Disordered Materials: Glass physics

Transcription

1 Disordered Materials: Glass physics > 2.7. Introduction, liquids, glasses > 4.7. Scattering off disordered matter: static, elastic and dynamics structure factors > 9.7. Static structures: X-ray scattering, EXAFS, (neutrons), data interpretation > Dynamic structures and the glass transition Hermann Franz Methoden moderner Röntgenphysik II July 2013

2 Time dependent structures, inelastic scattering Dynamic structure factor: S( q, ω ) = 1 N e iq dt ( R R ) iqu( R,0) iqu( R, t ) 2 π e e FT of the density-density correlation function Energy resolved inelastic scattering! Hermann Franz Master course mod. X-ray physics July Page 28

3 Time dependent structures Time correlation: speckle spectroscopy S( q, t) = 1 N e iq S( q, t) I( q,0) I( q, t) ( R R ) iqu( R,0) iqu( R, t ) However, we cannot measure the phases This is regardless of normalization - the time correlation function (see lecture 10) g ( Q, t) = I( Q,0) I( Q, t) / < I( Q) > 2 e e 2 Hermann Franz Master course mod. X-ray physics July Page 29

4 Dielectric spectroscopy Colliodal glass, 70 nm spheres 2000 frames 4 GB 400 s exposure Courtesy Ch. Gutt Hermann Franz Master course mod. X-ray physics July Page 30

5 Hermann Franz Master course mod. X-ray physics July Page 31

6 In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July Page 32

7 Dielectric spectroscopy U. Schneider et al. PRE (1999) Hermann Franz Master course mod. X-ray physics July Page 33

8 In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July Page 34

9 In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July Page 35

10 Nuclear resonant scattering Hermann Franz Master course mod. X-ray physics July Page 36

11 Nuclear resonant scattering Up to now all lectures treated scattering from electrons 2 e r e = = m = Å 2 mc electron : nucleus : 511 kev : 938,280 kev Thompson scattering of nuclei is negligible effect in the amplitude Hermann Franz Master course mod. X-ray physics July Page 37

12 Resonant scattering f ( ω ) = n ( E E ) n g D 0ΓR hω iγ T / 2 f ( ω ) 0 = D Γ T 0 ΓR / 2 excited state E g + hω 0 ground state holds for (any) resonance Hermann Franz Master course mod. X-ray physics July Page 38

13 Resonant scattering electrons: D = λ Å 2π 0.2 Γ ( ev R Γ T ) nuclei: D = λ Å π Γ Γ nev R T µ ev Re( f ( 57 ω 0, Fe ) 440r0 under resonance conditions the crosssection of nuclei excceeds the scattering from electrons Hermann Franz Master course mod. X-ray physics July Page 39

14 Resonant scattering Fe Resonance real and im. part [r0] energy [nev] Hermann Franz Master course mod. X-ray physics July Page 40

15 Excursion: The Mössbauer effect source sample detector energy (doppler velocity) Hermann Franz Master course mod. X-ray physics July Page 41

16 Experimental setup Undulator Collimation Focusing Fast detector High heat-load monochromator High resolution monochromator Hermann Franz Master course mod. X-ray physics July Page 42

17 Problem: electronic background intensity [a.u.] Black:Incident I blue: electronic scattering red: resonant scattering energy [mev] Resonant scattering is strong but limited to extremely narrow bandwidth (nev) Hermann Franz Master course mod. X-ray physics July Page 43

18 Way out: timing 25 intensity [a.u.] NOT TO SCALE time [ns] Due to the narrow bandwidth the response is slow (long life time, Heisenberg) Hermann Franz Master course mod. X-ray physics July Page 44

19 Way out: timing 25 intensity [a.u.] NOT TO SCALE time [ns] Electronic gating (of the detector) takes away the fast scattering off electrons Hermann Franz Master course mod. X-ray physics July Page 45

20 SO WHAT??? Is there any advantage in using scattering off the nuclei? Hermann Franz Master course mod. X-ray physics July Page 46

21 Yes! SR is an ideal source: no line broadening, no back ground (after gating), high brilliance, no radioactive source direct observation in time domain white incident radiation offers the possibility to perform inelastic measurements Hermann Franz Master course mod. X-ray physics July Page 47

22 Nuclear exciton The incident pulse excites all nuclei coherently, no nucleus is distinguished Thus the response is the sum of all scattering AMPLITUDES s i g n a l [a. u. ] sig nal [a.u.] energy [Γ] time [ns] Hermann Franz Master course mod. X-ray physics July Page 48

23 Types of hyperfine interactions Hermann Franz Master course mod. X-ray physics July Page 49

24 Time spectrum of FeBO 3 Hermann Franz Master course mod. X-ray physics July Page 50

25 Magnetic switching Determine switching angle and time Yu. Shvyd ko et al. PRL 1996 Hermann Franz Master course mod. X-ray physics July Page 51

26 Resonances suitable for NRS 57 Fe kev 141 ns 4.7 nev 151 Eu 21.5 kev 13.7 ns 48.3 nev 161 Dy kev 39.2 ns 16.2 nev 119 Sn kev 25.6 ns 25.8 nev 61 Ni kev 7.6 ns 87 nev and several more Hermann Franz Master course mod. X-ray physics July Page 52

27 Inelastic scattering excited state ground state Sample excitation with energy E ph = E X - (E e -E g ) excited state ground state Energies not to scale (kev and mev) Hermann Franz Master course mod. X-ray physics July Page 53

28 Phonon spectrum of α-iron 2 intensity [a.u.] Energy transfer [mev] Hermann Franz Master course mod. X-ray physics July Page 54

29 Quasielastic nuclear resonant forward scattering Intensity [a.u.] Phys.Bl. Götze Artikel von H. Cummins Neutron scattering Light scattering I ( ) 2( ) τ 8 2 t = I cos Ωt e F ( t) o t T time after excitation [ns] s relaxation function Butyl phthalate / ferrocene Exact treatment of QNFS: I. Sergueev, HF,.. PRB 2003 Hermann Franz Master course mod. X-ray physics July Page 55

30 Non ergodicity parameter 1 θ = 41 K T c = 202 K flm T [K] Square-root behaviour as predicted by mode-coupling theory Stretching exponent β = 0.48, independent of T Hermann Franz Master course mod. X-ray physics July Page 56