Atomic-scale modeling of Clear Band formation in FCC metals David Rodney GPM2/ENSPG INP Grenoble, France Special thanks to Y. Bréchet, M. Fivel and C. Pokor

Irradiation microstructures depend on the material and the irrad. conditions (temperature, flux and spectrum) In Copper: + Defects not visible in TEM: glissile interstitial loops (  < 1 nm) Vacancy-type defects stacking fault tetrahedra (  ~ 2 nm) (0.1dpa,100°C+anneal 300°C)[Singh,'01]316 steel (10dpa,375°C)[Pokor,'02] Interstitial defects black dots (  ~ 2 nm), Frank loops (  ~ 10 nm) In austenitic steels:

In all materials, irradiations induce a degradation of the mechanical properties: hardening (increase in yield stress) decrease in ductility plastic instability (upper yield point + softening) Polycrystal FCC steel BCC Mo Polycrystal FCC Cu Single crystal FCC Cu

Correlation between steps and clear bands in neutron irradiated copper [Sharp,'68,'72] The plastic instability corresponds to the localization of the deformation in clear bands (or defect free zones) Clear bands in Cu [Robach,'03] The band width saturates with the deformation, ~ 0.15  m Shear in the bands is high, ~ 0.5  m ≡ several thousand dislocations There are traces of cross-slip events There are pile-ups at the head of the channels

To understand clear band formation, atomistic input is needed, because: Interactions involve core contacts between dislocations and defects (+absorption/shear of the defects) Cross-slip traces are systematically observed in TEM Irradiation defects have sizes and separations in the nanometer range Glissile interstitial loops in Ni [Rodney&Martin,'99] Stacking fault tetrahedra in Cu [Wirth et al,'02 Osetsky&Bacon,'03] Voids and precipitates in Cu & Fe [Osetsky&Bacon,'03] Up to now, MD studies have focused on edge dislocations interacting with:

Our aim: Understand the dynamics of formation of clear bands in austenitic steels Systematic study of edge and screw dislocations interacting with interstitial Frank loops (austenitic) Study interaction mechanisms  Role of cross-slip, defect shape, temperature, chemistry Evaluate critical unpinning stresses  Use in larger scale simulations (DDD) and models (internal variable models) Since no potential for austenitic steels is available YET, we use Nickel as a prototypical FCC crystal

Outline: Simulation technique and boundary conditions Interaction Edge dislocation / Glissile loops Interaction Screw dislocation / Frank loops

Simulation technique

EAM Nickel potential [Angelo, Moody, Baskes, 1995] Molecular Statics (Conjugate Gradient) or Molecular Dynamics (Verlet Algorithm) Boundary conditions that construct infinite periodic glide planes  Y=[110] Z=[111] X=[112] Periodic condition in X (+Shift b/2 in Y dir.) and Y 2D dynamics in Z 20, 37, 60 nm 21.5 nm 17 nm Boundary conditions for screw dislocation: 

Edge dislocation in interaction with glissile interstitial loops [Rodney & Martin, PRL (1999), PRB (2000)]

MD simulation at T = 100 K,  = 150 MPa, 4-SIA loops "The vacuum cleaner effect" → removes all loops within a capture distance (~2 nm) → the dislocation climbs and broadens the band. Provides a mechanism for clear band formation but not for hardening Are clusters of dumbbells Are very mobile along their glide cylinder (Brownian motion) When in contact with core of edge dislocations: Collective flip of the dumbbells such that the final Burgers vector lies in the glide plane of the dislocation Absorption and drag by the moving dislocations b

Screw dislocation in interaction with interstitial Frank loops [Rodney, Acta Mater (2004)]

A D C B CC AA Frank loops have a {111} habit plane and a a/3 Burgers vector. For a screw dislocation, there are 2 non planar contact configurations:

A D C B CC AA Loop in a cross-slip plane of the dislocation Frank loops have a {111} habit plane and a a/3 Burgers vector. For a screw dislocation, there are 2 non planar contact configurations:

A D C B CC We consider hexagonal loops with edges in (austenitic steels and Nickel) or directions (Gold and Copper), with or without jogs on their border Diameter : 6 to 10 nm ; Density ~ m -3 → realistic values close to saturation values AA Loop in a cross-slip plane of the dislocation Loop not in a cross-slip plane of the dislocation Frank loops have a {111} habit plane and a a/3 Burgers vector. For a screw dislocation, there are 2 non planar contact configurations:

Initial configuration : Relaxed (CG) with no applied stress MD simulation at T = 100 K,  = 150 MPa Loop with perfect hexagonal shape and edges Burgers vector What do we see? Athermal cross-slip driven by the core interaction between disl./loop Disl. recombines with the loop edges Helical turn is sessile

Unpinning Mechanism from the helical turn Simulation at 425 MPa Unpinning involves an Orowan process Net result: transformation of the Frank loop into a perfect prismatic loop

What do we see? Configuration not favorable to recombination Emission of a constricted node The loop is not unfaulted but sheared + step Influence of the shape: Loop with edges Case of Austenitic steels and Nickel

Loops with Jogs Loops often contain jogs on their border, with a flower-like structure Can the jogs block the unfaulting reaction by impeding the cross-slips? We produced jogged loops by removing interstitials contained in smaller hexagons at the periphery of hexagonal loops Burgers vector direction CG simulation: Screw dislocation Loop diameter7 nm Jog height2 nm Applied stress150 MPa

What do we see? The jogs do not impede the cross-slips The helical turn has the complicated structure of the initial loop Vacancy clusters are produced (containing ~ 10 vacancies) Helical turn seen in the direction of the Burgers vector Full structure of the helical turn Vacancy clusters Burgers vector direction

Simulations with increasing applied stress with dislocation lengths ~ 20, 40, 60 nm Compare unpinning stress with Orowan stress [Scattergood & Bacon,'82] loops : D = 3.2 nm : D = 5.3 nm Effective size D close to real size Unpinning controlled by bowing out of the screw dislocation for screw dislocation (L=L y -D) with impenetrable obstacles (D) Evaluation of the Unpinning Stress

Summary Reactions involve athermal cross-slips promoted by the short-range interactions btwn dislocation/Frank loops and the applied stress The cross-slipped segments emitted from the loops can serve as dislocation sources in cross-slip planes The short-range core interactions may be directly responsible for the high number of cross-slip events observed in clear bands Cross-slipped segment emitted from a loop

Summary Importance of the shape of the loops : systematically unfaulted : sheared in 2 out of 3 cases Can the dislocation recombine with the loop edges? Suzuki et al. ('92) identified loops in proton-irradiated austenitic steels ; the loops were sheared in bands containing many debris

Shear of Frank loops is more frequent than assumed in the literature The same is observed with Stacking Fault Tetrahedra (Wirth, Osetsky, Bacon) Defect shearing also leads to the localization of the deformation, as in alloys hardened by coherent shearable precipitates A possible scenario, not considered up to now, could be that clear bands form by shearing the irradiation defects until they become unstable and/or are absorbed in dislocation cores, as in the case of glissile loops But this requires confirmation! Can shear be at the origin of the clear bands? Al-Li alloy SFT interacting with a screw dislocation

Perspectives PERFECT program At the micron scale (with Marc Fivel, GPM2) Import information in Dislocation Dynamics Account for non trivial effects : - Role of grain boundaries as sources - Role of pile-ups Obtain : - Clear band formation dynamics - Stress-Strain curve during clear band formation At the atomic scale Complete study with edge dislocations Consider solid-solutions to investigate alloying effects Ni-Al solid-solution (L. Proville, D. Rodney, Y. Bréchet, G. Martin) Dislocation gliding through glissile interstitial loops (M. Fivel, C. Lemaignan)