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E-grāmata: Thz Dynamics Of Liquids Probed By Inelastic X-ray Scattering, The

(Univ Of Wisconsin-madison, Usa)
  • Formāts: 324 pages
  • Izdošanas datums: 08-Jul-2021
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813229501
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Thz Dynamics Of Liquids Probed By Inelastic X-ray Scattering, ThePalielināt
  • Formāts: 324 pages
  • Izdošanas datums: 08-Jul-2021
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813229501
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Since its development toward the end of the past millennium, high-resolution Inelastic X-Ray Scattering (IXS) has substantially improved our knowledge of the collective dynamics of liquids at mesoscopic scales, that is, over distances and time-lapses approaching those typical of first neighboring atoms' interactions. However, despite the undoubted scientific relevance and the rapid evolution toward maturity, comprehensive monographs on this technique are not available. The primary purpose of this book is to partially fill this lack while providing a helpful reference for both mature scientists and less experienced researchers in the field.After a general introduction to the fundamental aspects of scattering measurements, the IXS cross-section is analytically derived, and the complementarity with Inelastic Neutron Scattering is discussed in detail.The remainder of the book reviews representative IXS studies on simple fluids focusing on topics as relevant as the dynamic crossover from the hydrodynamic to the kinetic regime, the onset of relaxation phenomena and related high-frequency viscoelasticity, the gradual emergence of quantum effects, the evidence of dynamic boundaries partitioning the supercritical domain, the prevalence of solid-like aspects in the high-frequency dynamics of fluids, and the dynamic fingerprints of the polymorphic nature of liquid aggregates.
Acknowledgements v
Symbols used throughout the text xiii
Chapter 1 Introductory topics
1(4)
References
3(2)
Chapter 2 Correlation functions and spectra
5(46)
2.1 Spectroscopic experiments and correlation functions (Berne and Pecora, 1976)
5(7)
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)
12(5)
2.3 Time averages and ensemble averages (Berne and Pecora, 1976)
17(2)
2.4 The Onsager's regression principle (Onsager, 1931a, Onsager, 1931, Batista)
19(4)
2.5 The linear response of the system (MacKintosh)
23(9)
2.6 The variable measured by a scattering measurement (Wang, 2012, Berne and Pecora, 1976)
32(4)
2.7 Further remarks on the outcome of spectroscopic measurements
36(2)
2.8 A simple method to derive some prototypical spectral shapes
38(2)
2.9 Some variables, correlation and spectral functions of interest (Balucani and Zoppi, 1994, Hansen and McDonald, 2006)
40(11)
Appendix 2A The Kramers-Kroenig relations
48(2)
References
50(1)
Chapter 3 The JXS technique
51(32)
3.1 Generalities on an IXS experiment
51(2)
3.2 Introducing the differential cross-section (Sakurai and Commins, 1995, Fowler, 2003)
53(5)
3.3 The crucial role of the cross-section in IXS measurements (Scopigno et al., 2005)
58(1)
3.4 From the Hamiltonian of the scattering process to the double differential cross section (Sinha, 2001, Scopigno et al, 2005)
59(6)
3.5 The cross-section in the adiabatic approximation (Bransden and Joachain, 1983, Sinha, 2001, Scopigno et al, 2005)
65(4)
3.6 An estimate of the count rate
69(14)
Appendix 3A The scattering problem: A time-independent theoretical description
71(7)
Appendix 3B A compact expression for the double differential cross-section in the adiabatic approximation
78(3)
References
81(2)
Chapter 4 Complementary aspects of IXS and INS
83(34)
4.1 Generalities on the INS technique (Lovesey, 1984, Squires, 2012)
83(2)
4.2 The cross-section of inelastic neutron scattering (see (Lovesey, 1984))
85(3)
4.3 Kinematic limitations (Squires, 2012)
88(4)
4.4 The roles of instrumental resolution and spectral contrast
92(5)
4.5 Three-axis and time of flight techniques (Windsor, 1981, Squires, 2012, Shirane et ai, 2002)
97(3)
4.6 A few critical features of IXS spectrometers
100(2)
4.7 An example of state-of-the-art spectrometers: ID28 beamline at ESRF
102(4)
4.8 Towards new generation IXS spectrometers
106(2)
4.9 A closer comparison between IXS and INS
108(9)
4.9.1 Advantages of IXS
109(2)
4.9.2 Advantages of INS
111(3)
References
114(3)
Chapter 5 From the Mori--Zwanzig formalism to the lineshape model
117(18)
5.1 Some general considerations on the memory function formalism (Berne and Pecora, 1976)
118(1)
5.2 The Generalized Langevin Equation (Berne and Pecora, 1976)
119(5)
5.3 Identifying a set of slow variables (Keyes, 1977)
124(4)
5.4 Beyond the Markov approximation (Balucani and Zoppi, 1994)
128(3)
5.5 From the memory function to the spectral lineshape
131(4)
References
132(3)
Chapter 6 A model for the lineshape
135(34)
6.1 The two opposite regimes of the spectral shape
137(12)
6.1.1 The hydrodynamic regime (Berne and Pecora, 1976)
138(4)
6.1.2 General considerations on the physical nature of hydrodynamic modes (Boon and Yip, 1980)
142(4)
6.1.3 The single-particle regime
146(3)
6.2 Modelling the lineshape at the departure from the hydrodynamic limit
149(13)
6.2.1 Generalized Hydrodynamics models
151(1)
6.2.2 Single timescale approximation of the memory decay, or pure viscoelastic model
152(3)
6.2.3 Molecular Hydrodynamics models
155(3)
6.2.4 Viscoelasticity and generalized transport parameters
158(4)
6.3 Approximating the measured spectral shape: few general and practical issues
162(7)
Appendix 6A The high and low-frequency limit of the memory function: The Damped Harmonic Oscillator model
165(2)
References
167(2)
Chapter 7 The Q-evolution of the spectral shape from the hydrodynamic to the kinetic regime
169(46)
7.1 Using THz spectroscopy to detect mesoscopic collective modes: Early results
169(2)
7.2 Evidence of extended Brillouin peaks at mesoscopic scales
171(7)
7.3 Further considerations on the different behavior of noble gases and liquid metals
178(4)
7.4 The kinetic theory approach: A few introductory topics
182(3)
7.5 The onset of kinetic regime probed by IXS measurements on deeply supercritical neon
185(4)
7.6 The crossover from the collective to the single-particle regime: Some qualitative aspects
189(3)
7.7 Using IXS as a probe of the single-particle regime
192(1)
7.8 Final states effects
193(2)
7.9 The case of molecular systems
195(3)
7.10 Gaining insight from spectral moments: The onset of quantum effects
198(2)
7.11 IXS studies of quantum effects in simple liquids
200(15)
Appendix 7A Brief hints on the Enskog theory formalism (Kamgar-Parsi et ai, 1987)
205(5)
Appendix 7B Handling quantum effects analytically (Fredrikze, 1983)
210(2)
References
212(3)
Chapter 8 Terahertz relaxation phenomena in simple systems probed by IXS
215(40)
8.1 Introductory topics
215(4)
8.2 Investigating viscoelastic phenomena by mesoscopic spectroscopy: The Q- and T-dependence of transport parameters
219(4)
8.3 Structural relaxations
223(3)
8.4 Brief remarks on the temperature dependence of relaxation time
226(3)
8.5 Quantitative insight on the structural relaxations: The case of water
229(10)
8.5.1 Gaining insight on the relaxation process from the spectral shape
231(2)
8.5.2 An IXS measurement of the structural relaxation time of water
233(3)
8.5.3 The longitudinal viscosity of water
236(1)
8.5.4 The microscopic contribution to the viscosity
237(2)
8.6 Collisional relaxations
239(2)
8.7 Other types of relaxation phenomena
241(2)
8.8 The adiabatic-to-isothermal transition
243(3)
8.9 Approximating the Rayleigh contribution to the memory function
246(9)
Appendix 8A
249(2)
References
251(4)
Chapter 9 A few emerging, controversial or unsolved topics in IXS investigations of simple fluids
255(44)
9.1 How do relaxation processes depend on thermodynamic conditions?
255(3)
9.2 Liquid-like and compressed gas behaviour
258(5)
9.3 Evidence of (thermo)dynamic boundaries
263(5)
9.4 The Prenkel line
268(2)
9.5 To what extent does the dynamics of a disordered system resemble the one of a solid?
270(6)
9.5.1 Sound damping, structural disorder and elastic anisotropy
271(5)
9.6 Generalities on the propagation of a shear wave in a liquid
276(14)
9.6.1 A transverse mode in the spectrum of water
278(9)
9.6.2 The onset of a transverse dynamics in monatomic systems
287(3)
9.7 Polyamorphism phenomena in simple systems investigated by IXS
290(9)
References
293(6)
Conclusive remarks 299
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