On the Modelling of Thermal Aging through Neutron Irradiation and Annealing

A newmethod predicting long-term thermal embrittlement of steel caused by P segregation is verified.-emethod is based on the results of impact strength or fracture toughness tests using specimens after relatively short-term neutron irradiation followed by annealing. 2Cr–Ni–Mo–V steel used in reactor pressure vessels of WWER-1000 type is investigated in four conditions: initial condition, after thermal aging, after neutron irradiation, and postirradiation annealing. -e results of impact strength and tensile tests and SEM investigation are presented.-e brittle fracture features are considered for different material conditions. Calculative estimation on neutron irradiation effect on P diffusion in steels is carried out. Experimental data are reported which confirm an intense P diffusion acceleration under neutron irradiation.


Introduction
ermal aging is the dominant degradation mechanism proceeding in unirradiated component (e.g., nozzle shell) materials for WWER-type reactor pressure vessels (RPVs).erefore, thermal aging of RPV materials during NPP operation should be predicted for an adequate structural integrity assessment of unirradiated RPV components.e WWER-1000 RPV operation temperature is 290-320 °C.Lifetime for this type reactor is planed to be extended at least up to 60 years.e prediction of thermal aging of RPV materials for 60 years is rather a complicated task.e point is that thermal aging of surveillance specimen sets proceeds at the same temperature as that of RPVs.erefore, surveillance specimen test results are relevant only to the current condition of RPV materials (for the moment of taking out surveillance specimens).Further material aging process can be predicted only through extrapolation.
Long-term prediction of thermal aging of materials is usually based on the test results of specimens subjected to accelerated aging at temperatures higher than the RPV operation temperatures.Such an approach results from the assumption that the material aging is controlled only by diffusion processes, and the equilibrium concentration of a diffusing element on some sinks (e.g., on grain boundaries) is temperature-independent.For this case, long-term prediction of thermal aging is usually based on the Arrhenius equation [1][2][3].In particular, the Hollomon parameter which determines the degree of material aging depending on exposure time and temperature is one of the most commonly used [4,5].
e phosphorus content for unirradiated RPV component materials is up to 0.020% as per relevant technical specifications.High P contents are known to result in thermal embrittlement of metal due to P segregation at grain boundaries (GBs).e equilibrium grain boundary P concentration is a temperature-dependent parameter, decreasing with increase of temperature [2,3,6].erefore, the prediction of P aging for the WWER-type RPV materials on the basis of the results of accelerated aging at higher temperatures and the Hollomon parameter application can be inadequate and nonconservative.
e above gave impetus to the development of a new method predicting "phosphorus" embrittlement of RPV steels.
is new method was reported in the paper [7].
Its main idea consists in accelerating P segregation processes by neutron irradiation at a temperature corresponding to that of RPV operation (T oper ).Unlike the acceleration of P segregation processes only due to increasing a temperature, neutron irradiation hardly affects equilibrium P segregation [8,9].At the same time, irradiation accelerates the kinetics of P segregation through radiation-enhanced diffusion [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. is acceleration results from the fact that the P diffusion coefficient increases considerably through the generation of point defects under irradiation [8,9,[11][12][13][14].As can be seen, the mechanism of forming P segregations is the general mechanism of metal embrittlement under thermal aging and neutron irradiation.e P diffuses towards different intragranular interphase boundaries (e.g., interphase carbidematrix boundaries) as well as towards GBs and forms local segregations [3,10,19,[23][24][25].As should be noted that P segregation does not lead to material hardening as P segregates mainly on GBs and on various intragranular barriers for dislocations that exist before irradiation (e.g., carbides).It means that P does not form new additional barriers for moving dislocations.At the same time, P segregations decrease the strength of interphase boundaries (e.g., carbidematrix boundaries) or grain boundaries that makes the initiation of cleavage microcracks or intergranular brittle microcracks easier and, as a consequence, leads to material embrittlement [3,19,[26][27][28][29].Since the above mechanism of material embrittlement does not result in its hardening, such an embrittlement mechanism is referred to as a nonhardening mechanism [26,27,30].
It is necessary to note also that P also segregates on dislocation loops and precipitations [19,31,32].Such segregations hardly affect material hardening [10].
e proposed method [7] consists in determining material embrittlement after the following two-stage treatment.At the first stage, accelerated neutron irradiation for short time with high neutron flux is conducted at T � T oper , which hardly changes the value of equilibrium P segregation and, at the same time, accelerates the formation of P segregations due to radiation-enhanced diffusion.At the second stage, the irradiated material is annealed at a temperature which deletes material hardening caused by neutron irradiation and leads to P dissociation from the intragranular interphase boundaries, but, at the same time, does not lead to P dissociation from GBs.For the WWER-1000 RPV materials, this annealing temperature T anneal � 450 °S [7].In addition, for the effective P diffusion coefficient to be determined, thermal aging should be carried out at the temper brittleness temperature [7].
According to the [7] time dependence of transition temperature shift due to P thermal aging, ΔT k (t) is determined on the basis of the following considerations.e dependence ΔT k (t) has been deducted when using the McLean equation [6], the theory of radiation-induced diffusion [11][12][13][14][15][16][17][18][19][20][21][22], and the introduced relation between the transition temperature T k and P concentration on the interphase boundaries and/or GBs at the current moment of time (C t p ) [7]. e transition temperature is taken as the temperature at which the Charpy impact strength equals 47 J or fracture toughness for specimens with thickness of 25 mm equals 100 MPam 1/2 for the fracture probability of 50%.
e McLean equation is presented in the form where C 0 p , C t p , and C ∞ p are the P concentrations at the interfaces and/or GBs at the given temperature at the initial moment of time (t � 0), at the time t, and at t � ∞, respectively; D P is the P diffusion coefficient in general depending on temperature and neutron flux (neutron dose rate) [14]; d is the GB thickness; c � C ∞ p /C v p where C v p is the bulk P concentration in atomic percentage.
e relation between T k and C t p takes into account possible P segregations in the material in the initial condition and after thermal aging during time t.It is taken in the form [7].
where α and β are some material constants.
Based on (1) and ( 2), the dependence ΔT k (t) is presented in the form [7]: where T ∞ k is the value of T k at t � ∞; T k0 is the value of T k in the initial condition; and D eff is the effective diffusion coefficient, Under irradiation, the P diffusion coefficient of an element (e.g., phosphorus) is calculated taking into account the production and recombination of vacancies and interstitial atoms, annihilation of point defects on the various sinks, mainly dislocations (for more details, see Section 3).In case of no irradiation, the temperature dependence of P diffusion coefficient is calculated by the well-known equation in [3] similar to the Arrhenius equation.
After the material two-phase treatment (irradiation + annealing), the value of transition temperature T k is determined for this material.Knowing T k0 , the value of T k for material condition after postirradiation annealing and value of D eff under irradiation, the value of T ∞ k corresponding to the RPV operation temperature is determined from (3) where ΔT k � T k −T k0 .e dependence ΔT k (t) for unirradiated material is calculated by (3) on the basis of determined value of T ∞ k and calculated value of D eff for T� T oper when there is no irradiation [7].
So, the main idea of the method proposed in [7] is the formation of the grain boundaries P segregation during shortterm irradiation due to strong acceleration of P diffusion under neutron irradiation at operation temperature of RPV.Strong acceleration of P diffusion under neutron irradiation up to now has not been proved directly.At the same time, there are some indirect proofs.In particular, it is well known that neutron irradiation leads to significant increase in the vacancies and interstitials concentrations and, as a result, to significant increase in the self-diffusion coefficient [11][12][13][14][15][16][17][18][19][20][21][22].Experimental studies [10,28] have also revealed that P segregations can be formed under neutron irradiation at sufficiently low temperature (T � 50 °C) when thermodiffusion of phosphorus is very small.

Advances in Materials Science and Engineering
Phosphorus is subsized element (atomic radius of P is less than Fe radius); therefore, P diffusion may occur by both vacancy and interstitial mechanisms.Hence, it may be expected that an increase in the vacancies and interstitials concentrations under irradiation may increase equally both the self-diffusion coefficient and P diffusion coefficient.At present, there are only theoretical justifications for this consideration [8,9,[11][12][13][14]; however, experimental data proving it are absent.
e aim of the present work is to obtain experimental data showing strong influence of neutron irradiation on P diffusion, that is, to prove that neutron irradiation increases equally both the self-diffusion coefficient and P diffusion coefficient.

Statement of the Problem
e effect of temperature on P diffusion and equilibrium P segregation at GBs has been studied well enough by now [3,6,29].e formation of P segregations at GBs leads to intergranular brittle fracture (IBF) [2,3,19,29].With a higher P concentration at GBs, the portion of IBF increases.According to (1), the P concentration at GBs is determined by the product D eff • t.Hence, the portion of IBF is controlled by the product D eff • t.
en, if the basic consideration of the new method is true and the condition met, the portion of IBF (when the nonhardening brittle fracture mechanism occurs) should be approximately the same both for thermally aged material and material after neutron irradiation and annealing.In the above condition, D T eff is the effective thermal diffusion coefficient of phosphorus, t T is the exposure time at a higher temperature, D F eff is the effective diffusion coefficient of phosphorus under neutron irradiation, and t F is the time of neutron irradiation.
us, the following experimental procedure may be proposed for justification of the proposed method in [7].Two different treatments should be carried out for the investigated material.One treatment is thermal aging and the another is two-phase treatment (irradiation + annealing).
e regimes for these treatments should be those for which the condition Here, the D F eff parameter should be calculated with the assumption that neutron irradiation increases practically equally both the self-diffusion coefficient and P diffusion coefficient (i.e presented hereafter in Section 3).Postirradiation annealing allows one to exclude any influence of irradiation-induced defects on material embrittlement except for the influence of grain boundaries P segregations that is typical for thermal aging.
Specimens machined from thermally aged material and material after postirradiation annealing should be tested over brittle fracture temperature range, and SEM examination of fracture surfaces should be performed to compare the portions of IBF for these materials.
If the portions of IBF for these material conditions coincide, then it may be concluded that the aim of the present paper is reached and the method proposed in [7] for prediction of thermal embrittlement is verified.

Calculative Estimation of the P Diffusion Coefficient under Neutron Irradiation
Radiation-enhanced diffusion coefficients of self-diffusion (hereinafter Fe atoms) D Fe and impurity atoms (hereinafter P atoms) D p can be written neglecting the correlation factors as follows [8,9,33]: where  [33] was used in ( 4) and (5).
Neglecting the thermal equilibrium concentration at the irradiation temperature, one can write for the average vacancy concentration [8,9,33]: where K is the PD production rate, ρ s is the PD sink strength, μ R is the recombination coefficient accounting for PD recombination at the rate μ R d i C i C v , and ε is the cascade efficiency in producing freely migrating PD (usually in the range 0.1 ÷ 1).Equation ( 6) can be rewritten as follows: where the parameter Q � 4εKμ R /d v ρ 2 s .We can consider two limiting cases: (1) PD sinks are dominated or Substituting these concentrations in ( 4) and ( 5) one can obtain the following estimates of the above two cases: for

Advances in Materials Science and Engineering
and for Q ≫ 1 where d v0 is the preexponential factor of vacancy diffusivity d v .
It is seen from ( 10) and ( 11) that D Fe1 and D P1 do not depend on d v and D P1 decreases with increasing temperature whereas Here, we adopt the following parameters: K � 6 × 10 −8 dPa/sec for a neutron flux of 6.07 × 10 17 n/m 2 •s from the relation 1 dPa per 10 25 n/m 2 (E > 0.5 MeV), ε � 0.1 for neutron irradiation [33], d v � 2 × 10 −4 exp (−1.3 eV/kT) m 2 /s from [11], μ R � 8•10 20 m −2 (assuming recombination volume on the order of 100 lattice parameter), and E b eff � 0.3 eV as an effective binding energy of mixed Fe-P dumbbells [33].e ρ s is taken to be equal to the dislocation density for RPV steel in initial condition.e ρ s may be assumed to be equal to 10 14 m −2 [7].
Taking into account that not much is known on the diffusion parameters of self-diffusion and P diffusion in RPV steels, justification of the above parameters is based on the following analysis.
e values taken for our estimations are following values: E m Fen �1.24 eV and E b pi � 0.17 eV (binding energy of mixed Fe-P dumbbells) and E b pn ≈ 0.3 eV that were used in [34,35] for modelling of P accumulation at GBs in dilute Fe-P alloys.
e models were applied successfully to fit experimental data on P accumulation at GBs in RPVs at a dose of 0.01 dPa.Modelling of P accumulation at GBs in Fe-Ni-P alloys was performed [8,9] taking into account radiation-enhanced P diffusion via both vacancy and interstitial mechanisms, radiation-induced segregation in the matrix near GBs and the Gibbsian adsorption at GBs. Vacancy migration energies in the range from 0.6 eV to 1.2 eV, interstitial migration energies from 0.1 eV to 0.30 eV, and binding energies between a P atom and an interstitial from 0.3 eV to 0.15 eV were considered.Later on, this model was applied successfully to fit experimental surveillance data for several units of WWER-440 [36] where radiation embrittlement enhancement has been observed at neutron fluences above (2-3) × 10 24 n/m 2 .
In recent years, much attention has been paid to modelling of self-diffusion and P diffusion in Fe and dilute Fe-P alloys.Molecular dynamics, ab initio, and kinetic Monte Carlo calculations are applied to elucidate the mechanisms and diffusion parameters [37][38][39][40][41]. Ab initio calculations reveal relatively high binding energies between P atoms and vacancies (vacancy drag effect) and very high binding energies of mixed Fe-P dumbbells on the order of 1 eV and their high mobility.In addition, a new mechanism of P atoms mobility via octahedral positions in the lattice was found as a result of interaction of a self-interstitial atom with a substitutional P atom.Formation energies and diffusivities of both mobile states are similar.However, attempts to use these diffusion parameters to fit experimental data at GB phosphorus accumulation in RPVs fail to succeed.Atomic transport via interstitials in dilute Fe-P alloys was used for modelling of GB phosphorus accumulation in RPVs [38] as applied to experimental data considered before [34,35].e predictions highly overestimate the data.e authors suppose that a significant portion of P atoms is trapped in stable two-P complexes or segregated on point defect clusters.Both vacancy and interstitial (via mixed Fe-P dumbbells and via octahedral positions) diffusion of P atoms were used [39,41] to fit some experimental data on GB phosphorus accumulation in RPVs at neutron fluences up to 10 24 n/m 2 .For fitting the data, an unreally high PD sink strength of 2 × 10 18 m −2 was adopted in calculations.Possibly, reliable data on self-diffusion and P diffusion in RPVs could be obtained in molecular dynamics modelling accounting for all most important alloying and impurity elements.

Material, Conditions, and
Results of Experiment e material selected for investigations (2Cr-Ni-Mo-V steel) used for WWER-1000 RPVs was similar to those used previously in [7].e chemical composition of this steel is given in Table 1.e transition temperature in the initial condition T k0 is equal to −5 °C, yield strength (σ Y ) at T � 20 °C is equal to 585 MPa.Several sets of Charpy specimens from the above steel were machined.
On the basis of equation describing the temperature effect on D P [3] and estimation of D P under neutron irradiation presented above, the following regimes of neutron irradiation and thermal aging were specified to provide the condition D T eff • t T ≈ D F eff • t F .Charpy specimens were subjected to neutron irradiation in the research WWR-M reactor (St.Petersburg Institute of Nuclear Physics by B. P. Konstantinov of NRC "Kurchatov Institute") at the irradiation temperature T≈ 300 °C with a neutron flux of 6.07 × 10 17 n/m 2 •s for ≈1000 hours.
en, the specimens were divided into two sets.e first set was investigated in the irradiated condition, the second set was annealed at T � 450 °C for t � 50 and for 100 hours.
e temperature dependence of impact strength was determined for each from two sets on the basis of impact tests.with exposures for 10 and 1000 hours.e temperature of thermal aging was taken to be equal to the temperature leading to the maximum degree of embrittlement with isothermal exposures of the same duration.After each exposure (10 and 1000 hours), the set of specimens was taken out from the furnace and impact tested with determining T k .
Additionally, the steel in initial condition was annealed at T � 450 °C for t � 50 and 100 hours.Such material condition was investigated to compare the fracture modes after annealing of irradiated material and material in initial condition.
For steel in the irradiated condition and that after irradiation and annealing, tension tests were performed at the temperature T � 20 °C using cylindrical specimens 3 mm in diameter and 15 mm in the gouge length.Tensile specimens were machined from the halves of broken Charpy specimens.
Some broken Charpy specimens from each tested set were investigated by SEM.Additionally, SEM investigation was applied to broken specimens from steel in the initial condition subjected to annealing.
All SEM investigations were made on the scanning electron microscope Hitachi ™ 3000 placed in the "hot cell" in the laboratory of CRISM "Prometey."e results of mechanical tests and SEM investigations are presented in Table 2, Figures 1 and 2. As can be seen from Table 2, after thermal aging with an exposure for 1000 hours, the portion of intergranular brittle fracture achieves 80%.
Neutron irradiation results in the intensive material embrittlement (ΔT k � 185 °C), even though, the portion of IBF is insignificant and fails to exceed 12% (Table 2, Figure 2).After annealing, the degree of material embrittlement decreases (Table 2) but, at the same time, the portion of IBF increases.is phenomenon will be explained in the following section.
It should be noted that annealing of the steel in the initial condition at a temperature of 450 °C does not result in significant increase in IBF (Table 2).It means that neutron irradiation, but not annealing, results in significant increase in P concentrations on GBs and hence, significant increase of the portion of IBF.
Based on the results obtained for ΔT k and corresponding exposure time, the values of T ∞ k and D eff were calculated for material under aging at T � 500 °C and T ∞ k was calculated for material under irradiation at T � 300 °C according to the method proposed in [7].Calculations of D eff under irradiation are presented below (Section 3).Table 3 presents the calculated values of T ∞ k and D eff • t for different material conditions.Also, Table 3 gives the value of D eff • t calculated at a temperature of 300 °C.

Discussion
e presented experimental data show that the portion of IBF after irradiation does not exceed 12% and after postirradiation annealing, it reaches 70% (Figure 1) though embrittlement degree for annealed material is much less than for irradiated material.Before comparing the portion of IBF of irradiated and thermally aged material, it is essential to understand the cause of a significant difference in the fracture modes for irradiated condition and that after postirradiation annealing.Relying on the referenced work [26], this result can be explained from the diagram presented in Figure 3.
For polycrystalline, metal grain boundary may be schematized as narrow zone with extremely damaged lattice [43] that results in three consequences.Firstly, it is very difficult to nucleate atomically sharp intercrystalline microcrack as damaged lattice results in microcrack tip blunting.Secondly, the anisotropy of grains gives rise to additional shear stresses acting along GBs.erefore, the intercrystalline  Advances in Materials Science and Engineering microcrack blunting due to dislocation emission from its tip becomes more probable than for a transgranular microcrack.
irdly, propagation of intercrystalline microcrack is practically impossible without dislocation emission from its tip (in contrast to transcrystalline microcrack which may propagate on cleavage plane without dislocation emission) that requires large expenditure of energy.erefore, for unirradiated steels, it may be taken that the resistance to nucleation and propogation of transcrystalline microcrack is less than the resistance to intercrystalline microcrack.us, for material in the initial condition, resistance of transgranular brittle fracture (TBF) is lower than the resistance of IBF.erefore, material in the initial condition is mainly fractured by transgranular mode.Neutron irradiation leads to the formation of point defects, dislocation loops, precipitates and also leads to the formation of P segregations on the intragranular interphase boundaries and GBs.Microcracks resulting in brittle fracture cannot be nucleated on point defects, dislocation loops, and precipitates as these microcracks are much larger than sizes of these radiation defects [26,27].erefore, the role of these radiation defects is hardening of material (increase of σ Y ) that results in embrittlement due to increase of stresses near notch or crack tip in specimen.P segregations caused by irradiation decrease the resistance to nucleation of both transgranular and intergranular microcracks and also decrease the resistance to intergranular microcracks propagation due to the weakening of atomic bonds [10,19,23,26,36].Hardening of material and intragranular and intergranular P segregations results in strong decrease of both TBF and IBF resistance in such manner that TBF resistance is lower than IBF.us, a degree of material embrittlement increases strongly (Figure 1), but the fracture mode remains similar to material in initial condition.erefore, irradiated material is mainly fractured by transgranular mode as well as material in the initial condition.
Another situation is observed for brittle fracture of steels annealed after irradiation.It is shown [42,44] that temperature for dissociation of P segregations in a grain is less than temperature for dissociation of grain boundary   2).As a result, both TBF resistance and IBF resistance increase.TBF resistance is fully recovered up to value corresponding material in initial condition.IBF resistance is recovered partially, as intergranular P segregations do not dissociate.
us, the relation of transgranular and intergranular brittle fracture resistance is changed that leads to fracture mainly on GBs.As the minimum brittle fracture resistance for material after annealing is less than for material in initial condition, only the partial recovery of material embrittlement occurs that is a characterized residual value of ΔT k (see Figure 1). is ΔT k is connected with intergranular P segregations only.
us, the portion of IBF does not always correlates univocally with the degree of material embrittlement.With increase of IBF portion ΔT k may decrease.
Since the subject of interest is phosphorus diffusion, that is, the process leading to the nonhardening mechanism of material embrittlement, the comparison should be made for material conditions when the hardening mechanism is excluded.erefore, two material conditions are considered: after thermal aging and after postirradiation annealing.
SEM investigations (Table 2, Figure 2) show that the portion of IBF after thermal aging achieves 80%.After postirradiation annealing, it makes up 70%.ese results allow the conclusion to be made that intergranular P concentration for both material conditions is nearly the same.
A similar conclusion follows from the calculations presented in Table 3.Indeed, parameter controlling accumulation of P in GBs under irradiation D F eff • t F � 0.15 is close to parameter D T eff • t T � 0.19 for thermal diffusion of P. So, the condition D T eff • t T ≈ D F eff • t F is met.us, the predictions obtained are in close agreement with the results of SEM investigations.So, the estimated values of the effective diffusion phosphorus coefficient under neutron irradiation are supported experimentally.Really, neutron irradiation increases the P diffusion coefficient by some orders.e last row of Table 3 includes the value of D eff • t with no influence of neutron irradiation, that is, only due to thermal action at the RPV operation temperature.It can be seen that the values of D eff • t in the first and the third rows of Table 3 are different by some orders that points to a very strong effect of neutron irradiation on the P diffusion coefficient.e results obtained have shown that neutron irradiation affects practically equally the self-diffusion coefficient and P diffusion coefficient.
So, the obtained experimental results and performed calculative estimation allow one to conclude that the proposed method [7] may be used for prediction of long-term thermal embrittlement on the basis of test results for material annealed after short-term neutron irradiation.

Conclusions
(1) 2Cr-Ni-Mo-V steel has been investigated in different conditions, namely, in initial conditions, after thermal aging at 500 °C, after neutron irradiation at 300 °C, after postirradiation annealing, and after annealing of the steel in initial condition.On the basis of impact strength tests results, the effect of different treatments (thermal aging, irradiation, and annealing) on degree of material embrittlement has been determined in terms of the transition temperature of brittleness.For each material condition, SEM investigation has been carried out and intergranular brittle fracture portion has been determined.(2) On the basis of performed investigations, the method using the test results of irradiated and annealed specimens has been verified that was proposed for prediction of long-term embrittlement of RPV steels (in terms of the transition temperature) caused by P segregation.(3) A strong effect of neutron irradiation on the P diffusion coefficient has been verified experimentally.e effect of neutron irradiation on the self-diffusion coefficient and on the P diffusion coefficient is nearly the same.(4) It is shown that postirradiation annealing considerably decreases the degree of material embrittlement in terms of transition temperature; however, after annealing, the portion of intergranular brittle fracture increases.ese results are explained from the physical point of view.us, it is possible situation when with increase of portion of intergranular brittle fracture, material toughness increases also.

Figure 1 :
Figure 1: e portion of IBF and the ΔT k value for different conditions of 2Cr-Ni-Mo-V steel: , portion of IBF; ○-ΔT k , °C.

Figure 2 :
Figure 2: Typical fracture surfaces of broken Charpy specimens from 2Cr-Ni-Mo-V steel in (a) initial condition, (b) after thermal aging at 500 °C for 1000 hours, and (c) after postirradiation annealing at 450 °C for 100 hours.

Figure 3 :
Figure 3: Schematic representation of brittle fracture resistance for 2Cr-Ni-Mo-V steel in three conditions: initial condition, irradiation condition, and postirradiation annealing condition.
C v and C i are the average vacancy and interstitial concentrations in the bulk depending on the point defect (PD) generation rate and sink density, d n and d pn (n � v, i) are the Fe and P diffusivities via vacancy and interstitial mechanisms, ξ pn accounts for the binding energies E b pn of P atoms with PD as ξ pn � exp(E b pn /kT), ξ n accounts additionally for the difference in migration energies of Fe E m Fen and P E m � exp(E b eff /kT), where E b eff is some effective binding energy.e equality d v C v ≈ d i C i corresponding to steady irradiation

Table 1 :
Chemical composition of 2Cr-Ni-Mo-V steel under investigation.

Table 2 :
Material conditions, mechanical properties, and the portion for IBF of 2Cr-Ni-Mo-V steel.Note.ΔT k � T k −T k0 ; Δσ Y � σ Y -σ Y0, where T k and σ Y are values for considered material condition; T k0 and σ Y0 are values for material in initial condition.

Table 3 :
D eff • t and T ∞ k values for different conditions of 2Cr-Ni-Mo-V.