1. Diffusion of radiation damage in Fe and Fe–P systems Stewart Gordon Loughborough University, UK

2. Introduction  Collision cascade – result of radiation damage  Classical MD of limited timescale  Problem: to predict what will happen in the long run  Key: discovering the state transitions

3. The dimer method – 1  Algorithm to find saddle points on a potential surface  System of N atoms – 3N-dimensional potential surface  No need to guide – exceeds limitations of molecular statics  Previously applied to surface diffusion

4. The dimer method – 2  Dimer – two nearby points on the potential surface  Dimer is rotated to line of lowest curvature  Then translated towards the saddle using an effective force  Determines minimum energy barriers

5. Methodology – 1  Fe bcc lattice size: 14 3 unit cells  Isolated defects  Total number of atoms: 9827  Relaxed using damped MD  Cubic region defines range of moving atoms

6. Methodology – 2  Interatomic potentials: Ackland (Fe–Fe) and Morse (Fe–P)  Calculation of transition times:  Assume standard attempt frequency of = 10 13 Hz

7. Fe self-interstitial structure  Fe bcc lattice  Defect:  110  dumbbell  Most common defect in collision cascades Fe atom on lattice site Fe interstitial atom Vacancy

8. Fe transitions – 1  Transition from  110  dumbbell to  111  crowdion  Energy barrier: 0.160 eV  Transition time at 300 K: 49 ps

9. Fe transitions – 2  The  111  crowdion translates in the  111  direction  Energy barrier: 0.0024 eV  Transition time at 300 K: 0.1 ps

10. Barrier convergence – Fe  111  crowdion transitions Moving atoms Translation To  110  dumbbell 10250.0026910.035078 20010.0024470.034672 54890.0023870.034562 67510.0023810.034565

11. Fe diffusion mechanism   110  dumbbell changes to  111  crowdion – controlling transition  Crowdion then translates  Returns to  110  dumbbell  Can then explore other  111  directions

12. P atoms in bcc Fe  P atoms prefer to sit in substitutional sites  Can be displaced into interstitial sites by radiation damage  P atoms in substitutional sites can attract Fe interstitial clusters  Here the mechanism for the motion of isolated interstitial P is investigated

13. P interstitial defect in Fe   110  Fe–P dumbbell  Some very different diffusion mechanisms to be seen Fe atom on lattice site Fe interstitial atom Vacancy P interstitial atom

14. Fe–P diffusion mechanisms – 1   110  dumbbell changes to tetrahedral  Energy barrier: 0.293 eV  Transition time: 8.4 ns  Then forms new  110  dumbbell  Energy barrier: 0.257 eV  Transition time: 2.1 ns  Diffusion through lattice possible

15.  Dumbbell pivots via  551  and  643  states  Key transition:  551  to  643   Energy barrier: 0.257 eV  Transition time: 2.1 ns Fe–P diffusion mechanisms – 2 [110] [551] [643] [634][515] [101]

16. Fe–P transitions – summary  643  dumbbell 0.0037 0.0027 0.257 0.066 0.085 0.227 0.041 0.293 0.257 0.289 0.254 0.0988 0.0796 0.111 0.260  551  dumbbell Face diagonal Offset tetrahedral  110  dumbbell Tetrahedral

17. Conclusions  Dimer method can be applied to bulk problems  More moving atoms needed than for surfaces  Unusual transitions can be identified  Diffusion mechanisms for P in Fe have been determined

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