Materials Analysis With Nuclear Reactions And Scattering

Type of physical science: Nuclear physics

Field of study: Nuclear techniques

Projectiles of various types interact with atomic nuclei by means of a number of processes that may be classified as nuclear reactions and/or nuclear scattering. In addition, the particles that result from the radioactive decay of nuclei or from other nuclear processes interact with bulk matter. The details of these interactions, which are dependent upon the nature of the material in which the interaction occurs, can be used to analyze the material.

Overview

Materials analysis involves the determination of the composition, structure, and properties of materials. The principles and techniques of nuclear physics are applied to the analysis of materials in two primary ways. The first involves the interactions of projectiles of various kinds with the individual nuclei of the matter under study. The second is based on the interactions of projectiles, some of which result from the decay of unstable nuclei, with bulk matter--that is, with large numbers of atoms and/or nuclei.

Nuclear interactions result when projectiles collide with atomic nuclei or when unstable nuclei decay. If the collision results in a change in the identity or properties of the target nucleus, the process is commonly referred to as a nuclear reaction. For example, if target nucleus X is bombarded by projectile a, resulting in nucleus Y and outgoing particle b, the nuclear reaction may be written as follows: a + X → Y + b. This reaction is often abbreviated: X(a,b)Y.

Associated with each reaction process is a reaction energy, Q, which may be defined as the total energy released as a result of the reaction. More correctly then, a + X → Y + b + Q. Reactions for which Q is positive are exoergic and result in the release of energy. Reactions with negative values of Q are endoergic and require an input of energy to proceed. If nuclear reactions are to be applied for the purpose of materials analysis, knowledge of the Q value of the specific reaction is essential to ensure that the projectile has sufficient energy to trigger the desired reaction, or so that the reaction products Y and b can be positively associated with the occurrence of a specific reaction.

A nuclear reaction in which the particles a and b are identical is conventionally known as a scattering event. While the nuclei, X and Y, are necessarily identical, they need not be in the same energy state: X(a,a')X. Scattering events for which the kinetic energy of the incident particle, a, and the outgoing particle, a', are equal (Q=0) are elastic scatterings, while all other scattering events (Q ≠ 0) are inelastic.

Also associated with each reaction process or scattering event is a cross section, which is a measure of the probability that the incident particle will undergo the reaction or scattering being considered. The cross section is of primary importance in the application of nuclear physics principles to materials analysis, since it is the quantity that relates the observed results of a reaction or scattering to the properties of the particles and nuclei involved in the process. The cross section varies in a general way from one type of reaction to another. Among other variables, the cross section for a specific reaction or scattering depends upon the identity, energy, and orientation (as determined by the spin angular momentum) of the incident particle. It also depends upon the identity, state of excitation, orientation, and electric and magnetic environment of the target nucleus. It is these dependencies that are exploited in the analysis of materials.

If, in the general nuclear reaction described above, there is no projectile particle (a), the reaction corresponds to a spontaneous radioactive decay of the nucleus, or a fission decay of the nucleus: X → Y + b + Q or X( ,b)Y. Often, the nucleus that results when a projectile collides with a target nucleus will itself be unstable against radioactive or fission decays. The details of the decay can then yield information about the original reaction.

Such a decay is characterized by a Q value and by a half-life, T_1/2, the time required for one-half of the initial number of unstable nuclei to decay. The particles emitted in decays of unstable nuclei are known as nuclear radiation, and their interactions with matter are useful in materials analysis.

Under some circumstances, projectiles that impinge on a sample of material interact with more than one nucleus or atom. This type of continuous or extended interaction between the projectile and bulk matter typically results in the attenuation or slowing of the incident particle beam, or some alteration of the properties of the particle beam.

In the majority of applications of nuclear physics principles to materials analysis, a beam of particles or electromagnetic radiation is caused to interact in some way either with individual nuclei or with a large number of atoms and nuclei in the sample under investigation.

The results of the interaction can then be interpreted--using concepts such as the cross section, Q value, and half-life--to yield information about the composition, structure, and properties of the material.

In a typical application of a nuclear reaction or scattering to materials analysis, a beam of particles of known energy and polarization is directed at a sample of the material. The degree of interaction between the projectiles and the various target nuclei in the sample is measured by determining the attenuation of the beam, detecting the reaction products, or measuring the energy, polarization, and direction of the scattered projectile particles. These measurements allow for the determination of the reaction or scattering cross sections. Since the cross sections depend upon the properties of the target nuclei, the presence of specific types of nuclei may be verified and quantified. Other properties of the target nuclei, such as polarization, state of excitation, and electric and magnetic properties, can also be determined from such a cross-section measurement.

Many different types of projectiles are employed. The most commonly used projectiles are stable charged particles that can be accelerated directly by various types of accelerators.

These include electrons, protons, and nuclei; the latter are usually referred to as ions, since they are generally not bare nuclei, but retain one or more electrons of the atoms from which they came. The α particle, which results from certain radioactive decays and has always been a mainstay of nuclear research, is an example of such an ion (the nucleus of a helium atom).

Similarly, the β radiation that results from some radioactive decays consist of high-energy electrons. Accelerators are also capable of producing beams of unstable charged particles such as muons, antiparticles, mesons, and radioactive nuclei. These unstable particles are produced in reactions that occur at the target of a primary accelerator beam and are then subsequently focused into a secondary beam. Beams of neutral particles such as neutrons and neutrinos can be produced in a similar fashion. Finally, sources of electromagnetic radiation can provide beams of photons with a wide range of energies. These sources include synchrotrons as well as radioactive nuclei, which decay by means of γ-ray emission.

The radioactive or fission decay of unstable nuclei can be utilized for purposes of materials analysis in two primary ways. The first utilizes the characteristics of the nuclear radiation emitted by unstable nuclei as a signature for the presence of those nuclei. The amount of such radiation fixes the quantity of those unstable nuclei in the sample. The unstable nuclei may occur naturally in the sample of material or may be artificially produced by bombarding the sample with appropriate projectiles. This method of artificially producing unstable nuclei is known as activation analysis. Although predominantly achieved by bombarding the sample with neutrons, activation analysis can also be carried out using charged particles as projectiles. The second use of radioactive decay and nuclear fission is as a source of nuclear radiations. Nuclear radiations can be used as primary sources for an accelerator beam, which is then exploited as described above. The nuclear radiations can also be used directly through their interactions with bulk matter to carry out materials analysis.

The various nuclear radiations interact with matter in characteristic ways that can be exploited for analysis of materials. Nuclear radiations are of four basic classes: heavy charged particles with masses comparable to nuclear masses (protons, α particles, nuclei), light charged particles (elecrons and their antiparticles, positrons), electromagnetic radiations (γ rays and X rays), and neutrons. Mesons, such as pions and muons, which are often involved in nuclear processes, have behaviors that fall between those of the light and the heavy charged particles.

Heavy charged particles of a fixed energy travel a well-defined distance, or range, before coming to rest in matter. These particles lose energy in small increments primarily by means of the excitation and ionization of the atoms of the matter. The range of the charged particle depends on the density of the material through which it travels, as well as the ionization potential and atomic number of the atoms of the material (identity of the atoms).

Light-charged particles lose energy by means of two mechanisms: ionization of the atoms of the material through which they travel; and bremsstrahlung, which is electromagnetic radiation that is caused by the scattering of charged particles. Bremsstrahlung becomes relatively more important as the energy of the charged particle increases. Since light-charged particles are more easily deflected than their heavy counterparts, their range in matter is not well defined.

These particles exhibit a phenomenon known as straggling, an erratic path through matter. In spite of this, the interaction of light charges with matter is dependent upon the properties of the absorbing material.

Electromagnetic radiations or photons interact less effectively with matter, since they are electrically uncharged. Nevertheless, photons do interact with the material through which they travel by scattering and absorption. At low incident energies, photons are predominantly absorbed by means of the photoelectric effect. At intermediate incident energies, the photon energy is gradually degraded by Compton scattering, while at high energies the process of pair production removes photons from the incident beam. These three mechanisms cause the photon beam to be exponentially attenuated over a characteristic distance that is dependent upon the nature of the absorbing medium.

Neutrons interact with matter by means of two main mechanisms that differ from those described above because of the uncharged nature of the neutron. These two mechanisms are absorption by atomic nuclei and the scattering of neutrons caused by the interaction of the neutron's magnetic field with the magnetic field of the material through which it travels. While the cross sections for the various interactions of charged particles and photons with matter change in a smooth way with the atomic number of the absorbing material, neutrons exhibit cross sections that change erratically from one nuclear species to the next. This makes neutrons very useful for the identification of specific nuclei.

Applications

The great variety of observed nuclear interactions contributes to their versatility as a tool for materials analysis. This variety also prohibits a comprehensive description of all the materials analysis techniques that, in one way or another, utilize nuclear interactions.

The use of nuclear scattering in materials analysis is exemplified by the interaction of neutrons with matter. When a fast neutron moves through matter, it undergoes scattering by the individual nuclei of the matter, losing some energy in each scattering event. The amount of energy lost in each event depends upon the mass of the scattering nucleus. The less massive the nucleus, the greater the energy loss of the neutron. The neutron continues to undergo these scatterings until its energy is of the same order as the thermal energy of the material through which it moves. The neutron is then known as a thermal neutron. Thermal neutrons have a high probability (or large cross section) of being captured by nuclei, although the cross section varies considerably with the species of nucleus.

One application of this scattering of fast neutrons and absorption of thermal neutrons is to well logging, which is carried out by the drilling industry to probe geologic formations and locate petroleum and hydrocarbon resources. Fast neutrons are generated in miniaturized accelerators that can be lowered into test wells. The accelerator produces fast neutrons by bombarding a tritium (a heavy isotope of hydrogen) target with an accelerated deuteron (another heavy isotope of hydrogen) beam.

One possible result of the interaction of the neutrons with the surrounding material is the production of γ rays caused by the inelastic scattering of the fast neutrons by carbon nuclei. The yield of such γ rays is dependent upon the identity of the scattering nuclei and can therefore be used to establish the quantity of carbon present in the material surrounding the test wall. The presence of carbon indicates that hydrocarbons, such as oil or gas, may be present.

A second possible result of the interaction of neutrons with surrounding material is the production of a well-defined thermal neutron pulse that is caused by the rapid slowing of the fast neutrons by hydrogen (the nucleus that has the smallest mass). A short-duration thermal neutron pulse signals the presence of chlorine in addition to hydrogen, since chlorine is a very effective absorber of thermal neutrons (high-absorption cross section), and indicates the presence of saltwater. If the thermal neutron pulse is relatively long-lasting, the presence of chlorine is not indicated, and hydrocarbons may be present.

Excellent examples of the application of nuclear reactions to materials analysis are provided by the interaction of ion beams with matter. Accelerators are capable of producing intense beams of a variety of ions that have a wide range of beam energies.

Most nuclear reactions exhibit a very sharp resonance behavior in their cross sections.

That is, the probability of the reaction occurring is very sensitive to the energy of the projectile and is significant only within a narrow range. When an ion beam of a specific energy is incident on a sample of material, its energy decreases in a well-understood way. The beam has a range that depends on the incident energy and the material through which the beam travels. These properties of the ion beam may be used to determine the depth distribution of impurity atoms or nuclei embedded in materials. This technique has excellent depth resolution--about 5 nanometers. It is also highly sensitive and can detect impurity concentrations as low as 1 part per million. The detection of impurities and their distribution within a sample of material finds application in the characterization of doped semiconductor materials, in the determination of hydrogen contamination of metals, which causes them to become brittle, and in the measurement of contamination of components used in nuclear reactors.

Another application of ion beams to materials analysis is ion implantation. Accelerated beams of ions (nuclei) can be implanted into a target crystal at any desired depth. This is caused by the specific range that ions of a given energy have in a particular material. The information gained by this implantation technique is the result of the interaction between the electromagnetic environment of the host crystal. These interactions give information about the vibrational modes of the crystal, and the electric and magnetic properties of the crystal, among other things. This is one of the few methods available for the study of magnetic properties of materials on the microscopic scale, and is valuable for the development of new materials with specific magnetic properties.

The interactions of various projectiles with bulk matter provide another source of information about materials. In general, as described above, charged particles lose their incident energy over some characteristic distance as they travel through a sample of material. When the target material is a crystal, the energy loss of both heavy and light charged projectiles may be strongly influenced by the orientation of the crystal. Particles that are incident along a relatively open crystallographic direction have minimal energy loss per unit length, penetrating unusually deeply into the material. Along these directions, the adjacent rows of atoms of the crystal lattice structure form "tunnels" within which the projectile particles encounter very little scattering. This process, known as channeling, is very useful in the study of the structure and properties of crystalline materials. The crystal structure can be investigated and the locations of impurities and some of the impurity properties can be determined.

The development of intense positively and negatively charged muon beams has provided another tool for the investigation of properties of materials. Muons are members of a class of elementary particles known as mesons, and are produced as a result of some nuclear reactions. Muons are similar to electrons but have masses that fall between those of electrons and protons. Muons are also unstable, decaying into lighter particles (electron and neutrinos). The electron and its antiparticle, the positron, have been used for some time in the study of materials, but the muon, with its intermediate mass and decay characteristics, is a valuable new probe of materials, complementing the use of electrons, positrons, and heavy charged particles. A unique property of the muons produced in accelerators is the nearly 100 percent spin polarization of the beam. Since nearly all muons are initially oriented toward the same direction, any alteration of the beam's polarization as it passes through a sample of material can be related to the magnetic properties of the material. This technique of muon spin rotation complements other magnetic sampling techniques such as neutron scattering, Mossbauer spectroscopy, and nuclear magnetic resonance (NMR) spectroscopy.

Context

The quest to understand the fundamental structure of matter has been the primary driving force behind the development of the physical sciences. Therefore, although it is usually viewed as a relatively recent technological application, materials analysis has in fact been a subject of study for a very long time. In some sense, speculation about and inquiry into the composition and structure of matter has been evolving and intensifying since the earliest philosophical considerations of Democritus, Epicurus, and Lucretius in ancient Greece. While these early speculations concerning the nature of materials are quite different from the modern techniques that are applied, they serve to emphasize that there is a strong link between materials analysis and the types of probes that are available.

A history of the development of materials analysis is very much a history of the isolation, characterization, and manipulation of new, ever smaller and more energetic particles or radiations. As knowledge of the fundamental structure of matter has opened up the realms of the atom, the nucleus, and the elementary particle, the newly discovered particles and radiations have served as probes of still deeper and more fundamental structure.

This progression began with the development of chemistry in the eighteenth and nineteenth centuries. The work of Robert Boyle, Antoine-Laurent Lavoisier, Joseph-Louis Proust, John Dalton, and others clarified the rules governing the behavior of atoms and molecules, and in so doing provided a technique that could be applied to the analysis of materials--chemical analysis. The combined investigations of James Clerk Maxwell, Wilhelm Conrad Rontgen, and Sir Joseph John Thomson, among others, indicated a deeper structure within the atom. Ernest Rutherford, Niels Bohr, and Albert Einstein each contributed to the understanding of that deeper structure in the form of a model of the nuclear atom. As a result, new probes in the forms of ions and electrons became available. With the theoretical framework of quantum mechanics provided by Werner Heisenberg, Erwin Schrodinger, and Paul Adrien Maurice Dirac, and probes resulting from radioactive decay, the structure and components of the nucleus itself were revealed, and neutrons, protons, and other more exotic particles could be used as probes of materials. Simultaneous with the discovery of new and different particles was the development, by Robert Van de Graaff, Ernest Orlando Lawrence, and others, of new accelerator technologies for the production of higher-energy beams of those particles.

Work on a more detailed understanding of the nucleus and the nuclear force holds the promise of new techniques and probes for the investigation and characterization of the properties of materials. These techniques, based upon principles of nuclear physics, complement atomic, acoustic, chemical, and other methods for the analysis of materials. In addition, many of the materials analysis techniques that are based on nuclear physics principles are being used for the development of tailor-made materials with specific properties.

Principal terms

BULK MATTER: a sample of a material that consists of a very large number of atoms and nuclei

CROSS SECTION: the measure of the probability that a specific type of reaction or scattering process will occur

ELECTROMAGNETIC RADIATION: electromagnetic waves, or photons, that span all parts of the electromagnetic spectrum, from radio waves to γ rays

FISSION: the decay of an unstable nucleus in which the two products of the decay are of comparable mass polarization

PROJECTILE: a particle (including the photon) that has a known energy and direction and that is used to produce a collision with a target

NUCLEAR RADIATION: particles or electromagnetic radiations resulting from the decay of a nucleus, including α particles, β radiation, γ radiation, neutrons, and nuclei

NUCLEAR REACTION: the interaction of an atomic nucleus with a projectile, or the decay of an unstable nucleus

NUCLEAR SCATTERING: a nuclear reaction in which the projectile and the target nucleus are identical to the scattered particle and the resulting nucleus

RADIOACTIVE DECAY: the decay of an unstable nucleus by the emission of α, β, or γ nuclear radiation

TARGET: an individual nucleus or a sample of bulk matter at which a projectile is directed

Bibliography

Asimov, Isaac. THE HISTORY OF PHYSICS. New York: Walker, 1984. This is a republication of Asimov's outstanding three-volume set, UNDERSTANDING PHYSICS. Gives a fascinating historical account of the development of physics in general, and in part 3, Asimov specifically considers the structure of the atom.

Hodgson, P. E. GROWTH POINTS IN NUCLEAR PHYSICS. 3 vols. Elmsford, N.Y.: Pergamon Press, 1980-1981. This series of small books contains short articles dealing with advances in nuclear physics and their applications in the late 1970's and early 1980's. Written for the nonspecialist, these remain a valuable resource.

Pais, Abraham. INWARD BOUND. New York: Oxford University Press, 1986. This book is similar to the volume by Segre mentioned below, but it is far more detailed both scientifically and historically. Contains extensive footnotes and references original scientific works. The subject index and index of names are very detailed.

Rozsa, Sandor. NUCLEAR MEASUREMENTS IN INDUSTRY. New York: Elsevier, 1989. This book gives many detailed examples of the application of nuclear physics principles to industrial situations, such as density and thickness measurements and determination of moisture content. Although much numerical information is provided, the text can be followed easily by the layperson.

Segre, Emilio. FROM X-RAYS TO QUARKS. New York: W. H. Freeman, 1980. This volume presents an excellent qualitative description of the development of modern nuclear and particle physics from 1895 through the 1970's. In addition to the excellent presentation of scientific discoveries, some fascinating personal glimpses are included. Ten appendices provide mathematical details for the interested student.

Trefil, James. FROM ATOMS TO QUARKS. New York: Charles Scribner's Sons, 1980. A popular work that has elementary particle physics as its main emphasis. Contains several chapters that deal with nuclear physics in general and accelerators in particular.

Nuclear Reactions and Scattering

Radiation: Interactions with Matter

Radioactive Nuclear Decay and Nuclear Excited States