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Dynamical Scattering of X-Rays in Crystals
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Dynamical Scattering of X-Rays in Crystals

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Dynamical Scattering of X-Rays in Crystals

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Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

01.02.2012

Verlag

Springer Berlin

Seitenzahl

514

Maße (L/B/H)

23.5/15.5/2.9 cm

Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

01.02.2012

Verlag

Springer Berlin

Seitenzahl

514

Maße (L/B/H)

23.5/15.5/2.9 cm

Gewicht

797 g

Auflage

Softcover reprint of the original 1st ed. 1978

Sprache

Englisch

ISBN

978-3-642-81209-5

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  • Dynamical Scattering of X-Rays in Crystals
  • 1. Introduction.- 2. Wave Equation and Its Solution for Transparent Infinite Crystal.- 2.1 Wave Equation and Its Solution.- 2.2 Two-Wave Approximation. Dispersion Surface.- 3. Transmission of X-Rays Through a Transparent Crystal Plate. Laue Reflection.- 3.1 Wave Fields Inside a Crystal.- 3.1.1 Semi-infinite Crystal. Connection with Experimental Conditions. Refraction Effect.- 3.1.2 Wave Amplitudes; Pendulum Solution. Extinction. Quasi-standing Waves.- 3.2 Transmission and Reflection Coefficients. Analysis of Pendulum Solution in the Case of Plane-Parallel Plate.- 3.3 Transmission Through a Wedge-Shaped Plate.- 4. X-Ray Scattering in Absorbing Crystal. Laue Reflection.- 4.1 Atomic Scattering and Absorption.- 4.2 Complex Form of Dynamical Scattering Parameters.- 4.3 Derivation of Exact Formulae for Transmission (T) and Reflection (R) Coefficient in the Case of an Absorbing Crystal.- 4.4 Derivation of Approximate Equations for Transmission Coefficient T and Reflection Coefficient R.- 4.5 Analysis of Approximate Equations for the Transmission Coefficient T and the Reflection Coefficient R.- 4.5.1 Symmetrical Reflection.- 4.5.2 Asymmetrical Reflection.- 4.6 Integrated Values of Reflection Ri and Transmission Ti in the Case of Absorbing Crystal.- 4.7 Analysis of Expressions for Integrated Values Ri and Ti as Applied to Important Particular Cases.- 5. Poynting’s Vectors and the Propagation of X-Ray Wave Energy.- 5.1 Averaged Poynting’s Vector in the General Case.- 5.2 The Triply Averaged Poynting’s Vector in Transparent Crystal.- 5.3 Triply Averaged Poynting’s Vector in Absorbing Centro-symmetrical Crystal.- 5.4 Energy Propagation in Absorbing Crystal Without a Centre of Symmetry, Taking into Account the Periodic Component of Poynting’s Vector. Additional Remarks.- 6. Dynamical Theory in Incident-Spherical-Wave Approximation.- 6.1 Dynamical Theory in a Two-Wave Approximation with Spherical Wave Incident on Crystal. Application to Scattering in Transparent Plane-Parallel and Wedge-Shaped Crystals.- 6.2 Application of the Theory Described to Scattering in Absorbing Crystal.- 7. Bragg Reflection of X-Rays. I. Basic Definitions. Coefficients of Absorption; Diffraction in Finite Crystal.- 7.1 Reflection from Transparent Crystal.- 7.2 True Absorption in Bragg Reflection. Investigation of Coefficient of Absorption ? from Plane-Parallel Plate.- 7.3 Diffraction in Finite Crystal in Incident-Spherical Wave or Incident Wave Packet Approximation.- 8. Bragg Reflection of X-Rays. II. Reflection and Transmission Coefficients and Their Integrated Values.- 8.1 Deriving General Expressions for Reflection and Transmission Coefficients.- 8.2 Bragg Reflection from Transparent Crystal.- 8.3 Bragg Reflection from Thick Absorbing Crystal.- 8.4 Integrated Reflection from Absorbing Crystal in Bragg Case.- 9. X-Ray Spectrometers Used in Dynamical Scattering Investigations. Some Results of Experimental Verification of the Theory.- 9.1 Estimating Wavelength Spread and Angular Divergence of X-Ray Tube Radiation.- 9.2 Two-Crystal Spectrometer, Using Bragg Reflections in Both Crystals (Bragg-Bragg Scheme).- 9.3 Three-Crystal Spectrometer.- 9.4 Other Types of Diffractometers.- 9.4.1 Double-Crystal Spectrometers of the Bragg-Laue and Laue-Laue Type.- 9.4.2 Multi-Crystal Diffractometers with MCC, with Symmetrical and Asymmetrical Bragg Reflections.- 9.4.3 Rigorous Theory of X-Ray Diffractometers.- 9.4.4 Investigation and Utilization of Bragg-Reflection Curves.- 9.4.5 Investigations into the Interference Effects of the Pendulum Solution.- Determining the Absolute Values of Atomic Amplitudes.- Some Other Pendulum Solution Investigations.- 10. X-Ray Interferometry. Moiré Patterns in X-Ray Diffraction.- 10.1 Three-Crystal Interferometers.- 10.2 Two-Crystal Interferometer.- 10.3 Formation and Utilization of X-Ray Moiré Patterns.- 10.4 Experimental Investigations. Three-Crystal Interferometer.- 10.4.1 Double-Crystal Interferometer.- 11. Generalized Dynamical Theory of X-Ray Scattering in Perfect and Deformed Crystals.- 11.1 Deriving Fundamental Equations in the General Case of Deformed Crystal.- 11.2 X-Ray Diffraction in Perfect Crystal Under Conditions of Space-Inhomogeneous Dynamical Problem. Influence Functions of Point Source.- 11.3 Laue Reflection in Perfect Crystal.- 11.4 Bragg Reflection in Perfect Crystal.- 11.5 Application of Generalized Theory to Deformed Crystal. Relationship Between Angular Variable ?n and Deformation Field.- 11.6 Fundamental Equations of Geometrical Optics of X-Rays.- 11.7 Approaches Based Upon Wave Theory.- 11.7.1 Rigorous Theory of Laue Diffraction of X-Rays in Crystal with Uniform Strain Gradient.- 11.7.2 Integral Formulation of Huygens-Fresnel Principle.- 11.7.3 Quasi-classical Wave Field Asymptotes.- 11.7.4 Ray Trajectories.- 11.7.5 Integrated Intensity of Diffracted Wave.- 11.7.6 Conclusion.- 12. Dynamical Scattering in the Case of Three Strong Waves and More.- 12.1 Scattering in Nonabsorbing Crystal. Reference Coordinate Systems.- 12.2 System of Fundamental Equations in the Case of Three Strong Waves, and the Dispersion Surface Equation.- 12.3 Another Method of Deriving the Dispersion Surface Equation in a Three-Wave Case.- 12.4 Analysis of the Dispersion Surface Equation in the Case of Nonabsorbing Crystal.- 12.5 Deriving the Dispersion Surface Equation in the Case of Four Strong Waves.- 12.6 Coefficients of Transmission and Reflection for a Plane-Parallel Plate. Laue Reflection.- 12.7 Scattering in Absorbing Crystal. Introducing Complex Parameters of Scattering and the Coefficient of Absorption.- 12.8 The Relationship Between the Coefficient of Absorption and the Shape of the Dispersion Surface. EWALD’s Criterion.- 12.9 Asymptotic Properties of the Dispersion Surface. Transition from the Multiwave to the Two-Wave Region.- 12.10 Symmetrical Cases of Multiwave Diffraction. Nonlinear Borrmann Effect.- 12.11 Scattering in Germanium and Silicon Crystals.- 12.12 Bragg Reflection of X-Rays in Multiwave Diffraction.- 12.13 Methods for Numerical Determination of Dispersion Surface and Electric Displacement Vectors.- Appendix A.- Appendix B.- Appendix C.- References.