1. Ion-beam, photon and hyperfine methods in nano-structured materials
Erasmus Intensive Program
Ion-beam, photon and hyperfine methods in nano-structured materials
Lyon — 14–23 May 2006
Elements of
MÖSSBAUER SPECTROSCOPY by G. Principi (Padova) and D.L. Nagy (Budapest)

2. Mössbauer spectroscopy Probability of the recoil-free process
The Mössbauer effect
Mössbauer spectroscopy
Probability of the recoil-free process
Line shape Hyperfine interactions
Isomer shift
Quadrupole splitting
Magnetic hyperfine splitting
Relaxation effects
Methodology
Spectrometers
Sources
Absorbers
Calibration
Conversion-electron Mössbauer spectroscopy (CEMS)
Fitting of spectra
Some examples of application to thin films
Ion-beam mixing of Fe-Pd bilayers
Epitaxial Fe0.5Pd0.5 films
Depth selectivity
Structural evolution of annealed metallic multilayers
Granular AgFe films

3. resonant absorption    •    photon emitter absorber
Recoil momentum
Recoil energy

6. (Gonser, 1975)

8. Mössbauer spectroscopy
EDoppler = E (v/c)

9. Classical calculation
Probability of the recoil-free process
Classical calculation
Debye model
(solid with a quadratic law of oscillator frequencies from 0 to D)
low T/D
low operating temperature
low E (low k)
for a strong ME

10. hyperfine interactions - electric monopole  isomer shift
- electric quadrupole  quadrupole splitting
- magnetic dipole  nuclear Zeeman effect
isomer shift
interaction of nuclear charge distribution
with the electron density at the nucleus
(in source and absorber)
nuclear property
electronic property

11. quadrupole splitting interaction of nuclear quadrupole moment eQ
with the electric field gradient at the nucleus
splits the nuclear state into sublevels
for 57Fe and 119Sn, I = 3/2, then

12. nuclear Zeeman effect interaction of nuclear magnetic moment n
with internal or applied magnetic field H splits the nuclear state of spin I into 2I+1 sublevels

13. The effect of the magnetic field direction on the line intensities

14. Polarimetry with Zeeman-split source and absorber+ 
a = mm / s
b = mm / s

15. Polarimetry with Zeeman-split source and absorber
Shift
Overlapping Peaks
Intensity
Polarisation
4a+b
1,6 9
parallel
3a+b
1,5; 2,6 24
perpendicular
2a+b
1,4; 2,5; 3,6 22 2a
1,3; 4,6 6
a+b
2,4; 3,5 8 a
1,2; 2,3; 4,5; 5,6 32 b
3,4 1
1,1; 2,2; 3,3; 4,4; 5,5; 6,6 52

16. Polarimetry with Zeeman-split source and absorber
Habsorber H
Hsource

18. typical experimental arrangement for transmission geometry

21. conversion-electron Mössbauer spectroscopy (CEMS)

22. ion-beam mixing of Fe-Pd bilayers (Gupta et al., 1990)

24. epitaxial Fe0.5Pd05 films
(Gehanno et al., 1998)

25. depth selectivity oxidation state of Sn at the
surface of an industrial glass
(Principi et al., 1993)
selection of high energy and
low energy electrons
from flowing gas proportional counter

26. buried FeSi2 layers by Fe implantation in Si (Walterfang et al., 2000)

28. annealing of (10nm Fe-14nm Al)15 multilayers
(Checchetto et al., 2001)

29. granular AgFe films (Alof et al., 2000)
Fe concentration (at. %) 30.0(5) 33.5(5) 36.5(5) 41.5(5)
Interface/bulk ratio R
Particle radius rp (nm)
Calculated number of
atoms per particle

30. CEMS polarimetry with Zeeman-split source and scatterer
H(s)
CEMS
Detector H k
Polariser

31. CEMS polarimetry with Zeeman-split source and scatterer: the bulk-spin-flop in a MgO(001)[57Fe(26Å)/Cr(13Å)]20 multilayer

32. Circular polarimetry with an in-plane magnetised and tilted 57Co:-Fe source

33. Circular polarimetry with a 57Co:-Fe source magnetised along the optical axis
The overlapping of the 44 allowed transitions of source and absorber result in 9 resonance lines 3 and 6 of which belong to parallel and antiparallel field orientations, respectively.

34. Circular polarimetry with an in-plane magnetised and tilted 57Co:-Fe source
 = 10°

35. Problem 1.
In an undergraduate examination in 1960 at Oxford University, Josephson received the problem to calculate the change in frequency of an oscillator, which suddenly changes its mass. He had read about the Mössbauer effect and realised that there was a connection with the emission of a gamma ray by a nucleus. He calculated that in the emission process there is a decrease in the energy of the emitted gamma ray given by
Try to reproduce the Josephson's calculation.
(Hint: consider the relativistic relation between mass and energy).

36. Problem 2.
A Mössbauer source is 24 m high and the absorber is at the ground level. Source and absorber are in identical crystalline lattices. Due to the gravitational shift, it is necessary to move the source with a velocity v with respect to the absorber in order to obtain a perfect resonance. Determine this velocity and its ratio with respect to the linewidth if the source is 57Co or 119mSn. Which isotope is better suited to the experiment?
(Hint: consider the relativistic relation between mass and energy).

37. Problem 3.
The electric quadrupole interaction for iron and tin gives a doublet. For europium the situation is more complicated. Find the number of lines observed in this case. Neglect the possible multipolarity mixing of the transition.
(Hint: from Table 1 and Eq. (11) …).

38. Problem 4.
An iron-based magnetic material gives rise to a Mössbauer sextet with line intensity ratio 3:3:1. Determine the direction of magnetisation with respect to the propagation direction of gamma rays perpendicular to the sample surface.
(Hint: look at table of Page 12…).

39. Problem 5.
The nucleus of a Mössbauer isotope is subjected to a magnetic field, which inverts stochastically its direction. The average period of inversions i is equal to the mean lifetime n of the excited state. The field intensity is high enough to result in a good separation of the spectral lines. Estimate the increment in the linewidths of the spectrum.
(Hint: on the basis of the Heisenberg principle …).