High Temperature Cascades

The next generation of nuclear reactors employing a graphite core will operate at 900◦C. To demonstrate the effect of the increased temperature cascades, the initial 20 directions have been simulated using an initial temperature of 900◦C and initial PKA energy 1000 eV. The results of two cascades simulations are presented below.

Figure 4.34 represents a cascade through graphite with the initial temperature set to 900◦C, initial PKA energy set to 1000 eV and the initial PKA direction 1 from table 3.1.

Figure 4.34:Graphite cascades with initial PKA energy 1000 eV after: (a) 0.04 ps, (b) 0.08 ps, (c) 0.18 ps, (d) 0.37 ps, (e) 0.71 ps and (f) 2.365 ps. Initial PKA direction 1 from table 3.1. Initial Temperatures (1)

900◦C and (2) 300◦C. The red circles denote interstitials and the blue squares denote vacancies. The path of each displaced atom is traced.

proceeds, secondary cascades begin to form, these can be observed in figures 4.34 (1c), (1d) and (1e). The cascade begins to stabilise, after 2.365 ps, figure 4.34 (1f). After the cascade has stabilised there are 15 interstitials and vacancies present in the cell. Figure 4.34 (2), shows the same cascade simulated at 300◦C. Figures 4.34 (1) and 4.34 (2) on the surface look close to being identical. Further analysis of the data produced highlights slight differences. The final number of interstitials and vacancies present in the cell in the 300◦C is 18, three more than seen in the 900◦C.

Figure 4.35 highlight the differences found within the simulations.

Figure 4.35:Graph indicating the number of defects present during a graphite cascade at 1000 eV. Initial PKA direction 1 from table 3.1. Initial Temperatures 900◦C (blue) and 300◦C (red).

The cascades both have an initial peak followed by a decrease in the number of defects present in the cell. At 300◦C, figure 4.35 there is evidence of channelling between 0.041 and 0.050 ps, a phenomenon which is not seen at 900◦C. The maximum number of defects present during both cascades is 33 and occurs at 0.041 ps during the 300◦C cascade and 0.063 ps during the 900◦C. Both graphs continue to see small changes in the number of defects present until they stabilise.

Figure 4.36:Graphite cascade with initial PKA energy 1000 eV after: (a) 0.04 ps, (b) 0.11 ps, (c) 0.021 ps, (d) 0.50 ps, (e) 0.92 ps and (f) 2.397 ps. Initial PKA direction 1 from table 3.1. The colour of the scalar bar indicates the distance moved by atoms during the cascade. Initial Temperatures(1)900◦C and(2)300◦C.

Figure 4.36 (1) and 4.36 (2) form very similar cascade patterns. The defect discrepancy can be seen by comparing Figures 4.36 (1f) and 4.36 (2f). Figure 4.36 (1f) has three more defects present in final cell than in figure 4.36 (2f). The final displacement of the PKA at 300◦C is 15.52Å and the final displacement of the PKA at 900◦C is 15.41Å.

Figure 4.37 shows a cascade in graphite simulated with an initial PKA energy of 1000 eV, initial PKA direction 15 from table 3.1 and initial temperatures set to 900◦C and 300◦C.

Figure 4.37:Graphite cascade with initial PKA energy 1000 eV after: (a) 0.00 ps, (b) 0.01 ps, (c) 0.03 ps, (d) 0.08 ps, (e) 0.63 ps and (f) 4.87 ps. Initial PKA direction 15 from table 3.1. Initial Temperature (1)

900◦C and (2) 300◦C. The red circles denote interstitials and the blue squares denote vacancies. The path of each displaced atom is traced.

Image (a) in figures 4.37 (1) and (2) shows the initial direction of the PKA. The two cascades follow the same path throughout the simulation. After 0.01 ps, secondary cascade collisions can be seen forming alongside the path of the initial PKA direction, (images (b), (c), (d), (e) and (f)). The cell stabilises after 0.70 ps leaving 14 interstitials and vacancies present in the 300◦C cell and 15 in the 900◦C.

Figure 4.38 denotes each displaced atom at any given point in time during the 900◦C and 300◦C cascades.

Figure 4.38:Graph indicating the number of defects present during a graphite cascade at 1000 eV. Initial Temperatures 900◦C (blue) and 300◦C (red). Initial PKA direction 15 from table 3.1.

The cascades are identical until the final stage of the simulation where there is one more interstitial formed in the 900◦C cascade than there is in the 300◦C cas- cade. The maximum peak of 32 defects occurs at 0.073 ps in figure 4.38. There is no channelling observed in either of these cascades. The slight variation in the number of defects present after 0.2 ps is a direct result of the carbon atoms at the edge of the secondary cascades reaching their threshold energies. Once the atoms have reached their threshold energies they no longer have enough kinetic energy to break away from the lattice sites. However, the carbon atoms may have enough kinetic energy to move slightly out of their position in the lattice, without breaking any bonds and form an interstitial between planes. The atoms may stay in their defect position or they may re-combine with the lattice in which case there will no longer be a defect present. In the case of these two cascades, this phenomena affects the number of interstitials and va- cancies present in the final lattice.

Figure 4.39 shows the distance travelled by displaced atoms during the graphite cascade. To begin with, the PKA follows the same initial path in both cascades. It is only in the final stages that the displacements of the PKA and surround- ing atoms alter. The PKA’s kinetic energy falls below its threshold energy at 0.56 ps in figure 4.39 (1d) compared to 0.66 ps in figure 4.39 (2d). The dif- ference in time for the PKA’s kinetic energy to fall less than the threshold energy contributes to the displacement of the PKA being greater in the 300◦C cascade. Images (1f) and (2f) from figure 4.39 highlight the difference in the number of interstitials and vacancies in the final lattice cell. The extra atom which appears in the 900◦C cascade has a displacement less than 1Å. As the displacement of the atom is so small, this supports the postulation that the

atom has just enough kinetic energy to leave the lattice site and form a defect within the plane but not enough kinetic energy to break the bonds and create further secondary cascades. The final displacement of the initial PKA is 48.6Å in the 900◦C cascade and 55.21Å in the 300◦C cascade.

Figure 4.39:Graphite cascade with initial PKA energy 1000 eV after: (a) 0.005 ps, (b) 0.022 ps, (c) 0.040 ps, (d) 0.066 ps, (e) 0.127 ps and (f) 3.320 ps. Initial PKA direction 15 from table 3.1. The colour of the scalar bar indicates the distance moved by atoms during the cascade. Initial Temperatures(1)900◦C and(2)300◦C.

High temperature graphite cascades, 900◦C, have produced results similar to those found during cascades at 300◦C. Whilst there are slight differences be- tween the final number of defects present in the final lattice, the collisions occurring at both temperature mirror each other. Further discussion of high temperature cascades can be found in Chapter 6.