Introduction to Nuclear Inelastic Scattering

1. Introduction to Nuclear Inelastic Scattering Aleksandr Chumakov European Synchrotron Radiation Facility HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

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

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

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

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

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

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

9. 57 Fe 26 706.4 366.8 136.5 14.412 keV E = 14.412 keV E = 7.112 keV = 256 10 cm - 20 2 = 26 10 cm s × - 20 2 s × n e G 2 eV t0 0.33 fs G = 4.7 10-9 eV t0 = 141 ns What is nuclear inelastic scattering: Electronic and nuclear levels: HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

10. What is nuclear inelastic scattering: Very narrow level: G= 4.7 neV Very long time: t0= 141 ns Interaction occurs ONLY for the selected isotope: element selectivity isotope selectivity site selectivity HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

12. Absorption monochromatorDE ~ 1 meV Energy energy scan detector pulsed structure of synchrotron radiation: 0.1 ns 176 ns counts time time gate What is nuclear inelastic scattering: ac and Sturhahn, Hyperfine Interact. 123/124 (1999) 781 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

14. 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 neutrons X-rays Exact density of phonon states in an entire energy range at “any” temperature HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

16. 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 isisotope-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, andXe(in nearest future, possibly also with Ge, Baи 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 , inabsolute numbers of phonon states. HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

18. Total DOS: area = 1/3N 0.28 0.23 ferrocene FeC10H10 0.14 0.30 Partial DOS: area = ??? rigid body: stretching: Why “less” is “better” Only partialdensity of phonon states: How do atoms move relative to each other? ac et al, Structural Chemistry 14 (2003) 109 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

19. Why “less” is “better” Only selected elements: How does the functional centre of a protein move? Fe 581 cm-1 594 cm-1 Сourtesy of Prof.Schuenemann. J. Am. Chem. Soc. 134, 4216 (2012). HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

20. Why “less” is “better” Only selected elements: How does the protein move? 69 cm-1 Сourtesy of Prof.Schuenemann. J. Am. Chem. Soc. 134, 4216 (2012). HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

21. ground ground + excited Fe C (CN3H6)2 [Fe(CN)5NO] N O excitedI-state excitedII-state groundstate ground excited Why “less” is “better” Only selected elements: What is the structure of the molecule? guanidiumnitroprusside: Paulsen et al, JACS 124 (2002) 3007 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

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

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

25. But: only Mössbauer isotopes... Nuclear inelastic scattering isisotope-selective: it proceeds only for selected nuclear isotopes Now: Fe, Sn, Sm, Eu, Dy, K, Kr, Sb, Te и Xe in nearest future: Ge, Baи Os Can we study, for instance, SiO2 ? HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

27. additional vibrational states? DOS g(E): additional vibrational states ! Reduced DOS g(E)/E2: the boson peak ! A.Wischnewski et al., PRB 57,2663,1998 Debye: ~E2 C.A.Angel et al., J.Phys.:Cond.Matt. 15,S1051,2003 The puzzle of glasses: ×5 R.C.Zelleret al., PRB 4,2029,1971 At low temperatures, heat capacity for glasses is larger than for crystals Debye: ~T3 g(E) g(E) / E2 HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

29. The puzzle of glasses: ambient glass densified glass SiO2 amorphous amorphous a-cristobalite a-quartz coesite tetragonal trigonal monoclinic HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

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

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

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

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

34. The puzzle of glasses: How disorder increases the heat capacity? It does not do it: the higher heat capacity of glasses is caused by their lower density HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

35. 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 isisotope-selective: thus gives site-selectivity HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014

36. Time to stop now... Thank you for your attention HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays, 16 Sept. 2014