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Diffusion of radiation damage in Fe and Fe–P systems

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

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Diffusion of radiation damage in Fe and Fe–P systems

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  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: 143 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 n = 1013 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

  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 P interstitial atom Vacancy

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

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

  18. Fadeout slide

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