15 Elementray Excitations

Mahavir Singh

Learning Outcomes

After studying these modules, you shall be able to

• Learn about the combined effect of electrical and magnetic properties of materials and their importance in the technological applications.
• Learn about the physics of MÖssbauer parameter and the basics theory involved
• Know the a) types of interactions and b) how they are different from each other
• Learn about the journey of resonant florescence from atomic to nuclear level
• Learn about the analogy of recoil free event between daily life experience and atomic & nuclear experiment

    1.Introduction

MÖssbauer Spectroscopy is Spectroscopic technique based upon recoilless resonant emission and absorption of gamma rays in solids. This resonant emission and absorption was first observed by Rudolf MÖssbauer during his graduate studies in 1957, called the Mossbauer Effect in his honor. Like NMR, MÖssbauer spectroscopy probes tiny changes in the energy levels of nucleus in response to its environment. Typically three types of nuclear interaction can be observed: an isomer shift; quadrupole splitting; and magnetic or hyperfine splitting also known as Zeeman Effect. Due to high energy and extremely narrow line widths of gammas rays , MÖssbauer spectroscopy is one of the most sensitive techniques in terms of energy resolution , capable of detecting change in just a few parts per 1011.

2.Basic principle

Just as a gun recoils when a bullet is fired, conservation of momentum requires a free nucleus to recoil during emission or absorption of a gamma ray(photon). If a nucleus at rest emits a gamma ray, the energy of the gamma ray is slightly less than the natural energy of the transition, but in order for a nucleus at rest to absorb a gamma ray, the gamma ray’s energy must be slightly greater than the natural energy, because in both cases energy is lost to recoil. This means that nuclear resonance (emission and absorption of the same gamma ray) is unobservable with free nuclei, because the shift in energy is too great and the emission and absorption spectra have no significant overlap

Nuclei in a solid crystal, however, are not free to recoil because they are bound in place in the crystal lattice. When a nucleus in a solid emits or absorbs a gamma ray, some energy can still be lost as recoil energy, but in this case it always occurs in discrete packets called phonons (quantized vibrations of the crystal lattice). Any whole number of phonons can be emitted, including zero, which is known as a “recoil-free” event. In this case conservation of momentum is satisfied by the momentum of the crystal as a whole, so practically no energy is lost. This was the major breakthrough done by MÖssbauer so to observe first nuclear floresence.

As an analogy, imagine jumping from a boat to shore, and imagine that the distance from boat to shore is the longest you can possibly jump (on land). If the boat is floating in water, you will fall short because some of your energy goes into pushing the boat back. If the water is frozen solid, however, you will be able to make it.

Mössbauer found that a significant fraction of emission and absorption events will be recoil free, which is quantified using the Lamb–Mössbauer factor. This fact is what makes Mössbauer spectroscopy possible, because it means gamma rays emitted by one nucleus can be resonantly absorbed by a sample containing nuclei of the same isotope, and this absorption can be measured.

3.Typical method

In Mössbauer absorption spectroscopy, a solid sample( in the form of powder or thin film) is exposed to a suitable beam of gamma radiation (Mossbauer probe), and a detector measures the intensity of the beam transmitted through the sample. The atoms in the source emitting the gamma rays must be of the same isotope as the atoms in the sample absorbing them.If the emitting and absorbing nuclei are in identical chemical environments, the nuclear transition energies would be exactly equal and resonant absorption would be observed with both materials at rest. The difference in chemical environments, however, causes the nuclear energy levels to shift in a few different ways in terms of electric and magnetic hyperfine interactions. Although these energy shifts are tiny (often less than a micro-electronvolt), the extremely narrow spectral linewidths of gamma rays for some radionuclides make the small energy shifts correspond to large changes in absorbance. To bring the two nuclei back into resonance it is necessary to change the energy of the gamma ray slightly, and in practice this is always done using the Doppler effect.

During Mössbauer absorption spectroscopy, the source is accelerated through a range of velocities using a linear motor to produce a Doppler effect and scan the gamma ray energy through a given range. A typical range of velocities for 57Fe, for example, may be ±10.047 mm/s (1 mm/s = 48.075 neV). In the resulting spectra, gamma ray intensity is plotted as a function of the source velocity. At velocities corresponding to the resonant energy levels of the sample, a fraction of the gamma rays are absorbed, resulting in a drop in the measured intensity and a corresponding dip in the spectrum. The number, positions, and intensities of the dips (also called peaks; dips in transmitted intensity are peaks in absorbance) provide information about the chemical environment of the absorbing nuclei and can be used to characterize the samples.

4.Selecting a suitable source

Mössbauer spectroscopy is limited by the availability of a suitable gamma-ray source. Usually, this consists of a radioactive parent that decays to the desired isotope. For example, the source for 57Fe consists of 57Co, which decays by electron capture to an excited state of 57Fe, then subsequently decays to a ground state emitting the desired gamma-ray of energy 14.4KeV known as MÖssbauer Probe for all iron contain samples especially magnetic materials. Similarly for semiconductor type samples we use Tin as MÖssbauer probe so as to study semiconductor properties. In superconductor we use Europium as MÖssbauer probe. Ideally the parent isotope will have a sufficiently long half-life to remain useful, but will also have a sufficient decay rate to supply the required intensity of radiation. Also, the gamma-ray energy should be relatively low, otherwise the system will have a low recoil-free fraction resulting in a poor signal-to-noise ratio and requiring long collection times.

5.Analysis of Mössbauer spectra

As described above, Mössbauer spectroscopy has an extremely fine energy resolution and can detect even subtle changes in the nuclear environment of the relevant atoms. Typically, there are three types of nuclear interactions that are observed, isomer shift (or chemical shift),quadrupole splitting and hyperfine splitting (or Zeeman splitting). Isomer shift is linked with monopole interaction, quadrupole splitting arise due to change in shape of nuclei which is further linked with Electric Field Gradient (EFG),Hyper fine splitting tells us about strengthof magnetic field locally so as understand the magnetic interactions (Ferromagnetic,ferrimagnetic,antiferromagnetic etc.)

6.Applications of Mössbauer spectroscopy

Mössbauer spectroscopy is unique in its sensitivity to subtle changes in the chemical environment of the nucleus including oxidation state changes, the effect of covalency on a particular atom, and the magnetic environment of the sample..It has been especially useful in the field of geology for identifying the composition of iron-containing specimens including meteors and moon rocks. Because of high precision and resolution , MÖssbauer spectroscopy is highly useful in Forensic Science for Finger Printing. In situ data collection of Mössbauer spectra has also been carried out on iron rich rocks on Mars.

Another significant application of Mössbauer spectroscopy is the study of phase transformations that occur in iron catalysts during Fischer–Tropsch synthesis. While these catalysts initially consist of hematite (Fe2O3), during reaction they are transformed into a mixture of magnetite (Fe3O4) and several iron carbides. The formation of carbides appears to improve catalytic activity, however it can also lead to the mechanical break-up and attrition of the catalyst particles. This can cause difficulties in the final separation of catalyst from reaction products. Mössbauer spectroscopy has also been used to determine the relative concentration change in the oxidation state of antimony (Sb) during the selective oxidation of olefins. During calcination all the Sb ions in an antimony-containing tin dioxide catalyst transform into the +5 oxidation state. Following the catalytic reaction, almost all Sb reverts from +5 to a +3 oxidation state. A significant change in the chemical environment surrounding the antimony nucleus occurs during the oxidation state change which can easily be monitored as an isomer shift in the Mössbauer spectrum. In synthesis of Ferritesome times Fe3+ converts into Fe2+ during sintering process so as to deteriorate the magnetic character of ferrite.Through Mossbauer analysis we can know the ratio of Fe2+ and Fe3+ ions.More recently, Mössbauer spectroscopy has been instrumental in developing an understanding of the structure and function of iron containing enzymes and the model complexes synthesized to mimic the functions of these enzymes.

7.Mössbauer spectrometer

A Mössbauer spectrometer is a device that performs Mössbauer spectroscopy, or a device that uses the Mössbauer effect to determine the chemical environment of Mössbauer nuclei present in the sample. It is formed by three main parts; a source that moves back and forth to generate a doppler effect, a collimator that filters out non-parallel gamma rays and select suitable energy of gamma raysay 14.4Kev for iron and a detector(Proportional counter). Through Multichannel arrangement data can be collected and displayed on the screen. Large number of counts (in lakhs) justify the good quality of Spectra. After fitting with minimum Chi square values we can calculate Isomer Shift, Quadrupole moment,magnetic dipole moment by using recommended soft ware.

8 Summary : The interdisciplinary nature of Mossbauer effect and low cost technique are highly useful in emerging technological areas such as nano magnetic system, metallurgy, biology and forensic science. Information on the type of magnetism, the onset of magnetic ordering ,the magnetic structure and magnetization can be obtained. The Mossbauer spectra of such substances frequently show interesting features in the critical region near magnetic ordering transitions. The nature and properties of superconductor and semiconductor can be better understood by using MÖssbauer spectroscopy.But fact of the matter is this technique is not so used in India.

   Value Addition:

Do You Know?

The Mossbauer effect or recoilless nuclear resonance florescence,is a physical phenomenon discovered by Rudolf Mossbauer in 1958 during his master programme .It involves the resonant and recil-free emission and absorption of gamma radiation by nuclei bound in a solid. Precise resolution is the key factor in this phenonmenon.The discovery was rewarded with the Noble prize in Physics in 1961.This spectroscopy can be use from low temperature to high temperature including room temperature.Mossbauer spectrum is characterized by the number,shape,position and relative intensity of the various absorption lines.These features result from the nature of the various hyperfine interactions and their time dependence,as well as on any motion of the Mossbauer nuclei.The total absorption intensity of the spectrum is a function of the concentration of Mossbauer nuclei in the absorber and the cross-sections of the processes involved.This absorption intensity ,together with the signal to noise ratio of the detection system and the total number of counts ,determine the quality and accuracy of Mossbauer spectrum.

Suggested Reading

Electronic spin relaxation and superparamagnetic relaxation play the crucial role for which Mossbauer spectroscopy help us to understand these phenomenon in depth. Time dependent effects, relaxation and dynamics need to be understand at advanced level so as to understand cryogenic in field experiments.

For More Details ( on this topic and other topics discussed in Text Module) See

1. Wickman H. H. Mossbauer Effect Methodolgy Vol. 2, New York, Plenum Press 1966
2. Goldanskii V. I. and Makarov E.F. Chemical Applications of Mossbauer Spectroscopy, New York, Academic Press, 1986

    For General Study on Mossbauer spectroscopy

Wertheim G.K. : Mössbauer Effect – Principles and Applications. Academic Press, New York, 1964.

Dominic P.E.Dickson,Frank J.Berry Mössbauer Spectroscopy Cambridge University Press London ,New York 1986.

Glossary:

Isomer Shift or Chemical Shift : difference of local, chemical environment between source and sample.

Quadrupole splitting

If the nucleus is subjected to an electric field gradient, local symmetry of the nucleus changes which is nothing but Quadrupole splitting. If Q.S is zero then nucleus is spherical, if Q.S is non zero then nucleus is either oblate or prolate.

Magnetic Splitting

In the presence of magnetic field the nuclear spin moment experience a dipolar interaction with the magnetic field that is Zeeman splitting.

Super paramagnetic state

With the help of Mossbauer analysis we can distinguish ferro,para and super paramagnetic state.For example if spectra consists of six lines then it is ferro or ferri, if it consists of doublet then it is para and if it consists of singlet then it is superpara.