Mössbauer Spectroscopy
Rudolf L. Mössbauer
1929 ‐ 2011
1958 
Recoilless Nuclear Resonance 
Absorption of Gamma‐Radiation
= the Mössbauer Effect (during PhD)
1961
Nobel Prize in Physics
The Mössbauer resonance line is
extremely narrow and allows
hyperfine interactions to be resolved
and evaluated, quadrupole splitting 
and an isomer shift 
1
The Mössbauer Effect
2
Recoilless Nuclear Resonance Absorption and
Fluorescence of -Radiation
3
2
2
2mc
E
ER


ge EEE 0
REEE  0
Nuclear Decay Scheme for 57Fe
Mössbauer Resonance
4
15 %
Mössbauer Emission
Radioactive 57Co (halflife 270 d) is
generated in a cyclotron and 
diffused into Rh
serves as the gamma radiation 
source for 57Fe Mössbauer
spectroscopy
10 ns, 122 keV
Nuclear Resonance Absorption
5
Mössbauer Active Elements
6
Nuclides suitable for Mössbauer spectroscopy:
Excited nuclear state lifetimes 10‐6 ‐ 10‐11 s 
Transition energies 5 ‐180 keV. 
Longer (shorter) lifetimes = too narrow (broad) emission and absorption lines, no 
effective overlap
Transition energies > 180 keV = too large recoil, < 5 keV = absorbed in the source and 
absorber material
The Mössbauer effect detected in 80 isotopes of 50 elements, 
only 20 elements studied in practice Fe, Sn, Sb, Te, I, Au, Ni, Ru, Ir, W, Kr, Xe, rare earth
elements, Np. More than 90 % of publications refer to 57Fe 
Nuclear Parameters for Selected
Mössbauer Isotopes
7EC = electron capture, β–=beta-decay, IT = isomeric transition, α = alpha-decay
Mössbauer Source
Activity = 10 ‐270 mCi, lifetime 10 y
1 Ci = 37 GBq
Reference Absorbers
8
Mössbauer Source
119mSn source = CaSnO3 matrix with 119mSn 
Activity = 2 ‐ 40 mCi, lifetime 10 y
9
Mean Lifetime  of Excited State and
Natural Line Width 
10
An excited state (nuclear or electronic) of mean lifetime  does not have a
sharp energy value, but only a value within the energy range E
the Heisenberg Uncertainty Principle:
 E  t  ħ
natural line width  = ħ / 
Transitions from an excited
(e) to the ground state (g)
involve all energies within
the range of E
The transition probability or
intensity as a function of E
= a spectral line centered
around the most probable
transition energy E0
Transition Probability
11
Lorentzian formula for spectral line shape
Resonance absorption is observable only if the emission and absorption lines
overlap sufficiently. This is not the case when the lines are too narrow or too
broad
Suitable for Mössbauer spectroscopy: lifetime = 10-6 - 10-11 s
The width at half maximum of
the spectral line = natural line
width  determined by the mean
lifetime 
57Fe (14.4 keV)
 =1.43 10-7 s
 = 4.6 10-9 eV
Recoil Effect
12
57Fe (14.4 keV)
 = 4.6 10-9 eV
Recoil energy ER = 2 10-3 eV
Much larger (5‐6 orders of magnitude) than the natural line width
= no resonance possible between free atoms
The Mössbauer effect cannot be observed for freely moving atoms or
molecules, i.e. in gaseous or liquid state
2
2
2mc
E
ER


Recoil Effect
13
57Fe (14.4 keV)
 = 4.6 10-9 eV
Recoil energy ER = 2  10-3 eV
Much larger (5‐6 orders of magnitude) than the natural line width
= no resonance possible between free atoms
The Mössbauer effect cannot be observed for freely moving atoms or
molecules, i.e. in gaseous or liquid state
2
2
2mc
E
ER


Recoilless Emission and Absorption
14
Solid state, crystalline or non‐crystalline = atoms tightly bound in the lattice
Unshifted transition lines overlap = nuclear resonance absorption observed
Large mass M of a solid particle as compared to an atom = the linear momentum
created by emission and absorption of a gamma quantum practically vanishes
The recoil energy is mostly transferred to the lattice vibrational system. 
The vibrational energy of the lattice can only change by discrete amounts 0, ħ, 
2ħ, …
The probability f (Debye‐Waller or Lamb‐Mössbauer factor) that no lattice excitation 
(zero‐phonon processes) takes place during γ‐emission or absorption.
f denotes the fraction of nuclear transitions which occur without recoil. Only for this 
fraction is the Mössbauer effect observable.
2
2
2mc
E
ER


Debye-Waller or Lamb-Mössbauer Factor
15
f increases with:
* decreasing recoil energy ER
* decreasing temperature T
* increasing Debye temperature θD = hωD/2πkB
ωD = vibrational frequency of Debye oscillator, kB = Boltzmann factor
θD = a measure for the strength of the bonds between the Mössbauer atom and 
the lattice
Mössbauer-Experiment
16
The resonance perturbed by electric and 
magnetic hyperfine interactions between
the nuclei and electric and magnetic fields
set up by electrons
Hyperfine interactions shift and split
degenerate nuclear levels resulting in 
several transition lines
The Mössbauer source emits a single transition line E (assume the absorber shows also
only one transition line A). 
E and A have slightly modified transition energies, perturbation energies 10‐8 eV 
comparable to the natural linewidth, shifts the transition lines away from each other
such that the overlap decreases or disappears entirely
Overlap restored by the Doppler effect, i.e. by moving the absorber and the source 
relative to each other
Mössbauer-Experiment
17
Source and absorber are moved relative to each other
Doppler velocity
57Fe :Γ0 = 4.7∙10‐9 eV, Eγ= 14400 eV, v = 0.096 mm s‐1
c = speed of light
E
cv 0

Mössbauer-Experiment
18
Non‐resonant
background 
radiation rejected
4.2 K b.p. of liquid He
1.5 K by pumping on 
the liquid He vessel
Several hundred channels
synchronised with the
vibrator
synchronises a triangular voltage
waveform yielding a linear
Doppler velocity scale as the
channel address advances
controls the electro‐
mechanical vibrator
the difference between the
monitored signal and the
reference signal drives the
vibrator at the same
frequency (typically 50 Hz)
Mössbauer-Experiment
19
Constant acceleration
Constant velocity
Mössbauer-Experiment
20
the source is moved to Doppler shift the
center of the emission spectrum
(brown) from smaller to larger energies,
relative to the center of the absorption
spectrum (red ), whose center, the
quantized transition energy, is fixed.
The level of the transmission spectrum
(blue) at each value of velocity, v, is 
determined by how much the shifted
emission spectrum overlaps the
absorption spectrum, such that greater
overlap results in reduced transmission
owing to resonant absorption. The
evolution of the transmission spectrum
from large negative (source moving
away from absorber) to large positive 
values of velocity may be followed
from the top to the bottom rows.
Correlation of count rate with channel
number and relative velocity
21
Mössbauer spectrum of metallic Fe. The 
count rate is plotted as function of the 
channel number
Doppler velocity as a function of the channel 
number
Hyperfine Interactions between Nuclei
and Electrons
22
Mössbauer Parameters
—Electric Monopole Interaction = Isomer Shift 
—Electric Quadrupole Interaction = Quadrupole Splitting EQ
—Magnetic Dipole Interaction =  Magnetic Splitting EM
Hyperfine Interactions
23
Electric monopole interaction (Coulombic) 
between protons of the nucleus and s‐electrons penetrating the nuclear field. 
Different shifts of nuclear levels A and E.
Isomer shift values give information on the oxidation state, spin state, and 
bonding properties, such as covalency and electronegativity.
Electric quadrupole interaction
between the nuclear quadrupole moment (eQ ≠ 0, I > ½) and an inhomogeneous
electric field at the nucleus (EFG ≠ 0). Nuclear states split into I + ½ substates.
The quadrupole splitting gives the information on oxidation state, spin state and 
site symmetry.
Magnetic dipole interaction
between the nuclear magnetic dipole moment (μ≠ 0, I > 0) and a magnetic field (H 
≠ 0) at the nucleus. Nuclear states split into 2I+1 substates with mI= +I, +I‐1, .…,‐I
The magnetic splitting gives information on the magnetic properties of the 
material under study ‐ ferromagnetism, antiferromagnetism.
Isomer Shift
24
The nuclear radius in the excited state is different (in 57Fe smaller) than that in 
the ground state: Re ≠ Rg. 
The electronic densities of all s‐electrons (1s, 2s, 3s, etc.) are different at the
nuclei of the source and the absorber: ρS ≠ ρA. 
The result is that the electric monopole interactions (Coulomb interactions) 
are different in the source and the absorber and therefore affect the nuclear
ground and excited state levels to a different extent. This leads to the
measured isomer shift δ.
Isomer Shift
25
δ = EA – ES = C (ρA – ρS)(Re
2 – Rg
2)    
C = (2/3)πZe2.
The energy levels of the ground and 
excited states of a bare nucleus are 
perturbed and shifted by electric
monopole interactions. The shifts in the
ground and excited states differ = different
nuclear radii and different Coulombic
interactions. 
The energy differences ES and EA in the
source and absorber also differ because of
the different electron densities in the
source and absorber material. 
The individual energy differences ES and EA
cannot be measured individually, a 
Mössbauer experiment measures only the
difference of the transition energies
δ = EA – ES, isomer shift.
Isomer Shift
26
The isomer shift depends directly on the s‐electron densities and are influenced
indirectly via shielding by p‐, d‐, and f‐electrons which are not capable (relativistic
effects) of penetrating the nuclear field.
Influence on |Ψ(0)|2: 
Direct = change of electron population in s‐orbitals (mainly valence s‐orbitals) 
changes directly |Ψ(0)|2
Indirect = shielding by p‐, d‐, f‐electrons, increase of electron density in p‐, d‐, f‐
orbitals increases shielding effect for s‐electrons from the nuclear charge
→ s‐electron cloud expands, |Ψ(0)|2 at nucleus decreases.
119Sn Mössbauer Spectra
27
(Re
2 – Rg
2)  0
Compound / mm s‐1 Compound / mm s‐1
SnF4 0.36 Sn (metal) 2.50
SnO2 0.0 Sn (gray) 2.02
SnCl4 0.85 SnO 2.71
SnBr4 1.15 SnSO4 3.90
SnI4 1.55 SnF2 3.2
SnPh4 1.22 SnCl2 4.07
SnH4 1.27 SnBr2 3.93
Sn(IV)   2.00 mm s‐1 electron config. 5s0 – lower el. density at nucleus than neutral
atom = negative shift
Sn(II)   2.50 mm s‐1 electron config. 5s2 – higher el. density at nucleus than
neutral atom as no 5p shielding = positive shift
119Sn Mössbauer Spectra
28
(Re
2 – Rg
2)  0
119Sn Mössbauer Spectra
29
(Re
2 – Rg
2)  0
PcSnX2 complexes
119Sn Mössbauer Spectra
30
10.1016/j.matchemphys.2016.07.061
JACS 1970,92,1501
IC1971,10,1553
Electron Densities at the Nucleus (r = 0)
31
The partial electron densities refer to one electron each in 1s, 2s, 3s, 4s‐orbitals. 
The total s‐electron density at r = 0 is twice the sum of the partial one‐electron 
contributions (all s‐orbitals are doubly occupied).
Isomer Shifts of Iron Compounds
32
The most positive isomer shift occurs with iron(I) 
with spin S = 3/2.
The seven d‐electrons exert a very strong
shielding of the s‐electrons, this reduces the s‐
electron density ρA giving a strongly negative 
quantity (ρA – ρS), as (Re
2 – Rg
2)  0  for 57Fe, the
isomer shift becomes strongly positive. 
Strongly negative for iron(VI) with spin S = 1. 
There are only two d‐electrons, the shielding
effect for s‐electrons is very weak and the s‐
electron density ρA at the nucleus becomes high.
Iron(II) high spin with S=2 can be easily assigned. 
In other cases with overlapping δ values
ambiguous assignment. Need to consider the
quadrupole splitting parameter.
Effect of Ligand Electronegativity
33
The electronegativity increases from I to F 
In the same ordering the 4s‐electron 
population decreases and the s‐electron
density at the iron nucleus decreases
(Re
2 – Rg
2)  0  for 57Fe
the isomer shift increases from iodide to 
fluoride.
Fe(II) HS,  CN = 6 
Second-Order Doppler Shift
34
The isomer shifts δ, i.e. the resonance peak shifts observed in  Mössbauer
spectra, are composed of two terms:
δ = δC + δSOD(T) 
The first term is the chemical isomer shift δC which is temperature‐
independent. 
The second term is the second‐order Doppler shift δSOD. 
Since δSOD is T‐dependent, the observed isomer shift δ is also T‐dependent. 
The second‐order Doppler shift δSOD is related to the mean‐square velocity  v2
of lattice vibrations in the direction of the γ‐ray propagation which increases 
with increasing T. Accordingly, the Mössbauer resonance moves to a more 
negative velocity with increasing T : 
c
v
SOD
2
2

Electric Quadrupole Interaction
Quadrupole Splitting EQ
35
Electric Quadrupole Interaction
Electric quadrupole interaction occurs if at least one of the nuclear states involved
possesses a quadrupole moment eQ (for I > 1/2) and if the electric field at the
nucleus is inhomogeneous. 
57Fe: the first excited state (14.4 keV) has a spin I = 3/2 and therefore also an
electric quadrupole moment eQ.
36
Quadrupole Splitting EQ
EFG is non‐zero in non‐cubic valence 
electron distribution and/or in non‐cubic
lattice site symmetry
The precession of the quadrupole moment 
vector about the field gradient axis 
Splits the degenerate I = 3/2 level into two
substates with magnetic spin quantum
numbers mI = ±3/2 and ±1/2. 
Selection rule: mI = 0, 1
The ground state I = ½ 
‐no quadrupole moment 
‐unsplit
‐twofold degenerate
Electric Quadrupole Interaction
Quadrupole Splitting EQ
37
The energy difference between the two
substates EQ is observed in the
spectrum as the separation between
the two resonance lines
Electric Field Gradient (EFG)
38
Vij = (∂2V/∂i∂j) (i,j,k = x,y,z) 
3x3 second rank EFG tensor
A point charge q at a distance r = (x2+ y2+ z2)½ from the nucleus causes a 
potencial V(r) = q/r at the nucleus. The electric field E at the nucleus is
the negative gradient of the potential, –V, and the electric field gradient 
EFG is given by:
Only five Vij components are independent, because:
•symmetric form of the tensor, i.e. Vij = Vji, 
•Laplace: traceless tensor 
Principal axes system:  |Vzz| ≥ |Vxx| ≥ |Vyy|
Axial symmetry (tetragonal, trigonal) ‐ the EFG is given only by the tensor 
component Vzz ,  Vxx = Vyy →  = 0
Non‐axial symmetry – the asymmetry parameter η: 0≤ η ≤ 1 
= (Vxx–Vyy)/Vzz
Electric Field Gradient (EFG)
39
Energy levels
Two kinds of contributions to the EFG: (EFG)total = (EFG)val + (EFG)lat
or in the principal axes system and η = 0: (Vzz)total = (Vzz)val + (Vzz)lat
The lattice contribution(Vzz)lat = non‐cubic arrangement of the next nearest 
neighbours
The valence contribution (Vzz)val = anisotropic (noncubic) electron population
in the orbitals
Electric Field Gradient (EFG)
40
For 57Fe with Ie = 3/2, Ig = 1/2:
EQ (3/2, ±3/2) = 3eQVzz/12  for I = 3/2, mI= ±3/2
EQ (3/2, ±1/2) = ‐3eQVzz/12  for I = 3/2, mI= ±1/2
the quadrupole splitting energy
ΔEQ= EQ(3/2, ±3/2) ‐ EQ (3/2, ±1/2) =  eQVzz/2 
(in axially symmetric systems, η= 0)
[Fe(H2O)6]3+ 6A1
41
EFGlat = 0
EFGval= 0
[ML6] (Oh)
z2
x2–y2
xz
yz
xy
FeSO4•7H2O
42
[Fe(H2O)6]2+  Fe(II)‐HS, S = 2
EFGlat = 0  0
EFGval  0  0
Jahn‐Teller‐Distortion
compressed elongated
FeSO4•7H2O
43
K4[Fe(CN)6]
44
Fe(II)‐LS, S = 0 cubic
EFGlat = 0
EFGval = 0
K4[Fe(CN)6]
45
Fe(II)‐LS, S = 0 cubic
Na2[Fe(CN)5(NO)]
46
Fe(II)‐LS, S = 0  tetragonal
EFGlat  0
EFGval  0
Fe(II) + NO+
or
Fe(III) + NO 
Na2[Fe(CN)5(NO)]
47
Fe(II)‐LS, S = 0  tetragonal
Unusually large ΔEQ and too negative  for Fe(II) LS (‐0.165 mm/s) 
NO withdraws electron density from dxz a dyz (‐bonding dp)
Isomer Shifts and Quadrupole Splitting
48
1.0 1.5
1
-0.5 0.5
Isomer shift (mm/s)
0
2
3
4
0.0
[6]
Fe(II)
[6]
Fe(III)
[6]
Fe3+
[4]
Fe3+
[6]
Fe2+
[4]
Fe2+
[sq]
Fe2+
[8]
Fe2+
[5]
Fe3+
[5]
Fe2+
119Sn Mössbauer Spectra and Structures
of the Tin Halides
49
Magnetic Dipole Interaction
50
Magnetic Splitting EM
Magnetic dipole interaction = the precession of the magnetic dipole moment vector
about the axis of the magnetic field
Splitting of the states I,mI into 2I + 1 substates
Magnetic Dipole Interaction
51
Magnetic Splitting EM
The requirements for magnetic dipole interaction
‐ the nuclear states involved possess a magnetic dipole moment  (I > ½)
‐ a magnetic field is present at the nucleus
57Fe: the ground state with I = ½ and the first excited state with I = 3/2 
Selection rules: ΔI = ±1, ΔmI = 0, ±1.
Magnetic Dipole Interaction
52
The energies of the sublevels :
EM(mI) = – H mI / I = –gN N H mI
gN = the nulcear Landé factor, N = the nuclear Bohr magneton.
The separation between the lines 2 and 4 (also between 3 and 5) refers to the
magnetic dipole splitting of the ground state.
The separation between lines 5 and 6 (also between 1 and 2, 2 and 3, 4 and 5) refers
to the magnetic dipole splitting of the excited I = 3/2 state.
Internal Magnetic Field
53
A magnetic field Hint (r = 0) at the nucleus can originate in various ways:
Hint = HC + HD + HL + Hext = total internal magnetic field
Fermi Contact Interaction HC:
Electron spin S of valence shell (e.g. S = 5/2 of Fe3+) polarizes the s‐electron density at 
the nucleus: core polarisation
Spin density |Ψ(0)↓|2 > |Ψ(0)↑|2 magnetic field HC ≠ 0
Spin dipolar interaction HD:
The magnetic moment of the electron spin gives rise to dipolar interaction 
with the nucleus and causes a field at r = 0.
Internal Magnetic Field
54
Orbital dipolar interaction HL:
Electrons with orbital moment L ≠ 0 give rise to an orbital magne c moment 
accompanied by a magnetic field HL= ‐2 μB <r‐3> <L>
<L>: expectation value of orbital angular momentum.
Externally applied field Hext:
By applying an external magnetic field of known size and direction
one can determine the size and the direction of the intrinsic magnetic
field of the material under investigation.
Combined Magnetic Dipole and Electric
Quadrupole Interactions
55
Combined Magnetic Dipole and Electric
Quadrupole Interactions
56
Magnetic dipole interaction and electric quadrupole interaction may be present in 
a material simultaneously (together with the electric monopole interaction which
is always present). 
Relatively weak quadrupole interaction
The nuclear sublevels I,mI arising from magnetic dipole splitting are additionally
shifted by the quadrupole interaction energies EQ(I,mI)
The sublevels of the excited I = 3/2 state are no longer equally spaced. The shifts
by EQ are upwards or downwards depending on the direction of the EFG. 
This enables one to determine the sign of the quadrupole splitting parameter ΔEQ.
The quadrupole shift parameter  depends on the canting angle  of the spins
with respect to the electric field gradient (EQ) axis [111]
 = EQ(3 cos2  ‐ 1)/2 and thus yields values with opposite sign for AF ( = 0°) 
and WF ( = 90°) states.
Magnetic Dipole Interaction
57
Fe3(CO)12
58
[Fe3(3-O)(OAc)6(H2O)3]
59
Variable‐temperature 57Fe Mössbauer spectra
[Fe3(3-O)(OAc)6(3-Et-py)3]S
60
Variable‐temperature 57Fe MÖssbauer spectra
S = CH3CCl3
CH3CCl3 is valence‐trapped at
low temperature, increasing
temperature leads to valence 
detrapping near room
temperature. The ratio of the
area fractions of Fe(III) to 
Fe(II) is close to 2 at low
temperatures.
[Fe3(3-O)(OAc)6(3-Et-py)3]S
61
Variable‐temperature 57Fe MÖssbauer spectra
S = C6H6
CH3CN increasing temperature
leads to valence detrapping near
room temperature. 
The lattice packing controls
valence de/trapping. 
C6H6  possesses a stack type 
structure with strong
intermolecular interactions due
to overlapping pyridine ligands. 
CH3CN and CH3CCl3 arelayered.
CH3CN
C6H6 is valence‐
trapped from 120 
to 298 K on the
Mössbauer time
scale (given by the
lifetime of the
nuclear excited
state). 
γ-Radiolysis of
FeSO4· 7H2O (300 K)
62
Corrosion Products
63
Corrosion of α‐Iron
in H2O/SO2 atmosphere at 300 K
Corrosion product is β‐FeOOH
Iron(III) Oxides
64
Iron(III) Oxides
65
alpha‐Fe2O3 measured at 260 K 
near Morin transition temperature
Hematite
At < 260 K is antiferromagnetic (AF) with the 
spins oriented along the electric field gradient 
axis. 
At Morin temperature (TM), around 260 K, a 
reorientation of spins by about 90°, the spins
become slightly canted to each other (by 5°), 
causing the destabilization of their perfect 
antiparallel arrangement = weak (parasitic) 
ferromagnetism between Morin and Neel 
temperature (TN).
Above the Neel temperature of 950 K, hematite 
loses its magnetic ordering and is paramagnetic.
Iron(III) Oxides
66
Maghemite
Mössbauer spectrum of a well‐
crystallized gamma‐Fe2O3 at 4 K in 
an external field of 6 T.
Iron in French Red Wine
67