Radiation damage I. Steve Fitzgerald.

Radiation damage I Steve Fitzgerald http://defects.materials.ox.ac.uk/

Firstly an apology Radiation damage is a vast area of research I cannot hope to cover much in any detail I will try and introduce some important modelling techniques so you can understand research papers more easily There will be also be some more detailed case studies Classes will attempt to give practical experience in the methods Feedback is very welcome this is the first time the course has happened, so will probably be too fast / slow / hard / easy as well as disjointed, confusing and incoherent There may also be typos and other mistakes keep your eyes open! steven.fitzgerald@materials.ox.ac.uk Page 2

Overview Recap on fusion materials The radiation damage event Primary collision, Kinchin-Pease model, neutrons, ions Single-atom defects Vacancies, SIAs, gas atoms Intro to density functional theory Multi-atom defects Dislocation loops, voids and bubbles Introduction to molecular dynamics, rate theory and kinetic Monte Carlo Effect on mechanical properties Hardening, swelling, embrittlement Intro to dislocation dynamics Other topics Transmutation, stochastic dynamics, phase field models Research application talks Page 3

Fusion reactor materials Must have adequate mechanical properties Must not produce long-lived radioactive waste Must maintain these properties over a wide temperature range Must withstand severe, prolonged neutron irradiation ITER Page 5

Mechanical properties Strong Weak Ductile Brittle High thermal conductivity Low thermal conductivity Stable Unstable Safe Dangerous Page 6

Mechanical properties Strong Weak Ductile Brittle High thermal conductivity Low thermal conductivity Stable Unstable Safe Dangerous Page 7

Swelling Unirradiated fuel cladding tube After irradiation (L) 316 stainless steel Fast reactor fuel cladding 80dpa at 510C 33% volume increase (Below) V-Fe alloy Page 8

Radiation damage event displacement of atoms Electrons, ions and neutrons Cascades Threshold displacement energy Kinchin-Pease model (and modifications) DPA, dose and dose rate A good read by Prof Gary Was UMich (827 pages) Page 9

Timescales and events Time (s) Event Result 10-18 Energy transfer from incident particle 10-13 Displacement of lattice atoms by PKA 10-11 Energy dissipation, spontaneous recombination, clustering Primary knock-on atom created Local melting, displacement cascade Stable Frenkel pairs >10-8 Thermal migration of defects Recombination, clustering, trapping See G. Was, Fundamentals of Radiation Materials Science Page 10

Incident particles Neutrons What we re really interested in: fusion or fission reactors Transmutation samples can become radioactive High flux, fluence difficult to generate in lab Use test reactor (fission), takes time to build up dose (years), energies not the same as fusion neutrons Wait for IFMIF or CTF (component test facility) Electrons e - damage in HV electron microscope allows simple in situ observations Low energy cf. neutrons/ions, individual displacements, not cascade Ions Easy to accelerate and control Mimics the PKA No transmutation, so samples don t become radioactive Page 11

Some ion irradiation/implantation facilities Helmholtz Centre, Rossendorf As well as creating displacement damage with self ions, can implant other ions to mimic nuclear reaction products Page 12

PKA interactions As the PKA ploughs through the lattice, it loses energy by interactions with electrons electronic stopping ions nuclear stopping radiation radiative stopping Energy is transferred to the lattice causing atomic displacements How many for a given material and incident particle energy? What does this depend on? Can we calculate it? Page 13

Threshold displacement energy T D This is the minimum KE that an atom in a solid needs to receive to be permanently displaced from its lattice site Depends on the material and the orientation of the impact T D,min < T D < T D,max Must be at least the energy of a Frenkel pair (~few ev) Usually quite a bit more than this (FP production isn t a simple process, a stable FP is harder to form than an instantaneous one) Temperature can also affect this Typically few tens of ev Not easy to calculate (see DFT section ) Page 14

Threshold displacement energy Maximum KE that an incoming particle with KE E and mass m can transfer to a lattice atom of mass M is KE max = E non-relativistic approximation 4Mm (m + M) 2 from conservation of energy and momentum derive it What does this mean for n, e -, self ion irradiation? Relativistic formula is When do we need this? KE max = 2ME(E +2mc2 ) (m + M) 2 c 2 +2ME c 3 10 8 ms 1 maybe don t derive it Page 15

Displacement probability T > T D doesn t automatically guarantee a displacement will happen There s a spread, affected by orientation, temperature etc probability of displacement 1 0 T D,min T D,max transferred KE Page 16

Kinchin Pease model (1955) Assumptions: Cascade is sequence of two-body elastic collisions Ignore spread (i.e. prob.(dispt) = 1 for T > T D ) No energy loss to lattice i.e. T new = T old T transfer Electron stopping energy loss given by simple cut-off E c Atomic collisions happen only when T PKA < E c Energy transfer given by hard sphere model Ignore crystal structure, channeling Page 17

Kinchin Pease model (1955) Want to know how many atoms (N) are displaced in the cascade caused by a PKA with energy T Imagine the first collision of the PKA with a lattice atom. Let s say it transfers energy to the lattice atom. Then N(T )=N(T )+N( T D ) N(T )+N( ) because we re ignoring energy loss to lattice T D is unknown, so we need to average over it somehow m = M in max energy transfer formula, so 0 < Assume uniformly distributed energy transfers* < T *this can be derived more rigorously Page 18

Kinchin Pease model (1955) Assume uniformly distributed energy transfers, then prob. that transferred energy lies in Therefore N(T )= = 2 T Z T 0 Z T Not obvious split into two integrals, change variables What is N(T) for relatively low T? 0 d (, +d ) is just T (N(T )+N( )) d T N( )d Page 19

Kinchin Pease model (1955) For T < T D, N = 0 For T D < T < 2T D, N(T) = 1 why? So N(T )= 2 T = 2T D T Z TD 0 + 2 T 0d + Z T Z 2TD 2T D N( )d T D 1d + Z T 2T D N( )d! Multiply by T, differentiate w.r.t. T, get finally N(T )= N(T >E c )= E c and 2T D since we assumed electronic stopping absorbed any energy above E C T 2T D Page 20

Kinchin Pease model (1955) N(T) Finally N(T) = 0; T<T D 1; T D <T <2T D T ; 2T D <T <E c 2T D E c ; T E c 2T D Need to know T D and E c as inputs T D 2T D E c T Page 21

Kinchin Pease model (1955) Various modifications and alternatives (NRT,, ) have been proposed but this remains widely-used. See SRIM class later today Stoller et al, NIMB 2013 Page 22

DPA Stands for displacements per atom 1 DPA means every atom has been displaced once (on average). Fusion power plant lifetime first wall ~100 DPA A highly questionable and unreliable quantification of radiation damage # of stable Frenkel pairs = 0.4 T dam / T D T dam is the amount of deposited energy, 0.4 comes from NRT model (K-P overestimates damage) Ignores dose rate, cascade overlap Really a material-dependent measure of exposure Page 23

Thanks to Andy Calder, Liverpool http://www.liv.ac.uk/~afcalder/ < one picosecond Page 25

Thanks to Andy Calder, Liverpool http://www.liv.ac.uk/~afcalder/ picoseconds Page 26

Thanks to Andy Calder, Liverpool http://www.liv.ac.uk/~afcalder/ nanoseconds Page 27

Thanks to Andy Calder, Liverpool http://www.liv.ac.uk/~afcalder/ http://www.youtube.com/watch? feature=player_embedded&v=ypwsny0ww9u http://www.youtube.com/watch? feature=player_embedded&v=0bthd_8jfv4 Page 28