Mossbauer Effect

Type of physical science: Condensed matter physics

Field of study: Solids

The Mossbauer effect is a resonance phenomenon involving the emission of high-energy γ photons produced by nuclear decay in a radioactive source material and their subsequent reabsorption by nuclei in a suitable absorber material. By studying this effect, scientists can gain important insights into the electronic and nuclear structure of the absorber materials.

Overview

The Mossbauer effect involves the resonant absorption of γ photons by nuclei in a suitable absorber material and the subsequent transition of these nuclei from their ground state to excited nuclear states. The source of the γ photons must contain excited nuclei of the same isotope as the nuclei under study in the absorber. In order to understand the principles of the Mossbauer effect, one must examine the processes of photon emission and absorption by a free nucleus.

Suppose that a free nucleus at rest and initially in its excited nuclear state emits a γ photon with energy E_γ. In this emission process, the energy of the nucleus decreases from its initial excited state energy, E_excited, to its ground state energy, E_ground. This energy difference, E_excited-E_ground, is called the transition energy of the nucleus, or E₁. The energy of the emitted γ photon need not be equal to the transition energy. The difference between these two energies is caused by the recoil effect. Since linear momentum must be conserved in this process, the emitting nucleus must acquire a momentum that is equal and opposite to that of the emitted photon.

Energy must be conserved in this process as well; thus, the energy of the emitted photon must be less than the transition energy by an amount equal to the nuclear recoil energy, E_R, which is expressed as E_γ = E₁ - E_R.

A similar recoil effect occurs when a γ photon is absorbed by a free nucleus at rest and in its ground state in the absorber material. Upon absorption, the incident γ photon must possess enough energy to move the nucleus to its excited state (the transition energy) and supply the required kinetic energy to the recoiling nucleus to conserve linear momentum. Thus, as a result of the recoil effects, a γ photon emitted by an excited nucleus in the source material does not have sufficient energy for resonance reabsorption by a ground state nucleus in the absorber. This actual energy deficiency is equal to 2E_R.

In 1904, Robert W. Wood performed an experiment that demonstrated resonance in an atomic system. The experiment involved visible photons and transitions between electronic levels of an atom. This physical system is identical to the nuclear system described above, except that the transitions involved are between electronic levels in an atom. In Wood's experiment, yellow light from a sodium lamp was focused on a glass bulb that contained sodium metal. The bulb was heated by a flame, causing some of the metal to evaporate and form a vapor. When atoms of the vapor in the bulb absorbed the incident photons, some of their valence electrons were excited into higher electronic energy levels. As these electrons fell back to their ground state, they emitted visible photons of the same color as the incident light in all directions. This resonant absorption and emission process is also referred to as resonance fluorescence. Although the recoil effects still occur in this atomic system, they are small in comparison with the visible photon energies. The recoil effects are also masked to a large extent by the thermal motions of the emitting and absorbing atoms. As a result, resonant absorption and emission are experimentally observed, even in the presence of recoil, in this atomic system.

In contrast, the recoil effects in the nuclear system are large. The γ photon energies, which are determined by the difference in nuclear energy between the excited and ground states, are approximately ten thousand times greater than visible photon energies.

Therefore, the recoil effects, which depend on the square of the photon energy, are approximately 10⁸ times greater than in the atomic case. These nuclear recoil effects are large enough to prevent nuclear resonance from occurring in free nuclei.

The Mossbauer effect, discovered by Rudolf Ludwig Mossbauer in 1958, makes it possible to overcome this recoil energy loss problem. Mossbauer observed that the absorption of γ photons by the isotope iridium 191 increased as the temperature of the absorber nuclei was lowered. The Mossbauer effect can be observed if both the source and absorber nuclei are in solid form. In this situation, the nuclear recoil can excite lattice vibrations or elastic waves, which are commonly called phonons, in the solid. Phonons, which have quantized energies similar to photons, are emitted and absorbed by vibrating atoms located at the lattice points in a solid. An individual atom of a solid exchanges vibrational energy with its neighbors by the exchange of phonons.

Since the phonon energies are quantized, there exist fractions f and f' of all emissions and absorptions, respectively, which occur without changing the vibrational state of the solid. For these phonon-free emissions and absorptions, the recoil energy loss becomes extremely small in comparison to the transition energy, since it is taken up by the whole solid, which consists of a large number of nuclei. Thus, if both the radioactive source that emits the γ photons and the absorber nuclei are in a solid or crystalline form, the effects of recoil are negligible for the phonon-free processes. Under these conditions, resonant emission and reabsorption can occur. The recoil-free fractions, f and f', can be theoretically calculated for a particular solid by quantum mechanical methods. The results of a detailed analysis show that the recoil-free fractions increase with decreasing temperature, thus verifying Mossbauer's experimental observation.

The Mossbauer effect has been observed in at least eighty-eight different γ photon transitions in seventy-two isotopes of forty-two chemical elements. Although it is theoretically possible to observe it in any nucleus that decays by γ photon emission, the effect may be too feeble to be observed by current detection techniques. One of the most useful isotopes that displays the Mossbauer effect is the transition metal iron 57. Its Mossbauer effect resonance is easy to detect, and iron is contained in many materials of interest, particularly those of biological importance. The iron 57 isotope can exhibit a Mossbauer effect resonance; γ photons with an energy of 14.4 kiloelectronvolts (1 electronvolt = 1.602 x 10^-19 joules) are absorbed by a nucleus in a suitable absorber, exciting the nucleus from its ground state with a spin of 1/2 to its excited state with a spin of 3/2.

The 14.4-kiloelectronvolt photons are produced by the radioactive decay of a source material containing cobalt 57 into iron 57. The γ photons emitted by the decay of the excited nuclei of iron 57 in the source material are not strictly monochromatic or monoenergetic.

They are emitted with a distribution of energies 4.7 x 10^-9 electronvolts wide, centered on the mean energy of 14.4 kiloelectronvolts. This distribution of emitted energies, usually called the natural linewidth, may be explained using the Heisenberg uncertainty principle. The excited nuclear state of iron 57 is not infinitely stable; it is metastable, with a half-life of 97.7 x 10^-9 seconds. In other words approximately half of the excited iron 57 nuclei will decay to their ground state within this time. The Heisenberg uncertainty principle asserts that the energy distribution of the emitted γ photons is related to the half-life of the excited nuclear state.

The narrowness of the natural linewidth of the emitted γ photons as compared to their mean energy is one reason that the Mossbauer effect is a valuable laboratory technique. The ratio of the γ photon energy to its linewidth for iron 57 is approximately 3 x 10 to the power of 12 for the phonon-free emissions. If the lattice of the solid that contains the emitting nuclei were excited, thereby generating phonons, then the linewidth of the emitted photons would be much larger than in the phonon-free case. The γ photons used in a Mossbauer effect experiment are quanta of some of the most accurately defined electromagnetic radiation available.

The Mossbauer effect can be used as a form of spectroscopy to measure the various nuclear energy levels of an absorber material when the energy of the emitted γ photons is modulated or varied. Scientists move the source and thus shift the energy of the emitted photons via the Doppler effect. A Mossbauer effect spectrometer consists of a source of γ photons that can be moved relative to an absorber material and a detector system to measure the intensity of the γ radiation after it passes through the absorber. A Mossbauer spectrum of a particular absorber material is a plot of the intensity of the γ radiation transmitted through the absorber as a function of the source velocity. For iron 57, moving the source toward or away from the absorber with a relative velocity of 1 millimeter per second will shift the energy of the emitted γ photons sufficiently to destroy the condition for resonant reabsorption.

If there are no hyperfine interactions present in the absorber material, then the transition energy in the absorber equals that of the source. The Mossbauer spectrum in this case will consist of a single absorption line or dip centered at v = 0. The spectrum has the shape of a dip, since it was recorded in transmission geometry and thus displays the intensity of the Doppler-shifted γ photons that were not reabsorbed by the absorber nuclei. Only the γ photons incident on the absorber nuclei with the correct energy, here equal to the transition energy, can cause resonance absorption by the absorber nuclei.

Applications

Applications of the Mossbauer effect and Mossbauer spectroscopy can be found in the areas of relativity, general physics, nuclear physics, solid-state physics, biophysics, chemistry, and metallurgy. One of the first uses of the Mossbauer effect was in an experiment designed to verify the existence of the gravitational redshift, a prediction of the theory of relativity. The gravitational redshift principle states that the frequency and energy of a quantum of electromagnetic radiation (a photon) depend on the local strength of the gravitational field. In this experiment, first performed by Robert V. Pound and G. Rebka in 1960, the emitting source was placed at some known distance above the absorber in a uniform gravitational field. The redshift principle asserts that a γ photon will be emitted from the source with an additional potential energy caused by its position with respect to the absorber in the gravitational field. This additional gravitational energy may prevent resonant reabsorption of the γ photon in the absorber. The experimental method involved finding the velocity at which an emitting source must be moved away from an absorber in order to reestablish the resonance condition. The data of Pound and Rebka were in excellent agreement with the special theory of relativity, thus demonstrating the usefulness of the Mossbauer effect as an experimental technique.

Most applications for the Mossbauer effect are based on the existence of hyperfine interactions. Hyperfine interactions are the interactions or the influence of the electrons that surround a nucleus on its nuclear properties. The hyperfine interactions are caused by a coupling between the various electric and magnetic moments of the nearby electrons with the various electric and magnetic moments possessed by an absorber nucleus. Determining the hyperfine structure of a nucleus in an absorber material involves finding the splittings and spacings of the various nuclear energy levels caused by the hyperfine interactions. The three hyperfine interactions that can be studied by the Mossbauer effect are the isomer shift, the electric quadrupole interaction, and the magnetic hyperfine interaction.

The isomer shift, sometimes called the chemical shift, is the result of the electrostatic monopole interaction (the Coulomb interaction) between an absorber nucleus and its electrons.

The result of the isomer shift is a change, or shift, in position of a Mossbauer absorption line that is dependent on the density of electrons at the absorber nucleus. A measurement of the isomer shift for a particular absorber material may help determine chemical or electronic information such as the material's oxidation state (number of valence electrons), the degree of covalent bonding among electrons, and the coordination number or number of bonds with neighbor atoms.

The electric quadrupole interaction is the result of a different electrostatic interaction between an absorber nucleus and nearby electrons. The excited nuclei of many atoms have a nonspherical charge distribution. This nonspherical nuclear charge distribution often can be represented by a positive charge in the shape of an ellipsoid of revolution and described by a quadrupole moment. An oblate (flattened) nucleus has a negative quadrupole moment, whereas a prolate (elongated) nucleus has a positive quadrupole moment. Nuclei with spins less than or equal to 1/2 have spherically symmetric charge distributions and thus have zero quadrupole moment. This nonuniform charge distribution can interact with the local electric field at the site of the absorber nuclei, which are produced by the valence electrons and neighboring atom electrons, in such a way that the energy of the nuclei depends on the orientation of its quadrupole moment with respect to the electric field. Measurement of the electric quadrupole interaction by the Mossbauer effect can provide the sign of the quadrupole moment of the absorber nuclei, the distribution of valence electrons of the absorber nuclei in their various atomic orbitals, the spacings and energies of the various atomic orbitals of the absorber material, and insight into the crystal structure of atoms in the absorber. Studying the electric quadrupole interaction of an absorber material using the Mossbauer effect can give information about nuclear and electronic properties of these materials.

The magnetic hyperfine interaction is the result of an interaction between the nuclear magnetic dipole moment of an absorber nucleus and the net magnetic field at its site. The net magnetic field is the sum of any external magnetic field applied to the absorber material and the internal magnetic field produced by the valence electrons of the absorber nuclei. The magnetic hyperfine interactions result in splittings of the nuclear energy levels of the absorber material via the Zeeman effect. Measurement of the magnetic hyperfine interaction splittings by the Mossbauer effect can provide the values of the magnetic moments for the various nuclear spin states in the absorber, insight into the electronic structure of the absorber nuclei, and information about the causes and details of the internal magnetic field.

Context

The Mossbauer effect has evolved from an accidental experimental discovery to an important laboratory technique used in many branches of physics and chemistry. The experimental difficulties in achieving nuclear resonance were troublesome to many physicists during the first half of the twentieth century. Several experimental methods were devised to compensate for the recoil energy loss in nuclear resonance reabsorption experiments. The Mossbauer effect was the first experimental technique that eliminated the need to compensate for the recoil effects in nuclear resonance experiments.

As is the case with many landmark discoveries, the experimental observation of the Mossbauer effect led to intense activity by theoretical physicists to understand its mechanisms.

The routine use of the Mossbauer effect as a research tool is the result of the development of experimental techniques for its observation, the identification of physical systems that are suitable for study, and advances in the theoretical interpretation of the experimental data for these systems.

Research topics involving the Mossbauer effect and Mossbauer spectroscopy fall in two broad categories. In the first category, the Mossbauer effect is used primarily as an analytical tool. It is used to extract basic information about the general characteristics and properties of a particular absorber system. In the second category, the Mossbauer effect is used as a sophisticated probe to analyze the details of many physical properties of a specific absorber system.

Mossbauer effect studies of condensed matter systems are also useful because they can provide information that is complementary to that produced by other experimental techniques.

For example, information about a particular system may be provided by magnetic susceptibility, electron paramagnetic resonance (EPR), Raman spectroscopy, optical absorption spectroscopy, and nuclear magnetic resonance (NMR). When these data are combined with additional information provided by the Mossbauer effect, much insight can be gained into many aspects of the physics of these materials.

Principal terms

DOPPLER EFFECT: the change of frequency or energy of a wavelike or particle-like disturbance when there is a relative motion between the source or cause of the disturbance and the observer

ELECTRONIC STRUCTURE: information about the distribution of the valence electrons in the various atomic (electronic) orbitals, the energies of these orbitals, and their spacings in an atom; the valence or outermost electrons determine many of the chemical properties of an atom

HYPERFINE INTERACTION: the interaction of the electric and magnetic moments of the electrons in an atom with the electric and magnetic moments of its nucleus

HYPERFINE STRUCTURE: the result or effect of the hyperfine interactions on the nuclear energy levels of the absorber material; usually observed as shifts and splittings of the nuclear states

NUCLEAR ELECTRIC QUADRUPOLE MOMENT: the charge distribution characteristic of the excited nuclei of many atoms with protons that are nonspherically symmetric

NUCLEAR RECOIL: the subsequent motion that a nucleus, initially at rest, must acquire when it emits or absorbs a photon; a result of the principle of conservation of momentum

NUCLEAR SPIN: an intrinsic angular momentum and associated magnetic moment that a nucleus may possess; it was first postulated to explain the hyperfine structure observed in the electronic spectra of some atoms

PHOTON: a small packet or quantum of electromagnetic energy; a particle of light

RESONANCE: in a mechanical or electrical system, a phenomenon that occurs when energy is input to the system at or near one of its natural frequencies, causing some property of the system to vibrate or oscillate with a relatively large amplitude; in an atomic, nuclear, or quantum mechanical system, resonance refers to the fact that the system can emit or absorb energy only in amounts that equal the difference in two of its intrinsic (or natural) energy levels

SPECTROSCOPY: the study of the various energy levels of a material

Bibliography

Cranshaw, T. E., B. W. Dale, G. O. Longworth, and C. E. Johnson. MOSSBAUER SPECTROSCOPY AND ITS APPLICATIONS. Cambridge, England: Cambridge University Press, 1985. A concise volume that describes the basic principles of the Mossbauer effect. Contains chapters that describe applications of the Mossbauer effect in relativity, solid-state physics, biophysics, low-dimensional magnetism, metallurgy, and archaeology.

French, A. P. SPECIAL RELATIVITY. New York: W. W. Norton, 1968. Contains a brief but informative discussion of the processes of photon absorption and emission and their relation to the Mossbauer effect.

Greenwood, N. N., and T. C. Gibb. MOSSBAUER SPECTROSCOPY. London: Chapman and Hall, 1971. One of the first encyclopedic works on the subject. Contains a detailed discussion of the principles of the Mossbauer effect, a discussion of experimental techniques, and a lengthy discussion of the various hyperfine interactions. More than half of the book summarizes the wealth of experimental and theoretical results obtained before its publication, with an emphasis on studies using the iron 57 resonance.

Thosar, B. V., P. K. Iyengar, J. K. Srivastava, and S. C. Bhargava, eds. ADVANCES IN MOSSBAUER SPECTROSCOPY: APPLICATIONS TO PHYSICS, CHEMISTRY, AND BIOLOGY. Amsterdam: Elsevier Scientific, 1983. A superb collection of lengthy review articles on various applications of Mossbauer spectroscopy. Topics include Mossbauer studies of biomolecules and paramagnetic hyperfine structure.

Wertheim, Gunther K. MOSSBAUER EFFECT: PRINCIPLES AND APPLICATIONS. New York: Academic Press, 1964. A classic work that describes the basic principles of the Mossbauer effect. Contains a very clear description of the information that can be extracted from Mossbauer effect studies of hyperfine structure in various absorber materials.

The Effect of Electric and Magnetic Fields on Quantum Systems

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