“Nothing in Life is to be Feared. It is Only to be Understood.”

—Marie Curie

Interactions of high-energy radiation such as a-, b-, and, y-rays as well as subatomic particles such as electrons, protons, and neutrons with crystal lattices give rise to defects/imperfections such as vacancies, self-interstitials, ionization, electron exci­tation, and so on. Fission fragments and neutrons cause the bulk of the radiation damage. Other types of radiation either do not have enough energy or are not pro­duced in sufficient number density to cause any major radiation damage. In a nuclear reactor scenario, the microscopic defects produced in materials due to irradiation are referred to as radiation damage. These defects result in changes in physical, mechanical, and chemical properties, and these macroscopic material property changes in aggregate are referred to as radiation effects. Before discussing the effects of radiation on various properties, we need to know how to describe the radiation damage in a quantitative fashion. The timescales in which the damage and effects take place are quite different. While radiation damage events take place within a short time period of around 10~n s or less, the radiation effects occur in a relatively large timescale ranging from milliseconds to months. Radiation effects range from the migration of defects to sinks that takes place in milliseconds to changes in physical dimensions due to swelling and so on with much longer dura­tion. Quantitative characterization of radiation damage is covered in this chapter, while radiation effects are discussed in Chapter 6 after descriptions of various prop­erties of materials. We mainly consider neutron irradiation here and the reader is referred to other monographs for damage calculations when charged particles (such as heavy ions and protons) and photon (such as y-ray) irradiations are involved.

The binding energy of lattice atoms is very small (~10-60 eV) compared to the energy of the impinging particles so that a scattering event between them results in the lattice atom getting knocked off from its position. The atom will generally have such a high energy that it can interact with another lattice atom that will also get knocked off from the lattice position. The atom that was knocked off by the incoming high-energy particle is known as “primary knock-on atom” or PKA, which in turn knocks off a large number of atoms before it comes to rest in an interstitial position, thereby creating a Frenkel pair in which case the atom is

An Introduction to Nuclear Materials: Fundamentals and Applications, First Edition.

K. Linga Murty and Indrajit Charit.

© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

considered to have been “displaced.” However, if the atom is in proximity to a vacancy, it would occupy the vacant lattice position in which case it becomes a “replacement collision.” Thus, in general, a PKA can lead to a large number of higher order knock-on atoms (also known as recoil atoms and/or secondary knock — on atoms) resulting in many vacant lattice sites and this conglomeration of point defects is known as “displacement cascade.” If during these collision processes many nuclei go into higher energy states at their lattice position, thermal spike is created. Before the particle-lattice atom interactions, the incoming particle may interact with electrons leading to ionization. As will be seen later, there is an elec­tron energy cutoff above which no additional atomic displacements take place until the particle energy becomes lower than this cutoff value, as envisioned in the Kin­chin-Pease (K-P) model.

Brinkman [1] first came up with the displacement spike model, as shown in Figure 3.1a. In this model, PKA motion creates a core consisting of several vacan­cies surrounded by a periphery rich in interstitials. Later, Seeger [2] further refined the concept and showed that vacant lattice sites in proximity lead to zones devoid of atoms commonly referred to as depleted zones (Figure 3.1b). However, if these regions are large enough, they form voids that lead to decreased density or volume increase known as “swelling.” In cases where elements such as B, Ni, and Fe are present, (n, a)[1]* reactions will lead to the production of He that will stabilize these voids, in which case they are referred to as “cavities”. These cavities once formed are stable and cannot be removed by thermal annealing.

The following are the radiation defects induced by intense nuclear radiation, in particular high-energy {E > 0.1 MeV} neutrons:

• Vacancies.

• Interstitials.

• Impurity atoms — produced by transmutation.

• Thermal spikes — regions with atoms in high-energy states.

• Displacement spikes — regions with displaced atoms, vacancies, self-interstitials (Frenkel pairs) produced by primary and secondary knock-on atoms.

• Depleted zones — regions with vacancy clusters (depleted of atoms).

• Voids — large regions devoid of atoms.

• Bubbles — voids stabilized by filled gases such as He produced from (n, a) reactions with B, Ni, Fe, and so on.

• Replacement collisions — scattered (self) interstitial atoms falling into vacant sites after collisions between moving interstitial and stationary atoms and dissi­pating their energies through lattice vibrations.

A flux of neutrons then results in a large number of PKAs, which in turn produce higher order knock-on atoms, as illustrated in Figure 3.1. Our goal is to first calculate the number of PKAs produced due to a flux of neutrons with a range of energies comprising the neutron spectrum. Next step is to find the number of knocked-on atoms due to these PKAs with varied energies. Integration through the

whole neutron spectrum then yields the number of atoms displaced. The displace­ments per atom or dpa will give us a measure of quantitative radiation damage that can be later related to changes in the macroscopic properties of materials due to the given neutron spectrum. Earlier, the total fluence or dose (flux x time) in units of n cm-2 was commonly used, but this does not take into account the different spectral variations, and so dpa is a far better unit. It is commonly observed that the properties of irradiated materials depend on the specific neutron spectrum to which they are exposed and thus will be different for the same total neutron

dose. Figure 3.2 clearly demonstrates this behavior. The example here shows the correlation for mechanical properties, while other such relations can be found for other properties such as physical, thermal, electrical, and so forth, which are gener­ally referred to as radiation effects. It is important to note that many atomic dis­placements occur due to neutron-lattice interactions, but only a small fraction (~1%) survive since most of the defects anneal out in situ during irradiation mainly due to the proximity of the defects to the appropriate sinks and mutual recombination of vacancies and interstitials.

3.1