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5 Isomer Shift Derived from NFS (Including a Reference Scatterer)

5 Isomer Shift Derived from NFS (Including a Reference Scatterer)

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498



9.6



9 Nuclear Resonance Scattering Using Synchrotron Radiation



Magnetic Interaction Visualized by NFS



The investigation of magnetic interaction of diamagnetic or paramagnetic iron

centers with applied magnetic fields is of interest in many fields of research. It

benefits from NFS because additional external parameters (compared to conventional MS), like polarization and time structure of the probing radiation, can be

introduced into the protocol of applied experimental conditions. In order to gain

access to the information that can be obtained from time-resolved scattering

experiments, especially on randomly oriented scatterers (frozen solution or polycrystalline material), theoretical approaches have been developed for a computer

code by which NFS spectra can be simulated. The code that describes magnetic

hyperfine splittings in M€

ossbauer nuclei in the framework of the spin-Hamiltonian

formalism is SYNFOS [13, 14]; it has been successfully applied to several ironcontaining systems [7, 13, 23, 25, 30, 51–54].



9.6.1



Magnetic Interaction in a Diamagnetic Iron Complex

(Example: [FeO2(SC6HF4)(TPpivP)])



For the “picket-fence” porphyrin complex [FeO2(SC6HF4)(TPpivP)], which is a

biomimetic model for oxymyoglobin, NFS spectra have been recorded at 4.2 K in

applied fields (B ¼ 4 T) pointing in different directions within a plane that is

perpendicular to the synchrotron beam [25]. In Fig. 9.20 the angle y represents

the field orientation with respect to the polarization s of the beam, with y ¼ 0

corresponding to B||s. The iron in [FeO2(SC6HF4)(TPpivP)] is diamagnetic, and

therefore the only magnetic contribution in the analysis of the measured spectra is

the applied field. The field rotation in Fig. 9.20 shows that the NFS response on y is

clearly visible. The fit quality of the spectra, obtained either with CONUSS [9, 10]

or with SYNFOS [13, 14], is comparable.



9.6.2



Magnetic Hyperfine Interaction in Paramagnetic Iron

Complexes (Examples: [Fe(CH3COO)(TPpivP)]À with S ¼ 2

and [TPPFe(NH2PzH)2]Cl with S ¼ 1/2)



The application of magnetic fields to iron in the paramagnetic state, i.e., ferrous

high-spin (FeII, S ¼ 2), ferric low-spin (Fe, S ¼ 1/2), ferric high-spin (FeIII, S ¼ 5/2),

ferryl intermediate-spin (FeIV, S ¼ 1), and ferryl high-spin (FeIV, S ¼ 2), induces

electronic spin-expectation values and consequently magnetic hyperfine interaction in the iron nuclei. The latter is represented by a complex beat structure in

the NFS spectrum. Corresponding conventional magnetic M€ossbauer spectra of

polycrystalline iron complexes have been analyzed routinely by the spin-Hamiltonian



9.6 Magnetic Interaction Visualized by NFS



499



Fig. 9.20 Experimental NFS

spectra of FeO2(SC6HF4)

(TPpivP) recorded at 4.2 K in a

field of 4 T applied at

different angles y within a

plane which is perpendicular

to the synchrotron beam.

y ¼ 0 represents a field

orientation parallel to the

polarization of the beam. The

solid lines are fits with the

CONUSS program [9, 10].

(Taken from [25])



θ = 0°



θ = 15°



Counts



θ = 30°



θ = 45°



θ = 60°



θ = 75°



θ = 90°



0



100



200



Time (ns)



formalism [55]. It was challenging to apply this formalism to magnetic M€ossbauer

spectra in the time domain and to account for the complicated band of nuclear

resonances in a randomly oriented paramagnetic sample. These resonances, via

hyperfine interactions, are related to electronic spin-expectation values which depend

on the polar and azimuthal angles y and ’, respectively, of the applied field B with

respect to the molecular frame of reference. The program package SYNFOS was

designed to numerically evaluate NFS spectra for this general case [13].

The first test case was the ferrous high-spin state (FeII, S ¼ 2) in the “picketfence” porphyrin acetate complex [Fe(CH3COO)(TPpivP)]À [13, 23], which is a

model for the prosthetic group termed P460 of the multiheme enzyme hydroxylamine oxidoreductase from the bacterium Nitrosomonas europeae. Both the

“picket-fence” porphyrin and the protein P460 exhibit an extraordinarily large

quadrupole splitting, as observed by conventional M€ossbauer studies [56].

Figure 9.21 shows the measured and simulated NFS spectra of [Fe(CH3COO)

(TPpivP)]À. The solid lines are simulations with the SYNFOS program using S ¼ 2



500



9 Nuclear Resonance Scattering Using Synchrotron Radiation



Counts



a



5

2

103

5

2

102

5

2

101

5

2

100

5



0



50



100



150



200



150



200



Time (ns)



Counts



b



5

2

103

5

2

102

5

2

101

5

2

100

5



0



50



100

Time (ns)



Fig. 9.21 NFS spectra of the paramagnetic “picket-fence” porphyrin complex [57Fe(CH3COO)

(TPpivP)]– obtained at 3.3 K in a field of 6.0 T applied (a) perpendicular to both the synchrotron

beam and the polarization vector of the radiation and (b) perpendicular to the synchrotron beam

but parallel to the polarization vector of the radiation. The solid lines are simulations with the

SYNFOS program using S ¼ 2 and parameters described in the text. (Taken from [13])



and zero-field splitting D ¼ À0.8 cmÀ1, rhombicity parameter E/D ¼ 0, magnetic

hyperfine coupling tensor A/gnbn ¼ (À17, À17, À12) T, quadrupole splitting DEQ

¼ 4.25 mm sÀ1, asymmetry parameter  ¼ 0, and effective thickness teff ¼ 20.

These parameters have been obtained by conventional MS [56] and were used to

test this first application of SYNFOS.

To visualize the sensitive response of the time-dependent forward scattering to

small changes of hyperfine parameters, the time spectra for asymmetry parameters

 ¼ 0.0, 0.2, and 0.5 (keeping all other parameters the same) were simulated

(Fig. 9.22). Comparable sensitivity was achieved for other hyperfine parameters,

provided the measurements are performed to high enough delay times.

An additional application of SYNFOS to simulate the magnetic hyperfine pattern in time spectra is provided by the low-spin ferri-heme (Fe, S ¼ 1/2) complex



9.6 Magnetic Interaction Visualized by NFS



501



5

2



Rel. Intensity



1015

2



η =0



1005

2



10–15

2



10–25

2



10–3

0



50



100



150



200



5

2



Rel. Intensity



1015

2



1005



η = 0.2



2

10–15

2



10–25

2



10–3

0



50



100



150



200



5

2



Rel. Intensity



1015

2



1005



η = 0.5



2

10–15

2



10–25

2



10–3

0



50



100



150



200



Time (ns)



Fig. 9.22 NFS spectra calculated with SYNFOS for different values of the asymmetry parameter .

Other conditions are as described in Fig. 9.21a. (Taken from [13])



bis(3-aminopyrazole)tetraphenylporphyriniron(III) chloride, [TPPFe(NH2PzH)2]Cl

[57]. This complex is a model for cytochrome P450cam from Pseudomonas putida

[58] and for chloroperoxidase from Caldariomyces fumago [59]. The NFS spectra

were recorded at 4.2 K under applied field, varying in field strength and orientation with respect to the synchrotron beam (Fig. 9.23) [23, 51]. The solid lines

obtained with SYNFOS originate from parameters that are slightly different from

those resulting from conventional M€

ossbauer studies: i.e., Axx ẳ (46.9 ặ 2.0) T,



502



9 Nuclear Resonance Scattering Using Synchrotron Radiation



103



a



0.061T ⊥γ⏐⏐ σ e



b



1T ⊥γ⏐⏐ σ e



c



1T ⊥γ⊥σ e



d



6T⏐⏐ γ⊥σ e



e



6T⊥γ⏐⏐ σ e



f



6T⊥γ⊥σ e



102

101

103

102

101

103

Counts (ns)



102

101

103

102

101

103

102

101

103

102

101

20



40



60



80

100

Time (ns)



120



140



Fig. 9.23 NFS spectra of [TPPFe(NH2PzH)2]Cl recorded at 4.2 K in applied fields as indicated.

The solid lines represent the best fit of NFS spectra using SYNFOS. The dashed lines are SYNFOS

simulations with the parameters obtained from conventional M€

ossbauer studies. (Taken from [51])



Ayy ¼ (9.5 Ỉ 2.0) T, and Azz ¼ (13.6 Ỉ 1.5) T (NFS) vs. Axx ẳ (45.6 ặ 3.5) T,

Ayy ¼ (6.0 Ỉ 5.5) T, and Azz ¼ (16.9 Ỉ 2.5) T (conventional; dashed lines). This

again demonstrates the sensitivity of NFS for hyperfine interactions in nuclear

(57Fe) scatterers. There can be no doubt that NFS benefits from experimental

conditions such as polarization and time structure, and also from a beam diameter

in the submillimeter range of the probing radiation.

However, when it comes to the simulation of NFS spectra from a polycrystalline

paramagnetic system exposed to a magnetic field, it turns out that this is not a

straightforward task, especially if no information is available from conventional

M€ossbauer studies. Our eyes are much better adjusted to energy-domain spectra and

much less to their Fourier transform; therefore, a first guess of spin-Hamiltonian

and hyperfine-interaction parameters is facilitated by recording conventional

M€ossbauer spectra.



9.6 Magnetic Interaction Visualized by NFS



9.6.3



503



Magnetic Hyperfine Interaction and Spin–Lattice

Relaxation in Paramagnetic Iron Complexes (Examples:

Ferric Low-Spin (FeIII, S ¼ 1/2) and Ferrous High-Spin

(FeII, S ¼ 2))



The spin state of a paramagnetic system with total spin S will lift its (2S þ 1)-fold

degeneracy under the influence of ligand fields (zero-field interaction) and applied

fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei

is different for the 2S ỵ 1 spin states in magnitude and direction. Therefore, the

absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how

the electronic states are occupied at a certain temperature.

When, however, phonons of appropriate energy are available, transitions between

the various electronic states are induced (spin–lattice relaxation). If the relaxation

rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a “breakdown” of

the quantum-beat pattern is observed in the NFS spectrum.

To visualize the effects induced by paramagnetic relaxation, the time-dependent

forward-scattering intensity has been calculated by implementing the stochastic

relaxation between spin states |i i and |j i into the SYNFOS program package [30].

The transition rates from |i i to |j i with Ei > Ej are described by [53]

oi!j ¼ oo



jEi À Ej j3 =kB3

É

;

exp jEi À Ej j=kB T À 1

È



(9.8a)



and for the reverse transition by

È

É

oj!i ¼ oi!j exp jEi À Ej j=kB T :



(9.8b)



The scaling parameter oo in (9.8a) determines the strength of spin–phonon

coupling.

A simple case is when a polycrystalline ferric low-spin system (S ¼ 1/2), with

effective thickness teff ¼ 20 and values of Ax,y,z/gnbn ¼ À50 T and DEQ ¼

2 mm sÀ1, is exposed to an external field B ¼ 75 mT. The transition rate from i

(i.e., Sz ¼ À1/2) to j (i.e., Sz ¼ +1/2) is assumed to be given by (9.8a), and the rate

of the reverse transition by (9.8b). NFS spectra for increasing relaxation rates

(corresponding to increasing temperature) are shown in Fig. 9.24. As the orientation

of the applied field was chosen perpendicular to direction k and the direction of

polarization s of the incoming beam, only the two Dm ¼ 0 transitions are available.

Therefore, at slow relaxation (o ¼ 0 mm sÀ1) essentially only one magnetic hyperfine frequency is observed, which is slightly modulated due to the powder average

because this leads to different orientations of Vzz with respect to the effective magnetic

field at the position of the nuclei. At fast relaxation (o ¼ 100 mm sÀ1), the effective



504



9 Nuclear Resonance Scattering Using Synchrotron Radiation



101



ω = 100 mm s–1



100

10–1

101



ω = 20 mm s–1



100

10–1

101



Relative Intensity



ω = 5.5 mm s–1

100

10–1

101

ω = 4.5 mm s–1



100

10–1

101



ω = 1.0 mm s–1



100

10–1

101



ω = 0 mm s–1

100

10–1

0



50



100

Time (ns)



150



200



Fig. 9.24 Theoretical calculations of nuclear forward scattering for the relaxation rates as indicated for a system with electron spin S ¼ 1/2, hyperfine parameters Ax,y,z /gnbn ¼ 50 T, and

DEQ ¼ 2 mm sÀ1 in an external field of 75 mT applied perpendicular to k and s. The transition

probabilities o in ((9.8a) and (9.8b)) are expressed in units of mm sÀ1, with 1 mm sÀ1

corresponding to 7.3 Á 107 sÀ1. (Taken from [30])



9.6 Magnetic Interaction Visualized by NFS



505



magnetic field corresponds to the very small applied field of 75 mT so only the quadrupole beats are visible. Around o ¼ 5.5 mm sÀ1, which corresponds approximately

to the splitting between the two Dm ¼ 0 resonances, complete dephasing of the at

o ¼ 0 mm sÀ1 and o ¼ 100 mm sÀ1 coherently forward scattered waves occurs

with the complete disappearance of the quantum-beat pattern in the NFS spectrum.

Figure 9.21 shows the NFS spectra of the ferrous high-spin (FeII, S ¼ 2)

complex [Fe(CH3COO)(TPpivP)]À at 3.3 K in an applied field of 6 T. This situation

corresponds to the slow-relaxation limit (o ¼ 0 mm sÀ1). Figure 9.25 shows

NFS spectra obtained from the same complex at various temperatures in a field of

4 T applied perpendicular to the wave vector k and to the direction of polarization (electric-field vector) s of the incoming beam. The spectra recorded at

14 and 18 K clearly exhibit the progressive collapse of magnetic hyperfine splitting due to spin–lattice relaxation. The simulations with SYNFOS (solid lines in

Fig. 9.25) were performed for all temperatures by means of one single value of

3.65 Â 109 sÀ1 KÀ3 for the scaling parameter oo in (9.8a).



9.6.4



Superparamagnetic Relaxation (Example: Ferritin)



For many organisms, iron is an indispensable element. In order to prevent growthlimiting effects, a sufficient supply of iron must be guaranteed. Therefore, it is

not surprising that nature has evolved systems for intracellular iron storage. One

class of storage compounds is ferritins, which have been isolated from mammals,

bacteria, and plants. Ferritins are composed of a protein shell harboring an ironcontaining mineral core. The inner diameter of the protein shell is about 8 nm and

can be filled to varying degrees with an inorganic “hydrous ferric oxide-phosphate”

complex, (FeOOH)8(FeOPO4H2), up to a maximum of about 4,500 iron atoms in a

single ferritin molecule [60].

Conventional M€

ossbauer studies (in the energy domain) of iron-rich ferritin

show a well-resolved magnetic hyperfine pattern at 4.2 K that, by increasing

temperature, changes into a quadrupole doublet [55, 61]. The transition temperature, which is also termed “blocking temperature” (TB), depends on the size of the

iron core. This behavior occurs in small particles of magnetically ordered materials

and is called superparamagnetism. Figure 9.26 shows the temperature variation of

the superparamagnetic relaxation as it is documented in time-domain spectra,

recorded from ferritin of the bacterium Streptomyces olivaceus [7]. In the fast

relaxation limit (100 K), the quadrupole interaction is visible as a quantum-beat

spectrum with a single frequency. In the slow-relaxation limit (3.2 K), the full

magnetic hyperfine interaction causes a complicated interference pattern. In the

intermediate relaxation regime (about 7 K), the stochastic spin flips cause dephasing of the delayed electromagnetic radiation, yielding destructive interferences with

concomitant loss of quantum-beat structure.

For a quantitative estimate of the particle size of the iron-containing mineral

core, one has to make use of the relaxation rate f at which the magnetization



506



9 Nuclear Resonance Scattering Using Synchrotron Radiation



103



T = 30 K



102

101

100

103



T = 18 K



102

101

100



Counts



103



T = 14 K



102

101

100

103



T=7K



102

101

100

103



T=3K



102

101

100

0



50



100



150



200



Time (ns)



Fig. 9.25 Time dependence of the nuclear resonant forward scattering by the complex [Fe

(CH3COO)(TPpivP)]– measured in an external field of 4 T applied perpendicular to k and s at

the temperatures indicated. (Taken from [30])



direction in each superparamagnetic particle changes between easy magnetic

axes:

f ¼ fo expðÀKV=kB TÞ:



(9.9)



In (9.9) K is the magnetic anisotropy constant, V is the volume of the particle, kB

is the Boltzmann constant, T is the temperature, and fo is a constant of about 109 sÀ1



9.6 Magnetic Interaction Visualized by NFS



507



Fig. 9.26 NFS spectra from

ferritin of the bacterium

Streptomyces olivaceus.

(Taken from [7])



100 K



9K



Counts



8K



7K



6K



3.2 K



0



50



100



150



200



Time (ns)



[62]. Assuming that the anisotropy constant is the same for various ferritins [63],

the relation between the diameter of the iron core and the blocking temperature is

˚ ). A quantitative determination of TB, at which f is equal to

d ¼ (6.860TB)1/3 (in A

the nuclear Larmor frequency (corresponding to the magnetic hyperfine field),

yields about 8 K for TB and about 4 nm for d, which is consistent with the analysis

of energy-domain spectra [7]. For comparison, energy-domain spectra of human

(instead of bacterium) ferritin have yielded 50 K for TB and 7 nm for d [64].



508



9.6.5



9 Nuclear Resonance Scattering Using Synchrotron Radiation



High-Pressure Investigations of Magnetic Properties

(Examples: Laves Phases and Iron Oxides)



Nuclear resonant scattering is extremely well suited for high-pressure studies

because synchrotron radiation exhibits almost laser-like properties and can be

collimated by optical devices such as mirrors and X-ray lenses, to spot sizes

in the 10 mm range [65]. Pressures, applied with diamond-anvil cells (DAC) to

samples of this size, reach values on the order of 100 GPa (1 Mbar). Such DACdevices (Fig. 9.27) have been successfully used for low-temperature (down to 15 K)

high-pressure (up to 105 GPa) studies of RFe2 Laves phases (R ¼ Y, Gd, Sc) [66,

67] as well as for high-temperature (up to 700 K) and high pressure (up to 80 GPa)

studies of the same class of material (RFe2, R ¼ Y, Se, Lu) [65, 67], FeBO3

(3.5–600 K, up to 55 GPa) [68], BiFeO3 (295 K, up to 62 GPa) [69], and FeO

and Fe2O3 (up to 2,500 K and 100 GPa) [70].

Temperatures as high as 2,500 K have been achieved by laser heating (LH). For

such LHDAC experiments, the sample size was around 50–100 mm, the laser beam

was focused to about 40 mm, and the synchrotron beam was microfocused to about

10 mm in diameter [70]. The photon-flux for the 14.4 keV (57Fe) synchrotron

radiation at the focusing spot was about 109 photons s À1with a 1 meV energy

bandwidth. This flux was reduced by a 5 mm path through diamond, via photo

absorption, to 25% of its original value. For comparison: the flux of the 21.5 keV

radiation of 151Eu would be reduced to only 60%.

SR



Fig. 9.27 Diamond-anvil cell

used for NFS studies. The

synchrotron radiation (SR)

enters the cell along the

diamond-anvil axis



NFS



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