Hugendubel.info - Die B2B Online-Buchhandlung 

Merkliste
Die Merkliste ist leer.
Bitte warten - die Druckansicht der Seite wird vorbereitet.
Der Druckdialog öffnet sich, sobald die Seite vollständig geladen wurde.
Sollte die Druckvorschau unvollständig sein, bitte schliessen und "Erneut drucken" wählen.

Basic Concepts of X-Ray Diffraction

E-BookEPUB2 - DRM Adobe / EPUBE-Book
312 Seiten
Englisch
Wiley-VCHerschienen am10.02.20141. Auflage
Authored by a university professor deeply involved in X-ray diffraction-related research, this textbook is based on his lectures given to graduate students for more than 20 years. It adopts a well-balanced approach, describing basic concepts and experimental techniques, which make X-ray diffraction an unsurpassed method for studying the structure of materials.

Both dynamical and kinematic X-ray diffraction is considered from a unified viewpoint, in which the dynamical diffraction in single-scattering approximation serves as a bridge between these two parts. The text emphasizes the fundamental laws that govern the interaction of X-rays with matter, but also covers in detail classical and modern applications, e.g., line broadening, texture and strain/stress analyses, X-ray mapping in reciprocal space, high-resolution X-ray diffraction in the spatial and wave vector domains, X-ray focusing, inelastic and time-resolved X-ray scattering. This unique scope, in combination with otherwise hard-to-find information on analytic expressions for simulating X-ray diffraction profiles in thin-film heterostructures, X-ray interaction with phonons, coherent scattering of Mossbauer radiation, and energy-variable X-ray diffraction, makes the book indispensable for any serious user of X-ray diffraction techniques.

Compact and self-contained, this textbook is suitable for students taking X-ray diffraction courses towards specialization in materials science, physics, chemistry, or biology. Numerous clear-cut illustrations, an easy-to-read style of writing, as well as rather short, easily digestible chapters all facilitate comprehension.



Emil Zolotoyabko is Professor in the Department of Materials Science and Engineering at the Technion - Israel Institute of Technology (Haifa). He is holder of the Abraham Tulin Academic Chair and recipient of the 2001 Henry Taub Prize for Academic Excellence. Emil Zolotoyabko has authored more than 160 scientific publications, three books, and four book chapters devoted to the development of new X-ray diffraction methods and their applications for studying the structure and dynamical characteristics of different materials systems.mehr
Verfügbare Formate
E-BookEPUB2 - DRM Adobe / EPUBE-Book
EUR70,99
E-BookPDF2 - DRM Adobe / Adobe Ebook ReaderE-Book
EUR70,99

Produkt

KlappentextAuthored by a university professor deeply involved in X-ray diffraction-related research, this textbook is based on his lectures given to graduate students for more than 20 years. It adopts a well-balanced approach, describing basic concepts and experimental techniques, which make X-ray diffraction an unsurpassed method for studying the structure of materials.

Both dynamical and kinematic X-ray diffraction is considered from a unified viewpoint, in which the dynamical diffraction in single-scattering approximation serves as a bridge between these two parts. The text emphasizes the fundamental laws that govern the interaction of X-rays with matter, but also covers in detail classical and modern applications, e.g., line broadening, texture and strain/stress analyses, X-ray mapping in reciprocal space, high-resolution X-ray diffraction in the spatial and wave vector domains, X-ray focusing, inelastic and time-resolved X-ray scattering. This unique scope, in combination with otherwise hard-to-find information on analytic expressions for simulating X-ray diffraction profiles in thin-film heterostructures, X-ray interaction with phonons, coherent scattering of Mossbauer radiation, and energy-variable X-ray diffraction, makes the book indispensable for any serious user of X-ray diffraction techniques.

Compact and self-contained, this textbook is suitable for students taking X-ray diffraction courses towards specialization in materials science, physics, chemistry, or biology. Numerous clear-cut illustrations, an easy-to-read style of writing, as well as rather short, easily digestible chapters all facilitate comprehension.



Emil Zolotoyabko is Professor in the Department of Materials Science and Engineering at the Technion - Israel Institute of Technology (Haifa). He is holder of the Abraham Tulin Academic Chair and recipient of the 2001 Henry Taub Prize for Academic Excellence. Emil Zolotoyabko has authored more than 160 scientific publications, three books, and four book chapters devoted to the development of new X-ray diffraction methods and their applications for studying the structure and dynamical characteristics of different materials systems.
Details
Weitere ISBN/GTIN9783527681181
ProduktartE-Book
EinbandartE-Book
FormatEPUB
Format Hinweis2 - DRM Adobe / EPUB
FormatFormat mit automatischem Seitenumbruch (reflowable)
Verlag
Erscheinungsjahr2014
Erscheinungsdatum10.02.2014
Auflage1. Auflage
Seiten312 Seiten
SpracheEnglisch
Dateigrösse12922 Kbytes
Artikel-Nr.2974660
Rubriken
Genre9201

Inhalt/Kritik

Inhaltsverzeichnis
Preface
Introduction

DIFFRACTION PHENOMENA IN OPTICS

WAVE PROPAGATION IN PERIODIC MEDIA

DYNAMICAL DIFFRACTION OF PARTICLES AND FIELDS: GENERAL CONSIDERATIONS
The Two-Beam Approximation
Diffraction Profile: The Laue Scattering Geometry
Diffraction Profile: The Bragg Scattering Geometry

DYNAMICAL X-RAY DIFFRACTION: THE EWALD-LAUE APPROACH
Dynamical X-Ray Diffraction: Two-Beam Approximation

DYNAMICAL DIFFRACTION: THE DARWIN APPROACH
Scattering by a Single Electron
Atomic Scattering Factor
Structure Factor
Scattering Amplitude from an Individual Atomic Plane
Diffraction Intensity inthe Bragg Scattering Geometry

DYNAMICAL DIFFRACTION IN NONHOMOGENEOUS MEDIA. THE TAKAGI-TAUPIN APPROACH
Takagi Equations
Taupin Equation

X-RAY ABSORPTION

DYNAMICAL DIFFRACTION IN SINGLE-SCATTERING APPROXIMATION: SIMULATION OF HIGH-RESOLUTION X-RAY DIFFRACTION IN HETEROSTRUCTURES AND MULTILAYERS
Direct Wave Summation Method

RECIPROCAL SPACE MAPPING AND STRAIN MEASUREMENTS IN HETEROSTRUCTURES

X-RAY DIFFRACTION IN KINEMATIC APPROXIMATION
X-Ray Polarization Factor
Debye-Waller Factor

X-RAY DIFFRACTION FROM POLYCRYSTALLINE MATERIALS
Ideal Mosaic Crystal
Powder Diffraction

APPLICATIONS TO MATERIALS SCIENCE: STRUCTURE ANALYSIS

APPLICATIONS TO MATERIALS SCIENCE: PHASE ANALYSIS
Internal Standard Method
Rietveld Refinement

APPLICATIONS TO MATERIALS SCIENCE: PREFERRED ORIENTATION (TEXTURE) ANALYSIS
The March-Dollase Approach

APPLICATIONS TO MATERIALS SCIENCE: LINE BROADENING ANALYSIS
Line Broadening due to Finite Crystallite Size
Line Broadening due to Microstrain Fluctuations
Williamson-Hall Method
The Convolution Approach
Instrumental Broadening
Relation between Grain Size-Induced and Microstrain-Induced Broadenings of X-Ray Diffraction Profiles

APPLICATIONS TO MATERIALS SCIENCE: RESIDUAL STRAIN/STRESS MEASUREMENTS
Strain Measurements in Single-Crystalline Systems
Residual Stress Measurements in Polycrystalline Materials

IMPACT OF LATTICE DEFECTS ON X-RAY DIFFRACTION

X-RAY DIFFRACTION MEASUREMENTS IN POLYCRYSTALS WITH HIGH SPATIAL RESOLUTION
The Theory of Energy-Variable Diffraction (EVD)

INELASTIC SCATTERING
Inelastic Neutron Scattering
Inelastic X-Ray Scattering

INTERACTION OF X-RAYS WITH ACOUSTIC WAVES
Thermal Diffuse Scattering
Coherent Scattering by Externally Excited Phonons

TIME-RESOLVED X-RAY DIFFRACTION

X-RAY SOURCES
Synchrotron Radiation

X-RAY FOCUSING OPTICS
X-Ray Focusing: Geometrical Optics Approach
X-Ray Focusing: Diffraction Optics Approach

X-RAY DIFFRACTOMETERS
High-Resolution Diffractometers
Powder Diffractometers

Indexmehr
Leseprobe
2
Wave Propagation in Periodic Media

Let us consider, following the ideas of Brillouin [4], the propagation of plane waves within a medium. A plane wave is defined as

2.1

where Y stands for a physical parameter that oscillates in space (r) and time (t), while Y0, , and are the wave amplitude, wave vector, and angular frequency, respectively. The term in circular brackets in Eq. (2.1), that is,

2.2

is the phase of the plane wave. At any instant t, the surface of steady phase = const is defined by the condition = const. The latter is the equation of a geometrical plane perpendicular to the direction of wave propagation and, therefore, this type of wave has accordingly been so named (plane wave).

Considering, first, a homogeneous medium, we can say that a plane wave having wave vector at a certain point in its trajectory will continue to propagate with the same wave vector because of the momentum conservation law. Note that the wave vector is linearly related to the momentum via the Planck constant : that is, = . We also remind the readers that the momentum conservation law is a direct consequence of the particular symmetry of a homogeneous medium, known as the homogeneity of space [5].

The situation drastically changes for a nonhomogeneous medium, in which the momentum conservation law, generally, is not valid because of the breaking of the above-mentioned symmetry. As a consequence, in such a medium, one can find wave vectors differing from the initial wave vector . The simplest case is realized when the medium comprises two homogeneous parts with dissimilar characteristics. Such breaking of symmetry is the origin of the refraction of waves at the interface between two parts. Refraction phenomena will also be touched upon later in this book (see Chapter 23). However, our focus in the current chapter is on the particular nonhomogeneous medium with translational symmetry, which comprises scattering centers in specific points rs only, that is,

2.3

the rest of the space being empty. Here, in Eq. (2.3), the vectors , , , are three noncoplanar translation vectors, while , , , are integer numbers (both positive, negative, and zero). Currently, this is our model of a crystal.

On the basis of the translational symmetry only, we can say that, in an infinite medium with no absorption, the magnitude of the plane wave Y should be the same in close proximity to any lattice node described by Eq. (2.3). It means that the amplitude Y0 is the same at all points , whereas the phase can differ by an integer number of (see Eq. (2.1)). Let us suppose that the plane wave has the wave vector at the starting point = 0 and = 0. Then, according to Eq. (2.2), = 0. If so, at point rs, the phase of the plane wave should be equal to . Note that the change of the wave vector from to physically means that the wave obeys scattering at point (see Figure 2.1). In this chapter, only elastic scattering (with no energy change) is considered. So

2.4

where stands for the radiation wavelength. Note also that Eq. (2.4) is equivalent to Eq. (1.1) introduced in Chapter 1.


Figure 2.1 Illustration of X-ray scattering in a periodic medium.


For further analysis, we recall the linear dispersion law for electromagnetic waves in vacuum, that is, the linear relationship between the absolute value of the wave vector and the angular frequency given by

2.5

where c is the speed of wave propagation. With the aid of Eq. (2.4) and Eq. (2.5), we can express the time interval for a wave traveling between points and as

2.6

By using Eq. (2.2), Eq. (2.4), Eq. (2.5), and Eq. (2.6), we calculate the phase of the plane wave, , after scattering at point as

2.7

Since the initial phase = 0, Eq. (2.7) determines the phase difference due to wave scattering. The difference vector between the wave vectors in the final and initial wave states is known as the wave vector transfer or the scattering vector:

2.8

Substituting Eq. (2.8) into Eq. (2.7) finally yields the phase difference as

2.9

According to Eq. (2.8), different values of are actually permitted, but only those that provide a scalar product in Eq. (2.9), that is, a scalar product of a certain scattering vector and different vectors from the lattice (Eq. (2.3)), equal to an integral multiple m of :

2.10

The vector is also called the diffraction vector. In order to avoid the usage of factor in Eq. (2.10), another vector is introduced as

2.11

for which Eq. (2.10) is rewritten as

2.12

By substituting Eq. (2.3) into Eq. (2.12), we finally obtain

2.13

In order to find the set of allowed vectors satisfying Eq. (2.13), the reciprocal space is introduced, which is based on three noncoplanar vectors , , and . Real space and reciprocal space are related to each other by the orthogonality conditions

2.14

where is the Kronecker symbol, equal to 1 for i = j or 0 for i j (i, j = 1, 2, 3). In order to build the reciprocal space from real space, we use the following mathematical procedure:

2.15

where stands for the volume of the parallelepiped built in real space on vectors a1, a2, a3:

2.16

By using Eq. (2.16), it is easy to directly check that the procedure (Eq. (2.15)) provides the orthogonality conditions (Eq. (2.14)). For example, a1 · b1 = a1 · [a2 × a3]/ = / = 1, whereas a2 · b1 = a2 · [a2 × a3]/ = 0. More information on the reciprocal space construction can be found, for example, in [6, 7].

In the reciprocal space, the allowed vectors are linear combinations of the basic vectors , , :

2.17

with integer projections (hkl), known as the Miller indices. The ends of vectors , being constructed from the common origin (000), form the nodes of a reciprocal lattice (see Figure 2.2). For all vectors , which are called vectors of reciprocal lattice, Eq. (2.13) is automatically valid because of the orthogonality conditions (Eq. (2.14)). So, in a medium with translational symmetry, only those wave vectors may exist that are related to the initial wave vector as follows:


Figure 2.2 Reciprocal lattice (black spots) and the Ewald's sphere construction. Wave vectors of X-rays in the initial and final states are, respectively, indicated by and .


2.18

where the vectors are given by Eq. (2.17). Sometimes, Eq. (2.18) is called the quasi-momentum (or quasi-wave vector) conservation law in the medium with translational symmetry, which should be used instead of the momentum conservation law in a homogeneous medium. Note that the latter law means = = = 0, that is, = . Graphical representation of Eq. (2.18), which leads to the famous Bragg law, is given in Figure 2.3. This important point will be elaborated in more detail below.


Figure 2.3 Graphical representation of Eq. (2.18).


Actually, Eq. (2.18) describes the kinematics of the diffraction process in an infinite periodic medium, since the presence of waves propagating along different directions , in addition to the incident wave with wave vector , is the essence of the diffraction phenomenon. According to Eq. (2.18), the necessary condition for the diffraction process is the quasi-momentum (or the quasi-wave vector) conservation law, which defines the specific angles 2 between wave vectors and , at which diffraction intensity could, in principle, be observed (see Figure 2.3). Solving the wave vector triangle in Figure 2.3, together with Eq. (2.4), yields

2.19

Note that each vector of reciprocal lattice, that is, = hb1 + kb2 + lb3, is perpendicular to a specific crystallographic plane in real space. This connection is directly given by Eq. (2.12), which defines the geometric plane for the ends of certain vectors rs, the plane being perpendicular to the specific vector (see Figure 2.4). Using Eq. (2.19) and introducing a set of parallel planes of this type, which are separated by the d-spacing

2.20

we finally obtain the so-called Bragg law:

2.21

which provides the relation between the possible directions for the diffracted wave propagation (via Bragg angles ) and interplanar spacings (d-spacings) d in crystals. By using Eq. (2.15), Eq. (2.16), Eq. (2.17), and Eq. (2.20), one can calculate the d-spacings in crystals, as functions of their lattice...
mehr