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Moessbauer Spectroscopy

1. Introduction Since the discovery of the recoilless nuclear resonance absorption of γ rays, the Moessbauer spectroscopy developed 1958 by Rudolf Moessbauer (Physics Nobel Prize 1963) into an important research method in solid-state physics and chemistry. It is a spectroscopy of the nuclear energy levels, which reacts sensitively to changes of their electronic and magnetic environment. Although most elements possess isotopes that show the Moessbauer effect (Figure.1), only a few are suitable for practical applications. Among the most important isotopes for solid state chemistry we find 57Fe, 119Sn, 121Sb and 151Eu.

1 18

H 2 13 14 15 16 17 He Li Be B C N O F Ne Na Mg 3 4 5 6 7 8 9 10 11 12 Al Si P S Cl Ar 1K1 1Ca1 Sc Ti V Cr Mn 1Fe2 Co 1Ni1 Cu 1Zn1 Ga 1Ge2 As Se Br 1Kr1 Rb Sr Y Zr Nb Mo 1Tc1 2Ru2 Rh Pd Ag Cd In 2Sn2 1Sb1

1Te1 2I2 2Xe2

1Cs1 1Ba1 1La1 4Hf4 1Ta2 4W7 1Re1 4Os62Ir4 1Pt2 1Au1

2Hg2 Tl Pb Bi Po At Rn Fr Ra Ac

Ce 1Pr1 1Nd2 2Pm2 6Sm6 2Eu4 6Gd9 1Tb1 4Dy6 1Ho1 5Er5 1Tm1 5Yb6 1Lu1

1Th1 1Pa1 3U3 1Np1 1Pu1 1Am1 Cm Bk Cf Es Fm Md No Lw

i Fe t

i: Number of isotopes that show Moessbauer effect t: Number of transitions observed. Figure 1. Periodic system of the Moessbauer nuclei In this experiment, the basics of the Moessbauer spectroscopy and its application in chemistry will be explored using 57Fe as an example.

2. Spectroscopy with γ quanta The decay of the majority of radioactive nuclides produces usually highly excited daughter nuclei.. These can decay to the ground state by emission of γ quanta. The excited state of 57

26 Fe can be formed by K-electron capture from the radioactive isotope 57

27 Co : 57 * 0 5727 1 26Co e Fe−+ → . The γ emission processes following this capture are

shown in Figure 2.

2

The transition with E0 = 14.4 keV is particularly favorable for spectroscopic applications. The nuclear excited state has a lifetime τN = 1.41 × 10-7 s and therefore no sharp energy. The intensity distribution of the γ ray source is Lorentzian and has a natural half width Γnat given by the Heisenberg uncertainty relation. The emitted radiation is in this sense monochromatic.

2

2 20

I(E)4(E E )

Γ≈

− + Γ (1)

N

7 9½N nat 0

wheret 1.41 10 s, 4.66 10 eV and E 14.4 keV

ln 2− −

Γ τ =

τ = ≈ × Γ = × =

In order to measure the intensity of absorption as a function of the energy and thus to record the γ-radiation spectrum, the emission energy must be varied continuously over a certain range. This modulation can be achieved by using the Doppler effect resulting from the motion of the source and absorber relative to each other:

0

vE E 1

cγ

= ±

, (2)

where the plus sign indicates a movement of the source toward the absorber. In the spectrometer used (Figure. 3), a periodic triangular voltage is produced by a digital function generator in 512 steps. It moves the source drive back and forth according to the loudspeaker principle. The absorber remains at rest.

Co57

57 Fe

27

26

136.32 keV

14.4 keV

0

ΓI02

I0

E 0 = 14.4 keV = EaEg

E

K-capture

E EτN = 1.4 * 10

-7s

τN 270 d

,

Figure 2.- Energy diagram and emission spectrum of 57Fe. The natural line width of the 14.4 keV decay is 4.66 × 10-9 eV.

3

The γ-quanta emitted by the source are partially absorbed by the sample. The transmitted quanta hit on a NaI(Tl) scintillation crystal and excite luminescence on the Tl centers. The photomultiplier converts the emitted flashes into pulsed voltages, whose height is proportional to the energy of the γ-quanta. The pulses are collected into a multichanel analyzer, where the source energy spectrum is displayed. An energy window can be set to let through only energies around 14.4 keV. The peak height analysis serves only to adjust this window, which filters out most of the background radiation, such as x-rays from the sample, and the rest of the nuclear energy levels not used for the measurement. When recording a Moessbauer spectrum the multichanal analyzer is operated differently. The channels are successively opened by the digital function generator. The continuous switching of the channels is synchronized by trigger pulses of the function generator so that the channel number is proportional to the relative velocity. A channel is then opened only for a velocity interval ∆v = vmax / 512. The impulses falling into the range of the energy window are passed on to the multichanal analyzer as standardized counting pulses and added to existing channel contents. Thus a Moessbauer spectrum consists of counting

Figure 3. Block diagram of the Moessbauer spectrometer for transmission experiments

U

t

t

v

512Channelnumber

T/%

High voltage supply

D e t ect o r

Absorber Source

Amplifier Single-channel a nalyzer

Multichannelanalyzer

Data processing

Funct iongenerator

Source drive

( Probe)

4

pulses summed up over many runs versus the channel number, or versus its equivalent, the relative velocity between source and absorber. The scintillation counter resolution is only 5 keV. Therefore in the peak height analysis the emission line spectrum will be 5 keV broad. On the other hand when acquiring a Moessbauer spectrum, the absorption line is scanned with an emission line of both of natural line width, so that the theoretical resolution in a Moessbauer spectrum corresponds to the sum of the natural line widths of source and absorber; i.e. 2 Γnat = 9.32 × 10-9 eV.

3. Nuclear γ-resonance absorption A γ-quantum, which is emitted during the transition of an excited nucleus to the ground state, can be resonantly absorbed by another nucleus of the same nuclide, if emission and absorption lines overlap (Figure. 4). After a halflife time τN the newly excited nucleus goes back to the ground state by emission of γ radiation or conversion electrons. Conversion electrons are produced when the energy of the excited nucleus is not transferred in the form of γ quanta, but to s-electrons passing the core, which possess thereby sufficient energy to leave the atom. Because of the conservation of momentum, when the nucleus of a free atom (e.g. in gases or liquids) emits a γ-quantum, it will recoil in such a way that pnucl is equal and opposite to pγ, nuclp pγ= − (3) and according to the de Broglie relation:

Eh hpc

γγ

ν= = =

λ λν, (4)

where λ is the wavelength, ν the frequency, c the speed of light and h Planck's constant. Because of conservation of energy, the energy of the γ-quantum is decreased by the recoil energy ER when it is emitted from the nucleus of the source. A

0 RE E Eγ = + (5) In the process of absorption, the pγ is transferred to the absorbing nucleus and a higher γ-energy is needed for the resonance absorption: A

0 RE E Eγ = + (6) If the nuclei are at rest before the emission and absorption, then the recoil energy is

2 22

2 nuclR 2

p Ep1E m v2 2 m 2 m 2 m c

γ γ= = = = , (7)

where m is the nuclear mass and v the velocity after emission or absorption.

5

Resonance absorption requires that R2 E ≤ Γ (see also Figure. 4). For a free Fe nucleus, using Equation (7) we can calculate ER = 1.96 × 10-3 eV, so the resonance absorption is extremely small. However, in solids the recoil energy is taken up not by an individual atom, but by the entire crystal lattice:

2

R 2

EE

2 M cγ= , (8)

where M is the mass of the crystal. The recoil energy in the crystal becomes extremely

small (2

242

E10

2 m cγ−≈ for a mol). However recoil effects can arise in the solid if the

energy of the γ-transition is enough to excite a lattice phonon. There is still a finite probability for so-called zero-phonon processes, in which no change of oscillation transition takes place. The fraction of zero-phonon transitions is indicated by Lamb-Moessbauer factor f. For a harmonic oscillator f can be expressed as:

( )

22

2

Ef exp x , 0 f 1

cγ

= − < <

(9)

where 2x is the mean square amplitude of the oscillations of the nuclei in the direction

of the γ-rays. Large f values in general correspond to solids with strongly bound atoms, which possess small mean square amplitude. The exact form of 2x depends on the oscillation density of states of the specific solid lattice. In real solids these are usually very complex and there are no suitable models available. In first approximation, for a simple site in octahedral surroundings, the Debye

E 0 E 0

E0E

E

E

AS

ES Aγγ

ER

ER

Emission Absorption

Source Absorber

E

E

E

a

g

Figure 4. Nuclear resonance absorption and recoil effect

6

N( )

maxν ν

ν

Figure 5. Oscillator density of states according to the Debye model

model calculates the density of the continuum of a harmonic oscillator as ( ) 2N constant*ν = ν and a maximum critical frequency νmax.

Applying this model the Lamb-Moessbauer factor f can be written as

D

2T

Rx0

D D

6E 1 T xdxf expk 4 e 1

θ = − + θ θ − ∫ (10)

The Debye temperature is a measure of the bond strength in the crystal. Equation (10) shows that f becomes larger for low temperatures and large θD.

Two extreme cases can be analyzed: a) At low temperature D Tθ and θD.

2 2

R2

D D

E 3 Tf expk 2

π= − + θ θ

(11)

Even at T = 0, we get f < 1, and it depends both on ER

b) At high temperatures D Tθ

R2D

6E Tf expk

= − θ

(12)

Recoilless emission and absorption is then favored at low temperatures with nuclei which are strongly bound into a crystal lattice. For quantitative applications, the Lamb-Moessbauer factor must be known. However f is not a crystal-specific constant, but a local characteristic. As Equation 8 clarifies shows, f depends also strongly on the energy of the emitted radiation. Very high energy processes (≈100 keV) can be observed without recoil only at very low temperatures.

lnf

T

Figure 6. Temperature dependence of ln f

7

4. Hyperfine structure (HFS) in the 57Fe Moessbauer spectra. The practical application of Moessbauer spectroscopy is not so much concerned with the observation of the effects itself, but mostly with the effects of the sample's own internal electrical and magnetic fields on the energy of the nuclear states. These effects contain information about the chemical environment of the observed atomic nuclei. Although the magnitude of these energy variations ( )8 6

HFE 10 10 eV− −≅ − is very small compared to

the main effect (Eγ = 14400 eV), they can be resolved in the Moessbauer spectrum, since the resonance absorption line is comparatively very sharp. Among all spectroscopy,

Moessbauer spectroscopy is the one with the highest resolving power 13nat2 6.5 10E

−

γ

Γ= × .

4.1 Electrical hyperfine interactions The whole electrostatic interaction Eel between a nuclear charge distribution ρn and an electrical potential V can be described by the following expression

n n , nel 0,

, 1, 2,3

1E V d V x d V x x d ........

2!

α α α β α βα α β

α β =

= ρ τ+ ρ τ+ ρ τ+∑ ∫ ∫∑∫ (13)

The first term describes the electrostatic interaction energy of the nucleus as point charge with the surrounding charges in the entire solid. However, this energy does not affect the splitting of the different nuclear levels and therefore is of no further interest here. The second term contains the electrical dipole moment, which vanishes due to the symmetry of the nuclear charge distribution. Thus only the third term, the electric quadrupole, is actually important for Moessbauer spectroscopy. The energy contributions of higher

order terms of are too small and can be neglected. The components 2VV

x xαβα β

∂=

∂ ∂of the

electrical field gradient form a tensor. In the symmetry-adapted coordinate system, this tensor is reduced to its diagonal elements Vαα. Under these conditions, the third term of Equation (13) can be written as:

8

23 3 22n nel 0 0

1 1

32

n01

r1 1E V (r) x d V (r) x d32 2

1 V (r) r d6

αα αα α α α= α=

αα

α=

= ρ τ= ρ − τ∑ ∑∫ ∫

+ ρ τ∑ ∫

(14)

where 3

2 2 2 2 2

1r x x y zα

α=

= = + +∑ (14)a

After adding and subtracting in equation(14), the definition of the nuclear quadrupole moment tensor in terms of its diagonal elements Qαα is given by: ( ) ( )2 2

nQ r 3x r dαα α= ρ − τ∫ (15) Further, the Poisson' equation, well-known from classical physics, is applied:

( )3

e

1 0

V 0ααα=

ρ+ =

ε∑ , (16)

with ( ) 2

e e 0ρ = − Ψ is the charge density produced by the electrons at the nuclear site, so that:

( ) ( )3 2

01 0

eV 0ααα=

= ψε∑ (17)

The total energy Eel at the nuclear site turns out to be:

( ) ( ) ( )23 22 2

el n n01 0

1 r 1E V (r) x d e 0 r r d2 3 6αα α

α=

= ρ − τ + ψ ρ τ ε

∑ ∫ ∫ (18)

The first term represents the electrical quadrupole interaction with electrical field gradients. We have already met this interaction in the description of the nuclear quadrupole interaction in NMR spectroscopy. However the second term describes the electrical monopole interaction at the nuclear site, which results from the spatial charge distribution of electrons at the nucleus.

9

4.1.1 Electrical monopole interaction: isomer shift As opposed to the first constant term in equation(13), the second term in equation (18) describes the monopole interaction of the electronic charge density over the spatial expansion of the nuclear charge, i.e. the nucleus. Its diameter is described by the effective radius. During the excitation of the nucleus, the charge pattern and also the effective radius change, and therefore the shift of the energy levels of the ground and excited states are different. So that the energy levels are differently shifted of reason and put on condition. The larger the size difference of the nucleus in both levels, the larger is the difference of the shift of the nucleus in the excited state.

( ) ( )2a e 2n

0

1E e 0 r r d in the excited state6

= ψ ρ τε ∫ (19)

( ) ( )2g g 2n

0

1E e 0 r r d in the ground state6

= ψ ρ τε ∫ (20)

Similar conditions apply to the sample (the absorber). However, the electron density at

the nucleus ( )( )20Ψ is different in the sample compared with the source. That is the

reason for the different shifts:

( ) { }

( ) { }

2e g e 2 g 2S S S S SS

0

2e g e 2 g 2A A A A AA

0

1E E E e 0 (r) r d (r) r d6

1E E E e 0 (r) r d (r) r d6

∆ = − = ψ ρ τ − ρ τε

∆ = − = ψ ρ τ − ρ τε

∫ ∫

∫ ∫ (21)

As a good approximation, polarization effects of the nuclei by the electronic surroundings can be neglected ( ) ( ) ( ) ( )e e g g

S A S Ar r and r rρ = ρ ρ = ρ , the isomer shift of the absorber relative to the source is then equal to the energy difference between the two states:

( ) ( ){ }{ }2 2 e 2 g 2A S A S

0

1E E e 0 0 (r) r d (r) r d6

δ = ∆ − ∆ = ψ − ψ ρ τ − ρ τε ∫ ∫ (22)

The mean value of the square of the nucleus radius is proportional to the second momentum of the nuclear charge distribution:

( )( )

2n2

n

r r dr

r d

ρ τ=

ρ τ∫∫

(23)

but since ( )n r d Zeρ τ =∫ , it follows that

( ) 2 2n r r d Ze rρ τ =∫ (24)

10

This second moment can be determined according to the formula above in principle for any nuclear charge distribution. If one accepts a spherical distribution, applies. Given a spherical charge distribution, we get:

2 23r R5

= (25)

and therefore for the isomer shift:

( ) ( ){ }( )2 22 2 2e gA S

0

1 Ze 0 0 R R10

δ = ψ − ψ −ε

(26)

I

v/mms -1(+)(-) 0

δ

Source Absorber

EE

g

e

SA

E0E0

E

E

Fe(II) S=2

Fe(II) S=0

Fe(III) S=5/2

Fe(III) S=1/2

0 +1

Fe(I) S=3/2Fe(I) S=1/2

Fe(II) S= 1

Fe(III) S=3/2

Fe(IV) S=2

Fe(IV) S= 1Fe(VI) S=1

-1δ/mms

∆∆

-1 +2

The isomer shift effect is shown in figure 7. Moessbauer nuclei, for which changes very strongly between excited and ground states, have a very large isomer shift and therefore react more sensitively to small differences in the chemical environments. The isomer shift reacts very sensitively to differences in the oxidation states. The electron density at the nucleus can be affected directly by the change in the number of bonding electrons in orbitals with s-character, and indirectly by screening of the s-electrons caused by p or d electrons which themselves do not have a finite probability density at the nuclear site Since the difference ( )2 2

e gR R− in Equation (26) is negative for 57Fe, δ becomes more positive, as one goes from Fe0 (configuration 3d64s2) to Fe2+ (3d6), since the number of the s-electrons decreases. On the other hand Fe2+ possesses a more positive isomer shift than Fe3+ (3d5), since the number of the d-electrons in the Fe2+ is larger and thus the

Figure 7. Isomer shift: E0 represents the energy difference between the ground (Eg) and the excited Ee states, without taking into account the surrounding electrons. ∆ES and ∆EA apply to nuclei with different s-electron density. The isomer shift δ equals to ∆EA-∆ES. The picture in the right is an overview of the isomer shift of different Fe-compounds with various oxidation states relative α-Fe

11

nucleus becomes more strongly shielded from s-electrons. For Fe complexes, the isomer shift depends also on the spin state, e.g., the δ values for Fe2+ and Fe3+ in high spin complexes are separated in the isomer shift scale (figure 7), while the appropriate low spin complexes show no difference in the isomer shift. The octahedral complexes of 3d-metals with ligands like CN -, CO or NO+ possess π orbitals. The proportion of the ligand and/or of the metal orbital in the molecule orbitals is inversely proportional to the energy content of the orbital. Therefore the πb-orbitals have predominantly a ligand character, i.e. the electrons in this MO predominantly are with the ligands. On the other hand the s-electron density at the central atom can be increased directly by σL-M donation and thus the isomer shift is decreased (figure 8).

A1g

zy

x

s

z

x

y

zy

x

d 2Z

M etal Ligand Ligand

T1u

zy

x

M etal

yz

x

pzΣa

y

x

d -x2 y 2

Eg

yz

x

Σ x - y2 2

Σz

Eg

zy

x

Σz2

(p p analog)x, y

This way, for Fe(II) complexes of [Fe2+(CN)5Xn-](3+n)- δ becomes more negative in the series H2O< NH3 < NO2

- < SO42-< CO < < NO+ (see spectrochemical series) .

The πM-L backbonding increases indirectly the s-electron density at the nucleus by reducing of the screening of the T2g electrons on the s-electrons. The Fe2+/3+-low-spin complexes are present with ligands with strong σM -L bonding and πM-L backbonding. In K4[ Fe (CN)6 ]·3H2O additional electron compared with K3[Fe (CN)6] is with the ligands. Therefore the isomer shift is almost the same for both complexes.

Figure 8a. Representation of the 6 metal ions orbitals and their symmetry-adapted ligand orbitals. By superimposing the coordinate origin in each pair the overlaps resulting in a σ bond become evident.

12

Metal Ligand

z

x

yz

y

x

dxz

T2g

S xz

Figure 8b. d-orbitals of the metal ion with symmetry-adapted ligand ligand orbitals from p-orbitals in the right position for π-bonding. The bond type can be recognized again by overlapping the coordinate origins.

(n+1)p

(n+1)s

nd

*Π

Π

Σ

A1g Eg

T1u

, ,

T1u

T1u

A 1g

T1u

Eg

T2g

T2g

T1gT2u

T2u T1g

T 2g

E

bσ,

:

πbπb

πb

π

σ*

π*π*

π*

π*σ * :

::

:

:

:

::

:

b

Metalorbitals

Molecularorbitala

Ligandorbitals

,

Figure 8c. Qualitative molecular orbital diagram for a complex of type [Me(CN)6]n-

13

4.1.2 Electrical quadrupole interaction The first term in Equation (18) describes the electrical quadrupole interaction. It exists for all nuclear levels with angular momentum quantum numbers I > 1/2. A nuclear quadrupole moment is present when the nuclear charge distribution is not spherically symmetric This core quadrupole moment interacts with electrical field gradients, which are caused by the deviation from spherical symmetry in the electronic environments of the nucleus. A detailed description of this interaction is in the text Nuclear quadrupole interaction in the NMR spectroscopy. For the quadrupole interaction energy we get:

( )1/ 22

2zzQpI

eQVE 3m I I 1 14I(2I 1) 3

η = − + + − (27)

with

xx yy

zz

V VV−

η = (28)

Here is eQ the scalar quadrupole moment. The quadrupole interaction energy depends thus only from the square of the azimuthal quantum number m. Since for Fe, only the excited state has a quadrupole moment (I = 3/2), and given the selection rule ∆ml =0, ± 1, only two transitions are observed.

0 v/mms(+)(-) -1

Q

δ

Q

Isomershift

Quadrupolesplitting

I=3/2

I=1/2

mI3/2

1/2

+-

+-

1/2+-

I

S

S

Figure 9. Quadrupole splitting (QS) and isomer shift in the 57Fe example.

14

For the case of 57Fe, the quadrupole splitting can be calculated from Equation (27) as:

2

1/ 2zz

1QS eQV (1 )2 3

η= + . (29)

This is dominated by the value of the electrical field gradient along the major axis Vzz , which supplies information about the symmetry of the electronic charge environment. In a more cubic symmetry, e.g. ideally tetrahedral or octahedral environment, Vzz = 0 and therefore QS = 0. Generally two contributions need to be considered: Vzz = Vzz (lattice) + Vzz (valence) (30)

Lattice or ligand contribution: A non-cubic arrangement of ligands around the Moessbauer central atom or the presence of chemically different ligands produces an inhomogeneous electrical field at the nucleus. The same applies to point charges or defects that are not cubically arranged in the lattice.

Valence contribution: This contribution is the product of a non-cubic distribution of the electrons in the valence orbitals of the Moessbauer . In an octahedral ligand field the 5-fold degenerated orbitals split into a two groups: 2-fold degenerate eg ( )2 2 2z x y

d and d−

, and a 3-fold degenerate

t2g(dxy, dyz and dxz). The associated electron density has cubic symmetry and therefore supplies no valence contribution. That valence contribution will not vanish in high or low spin complexes of Fe2+ and Fe3+ if the octahedral symmetry is disturbed (Figure 10). The effect of a tetragonal distortion (stretching or compression) lifts the electronic degeneracy of the d orbitals: partly for the t2g set and completely for the eg, according to the Jahn-Teller theorem: An electronically degenerated nonlinear system is unstable and will try to degrade its symmetry by a distortion of the structure that breaks the degeneracy and the total energy of the system will be lowered by an increase in the population of the energy levels whose energy is lowered by the distortion Boltzmann distribution). For Fe2+ low spin and Fe3+ high spin complexes, the initial state is not degenerate and no stabilization can be brought about by a therefore a tetragonal distortion (Vzz=0). However a tetragonal stretch of the octahedron of low-spin- Fe3+complexes leads to the lowering of the energy of one of the dxz and dyz orbitals, while the energy of the dxy is increased. This results in a net stabilization given the asymmetrical charge pattern (in the XY-plane is larger than in the z-direction with eq ≠ 0). The quadrupole splitting (QS) depends also on the bonding characteristics, as can be seen for example in the complexes of type[Fe2+(CN)5Xn-](3+n) -. In a first approximation one can assume that the valence contribution to the QS is caused by an imbalanced occupancy in the 3d orbitals. The changes in EFG are caused by the variation of Xn- and not because of the change in [Fe (CN)5]3-. In [Fe (CN)6]4-in contrast, the electron bonding structure has cubic molecular symmetry and no QA is present.

15

∆ o Π

E

d ,low spin, Ooctahedral

V = 0

6

zz

h

Eg

T2g

x. - y2 2 2zz

xz yz xy

∆ <o Π

E

d ,high spin, Dtetragonal compression

V >0

6

zz

d ,high spin, Ooctahedral

V = 0

6

zz

h 4h d ,high spin, Dtetragonal stretch

V < 0

6

zz

4h

Eg

T2g

x. - y2 2 2zz2zz

2zzx. - y2 2

x. - y2 2

xz yz xy xz yz

xy

xy

xz yz

∆ o Π

E

d ,low spin, Dtetragonal compression

V > 0zz

d ,low spin, Ooctahedral

V = 0zz

h 4h d ,low spin, Dtetragonal stretch

V < 0zz

4h

Eg

T2g

x. - y2 2 2zz2zz

2zzx. - y2 2

x. - y2 2

xz yz xyxz yz

xy

xy

xz yz

∆ <o Π

E

d ,high spin, Ooctahedral

V = 0zz

h

Eg

T2g

x. - y2 2 2zz

xz yz xy

>

5 5 5

>

5

3/5

2/5

∆ o

∆ o

Figure 10: Schematic energy level diagram for electronic configuration of Fe2+/3+ in an octahedral ligand field and the same with tetragonal distortion. A high-spin complexe is formed when the ligand field splitting energy ∆0 is smaller than the spin pairing energy Π. In the reverse case (∆0 > Π), a low spin complex is formed.

16

The response of the QS to the substitution of CN- by Xn- will manifest in either of these two ways: if Xn- a stronger σ-donor than CN-, the electron density in the 2z

d orbital will be larger than in the 2 2x y

d−

orbital (taking the Fe-Xn- axis as z-axis). In the case that Xn- is

a stronger π-acceptor than CN-, charge will be delocalized from the central atom to the ligands and so that the contribution to Vzz (valence) happens in opposite direction. The resulting effect then depends both on theσ-donor and on the π-acceptor. Table1: Isomer shift δ and quadrupole splitting QS for different Fe(II) complexes, at 298 K relative to Fe/Rh.

Complex δ/mms-1 QS/mms-1

[Fe (CN)5 NO]2- -0,38 1,70

[Fe (CN)5 CO]3- -0,22 0,43

[Fe (CN)5 SO3]5- -0,15 0,80

[Fe (CN)5 NO2]4- -0,11 0,98

[Fe (CN)5 NH3]3- -0,11 0,67

[Fe (CN)5 H2O]3- -0,06 0,80

4.2 Magnetic splitting The Zeeman effect between the magnetic moment of the nucleus and the magnetic field at the nuclear site leads to a further splitting of the nuclear levels according to the different possible values of the azimuthally quantum numbers m. The largest component of the nuclear magnetic moment µ in field direction is: I I Iµ = γ . This formula applies for the ground and excited states which have different I and µI and therefore different γI.

I

I I Im,I

mE m B BI

= − γ = −µ (31)

This type of interaction forms the basis of the NMR spectroscopy. For 57Fe, the selection rules (∆I=1, ∆m = 0, ±1) lead to a hyperfine splitting in 6 lines (Figure 11).

17

I=3/2

I=1/2

mI+3/2

+1/2

-1/2-3/2

-1/2

+1/2Isomershift Zeeman splitting Zeeman and Quadrupolar

splittings

B ≠ 0, V = 0zz

I

v/mms-1

B ≠ 0, V > 0zz

δ

The magnetic field at the nuclear site can be an external field or an internal one, generated by local magnetic moments of unpaired electrons. However, at room temperature these moments may be subjected to temporal fluctuations which compared to the halflife of the excited state are very fast. In this case, the time average of B vanishes. This time averaging can be prevented by reducing the spin-spin interaction as a result of large spatial dilution or by cooling down to very low temperature.

Figure 11. Magnetic splitting (B ≠ 0) in 57Fe without (B ≠ 0, Vzz = 0) and with electrical quadrupole interaction (B≠0, Vzz > 0) and resulting Moessbauer spectra (schematic). The isomer shift is measure from the center of gravity of the multiplets.

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1

0 1

B(T)/B(0)

T/Tc

770 C

740 C

22 C

o

o

o

-6 0 +6 v/mms-1

Figure 12: Temperature dependence of the magnetic splitting in Fe-metal: Saturation magnetization / B0 and spectra at different temperatures Magnetic hyperfine splitting is easy to observe, if the magnetic moments in the sample (at least locally) have a stationary preferred orientation, as they have in ferro- and antiferromagnetic systems below the ordering temperature

5. Summary In the preceding text only the most important measuring parameters of the Moessbauer spectroscopy have been presented. But also, depending on the specifics of the problem, the following parameters can supply important information: line form and width, resonance intensity, effect of an external magnetic field, angle dependence of the spectra, single crystals and temperature and pressure dependence. Moessbauer spectroscopy has made important contributions to the determination of oxidation numbers, local bonding symmetry and magnetic structure in many crystalline and amorphous solids. A substantial disadvantage of the method is however in its restriction to a few suitable nuclear isotopes and the stagnating level of development in spectroscopic methodology observable at present.

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6. Tasks

6.1 Isomer splitting and quadrupole splitting Measurement of the spectra of:

• Na2[Fe(CN)5NO]·H2O with QS = 17015 ± 0.0002 mm/s for the velocity calibration of spectra

• two Fe hexacyanoferrate samples (sample I, II) and determination of the respective oxidation state. (The x-ray diffraction experiments suggest octahedral coordination for both samples)

• FeSO4·7 H2O • Interpretation of the isomer shift (IS) for the measured spectra and discussion of

the process of the IS and QS data in table 1 (configuration, spin state, coordination) on the basis the theories described in the text.

• Comparison of the line width with Γnat.

6.2 Magnetic splitting

• Measurement of the spectra of α-Fe and steel • Calculation of IS, Band µe, the magnetic moment of the nuclei, in the excited

state, knowledge of µg (magnetic moment in the nuclear ground state). • Interpretation of different magnetic splitting with help of Figure. 11. The

maximum magnetic moment component in the ground state equals to µg= 4.561 10-28 J/T.

• Comparison of the line widths of α-Fe and steel with Γnat. For the energy conversion use E=E0 v/c.

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7. Appendix

Table 2. Typical nuclear and electronic interaction energies

Interaction energy kJ/mol

Moessbauer-γ-radiation energy 106 - 107

Chemical bond and latttice energy 102 - 103

Electronic transitions 50 - 500

Molecular vibrations 5 - 50

Lattice vibrations 0,5 - 5

Recoil and Doppler energies 10-2 - 1

Nuclear quadrupole splitting energy < 10-3

Nuclear Zeeman interaction energy < 10-3

Heisenberg line width 10-7 - 10-4

Table 3. Energy conversion factors

57Fe (14,4 keV) J kJ/mol eV Hz

1 mm/s 7,701*10-27 4,638* 10-6 4,806*10-8 11,62*106

8. Literature

For the introduction: P. Gütlich, Chemie in unserer Zeit, 4(1970), 133-144 and 5, (1971), 131-141 P. Gütlich, Moessbauer Spectroscopy in Chemistry, in U. Gonser, Moessbauer Spectroscopy, Springer Verlag, Berlin 1975, 52-96

Further reading T. C Gibb, Principles of Moessbauer Spectroscopy, Chapman and Hall, London 1976 CD Barb, Grundlagen and Anwendungen of the Moessbauer spectroscopy, Academie Verlag, Berlin-Ost, 1980

For chemistry, crystal field and MO theory: Cotton, Wilkinson, Anorganische Chemie, Verlag-Chemie, Weinheim