Atomistic KMC for Fe-Cr alloys

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Atomistic KMC for Fe-Cr alloys α – α’ decomposition during thermal ageing Radiation Induced Segregation F. Soisson (CEA Saclay, SRMP) O. Senninger, E. Martinez (LANL), C.-C. Fu, M. Nastar, Y. Bréchet (SIMAP)

Interaction and diffusion model for Fe-Cr alloys magnetic properties of Fe-Cr alloys :  special thermodynamic properties (ordering/unmixing tendencies, asymmetrical phase diagram)  special diffusion properties (non-arrhenian behavior, acceleration of diffusion near Tc) effects on the kinetics of segregation and decomposition ? Interaction and diffusion model : Magnetic Cluster Expansion (M. Lavrentiev et al.) Clear physical basis, efficient at 0K, but no diffusion of defects for the time being and difficult to handle by AKMC simulations Alternative approach : concentration and temperature dependent pair interactions fitted on - DFT calculations at 0K (ΔHmix , vacancy formation and migration energies) - Experimental data at high temperature: Tc (α-α’) and diffusion coefficients - takes into account the magnetic transition and vibrational entropic contributions

Thermodynamics properties (Levesque et al. PRB 2011) pair interactions on a rigid BCC lattice - Composition dependence fitted on DFT calculations of ∆Hmix (SQS, PWSCF, GGA-PAW) - A linear temperature dependence fitted on the experimental α-α’ critical temperature Phase diagram : good agreement with the modified CALPHAD diagram (Bonny et al, 2010) -> asymmetrical miscibility gap, non-vanishing Cr solubility at low T

Diffusion properties : dilute alloys (Senninger et al. 2012) at 0K : DFT calculations of vacancy migration barriers in ferromagnetic iron and non-magnetic chromium -> saddle-point interactions acceleration at the ferro-paramagnetic transition in the α phase -> corrections of the migration barriers, fitted on experimental tracer and interdiffusion coefficients tracer diffusion coefficients in iron in chromium strong acceleration of the diffusion at Tc Tc decreases with the Cr concentration

Diffusion properties: concentrated alloys ~ The interdiffusion coefficients strongly decrease with the Cr content: may explain the small effect of the composition on the decomposition kinetics Its important to take into account the real vacancy concentration [1] Braun & Feller-Kniepmeier, 1985 [2] Jönsson 1995

Diffusion properties: concentrated alloys The interdiffusion coefficients strongly decrease with the Cr content: may explain the small effect of the composition on the decomposition kinetics Its important to take into account the real vacancy concentration [1] Braun & Feller-Kniepmeier, 1985 [2] Jönsson 1995

AKMC: α-α’ decomposition during thermal ageing Fe-20%Cr T = 500°C AKMC (E. Martinez, O. Senninger, CEA) 3D atom probe (Novy et al, GPM Rouen, 2009)

Kinetics of α-α’ decomposition: AKMC vs SANS Small Angle Neutron Scattering experiments : 500°C: Bley (1992) 540°C: Furusaka et al. (1986) - F/P transition : strong acceleration of the decomposition between above 35% Cr (lower TC) - better agreement with experimental kinetics 500°C 540°C  SANS experiments  AKMC simulations  AKMC simulations without magnetic correction

Under irradiation: self-interstitial properties DFT calculations (PWSCF-GGA-PAW) - in Fe-rich ferromagnetic configurations Fe-Fe dumbbell 110 more stable than 111 (ΔEfor ≈ 0.7 eV) weak Cr-dumbbell interactions - in Cr-rich AFM configurations: Cr-Cr dumbbell 110 slightly more stable than 111 very strong Fe-dumbbell attraction (ΔEfor ≈ 0.1 eV) - SIA migration barriers Integration in AKMC: <110> dumbbells Dilute Fe-Cr configurations Measurements of Lij  Radiation Induced Segregation Ebin AKMC (eV) Ebin DFT (eV) May 7, 2019

AKMC : measurements of Onsager coefficients The coupling between fluxes of point defects and the flux of solute is controlled by the Onsager coefficients : LCr-V < 0 LCr-SIA > 0 -> Cr depletion at sinks -> Cr enrichment at sinks No significant effect of the Cr content

AKMC : simulations of radiation induced segregation Evolution of the Cr concentration profiles at a grain boundary Fe-10at%Cr 2 x 10-3 dpa/s T = 650 K T = 850 K different behaviors, depending on the temperature and the dose/rate, but… initial state steady-state %Cr %Cr Atomic plane Atomic plane

SIA migrations barriers AKMC vs DFT migration (110 dumbbells): The diffusion model must be improved, especially for SIA migration barriers in non-dilute configurations

Conclusions A model with composition and temperature dependant pair interactions on rigid lattice: gives reasonable thermodynamic and diffusion properties kinetics of decomposition in good agreement with experimental results take into account the effect of the F/P magnetic transition Alloys under irradiation – the description of SIAs must be improved A phenomenological model : - lack experimental data at low T and in the Cr rich phase - ad hoc corrections of the migration barriers only - probably an effect of the F/P transition on the formation energies too … A more physical model (with interactions between magnetic moments) would provide more information

Acceleration of the diffusion at the ferro-to-paramagnetic transition T c = 1043 K in pure Fe, decreases with %Cr  introduction of an empirical correction on the migration barriers fitted on: - tracer diffusion coefficients in pure iron - concentration dependence of Tc - tracer diffusion coefficients at 50%wt Cr 7 mai 2019 CEA | 10 AVRIL 2012