The mechanism of radiation-induced segregation in ferritic–martensitic alloys

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ScienceDirect Acta Materialia 65 (2014) 42–55 www.elsevier.com/locate/actamat

The mechanism of radiation-induced segregation in ferritic–martensitic alloys Janelle P. Wharry ⇑, Gary S. Was University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109, USA Received 3 February 2013; received in revised form 20 September 2013; accepted 29 September 2013 Available online 20 December 2013

Abstract The mechanism of radiation-induced segregation in Fe–Cr alloys was modeled using the inverse Kirkendall mechanism and compared to experimental measurements over a range of temperatures, bulk Cr compositions, and irradiation dose. The model showed that over a large temperature range chromium was enriched at sinks by interstitial migration, and at very high temperatures it was depleted by diffusing opposite to the vacancy flux. Experimental results and model predictions were in good qualitative and quantitative agreement with regard to the temperature dependence of segregation and the crossover from Cr enrichment to Cr depletion. The inverse Kirkendall mechanism was also in agreement with experimental findings that observed a decreasing amount of Cr enrichment with increasing bulk Cr composition. The effects of solute drag were modeled within the inverse Kirkendall framework, but were unable to account for either the crossover from Cr enrichment to Cr depletion or the magnitudes of segregation measured in experiments. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Radiation-induced segregation; Ferritic–martensitic; Proton irradiation

1. Introduction The renewed interest in nuclear energy as a source of carbon-free electricity has reinvigorated research on the effects of irradiation in ferritic–martensitic (F–M) alloys, which are the leading candidates for cladding and structural components in some advanced nuclear reactor concepts. These steels have high strength at elevated temperatures, are resistant to thermal stresses and are dimensionally stable under irradiation [1]. However our understanding of nucleation and growth of defect clusters (loops, voids), phase stability, radiation-induced segregation and irradiation creep is lacking. Radiation-induced segregation (RIS), in particular, suffers from very few and conflicting observations, confounding a mechanistic understanding of its origin. ⇑ Corresponding author. Present address: Boise State University, 1910 University Drive, Boise, ID 83725, USA. Tel.: +1 734 936 0266; fax: +1 734 763 4540. E-mail address: [email protected] (J.P. Wharry).

Lu et al. [2] recently surveyed the literature on the RIS behavior of F–M alloys and identified only 15 experimental studies on RIS in a variety of model and commercial F–M alloys (5–13% Cr), irradiated over a range of temperatures (250–800 °C), doses (0.5–118 dpa), and fluxes (105–101 dpa s1), and with a variety of irradiating particles. Lu et al.’s survey revealed small amounts of Cr enrichment (<5 wt.% Cr) at grain boundaries in some studies and depletion in others. Given the inconclusive, inconsistent data and the varying conditions under which the experiments were performed, it was impossible to extract trends in the data or any mechanistic understanding of RIS. The finding of grain boundary Cr enrichment in F– M alloys was contrary to the highly consistent and repeatable measurements of Cr depletion in austenitic alloys, which has been accurately predicted by the inverse Kirkendall (IK) mechanism [3]. Thus, the IK mechanism was initially suspected to be irrelevant to F–M alloys. Until this work, however, a thorough investigation of the IK mechanism using material parameters appropriate for

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.09.049

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

body-centered-cubic (bcc) Fe–Cr alloys, had not been performed. Other mechanisms were investigated in attempts to explain the inconsistent experimental results of Cr RIS. The solute drag mechanism, in which tightly bound solute-defect complexes diffuse significant distances before dissociating, was proposed as a possible mechanism of RIS in F–M alloys. However, most investigations of the solute drag mechanism [4–7] focused on minor elements such a P, S and B rather than on major alloying components like Cr in Fe. Recent modeling efforts calculated attractive binding energies between Cr atoms and vacancies as well as between Cr atoms and interstitials [8–10], suggesting that Cr would enrich via solute drag. Prior to this work, only Johnson and Lam [11,12] had accounted for the effects of solute drag in a rate theory (i.e. IK-type) model, but their results were inconclusive and were presented only for ternary face-centered cubic (fcc) Fe–Cr–Ni systems. Recent work has suggested a link between RIS in Fe–Cr alloys and atomic-level electronic and magnetic properties, manifest as a change of sign of mixing enthalpy near 10% Cr [13–18]. These models reinforced experimental observations [19–21] that at low Cr concentrations, Cr atoms order as far apart from one another as possible [15,22], but with increasing Cr concentration, Cr–Cr interactions become unavoidable, leading to positive formation enthalpy [22]. This theory offers a plausible explanation for why highCr steels would have clusters, precipitates and grain boundaries enriched in Cr. However, mixing enthalpy cannot explain the underlying mechanism of RIS, since it does not consider how atomic species are transported toward or away from grain boundaries, nor can it explain Cr enrichment in low-Cr steels, as observed in Refs. [23,24]. The solute size effect has also been addressed. Wong et al. [8] and Choudhury et al. [10] calculated that Cr is an undersized solute in the Fe matrix, while Terentyev et al. [25] calculated that Cr is oversized. Lu et al. [2] also argued the solute size effect, based upon atomic radii differences, suggesting that with increasing concentrations of oversized impurities (e.g. W, Nb, Mo, Ti), the relative size of Cr, and thus the tendency of Cr to deplete, decreases. While a number of theories for Cr RIS in bcc Fe–Cr alloys have been proposed and investigated, none could consistently and comprehensively explain experimental observations. In addition, it was not until Wharry and Was [24] presented the first systematic experimental study of RIS in F–M alloys, that the dependencies of RIS on irradiation parameters and on Cr content could be established. The authors found small amounts of Cr enrichment (<2 wt.%) in all but one dose/temperature condition, and found that Cr enrichment followed a bell-shaped temperature dependence. In T91 irradiated to 3 dpa, Cr enrichment was at a minimum at 300 °C and 600 °C, and a maximum at 450 °C; Cr depletion only occurred at 700 °C. The extent of Cr enrichment decreased with increasing bulk Cr content, following 400 °C irradiation to 3 dpa. Lastly, the authors found little dose dependence of Cr RIS in T91 irra-

43

diated at 400 °C to 1, 3, 7 and 10 dpa. Understanding these systematic variations of RIS with key parameters is a prerequisite to identifying the mechanism(s) driving RIS and in developing a predictive model. This paper aims to determine the mechanism of RIS in a binary Fe–Cr (bcc) system by comparing model calculations of RIS based on the IK mechanism against experimental measurements. Since the IK mechanism is both well known and has been applied to austenitic Fe–Cr–Ni alloys, it is selected as the reference case for investigation of RIS in bcc Fe–Cr alloys. The effects of solute drag will then be incorporated into the IK model. Model calculations will be compared to the experimental measurements presented in Ref. [24]. Model–experiment comparisons will demonstrate whether RIS in F–M alloys is consistent with the IK and solute drag mechanisms. Finally, experimental measurements of RIS published in the open literature will be considered in the context of the results of this paper. 2. Inverse Kirkendall model for binary Fe–Cr alloys The purpose of this section is to describe the inverse Kirkendall modeling methodology for Fe–Cr alloys and the sensitivity of variables to input parameters. Appropriate input parameters will be chosen for an Fe–9Cr bcc alloy system. Finally, the method for comparing model results to experimental measurements will be described. 2.1. The inverse Kirkendall model The one-dimensional (1-D) inverse Kirkendall model used in this study was based upon the framework of the Perks [26,27] rate theory model. In this framework, a system of equations representing the concentrations of the major alloying elements and the point defects is solved simultaneously as a function of space and time. These equations are written for a binary A–B alloy as: @C A ¼ r½DA arC A þ N A ðd Av rC v  d Ai rC i Þ: @t @C B ¼ r½DB arC B þ N B ðd Bv rC v  d Bi rC i Þ: @t @C i ¼ r½d Ai N i arC A  d Bi N i arC B þ Di rC i  þ K 0  R  S i ; @t @C v ¼ r½d Av N v arC A  d Bv N v arC B þ Dv rC v  þ K 0  R  S v : @t

ð1Þ ð2Þ ð3Þ ð4Þ

Eqs. (1)–(4) represent the time rate of change of the concentrations of atoms A and B, interstitials and vacancies, respectively, at a fixed position in space. The right-hand sides of Eqs. (1) and (2) represent the positional flux of the given atomic specie. The right-hand sides of Eqs. (3) and (4) consider defect production (K0), loss of defects to recombination (R) and sinks (Si or Sv), and the positional flux of defects (bracketed terms). In all of the above equations, variables are concentration C, time t, diffusion coefficients D, diffusivities d, number density N and

44

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thermodynamic factor a; subscripts are X = {A, B} for an atomic specie, y = {v, i} for vacancies or interstitials, and Xy for the diffusion of atomic specie X via defect y. The model was initially written to describe RIS in the austenitic (fcc) Fe–Cr–Ni ternary alloy. In this work, it is adapted for the bcc Fe–Cr binary system. The IK model is coded in Fortran and uses the GEAR software package [28–30] to solve a system of differential equations (each equation representing the time rate of change of the concentration of each atomic specie and both types of point defects) with initial and boundary conditions, by using finite differences to solve spatial derivatives with a continuous time variable [28–30]. The IK model is compiled, debugged and executed using SilverFrost Fortran 95 [31] for MicrosoftÒ Windowse. The IK model solves Eqs. (1)–(4) across a plane foil at user-defined time steps. One surface of the plane foil is fixed to simulate the grain boundary and to act as an unbiased point defect sink. Symmetry is assumed across the grain boundary. The dimension of the foil is divided into a three-region mesh, as shown in Fig. 1. In the first region the solution changes rapidly so a fine mesh (0.25 nm) is used for the first 4 nm from the boundary. In the second region extending from about 4 to 18 nm, a 1 nm mesh spacing is used. In the third region, the solution reaches steadystate, so small intervals are unnecessary; points with a few hundred nm spacing are sufficient. A number of inputs are required for model execution. A complete list of the input parameters, with their definitions, values and units, is provided in Table 1. The selection of values for each of these input parameters will be addressed in Section 2.1.2, but it is helpful to understand the sensitivity of the model to each of the parameters first. 2.1.1. Sensitivity analysis Model sensitivity was defined as the derivative of the grain boundary Cr concentration with respect to an input parameter, oC/oP. For calculational purposes, the sensitivity was approximated as the ratio of the change in grain boundary Cr concentration to the change in input parameter, dC/dP, when the input parameter was varied by a factor of 104 about its reference value. The sensitivity was expressed as:

Fig. 1. Schematic of 1-D positional regions in IK model.

@C dC C 0  C reference  ¼ 0 ; @P dP P  P reference

ð5Þ

where Creference is the grain boundary Cr concentration calculated at Preference and C0 is the resulting grain boundary Cr concentration calculated at P0 . The sensitivity can be expressed as a significance, S CP , which is the fractional change in calculated grain boundary Cr concentration relative to the fractional change in input parameter. The significance of C given P is defined as: S CP ¼

C 0  C reference P reference  : P 0  P reference C reference

ð6Þ

It follows, then, that the variable of interest, grain boundary Cr concentration, is most sensitive to those parameters that have the largest magnitude of the significance. Significance was calculated at two temperatures, 320 °C and 500 °C, for Fe–9Cr irradiated to a steady-state dose of 15 dpa at 105 dpa s1; results are shown in Fig. 2. Significance results for the two temperatures are nearly identical, suggesting that significance is not highly sensitive to temperature. Furthermore, the grain boundary Cr concentration is highly sensitive to four parameters: the vacancy and migration energies of both Cr and Fe. The Cr concentration is relatively insensitive to all other parameters studied. The high sensitivity to point defect migration energies and insensitivity to other material parameters was substantiated by Allen and Was [3] for austenitic alloys. 2.1.2. Input parameter selection Given the significance of the point defect migration energies demonstrated in the preceding section, selecting appropriate values for these energies was critical to obtaining useful, relevant results from the IK model. Input parameter values appropriate for a bcc Fe–9Cr alloy are given in Table 1; these values were taken from experiments or, when experimental data were unavailable, from model simulations. Migration energies, given their high significance, will be discussed in greater detail in this section. Identification of appropriate values for the Fe and Cr vacancy and interstitial migration energies relied on ab initio modeling, since limited experimental studies examining point defect migration in bcc Fe–Cr alloys utilized the resistivity recovery technique exclusively, which provided only qualitative results [32–35]. Quantitative experiments using positron annihilation or tracer diffusion techniques were performed only on pure bcc a-Fe or pure bcc Cr, and thus provided only a bounding limit of point defect migration energies [34,36–39]. However, recent ab initio models [8,10,16,25,40–42] calculated energies of vacancy and interstitial jumps, the orientations of which have been defined by LeClaire [43,44]. In the following sections, ab initio calculations will be used to determine the migration energies input to the IK model, and will be compared against bounding qualitative experimental results.

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45

Table 1 List of values for input parameters to IK model, or IP0. Definition

Symbol

Unit

Value

Reference

Vacancy production efficiency Interstitial production efficiency Number density Jump distance Vacancy jump correlation factor, Fe Vacancy jump correlation factor, Cr Interstitial jump correlation factor, Fe Interstitial jump correlation factor, Cr Vacancy jump frequency, Fe Vacancy jump frequency, Cr Interstitial jump frequency, Fe Interstitial jump frequency, Cr Interstitial migration energy, Fe Interstitial migration energy, Cr Vacancy formation enthalpy Vacancy migration energy, Fe Vacancy migration energy, Cr Vacancy formation energy, Fe Vacancy formation energy, Cr GB formation energy Dose rate Dislocation density Debye frequency, vacancy Debye frequency, interstitial Thermodynamic factor Number of neighbour atoms

ev ei N k fvFe fvCr fiFe fiCr xvFe xvCr xiFe xiCr EFe mi ECr mi Sfv EFe mv ECr mi EFe fv ECr fv EGb f K0 qd mv mi a z

unitless unitless at m3 m unitless unitless unitless unitless s1 s1 s1 s1 eV eV eV m1 eV eV eV eV eV dpa s1 m2 s1 s1 unitless unitless

0.3 0.3 8.34  1028 2.48  1010 0.727 0.777 0.727 0.727 1.60  1013 2.40  1013 2.90  1012 4.20  1012 0.35 0.28 1.00 0.63 0.55 1.6 2.25 0.87 105 0 1.50  1013 1.50  1012 1 8

[62] [62]

α E GB f

320°C 500°C

E Cr fv E fvFe Cr Emv Fe Emv S

fv

Cr Emi Fe Emi ω iCr ω iFe ω vCr ω

vFe

f

iCr

f iFe f

vCr

f

vFe

-60

-40

-20

0

20

40

60

Significance Fig. 2. Results of sensitivity analysis of inverse Kirkendall model.

2.1.2.1. Vacancy migration energies. Vacancy migration energies of both Fe and Cr were determined from ab initio calculations of bcc Fe containing dilute additions of Cr. In this alloy system, a number of Fe-vacancy or Cr-vacancy jump configurations exist. This section will identify which of the jumps were considered in the migration energy values used in the IK model. There are six Fe-vacancy jumps to consider: w3, w4, w3’, w4’, w3’’ and w4’’, as defined by LeClaire [43,44]; the energies of these jumps have been calculated by ab initio

[63–65] [66] [67] [67] [68] [68] [69] [69] See Section See Section [3] See Section See Section [36,70] [71] [72]

2.1.2 2.1.2 2.1.2 2.1.2

[3] [3] [3]

methods in dilute Fe–Cr alloys by Choudhury et al. [10], Wong et al. [8] and Nguyen-Manh et al. [40]. These energies are compiled in Table 2. The average of these migration energies is 0.63 eV, which shall be used for the Fe-vacancy migration energy in this work. Because the IK model does not discretely consider all jump configurations, the use of an average migration energy is an attempt to account for all jump configurations within the limitations of the IK model. Ab initio calculations suggest that the addition of dilute amounts of Cr to bcc Fe causes the Fe-vacancy migration energy to decrease [8,10], which is consistent with the 0.63 eV Fe-vacancy migration energy in dilute Fe–Cr alloys being lower than the 0.68 eV migration energy in pure bcc a-Fe [45]. The w2 jump in dilute bcc Fe–Cr alloys will be used for Cr-vacancy diffusion. The w2 migration energy has been calculated by Choudhury et al. [10], Wong et al. [8], Nguyen-Manh et al. [40] and Olsson et al. [16], the results of which are summarized in Table 2, and average 0.55 eV, which will be used for the Cr-vacancy migration energy in this study. The Fe-vacancy and Cr-vacancy migration energies determined here imply that Cr preferentially migrates via vacancies. This was confirmed by resistivity recovery experiments, which showed that vacancies become mobile at a lower energy in binary Fe–Cr (205-201 K) [32,33] than in pure bcc Fe (220 K) [34]. 2.1.2.2. Interstitial migration energies. Interstitial migration energies of Fe and Cr were also determined from ab initio

46

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

Table 2 Solute-defect migration energies (eV) determined from ab initio models. Migration energy, Em (eV)

Jump configuration

Ref. [10]

Ref. [8]

Fe-vacancy

w3 w4 w03 w04 w003 w004 5Fe + 1Cr

0.69 0.65 0.67 0.63 0.64 0.62

0.66 0.62 0.65 0.59 0.60 0.57

Ref. [40]

Ref. [16]

Ref. [41]

Ref. [42]

Average

Variation in Ema

0.63

0.06

0.627

Cr-vacancy

w2

0.58

Fe-interstitial

w0 w4 w6

0.35 0.39 0.36

Cr-interstitial

w1 w2

0.25 0.33

0.52

0.571

0.54 0.34

0.55

0.03

0.34 0.35

0.35

0.04

0.23 0.33

0.28

0.05

a

Variation is calculated as the largest absolute difference between the average migrationz energy (column 9) and either the maximum or minimum migration energy calculated by ab initio methods (columns 3-8).

calculations of bcc Fe containing dilute Cr additions. A number of interstitial jump configurations exist for both Fe and Cr. However, models have suggested that it may be energetically favorable for the interstitial to diffuse as a dumbbell [8,25,41], so the orientation of the interstitial must be considered first. Fu et al. [41] showed that in pure a-Fe, the h1 1 0i dumbbell is the most energetically favorable interstitial. Other models corroborated this finding in both dilute and concentrated Fe–Cr alloys [8,25]. Additionally, Terentyev et al. [25] demonstrated that this orientation accounts for >99% of interstitials in concentrated Fe–Cr alloys. Thus, for the purpose of this work, it will be assumed that all interstitials are of the h1 1 0i dumbbell orientation. Three h1 1 0i interstitial dumbbell jump configurations are Fe-interstitial jumps: w0, w4 and w6. The calculations of Choudhury et al. [10], Fu et al. [41] and Olsson [42] are summarized in Table 2, and average to 0.35 eV, which shall be used for the Fe-interstitial migration energy in this work. This value is in good agreement with the mono-interstitial migration energy of 0.33 eV in pure bcc a-Fe [45]. The w1 and w2 jumps are Cr-interstitial jumps. The calculations of Choudhury et al. [10] and Olsson [42] are summarized in Table 2, and average to 0.28 eV, which will be used for the Cr-interstitial migration energy in this work. Resistivity recovery experiments have shown that the addition of Cr to a-Fe stabilized mixed-dumbbell selfinterstitial atoms (SIA)s, confirming that Cr is a faster interstitial diffuser than Fe [35]. Similarly, Terentyev et al. [25] calculated that the migration energy of single SIAs decreased with increasing Cr concentration. Both experiments [35] and models [10,25,41,42] agree that Cr is a faster diffuser than Fe by way of interstitials. 2.2. Consideration of the solute drag mechanism This section describes the incorporation of the solute drag mechanism for RIS into the existing IK model

framework. This mechanism was initially described by Aust et al. [46] and Anthony [47] and it considers both solute-interstitial and solute-vacancy complexes. Soluteinterstitial complexes are considered as di-interstitial dumbbells. For solute-vacancy complexes, atomic species strongly bound to vacancies would be carried, or “dragged”, along with the vacancy flux to grain boundaries. In this work, the solute drag mechanism was modeled by adding the diffusion of solute-vacancy and solute-interstitial complexes to the existing rate-theory IK model presented in the preceding sections. The formulation of Johnson and Lam [11,12] aided in defining the appropriate kinetic rate equations for solute-defect complexes: @C iCr ¼ DiCr r2 C iCr þ K iCr C i C Cr  K 0iCr  K viCr C v C iCr ; @t

ð7Þ

@C vCr ¼ DvCr r2 C vCr þ K vCr C v C Cr  K 0vCr  K ivCr C i C vCr ; @t

ð8Þ

which state that the time rate of change of solute-defect complex concentrations are given by diffusion plus formation, minus the dissociation and annihilation of complexes. In these expressions, D are diffusion coefficients, C are concentrations and K are rate constants; subscripts are iCr for Cr-interstitial complexes, vCr for Cr-vacancy complexes, v-iCr for the annihilation of Cr-interstitial complexes with a mono-vacancy and i-vCr for the annihilation of a monointerstitial with a Cr-vacancy complex. Diffusion coefficients and rate constants were also adapted from Johnson and Lam [11,12], for example: K 0icr ¼ 4vi expððEmi þ EbiCr Þ=kT Þ; K 0vcr

¼ 7vi expððEmv þ EbvCr Þ=kT Þ;

ð9Þ ð10Þ

where Emi and Emv are the interstitial and vacancy migration energies, and EbiCr and EbvCr are the binding energies of the Cr-interstitial and Cr-vacancy complexes, respectively. The solute drag model requires input of migration and binding energies of the Cr-interstitial and Cr-vacancy

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

complexes. Unfortunately, there are no experimental measurements of these energies, so models and approximations were used. The migration energies EmiCr and EmvCr are the energies required for diffusion of a bound Cr-interstitial complex or a bound Cr-vacancy complex, respectively. Since the single interstitial migration energies used in the IK model were actually dumbbell migration energies, it is reasonable to approximate EmiCr as the Cr-interstitial migration energy from the IK model, 0.28 eV. Cr-vacancy complexes have not been studied, so it is unknown what an appropriate value of EmvCr may be. A conservative estimate for EmvCr is the Cr-vacancy migration energy from the IK model, 0.55 eV. The energies EbiCr and EbvCr are the binding energies of a Cr-interstitial complex and a Cr-vacancy complex, respectively. The convention used in this work shall denote attraction with a positive binding energy, and repulsion with a negative binding energy. Using ab intio methods, Choudhury et al. [10] calculated a weak attractive EbvCr of 0.01-0.05 eV. Wallenius et al. [9] calculated EbiCr in Fe–5Cr to be as high as 0.27 eV or as low as 0.05 eV, depending on which embedded atom method potential was used [48]. These binding energies, listed in Table 3, suggest that Cr should enrich by both Cr-vacancy and Crinterstitial solute drag. 2.3. Convolution of model results There are imprecisions in the measured grain boundary Cr composition profiles to which model results will be compared, due to finite size of the electron beam and beam broadening as it traverses the foil. The scanning transmission electron microscopy-measured composition profile is the convolution of the actual composition profile with the electron beam; this is illustrated in Fig. 3, which shows how convolution causes a narrow and sharply peaked concentration profile to broaden and decrease in magnitude at the grain boundary. When comparing model calculations to experimental measurements, the model-calculated composition profile must be convoluted with the electron beam for a fair comparison. In this work, model results were convoluted with the electron beam profile following the method of Carter et al. [49]. Fig. 4 illustrates the effect of convolution on a Cr concentration profile calculated by the IK model; the true concentration profile is more sharply peaked than the convoluted profile. Henceforth, all model results presented in this paper have been passed through the convolution process.

Table 3 Binding energies of Cr-interstitial complexes and Cr-vacancy complexes for the solute drag mechanism. Parameter

Binding energy (eV)

Attractive or repulsive?

Reference

EbiCr EbvCr

0.05–0.27 0.01–0.05

attractive attractive

[9] [10]

47

3. Results and discussion In this section, model calculations will be compared to the experimental measurements presented in Ref. [24] to determine whether the IK and solute drag mechanisms are consistent with the experimental results. It is critical to first establish which behaviors are important to the comparison. In the experimental study of Wharry and Was [24], three distinct features of Cr RIS behaviors were presented: (1) a bell-shaped temperature dependence and a “crossover” between Cr enrichment and Cr depletion, (2) decreasing amount of RIS with bulk Cr concentration and (3) minimal dependence of RIS on irradiation dose, with possible saturation of RIS at higher doses. Each of these three behaviors will be the focus of one of the following sections, in which first the IK, then the solute drag, models will be compared against experimental measurements. 3.1. Temperature dependence The IK model was executed for Fe–9Cr, at a steadystate dose of 15 dpa, dose rate of 105 dpa s1 and dislocation density of 0 m2, using the set of input parameters from Table 1 (henceforth referred to as “IP0” of the IK input parameter set). This simulation exhibited a bellshaped temperature dependence, in which the RIS was maximized at a moderate temperature and suppressed at low and high temperatures, Fig. 5 (solid line). The IK model also predicted that Cr enrichment would flip to Cr depletion at higher temperatures (henceforth referred to as the “crossover”). These behaviors are similar to those measured experimentally by Wharry and Was [24] in T91 (Fe–9Cr commercial alloy), irradiated with 2.0 MeV protons to 3 dpa at 105 dpa s1. But given the high significance values (Section 2.1.1) of migration energies used in the model, it could be determined whether modelexperiment agreement could be achieved by varying the migration energies within the known experimental/calculational error range. The values chosen for the solute-defect migration energies (Section 2.1.2) were the average of several ab initio calculations. As shown in Table 2, each migration energy has an associated variation between the average value and the ab initio values in the data set. The range over which the given migration energies could fall is thus the average migration energy ± the variation. Adjusting any one, or more, migration energy will alter the IK results. For example, in Fe–9Cr at steady-state dose, 105 dpa s1, dislocation density 0 m2, a 0.03 eV decrease in Fe-vacancy migration energy caused the crossover temperature and the temperature of peak segregation to fall into better agreement with experimental measurements, Fig. 5 (dashed line). This modified set of input parameters shall henceforth be called “IP1” of the input parameter set; see Table 4.

48

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Fig. 3. Schematic illustrating the effect of convolution on a RIS profile calculated by the model, after Carter et al. [49].

3

11.5

-5

o

Fe-9Cr, 3 dpa, 10 dpa/sec

-5

IK model before convolution

11

10.5

convoluted

10

Fe

IP0 (E =0.63) mvFe IP1 (E =0.60) mv T91 Experiment

2.5

Δ GB Cr concentration (at%)

Cr concentration (at%)

Fe-9Cr, 400 C, 10 dpa/sec, 15 dpa

2 1.5 1 0.5 0 -0.5

9.5

0

0.5

1

1.5

2

2.5

Distance from GB (nm) Fig. 4. Chromium concentration profile at the grain boundary, from the IK model reference case of Fe–9Cr irradiated at 400 °C to steady-state dose of 15 dpa, at a dose rate of 105 dpa s1. Model result prior to convolution is shown as a solid line; convoluted model result is shown as dashed line.

The calculated temperature dependence, and the effect of decreasing the Fe-vacancy migration energy, can be explained by referring to the diffusion coefficient ratios of Cr to Fe for both vacancies and interstitials, Fig. 6. The crossover occurs because the ratio of the vacancy diffusion coefficient in Cr to that in Fe crosses the ratio for interstitials, resulting in a change in Cr RIS direction. When the interstitial and vacancy diffusion coefficient ratios are equal (i.e. at the crossover), the contribution of Cr enrichment by interstitials is balanced by the contribution of Cr depletion by vacancies. Below the crossover temperature, Cr enrichment by interstitials dominates Cr depletion by vacancies, resulting in a net Cr enrichment. Conversely, above the crossover temperature, Cr depletion by vacancies dominates Cr enrichment by interstitials, resulting in a net Cr depletion. In Fig. 6, it is shown that decreasing the Fevacancy migration energy by 0.03 eV shifted the vacancy diffusion coefficient ratio such that the crossover temperature increased from 530 °C to 625 °C. Clearly, the

-1 100

200

300

400

500

600

700

800

900

o

Temperature ( C) Fig. 5. Comparison of temperature dependence of Cr RIS between IK input parameter set IP0 and IP1 for Fe–9Cr, and experimental measurements for T91, at 3 dpa, 105 dpa s1. Difference between IP0 and IP1 is that Fe vacancy migration energy value is changed from 0.63 eV to 0.60 eV, respectively.

RIS profile is sensitive to variations in the migration energy barriers that are small enough to fall within the margins of error of the ab initio calculations. Despite this limitation, the ab initio results are the best estimates of the values of the migration energy barriers, since the barriers have not been measured experimentally. The IK model also over-predicted the magnitude of Cr RIS. Calculations can be brought into better agreement with experimental measurements if point defect sinks are considered. The IK model treats sinks by considering an equivalent dislocation line density, qd, in units of m2, and distributing them homogeneously throughout the volume being considered. In a related work [50], equivalent dislocation line densities of T91 and Fe–9Cr were calculated by accounting for grain boundaries, precipitates and dislocation loops and lines in the as-received alloys and following irradiation to 1-10 dpa at 400 °C. These measurements are provided in Tables 5 and 6, and demonstrate consistency with literature. From Table 5, one can

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49

Table 4 Differences between the versions of the IK input parameter sets. Parameter

Symbol

Unit

IP0

IP1

IP2

IP3

Interstitial migration energy, Fe Interstitial migration energy, Cr Vacancy migration energy, Fe Dose rate Dislocation density

EFe mi ECr mi EFe mv

eV eV eV dpa s1 m2

0.35 0.28 0.63 105 0

0.35 0.28 0.60 105 0

0.35 0.28 0.60 105 7.5  1014

c.d. c.d. 0.60 105 7.5  1014

K0 qd

c.d. = composition-dependent (see Table 7 for values).

calculate the average spacing between lath boundaries is 440 nm, 207 nm between carbides, 40 nm between dislocation lines and 66 nm between loops. Since the irradiationenhanced diffusion length is 16.8 nm at 400 °C, point defects produced at the nearest lath boundary or carbide will likely never reach the grain boundary of interest, and these sinks should have very little, if any, influence on RIS. Dislocation loops and lines, however, could influence RIS, and their contribution dominates the total sink strength shown in Table 5. Thus, the total sink strengths in Tables 5 and 6 over-predict the actual sink strengths that influence RIS. The IK model was reevaluated using a range of equivalent dislocation line and loop densities as shown in Fig. 7. This figure demonstrates that the absence of sinks (0 m2) over-predicted the amount of Cr RIS, while an extremely high dislocation density (1017 m2) under-predicted the amount of RIS. The closest fit of the IK calculations to experimental measurements was from a dislocation line density of 7.5  1014 m2, or 75% of the measured value of 1015 m2 from as-received T91 (see Table 5). As noted previously, due to the diffusion length in the material, it is unsurprising that the best-fit dislocation line density is lower than the measured value. The IK model input o

Temperature ( C) 727

2

ln[D(Cr) / D(Fe)]

560 Tcross shift

977 2.2

441

352

282

Interstitials

1.8

E 1.6

E

Vacancies = 0.63 eV

IP0

mvFe

Vacancies = 0.60 eV

IP1

mvFe

1.4

1.2 0.0008

0.001

0.0012

0.0014

0.0016

0.0018

-1

1/T (K ) Fig. 6. Effect of migration energy variations on the Cr:Fe vacancy and interstitial diffusion coefficient ratios for F–M alloys.

parameters in IP1 were updated to include the best-fit dislocation density of 7.5  1014 m2, as given in Table 4, resulting in input parameter set IP2. 3.2. Composition dependence The dependence of Cr RIS on bulk Cr composition was calculated using input parameter set IP2 for Fe–7Cr through Fe–15Cr, at 400 °C, steady-state dose, 105 dpa s1, 7.5  1014 m2 dislocation density. The results, Fig. 8 (dashed line), were compared to experimental measurements from T91, HT9, HCM12A and Fe–9Cr, irradiated with 2.0 MeV protons at 400 °C to 3 dpa. Clearly, the IK model predicted that Cr RIS would increase with bulk Cr concentration, whereas experimental results showed Cr RIS decreased. This discrepancy is attributed to composition-dependent interstitial migration energies. The IK simulation used fixed interstitial migration energies for all bulk Cr concentrations. But both models and experiments [25,35] have suggested that this quantity is dependent upon the alloy composition. The results of Terentyev et al. [25] were interpolated to calculate composition-dependent Fe and Crinterstitial migration energies for the IK model. Since the preceding section showed agreement between the IK model for Fe–9Cr and experimental data from T91, compositiondependent interstitial migration energies were used only for Fe–xCr, where x – 9. The new set of IK model input parameters shall henceforth be referred to as input parameter set IP3; see Table 4. Using concentration-dependent interstitial migration energies from Table 7, the IK model predicted the same behavior as the experiment – decreasing Cr enrichment with increasing Cr concentration, solid line in Fig. 8. Implementing composition-dependent interstitial migration energies caused the interstitial diffusion coefficient ratio of Cr to Fe, to change, as illustrated in Fig. 9 for the 11–12 wt.% Cr-interstitial migration energies (solid line) compared to the original 9 wt.% Cr-interstitial migration energies (dashed line). The shift in the interstitial diffusion coefficient ratio caused two significant effects: (1) the crossover temperature decreased to 550 °C, and (2) the difference between the vacancy and interstitial diffusion coefficient ratios at 400 °C decreased. The latter effect explains the observed decrease in Cr enrichment as a function of increasing bulk Cr concentration at a fixed temperature.

50

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

Table 5 Microstructure measurements and sink strength calculations for alloy T91 as-received and irradiated at 400 °C, from Ref. [50]. Dose (dpa) Source of data

0 Measurement

1 Measurement

3 Measurement

7 Measurement

10 Measurement

0-10 Range reported in Refs. [1,23,73,74]

Grain boundaries

Lath length (106 m) Lath width (106 m) Sink strength (1012 m2)

5.07 0.44 10.76

5.07 0.44 10.76

5.07 0.44 10.76

5.07 0.44 10.76

5.07 0.44 10.76

4.2-13.5 0.25-0.64 –

Carbides

Diameter (106 m) Density (1020 m3) Sink strength (1012 m2)

0.156 1.13 220.82

0.159 1.16 232.38

0.161 1.23 248.76

0.164 1.20 247.47

0.160 1.24 249.00

0.08-0.2 0.20-3.57 –

Dislocation lines

Density (1014 m2) Sink strength (1012 m2)

6.25 888

6.25 888

6.25 888

6.25 888

6.25 888

4.5-13.0 –

Dislocation loops

Diameter (109 m) Density (1021 m3) Sink strength (1012 m2)

0 0 0

15.7 3.41 673

28.5 9.10 3259

31.8 13.9 5567

49.0 14.0 8621

11.3-55.7 2.0-17.8 –

Total

Sink strength (1012 m2)

1120

1804

4407

6713

9769

–

79

87

94

96

97

–

% of total sink strength due to lines and loops

The IK model is a simplified model of RIS and it does not account for all variations between alloys, such as minor and impurity element differences and microstructural differences. These features could affect the experimentally observed Cr RIS. But, without considering these effects, the IK model has so far calculated good agreement with the experimental data of Cr RIS. 3.3. Irradiation dose dependence The input parameter set IP3 was used to test the dose dependence of Cr RIS in Fe–9Cr irradiated at 400 °C, 105 dpa s1, with qd = 7.5  1014 m2. The model result is shown in Fig. 10 (solid line), in which it is compared to experimental measurements of Cr RIS from T91 and 9Cr model alloy, irradiated with 2.0 MeV protons at 400 °C to doses ranging from 1 dpa to 10 dpa. Upon initial inspection, there was little similarity between the experiment and model results shown in Fig. 10. Most notably, the IK results indicated that the onset of RIS should occur almost immediately, with 0.5 at.% Cr enrichment by 0.0001 dpa, whereas experimental data showed this amount of enrichment at 1 dpa. Furthermore, the IK model calculated steady-state RIS would occur by 1 dpa, whereas in experiments on T91 and the 9Cr model alloy, the onset of what may be a steady-state regime does not occur until higher doses. Implementing dose-dependent sink strengths (taken from Tables 5 and 6) into the IK model resulted in the reduction in Cr RIS magnitudes at higher doses, as shown in Fig. 10 (dashed lines). The IK calculated amount of Cr enrichment decreased as soon as the sink density increased at 1 dpa, which was not the case in experimental measurements. Clearly, a dose-dependent dislocation density alone explains neither the buildup of Cr RIS between 0 and 7 dpa, nor the decrease in Cr RIS in T91 from 7 to 10 dpa.

There remains the issue of the earlier onset of RIS and steady-state RIS in the IP3 result than in experiment. This inconsistency could be attributed to microstructural evolution in the alloys. Dislocation loops are strong sinks, having a total strength an order of magnitude larger than that of any other feature (grain boundaries, carbides, dislocation lines) [50]. As such, nucleation and growth of dislocation loops may be such a strong sink that point defects take a longer time (i.e. a higher irradiation dose) to arrive at grain boundaries. This would delay the onset of RIS compared to that predicted by the IK model, which does not consider sinks discretely or individually. There remain unresolved issues between the measured and calculated Cr RIS dose dependence, which prevent determination of whether the observed dose dependence is consistent with the IK mechanism. However, both experiment and model have exhibited some steady-state behavior. The differences may be due to microstructural evolution. 3.4. Solute drag In this section, it will be determined whether solute drag effects can explain or contribute to observed Cr RIS. By inspection of the binding energies of Cr-interstitial and Cr-vacancy complexes (Table 3), it is clear that the solute drag mechanism is unable to account for the crossover from Cr enrichment to Cr depletion, because the attractive binding energies will always produce Cr enrichment via solute drag. Therefore, Cr depletion will not occur if solute drag is a dominant process. Nevertheless, solute drag effects were evaluated using the IK input parameter set IP3 for Fe–9Cr at 105 dpa s1, steady-state dose and qd = 7.5  1014 m2. In Fig. 11, solute drag (region bounded by dashed lines) is compared to measurements (points) and IK calculations (solid line) for

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

51

Table 6 Microstructure measurements and sink strength calculations for 9Cr model alloy as-received and irradiated at 400 °C, from [50]. Dose (dpa) 6

1

3

7

10

Grain boundaries

Lath length (10 m) Lath width (106 m) Sink strength (1012 m2)

4.63 0.40 12.96

4.63 0.40 12.96

4.63 0.40 12.96

4.63 0.40 12.96

4.63 0.40 12.96

Carbides

Diameter (106 m) Density (1020 m3) Sink strength (1012 m2)

0.126 0.121 19.12

0.127 0.124 20.46

0.129 0.122 19.65

0.128 0.127 19.40

0.129 0.128 20.52

Dislocation lines

Density (1014 m2) Sink strength (1012 m2)

1.62 217

1.62 217

1.62 217

1.62 217

1.62 217

Dislocation loops

Diameter (109 m) Density (1021 m3) Sink strength (1012 m2)

0 0 0

13.2 1.57 260

26.7 4.32 1449

33.5 5.87 2472

40.6 6.02 3072

Total

Sink strength (1012 m2)

249

511

1699

2722

3322

87

93

98

99

99

% of total sink strength due to lines and loops

3

2.5

-5

Fe-9Cr, 3 dpa, 10 dpa/sec 14

Δ GB Cr concentration (at%)

-2

d

ρ = 7.5 x 10 m d 14

14

-2

15

-2

ρ = 10 m

-2

d

ρ = 10 m d

1 16

-2

ρ = 10 m d 17 -2 ρ = 10 m

0.5

-5

mi

ρ = 0 m (IP1)

2 1.5

o

3 dpa, 400 C, 10 dpa/sec Fe IP2 (E =0.35 eV, E

-2

IP2 (ρ =7.5 x 10 m ) d T91 Experiment

2.5

Δ GB Cr concentration (at%)

0

d

0

Cr mi

=0.28 eV) Fe

Cr

&E ) IP3 (composition-dependent E mi mi Experiment

2

1.5

1

0.5

-0.5 -1 100

200

300

400

500

600

700

800

900

o

Temperature ( C) Fig. 7. Effect of sink density on temperature dependence of Cr RIS, comparison between IK model input parameter sets IP1 and IP2 for Fe– 9Cr, and experimental measurements for T91, at 3 dpa, 105 dpa s1. Difference between IP1 and IP2 is dislocation density.

(a) Cr-interstitial complexes and (b) Cr-vacancy complexes. In these figures, the binding energy ranges taken from Table 3 define a region over which solute drag effects predict that Cr enrichment will occur. Considering first the solute drag of only Cr-interstitial complexes, the extent of Cr enrichment was overpredicted at all temperatures. At 450 °C, for example, solute drag predicted 4-42% Cr enrichment, compared to 1.75% Cr enrichment measured experimentally and predicted by the IK model. Solute drag of Cr-vacancy complexes also overpredicted Cr enrichment at most temperatures. In modeling solute drag, binding energy was added to migration energy, as shown in Eqs. (9), (10). Thus, if the binding energy exceeds the variation in migration energy (Table 2), the IK model cannot account for binding of solute-defect complexes. This idea is illustrated in Fig. 11, in

0

6

8

10

12

14

16

Bulk Cr concentration (at%) Fig. 8. Comparison of composition dependence of Cr RIS between IK input parameter sets IP2, IP3, and experimental measurements, for alloys ranging from Fe–7Cr through Fe–15Cr, at 400 °C, 3 dpa, 105 dpa s1. Difference between IP2 and IP3 is the inclusion of composition-dependent interstitial migration energies in the latter.

which the IK model prediction is surrounded by a shaded region indicating the range over which the IK prediction would vary if migration energies varied. In Fig. 11a, the IK range does not overlap with the Cr-interstitial solute drag range, suggesting that IK cannot account for Cr-interstitial binding. In Fig. 11b, there is slight overlap between the IK and Cr-vacancy solute drag ranges <650 °C, which is consistent with the original argument against the solute drag mechanism: attractive Cr-vacancy and Crinterstitial binding cannot explain Cr depletion. 4. Literature data in the context of this work This paper has shown that the RIS measurements of Wharry and Was [24] are consistent with the IK

52

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

Table 7 Composition dependence of Cr-interstitial migration energy, as calculated by Terentyev et al. [25], which is used as the basis for interpolation of the Feinterstitial and Cr-interstitial migration energies for the IK input parameter set IP3 containing composition-dependent interstitial migration energies. Alloy

Fe Fe–0.2Cr Fe–5Cr Fe–7Cr Fe–7.5Cr Fe–8Cr Fe–9Cr Fe–10Cr Fe–11Cr Fe–12Cr Fe–13Cr Fe–14Cr Fe–15Cr *

Terentyev et al. [25] calculated migration energy of single SIA in Fe–Cr alloys (eV)

Migration energy interpolated based on slope of Terentyev data (eV) Fe-interstitial, EFe mi

Cr-interstitial, ECr mi

0.31 0.29 0.28 n/a 0.26 n/a n/a 0.25 n/a n/a n/a n/a 0.23

n/a n/a n/a 0.36 n/a 0.36 0.35* 0.35 0.34 0.34 0.33 0.33 0.32

n/a n/a n/a 0.29 n/a 0.29 0.28* 0.28 0.27 0.27 0.26 0.26 0.25

Fe–9Cr interstitial migration energy is fixed; non-asterisked migration energies were interpolated based upon the slope of the Terentyev data.

o

2.5

Temperature ( C) 560

2

ln[D(Cr) / D(Fe)]

441

352

Interstitials IP2 E Fe = 0.35 eV, ECr=0.28 eV mi

Vacancies

mi

1.8

Interstitials IP3 comp-dependent E Fe& E Cr mi

o

mi

1.6

-5

Fe-9Cr, 400 C, 10 dpa/sec IP3 with ρd from T91 or Fe-9Cr T91 Experiment Fe-9Cr Experiment

282

Δ GB Cr concentration (at%)

727

Tcross shift

977 2.2

2

1.5

1

0.5

1.4

0 0.001 1.2 0.0008

0.01

0.1

1

10

100

Dose (dpa) 0.001

0.0012

0.0014

0.0016

0.0018

-1

1/T (K ) Fig. 9. The effect of composition-dependent interstitial migration energies on the Cr to Fe-interstitial diffusion coefficient ratio for 11-12 wt.% Cr F– M (solid lines) compared to that for 9 wt.% Cr (dashed line); vacancy diffusion coefficient ratio is not affected by composition-dependent interstitial migration energies.

mechanism. A more rigorous test, however, is to determine whether RIS measurements from literature can be explained by the IK mechanism, which will be done in this section. The IK model predicts that Cr enrichment will change to depletion at a concentration-dependent crossover temperature; this trend is an effective way to compare the IK mechanism to literature measurements, as shown in Fig. 12. Observations of Cr enrichment should fall below the crossover temperature line, while observations of Cr depletion should fall above the crossover. It is recognized

Fig. 10. Comparison of dose dependence of Cr RIS between IK input parameter set IP3 and experimental measurements for T91 and Fe–9Cr at 400 °C and 105 dpa s1. The effect of dose-dependent dislocation densities is also considered in the IK model.

that while the literature data are predominantly from commercial alloys containing a number of minor elements, the IK model does not account for elements other than Fe and Cr. The effect of minor elements on the crossover temperature, and on Cr RIS behavior in general, is not well known. However, the good match between measurement and model for the temperature dependence of RIS in T91 using sink densities that are close to those calculated from the measured microstructure, indicate that the effect of the minor elements cannot be large. Thus, the crossover temperature for T91 is likely close to that for Fe–Cr. Four authors measured Cr enrichment consistent with the IK model prediction, all of which presented robust experimental techniques. Gupta et al. [23] measured Cr

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

53

Fig. 11. Temperature dependence of Cr RIS calculated by IK model and with solute drag of (a) bound Cr-interstitial complexes, and (b) bound Cr-vacancy complexes for Fe–9Cr, steady-state dose, 105 dpa s1.

and V enrichment and Fe depletion in T91 irradiated with 2 MeV protons. Little et al. [51] observed Cr, P, Si, Mn and Mo enrichment and Fe depletion in 12CrMoVNb following fast neutron irradiation at 465 °C. Clausing et al. [52] measured Cr enrichment in HT9 neutronirradiated at 410 °C, but found no Cr segregation at 520 °C and 565 °C. This is reasonable, since near the crossover temperature (515 °C for HT9), little segregation in either direction will occur. Lastly, Kato [53] irradiated

Fe–10Cr–xMn–3Al, where x = 5, 10 and 15, with 1 MV electrons and found Cr enriched in all cases. Two experiments measured Cr depletion consistent with the IK calculation. Hamaguchi et al. [54] irradiated SUS410L (12.34 wt.% Cr in bulk) with 11 MeV protons over 497-647 °C. Although the temperature range of this experiment was large, it falls almost entirely above the 520 °C crossover temperature, so it is reasonable to have observed Cr depletion. Neklyudov and Voyevodin [55]

Fig. 12. Experimental measurements of the directions of Cr RIS in F–M alloys published in the literature (open symbols), as compared to the crossover temperature calculated in this work and experimental measurements of Cr RIS from Ref. [24] (closed symbols).

54

J.P. Wharry, G.S. Was / Acta Materialia 65 (2014) 42–55

measured Cr depletion in 13Cr–2MoVNbB irradiated with 1 MeV Cr3+ ions at 575 °C. Several experiments were conducted using techniques that make it difficult to determine the true direction of Cr RIS. Neklyudov and Voyevodin [55] irradiated 13Cr– 2Mo + TiO2 with 1–5 MeV Cr3+ ions at 270-800 °C, to 0.1-200 dpa. With such copious variations in irradiation conditions, it was impossible to judge whether this experiment is consistent with the IK calculation. Ohnuki et al. [56] irradiated Fe–13Cr alloys with 200 keV C+ ions, and analyzed the implantation surface. Given the shallow damage profile and its proximity to the surface, it is likely that the measured composition was unduly influenced by the surface. The same issue arises for the 250 keV Ni+ ion irradiation on pre-perforated foils of E911, by Lu et al. [57]. Scha¨ublin et al. [58] reported both Cr and Fe depletion, and no enrichment, following proton irradiation of F82H, which is difficult to rationalize. Takahashi et al. [59] observed Cr depletion in 400 °C electron irradiated Fe–5Cr and Fe–13Cr, with concentration profiles having FWHM 200 nm – over an order of magnitude greater than that in most experimental studies of RIS. Lastly, Marquis et al. [60,61] found significant variability in Cr RIS behavior as a function of depth into the damage profile in Fe–14.25Cr and a model Fe–12Cr ODS alloy, using 0.5 and 2.0 MeV Fe+ ions; the acquisition of RIS measurements at or near one of the Fe implantation peaks made it difficult to assess the true direction of Cr RIS. 5. Conclusions The behavior of Cr (and Fe) RIS in F–M alloys was found to be largely consistent with the IK mechanism, but not with the solute drag mechanism, supporting IK as the dominant mechanism of Cr RIS in F–M alloys. Chromium RIS can be explained by the Cr:Fe diffusion coefficient ratios for vacancies and interstitials. Because these diffusion coefficient ratios are both greater than one, preferential diffusion of Cr occurs via both vacancies and interstitials. The direction of RIS is determined by the relative magnitudes of the diffusion coefficient ratios at the given temperature. The diffusion coefficient ratios intersect at a “crossover” temperature, below which Cr enrichment via interstitials is dominant, and above which Cr depletion via vacancies is dominant. The solute drag mechanism cannot account for the crossover from Cr enrichment to Cr depletion, and thus solute drag cannot be the dominant mechanism of Cr RIS in F–M alloys. The IK mechanism also explains the measured decrease in Cr enrichment with increasing bulk Cr concentration. The Cr:Fe diffusion coefficient ratio for interstitials decreases with increasing bulk Cr concentrations causing (1) the predicted crossover temperature to decrease, and (2) the difference between the diffusion coefficient ratio of interstitials and that of vacancies to decrease, thus reducing the expected amount of Cr enrichment at a fixed temperature below the crossover temperature.

Acknowledgements Research was funded by the DOE Office of Nuclear Energy’s Nuclear Energy University Programs under awards DE-FG07-07ID14828 and DE-FG07-07ID14894. This research was supported in part by Oak Ridge National Laboratory’s SHaRE User Facility, which is sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. The authors also wish to acknowledge the assistance of Ovidiu Toader and Fabian Naab of the Michigan Ion Beam Laboratory, and Kai Sun of the Electron Microbeam Analysis Laboratory at the University of Michigan. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

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