ASTM Conference, Feb 6 2013, Hyderabad, India Effect of Hydrogen on Dimensional Changes of Zirconium and the Influence of Alloying Elements: First-principles and Classical Simulations of Point Defects, Dislocation Loops, and Hydrides M. Christensen, W. Wolf, C. Freeman, E. Wimmer, Materials Design Inc., Santa Fe, NM, USA R. B. Adamson, Zircology Plus, Freemont, CA, USA L. Hallstadius, Westinghouse Electric Sweden, Västerås, Sweden P. Cantonwine, Global Nuclear Fuels, Wilmington, NC, USA E. V. Mader, Electric Power Research Institute (EPRI), Palo Alto, CA, USA
Overview EPRI Channel Distortion Program: objectives of the atomistic simulations Atomistic ab-initio and forcefield based simulation methods Dimensional changes in Zr and hydrides due to H pickup Solubility of H in Zr vs. temperature, effect of strain Vacancies and interstitials in Zr Dislocation loops in Zr and the impact of H, volume effect Diffusivity of vacancies and interstitials, H and O Effect of alloying elements Fe, Cr, Ni, Nb, Sn and O impurity Summary 2
Atomistic Modeling for Channel Distortion Issues Helping to understand mechanisms channel distortion Fluence-gradient bow Shadow corrosion-induced bow Hydrogen pickup Alloy dependence Prediction of materials properties Solubility of H in Zr Dimensional changes of Zr and hydrides as a function of H concentration Mechanical and elastic properties - stress Diffusion of H, vacancies, interstitials and impurities in Zr Influence of alloying elements (Fe, Cr, Ni, Nb, Sn) and impurities (O) on the above properties Dislocation loop formation, as affected by H and alloying elements 3
Computational procedures involved MedeA computational environment Structural models with periodic boundary conditions (~100 atoms for abinitio, ~10000 atoms for forcefields) Discrete sampling of hydride structures Ab-initio calculations (VASP) for geometries and total energy for stable structures and transition states Ab-initio phonon calculations for temperature effects within a (quasi)harmonic approximation Configurational entropy from an independent two-site model for impurities in Zr (solubility, absorption isotherms) Eyring s transition state theory for diffusivities Embedded atom potentials fitted to ab-initio data and applied for large timeand length-scale molecular dynamics simulations (LAMMPS): structure and energy of dislocation loops, diffusivities 4
Zirconium, Hydrogen and Hydrides 5
Swelling Due to Hydrogen Pickup ZrH 2 ZrH H in solution Zr Hydride 6
Swelling Due to Hydrogen Pickup Volume vs. H concentration in hydrides increases non-linearly tending to a plateau at ZrH 2 ZrH 2 ZrH H in solution Zr Hydride 7
Gibbs Free Energy of H Solution in Zr H mostly in tetrahedral sites Effect of strain Like sponge : Solubility higher under tensile strain, lower under compression Computed DH 0 298 = -41.3 kj/mol Experimental: -32.5 to -64 kj/mol 8
H Solubility in a-zr Solubility of H increases with temperature Computed Experiment Terminal solubility Computed terminal solubility: S[wt-ppm] = 546577exp(-5450/T[K]) at 300 ºC: S = 41 wt-ppm at 25 ºC: S = 0.006 wt-ppm 9
Zr-H Phase Diagram EOF/atom: -54 kj/mol e-zrh 2 I4/mmm a = 3.537 Å (+0.48%) c = 4.458 Å (+0.21%) c 11 = 225 GPa c 12 = 88 GPa c 33 = 157 GPa c 13 = 108 GPa c 44 = 30 GPa B = 130 GPa G = 24 GPa E = 68 GPa d-zrh 2 Fm-3m cubic, tetrahedral sites filled EOF/atom: -53 kj/mol a = 4.821 Å (+0.92%) Elastically unstable with 1:2 stoichiometry ε δ Zr P6_3/mmc EOF/atom: -40 kj/mol a = 3.243 Å (+0.00%) c = 5.022 Å (+1.50%) ZrH P4_2/mmc g EOF/atom: -31 kj/mol a = 3.283 Å (+1.23%) c = 5.012 Å (+1.30%) g-zrh I-4m2 EOF/atom: -23.7 kj/mol a = 4.660 Å Zr 2 H Pn-3m EOF/atom: -20.2 kj/mol a = 3.263 Å (-1.1%) c = 10.824 Å (+5.2%) z-zr 2 H P-3m1 10
Phase Stability ZrH 2 AF30874 d Fm-3m hydride stable with H vacancies 6 February 2013 ASTM Conference, Hyderabad, India - Atomistic Modeling for Channel Distortion, Materials Design, Inc.
Phase Stability ZrH 2 AF30874 e I4/mmm hydride (ordered) most stable if fully stoichiometric 6 February 2013 ASTM Conference, Hyderabad, India - Atomistic Modeling for Channel Distortion, Materials Design, Inc. c contracts by 7.5% a expands by 3.8%
Elastic Moduli for Stable Structures Increase of bulk modulus with H embrittlement Elastic moduli for most stable structures for each stoichiometry 6 February 2013 ASTM Conference, Hyderabad, India - Atomistic Modeling for Channel Distortion, Materials Design, Inc.
Vacancies and Interstitials in Zirconium 14
Vacancies in Zr DV V 1 V V 0 V 1 = V 0 DV + V Zr lattice shrinks around vacancies: by removing 1% of Zr atoms, the volume shrinks by 0.44%; counting also the removed Zr atoms, the total volume V 1 of the system increases by 0.56% The shrinkage is anisotropic: 0.25% in the a-direction and 0.43% in the c-direction. The vacancy formation energy is computed as 193 kj/mol
Trapping of H in Vacancies A single vacancy can trap up to 9 hydrogen atoms 16
Self-Interstitials in Zr DV V 0 V 1 = V 0 + DV Zr lattice expands around self-interstitials: by adding 1% of interstitial Zr atoms, the volume increases by 1.02 to 1.18% depending on the location of the interstitial; the expansion is between 0.02 and 0.18% for a constant number of Zr atoms The expansion is anisotropic; for interstitials in the basal plane there the lattice expands principally in the a directions. The formation energy of Zr interstitials at octahedral and tetrahedral sites is computed as 315 and 331 kj/mol, respectively. The binding energy of H near an interstitial is 14 kj/mol less than in defect-free Zr. H is repelled from self interstitials.
Formation of dislocation loops, impact of hydrogen 18
Formation of Loops a [0001] c c-loop a [10-10] [10-10] a a-loop [10-10] [11-20] [11-20] a-loop 19
Vacancy c-loops A B A Simulations indicate that vacancy c-loops collapse into cone-like 3-D structures Upon collapse the system shrinks in the c-direction 20
Vacancy c-loop with H Hydrogen atoms are attracted into vacancy loops and can retard or prevent collapse
Interstitial c-loops Crowdions are more stable than small (~5 Å) interstitial c-loops Larger interstitial c-loops are lens-shaped In the presence of interstitial c-loops hydrogen is most stable at the rim and thus has only marginal influence on this type of loop 22
Role of Dissolved Hydrogen Hydrogen mostly affects vacancy loops in c-loops H can retard the collapse, but collapsed loops are thermodynamically more stable Collapse of H-rich c-loop can lead to supersaturated Zr leading to nucleation of hydride H in <10-10> a-loop prevents collapse, thus causing an effective expansion of the lattice in the a-direction, which would not be present in H-free Zr or if H cannot reach the a-loops H has relatively little effect on interstitial loops 23
Diffusion vacancies, interstitials, H and O 24
Diffusion Self-interstitial diffusion: FAST, anisotropic (a>c) Hydrogen diffusion: D H = 1.13x10-7 e -42/(RT) (m 2 /s) MEDIUM, isotropic Vacancy diffusion: D basal = 8.62x10-6 e -69/(RT) (m 2 /s) D axial = 9.87x10-6 e -73/(RT) (m 2 /s) SLOW, isotropic Barrier heights in kj/mol 25
Diffusion of H and O in Zr Diffusion paths: Diffusion barriers (kj/mol): H O Octahedral to tetrahedral: 34.7 173.3 Tetrahedral to octahedral: 39.8 91.8 Tetrahedral to tetrahedral: 12.4 1.5 Octahedral to octahedral: 41.2 281.7 Diffusion rates Hydrogen: D H = 1.13x10-7 e -42/(RT) (m 2 /s) Oxygen: D planar = 6.13x10-5 e -175.7/(RT) m 2 /s D axial = 4.64x10-5 e -173.7/(RT) m 2 /s 26
Diffusion of Oxygen in Zr Computed: Red: Diffusion along c-axis Blue: Diffusion in basal plane D GB : grain boundary diffusion D V : volume diffusion LT low temperature (<973 K) HT high temperature (a) Internal friction and strain ageing measurements (b) AES (c) XPS (d) XPS (e) AES (f) AES Figure from: B.J. Flinn, C.-S. Zhang and P.R. Norton PRB 47, 16499 (1993) 27
Effect of Cr, Ni, Fe, Sn, Nb; O 28
Volume Effect of Alloying 29
Effect of Alloying on Hydride Stability Alloying elements impede the formation of hydrides, because they are less stable inside a hydride than in solution Sn has the largest effect at high H concentrations 30
Surface Segregation of Alloying Elements Impurity prefers surface Impurity prefers bulk Sn and Ni have significant thermodynamic driving force to segregate to surface Fe and Cr have smaller driving force Nb prefers bulk M. Christensen, T. M. Angeliu, J. D. Ballard, J. Vollmer, R. Najafabadi, and E. Wimmer, J. Nucl. Mat. 404, 121 (2010) 31
Effect of Alloying Elements on Interstitial Diffusion from ab-initio Substitutional Cr, Fe, and Ni exchange position with interstitial Zr and become fast interstitial diffusers Interstitial Cr and Fe diffuse anisotropically with fast motion along c-axis; for Ni anisotropic diffusion is less pronounced Nb remains on substitutional site and retards interstitial Zr diffusion Substitutional Sn has no pronounced effect on interstitial Zr diffusion 32
Self interstitial diffusion in presence of Fe, Cr and Ni from molecular dynamics Substitutional Cr, Fe, and Ni exchange position with interstitial Zr Initial rapid diffusion of Fe, Cr, and Ni mainly in the c-direction The alloying elements start to cluster thereby forming a precursor of an intermetallic phase, which halts the diffusion 33
Self Interstitial diffusion in presence of Nb and Sn from molecular dynamics Nb stops diffusion of self interstitials The diffusion of self interstitial atoms is impeded by Nb and, to a lesser extent, by Sn. 34
Self interstitial diffusion in presence of Sn from molecular dynamics a-direction c-direction Diffusion of self interstitial atoms is anisotropic: faster in basal plane The diffusion of self interstitial atoms is empeded by Sn at low temperatures. At high temperatures there is little effect on self interstitial diffusion 35
Effect of Single Alloying Elements Cr Fe Ni Nb Sn O Site preference Subst. Sub./Int. Subst. Subst. Subst. Interst. Volume effect (%) for 1 wt% -0.81-0.72-0.85-0.27-0.06 1.26 Tendency to segregate to surface (kj/mol) -41-32 -64 5-82 -36 Tendency to segregate to grain boundary -59-67 -60-7 -13 31 Attracts H (kj/mol) (+ means repulsion) -26-56 -18 +2 +3 +1 Attracts vacancy (kj/mol) (+ means repulsion) -12-74 -18-5 -6 1 Attracts interstitial Zr (kj/mol) (* = exchange) -270 * -350 * -273 * -61 11-5 Effect on diffusion of interstitial Zr Fast-c Fast-c Fast-c pin retard small Effect on diffusion of vacancy retard retard small retard small Effect on hydride formation Alloying elements retard hydride formation, most for high H content Effect on a-loop formation diminish Zr interstitials reaching a-loops due to exchange impedes int. loops retards int. loops Effect on c-loop formation enriches c-loops with alloying elements impedes int. loops retards int. loops 36
Scenario for Loop Formation interstitial c-loop vacancy c- loop vacancy interstitial Zr a-loops perfect crystalline Zr vacancies and interstitials; lattice expands isotropic diffusion of vacancies and faster diffusion of interstitials in the a-direction should lead to c-loops being dominantly vacancy loops and a-loops more interstitial loops c-loops c-loops a-loops a-loops small net lattice contraction after collapse of vacancy c-loops, expansion in a-direction due to interstitial a-loops H in vacancy a-loops can prevent collapse: more expansion in a- direction 37
Effect of Fe, Cr, Ni Fe interstitial Fe c-loops a-loops vacancies and interstitials; lattice expands Fe removes interstitial Zr by exchange fast diffusion of interstitial Fe in c-direction fills vacancies, leading to smaller vacancy loops and Fe-decorated interstitial loops: overall smaller effect 38
Effect of Nb Nb c-loops a-loops vacancies and interstitials; lattice expands slower formation of interstitial loops due to Nb-induced slowdown of interstitial Zr diffusion, less expansion in a-direction; faster vacancy diffusion and Frenkel pair recombination possibly impedes formation of interstitial a-loops 39
Effect of Sn Sn Sn tends to segregate to surfaces and may help in the formation of protective oxide layers and diffusion barrier of H If atomically dispersed, Sn can retard the diffusion of self interstitial atoms Sn inhibits the formation of hydrides 40
Summary Present atomistic simulations using the MedeA software environment provide deeper insight and improved, quantitative materials property data: H in pure Zr, vacancies, self interstitials: anisotropic deformations Solubility of H in Zr, terminal solubility Volumetric, thermodynamic, and elastic properties of hydrides as a function of composition Interaction of H with alloying (impurity) elements Fe, Cr, Ni, Nb, Sn; O Inhibition of hydride formation by alloying (impurity) elements Vacancy and interstitial diffusion and loop formation: anisotropy of interstitial diffusion plays key role Impact of H on the collapse of dislocation loops and nucleation of hydrides Effect of alloying elements on diffusivity of H, vacancies and self interstitials: Nb stops interstitial diffusion The present work establishes a firmer basis for thermodynamic, kinetic, and micromechanical models