1. Slide: 1 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

2. Slide: 2 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Methods to study dynamics: Dispersion relations: S(q,E) Density of states: g(E) Thermal diffuse scattering: p(q)

3. Slide: 3 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Methods to study dynamics: Dispersion relations: S(q,E) Density of states: g(E) Thermal diffuse scattering: p(q) ~meV ~eV Averaging over momentum transfer  q using many detectors (many scattering angles)

4. Slide: 4 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Methods to study dynamics: Dispersion relations: S(q,E) Density of states: g(E) Thermal diffuse scattering: p(q) ~meV ~eV Averaging over momentum transfer  q using LONG TIME of interaction

5. Slide: 5 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Another view of inelastic scattering: Inelastic scattering = diffraction on moving super-lattice Periodic variation of density caused by moving atoms Bragg law (diffraction condition): Doppler effect (incidence on a moving surface):

6. Slide: 6 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Another view of inelastic scattering: During LONG TIME of interaction super-lattice disappeared Periodic variation of density caused by moving atoms no diffraction, incoherent scattering Doppler effect (incidence on a moving surface):

7. Slide: 7 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Another view of inelastic scattering: Nuclear Inelastic Scattering physically: nuclear inelastic absorption Kohn and ac, J.Phys.:Condens.Matter 14 (2002) 11875

8. Slide: 8 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Content: What is Nuclear Inelastic Scattering: physics, method, properties, data treatment What is interesting in Nuclear Inelastic Scattering: partial density of states, element selectivity, isotope selectivity, site selectivity (selected examples of applications) An extension of Nuclear Inelastic Scattering: Inelastic X-ray Scattering with Nuclear Resonance Analysis (application to glass dynamics)

9. Slide: 9 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 What is nuclear inelastic scattering:   2 eV  0  0.33 fs E = 7.112 keV  e =26  10 -20 cm 2  = 4.7  10 -9 eV  0 = 141 ns E = 14.412 keV  n = 256  10 -20 cm 2 14.412 keV 136.5 366.8 706.4 Fe 57 26 Electronic and nuclear levels:

10. Slide: 10 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 What is nuclear inelastic scattering: Very narrow level:  = 4.7 neV Very long time:  0 = 141 ns Interaction occurs ONLY for the selected isotope: element selectivity isotope selectivity site selectivity

11. Slide: 11 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Narrow resonance: Narrow resonance is a built-in energy analyzer No need to analyze the energy of scattered radiation inelastic scattering (neutron of x-ray) М А D S monochromatorsampledetector analyzer E in + E ph = E out Inelastic Nuclear Absorption: М S monochromator sample (alias analyzer) E in + E ph = E N D detectorр products of nuclear absorption N eKeK eLeL conversion electrons atomic fluorescence Monitoring the products of nuclear absorption: 0 fluorescence energy Seto et al, PRL 74 (1995) 3828

12. Slide: 12 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 What is nuclear inelastic scattering: Energy Absorption detector monochromator  E ~ 1 meV 0.1 ns176 ns time counts pulsed structure of synchrotron radiation: time gate energy scan ac and Sturhahn, Hyperfine Interact. 123/124 (1999) 781

13. Slide: 13 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 What is nuclear inelastic scattering: 57 Fe nuclei v+v+ v-v- E = E res (1+v/c) Classical interpretation of Nuclear Inelastic Scattering: monitoring velocity distribution of vibration atoms pair correlation does not matter: no sensitivity wave vector !!!

14. Slide: 14 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 NIS: simple and accurate Absorption - ideal averaging over wave vectors - no corrections for multiple scattering events - no corrections for contribution of coherent scattering Isotope selectivity: - no corrections for empty can High energy of incidence radiation (~10-30 keV): - no kinematic limitations (full range of wave vectors and energy) - work in “loss-energy” region - fixed instrumental function over an entire energy range neutronsX-rays Exact density of phonon states in an entire energy range at “any” temperature

15. Slide: 15 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 NIS: simple and accurate Determination of the density of states from the energy dependence of Nuclear Inelastic Scattering Fourier logarithm Fourier 0 absorption energy absorption probability density of states: normalization Kohn and ac, Hyperfine Interact. 125 (2000) 205

16. Slide: 16 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Intermediate summary: Nuclear Inelastic Scattering - inelastic absorption of x rays by nuclei with low- energy nuclear resonances accompanied by creation and annihilation of phonons Nuclear inelastic scattering is isotope-selective: it proceeds only for a particular nuclear isotope with a selected energy of nuclear resonance. Presently, it can be performed with Fe, Sn, Sm, Eu, Dy, K, Kr, Sb, Te, and Xe (in nearest future, possibly also with Ge, Ba и Os). Nuclear inelastic scattering allows for measurements of the partial density of phonon states of the selected isotope in the studied sample. Nuclear inelastic scattering allows for determination of the density of states with high accuracy, in absolute numbers of phonon states.

17. Slide: 17 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 But: Only partial density of states (not a complete one) Only for selected elements (not for all of them) Is it good or bad ?

18. Slide: 18 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only partial density of phonon states: How do atoms move relative to each other? ferrocene FeC 10 H 10 rigid body:stretching: 0.30 0.14 0.23 0.28 Total DOS: area = 1/3N Partial DOS: area = ??? ac et al, Structural Chemistry 14 (2003) 109

19. Slide: 19 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only selected elements: How does the functional centre of a protein move? 581 cm -1 594 cm -1 Fe

20. Slide: 20 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only selected elements: How does the protein move? 69 cm -1

21. Slide: 21 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only selected elements: What is the structure of the molecule? guanidium nitroprusside: (CN 3 H 6 ) 2 [Fe(CN) 5 NO] Fe C N O ground state excited I-state excited II-state groundground + excited groundexcited Paulsen et al, JACS 124 (2002) 3007

22. Slide: 22 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only selected isotopes: How do atom move in the first (second, third) atomic layer? 57 Fe 56 Fe W Ślęzak et al, PRL 99 (2007) 066103

23. Slide: 23 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Only selected isotopes in selected sites: What determines the anomalous elasticity of nano-composite? Why “less” is “better” composite model магнитное поле nano-grain grain surface interface Mössbauer spectroscopy: Magnetic field

24. Slide: 24 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Why “less” is “better” Only selected isotopes in selected sites: What determines the anomalous elasticity of nano-composite? grains interface Stankov et al, PRL 100 (2008) 235503 Atomic dynamics of nano-grains and bulk is the same All anomalies comes from atomic dynamics of interface

25. Slide: 25 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 But: only Mössbauer isotopes... Nuclear inelastic scattering is isotope-selective: it proceeds only for selected nuclear isotopes Now: Fe, Sn, Sm, Eu, Dy, K, Kr, Sb, Te и Xe in nearest future: Ge, Ba и Os Can we study, for instance, SiO 2 ?

26. Slide: 26 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Not only Mössbauer isotopes! Inelastic X-ray Scattering with Nuclear Resonance Analysis Inelastic X-ray Scattering: Nuclear Inelastic Scattering: Crystal analyzers:  E = 1.4 meV or 3 meV  Q = 0.03 nm -1,  Q = [1-7] nm -1 nuclear analyzer:  E = 0.5 meV  Q = [3-14] nm -1 Move resonance from sample to detector !!! ac et al, PRL 76 (1996) 4258.

27. Slide: 27 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses: C.A.Angel et al., J.Phys.:Cond.Matt. 15,S1051,2003 A.Wischnewski et al., PRB 57,2663,1998 Debye: ~E 2 g(E) g(E) / E 2 R.C.Zeller et al., PRB 4,2029,1971 DOS g(E): additional vibrational states ! Reduced DOS g(E)/E 2 : the boson peak ! Debye: ~T 3 additional vibrational states? ×5×5 At low temperatures, heat capacity for glasses is larger than for crystals

28. Slide: 28 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses:

29. Slide: 29 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses:  -cristobalite tetragonal  -quartz trigonal coesite monoclinic ambient glass amorphous densified glass amorphous

30. Slide: 30 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses: ambient glass densified glass nuclear resonance analysis crystal analyzers  -cristobalite  -quartz coesite ac et al, PRL 112 (2014) 025502

31. Slide: 31 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses: excess states all states in this energy region Debye level: how many states one can expect for acoustic sound waves  -quartz

32. Slide: 32 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses:  -cristobalite ambient glass  -quartz densified glass excess states: all states: 5.6(3)% 8.4(5)% excess states: all states: 5.3(3)% 8.4(5)% excess states: all states: 5.9(4)% 12.8(8)% excess states: all states: 6.6(4)% 11.5(7)% 12 atoms in unit cell 9 atoms in unit cell

33. Slide: 33 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses: The low-density glass and crystal The high-density glass and crystal  -cristobalite  = 2.29 g/cc  -quartz  = 2.65 g/cc ambient glass  = 2.20 g/cc densified glass  = 2.67 g/cc R.C.Zeller et al., PRB 4,2029,1971 typical glass vs typical crystal (quartz) low-density glass vs high-density crystal

34. Slide: 34 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 The puzzle of glasses:

35. Slide: 35 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Summary: Nuclear Inelastic Scattering (NIS): inelastic absorption of x rays Nuclear levels are narrow: ~neV this gives an ideal built-in energy analyzer Nuclear interaction is slow: ~ns this gives an ideal averaging of wave vectors (q) NIS gives the partial density of states this shows how atoms move NIS is isotope-selective: thus gives site-selectivity

36. Slide: 36 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014 Time to stop now...