Basic Concepts of X-Ray Diffraction

Emil Zolotoyabko

• Publisher: Wiley-VCH
• Year: 2014
• ISBN:
  9783527681181
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

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.

1

Diffraction Phenomena in Optics

The term diffraction in optics is usually used to explain the deviations of light propagation from the trajectories dictated by geometrical (ray) optics. One of the most famous examples is the so-called Fraunhofer diffraction, which explains the transmission of an initially parallel beam of light through a circular hole of radius D fabricated in a nontransparent screen. Within the framework of geometrical optics, behind the screen, the nonzero transmitted intensity will be detected just in front of the hole (see Figure 1.1). It means that, after passing through the screen, the direction of light propagation does not change; the only effect is a reduction in the total light intensity in a proportion dictated by the area of the hole S = πD² with respect to the cross section of the incident beam. However, light scattering by the border of the hole can substantially modify this result and provide additional transmitted intensity in spatial directions that differ by angle Θ from the initial direction of light propagation before the screen (see Figure 1.2, upper panel). In other words, after passing through the screen, light propagates not only in one direction, which is defined by the initial wave vector

, but also in many other directions defined by the vectors

=

+

. Here,

is a variable wave vector transfer to the screen during scattering events (see Figure 1.3). Note that, for elastic scattering processes

1.1

where λ is the wavelength of light. Taking into account Eq. (1.1) and the axial symmetry of the particular scattering problem (at a fixed scattering angle Θ, see Figure 1.3), we find that

1.2

Figure 1.1 Light transmission through a circular hole of radius D in the limit of geometrical optics.

Figure 1.2 Light transmission (upper panel) through a circular hole of radius D, taking into account diffraction phenomenon (Fraunhofer diffraction). Bottom panel: transmitted intensity as a function of angular deviation Θ.

Figure 1.3 Wave vector change

in the course of elastic scattering of propagating light.

For each

-value, the light scattering amplitude is given by the Fourier component

of the wave field

just after the screen [1]:

1.3

However, in the first approximation, we can set u =

, that is, equal the amplitude of the homogeneous wave field before the screen, and then express the scattering amplitude

as

1.4

where the integration proceeds over the entire area S of the hole. The diffraction intensity (relative to that in the incident beam) for a given

-value within an element of solid angle Ω is expressed as follows [1]:

1.5

In order to find

, let us introduce the polar coordinates

and

within the circular hole. In this coordinate system, Eq. (1.4) transforms into

1.6

where J₀ is the Bessel function of zero order. Note that, in deriving Eq. (1.6), we used the fact that, for small scattering angles Θ, the vector

is nearly situated in the ...

Table of contents

• Cover
• Related Titles
• Title Page
• Copyright
• Dedication
• Preface
• Introduction
• 1: Diffraction Phenomena in Optics
• 2: Wave Propagation in Periodic Media
• 3: Dynamical Diffraction of Particles and Fields: General Considerations
• 4: Dynamical X-Ray Diffraction: The Ewald–Laue Approach
• 5: Dynamical Diffraction: The Darwin Approach
• 6: Dynamical Diffraction in Nonhomogeneous Media: The Takagi–Taupin Approach
• 7: X-Ray Absorption
• 8: Dynamical Diffraction in Single-Scattering Approximation: Simulation of High-Resolution X-Ray Diffraction in Heterostructures and Multilayers
• 9: Reciprocal Space Mapping and Strain Measurements in Heterostructures
• 10: X-Ray Diffraction in Kinematic Approximation
• 11: X-Ray Diffraction from Polycrystalline Materials
• 12: Applications to Materials Science: Structure Analysis
• 13: Applications to Materials Science: Phase Analysis
• 14: Applications to Materials Science: Preferred Orientation (Texture) Analysis
• 15: Applications to Materials Science: Line Broadening Analysis
• 16: Applications to Materials Science: Residual Strain/Stress Measurements
• 17: Impact of Lattice Defects on X-Ray Diffraction
• 18: X-Ray Diffraction Measurements in Polycrystals with High Spatial Resolution
• 19: Inelastic Scattering
• 20: Interaction of X-Rays with Acoustic Waves
• 21: Time-Resolved X-Ray Diffraction
• 22: X-Ray Sources
• 23: X-Ray Focusing Optics
• 24: X-Ray Diffractometers
• References
• Index