22.08.2015   Comprehensive nuclear materials

Review of Aspects of Radiation Damage Relevant to Ion Irradiation

1.07.3.1 Defect Production

The parameter commonly used to correlate the dam­age produced by different irradiation environments is the total number of displacements per atom (dpa). Kinchin and Pease7 were the first to attempt to deter­mine the number of displacements occurring during irradiation and a modified version of their model known as the Norgett-Robinson-Torrens (NRT) model8 is generally accepted as the international standard for quantifying the number of atomic dis­placements in irradiated materials.9 According to the NRT model, the number of Frenkel pairs (FPs), nNRT(T), generated by a primary knock-on atom (PKA) of energy T is given by

kEd(T )
2 Ed

where ED(T) is the damage energy (energy of the PKA less the energy lost to electron excitation), Ed is the displacement energy, that is, the energy needed to displace the struck atom from its lattice position, and к is a factor less than 1 (usually taken as 0.8). Integration of the NRT damage function over recoil spectrum and time gives the atom concentration of displacements known as the NRT displacements per atom (dpa): f(E)vNRT(T)a(E, T)dTdE where f(E) is the neutron flux and s(E, T) is the proba­bility that a particle of energy E will impart a recoil energy Tto a struck atom. The displacement damage is accepted as a measure of the amount of change to the solid due to irradiation and is a much better measure of an irradiation effect than is the particle fluence. As shown in Figure 1, seemingly different effects of

image467image468

Figure 1 Comparison of yield stress change in 316 stainless steel irradiated in three facilities with very different neutron energy flux spectra. While there is little correlation in terms of neutron fluence, the yield stress changes correlate well against displacements per atom (dpa). Reprinted, with permission, from ASTM, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.

Подпись: Figure 2 Energy spectrum for neutrons from a variety of reactor types and a monoenergetic proton beam. Reproduced from Stoller, R. E.; Greenwood, L. R. J. Nucl. Mater. 1999, 271-272, 57-62.
Подпись: Figure 3 Displacement-damage effectiveness for various energetic particles in nickel. Reproduced from Kulcinski, G. L.; Brimhall, J. L.; Kissinger, H. E. In Proceedings of Radiation-Induced Voids in Metals; Corbett, J. W., laniello, L. C., Eds.; USAEC Technical Information Center: Oak Ridge, TN, 1972; p 453, CONF-710601.

irradiation on low temperature yield strength for the same fluence level (Figure 1 (a)) and disappear when dpa is used as the measure of damage (Figure 1(b)).

A fundamental difference between ion and neu­tron irradiation effects is the particle energy spectrum that arises because of the difference in the way the particles are produced. Ions are produced in accel­erators and emerge in monoenergetic beams with very narrow energy widths. However, the neutron energy spectrum in a reactor extends over several orders of magnitude in energy, thus presenting a much more complicated source term for radiation damage. Figure 2 shows the considerable difference in neutron and ion energy spectra and also between neutron spectra in different reactors and at different locations within the reactor vessel.

Distance into solid (m)

Another major difference in the characteristics of ions and neutrons is their depth of penetration. As shown in Figure 3, ions lose energy quickly because of high electronic energy loss, giving rise to a spa­tially nonuniform energy deposition profile caused

by the varying importance of electronic and nuclear energy loss during the slowing down process. Their penetration distances range between 0.1 and 100 pm for ion energies that can practically be achieved by laboratory-scale accelerators or implanters. By virtue of their electrical neutrality, neutrons can penetrate very large distances and produce spatially flat dam­age profiles over many millimeters of material.

Further, the cross-section for ion-atom reaction is much greater than for neutron-nuclear reaction giving rise to a higher damage rate per unit ofparticle fluence. The damage rate in dpa per unit of fluence is propor­tional to the integral of the energy transfer cross-section and the number of displacements per PKA, nNRT(T):

 

recoil atom to other target atoms. The fraction of recoils between the displacement energy Ed, and T is

 
image471

image472

T (eV)

Figure 4 Integral primary recoil spectra for 1 MeV particles in copper. Curves plotted are the integral fractions of primary recoils between the threshold energy and recoil energy, Tfrom eqn [6]. Reproduced from Averback, R. S.

J. Nucl. Mater. 1994, 216, 49.

 

a(E, r>NRT(T)dr

 

A

N f

 

[3]

 

Ed

 

where Rd is the number if displacements per unit vol­ume per unit time, N is the atom number density, and f is the particle flux (neutron or ion). In the case of neutron-nuclear interaction described by the hard — sphere model, eqn [3] becomes

 

_Rd_

N f

 

[4]

 

where g = 4mM/(m + M)2, M is the target atom mass, m is the neutron mass, E is the neutron energy, and ss is the elastic scattering cross-section. For the case of ion — atom interaction described by Rutherford scattering, eqn [3] becomes

Rd_ TCZ^e4 /Mj gE

NI = 4EEd M2 Ej ’ []

 

E 106 105

 

1 MeV electrons T =60 eV e = 50-100%

 

where e is the unit charge, M1 is the mass of the ion, and M2 is the mass of the target atom. As shown in Figure 3, for comparable energies, 1.3 MeV protons cause over 100 times more damage per unit of fluence at the sample surface than 1 MeV neutrons, and the factor for 20 MeV C ions is over 1000. Of course, the damage depth is orders of magnitude smaller than that for neutron irradiation.

 
image473

1 MeV protons T=200eV e = 25%

 

103

 

102’Tp Te

-101

 

1 MeV heavy ions T =5keV e = 4%

 

E

 

E