Taken from Mossbauer Spectroscopy at Knox
College: http://nthome.knox.edu/student/ferazo/physics/moss
Mössbauer
Spectroscopy of Iron Porphyrins
Knox College
Hughes Fellowship Summer Research
Fernando J. Erazo
Prof. Charles Schulz, mentor
August 22, 1999
Introduction:
Mössbauer Spectroscopy is
the measurement of recoilless resonant gamma ray absorption by certain
nuclei. It was Rudolph Mössbauer who
first discovered the existence of recoilless nuclear resonance fluorescence in
1957 (Greenwood, pp. 1). After him, the
nuclear emission or absorption of a photon without energy lost to recoil is
known as the Mössbauer effect. The
measurements provided by this spectroscopy method are extremely precise and
have a great resolution, allowing scientist to detect otherwise unobservable
interactions between the nucleus and orbital electrons – called hyperfine
interactions.
Although in theory the
Mössbauer effect is present in all excited-state to ground-state nuclear
transitions, it has only been detected in a total of 88 gamma ray transitions
in 72 isotopes of 42 different elements (Greenwood, pp. 1). This is partly because of limitations in
current instrumentation but mostly because in the majority of transitions the
Mössbauer line width is too small to be measured. The most commonly studied
isotope in Mössbauer spectroscopy is 57Fe, specifically, this isotope’s first
excited state decay.
It is not a coincidence that
57Fe has been so largely documented and studied by using the Mössbauer
method. In Mössbauer spectroscopy, 57Fe
has a series of physical characteristics that qualify it as a very approachable
isotope. Also, an important factor
qualifying iron for such extensive Mössbauer analysis is this element’s
presence in very important biological molecules. A perfect example is hemoglobin.
In our summer study of
Mössbauer spectroscopy, we found the spectra of various tetraethylporphyrins
and tetrapropylporphyrins. Porphyrins
are planar atomic structures with an iron atom in the center; in this case they
are compounded with very long chains of amino acids to form large protein
molecules – such as hemoglobin. A
computer analysis of the obtained spectra returns precise information about the
hyperfine interactions around the iron nucleus in these proteins. The result is a better understanding of the
environment surrounding the iron nucleus in such proteins. Thanks to this information scientists can
learn more about the types of chemical reactions implicated in fundamental
biological processes.
The Mössbauer effect:
It is now widely known that
atoms and nuclei have excited states that consist of different electron,
proton, and, neutron configurations.
These excited states are sometimes accessible from the ground or
low-lying states through the absorption of gamma rays (photons). The excited states in nuclei, however, have
very narrow energy widths. Therefore,
in order to observe a good resonant absorption of gamma rays by nuclei we need
a highly precise and sharply defined incident gamma ray energy. For example, a 57Fe nucleus on its first
excited state can decay by emitting a photon with an energy of 14.4KeV. Since the energy levels in the nucleus have
a very narrow width (long lifetime), only a 14.4KeV photon can be absorbed by
another such nucleus. A photon with an
energy of 14KeV is completely useless to the 57Fe nucleus (Wiarda).
The
next obvious question is how to obtain gamma rays of the precise resonant
energy needed to excite the desired nuclei.
Obviously, a perfect source is an identical nucleus that is currently in
the excited state; when it decays it will emit a photon of precisely the needed
energy. The gamma ray source - excited
nuclei - can be obtained from decay products of
radioactive isotopes. In our study of
iron Porphyrins we use radioactive 57Co isotopes because when they decay into
57Fe they sometimes emit 14.4KeV photons.
The
challenge does not stop there. From a
mechanical perspective, if an excited 57Fe nucleus decays to its ground state
it won’t necessarily emit a photon of 14.4KeV.
The energy of that photon is not really 14.4KeV, but lower. Since the nucleus recoils while emitting the
particle, this recoil takes up some of the energy of the emitted photon. The energy lost to recoil, though relatively
very small, is sufficient so that at normal temperatures the photon cannot be
absorbed by another 57Fe nucleus.
In
1958, Mössbauer discovered that a photon could indeed be emitted with the full
transition energy. If encrusted in a
lattice – a lattice is the quantum mechanical perspective of a solid – a
nucleus can emit its photon with negligible loss of energy due to recoil. In the lattice the nucleus is bound by
elastic forces and the effective recoil mass is the entire solid. Similarly, in the absorbing nucleus – also
embedded in a solid – we can have a fraction of recoilless absorptions. “Mössbauer’s important contribution was the
discovery that a nucleus which is embedded in a solid can sometimes emit its
gamma ray with negligible energy loss to recoil” (Lang 4).
The
Mössbauer Spectrum:
One
of Mössbauer Spectroscopy’s main features is that it has made it possible to
resolve the elusive hyperfine interactions in the sample nuclei. This is allowed by the sharpness of the
Mössbauer line, and, the ability to determine the energies of the emitted gamma
rays from the source with respect to the absorber with great accuracy. The hyperfine interactions represent
associations and relations among a nuclear property and appropriate electronic
or atomic configurations. These
hyperfine relations are of great importance because they provide information
regarding electron- and spin-density distributions (Gonser 21).
The
advantage of the Mössbauer method to detect the hyperfine interactions arises
from the very narrow line width of the nuclear transitions involved in this
effect. The absorption of resonant
gamma rays is extremely sensitive to the smallest variations of the radiation
energy. Therefore, the otherwise
undetected interactions between the nucleus and the orbiting electrons manifest
themselves very markedly when analyzed under Mössbauer Spectroscopy (Danon 66).
There
are three main hyperfine interactions:
·
The
nuclear isomer shift – electric monopole interaction.
·
The nuclear quadrupole splitting – electric
quadrupole interaction.
·
The nuclear Zeeman effect – magnetic dipole
interaction.
First, the isomer shift
occurs due to the electrostatic interaction between the electron charge density
at the nucleus and the charge distribution of the nucleus itself over its
radius. The chemical environment that
surrounds both the emitting and the absorbing elements can change the electron
density at their nuclei. When that occurs,
electrostatic interaction also changes the levels of the nuclear ground and
excited states – therefore altering their transition energies. In our Mössbauer resonant measurements, the
difference between these transition energies is called the isomer shift. The isomer shift is identified in the
spectrum as the shift from zero-velocity of the center of the Mössbauer line.
The quadrupole splitting
arises from the interaction between the nuclear electric quadrupole moment and the
electric field gradient (EFG) at the nucleus.
The determinacy of such an electric quadrupole interaction by Mössbauer
Spectroscopy is one its most useful features.
The quadrupole splitting measurements help scientist determine
deformities in the nuclear charge distribution. The sign of the quadrupole moment depends solely on the charge
distribution deformation: a negative quadrupole moment indicates a nucleus that
is flat along the spin axis, while a positive quadrupole moment indicates a
nucleus is elongated (Greenwood et al, 54).
The quadrupole interactions resolved by using Mössbauer spectroscopy are
of fundamental importance in chemistry and solid state physics since they
provide a means to derive the electric field gradient at the nucleus. In the case of 57Fe, there is a considerable
uncertainty about the absolute value of the quadrupole moment of its first
excited state. Therefore, the
inaccuracy of its derived EFG is fairly high.
A perfect example of a spectrum that represents a quadropole splitting
follows this page.
The third hyperfine
interaction is the Zeeman effect. Also
called the magnetic dipole interaction, this property is present only when the
nucleus is under a magnetic field. The
applied magnetic field can vary in strength and can be originated from within
the atom itself or any other external source.
When the field originates from the atom’s own orbiting electrons, it is
called internal field. The result of
the Zeeman effect is the splitting of the nuclear state with spin I (I >0) into (2 I + 1) (Gonser, 24). After this page, a spectrum of a sample with a large magnetic
interaction has been included.
Besides the three main
interactions briefly described above, Mössbauer spectroscopy can also determine
perturbations or combined effects.
Sometimes, the splitting of a nuclear state can involve nuclear magnetic
dipole and electric quadrupole interactions simultaneously. In this case, the interpretation of the
obtained spectrum becomes much harder.
Relaxation effects can also be investigated when the hyperfine
interactions present involved time dependant features. Lastly, relativistic effects may also be
observed, these arise from the high frequency vibrations of the atoms in a solid,
the average square velocity of these oscillations causes a shift of the
resonance line – also called the second-order Doppler effect (Gonser, 32).
The apparatus:
The most basic Mössbauer
spectrometer is in itself a very simple experimental setup: all we need is a
source emitting a good fraction of recoil-free gamma rays, an absorber, and a
proportional counter aligned together in the obvious way. However, in order to observe the nuclear
resonant absorption of gammas, we must instead look for conditions where this
absorption does not occur. Thanks to
the very narrow resonance line width, it is sufficient to Doppler shift the
source or the absorber to sweep over the resonance. The velocity ranges of the Doppler shift applied depend on the
width of the resonance. In our study of
iron Porphyrins, the velocity used was 6 mm/sec. It most be made clear that the purpose of the Doppler shift
applied is solely to sweep over the resonance and not at all to compensate for
the fraction of the gamma rays with energy lost to recoil (Danon, 44). For our summer research, we chose to Doppler
shift the incoming gamma rays by using a velocity transducer on the 57Co
source. Also called a velocity sweep
device, the transducer consists of a multi-channel analyzer that allows the
inspection of the entire velocity spectrum simultaneously.
Besides the Doppler shift
velocity, there are more variables a scientist can control in a Mössbauer
experiment. For example: the magnetic
field applied to the absorber, and, its temperature. Towards that end, there are commercially available cryostats with
various temperatures ranges designed specifically to work in a Mössbauer
setup. Similarly, superconductive
magnets that apply very high fields to the sample in a Mössbauer experiment are
also available. All the samples that we
analyzed this summer were studied in a spectrometer capable of delivering a
magnetic field of up to 90.000 gauss and a constant temperature as low as 4.2
Kelvin.
The largest part of our
Mössbauer project this summer was the construction of a spectrometer that
utilizes a closed cycle cryostat. The
advantages of this type of spectrometer are primary financial: all it requires
to run is a cylinder of helium gas and a 250V electrical outlet! That contrasts sharply with the needs of our
current spectrometer, which uses up to 250 liters of liquid helium and about
100 liters of nitrogen to run at 4.2K and attain superconductivity. On this aspect, the close cycle cryostat
spectrometer is much more versatile and easy to setup. Another advantage of the closed cycle
cryostat is that it has a variable range of temperatures at which the Mössbauer
spectrum can be taken: from about 20 Kelvin up to room temperature. This versatility, of course, comes at a
price: the closed cycle cryostat’s lower temperature limit falls short of the
4.2 Kelvin that can be achieved on our current cryostat. Also, the magnetic field applied on the
closed cycle cryostat’s sample is barely 400-600 gauss. We attained this field by using 16
individual Neodymium magnets. Thus, the
field is variable – just reduce/add more magnets – but it has to be measured
with a probe, therefore introducing some uncertainty. The superconductive magnet used on our current spectrometer, on
the other hand, has a variable strength field of up to 90000 gauss regulated
from a control board.
Special considerations had
to made while designing the closed cycle cryostat stand to be used on the new
spectrometer. Vibration is a primordial
issue in Mössbauer spectroscopy that must be avoided at all cost. To that end, the frame of the stand was made
of hardened-steel framing and it was reinforced with aluminum plates. To insulate the system from outside
vibrations, a set of four air-cushion vibration isolators were used. It is important to realize how critical vibration
isolation is in a Mössbauer experiment.
In our research we only took spectra for 57Fe nuclides. Because of the 57Fe very narrow line width
and relatively high gamma ray energy, vibration can be a serious problem. It is no exaggeration that the following
rule of thumb is applied to a 57Fe spectrometer: “If one touches the equipment
lightly with the fingertips and notices any traces of vibration, the experiment
will fail (Frauenfelder, 40)!” The
vibration problem is even more marked for nuclides that have a narrower line
width, for example 67Zn. This isotope
has a resonance width of about 10-10 eV. Such a narrow width corresponds to a Doppler velocity of about 10-5
cm/sec. “That velocity is so small that
is barely faster than the speed at which human fingernails grow!” If vibration exists on a spectrometer used
for 67Zn, “an amplitude of a few times 10-8 cm can be sufficient to
destroy the resonance (Frauenfelder, 33)!”
A sketch of the Mössbauer Spectrometer we built follows this page.
Data analysis:
A computer program analyzed
all the spectra we obtained for the metalloproteins we studied. Expect for the simplest of the Mössbauer
spectra where no more than one interaction appears at a time, the aid of a
fitting program is required to make sense of a spectrum and learn the adequate
parameters. One of the projects that we
also undertook this summer was the translation of parts of this program from
FORTRAN into C++. The versatility and
modularity of C++ allows us to build a larger program that can use all the
modules and fitting programs into a single user-friendlier suite with a helpful
graphical user interface. Specifically,
the new segment we added to the Mössbauer Spectra Analyzer program was a Hamiltonian
fit module. Previously, the FORTRAN
version of this program used an Omega tensor method to approximate model fit
parameters of the analyzed spectra.
Thanks to the module we added to the analyzer we obtained better fits
for the spectra of the Porphyrins we studied, included after this page are two
examples of such fits for the spectra of Fe (III) Tetraethyl Porphyrin Chloride
and Fe (III) Tetrapropyl Porphyrin Chloride.
Conclusion:
Mössbauer Spectroscopy by
itself is a huge field that offers an infinite number of possible applications. The ten weeks spent this summer have served
me very well as an advanced and practical introduction to this singular
scientific method. After being
introduced into this field I have decided to continue the exploration of
Mössbauer Spectroscopy by taking an independent studies this term on that
topic. This time I will concentrate my
efforts on a particular subject within the Mössbauer ground.
References:
1.
Danon,
J. “Lectures on the Mössbauer Effect.” Gordon and Breach Science Publishers,
New York 1968.
2.
Frauenfelder,
Hans. “The Mössbauer Effect.” Frontiers in Physics, A Lecture Note and Reprint
Series, W.A. Benjamin, Inc. Publishers, New York 1962.
3.
Gonser,
U. Ed. “Mössbauer Spectroscopy.” Topics
in Applied Physics. From a strange effect
to Mössbauer Spectroscopy, Gonser.
Springer-Verlag Publishing, New York 1975.
4.
Greenwood,
N. N. and Gibb T. C. “Mössbauer Spectroscopy.” Chapman and Hall Ltd.
Publishing, London 1971.
5.
Wiarda,
Dorothea. “Taking a Mössbauer Measurement.” Aug. 1999 http://www.public.usit.net/wiarda/scientific/Moessbauer.html