Displacements per atom

A commonly used measure of irradiation damage is displacements per atom (dpa). A unit of 1 dpa means that on the average, every atom in the irradiated volume has been displaced once from its equiUbrium lattice site. The approximated dpa in the implanted region is given by equation 16 where 0 (ions/cm ) is the dose, and (NJE)) is the damage function given by equation 14. 

As discussed earlier, the first wall materials in next generation machines will receive from 0.005 to 30 displacements per atom. At the lower end of this range (<0.01 dpa) there are essentially no mechanical property changes expected in graphite materials. However, even at these low doses thermal conductivity and stored energy are of concern. For displacement levels >0.01 dpa other property... 

Displacement damage function, 14 436 Displacement desorption, factors governing choice of method, l 614t Displacement plating, 24 141 Displacements per atom (dpa), 14 436 Displays... 

To compare doses resulting from different types of radiation it is necessary to formulate a measure of radiation effects on the crystal structure doses can be recalculated to the number of displacements per atom (dpa). A dose of 0.1 dpa, for example, means that one of ten atoms was displaced from its initial position. Equivalent values in dpa units may be calculated for different types of radiation from the effects of its interaction with the crystal lattice. To recalculate a-dose to dpa the following formula is used ... 

According to the SRIM code (www.srim.org), lO cm Si ions introduced by the elastic energy losses about 130 displacements per atom (dpa), while Xe ions - less than 0.014 dpa. On the other hand, electronic energy losses of Si ions were -0.2 keV/nm, while for SHI they achieved 14keV/nm. Therefore, Si segregation and growth of the nanoprecipitates under Xe ion irradiation were mainly due to the electronic energy losses of SHI. 

The expression displacements per atom (dpa) is a quantity very often used for comparing the damage caused by ion bombardment in different targets by different types of bombarding particles. In most cases the displacements per atom are normalized to the total number of target atoms or atoms in a certain region of the target. 

In the ion beam experiments, the beam-current density is measured and converted to a flux, ion/cm s. The fluence (in ions/cm experienced by the specimen is the flux multiplied by time. In many papers, the measured fluence is converted to an ion dose in units of displacements per atom (dpa). This is essentially a measure of the actual amount of damage (i.e. number of atomic displacements) that results from cascade formation, but it does not consider subsequent relaxation or recrystallization events. The fluence-to-dose... 

Radiation Energy (mev) Flux (om seo-i) Time No. of displacements per atom in copper... 

The X-ray patterns shown in Figure 3 was obtained on a 500 Ma monazite containing 13% Th and 0.25% U. It can be calculated that this monazite experienced about 7 X 10 a/g. Meldrum et al. (1998) estimated that each a-decay in monazite produces 860 displacements. So this monazite should have suffered 3.7 displacements per atom, or one order of magnitude greater that the minimum dose necessary to make a mineral amorphous (Meldrum et al. 1997a). The crystalline integrity of this grain indicates that a mechanism must exist that is able to naturally restore monazite structure. 

Normally in implanted crystals, the resistance decreases very rapidly for displacement per atom (dpa) values below 1. Above 1, a saturation is observed and this indicates that the maximum o value due to disorder is reached. This happens if all the atoms have been displaced once. In MgO thin films for the fluence of 10 ions cm, it is noted that the films are not channeling amorphous as was demonstrated by XRD and RBS analysis. The increase in conductivity with fluence is attributed to the increase in the accumulation of the implanted ions in the crystal lattice. Also, it is revealed that the temperature dependence condnctivity with ln(a) being proportional to T" and T" ", and, therefore, electron transport occurs through a variable range hopping process in addition to the thermal process. 

The papers [72,73] give experimental results that fit the theoretical Shen model described earlier [65]. The Cu nanocrystals of 2.5.nm implanted into the Si02 matrix were irradiated with zinc ions of 5 MeV at -197°C. It has been established that a relatively low radiation dose of 0.16 displacement per atom (dpa) causes amorphization of copper [72]. The copper nanocrystals having a little bit larger size of 8 nm were not amorphized after exposure to the radiation by a considerably larger dose [73],... 

Stable operation of the demonstration reactor BN-600 in Russia with a nominal power output of 600MW(e) for 20 years and an average load factor of 72%, successful operation of the prototype reactors BN-350 in Kazakshstan and Phenix in France as well as the reliable operation of MOX fuel at high bumup (20% witti an irradiation dose in excess of 160 displacement per atom (dpa) in the cladding) in PFR (UK) and Phenix, are milestone in the implementation of LMFR technology. 

Studies carried out in some Member States showed that even low neutron irradiation doses (of about 2 displacements per atom) has significant effects on near-core structural material at low and high temperature. It was observed that near core structures — permanent for 40-50 years of service — have exhibited degradation due to the neutron environment. 

Both in Europe and Japan low carbon stainless steel of type 316L with controlled addition of nitrogen is recommended for use even at low temperature. At doses above about 15 displacements per atom the degree of embrittlement and the level of swelling in all materials tested are probably unacceptable for use in critical fixed reactor components. 

Immediately before refuelling operations in PFR three sweep arms were employed to ensure that there were no obstructions above the core which would prevent rotation of the rotating shield, as shown in Figure 8.1. At the start of a reload in 1988 the sweep arms were found to contact or partially contact objects in two core positions. These positions were identified as containing subassemblies with cold-worked EN58B steel wrappers, with a calculated dose of greater than 60 displacements per atom (dpa). 

In order to calculate P-T curves, values of toughness are needed at the 14-thickness and %-thickness locations in the RPV wall. Calculations are usually performed to determine the attenuation of neutron flux/fluence from the inside surface of the RPV into the wall. The best available method for making these projections is to use displacements per atom (dpa) as the measure of fluence change since dpa takes into account the change in neutron spectra that occurs as the neutrons are attenuated. Regulatory Guide 1.99, Revision 2 uses this approach and specifies a generic exponential decay function (f = where fx is fluence at depth x in RPV wall,... 

Another significant change was the attenuation model for fluence through the vessel wall. In Revision 1, the attenuation model used a fast neutron exposure (n/cm, E > 1 MeV) as the attenuated fluence, whereas Revision 2 used a displacements per atom (dpa) model for attenuation through the vessel wall. The attenuation using dpa is less than for fast neutron, which means that the projected embrittlement at 14-thickness and %-thickness is higher using the dpa model. 

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