and a suitable detector (such as the light bulb and the eye, respectively) are required to observe common objects. Atoms, however, are too small to be discerned using any visible light source, because atomic radii 1 range from a few tenths of an angstr¨om to a few angstr¨oms, and they are smaller than 1/1,000 of the wavelengths present in visible light (from ∼4,000 to ∼7,000 ˚A).

A suitable wavelength to observe individual atoms is that of X-rays. The latter are short-wave electromagnetic radiation discovered by W.C. Roentgen, 2 and they have

1 Atomic radius may be calculated self-consistently or it may be determined from experimental structural data. Effective size of an atom varies as a function of its environment and nature of

chemical bonding. Several different scales – covalent, ionic, metallic, and Van der Waals radii – are commonly used in crystallography.

2 Wilhelm Conrad Roentgen (1845–1923). German physicist who on November 8, 1895 discovered X-rays and was awarded the first ever Nobel Prize in Physics in 1901 “in recognition of

the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” For more information about W.C. Roentgen see http://www.nobel.se/physics/ laureates/1901/index.html on the Web.

108 6 Properties, Sources, and Detection of Radiation

Fig. 6.1 The illustration of an observer placed in the absolutely dark room with a book (left) and the same room with the light source producing visible rays of light (right).

the wavelengths that are commensurate with both the atomic sizes and shortest interatomic distances.

Unfortunately, the index of refraction of X-rays is near unity for all materials and they cannot be focused by a lens in order to observe such small objects as atoms, as it is done by glass lenses in a visible light microscope or by magnetic lenses in an electron microscope. Thus, in general, X-rays cannot be used to image

individual atoms directly. 3 However, as was first shown by Max von Laue in 1912 using a single crystal of hydrated copper sulfate (CuSO 4 · 5H 2 O ), the periodicity of the crystal lattice allows atoms in a crystal to be observed with exceptionally high resolution and precision by means of X-ray diffraction. As we will see later, the diffraction pattern of a crystal is a transformation of an ordered atomic structure into reciprocal space, rather than a direct image of the former, and the three-dimensional distribution of atoms in a lattice can be restored only after the diffraction pattern has been transformed back into direct space.

Particles in motion, such as neutrons and electrons, may be used as an alternative to X-rays. They produce images of crystal structures in reciprocal space because of their dual nature: as follows from quantum mechanics, waves behave as particles (e.g., photons), and particles (e.g., neutrons and electrons) behave as waves with

wavelength λ determined by the de Broglie 4 equation:

where h is Planck’s constant (h = 6.626 × 10 −34 Js ), m is the particle’s rest mass, and v is the particle’s velocity (mv = p, particle momentum).

3 Direct imaging of atoms is feasible using X-ray holography, in which the wave after passing through a sample is mixed with a reference wave to recover phase information and produce three-

dimensional interference patterns. See R. Fitzgerald, X-ray and γ-ray holography improve views of atoms in solids, Phys. Today 54, 21 (2001).

4 Louis de Broglie (1892–1987) the French physicist who postulated the dual nature of the electron. In 1929 was awarded the Nobel Prise in physics “for his discovery of the wave nature of electrons.”

See http://nobelprize.org/nobel prizes/physics/laureates/1929/broglie-bio.html for details.

6.1 Nature of X-Rays 109 For example, a neutron (rest mass, m = 1.6749 × 10 −27 kg) moving at a constant

velocity v = 3, 000 m/s will also behave as a wave with λ = 1.319 ˚

A. Moreover, charged particles, for example, electrons, can be focused using magnetic lenses. Thus, modern high-resolution electron microscopes allow direct imaging of atomic structures (for the most part in two dimensions on a surface) with the resolution suf- ficient to distinguish individual atoms. Direct imaging methods, however, require sophisticated equipment and the accuracy in determining atomic positions is sub-

stantially lower than that possible by means of diffraction techniques. 5 Hence, direct visualization of a structure with atomic resolution is invaluable in certain applications, but the three-dimensional crystal structures are determined exclusively from diffraction data. For example, electron microscopy may be used to determine unit cells or modulation vectors, both of which are valuable data that may be further employed in solving a crystal structure using diffraction methods, and specifically, powder diffraction.

Nearly immediately after their discovery, X-rays were put to use to study the in- ternal structure of objects that are opaque to visible light but transparent to X-rays, for example, parts of a human body using radiography, which takes advantage of varying absorption: bones absorb X-rays stronger than surrounding tissues. It is in- teresting to note that the lack of understanding of their nature, which did not occur until 1912, did not prevent the introduction of X-rays into medicine and engineer- ing. Today, the nature and the properties of X-rays and other types of radiation are well-understood, and they are briefly considered in this chapter.

6.1 Nature of X-Rays

Electromagnetic radiation is generated every time when electric charge accelerates or decelerates. It consists of transverse waves where electric (E) and magnetic (H) vectors are perpendicular to one another and to the propagation vector of the wave (k), see Fig. 6.2, top. The X-rays have wavelengths from ∼0.1 to ∼100 ˚A, which are located between γ -radiation and ultraviolet rays as also shown in Fig. 6.2, bottom. The wavelengths, most commonly used in crystallography, range between ∼0.5 and ∼2.5 ˚A since they are of the same order of magnitude as the shortest interatomic distances observed in both organic and inorganic materials. Furthermore, these wavelengths can be easily produced in almost every research laboratory.

5 Despite recent progress in the three-dimensional X-ray holography [e.g., see M. Tegze, G. Faigel, S. Marchesini, M. Belakhovsky, and A. I. Chumakov, Three-dimensional imaging of atoms with

isotropic 0.5 ˚ A resolution, Phys. Rev. Lett. 82, 4847 (1999)], which in principle enables visualization of the atomic structure in three dimensions, its accuracy in determining coordinates of atoms and interatomic distances is much lower than possible by employing conventional diffraction methods.

110 6 Properties, Sources, and Detection of Radiation E Wavelength, λ

microwave radio

10 −12 10 −11 10 −10 10 −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 Wavelength, λ (m)

Fig. 6.2 Top – the schematic of the transverse electromagnetic wave in which electric (E) and magnetic (H) vectors are mutually perpendicular, and both are perpendicular to the direction of the propagation vector of the wave, k. The wavelength, λ, is the distance between the two neigh- boring wave crests. Bottom – the spectrum of the electromagnetic waves. The range of typical X-ray wavelengths is shaded. The boundaries between different types of electromagnetic waves are diffuse.

6.2 Production of X-Rays

The X-rays are usually generated using two different methods or sources. The first is

a device, which is called an X-ray tube, where electromagnetic waves are generated from impacts of high-energy electrons with a metal target. These are the simplest and the most commonly used sources of X-rays that are available in a laboratory of any size, and thus, an X-ray tube is known as a laboratory or a conventional X-ray source. Conventional X-ray sources usually have a low efficiency, and their bright-

ness 6 is fundamentally limited by the thermal properties of the target material. The latter must be continuously cooled because nearly all kinetic energy of the accelerated electrons is converted into heat when they decelerate rapidly (and sometimes instantly) during the impacts with a metal target.

The second is a much more advanced source of X-ray radiation – the synchrotron, where high energy electrons are confined in a storage ring. When they move in a circular orbit, electrons accelerate toward the center of the ring, thus emitting elec-

tromagnetic radiation. The synchrotron sources are extremely bright (or brilliant 7 ) 6 Brightness is measured as photon flux – a number of photons per second per unit area – where

the area is expressed in terms of the corresponding solid angle in the divergent beam. Brightness is different from intensity of the beam, which is the total number of photons leaving the target, because intensity can be easily increased by increasing the area of the target irradiated by electrons without increasing brightness.

7 The quality of synchrotron beams is usually characterized by brilliance, which is defined as brightness divided by the product of the source area (in mm 2 ) and a fraction of a useful photon

6.2 Production of X-Rays 111 since thermal losses are minimized, and there is no target to cool. Their brightness

is only limited by the flux of electrons in the high energy beam. Today, the so-called third generation of synchrotrons is in operation, and their brilliance exceeds that of the conventional X-ray tube by nearly ten orders of magnitude.

Obviously, given the cost of both the construction and maintenance of a synchrotron source, owning one would be prohibitively expensive and inefficient for an average crystallographic laboratory. All synchrotron sources are multiple-user facilities, which are constructed and maintained using governmental support (e.g., they are supported by the United States Department of Energy and National Science Foundation in the United States, and by similar agencies in Europe, Japan, and other countries).

In general, there is no principal difference in the diffraction phenomena using the synchrotron and conventional X-ray sources, except for the presence of several highly intense peaks with fixed wavelengths in the conventionally obtained X-ray spectrum and their absence, that is, the continuous distribution of photon energies when using synchrotron sources. Here and throughout the book, the X-rays from conventional sources are of concern, unless noted otherwise.

6.2.1 Conventional Sealed X-Ray Sources

As noted earlier, the X-ray tube is a conventional laboratory source of X-rays. The two types of X-ray tubes in common use today are the sealed tube and the rotating anode tube. The sealed tube consists of a stationary anode coupled with a cathode, and both are placed inside a metal/glass or a metal/ceramic container sealed under high vacuum, as shown in Fig. 6.3.

The X-ray tube assembly is a simple and maintenance-free device. However, the overall efficiency of an X-ray tube is very low – approximately 1% or less. Most of the energy supplied to the tube is converted into heat, and therefore, the anode must be continuously cooled with chilled water to avoid target meltdown. The input power to the sealed X-ray tube ( ∼0.5 to 3kW) is, therefore, limited by the tube’s ability to dissipate heat, but the resultant energy of the usable X-ray beam is much lower than 1% of the input power because only a small fraction of the generated photons exits through each window. Additional losses occur during the monochromatization and collimation of the beam (see Sect. 11.2).

In the X-ray tube, electrons are emitted by the cathode, usually electrically heated tungsten filament, and they are accelerated toward the anode by a high electrostatic potential (30 to 60 kV) maintained between the cathode and the anode. The typical current in a sealed tube is between 10 and 50 mA. The X-rays are generated by the impacts of high-energy electrons with the metal target of a water-cooled anode, and they exit the tube through beryllium (Be) windows, as shown in Figs. 6.3 and 6.4.

energy, i.e., bandwidth (see, for example, J. Als-Nielsen and D. McMorrow, Elements of modern X-ray physics, Wiley, New York (2001)).

112 6 Properties, Sources, and Detection of Radiation

Coupling to a high voltage cable

Be window

Anode

Water in Fig. 6.3 The schematic (left) and the photograph (right) of the sealed X-ray tube. The bottom part

Water

Be windows

of the tube is metallic and it contains the anode (high purity copper, which may be coated with a layer of a different metal, e.g., Cr, Fe, Mo, etc., to produce a target other than copper), the windows (beryllium foil), and the cooling system. The top part of the tube contains the cathode (tungsten filament) and it is manufactured from glass or ceramics, welded shut to the metal canister in order to maintain high vacuum inside the tube. The view of two windows (a total of four) and the “water out” outlet is obscured by the body of the tube (right). High voltage is supplied by a cable through

a coupling located in the glass (or ceramic) part of the tube. Both the metallic can and the anode are grounded.

Windows, point focus

Cathode Cathode

Line focus

Point focus Anode

Anode Cathode

Cathode projection

Windows,

projection Fig. 6.4 The schematic explaining the appearance of two different geometries of the X-ray focus

line focus

in a conventional sealed X-ray tube (left) and the disassembled tube (right). The photo on the right shows the metallic can with four beryllium windows, two of which correspond to line- and two to point-foci. The surface of the anode with the cathode projection is seen inside the can (bottom, right ). What appears as a scratch on the surface of the anode is the damage from the high intensity electron beam and a thin layer deposit of the cathode material (W), which occurred during the lifetime of the tube. The cathode assembly is shown on top, right.

6.2 Production of X-Rays 113

A standard sealed tube has four Be windows located 90 ◦ apart around the cir- cumference of the cylindrical body. One pair of the opposite windows corresponds to a point-focused beam, which is mostly used in single crystal diffraction, while the second pair of windows results in a line-focused beam, which is normally used in powder diffraction applications, see Fig. 6.4.

Given the geometry of the X-ray tube, the intensities of both the point- and line- focused beams are nearly identical, but their brightness is different: the point focus is brighter than the linear one. The use of the linear focus in powder diffraction is justified by the need to maintain as many particles in the irradiated volume of the specimen as possible. The line of focus (i.e., the projection of the cathode visible

through beryllium windows) is typically 0.1 to 0.2 mm wide 8 and 8 to 12 mm long. Similarly, point focus is employed in single crystal diffraction because a typical size of the specimen is small (0.1 to 1 mm). Thus, high brightness of a point-focused beam enables one to achieve high scattered intensity in a single crystal diffraction experiment.

Recently, some manufactures of X-ray equipment began to utilize the so-called micro-focus sealed X-ray tubes. Due to a very small size of the focal spot, ranging from tens to a hundred of microns, power requirements of these tubes are two orders of magnitude lower when compared to conventional sealed tubes. Because of this, the micro-focus tubes are air-cooled and have long lifetimes, yet they produce brilliant X-ray beams comparable to those of rotating anode systems, see Sect. 6.2.3. These tubes find applications in diffraction of single crystals, including proteins, but their use in powder diffraction remains limited because of a small cross section of the beam.

6.2.2 Continuous and Characteristic X-Ray Spectra

The X-ray spectrum, generated in a typical X-ray tube, is shown schematically in Fig. 6.5. It consists of several intense peaks, the so-called characteristic spectral lines, superimposed over a continuous background, known as the “white” radiation. The continuous part of the spectrum is generated by electrons decelerating rapidly and unpredictably – some instantaneously, other gradually – and the distribution of the wavelengths depends on the accelerating voltage, but not on the nature of the anode material. White radiation, also known as bremsstrahlung (German for “braking radiation”), is generally highly undesirable in X-ray diffraction analysis applications. 9

While it is difficult to establish the exact distribution of the wavelengths in the white spectrum analytically, it is possible to establish the shortest wavelength that will appear in the continuous spectrum as a function of the accelerating voltage. Photons with the highest energy (i.e., rays with the shortest wavelength) are emitted

8 The projection of the cathode on the anode surface is wider, 1–2 mm, see Fig. 11.7. 9 One exception is the so-called Laue technique, in which white radiation is employed to produce

diffraction patterns from stationary single crystals, see Figs. 7.11 and 7.12.

114 6 Properties, Sources, and Detection of Radiation

y it

λ SW Intens K β

Wavelength, λ

Fig. 6.5 The schematic of a typical X-ray emission spectrum, for clarity indicating only the presence of continuous background and three characteristic wavelengths: K α 1 ,K α 2 , and K β, which have high intensities. The relative intensities of the three characteristic spectral lines are approximately to scale, however, the intensity of the continuous spectrum and the separation of the

K α 1 /Kα 2 doublet are exaggerated. Fine structure of the K β spectral line is not shown for clarity. The vertical arrow indicates the shortest possible wavelength of white radiation, λ SW , as determined by (6.4).

by the electrons, which are stopped instantaneously by the target. In this case, the electron may transfer all of its kinetic energy

= eV

to a photon with the energy

where m is the rest mass, v is the velocity, and e is the charge of the electron (1 .602×

10 −19 C), V is the accelerating voltage, c is the speed of light in vacuum (2 .998 ×

10 8 m /s), h is Planck’s constant (6.626 × 10 −34 Js ), ν is the frequency and λ is the wavelength of the wave associated with the energy of the photon. After combining the right-hand parts of (6.2) and (6.3), and solving with respect to λ, it is easy to obtain the equation relating the shortest possible wavelength ( λ SW in ˚

A) and the accelerating voltage (in V).

The three characteristic lines are quite intense and they result from the transitions of upper level electrons in the atom core to vacant lower energy levels, from which an electron was ejected by the impact with an electron accelerated in the X-ray tube. The energy differences between various energy levels in an atom are element-

6.2 Production of X-Rays 115 Table 6.1 Characteristic wavelengths of five common anode materials and the K absorption edges

of suitable β-filter materials. 10 Anode

β filter K absorption material

Wavelength ( ˚ A)

edge ( ˚ A)

Cr 2.29105 2.28975(3)

2.08491(3) V 2.26921(2) Fe 1.93739 1.93608(1)

1.75664(3) Mn 1.896459(6) Co

1.62082(3) Fe 1.743617(5) Cu

1.39225(1) Ni 1.488140(4) Nb

0.653134(1) Mo

0.63230(1) Zr 0.688959(3) a The weighted average value, calculated as λ average = (2 λ K α1 +λ K α2 )/3.

specific and therefore, each chemical element emits X-rays with a constant, that is, characteristic, distribution of wavelengths that appear due to excitations of core electrons by high energy electrons bombarding the target, see Table 6.1. Obviously, before core electrons can be excited from their lower energy levels, the bombarding electrons must have energy, which is equal to, or exceeds that of the energy difference between the two nearest lying levels of the target material.

The transitions from L and M shells to the K shell, that is, L → K and M → K are designated as K α and Kβ radiation, 11 respectively. Here K corresponds to the shell with principal quantum number n = 1, L to n = 2, and M to n = 3. The K α component consists of two characteristic wavelengths designated as Kα 1 and K α 2 , which correspond to 2p 1 /2 → 1s 1 /2 and 2p 3 /2 → 1s 1 /2 transitions, respectively, where s and p refer to the corresponding orbitals. The subscripts 1 / 2 and 3 / 2 are equal to the total angular momentum quantum number, j. 12 The K β component also consists of several discrete spectral lines, the strongest being K β 1 and K β 3 , which are so close to one another that they are practically indistinguishable in the X-ray spectra of many anode materials. There are more characteristic lines in the emission spectrum (e.g., L α − γ and Mα − ξ ); however, their intensities are much lower, and their wavelengths are greater that those of K α and Kβ. Therefore, they are not used in X-ray diffraction analysis and are not considered here. 13

10 The wavelengths are taken from the International Tables for Crystallography, vol. C, Second edi- tion, A.J.C. Wilson and E. Prince, Eds., Kluwer Academic Publishers, Boston/Dordrecht/London

(1999). For details on absorption and filtering, see Sects. 8.6.5 and 11.2.2. 11 According to IUPAC [R. Jenkins, R. Manne, J. Robin, C. Cenemaud, Nomenclature, symbols,

units and their usage in spectrochemical analysis. VIII Nomenclature system for X-ray energy and polarization, Pure Appl. Chem. 63, 735 (1991)] the old notations, e.g., Cu K α 1 and Cu K β should be substituted by the initial and final levels separated by a hyphen, e.g., Cu K −L 3 and Cu K −M 3 , respectively. However, since the old notations remain in common use, they are retained throughout this book.

12 j = ℓs when ℓ > 0 and j = 1 / 2 when ℓ = 0, where ℓ is the orbital, and s is the spin quantum numbers. Since ℓ adopts values 0, 1, 2, . . . , n-1, which correspond to s, p, d, . . . orbitals and

s =± 1 / 2 , j is equal to 1 / 2 for s orbitals, 1 / 2 or 3 / 2 for p orbitals, and so on. 13 Except for one experimental artifact shown later in Fig. 6.10, where two components present in

the L α characteristic spectrum of W (filament material contaminating Cu anode of a relatively old

116 6 Properties, Sources, and Detection of Radiation In addition to their wavelengths, the strongest characteristic spectral lines have

different intensities: the intensity of K α 1 exceeds that of K α 2 by a factor of about two, and the intensity of K α 1 ,2 is approximately five times that of the intensity of the strongest K β line, although the latter ratio varies considerably with the atomic number. Spectral purity, that is, the availability of a single intense wavelength, is critical in most diffraction applications and therefore, various monochromatization methods (see Sect. 11.2.2) are used to eliminate multiple wavelengths. Although the continuous X-ray emission spectrum does not result in distinct diffraction peaks from polycrystals, its presence increases the background noise, and therefore, white radiation must be minimized.

Typical anode materials that are used in X-ray tubes (Table 6.1) produce characteristic wavelengths between ∼0.5 and ∼2.3 ˚A. However, only two of them are used most commonly. These are Cu in powder and Mo in single-crystal diffractometry. Other anode materials can be used in special applications, for example, Ag

A) can be used to increase the resolution of the atomic structure since using shorter wavelength broadens the range of sin θ/ λ over which diffracted intensity can be measured. Bragg peaks, however, are observed closer to each other, and the resolution of the diffraction pattern may deteriorate. On the other hand, Cr, Fe, or Co anodes may be used instead of a Cu anode in powder diffraction (or Cu anode instead of Mo anode in single crystal diffractometry) to increase the resolution of the diffraction pattern (Bragg peaks are observed further apart), but the resolution of the atomic structure decreases.

anode ( λKα 1 = 0.5594218 ˚

6.2.3 Rotating Anode X-Ray Sources

The low thermal efficiency of the sealed X-ray tube can be substantially improved by using a rotating anode X-ray source, 14 which is shown in Fig. 6.6. In this design,

a massive disk-shaped anode is continuously rotated at a high speed while being cooled by a stream of chilled water. Both factors, that is, the anode mass (and therefore, the total area bombarded by high energy electrons) and anode rotation, which constantly brings chilled metal into the impact zone, enable a routine increase of the X-ray tube input power to ∼15−18kW and in some reported instances to 50–60 kW, that is, up to 20 times greater when compared to a standard sealed X-ray tube.

The resultant brightness of the X-ray beam increases proportionally to the input power; however, the lifetime of seals and bearings that operate in high vacuum is limited. 15 The considerable improvement in the incident beam brightness yields

X-ray tube) are clearly recognizable in the diffraction pattern collected from the oriented single crystalline silicon wafer.

14 For more details on rotating anode X-ray sources see W.C. Phillips, X-ray sources, Methods Enzymol. 114, 300 (1985) and references therein.

15 In the laboratory of one of the authors (VKP) the direct drive rotating anode source manufactured by Rigaku/MSC has been in continuous operation (the anode is spinning and the X-rays are on

24 h/day, 7 days/week) for 8 years at the time of writing this book. The anode requires periodic

6.2 Production of X-Rays 117

Rotating anode

Cathode projection

Water in Water out

Fig. 6.6 The schematic (left) and the photograph (right) of the direct drive rotating anode assembly employed in a Rigaku TTRAX powder diffractometer. PF is point focus and LF is line focus. The trace seen on the anode surface on the right is surface damage caused by high-energy electrons bombarding the target and a thin layer deposit of the filament material (W), which occurred during anode operation.

much better diffraction patterns, especially when diffraction data are collected in conditions other than the ambient air (e.g., high or low temperature, high pressure, and others), which require additional shielding and windows for the X-rays to pass through, thus resulting in added intensity losses.

6.2.4 Synchrotron Radiation Sources

Synchrotron radiation sources were developed and successfully brought on line, beginning in the 1960s. They are the most powerful X-ray radiation sources today. Both the brilliance of the beam and the coherence of the generated electromagnetic waves are exceptionally high. The synchrotron output power exceeds that of the conventional X-ray tube by many orders of magnitude. Tremendous energies are stored in synchrotron rings (Fig. 6.7, left), where beams of accelerated electrons or positrons are moving in a circular orbit, controlled by a magnetic field, at relativistic velocities.

refurbishing, which includes replacement of bearings and seals, and rebalancing approximately every six months.

118 6 Properties, Sources, and Detection of Radiation X-ray

beam

Storage ring

Electron beam

Wavelength, λ Bending magnet

Fig. 6.7 Schematic diagram of a synchrotron illustrating X-ray radiation output from bending magnets. Electrons must be periodically injected into the ring to replenish losses that occur during normal operation. Unlike in conventional X-ray sources, where both the long- and short-term stability of the incident photon beam are controlled by the stability of the power supply, the X-ray photon flux in a synchrotron changes with time: it decreases gradually due to electron losses, and then periodically and sharply increases when electrons are injected into the ring.

Electromagnetic radiation ranging from radiofrequency to short-wavelength X- ray region (Fig. 6.7, right) is produced due to the acceleration of charged particles toward the center of the ring. The X-ray beam is emitted in the direction, tangential to the electron/positron orbit.

Since there is no target to cool, the brilliance of the X-ray beam that can be achieved in synchrotrons is four (first generation synchrotrons) to twelve (third generation synchrotrons) orders of magnitude higher than that from a conventional X-ray source. Moreover, given the size of the storage ring (hundreds of meters in diameter), the average synchrotron beam consists of weakly divergent beams that may be considered nearly parallel at distances typically used in powder diffraction (generally less than 1 m). This feature presents an additional advantage in powder diffraction applications since the instrumental resolution is also increased.

Another important advantage of the synchrotron radiation sources, in addition to the extremely high brilliance of the X-ray beam, is in the distribution of the beam intensity as a function of wavelength (Fig. 6.7, right). The high intensity, observed in a broad range of photon energies, allows for easy selection of nearly any desired wavelength. Further, the wavelength may be changed when needed, and energy dis- persive experiments, in which the diffraction angle remains constant but the wavelength varies, can be conducted.

Thus, synchrotron radiation finds more and more use today, although its availability is restricted to the existing synchrotron sites. 16 However, some synchrotron sites are equipped with high-throughput automated powder diffractometers that are

16 Room-size synchrotron is under development by Lyncean Technologies, Inc. using laser beam instead of bending magnets to move electrons in a circular orbit. This reduces the diameter of

the ring by a factor of about 200, e.g., from 1,000 ft to only 3–6 ft. More information about The Compact Light Source project can be found at http://www.lynceantech.com.

6.3 Other Types of Radiation 119 made available to a broad scientific community. For example, beamline 11-BM,

designed by Brian Toby at the APS, is equipped with a 12-channel analyzer system and 100+ samples robotic changer, and is available for rapid access using mail-in

service. 17 Some of the well-known sites are the ALS – Advanced Light Source at Berkeley Lab, APS – Advanced Photon Source at Argonne National Laboratory, NSLS – National Synchrotron Light Source at Brookhaven National Laboratory, SRS – Synchrotron Radiation Source at Daresbury Laboratory, ESRF – European Synchrotron Radiation Facility in Grenoble, and others. 18

6.3 Other Types of Radiation

Other types of radiation that are commonly used in diffraction analysis are neutrons and electrons. The properties of both are compared with those of X-rays in Table 6.2.

Neutrons are usually produced in nuclear reactors; they have variable energy and therefore, a white spectrum. Maximum flux of neutrons is usually obtained in an angstrom range of wavelengths. The main differences when compared to X-rays are as follows: (i) neutrons are scattered by nuclei, which are much smaller than electron clouds, and the scattering occurs on points; (ii) scattering factors of elements remain constant over the whole range of Bragg angles; (iii) scattering functions are not proportional to the atomic number, and they are different for different isotopes of the same chemical element. Furthermore, since neutrons have spins, they interact with the unpaired electron spins (magnetic moments) and thus neutron diffraction data are commonly used to determine ordered magnetic structures. Other differences between neutrons and X-rays are nonessential in the general diffraction theory.

One of the biggest disadvantages of the conventional (reactor-generated) neutron sources is relatively low neutron flux at useful energies and weak interactions of neutrons with matter. Hence, a typical neutron experiment calls for 1 to 5 cm 3 of

a material. 19 This problem is addressed in the new generation of highly intense pulsed (spallation) neutron sources. 20 In a spallation neutron source, bunches of protons are accelerated to high energies, and then released, bombarding a heavy metal target in short but extremely potent pulses. The collision of each proton with

a heavy metal nucleus results in many expelled (spalled or knocked out) neutrons at various energies. The resultant highly intense ( ∼10 2 times higher flux than in any

17 See http://11bm.xor.aps.anl.gov/. 18 Web links to worldwide synchrotron and neutron facilities can be found at http://www.iucr.org/

cww-top/rad.index.html. 19 This volume is a few orders of magnitude greater than needed for an X-ray diffraction ex-

periment. Some of the third generation, high-flux neutron sources allow measurements of much smaller amounts, e.g., as little as 1 mm 3 , but acceptable levels of the scattered intensity are generally achieved by sacrificing resolution. 20 The most powerful operational pulsed neutron source is SNS – the Spallation Neutron Source –

at the Oak Ridge National Laboratory (http://www.sns.gov/). The next is ISIS, which is located at the Rutherford Appleton Laboratory in the UK (http://www.isis.rl.ac.uk/).

120 6 Properties, Sources, and Detection of Radiation Table 6.2 Comparison of three types of radiation used in powder diffraction.

Electrons Nature

X-rays (conv./synch.)

Neutrons

Particle Medium

Wave

Particle

Atmosphere Atmosphere High vacuum Scattering by

Electron density

Nuclei and

Electrostatic magnetic spins of

potential

electrons

Scattering function f (s) ∝ Z a f is constant at all s f (s) ∝ Z 1 /3,b Wavelength range, λ

0.02–0.05 ˚ A Wavelength selection

0.5–2.5/0.1–10 ˚ A ∼1 ˚A

Variable c Variable c Focusing

Fixed , c K α, β/variable

Magnetic lenses Lattice image

None

Direct, reciprocal Direct structure image

Reciprocal

Yes Applicable theory of

Dynamical diffraction Use to determine atomic

Kinematical

Very complex structure a s b If unknown, electron scattering factor f − sinθ/λ, Z – atomic number, f – atomic scattering function. e (s) may be derived from X-ray scattering factor f x (s) as

Relatively simple

f e (s) = k[Z − f x (s)]/s 2 , where k is constant. 21 c According to Moseley’s 22 law, X-ray characteristic frequency is ν = c/λ = C(Z − σ) 2 , while for

neutrons and electrons λ = h/mv = h(2mE) −1/2 , where C and σ are constants, m is mass, v is velocity, and E is kinetic energy of a particle.

conventional reactor) neutron beams have a nearly continuous energy spectrum, and they can be used in a variety of diffraction studies, mostly in the so-called time- of-flight (TOF) experiments. In the latter, the energy (and the wavelength) of the neutron that reaches the detector is calculated from the time it takes for a neutron to fly from the source, to and from the specimen to the detector.

In addition to the direct imaging of crystal lattices (e.g., in a high-resolution transmission electron microscope), electrons may be used in diffraction analysis. Despite the ease of the production of electrons by heating a filament in vacuum, electron diffraction is not as broadly used as X-ray diffraction. First, the experiments should be conducted in a high vacuum, which is inconvenient and may result in decomposition of some materials. Second, electrons strongly interact with materials. In addition to extremely thin samples, this requires the use of the dynamical theory of diffraction, thus making structure determination and refinement quite complex. Finally, the complexity and the cost of a high-resolution electron microscope usually considerably exceed those of a high-resolution powder diffractometer.

Neutron diffraction examples are discussed when deemed necessary, even though in this book we have no intention of covering the diffraction of neutrons (and elec-

21 Electron diffraction techniques, Vol. 1, J. M. Cowley, Ed., Oxford University Press, NY (1992). 22 Henry Gwyn Jeffreys Moseley (1887–1915). British physicist, who studied X-ray spectra of

elements and discovered a systematic relationship between the atomic number of the element and the wavelength of characteristic radiation. A brief biography is available on WikipediA at http://en.wikipedia.org/wiki/Henry Moseley.

6.4 Detection of X-Rays 121 trons) at any significant depth. Interested readers can find more information on

electron and neutron diffraction in some of the references provided at the end of this chapter.

6.4 Detection of X-Rays

The detector is an integral part of any diffraction analysis system, and its major role is to measure the intensity and, sometimes, the direction of the scattered beam. The detection is based on the ability of X-rays to interact with matter and to produce certain effects or signals, for example, to generate particles, waves, electrical current, etc., which can be easily registered. In other words, each photon entering the detector generates a specific event, better yet, a series of events that can be recognized, and from which the total photon count (intensity) can be determined. Obviously, the detector must be sensitive to X-rays (or in general to the radiation being detected), and should have an extended dynamic range and low background noise. 23

6.4.1 Detector Efficiency, Linearity, Proportionality and Resolution

An important characteristic of any detector is how efficiently it collects X-ray photons and then converts them into a measurable signal. Detector efficiency is determined by first, a fraction of X-ray photons that pass through the detector window (the higher, the better) and second, a fraction of photons that are absorbed by the detector and thus result in a series of detectable events (again, the higher, the better). The product of the two fractions, which is known as the absorption or quantum efficiency, should usually be between 0.5 and 1.

The efficiency of modern detectors is quite high, in contrast to the X-ray film, which requires multiple photons to activate a single grain of photon-sensitive silver halide. It is important to keep in mind that the efficiency depends on the type of the detector and it normally varies with the wavelength for the same type of the detector. The need for high efficiency is difficult to overestimate since every missed (i.e., not absorbed by the detector) photon is simply a lost photon. It is nearly impossible to account for the lost photons by any amplification method, no matter how far the amplification algorithm has been advanced.

The linearity of the detector is critical in obtaining correct intensity measurements (photon count). The detector is considered linear when there is a linear depen- dence between the photon flux (the number of photons entering through the detector window in one second) and the rate of signals generated by the detector (usually the

23 For the purpose of this consideration, the dynamic range is the ability of the detector to count photons at both the low and high fluxes with the same effectiveness, and by the background noise

we mean the events similar to those generated by the absorbed photons, but occurring randomly and spontaneously in the detector without photons entering the detector.

122 6 Properties, Sources, and Detection of Radiation number of voltage pulses) per second. In any detector, it takes some time to absorb

a photon, convert it into a voltage pulse, register the pulse, and reset the detector to the initial state, that is, make it ready for the next operation. This time is usually known as the dead time of the detector – the time during which the detector remains inactive after it has just registered a photon.

The presence of the dead time always decreases the registered intensity. This effect, however, becomes substantial only at high photon fluxes. When the detector is incapable of counting every photon due to the dead time, some of them could be absorbed by the detector but remain unaccounted, that is, become lost photons. It is said that the detector becomes nonlinear under these conditions. Thus the linearity of the detector can be expressed as: (i) the maximum flux in photons per second that can be reliably counted (the higher the better); (ii) the dead time (the shorter, the better), or (iii) the percentage of the loss of linearity at certain high photon flux (the lower percentage, the better). The latter is compared for several different types of detectors in Table 6.3 along with other characteristics.

The proportionality of the detector determines how the size of the generated voltage pulse is related to the energy of the X-ray photon. Since X-ray photons produce

a certain amount of events (ion pairs, photons of visible light, etc.), and each event requires certain energy, the number of events is generally proportional to the energy of the X-ray photon and therefore, to the inverse of its wavelength. The amplitude of the generated signal is normally proportional to the number of these events and thus, it is proportional to the X-ray photon energy, which could be used in pulse- height discrimination. Usually, the high proportionality of the detector enables one to achieve additional monochromatization of the X-ray beam in a straightforward fashion: during the registration, the signals that are too high or too low and thus correspond to photons with exceedingly high or exceedingly low energies, respectively, are simply not counted.

Finally, the resolution of the detector characterizes its ability to resolve X-ray photons of different energy and wavelength. The resolution (R) is defined as follows:

Table 6.3 Selected characteristics of the most common detectors using Cu K α radiation. Property /

Linearity loss at Proportionality Resolution Energy per No. of Detector

40,000 cps a for Cu K α event (eV) events b Scintillation <1%

350 23 Proportional <5%

Very good

Good, but fails at high 14%

photon flux

Solid state Up to 50%

3.7 2,200 a cps – counts per second. b Approximate number of ion pairs or visible light photons resulting from a single X-ray photon

Pileup in mid-range

assuming Cu K α radiation with photon energy of about 8 keV.

6.4 Detection of X-Rays 123 where V is the average height of the voltage pulse and δV is the spread of voltage

pulses. The latter is also defined as the full width at half-maximum of the pulse height distribution in Volts. The resolution for Cu K α radiation for the main types of detectors is listed in Table 6.3. Thus, the resolution is a function of both the number of the events generated by a single photon and the energy required to generate the event, and it is critically dependent on how small is the spread in the number of events generated by different photons with identical energy. In other words, high resolution is only viable when every photon is absorbed completely, which is difficult to achieve when the absorbing medium is gaseous, but is nearly ideal in the solid state simply due to the difference in their densities (see Sect. 8.6.5).

6.4.2 Classification of Detectors

Historically, the photographic film is the first and the oldest detector of X-rays, which was in use for many decades. Just as the visible light, the X-ray photons excite fine particles of silver halide when the film is exposed to X-rays. During the development, the exposed halide particles are converted into black metallic silver grains. Only the activated silver halide particles, that is, those that absorbed several X-ray photons (usually at least 3–5 photons), turn into metallic silver.

This type of detector is simple but is no longer in common use due to its low proportionality range, and limited spatial and energy resolution. Moreover, the film- development process introduces certain inconveniences and is time consuming. Finally, the information stored on the developed photographic film is difficult to digitize.

In modern detectors the signal, which is usually an electric current, is easily dig- itized and transferred to a computer for further processing and analysis. In general, detectors could be broadly divided into two categories: ratemeters and true counters. In a ratemeter, the readout is performed after hardware integration, which results, for example, in the electrical current or a voltage signal that is proportional to the flux of photons entering the detector. True counters, on the other hand, count individual photons entering through the detector window and being absorbed by the detector.

Hence, the photographic film vaguely resembles a ratemeter, because the intensity is extracted from the degree of darkening of the spots found on the film – the darker the spot, the higher the corresponding intensity as a larger number of photons have been absorbed by the spot on the film surface. The three most commonly utilized types of X-ray detectors today are gas proportional, scintillation, and solid- state detectors, all of which are true counters.

Yet another classification of detectors is based on whether the detector is capable of resolving the location where the photon has been absorbed and thus, whether they can detect the direction of the beam in addition to counting the number of photons. Conventional gas proportional, scintillation, and solid-state detectors do not support

124 6 Properties, Sources, and Detection of Radiation

f(2 θ)

Fig. 6.8 The schematic explaining the difference between point (the set of discrete dots), line (solid rectangle ), and area (the entire picture) detectors, which are used in modern powder diffractometry. The light trace extended from the center of the image to the upper-left corner is the shade from the primary beam trap. The Bragg angle is zero at the center of the image and it increases along any line that extends from the center of the image as shown by the two arrows (also see Fig. 8.4).

spatial resolution and therefore, they are also known as point detectors. A point detector registers only the intensity of the diffracted beam, one point at a time. In other words, the readout of the detector corresponds to a specific value of the Bragg angle as determined by the position of the detector relatively to both the sample and the incident beam. This is illustrated as the series of dots in Fig. 6.8, each dot corresponding to a single position of the detector and a single-point measurement of the intensity. Thus, to examine the distribution of the diffracted intensity as a function of Bragg angle using a point detector, it is necessary to perform multiple- point measurements at varying Bragg angles.

Detectors that support spatial resolution in one direction are usually termed as line detectors, while those that facilitate resolution in two dimensions are known as area detectors. Again, photographic film is a typical example of an area detector because each point on the film can be characterized by two independent coordinates and the entire film area is exposed simultaneously. The following three types of line and area detectors are in common use in powder diffractometry today: position sensitive (PSD), charge coupled devices (CCD), and image plates (IPD). The former is a line detector (its action is represented by the rectangle in Fig. 6.8) and the latter two are area detectors (the entire area of Fig. 6.8 represents an image of how the intensity is measured simultaneously). Both line and area detectors can measure diffracted intensity at multiple points at once and thus, a single measurement results in the diffraction pattern resolved in one or two dimensions, respectively.

6.4 Detection of X-Rays 125

6.4.3 Point Detectors

A typical gas-proportional counter detector usually consists of a cylindrical body filled with a mixture of gases (Xe mixed with some quench gas, usually CO 2 , CH 4 , or a halogen, to limit the discharge) and a central wire anode as shown schematically in Fig. 6.9 (left). High voltage is maintained between the cathode (the body of the counter) and the anode. When the X-ray photon enters through the window and is absorbed by the gas, it ionizes Xe atoms producing positively charged ions and electrons, that is, ion pairs (see Table 6.3). The resulting electrical current is measured and the number of current pulses is proportional to the number of photons absorbed by the mixture of gases. The second window is usually added to enable the exit of the nonabsorbed photons, thus limiting the X-ray fluorescence, which may occur at the walls of the counter. In some cases, the cylinder can be filled by a mixture of gases under pressure exceeding the ambient to improve photon absorption and, therefore, photon detection by the detector.

Chapter 6 Properties, Sources, and Detection of Radiation