X-Ray Scattering from Semiconductors and Other Materials: 3rd Edition

Description

This third edition has been extended considerably to incorporate more information on instrument influences on the interpretation of X-ray scattering profiles and reciprocal space maps. Another significant inclusion is on the scattering from powder samples, covering a new theoretical approach that explains features that conventional theory cannot. The new edition includes some of the latest methodologies and theoretical treatments, including the latest thinking on dynamical theory and diffuse scattering. Recent advances in detectors also present new opportunities for rapid data collection and some very different approaches in data collection techniques; the possibilities associated with these advances will be included. This edition should be of interest to those who use X-ray scattering to understand more about their samples, so that they can make a better judgment of the parameter and confidence levels in their analyses, and how the combination of instrument, sample and detection should be considered as a whole to ensure this. Contents Acknowledgements Symbols used throughout the text Chapter 1: Introductory topics Chapter 2: Correlation functions and spectra 2.1. Spectroscopic experiments and correlation functions (Berne and Pecora, 1976) 2.2. An example of a correlation function: The velocity autocorrelation function and the single-particle dynamics (Boon and Yip, 1980; Yip, 2003; Balucani and Zoppi, 1994) 2.3. Time averages and ensemble averages (Berne and Pecora, 1976) 2.4. The Onsager’s regression principle (Onsager, 1931a, Onsager, 1931, Batista) 2.5. The linear response of the system (MacKintosh) 2.6. The variable measured by a scattering measurement (Wang, 2012, Berne and Pecora, 1976) 2.7. Further remarks on the outcome of spectroscopic measurements 2.8. A simple method to derive some prototypical spectral shapes 2.9. Some variables, correlation and spectral functions of interest (Balucani and Zoppi, 1994, Hansen and McDonald, 2006) Appendix 2A: The Kramers-Kroenig relations References Chapter 3: The IXS technique 3.1. Generalities on an IXS experiment 3.2. Introducing the differential cross-section (Sakurai and Commins, 1995, Fowler, 2003) 3.3. The crucial role of the cross-section in IXS measurements (Scopigno et al., 2005) 3.4. From the Hamiltonian of the scattering process to the double differential cross section (Sinha, 2001, Scopigno et al., 2005) 3.5. The cross-section in the adiabatic approximation (Bransden and Joachain, 1983, Sinha, 2001, Scopigno et al., 2005) 3.6. An estimate of the count rate Appendix 3A: The scattering problem: A time-independent theoretical description Appendix 3B: A compact expression for the double differential cross-section in the adiabatic approximation References Chapter 4: Complementary aspects of IXS and INS 4.1. Generalities on the INS technique (Lovesey, 1984, Squires, 2012) 4.2. The cross-section of inelastic neutron scattering (see (Lovesey, 1984)) 4.3. Kinematic limitations (Squires, 2012) 4.4. The roles of instrumental resolution and spectral contrast 4.5. Three-axis and time of flight techniques (Windsor, 1981, Squires, 2012, Shirane et al., 2002) 4.6. A few critical features of IXS spectrometers 4.7. An example of state-of-the-art spectrometers: ID28 beamline at ESRF 4.8. Towards new generation IXS spectrometers 4.9. A closer comparison between IXS and INS 4.9.1. Advantages of IXS 4.9.2. Advantages of INS References Chapter 5: From the Mori–Zwanzig formalism to the lineshape model 5.1. Some general considerations on the memory function formalism (Berne and Pecora, 1976) 5.2. The Generalized Langevin Equation (Berne and Pecora, 1976) 5.3. Identifying a set of slow variables (Keyes, 1977) 5.4. Beyond the Markov approximation (Balucani and Zoppi, 1994) 5.5. From the memory function to the spectra llineshape References Chapter 6: A model for the lineshape 6.1. The two opposite regimes of the spectral shape 6.1.1. The hydrodynamic regime (Berne and Pecora, 1976) 6.1.2. General considerations on the physical nature of hydrodynamic modes (Boon and Yip, 1980) 6.1.3. The single-particle regime 6.2. Modelling the lineshape at the departure from the hydrodynamic limit 6.2.1. Generalized Hydrodynamics models 6.2.2. Single timescale approximation of the memory decay, or pure viscoelastic model 6.2.3. Molecular Hydrodynamics models 6.2.4. Viscoelasticity and generalized transport parameters 6.3. Approximating the measured spectral shape: few general and practical issues Appendix 6A: The high and low-frequency limit of the memory function: The Damped Harmonic Oscillator model References Chapter 7: The Q-evolution of the spectral shape from the hydrodynamic to the kinetic regime 7.1. Using THz spectroscopy to detect mesoscopic collective modes: Early results 7.2. Evidence of extended Brillouin peaks at mesoscopic scales 7.3. Further considerations on the different behavior of noble gases and liquid metals 7.4. The kinetic theory approach: A few introductory topics 7.5. The onset of kinetic regime probed by IXS measurements on deeply supercritical neon 7.6. The crossover from the collective to the single-particle regime: Some qualitative aspects 7.7. Using IXS as a probe of the single-particle regime 7.8. Final states effects 7.9. The case of molecular systems 7.10. Gaining insight from spectral moments: The onset of quantum effects 7.11. IXS studies of quantum effects in simple liquids Appendix 7A: Brief hints on the Enskog theory formalism (Kamgar-Parsi et al., 1987) Appendix 7B: Handling quantum effects analytically (Fredrikze, 1983) References Chapter 8: Terahertz relaxation phenomena in simple systems probed by IXS 8.1. Introductory topics 8.2. Investigating viscoelastic phenomena by mesoscopic spectroscopy: The Q- and T-dependence of transport parameters 8.3. Structural relaxations 8.4. Brief remarks on the temperature dependence of relaxation time 8.5. Quantitative insight on the structural relaxations: The case of water 8.5.1. Gaining insight on the relaxation process from the spectral shape 8.5.2. An IXS measurement of the structural relaxation time of water 8.5.3. The longitudinal viscosity of water 8.5.4. The microscopic contribution to the viscosity 8.6. Collisional relaxations 8.7. Other types of relaxation phenomena 8.8. The adiabatic-to-isothermal transition 8.9. Approximating the Rayleigh contribution to the memory function Appendix 8A References Chapter 9: A few emerging, controversial or unsolved topics in IXS investigations of simple fluids 9.1. How do relaxation processes depend on thermodynamic conditions? 9.2. Liquid-like and compressed gas behaviour 9.3. Evidence of (thermo)dynamic boundaries 9.4. The Frenkel line 9.5. To what extent does the dynamics of a disordered system resemble the one of a solid? 9.5.1. Sound damping, structural disorder and elastic anisotropy 9.6. Generalities on the propagation of a shear wave in a liquid 9.6.1. A transverse mode in the spectrum of water 9.6.2. The onset of a transverse dynamics in monatomic systems 9.7. Polyamorphism phenomena in simple systems investigated by IXS References Conclusive remarks Using IXS as a tool to advance terahertz phononics The critical role of the spectrometer performance Revisiting the lineshape analysis The critical role of molecular dynamic simulations References