22.08.2015   Comprehensive nuclear materials

Damage Rate Effects

As differences in dose rates can confound direct comparison between neutron and ion irradiations, it is important to assess their impact. A simple method for examining the tradeoff between dose and temper­ature in comparing irradiation effects from different particle types is found in the invariance requirements. For a given change in dose rate, we would like to know what change in dose (at the same temperature) is required to cause the same number of defects to be absorbed at sinks. Alternatively, for a given change in dose rate, we would like to know what change in temperature (at the same dose) is required to cause the same number of defects to be absorbed at sinks. The number of defects per unit volume, NR, that have recombined up to time t, is given by Mansur14

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t

 

Ci Cv dt

 

[12]

 

Nr

 
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0

 
image487
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where kSj is the strength of sink j and Cj is the sink concentration. The ratio of vacancy loss to interstitial loss is

 
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Nsv

Nsi

 

[14]

 

Rs

 

where j = v or i. The quantity Ns is important in describing the microstructural development involving total point defect flux to sinks (e. g., RIS), while Rs is the relevant quantity for the growth of defect aggregates such as voids that require partitioning of point defects to allow growth. In the steady-state recombination dominant regime, for Ns to be invariant at a fixed dose, the follow­ing relationship between ‘dose rate (K) and temperature (Ti)’ must hold:

 

Figure 9 shows plots of the relationship between the ratio of dose rates and the temperature difference required to maintain the same point defect absorption at sinks (a), and the swelling invariance (b).

The invariance requirements can be used to prescribe an ion irradiation temperature-dose rate combination that simulates neutron radiation. We take the example of irradiation of stainless steel under typical BWR core irradiation conditions of ^4.5 x 10-8 dpa s-1 at 288 °C. If we were to conduct a proton irradiation with a characteristic dose rate of 7.0 x 10-6dpas-1, then using eqn [15] with a vacancy formation energy of 1.9 eV and a vacancy migration

 

£M t

 

[15]

 
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where Evm is the vacancy migration energy. In the steady-state recombination dominant regime, for Rs to be

 

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Figure 9 Temperature shift from the reference 200 °C required at constant dose in order to maintain (a) the same point defect absorption at sinks, and (b) swelling invariance, as a function of dose rate, normalized to initial dose rate. Results are shown for three different vacancy migration energies and a vacancy formation energy of 1.5 eV. Adapted from Mansur, L. K. J. Nucl. Mater. 1993, 206, 306-323; Was, G. S. Radiation Materials Science: Metals and Alloys; Springer: Berlin, 2007.

 

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Подпись: Table 2 Minimum displacement energies in pure metals, semiconductors, and stainless steel (SS) Materials Al Cgraph Cu Fe Ge Mo Ni W Si SS Tm(eV) 16 25 19 17 15 33 23 41 13 18
Подпись: Source: Lucasson, P. In Fundamental Aspects of Radiation Damage in Metals; Robibnson, M. T., Young, F. W., Jr., Eds.; ERDA Report CONF-751006; 1975; p 42; Andersen, H. H. Appl. Phys. 1979, 18, 131.

energy of 1.3 eV, the experiment will be invariant in Ns with the BWR core irradiation (e. g., RIS) at a proton irradiation temperature of 400 °C. Similarly, using eqn [16], a proton irradiation temperature of 300 °C will result in an invariant Rs (e. g., swelling or loop growth). For a Ni2+ ion irradiation at a dose rate of 10~3 dpas, the respective temperatures are 675 °C (Ns invariant) and 340 °C (Rs invariant). In other words, the temperature ‘shift’ due to the higher dose rate is dependent on the microstructure feature of interest. Also, with increasing difference in dose rate, the AT between neutron and ion irradiation increases substantially. The nominal irradiation tem­peratures selected for proton irradiation, 360 °C and for Ni2+ irradiation, 500 °C represent compromises between the extremes for invariant Ns and Rs.