Journal of Nuclear Materials 85 & 86 (1979) 621-625 0 North-Holland Publishing Company
PREDICTING lHE EFFECTS OF RADIATICWUPQY THE CCXTITUl’[email protected]
OF FUSI(3N REACIOR MATERIALS J.H. GIlTUS+ and A.P. MIOD(XYNIK* +UKAEA SNL Springfields,
*Metallurgy Department, University
of Surrey, Guildford,
Surrey, United Kingdom
The intense irradiation bombardment to which the first wall and other parts of the fusion reactor are subjected is known to produce radiation damage effects. These include void and bubble formation, blistering, spalling, exfoliation, erosion and the emission of macroscopic particles of the material itself. This paper is concerned with an additional effect which has only recently been appreciated: the change in actual constitution which may be produced by these intense radiation fields. While the number and type of phases which are present in metallic alloys is conventionally determined by thermodynamic considerations, the free energy balance, which governs constitution, is disturbed significantly by intense particle-irradiation so that phases which do not form normally may be caused to appear and others, normally to be expected, may dissolve. This effect is quite distinct from the well ~~VWIIphenomenon of irradiationenhanced diffusion which can accelerate the attainment of equilibria structures but which is not itself a cause of a shift in the equilibrium. In the present paper a scheme is presented which permits the radiation levels at which such effects are likely to occur to be predicted. lhe method is exemplified by reference to stainless steels and nickel based alloys under fusion reactor fluxes and temperatures, but may well be of more general application.
INTRODUCTI CN ‘Ihe appearance of precipitates in otherwise sub-saturated solid solutions, and/or the appearance of precipitates with a different structure from that expected under normal equilibria conditions has now been reported In many cases in numerous systems (Table I). it is difficult to be certain that radiation is not just accelerating changes which are too slow to take place under normal circwrstances, but in the case of nickel-silicon alloys there now seems to be incontrovertible evidence that irradiation induced precipitation of Nisi redissolves when irradiation ceases but all other variables are kept constant (20). Reference to (Table I) shms that only the Ni-Si system has been studied sufficiently to obtain sane idea of the temperature-dose rate dependence of such anomalous precipitation. Consequently we have chosen this system as a prototype in or&r to define some general grolrnd rules for irradiation induced precipitation in sub-saturated solid solutions.
Once the structure of a material has been designed for optimwn performance, it is clearly undesirable to have changes occurring in that structure in service. Hmeve r since many properties depend on non-equilibrium structures, it is necessary in practise to allm for changes due to diffusional processes, especially at hi& temperatures. Such allowances are tolerable if based on predictable transitions between rmztastable and stable phases, or the growth of such phases, so that the presence of radiation enhanced diffusion does not by itself necessitate any major change in methodology. However the appearance of unexpected phases in the Dresence of irradiation creates new proble;, insofar that (a) it is currently unpredictable, (b) there seems to be a relationship between such irradiation induced precipitation and the reclination or irradiation induced vacancies and interstitials, and (c) that swelling behaviour may therefore be significantly affected by such precipitates.
J.H. Gittus and A.P. Miodownik /Predicting the effects of radiation
The rationale of our approach is srmmmrised in Figure 1. ‘Ihe cotiined results of previous work on Ni-Si alloys can be represented in the form of a TransformationTemperature-Dose-Pate (TTD) Diagram, Figure 1C. Ihe lower curves in this diagram arise from diffusion control, and are entirely analogous to the equivalent regions of the more familiar Transformation-Time-Terrperature (TTT) Diagrams. Pursuing this analogy, the upper curves ¬e the presence of a driving force for precipitation, increasing as the temperature decreases ; in the present instance, this driving force is provided via the irradiation flux. Although the analogy is useful in providing an approach to the problem in hand, the inherent differences between TI’D and TIT diagrams should also be noted. Firstly, the “start of transformation” curves in the TTD
diagram imply that if the dose rate is reduced sufficiently, the precipitate will redissolve, i.e. the transformation under consideration is reversible, which is not the case in the TIT analogue. Secondly, since one is here considering sub-saturated solid solutions the change in chemical potential associated with
The “start of transformatim” curves in the high temperature region of the TI’D diagram therefore correspond to a point of balance where the chemical driving force and the irradiation induced driving force are equal in magnitude. Ihis is indicated in Figure (la) , which also shows that it should therefore be possible to obtain a measure of this driving force at various temperatures provided that the appropriate free energy data is available for the alloy system concerned.
COMPOSITION SHOWING PRECIPITATION UNDER IRRADIATION CONDITIONS
600 boo 200 0 I
FIG. (1) General Scheme for Relating Time-Transformation Dose Fate Curves with the! Free Energy of Transformation
J.H. Gittusand A.P. Miodownik /Predicting
the effects of radiation
TABLEI Alloy Systems Exhibiting Material
316 + Si
In the case of the Ni-Si sys tern, the available experimental data axe incomplete, being largely concerned with the liquid phase, and the various compounds in’ the sys tern (21) . hiobresurprisingly, the equilibrium diagram is also rather incompletely known, with the solid solubility region being rather sketchily outlined, (Figure 2). Fortunately it is possible to make up for the missing data by combining the two sources of info~tion and applying some of the self consistent phase diagram-thermochemical techniques naw available (24). Full details of such calculations are being ptilished elsewhere (25), but the salient features are summarised below.
FIG. (2) Compariscn of Experimental and Calculated
a(a + Nisi)
in which Irradiation
Transus and Region Induced Precipitation
has been observed
a)Data from the liquid state are first used to produce a fo~~ati~ for the free energy of the nickel-silicon solid solution which is consistent with the known maximumsolubility of silicon in nickel. b) This is, then combined with a formulation for the free energy of the Ni3Si phase to yield the equilibrium a(a + Ni3Si) transus. c) Finally, the same free energy curves are used to calculate the excess free energy bG*‘ required to allow Ni3Si to precipitate from solid s,olutions whose silicon content is lower than the equilibrium value (at some chosen temperature). (Fig. 2) shows the resultant calculated a(a + Ni3Si) transus together with the limited available experismntal data and also the compositions at which Ni3Si has been observed to precipitate under irradiation.
J.H. Cittus and A.P. Miodownik /Predicting the effects of radiation TABLEII Calculated
Free Energy (AG* J mol-‘)
with the Precipitation
of NigSi from Sub-
Saturated Nickel-Silicon Composition
(Table II) lists the values of AG* (as defined in Fig. (lb)) for various compositions and temperatures. This parameter (AG*) represents the minimumfree energy shift which has to be addem system in order to obtain equilibrium between the chosen subsaturated solution and Ni3Si. This is not the only criterion that could be used, but is definable with the minimumnunber of assumptions. Since the data of Martin and Barbu (6) defines the minimumdose rate r required to produce precipitation at various temperatures it is possible to relate the critical values of AG* and critical values of dose rate, Fig. (la). The general tendency is clearly that for a high degree of subsaturation it is necessary to use a larger dose rate to offset the greater chemical driving force associated witn any Nigi precipitates. It is encouraging to find that the rather extensive linear extrapolation used on one set of data (ref. 6) seems to adequately encompass the data of other workers (4,5,7,8) and also further unptilished data from Martin and his co-workers which refers to much lower radiation doses (26). The general order of coitus of the free energies which must be associated with radiation-induced precipitation as deduced by the present approach is similar to the values deduced previously for stainless steels by an entirely different method of approach (27,28). More calculations are clearly necessary before it is possible to say whether it can be established that this general or&r of magnitude for AG can be applied to other materials, which would clearly simplify the prediction of likely conditions for irradiation induced precipitation calculations are currently in progress on the free energies associated with normal phase equilibria in Fe-Ni-Cr-C and Fe-Ni-Cr-Si alloys (29) which comprise more commercially important alloy compositions used in intensive radiation Such calculations are now environments. relatively easily performed (30) and will allow
some direct checks with accumulated data on ‘real’ alloys. 3.
Thermodynamic characterisation of the Nickel-Silicon system has been made to yield values of the chemical driving force which opposes irradiation induced precipitation, and which controls the composition at which such precipitation is likely to occur in subsaturated alloys. When reference is made to composition/temperature/dose-rate combinations known to exhibit such precipitation, the relevant driving forces are seen to be appreciable (0.5 + 1 KJ mol-1) , and give an indication of the forces associated with defect redistribution and solute-defect interaction. An approximately log-linear relationship appears to exist between the dose rate and the associated driving force in the system under investigation. Given the complementary relationship between driving force and precipitation, it will be possible to design alloys with a sufficiently high degree of sub-saturation to avoid subsequent precipitation in service. This may then avoid deleterious redistributicm of solutes and changes in a matrix camposition already selected to provide optimum recohination of vacancies and interstitials in order to reduce the swelling problem (31). REFERENCES 1. Cawthome C., Brcwn C., J.Nucl Mat. 66
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