COMPLICACIONES QUIRÚRGICAS

The initial 20 directions for cascades selected using the Thomson problem have been employed to accurately represent the possible directions a PKA could travel. To give a full picture of cascade results, there are other extreme direc- tions which are to be examined. The extreme directions are: directly along the plane and normal to the plane. The cascades have been simulated at 500 eV and the results are presented below.

Initial PKA Direction Through the Plane

In order to simulate a cascade through the plane, the initial PKA direction was selected to be x = 0.00, y = 0.90 and z = 0.00. Figure 4.24 follows the interstitials and vacancies which are formed throughout the cascade.

Figure 4.24:Graphite cascade with initial PKA energy 500 eV after: (a) 0.00 ps, (b) 0.01 ps, (c) 0.04 ps, (d) 0.11 ps, (e) 0.27 ps and (f) 2.97 ps. Initial PKA direction x = 0.00, y = 0.90 and z = 0.00. The cell temperature is 300◦C. The red circles denote interstitials and the blue squares denote vacancies. The path of each displaced atom is traced.

Figure 4.24 (a) shows the initial direction of the PKA. After 0.01 ps there are three clearly defined interstitials and vacancies (figure 4.24 (b)). As the cascade continues, a cluster of defects begins to form and displaced atoms continue to travel through the cell creating secondary cascades (figures 4.24 (c) and (d)). After 0.27 ps (figure 4.24 (e)) the cell begins to stabilise and by 2.97 ps the lattice is stable (figure 4.24 (f)). The total number of interstitials and vacancies

present in the final lattice is six.

Figure 4.25 shows the number of defects created during this simulation as a function of time.

Figure 4.25:Graph indicating the number of defects present during a graphite cascade at 500 eV. Initial PKA direction x = 0.00, y = 0.90 and z = 0.00. The cell temperature is 300◦C.

Figure 4.25 has an initial peak of defects, the maximum number of defects formed is 23 and occurs at 0.079 ps into the cascade. The number of defects begins to decrease until the system begins to stabilise at 0.2 ps.

Figure 4.26 tracks the distance travelled by displaced atoms. The PKA travels alongs its initial path for 0.32 ps before colliding with a carbon atom in the cell. The collision forces the PKA to alter its direction before re-combining in a lattice plane, figure 4.26 (f). The final displacement of the PKA is 4.40Å.

Figure 4.26:Graphite cascade with initial PKA energy 500 eV after: (a) 0.00 ps, (b) 0.01 ps, (c) 0.04 ps, (d) 0.11 ps, (e) 0.27 ps and (f) 2.97 ps. Initial PKA direction x = 0.00, y = 0.90 and z = 0.00. The colour of the scalar bar indicates the distance moved by atoms during the cascade. The cell temperature is 300◦C.

Initial PKA Direction Normal to the Plane

Examples of two simulations with an initial PKA direction normal to the plane are presented to highlight the directional dependence of cascades through graphite.

Figure 4.27 follows the interstitials and vacancies formed during a cascade with an initial PKA direction normal to the plane. The initial PKA direction was set to x = 0.00, y = 0.00 and z = -1.00.

Figure 4.27:Graphite cascade with initial PKA energy 500 eV after: (a) 0.00 ps, (b) 0.01 ps, (c) 0.04 ps, (d) 0.12 ps, (e) 0.25 ps and (f) 2.99 ps. Initial PKA direction x = 0.00, y = 0.00 and z = -1.00. The cell temperature is 300◦C. The red circles denote interstitials and the blue squares denote vacancies. The path of each displaced atom is traced.

Figures 4.27 (a) and (b) show the initial position of the PKA. There is little movement from displaced atoms in the x and y planes (figures 4.27 (c), (d), (e) and (f)). Figure 4.28 highlights the distance travelled by displaced atoms.

Figure 4.28:Graphite cascade with initial PKA energy 500 eV after: (a) 0.007 ps, (b) 0.025 ps, (c) 0.048 ps, (d) 0.070 ps, (e) 0.148 ps and (f) 2.991 ps. The colour of the scalar bar indicates the distance moved by atoms during the cascade. Initial PKA direction x = 0.00, y = 0.00 and z = -1.00. The cell temperature is 300◦C.

Figures 4.27 and 4.28 (from the perspective of the x and y directions) suggests the cascade formed a cluster of defects. However, this proposition is contra- dicted when studying the images in figure 4.28 (from the perspective of the y and z directions). The distance travelled by the PKA can be seen to be greater than 10Å after 0.025 ps (figure 4.28 (b)). If the cascade remained as a cluster of interstitials and vacancies a displacement of over 10Å of the PKA would be unlikely. Figure 4.29 shows the same cascade from the view point of the y and z directions.

Figure 4.29:Graphite cascade with initial PKA energy 500 eV after: (a) 0.007 ps, (b) 0.020 ps, (c) 0.048 ps, (d) 0.070 ps, (e) 0.148 ps and (f) 2.991 ps. The colour of the scalar bar indicates the distance moved by atoms during the cascade. Initial PKA direction x = 0.00, y = 0.00 and z = -1.00. The cell temperature is 300◦C.

The images in figure 4.29 demonstrate that the PKA travels through the cell. Figures 4.29 (a) and (b) show the initial path of the PKA. It is involved in a head-on collision with a carbon atom at 0.022 ps which causes it to retrace the original path for 0.026 ps before forming an interstitial between the graphite layers as seen in figure 4.29 (d). The second carbon atom continues to travel through the cell causing secondary cascades (figure 4.29 (e)) until the cell sta- bilises (figure 4.29 (f)). The final cell has eight interstitials and eight vacancies present and the PKA has a final displacement of 5.94Å.

Figure 4.30:Graph indicating the number of defects present during a graphite cascade at 500 eV. Initial PKA direction x = 0.00, y = 0.00 and z = -1.00. The cell temperature is 300◦C. The blue arrow indicates a head-on collision between the PKA and a neighbouring atom.

The head-on collision between the PKA and the second carbon atom is high- lighted by the blue arrow in figure 4.30. The second carbon atom proceeds through the cell creating a cascade of defects to be formed. The maximum number of defects formed is 17 at 0.101 ps. After the initial spike of de- fects, displaced atoms come to rest in vacant sites or collide with neighbouring atoms until the cell stabilises.

Figure 4.31 follows the interstitials and vacancies formed during a cascade with an initial PKA direction normal to the plane. The initial PKA direction was set to x = 0.00, y = 0.00 and z = 1.00.

Figure 4.31:Graphite cascade with initial PKA energy 500 eV after: (a) 0.00 ps, (b) 0.01 ps, (c) 0.04 ps, (d) 0.11 ps, (e) 0.26 ps and (f) 2.91 ps. Initial PKA direction x = 0.00, y = 0.00 and z = 1.00. The cell temperature is 300◦C. The red circles denote interstitials and the blue squares denote vacancies. The path of each displaced atom is traced.

Figures 4.31 (a) and (b) highlight the initial direction of the PKA. It collides with two carbon atoms and comes to rest forming an interstitial 0.04 ps into the cascades (figure 4.31 (c)). Figure 4.31 (c) shows that the displaced carbon atoms produce two individual secondary cascades in opposing directions. The secondary cascades continue to form interstitials and vacancies until 0.26 ps (figure 4.31 (e)) where channelling occurs resulting in the increased presence of interstitials and vacancies before the cell stabilises (figure 4.31 (f)). The number of interstitials and vacancies present in the final cell is 10.

Figure 4.32:Graph indicating the number of defects present during a graphite cascade at 500 eV. Initial PKA direction x = 0.00, y = 0.00 and z = 1.00. The cell temperature is 300◦C.

Figure 4.32 has an initial peak of 18 defects at 0.099 ps. The number of defects present in the cell gradually decreases as interstitials re-combine in the lattice. A second peak can be seen in figure 4.32. This is evidence of channelling and can clearly be seen between 0.2 and 0.4 ps. The second peak gradually decreases leaving the cell to stabilise. The maximum number of defects 23 occurs at 0.428 ps.

Figure 4.33 follows the distance travelled by displaced atoms.

Figure 4.33:Graphite cascade with initial PKA energy 500 eV after: (a) 0.007 ps, (b) 0.021 ps, (c) 0.046 ps, (d) 0.074 ps, (e) 0.128 ps and (f) 2.919 ps. The colour of the scalar bar indicates the distance moved by atoms during the cascade. Initial PKA direction x = 0.00, y = 0.00 and z = 1.00. The cell temperature is 300◦C.

Figures 4.33 (a) and (b) indicate the initial path of the PKA. As the cascade continues, the PKA collides with two carbon atoms. This alters the path of the PKA forcing it back along its initial path before the PKA comes to rest. In figure 4.33 (c) the red atom is not the PKA but rather it is a second carbon atom which was displaced as a direct result of a collision with the PKA. Figures 4.33 (d), (e) and (f) continue to track displaced atoms from secondary cascades. The final displaced atoms (figure 4.33 (f)) have travelled an average of 5.17Å. The final displacement of the PKA is 5.86Å.