Radiation rate dependence of microstructure evolution

Journal of Nuclear North-Holland

Materials

169 (1989) 89-94

89

RADIATION RATE DEPENDENCE OF MICROSTRUCTURE EVOLUTION M. KIRITANI Department of Nuclear Engineering, School of Engineering, Nagoya University, Nagoya 464, Japan Received

22 February

1989; accepted

12 September

1989

Analysis and discussion are given of the radiation rate dependence of each component reaction process in the microstructure evolution under irradiation with energetic particles. The criteria to have radiation rate dependence are discussed from a relaxation time analysis of component phenomena (typically the time for defects to disappear to sinks) in which the overlap of component processes is the origin of the dependence. Examples for electron and neutron irradiation in at presently available facilities are presented, and the disappearance of the rate dependence by the saturation of defect structure development is pointed out. Enhancement and suppression of the defect structure development by accelerated irradiation are categorized from the pseudo-order of reaction of each component process. A typical example of a combination of component processes is presented for the dislocation loop formation by electron irradiation with a high voltage electron microscope. Several other sources of the rate dependence, such as cascade relaxation and the reaction of transmutation products, are pointed out.

1. Introduction Major structural materials in the present atomic reactors and also in the future fusion reactors are designed to last for several tens of years. However, irradiation testing for the development of materials is not practical if it requires a comparable time, and accelerated testing with stronger irradiation facilities is always desirable. Examples of typical damage rates in the presently available irradiation facilities are plotted in fig. 1 together with the total damage achieved by available machine time. This figure tells us how widely spread is the damage rate among the irradiations with different facilities. Here, the question arises how the change of materials by a long irradiation with a lower irradiation rate can be predicted from the experimental results from the shorter irradiation with a much stronger irradiation rate. Major concern about the radiation rate effects started at the time that ion irradiation with accelerators was adapted to simulate neutron irradiation. Irradiation with ions from an accelerator can achieve an extraordinarily high efficiency in reaching a desired accumulation of displacement damage (see fig. 1). Efforts have been made to detect the radiation rate effects within the ion irradiation regime by changing the ion current for the same total dose [l-3]. The peak swelling temperature was found to be higher for higher dose rates in simple metals of copper [l] and nickel [2], but some more 0022-3115/89/$03.50 (North-Holland)

0 Elsevier Science Publishers

B.V.

complications have been pointed out [3]. At a fixed irradiation temperature the swelling in austenitic 316 steel was found to decrease with decreasing displacement rate [4]. If the swelling has a peak and the peak temperature shifts with irradiation rate, the increase of the swelling rate with increase of the displacement rate is also predicted within the same material depending on which of the swelling peaks the irradiation temperature is located. A comparison between ion irradiation with an accelerator and neutron irradiation with a reactor, which gives us several orders of magnitude difference in the displacement rate, showed a large shift of the swelling peak to higher temperatures with the higher dose rate of an accelerator [5]. All of these experimentally detected shifts of the swelling peak temperature have been analyzed and discussed principally in terms of the theory developed by Brailsford and Bullough [6]. This theory treats void swelling as the result of void growth, and the parallel shift of the peak swelling temperature with the dose rate has been attributed to the parallel shift of the production rate of point defects with the reaction rate of the radiation-induced point defects which increases with temperature. Further theoretical predictions have been made by Mansur [7], categorizing by the type of controlling limiting processes, whether limited by the mutual annihilation or by absorption to sinks, and by the mode of point defect absorption to voids - a surface reaction or diffusion controlled. In all the above experiments and analyses, they dealt

M. Kiritani / Radiation rate dependence of microstructure euolurion

. FFTF,

5 years

l

Ions, I hour

lHVEM, I day

lFFTF, lOmonths JOYO, I yeor .HVEM, . JOYO, 3 months l

Ihcur l

Ions, lmln i

DEPA Rate (eV/atom.s)

Fig. 1. Comparison of damage rate in various irradiation facilities. DEPA is the unit of average damage energy per atom. The a~umulat~ damage energy by the available machine time for each facility is aiso shown. 2 MeV He+, 1 A/cm2, at damage peak depth, Ions: High voltage electron microscope, 2 MeV, 10 HVEM: A/cm2 s, Fast-breeder reactor at HEDL (Hanford FFTF: Engineering Development Laboratory), 200 MW, Fast-breeder reactor at PNC (Power Reactor JOYO: and Nuclear Fuel Development Corporation}. 100 MW, Japan Materials Testing Reactor at JAERI JMTR: (Japan Atomic Energy Research Institute), 50 MW, Kyoto University Reactor (Research Reactor InKUR: stitute, Kyoto University), 5 MW, Rotating Target Neutron Source at LLNL RTNS-II: (Lawrence Livermore National Laboratory).

with the micro-structure evolution in which several complex reactions proceed in parallel and in series, and it is not easy to extract the principal reaction from which the radiation rate effects are reflected in the final defect-structure development. In this paper, apart from the effort to understand the complex phenomena, the first principle type of discussion will be given on the origin of the radiation rate dependence on microstructure evolution, in the expectation that the result may help in categorizing and extracting the mechanistic origin of the radiation-rate dependence of more complex phenomena. A more recent interest in radiation dose rate effects has arisen from the effort to establish a so called “fission-fusion correlation”. Presently available fusion neutrons are from an accelerator-type of neutron source [%-lo], and the damage rate with the source is generally several orders of magnitude smaller than in the fission neutron irradiation with a fission reactor (see fig. 1).

There have been several discussions about the comparison between the defect structure development by fusion neutrons and fission neutrons in a low-dose regime, pointing out the importance of the difference from the damage rate [11,12]. However, this fission-fusion problem cannot be simplified, for example the point-defect production rate, even more the mode of the production of free point defects, &might be appreciably different for fission and fusion neutrons for the same deposited damage energy [13].

2. Criteria for radiation rate effects An irradiation rate dependence appears only when the defects produced by collision events by an incident energetic particle interact with those produced by preceding or succeeding particles. In other words, there should be a limiting irradiation intensity below which no irradiation rate dependence appears. Within this limit, the reaction of defects produced by preceding collision events has already finished before the following collision event takes place. A large number of point defects produced by a cascade collision can be supposed to have been produced by a single collision event in the following analysis similar to the production of single Frenkel pair by electron irradiation, because the time duration of the cascade collision is much less than any of the reactions of point defects by thermal activation. 2.1. Flux limit for zero irradiation rate dependence Let us consider the cases in which the defects produced by a collision event disappear by diffusion to sinks. Preexisting sinks such as grain boundaries, specimen surfaces, dislocations as well as the defects produced by irradiation such as point defect clusters and high density of tangled dislocations should be taken into consideration as sinks for these point defects. The time pi required for defects to disappear to sinks of concentration Cs with a jump frequency of M is (MC,)-*, and the average time interval T? between two collision events in the diffusion volume Vn is where u is the collision cross-section of an (N+ev,)-‘, incident particle of dose rate #, and N the number of atoms in a unit volume. When 7, is smaller than r2, the defects produced by preceding collision have disappeared already before the next collision takes place, and 72 ’

71

or

MC, > iV+aY,

(1)

can be adopted as the condition not to have interaction between defects from separate collision events.

91

M. Kiritani / Radiation rate dependence of microstructure evolution Radiation

Rate

RadiationRote

Fig. 2. Analysis

of existence and nonexistence of radiation rate dependence from the relaxation time of point Collision cross-sections of 50 barn and 3 barn were used for electrons and neutrons, respectively.

The sink concentration C, and the diffusion V, are generally related to each other. When V,, are rewritten with diffusion distance R,,

C, = aa2/R,

and

volume Cs and

VD = /3Rb.

(4

where a is the distance of one defect jump, and (Y and /? are constants close to unity, the values of which depend on sink geometry. Then, eq. (1) which gives the condition not to have radiation rate dependence, becomes R& z ap-‘MN-?#-‘a-‘.

(3)

Relations among R,, M and + are illustrated in figs. 2(a) and (b) for irradiation with electrons and neutrons, using typical values of collision cross-section u of 50 and 3 barn, respectively. For simplicity the constants a: and B in eq. (3) were set to unity in drawing the figures. 2.2. Examples from electron and neutron irradiation Electron irradiation experiments with a HVEM are always performed with a thin foil observable with a microscope (So-500 nm in thickness) and with the irradiation intensity of the order of lOi to 102’ e/cm2 s. From fig. 2(a), the limiting thickness required to observe interstitial cluster formation, which takes place by the interaction among interstitials produced by separate collision events by electrons, is figured out. At room temperature and above, at which the interstitials have a jump frequency as large as lo* jumps/s, the diffusion distance, in practice in HVEM irradiation, corresponds to the thickness of the specimen foil, should

defect

diffusion.

be more than about 50 nm. This thickness corresponds to the actually observed limiting thickness to form interstitial types of dislocation loops, and also corresponds to the observed thickness of the denuded layer of interstitial loops along the surface of a thicker specimen [15,16]. When the thickness of the specimen is more than this limit, the phenomena falls into the range in which a radiation rate dependence should be considered from the scheme described in the following section. In neutron irradiations, the irradiation flux ranges from lOi n/cm2 s in the D-T neutron source RTNS-II to lOi n/cm2 s in the core of a fast-breeder reactor as FFTF. For this range, the diffusion distance relation in order not to have interactions among defects produced by separate neutron collision events is illustrated in fig. 2(b). For an example of a polycrystalline material, the grain size corresponds to the diffusion distance. In the normally annealed samples with a grain diameter of 0.1 mm or larger, the figure tells us that all the cases fall into the range in which there exists a mutual reaction between defects produced from separate cascades before they reach the grain boundaries. When the sample has a high density of dislocations, such as 10’“/cm2 in heavily deformed materials, the diffusion length goes down to the order of 0.1 pm. The limiting flux in order not to have radiation rate dependence goes down to lo3 n/cm2 s for vacancy phenomena with a jump frequency of lo2 jumps/s as a typical case at room temperature, and the limit goes up to lOi n/cm2 s for the phenomena of interstitials with a jump frequency of lo* jumps/s. The reason why Labbe et al. [17] did not find a temperature shift for peak swelling with reactor neu-

92

M. Kiriiani / Radiation rate dependence of microstructure evolution

tron dose rate may be thdught to belong to the region of the low flux limit, though the phenomena they observed are not simple component processes. They varied the neutron dose rate in ranges as low as lo-*-lo-‘dpa/s. The existence or nonexistence of a radiation rate dependence through the overlap of the defects produced by separate collision events depends on the combination of three parameters; the irradiation flux, the sink geometry and the irradiation temperature which determines the diffusion speed of participating defects. When there are interactions among defects from separate collision events, the radiation rate dependence may be understood by the scheme described in section 3. 2.3. Saturation

of radiabon-induced

defect structure

After a prolonged irradiation, it might be expected that a high density of radiation-induced defect structure could be produced which would change no more as a whole. An example is highly tangled dislocations started from the growth of interstitial type dislocation loops. Each dislocation may keep moving on a smaller scale by the absorption of continuously introduced point defects, but their density and configuration might not change as a whole. In the initial stage of this type of microstructure evolution, nucleation and initial stage of dislocation loop growth, there must be a strong radiation rate dependence from the two processes involved. One is the nucleation, which will be dealt in the next section, and the other is from the progressive increase of point defect sinks, which might go across the border illustrated in fig. 2. For example, a fully annealed pure nickel sample was found to contain a fairly homogeneous distribution of tangled dislocation of more than 109/cm2, after reactor irradiation at 400°C (Japan Material Test Reactor, 102’ n/cm2 with 1014 n/cm2 s (E > 1 MeV) [14]. This situation already extended down into the radiation rate independent region in fig. 2 as discussed for the highly deformed samples.

lation of point defects of different kinds, the nucleation of clustered defects by the remaining point defects, their growth, the conversion of one kind of defect to other kind, and so forth. Let us define the n th pseudo-order of reaction as a reaction that proceeds with speed 0 expressed as a function of the dose rate @ in the form of B=KqY”,

(4)

where K is a constant. The prefix pseudo- has been used because the value n does not necessarily mean the true order of the reaction occurring in the component process, but may mean the resultant apparent dependence on the irradiation flux through the combination of several elementary reactions. The accumulated amount 0 of the reaction by the irradiation time 7 is O= j’Bdr=

j‘K#‘dt=K#‘r

= K@#-‘,

(5)

where @ = +r is the total accumulated dose. With the simple expression of eq. (5), one can easily classify the rate dependence of each component process. Let us consider the consequence of accelerated irradiation keeping the total dose 4p fixed. Here, accelerated irradiation means irradiation with a stronger irradiation intensity or dose rate to achieve the desired total dose within a shorter irradiation time. Each process is enhanced or suppressed depending on whether the value of n greater or smaller than unity, as tabulated in table 1. The classification above is for those component processes which continuously make progress during the irradiation. There are other cases in which the radiation rate dependence is directly given as @=KI$“’

(6)

not as the accumulation throughout the irradiation, in which the rate dependence is more clear-cut. An example of this category will be given in the following as the nucleation of interstitial loops by electron irradiation with a high voltage electron microscope.

3. Analysis from pseudo-order of reaction The irradiation rate dependence is analyzed in this section starting from the apparent dependence of each component reaction on the irradiation rate. 3.1. Formal analysis Microstructure several component

evolution processes,

is generally composed of such as the mutual annihi-

Table 1 Variation of the consequence the value of the pseudo-order

of accelerated of reaction

irradiation

Pseudo-order of component process

Consequence of accelerated irradiation

?I>1 tl=l nil

enhanced unchanged suppressed

with

93

M. Kiritani / Radiation rate ~~endence o~~i~r~st~~~~e evolution 3.2. Example

of interstitial loop formation

The formation of interstitial clustered defects in the form of dislocation loops has been most thoroughly investigated by high voltage electron microscopy in which the electrons for the observation of structural change are simultaneously utilized as particles to cause displacement damage, and is adopted here as a typical example of radiation rate dependence analysis, The nucleation of interstitial clusters in a wide variety of pure metals is known to take place during the transient increase of interstitial con~ntration at the very beginning of an irradiation, with no further increase after the transient [18]. When a di-interstitial serves as the nucleus of the clusters, which is the case for large production rate of point defects in a high voltage microscope, their number density NIL is given by N,r = K,&‘/2,

d R rJd t = K,e$/2,

(8)

where K, contains a temperature dependent factor My2 through the jump frequency of vacancy diffusion Mv [20,21]. In order to compare the final state of dislocation loops at the same total dose with different irradiation rates, eq. (8) is rewritten as = K2@~-1/2.

The density of dislocations Nt, = 2nR,,N,,

= 2?rK,K,+t

(9) No is given by = 2nK,K,@,

(10)

supposing circular loops. And the amount of interstitial atoms in the dislocation loops is given by N1 = TR;,N,,/G

Defect structure

Number density of interstitial loops Loop size Dislocation density Number of interstitials in interstitial loops

Dependence on irradiation rate

Consequence of accelerated irradiation

+i/2 $- i/2 no dependence

enhanced suppressed unchanged

rp-“’

suppressed

the amount of interstitials in the loops (the total area of dislocation loops), while the dislocation density is kept unchanged.

(7)

where K, contains a temperature dependent factor of M;1/2 through the jump frequency of interstitial diffusion M, [15,18,19]. The growth speed of these dislocation loops of radius R,, at a high temperature at which vacancies are mobile is given by

R,, = K,#‘/‘t

Table 2 Dislocation loop data compared at the same total electron irradiation with different irradiation intensity

= ;K$$t2K,+1/2

= ;K,K;@2~-‘/2, (11)

where 52 is the atomic area of one interstitial atom on a loop. The dependence on irradiation rate and the consequence of accelerated irradiation are summarized in table 2 for these dislocation loop structure development. It should be noticed here that the consequence of accelerated radiation at the end of fixed total irradiation varies with the phenomena of interest. The enhancement and suppression are towards opposite directions between the number density of dislocation loops and

4. Further considerations and concluding remarks Analyses of radiation rate effect on microstructure evolution have been made so far in this paper from the relaxation time of defects produced and from the nature of component processes. There are still several important mechanisms undiscussed, which give rise to radiation rate dependence, and they will be pointed out below. 4. I. Reparation of cascade defects The extremely high density of energy deposited into a cascade collision volume [10,13] is expected to cool down within a time of the order of T = 10-l’ s 122,231. In order to have overlap of cascades within this cooling process, the neutron flux # should be

Ip > (NerI+)-‘,

(12)

where N is the number of atoms in unit volume, and (I is the collision cross-section to initiate the cascade collision of average size of V,. In a typical case of CI= 3 barn and V, = (20 nm)3 for 14 MeV neutrons, a neutron flux larger than lOI8 n/cm2 s is necessary to have a geometrical overlap during the cooling process, through which the irradiation rate dependence might be expected. Radiation rate dependence from this origin is not expected in the neutron irradiation facilities available at present or in the near future. The next step of the reaction which takes place among defects produced by the cascade collision is the mutual annihilation of opposite types of point defects,

94

M. Kiritani / Radiation rate dependence of microstructure evolution

and this will be followed by the outward diffusion of point defects to the surrounding volume as free point defects. The speed of these reactions is highly temperature dependent, and the time required is much longer than the cascade cooling time. Therefore, the defects localized at a cascade have a possibility of overlapping with the forthcoming cascade defects before they diffuse out to the wider space, at a much lower irradiation dose rate than that estimated for the overlap at the stage of cascade cooling. The overlap is expected to enhance the reaction of point defects and may lead to an important irradiation rate dependence in the final microstructures. The limiting dose rate for the overlap can be analyzed by the same scheme as that in section 3.2, replacing the sink geometry by the volume of outward diffusion from the cascade at which the defect density becomes so low that no further interaction among defects is expected. 4.2. Reaction of transmutation

products

The rate of transmutation reaction is precisely proportional to the irradiation intensity. However, the reaction of transmutation products with structural defects will have a radiation rate dependence whenever the reaction of the structural defects have any rate dependence. Moreover, the reaction of transmutation products themselves may have a strong radiation rate dependence. The simplest example may be found in the nucleation rate of bubbles and voids with helium atoms in which more than one helium atom is expected to participate. These will be the goals of a more detailed consideration and analysis. Finally a remark is made on the experiment to clarify the irradiation rate dependence on the microstructure evolution. In the case of electron irradiation with a high voltage electron microscope, an experiment with different dose rates can be easily carried out by changing the electron dose rate either by changing the total electron beam current or changing the electron beam size with the same total electron beam current. In the case of ion irradiation, this kind of experiment is not as easy as for the electron irradiation, but it is possible. Much more difficulty is involved in neutron irradiation. Logically, it is possible to derive the radiation rate dependence from the comparison of results of irradiations by different irradiation facilities with different irradiation strengths. However, difficulties remain because of the simultaneous change in the other irradiation parameters, such as the neutron energy spectrum in different fission reactors. The same kind of difficulties

remain even when we compare the results of irradiation at different locations with different dose rates in the same fission reactor. A strong proposal is made here to utilize the chance of long time occupation of the same reactor for short and long irradiation under the same or at least similar irradiation fields, such as the irradiation research project with the fast-breeder reactor FFTF for six years [24].

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