The mechanism of solute-enriched clusters formation in neutron-irradiated pressure vessel steels: The case of Fe-Cu model alloys
Graphical abstract
Introduction
Owing to efforts of many researchers, various irradiation-induced changes in the microstructure of reactor pressure vessel (RPV) steels have been identified to date, which result in the following two main effects contributing to material embrittlement (see Refs. [1], [2], [3], [4], [5]):
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grain body hardening;
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grain boundaries weakening.
The weakening is caused by formation of radiation-induced segregations of some elements, such as phosphorus, on the boundaries of grains. Grain body hardening is caused by two factors:
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formation of ensembles of small dislocation loops and point defect clusters;
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formation of ensembles of small size () quasi-spherical clusters enriched with solute elements, such Cu, Mn, Ni, and Si.
Objects forming the above ensembles serve to a varying degree as centers of dislocations pinning, thus causing hardening. This phenomenon raises many unavoidable questions: what are mechanisms of the objects formation? What is the strength and the lifetime of the objects as various type pinning centers?, etc. Answers to these questions should initiate solution of the problems of practical importance, such as:
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pressure vessel steels (PVS) composition optimization;
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creation of valid technique for determining neutron dose for PVS caused by the mechanisms of generation of pinning centers and formation of grain boundary segregations;
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optimization of PVS annealing modes in order to recover their properties; etc.
Ultimately, provided that the dose patterns are available both for the processes of the grain body hardening and the grain boundary weakening, the main goal of our research is to make a description of PVS embrittlement process at the polycrystalline level.
The objective of this study is to describe the mechanism of formation of solute-enriched clusters, the ensemble of which makes the main contribution to irradiation-induced hardening of RPV steels. As a result of examination [6], [7], [8] of irradiated samples of RPV steels and Fe-Cu model alloys using Atom Probe Field-Ion Microscopy (APFIM) [9], the following characteristics of clusters enriched with the solute elements were determined:
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usually, quasi-spherical shape with the size ≅ 1–4 nm;
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chemical composition of clusters formed on the basis of bcc-Fe matrix contains up to 30–70 at.% Cu, as well as Mn, Ni, and Si with concentrations exceeding by an order of magnitude the average concentration in the reference steel composition. The maximum value of the enrichment coefficient, i.e. the ratio of element concentration in a solute-enriched cluster to its reference value for copper is much higher than the enrichment coefficients of other solute elements, although their concentrations in the solute-enriched clusters can be much higher as compared to that of copper because the reference copper content may be ultimately low;
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in contrast to precipitates, the determinant feature of the solute-enriched clusters is the absence of a pronounced concentration boundary, while copper atoms are substitution atoms for bcc-iron or bct-iron lattice (see Fig. 1);
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The specific temperature of PVS irradiation by neutrons that initiates formation of an ensemble of solute-enriched clusters is T ≅ 560–580 K, at which diffusion processes in the steel are considerably suppressed. The neutron flux on PVS is also comparatively low. For the above two reasons it is rather unlikely an emergence of any collective processes, such as those occurring in case of steel irradiation in fast neutron reactors;
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the number density of solute-enriched clusters increases with the irradiation dose reaching saturation value at the density about 1018 cm−3.
Except vessel steels with bcc crystalline structure, bcc-Fe model alloys containing 1.4, 0.7, and 0.1 at.% Cu were irradiated and examined using APFIM in order to determine the contribution of copper to the effect under study. The observed ensembles of the copper-enriched clusters possessed all the above attributes. In this paper, the solute-enriched clusters formation model is developed by taking model alloys as examples and accounting the above considerations about low temperature and neutron flux properties. The proposed solute-enriched clusters formation mechanism is based on local high-speed processes caused by the thermal spike due to displacement cascade. Upon completion of the local processes and temperature equilibration, the formed copper-enriched cluster becomes “quasi-frozen”.
Section snippets
The basing of the problem
In order to prove the feasibility of the proposed mechanism of solute-enriched clusters formation, the following points should be demonstrated:
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first, there is a high probability that thermal spike caused by a localized energy release in the cascade generated by the primary knock-on atom (PKA) with energy EPKA ≅ 30 keV, which has a region with average temperature significantly exceeding the melting point () would initiate formation of a liquid phase;
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second, as the temperature decreases
The “solute drag” mechanism
Below we consider the model alloy Fe-Cu in the low-alloyed bcc-iron phase (with initial concentration or 1.4 at.%). As a result of cascade generation followed by thermal spike evolution, the quasi-spherical molten Fe-Cu domain is formed, which undergoes expansion and then constriction up to its complete disappearance. The end of progressive advance of the solid-liquid interface at the expansion stage is characterized by maximum molten domain extension radius Rmax, see Eq. (1). Because
“Solute-drag” process termination and estimates
The above considered mechanism of forced segregation termination related to an attenuation of thermodynamic barrier with increasing copper concentration, CCu, results in too high CCu in the cluster to the end of the segregation process and too small cluster radius, in strong contradiction with available experimental data (see Section 3 and [6], [7], [8]). The conclusion can be made that some other mechanisms exist, which would terminate the process somewhat earlier, i.e. at CCu ≅ 0.3 − 0.9 [6],
Discussion
To describe the mechanism of solute-enriched clusters formation we used the tools of quasi-equilibrium thermodynamics of solid solutions. Below, we discuss the applicability of such an approach. Being one of the most advanced branches of physics, quasi-equilibrium thermodynamics as well as rapidly developing non-equilibrium thermodynamics currently being used highly successfully to describe a wide range of phenomena, starting from physics and chemistry and ending with sociology and biology. In
Conclusions
In this paper we propose and solve the new model of “solute drag” process initiated by thermal spike in order to explain the available regular patterns of solute-enriched clusters obtained in experiments:
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level of copper atoms concentration in solute clusters;
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concentration pattern on the solute cluster boundary;
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linear dimensions of the solute clusters;
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residual level of solute atoms concentration outside solute cluster domain after solid-liquid interface transit;
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kinetics of solute clusters
Acknowledgements
Authors express their acknowledgements to Dr. T.B. Ivanova, and Dr. O.V. Ivanov from P.N. Lebedev Physical Institute for fruitful discussions and assistance in work.
References (61)
- et al.
J. Nucl. Mater.
(1987) - et al.
J. Nucl. Mater.
(1995) Int. J. Press. Vessels Pip.
(1999)- et al.
J. Nucl. Mater.
(2001) - et al.
J. Nucl. Mater.
(1995) - et al.
J. Nucl. Mater.
(1995) - et al.
Mater. Charact.
(2000) - et al.
J. Nucl. Mater.
(1999) - et al.
J. Nucl. Mater.
(2000)