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 > 11.7. Dynamic structures and the glass transition Hermann Franz Methoden moderner Röntgenphysik II July 2013
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 20113 Page 28
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 20113 Page 29
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 20113 Page 30
Hermann Franz Master course mod. X-ray physics July 20113 Page 31
In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July 20113 Page 32
Dielectric spectroscopy U. Schneider et al. PRE (1999) Hermann Franz Master course mod. X-ray physics July 20113 Page 33
In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July 20113 Page 34
In glassy systems f(q,t) = exp (-t/τ) β = exp (-t*λ) β Hermann Franz Master course mod. X-ray physics July 20113 Page 35
Nuclear resonant scattering Hermann Franz Master course mod. X-ray physics July 20113 Page 36
Nuclear resonant scattering Up to now all lectures treated scattering from electrons 2 e r e = = 2.818 10-15 m = 2.818 10-5 Å 2 mc electron : nucleus : 511 kev : 938,280 kev Thompson scattering of nuclei is negligible 0.0005 effect in the amplitude Hermann Franz Master course mod. X-ray physics July 20113 Page 37
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 20113 Page 38
Resonant scattering electrons: D = λ Å 2π 0.2 Γ 0.005 ( ev R Γ T ) nuclei: D = λ Å 2 0.2 π Γ 0.1 0. 8Γ 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 20113 Page 39
Resonant scattering 500 57 Fe Resonance 400 300 real and im. part [r0] 200 100 0-40 -30-20 -10 0 10 20 30 40-100 energy [nev] -200-300 Hermann Franz Master course mod. X-ray physics July 20113 Page 40
Excursion: The Mössbauer effect source sample detector -10-5 0 5 10 energy (doppler velocity) Hermann Franz Master course mod. X-ray physics July 20113 Page 41
Experimental setup Undulator Collimation Focusing Fast detector High heat-load monochromator High resolution monochromator Hermann Franz Master course mod. X-ray physics July 20113 Page 42
Problem: electronic background intensity [a.u.] 500 400 300 200 Black:Incident I blue: electronic scattering red: resonant scattering 100 0-4 -2 0 2 4 energy [mev] Resonant scattering is strong but limited to extremely narrow bandwidth (nev) Hermann Franz Master course mod. X-ray physics July 20113 Page 43
Way out: timing 25 intensity [a.u.] 20 15 10 5 NOT TO SCALE 0-10 90 190 290 390 time [ns] Due to the narrow bandwidth the response is slow (long life time, Heisenberg) Hermann Franz Master course mod. X-ray physics July 20113 Page 44
Way out: timing 25 intensity [a.u.] 20 15 10 5 NOT TO SCALE 0-10 90 190 290 390 time [ns] Electronic gating (of the detector) takes away the fast scattering off electrons Hermann Franz Master course mod. X-ray physics July 20113 Page 45
SO WHAT??? Is there any advantage in using scattering off the nuclei? Hermann Franz Master course mod. X-ray physics July 20113 Page 46
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 20113 Page 47
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. ] 1.1 1 0.9 0.8 0.7 sig nal [a.u.] 1.2 1 0.8 0.6 0.4 0.2 0.6-25 -15-5 5 15 25 energy [Γ] 0 0 50 100 150 200 time [ns] Hermann Franz Master course mod. X-ray physics July 20113 Page 48
Types of hyperfine interactions Hermann Franz Master course mod. X-ray physics July 20113 Page 49
Time spectrum of FeBO 3 Hermann Franz Master course mod. X-ray physics July 20113 Page 50
Magnetic switching Determine switching angle and time Yu. Shvyd ko et al. PRL 1996 Hermann Franz Master course mod. X-ray physics July 20113 Page 51
Resonances suitable for NRS 57 Fe 14.412 kev 141 ns 4.7 nev 151 Eu 21.5 kev 13.7 ns 48.3 nev 161 Dy 25.651 kev 39.2 ns 16.2 nev 119 Sn 23.88 kev 25.6 ns 25.8 nev 61 Ni 67.41 kev 7.6 ns 87 nev and several more Hermann Franz Master course mod. X-ray physics July 20113 Page 52
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 20113 Page 53
Phonon spectrum of α-iron 2 intensity [a.u.] 1 0-50 -30-10 10 30 50 Energy transfer [mev] Hermann Franz Master course mod. X-ray physics July 20113 Page 54
Quasielastic nuclear resonant forward scattering Intensity [a.u.] Phys.Bl. Götze Artikel von H. Cummins Neutron scattering Light scattering. 1000.0 100.0 10.0 1.0 I ( ) 2( ) τ 8 2 t = I cos Ωt e F ( t) o t T 1 + 0.1 0.0 100.0 200.0 300.0 400.0 500.0 time after excitation [ns] s 0.2 0.1 0.0-0.1 relaxation function Butyl phthalate / ferrocene Exact treatment of QNFS: I. Sergueev, HF,.. PRB 2003 Hermann Franz Master course mod. X-ray physics July 20113 Page 55
Non ergodicity parameter 1 θ = 41 K T c = 202 K flm 0.1 0.01 50 70 90 110 130 150 170 190 210 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 20113 Page 56