*3.3. Influence of Radiation Defects on Elastic Properties*

The effects of different vacancy types on elastic properties are shown in Figure 5. According to experimental results, the concentrations of Cr and Al in FeCrAl are generally from 12 wt.% and 5% respectively. In this work, the Fe8Cr5Al and Fe13Cr5Al alloys were selected as examples to show the effects of radiation defects on elastic constants. From these figures, it is clear that after the formation of radiation-induced vacancies, the *C*11, *C*12, *C*44, bulk modulus and shear modulus of these two alloys decrease in comparison to the perfect state. It should also be noted that when the vacancy clusters are formed, these elastic constants decrease slightly or are kept constants and then increase with an increase of vacancy cluster size but decrease of the number of vacancy clusters. The K/G value remains around 2.30, larger than 1.75, which is still a ductility alloy according to Pugh's rule [30].

The dependence of elastic properties on different numbers of dumbbell interstitials are shown in Figure 6 for Fe8Cr5Al and Fe13Cr5Al alloys. It is also clear that *C*11, *C*<sup>44</sup> and shear modulus decrease when the interstitials are formed in these two alloys. However, *C*<sup>12</sup> and bulk modulus increase when the number of interstitials increases, different from the results of *C*11, *C*<sup>44</sup> and shear modulus. Therefore, according to the definitions of bulk and shear modulus, it can be understood from the present results that the formation of interstitials could increase the ability of the alloys to resist the volume change under the effect of pressure but decrease the ability to resist the torsion applied on alloys. When

the materials are applied in a nuclear reactor, the interaction between dislocations and these interstitials could further affect the mechanical properties. Thus, the present results indicate that the formation of an interstitial should be included, even if these interstitials are distributed separately and before their interaction with dislocations.

**Figure 5.** (**a**–**e**) The effects of vacancy and void on *C*11, *C*12, *C*44, bulk modulus and shear modulus, (**f**) shows the value of K/G as a function of vacancy type. In these figures, *n* is the number of vacancies in each vacancy cluster or void and *m* is the number of vacancy clusters or voids.

When the Cr-rich precipitates are formed, the dependence of elastic properties on numbers of Cr precipitates are shown in Figure 7 for Fe8Cr5Al and Fe13Cr5Al alloys. From these results, it can be seen that after the Cr-rich precipitates are formed, these elastic properties of alloys increase but are kept as almost a constant, thus they are independent of the number and volume of precipitates. From previous studies, it is known that the precipitates would affect the mechanical properties. According to the present results, it can be understood that the effect of α precipitates on the mechanical properties of FeCrAl should be mainly due to their interaction with dislocations, different from the effects of vacancies, voids and interstitials, as shown in Figures 5 and 6. All results shown in Figures 5 and 6 indicate that an increase of Cr concentration would result in the decrease of elastic properties under the irradiation environment. Thus, the concentration of Cr in alloys should also be limited as indicated experimentally [3,9]. These results also indicate the radiation defects could result in larger decreases or increases of elastic properties than the Cr and Al concentrations. Furthermore, comparing the effects from vacancies, voids, interstitials and Cr-rich precipitates, it is clear that the interstitials have stronger effects on bulk and shear modulus than vacancies, voids and Cr-rich precipitates. It should also be noted the present results only consider the effects from radiation defects. The effect from the interaction between dislocations and radiation defects on mechanical properties should be investigated in future work.

**Figure 6.** (**a**–**e**) The dependence of *C*11, *C*12, *C*44, bulk modulus and shear modulus on number of dumbbell interstitials, (**f**) shows one example of statistical uncertainty for these elastic constants based on 50 simulations at 0 K.

**Figure 7.** (**a**–**e**) The dependence of *C*11, *C*12, *C*44, bulk modulus and shear modulus on number of Cr precipitates. (**f**) Example of statistical uncertainty for these elastic constants based on 50 simulations at 0 K.
