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Ni(Si)

Ni(Si). Ni. Si. Ni(Si). Ni 3 Si. Ni(Si) + Ni 3 Si. The Ni-rich region of the Ni-Si phase diagram. Dark-field image using Superlattice reflection. After irradiation. Before irradiation. Electron Diffraction Pattern. Before irradiation. After irradiation. zone axis = [100].

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Ni(Si)

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  1. Ni(Si) Ni Si Ni(Si) Ni3Si Ni(Si) + Ni3Si The Ni-rich region of the Ni-Si phase diagram

  2. Dark-fieldimage using Superlattice reflection After irradiation Before irradiation Electron Diffraction Pattern Before irradiation After irradiation zone axis = [100] Ni-4 at.% Si A. Barbu and A.J. Ardell, Scripta Metall. 9 (1975) 1233

  3. The formation of Ni3Si precipitates under 500 keV Ni+ ion irradiation is an early example of radiation-induced precipitation (RIP) as a consequence of radiation-induced segregation (RIS) of Si to point-defect sinks, in this case (mostly) faulted interstitial dislocation loops. The nucleation and growth of precipitates under conditions in which they are not thermodynamically stable is one important manifestation of RIS. RIP occurs when RIS proceeds to such an extent that the solubility limit is exceeded.

  4. RADIATION-INDUCED SEGREGATION AND PRECIPITATION IN ALLOYS Alan J. Ardell Department of Materials Science and Engineering University of California Los Angeles, CA 90095 USA

  5. OUTLINE • Brief description of the physical reasons for RIS and RIP, and their principal causes: Diffusion by solute-atom/point-defect complexes in dilute alloys; Diffusion of solute by the Inverse Kirkendall Effect (IKE). • Modeling RIS---brief discussion of different approches: Examples of the comparisons between experiments and predictions of rate models; A couple of examples of recent Kinetic Monte Carlo simulations. • Observations of RIS at Internal Boundaries in Austenitic and Ferritic Steels: Typical profiles for segregation of Fe, Ni and Cr at static boundaries; Effect of irradiation temperature; Segregation profiles at moving boundaries; Segregation at special boundaries; Effects of other solute elements on RIS. • The conundrum of Thermal Non-Equilibrium Segregation (TNES): TNES segregation profiles and the IKE; W-shaped segregation profiles • Effect of RIS on mechanical behavior in steels • Closing remarks

  6. PRINCIPAL MANIFESTATIONS OF RADIATION-INDUCEDSEGREGATION (RIS) • Long-range flow of solute atoms to point-defect sinks:(a) dislocation lines in a network---closed loops, faulted or not---(b) internal interfaces like stacking faults and grain boundaries---(c) free surfaces, including the surfaces of voids; • Formation of a new phase or phases in alloys that areundersaturated in the unirradiated condition. RIP occurs when the solubility limit for that phase is exceeded; • Enrichment or depletion of solute atoms at internal interfaces and surfaces, without necessarily forming a new phase; • Short-range flow of solute atoms to solute-rich clusters. This process can destabilize a solid solution, producing precipitation of a new phase (Cauvin and Martin, PRB, several papers, 1981,82).

  7. CONSEQUENCES OF RIS • Segregation of atoms and precipitation of new phases at grain boundaries and dislocations can lead to reduced fracture toughness at high temperatures; • In principle, enrichment or depletion of solute atoms to internal interfaces can reduce the resistance of an alloy to stress-corrosion cracking or simply reduce its resistance to corrosion; • It could be argued that there might be beneficial consequencesof RIS (e.g. strengthening at high temperatures), but it would be very difficult to convince a design engineer that something good can come of it.

  8. PRINCIPAL MECHANISMS OF RIS • Preferential strong binding of solute atoms to point defects, producingsolute-atom/point-defect complexes that induce the flow of atomsand point defects in the same direction; • Diffusive flow of unbound, or weakly bound, solute atoms in responseto fluxes of point defects induced by strong defect gradients nearpoint-defect sinks---this is referred to as the INVERSEKIRKENDALL EFFECT (IKE); • Both mechanisms can contribute to RIS in a given alloy containing 2 or more solute atoms, and therefore both will certainly be important in commercial alloys.

  9. DIFFUSION OF SOLUTE-ATOM/POINT-DEFECT COMPLEXES RIS by the diffusion of solute-atom/point-defect complexesis particularly effective for complexes involving interstitials andundersized solute atoms. It is believed to be main factor leadingto radiation-induced precipitation at void surfaces, dislocationloops, grain boundaries and free surfaces in a very large numberof alloys, including the stainless steel in which the radiation-inducedprecipitation of Ni3Si at void surfaces was first observed byOkamoto and Wiedersich, J. Nucl. Mater. 53 (1974) 336, As well as the undersaturated binary Ni-Si alloy in which radiation-induced precipitation of Ni3Si at interstitial dislocation loops wasfirst observed by Barbu and Ardell, Scripta Metall. 9 (1975) 1233.

  10. Other examples of RIP in undersaturated Ni-Si alloys

  11. Formation of Ni3Si in undersaturatedNi-Si alloys proton-irradiated to adose of 0.42 dpa: (a) 2% Si, 550 °C,at voids (arrows) and dislocation loops; (b) 8% Si, 450 °C, at stacking faults, discontinuous precipitation at GB; (c) 6% Si, 550 °C, coherent twin boundary; (d) 6% Si, 300 °C, modulated dislocation loop structure. Ardell and Janghorban, Phase Transformations During Irradiation, 1983, p. 301

  12. Solute-Atom/Interstitial Diffusion Displacement and rotation of mixed dumbbells Displacement and rotation of solvent and mixed dumbbells Wiedersich and Lam, PTDI, 1983, p. 17

  13. Solute-Atom/Vacancy Diffusion Jumps that must be accounted for when a solute atom (shaded),oversized in this case, is nearest neighbor to a vacancy or a solventatom which is itself nearest neighbor to a vacancy. W0, W1, W2,W3 and W4 represent 5 different jump frequencies, all of whichare difficult to calculate. Wiedersich and Lam, PTDI, 1983, p. 11

  14. The solute-atom/point-defect pairs depicted in the previous slidesare most meaningful when the solutions are very dilute. In concentrated solid solutions the probability of forming solute-solutedumbbells, and perhaps even more complex entities involving severalinterstitial atoms, increases. Similar complexities arise in the case ofvacancies, because any given vacancy will have several solute atomsas nearest neighbors.

  15. An exception to the ”Size Rule" is the observation by Barbu of Ni3Ge at assorted sinks in irradiated undersaturated Ni-Ge alloys, confirmed later by Rehn and Okamoto; Ge is an oversized atom in Ni solid solutions. A. Barbu, in Comportement sous Irradiation des Materiaux Metalliques et des Coeurs des Reacteurs Rapides, ed. by J. Poirier and J.M. Dupouy, CEA, Gif-sur-Yvette (1979). L.E. Rehn and P. R. Okamoto, PTDI 1983, p. 247. In general SA/I complexes lead to enrichment (and possibly radiation induced precipitation) at sinks when the solute is UNDERSIZED, and SA/V complexes lead to depletion at PD sinks when the solute is OVERSIZED. Depletion of an UNDERSIZED solute at sinks has never been observed.

  16. An alternative approach to RIS; the Inverse Kirkendall Effect(from Rehn and Okamoto, PTDI: 1983) Vacancy Mechanism If A diffuses faster than B the boundary (or free surface) will be depleted in A and enriched in B, and vice versa (this is enrichment in B by subtraction of A). This was first realized by T.R. Anthony, J. Appl. Phys. 41 (1970) 3969, and first associated with RIS by A.D. Marwick, J. Phys. F 8 (1978) 1849.

  17. Rate theories-continuum diffusion models: R.A. Johnson and N.Q. Lam, Phys. Rev. B 13 (1976) 4364. N.Q. Lam, P.R. Okamoto and H. Wiedersich, J. Nucl. Mater. 74 (1978) 101; A.D. Marwick, J. Phys. F 8 (1978) 1849. J.M. Perks and S.M. Murphy: Mater. For Nuclear Reactor Core Components, BNES (1987) 165. S.M. Murphy, Philos. Mag. A 59 (1989) 953. A.S. Bakai and A.A. Turkin, ASTM STP 1125 (1992) 709. T.R. Allen and G.S. Was, Acta Mater. 46 (1998) 3679. T.S. Duh, J.J. Kai, F.R. Chen and L.H. Wang, J. Nucl. Mater. 294 (2001) 267. N. Sakaguchi, S. Watanabe and H. Takahashi, J. Mater. Sci. 40 (2005) 889. R.P. Fernandes, N.K. Patel, A. Miotello and D.C. Kothari, Surf. Coatings Tech. 201 (2007) 8424. Mean-field lattice diffusion models: Y. Grandjean, P. Bellon and G. Martin, Phys. Rev. B 50 (1994) 4228. M. Nastar, P. Bellon, G. Martin and J. Ruste, MRS Symp. Proc. 481 (1998) 383. M. Nastar, Philos. Mag. 85 (2005) 641. Non-equilibrium segregation models (diffusion only by solute/PD complexes): R.G. Faulkner, N.C. Waite, E.A. Little and T.S. Morgan, Mater. Sci. Engr, A171 (1993) 241. R.G. Faulkner, S. Song and P.E.J. Flewitt, Metall. Mater. Trans. A, 27A (1996) 3381. C.C. Goodwin, R.G. Faulkner and S.B. Fisher, ASTM STP 1325 (1999) 634. Theories of RIS in Concentrated Binary Alloys

  18. Kinetic Monte Carlo Simulations of RIS: F. Soisson, Philos. Mag. 85 (2005) 489. F. Soisson, J. Nucl. Mater. 349 (2006) 235. J. Rottler, D.J. Srolovitz and R. Car, Philos. Mag. 26 (2007) 3945. Kinetic Monte Carlo Simulation of Homogeneous Nucleation: P. Krasnochtchekov, R.S. Averback and P. Bellon, Phys. Rev. B 75 (2007) 144107.

  19. CA, CB, Cv & Ci are concentrations of A atoms, B atoms vacancies and interstitials, respectively JA, JB, Jv & Ji are fluxes of A atoms, B atoms vacancies and interstitials, respectively G is the rate of production per unit volume of vacancies and interstitials by irradiation R is a constant expressing the recombination of vacancies and interstitials Theory of RIS in Concentrated Binary Alloys H. Wiedersich, P.R. Okamoto and N.Q. Lam, J. Nucl. Mater. 83 (1979) 98

  20. In concentrated solid solutions models describing transport by individual atom-vacancy and atom-interstitial complexes are not valid because complexes are rarely, if ever, isolated, so a different approach is required. Assuming that correlation coefficients are equal to unity, Wiedersich et al. describe the fluxes of A, B, v and i in terms of Partial Diffusion Coefficients Transport of A atoms is the partial diffusion coefficient of A via exchange with vacancies is the partial diffusion coefficient of vacancies via exchange with A atoms is the partial diffusion coefficient of A atoms via interstitial transport is the partial diffusion coefficient of interstitial A atoms via interstitial transport is the jump frequency of an interstitial A atom to a nearest-neighbor interstitial site where nAv is the jump frequency of an A atom to a nearest-neighbor vacant lattice site are concentrations expressed as atom fractions

  21. Fluxes of All Diffusing Species a is the thermodynamic factor

  22. The flux of A atoms depends on the usual Fickian term ( ) plus contributions from the vacancy gradient ( ) and the interstitial gradient ( ) Likewise, the fluxes of vacancies and interstitials depend not only on their own gradients, but also on the gradients of A and B atoms, giving rise to the second terms in both equations. In general

  23. Steady-State Assuming that all interstitials and vacancies are eliminated by recombination (restrictive physically, but instructive for predictive purposes), After some algebra

  24. When and CB CA Cv 0 0 0 distance from sink distance from sink distance from sink

  25. Cv 0 distance from sink CA 0 distance from sink Physical significance of these profiles The concentration of vacancies (and interstitials) always decreases at sinks from its value in the bulk, i.e. Because of the diffusion constants chosen the gradient of A atoms is also > 0, so the concentration of A is smaller at the sink than it is in the bulk. This is a manifestation of the IKE. THERE IS NO FLUX OF A ATOMS. THIS STEADY-STATE PROFILE OBTAINS WHEN THE FLUX OF A AWAY FROM THE SINK (IKE) IS BALANCED BY THE FLUX TOWARDS IT FROM NORMAL DIFFUSION.

  26. Does the model of Wiedersich et al. Have predicitive capability? RIS in undersaturated Ni-Si alloys produces surface films of Ni3Si

  27. Surface film of Ni3Si in a Ni-6% Si alloy; 400 keV H+, dose = 0.06 dpa, 500 °C. The lines in this dark-field TEM image are traces of anti-phase boundaries. Ardell and Janghorban, PTDI, 1983, p. 303

  28. Kinetics of growth of Ni3Si surface films in a Ni-12.7 at% Si alloy under 2 MeV He+ irradiation The model of Wiedersich et al., assuming strong coupling of Si atoms and interstitials, and boundary conditions for the growth of surface films, predicts that the film thickness varies as (dose)1/2, with an activation energy = to 1/4 that of motion of the slowest diffusing species (vacancies) at lower T (even though transport of Si to the film occurs by the motion of Si-interstitial complexes). At higher T the Arrhenius slope is positive and equal to half the vacancy formation energy. Note that the growth rates of the films (the slopes of the curves) first increase with T, then decrease. R.S. Averback, L.E. Rehn, W. Wagner, H. Wiedersich and P.R. Okamoto, Phys. Rev. B 28 (1983) 3100.

  29. Slope yields ≈ 0.3 eV ≈ Emv/4 Slope yields ≈ 0.75 eV, assumed to be ≈ Efv/2 No-theory region data of Averback et al. L.E. Rehn and P.R. Okamoto, PDTI, 1983, p. 267.

  30. Physical significance of these results The dominant process during RIS is recombination of interstitials and vacancies (there is no RIS if all interstitials and vacancies created by irradiation recombine); At low T the thermal equilibrium concentration of vacancies is negligible. Increasing T simply increases vacancy mobility (hence the dependence on Emv), increasingly enabling the escape of vacancies to sinks, thereby reducing recombination and increasing the growth rate of the film due to the increasing concentration of interstitial Ni-Si complexes; At high T the thermal equilibrium vacancy concentration becomes increasingly important (hence the dependence on Efv). As T increases Cv increases, thereby increasing recombination and reducing the concentration of interstitial Ni-Si complexes; At low T increasing the fluence (dose rate) has the same effect as increasing T at a fixed dose rate. Vacancies and interstitials are generated at faster rates, but recombination disproportionately increases and the growth rate decreases.

  31. RIS in Steels

  32. Representative behavior of RIS in austenitic stainless steels. Cr and Fe are depleted at grain boundaries, while Ni is enriched. At a given dose the width of the segregation profile increases with increasing irradiation temperature. D.I.R. Norris, C. Baker, C. Taylor and J.M. Titchmarsh, ASTM STP 1125 (1992) 603

  33. Examples of RIS in ferritic steels are much harder to find, but as shown below Cr is depleted at grain boundaries while Ni is enriched. T. Muroga, A. Yamaguchi and N. Yoshida, ASTM STP 1046 (1989) 396.

  34. RIS in an austenitic stainless steel at moving grain boundaries, illustrating the highly asymmetric segregation profiles found under this condition. D.I.R. Norris, C. Baker, C. Taylor and J.M. Titchmarsh, ASTM STP 1125 (1992) 603

  35. Other factors affecting RIS: Minor additions of oversized solute atoms; Minor additions of interstitial solute atoms; Grain boundary character; Grain boundary migration.

  36. Suppression of RIS at GBs in Type 316 stainless steel by the addition of Zr or Hf (Ti to a lesser extent) HVEM, 10.8 dpa T. Kato, H. Takahaski and M. Izumiya, J. Nucl. Mater. 189 (1992) 167.

  37. Suppression of RIS at GBs in Type 316 stainless steel by the addition of Pt or Hf L. Fournier, B.H. Spencer, G.S. Was, E.P. Simonen and S.M. Bruemmer, J. Nucl. Mater. 321 (2003) 192.

  38. • Interstitial carbon and nitrogen in stainless steel subjected to 12 MeV Ni+ at 573 K can affect RIS of substitutional elements, as shown here. • Kano, Fukuya, Hamada and Miwa, J. Nucl. Mater. 258-263 (1998) 1713.

  39. Trapping of vacancies by oversized solutes promotes recombination. This does not explain the effect of interstitial atoms, but the formation of small carbide and/or nitride precipitates could also serve to trap vacancies and promote recombination.

  40. Effect of grain boundary misorientation on RIS in an austenitic stainless steel. The enrichment of Ni and depletion of Cr at special boundaries is reduced because the efficiency of these boundaries as point-defect sinks is reduced compared to random GBs. The solid lines represent fitting to a continuum rate theory, modified to take the sink strength of GBs into account. N. Sakaguchi, S. Watanabe, H. Takahashi and R.G. FaulknerJ. Nucl. Mater. 329-333 (2004) 192.

  41. Results of the modeling by Sakaguchi et al. of RIS and radiation-induced grain boundary motion in an electron-irradiated austenitic steel. The model includes the GB velocity, which depends on the difference between the actual and equilibrium vacancy concentrqtions, via a parameter av,i (called the rearrangement factor). This parameter, substituted into the rate equations of Wiedersich et al., reproduces the correct behavior, though its physical meaning is not certain. N. Sakaguchi, S. Watanabe and H. Takahashi, J. Mater. Sci. 40 (2005) 889.

  42. Parameters used by Sakaguchi et al. to model RIS and radiation-induced grain boundary motion in an austenitic steel. The model also includes the GB velocity, which depends on the difference between the actual and equilibrium vacancy concentrations. N. Sakaguchi, S. Watanabe and H. Takahashi, J. Mater. Sci. 40 (2005) 889.

  43. A few other models of RIS; predicted behavior in steels

  44. The actual experimental dose was 6 dpa. The model assumes that RIS under 3 MeV Ni+ irradiation occurs exclusively by vacancy diffusion via the Inverse Kirkendall Effect. Quantitative agreement is poor. A.D. Marwick, R.C. Piller and M.E. Horton, Dimensional Stability and Mechanical Behaviour of Irradiated Metals and Alloys, BNES, London, 1984, p. 11

  45. The non-monotonic dependence of RIS on dose is reproduced only qualitatively. Comparison of the predictions of the CEA model (Grandjean et al., updated using 2 sets of parameters) with the data of Damcott, Allen and Was, J. Nucl. Mater. 225 (1995) 97. The quantitative agreement is very good for parameter set 2, which includes the effect of interstitials (parameter set 1 does not). The parameter set includes 18 physical quantities.

  46. KMC simulation of RIS in an ideal bcc solid solution (10 %A) under electron irradiation at 500 K and a dose rate of 10–3 dpa/s. The solid curves show the predictions of the rate theory model of Wiedersich et al. with dAV > dBV. For the parameters chosen there is a major contribution to RIS from the IKE. The non-monotonic dependence of the solute-concentration profile is apparent. THIS IS NOT A STEEL F. Soisson, J. Nucl. Mater. 349 (2006) 235.

  47. The Thermal Non-Equilibrium Segregation (TNES) Conundrum TNES refers to the enrichment of solute atoms at grain boundaries at intermediate cooling rates from high solution-treatment temperatures. In austenitic stainless steels TNES produces an enrichment of Cr at GBs in UNIRRADIATED alloys. Subsequent irradiation to moderate doses produces a “W-shaped” segregation profile for Cr atoms. Continued irradiation produces the depletion of Cr usually observed.

  48. Proton-irradition data (filled circles) from J.T. Busby, G.S. Was, S.M. Bruemmer, D.J. Edwards and E.A. Kenik, MRS Symp Proc 540 (1999) 540. Neutron-irradiation data (open circles) from C.C. Goodwin, R.G. Faulkner and S.B. Fisher, ASTM STP 1325 (1999) 634.

  49. At solution treatment temperature Xv = Xv,eq Vacancy flux Flux of Cr atoms from IKE Xv After moderately fast cooling Xv,GB < Xv,eq 0 distance from GB Vacancy and Atom Motion during TNES Since Cr is the fastest diffuser in austenitic stainless steels, the IKE predicts Cr DEPLETION at GBs for this type of heat treatment. Instead, ENRICHMENT of Cr is observed experimentally. TNES cannot be explained by the Inverse Kirkendall Effect.

  50. Vacancy flux Vacancy concentration Flux of Cr atoms from vacancy binding 0 distance from GB Explanation by Goodwin, Faulkner and Fisher, ASTM STP 1325 (1999) 634 Cr is oversized in austenitic SS, hence has a positive binding energy with vacancies. Unirradiated Stainless Steel Cr enrichment at GBs

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