- Email: [email protected]
Basic aspects of swelling in dense livuid metal fast breeder reactor fuels
Journal of the Less-Common
Metals, 121 (1986)
583
583 - 603
BASIC ASPECTS OF SWELLING IN DENSE LIQUID METAL FAST BREEDER REACTOR FUELS* H. BLANK
Commission of the European Communities Joint Research Centre, Karkruhe Establishment, European Institute for Transuranium Elements, Postfach 2340, D-7500 Karlsruhe (F.R.G.)
Summary The basic aspects of swelling in dense liquid metal fast breeder reactor fuels, alloys, carbides and nitrides, are analysed as functions of burn-up by use of a common reduced temperature scale. In addition to temperature and burn-up, swelling depends on stress and the composition and as-fabricated structure of the fuel. Therefore the technological boundary conditions, as defined by pin design and operation parameters, have to be respected in order to limit the analysis. This leads to the concepts of “hot” fuels, “cool” fuels as well as free swelling and swelling under restraint. With increasing bum-up the in-pile kinetics responsible for swelling are affected by the ingrowth of fission damage and the increasing concentration of fission products. The resulting phenomena are not yet well understood and represent a field of present and future research.
1. Introduction In contrast with the oxide fuels currently employed, swelling in dense liquid metal fast breeder reactor (LMFBR) fuels is a phenomenon which, if its implications are not properly taken care of, limits useful pin life. The technological requirements of the LMFBR fuel cycle provide the framework within which the swelling properties of dense fuels have to be determined. The present situation for fast reactors is characterized by the need to optimize the fuel cycle. This need also defines the boundary conditions on the choice of a particular fuel and for which the swelling problems have to be solved with regard to a high target burn-up. The boundary conditions may differ between different countries. At present three candidate fuels, metallic fuels, carbides and nitrides, exist whose swelling properties will be discussed from a basic point of view.
*Paper
presented
0022-5088/86/$3.50
at Actinides
85, Aix en Provence, 0 Elsevier
September Sequoia/Printed
2
- 6, 1985. in The Netherlands
584 TABLE 1 Properties of dense fuels Fuel ff-U
U+15Pu+lOZr
MN
MC
18.95
14.13
13.53
12.95
75 14.2
75 10.6
80 10.8
80 10.36
1405
1426
3050
2700
940 1045 -
-
-
-
about 910 about 935
-
-
Thermal conductivity (W cm-‘K-l ) 400 - 800 “C 800 - 1200 “C
0.18 - 0.25
-
-
-
-
0.17 - 0.22
0.17 - 0.22
Minimum rate of swelling (e 4 0.35) So% (at.%)-’
about 3
about 1.5
1.6 + 0.2
Heavy metal densities Theoretical density (g cmp3) Smear densitya (%) (g cmp3) Melting temperature
(K)
Transformation temperatures a-+P P+r a+b+{+a+{+y cr+{++y
Vurrent
(K)
pin design.
Some of the relevant properties of these fuels are summarized in Table 1. In spite of the large differences between their melting points it is possible to understand the relevant swelling mechanisms on a common basis. This is outlined in Section 2. In Section 3 their in-pile operating conditions are described, and in Section 4 the basic aspects of swelling in the three fuels are discussed in more detail.
2. Basic aspects of swelling - a survey 2.1. Lattice damage The first step in the understanding of the in-pile kinetics for a nuclear fuel is to know the fission damage to the fuel lattice. Basically it is the same regardless whether the fuel is metallic or ceramic, especially since all fuels regarded here possess metallic thermal and electrical conductivity. In each fission event one heavy atom (U,Pu) is fissioned and most of the energy of about 200 MeV is imparted as kinetic energy to the two fission fragments and the two to three fission neutrons. When the two fragments come to rest in the fuel matrix (after straight paths of 6 to 10 pm in length)
585
about 95% of their kinetic energy has been transformed into heat, increasing the fuel temperature locally, and the remainder into lattice damage by the formation of Frenkel pairs (lattice vacancies and interstiti~s~. These are mostly distributed in clusters on the branches of defect cascades. Owing to geometric effects in the fuel lattice the clusters are enriched in vacancies because the interstitials are transported further away by focused collisions [l, 21. For each fission event a volume uf of crystal (uf = lo-l7 cm3) is damaged in this way. Depending on the local temperature this damage will either remain, or anneal out quickly before the same volume is affected by another fission spike [3]. Since the lifetime of the interstitials is much shorter than that of the vacancies at low temperatures a mean fission rate induced vacancy concentration C,*(F, T,S)is reached which depends on the fission rate k, the temperature 2’ and the density S of appropriate sinks. These vacancies are available for interaction with the fission product atoms (solid and gaseous) or for supporting anisotropic irradiation growth as in the case of o-U [4]. Most of the interstitials and a proportion of the vacancies precipitate initially into small dislocation loops. These loops grow until they interact and form a dislocation network as shown in Fig. 1. 2.2. Behaviour of fission product atoms The second consequence of nuclear fission in an operating fuel is the increasing concentration of fission product atoms which in most cases are not soluble in the fuel matrix and tend to form precipitates. If these precipitates are solid their space requirements and hence their contribution to swelling is relatively low and cannot be changed. However, about 25% of the fission product atoms are rare gases (xenon, krypton) and precipitate as gas bubbles. These require additional space depending on the bubble size, temperature and pressure. The relation between bubble radius r and gas pressure p is
p=2y, r
+(J
Ts = 1000
erg cm-2
(1)
where ys is the surface energy of the fuel and u is a possible hydrostatic stress in the surrounding matrix which may be positive or negative depending on the fuel type and technologicat conditions. The connection between the gas pressure p in the bubble and the temperature is given by the equation of state of the gas. This may be approximated by a (modified) van der Waals equation in the case of bubbles with radii r < 0.2 pm and by the ideal gas law for larger ones. At very low fuel temperatures, i.e. T/T& 0.35where T, is the melting temperature, all fission product atoms remain more or less in dynamic solution in the fuel matrix (or form only extremely small precipitates at higher burn-up). Under these conditions the rate of fuel swelling is the lowest possible. Values of these lower bounds So for the rate of swelling are given in Table 1.
586
(a)
(b) Fig. 1. Lattice damage in a carbide fuel at 3.5 at.% burn-up as observed by transmission electron microscopy (TEM) showing dislocations, several types of precipitates and fission gas bubbles: (a) specimen tilted for dislocation contrast; (b) tilted for bubble contrast
[51.
After, for example, a bum-up of 12 at.% the fuel contains 12% more atoms compared with the initial metal (sub)lattice of which 21% are now impurity atoms, i.e. in addition to the volume increase the fuel has also drastically changed its overall composition.
587
2.3. Point defect kinetics in dense fuels and a common temperature scale From a fundamental point of view both the intrinsic lattice defects, vacancies and interstitials, and the extrinsic ones, the fission fragment atoms, represent a variety of point defect species i. These migrate in the fuel lattice according to their specific mobilities determined by their diffusion coefficients Di. The directions of motion are dictated by the local forces Fi = grad /Ji, where /Li is the chemical potential of species i which may in general contain chemical, thermal and mechanical contributions. Depending on their size, fission fragment atoms will combine with one or several lattice vacancies and correspondingly will migrate by either a simple or a more complex vacancy mechanism. The latter case is certainly true for the fission gas atoms xenon and krypton and for caesium. Hence the intrinsic lattice vacancies, either provided at low temperatures by the fission damage with a concentration C: or existing at high temperatures in the thermal equilibrium concentration C,, play a fundamental role in the kinetics of fuel swelling and in-pile restructuring. In order to compare the mobility of vacancies and impurity atoms between different substances it is convenient to use a common temperature scale by writing for each substance 8 = T/T,. The underlying concept is that the kinetic situation in different crystaIline substances is practically the same at the same fraction 8 of the absolute melting temperatures. This reduced temperature scale is generally valid for substances of simple crystal structures as in the present cases where it applies to the metal (sub)lattice of each fuel. It can be divided into three ranges. (a) 8 < 0.35. Thermally activated migration of vacancies is practically non-existent. Atoms are stochastically moved by high energy atomic collisions with a fission rate induced diffusion coefficient D* = lo-l8 cm* s-l and no biased point defect migration is possible. This implies that no precipitation of the fission products occurs and fission gas bubbles do not form [3]. The rate of swelling is given by So in Table 1. (b) 0.35 L 19< 0.5. Vacancies introduced into the lattice by quenching, plastic deformation or irradiation are mobile with a thermally activated vacancy diffusion coefficient D, = fa2v0 exp(-ML/RT) ,UYL is the migration energy of a metal vacancy in the lattice, f is the correlation factor, a the next neighbour distance and v. the frequency factor. Fission fragment atoms i sitting on a lattice position or in a vacancy cluster, e.g. xenon, krypton, caesium, may acquire additional mobile vacancies from the irradiation-induced concentration C,* and their diffusion coefficient Di in this temperature range becomes Di = AiEi(T)C:D,
= Di, exp(-&i/RT)
588
Aj and Ei are an entropy factor and an interaction energy term which depend on the details of the migration mechanism and on the interaction energy between vacancies and impurity atoms. These details are not known. However, at low impurity concentrations the factor E,(T) probably will not change the term AH& of eqn. (2) very much and the temperature dependence of Di will not differ very much from that of D,. Hence in the range 0.35 ,< 8 2 0.5 fission product atoms may migrate by a biased thermally activated vacancy mechanism with an activation energy similar to AH&. The in-pile kinetics are “‘slow” with a moderate temperature dependence. However, this picture will change with increasing concentrations of fission product atoms. As regards the fission gas, bubbles are nucleated in this temperature range with high densities and grow slowly. Consequently the rate of swelling is low. Gas release is negligible unless special release paths (e.g. open porosity) are built into the fuel in the fabrication process. Even then the rate of gas release is relatively low. (c) e > 0.5 In this temperature range the vacancy diffusion coefficient D, of eqn. (2) becomes very large and irradiation-induced vacancies anneal out very quickly. But thermal activation is now sufficiently strong to create a thermal equilibrium concentration C, = exp(-AHfVIkT) which replaces C,*. All diffusion coefficients Di are now faster with activation energies Qi near that of the lattice self-diffusion given by AH,’ + AH;. The in-pile kinetics are “fast” with a strong temperature dependence. Fission gas bubbles are nucleated with low densities and grow rapidly within the grains and on the grain boundaries. The rate of swelling is high. Grain boundary bubbles coalesce and form channels from which the fission gas can escape, see Fig. 2. Hence high swelling is accompanied by high gas release. The approximate temperature variation of the single gas atom diffusion coefficient D, in the three temperature ranges is plotted in the Arrhenius diagram in Fig. 3. The abscissa has the scale l/0 thus the diagram should in principle be valid for all nuclear fuels. It must, however, be regarded as a With increasing burn-up the situation rather qualitative representation. becomes more complex due to vacancy-impurity and impurity-impurity interactions and the diffusion coefficients Di will change in the ranges (b) and (c). Depending on the type and amount of fission product atoms going into solution in the matrix the pattern of Fig. 3 is expected to change slowly with increasing bum-up. For example, the difference in the solubility of the rare earth elements between carbide and nitride causes differences in the lattice parameter changes with burn-up. The lattice parameter of MC shrinks with increasing bum-up whereas that of MN remains practically constant [6]. Consequently differences in the development of the fission gas kinetics are to be expected as well. In addition solid fission product atoms may contaminate the surface of the fission gas bubbles and change the surface energy yS.
589
-e;l 0.6 -10
10
It
0.5
0.L
Tm
0.35
Dg lcm2/s1
Fig. 2. Grain boundary porosity in a helium-bonded carbide fuel at about 0.6 of a pellet radius at 5 at.%, Scanning electron micrograph of a fracture surface. Fig. 3. The approximate temperature dependence of the fission gas single atom diffusion coefficient D, in nuclear fuels. Arrhenius diagram with a common reduced temperature scale l/6 = T,/T valid at low burn-up (F Q 1 at.%). This pattern is expected to change noticeably with increasing bum-up. Three temperature ranges can be recognized: 6 > 0.5, 0.35 < 0 Q 0.5 and 0 < 0.35.
3. The technological boundary conditions for swelling The technological boundary conditions are fixed by three groups of parameters: (i) the initial fuel composition and structure which result from the specific fabrication procedure of each fuel; (ii) the pin concept and the detailed pin design; (iii) the operation conditions in the reactor. These technological factors determine the main parameters responsible for the swelling performance of a fuel, namely fuel temperature T, smear density /sof the fuel in a pin cross section, fuel-cladding restraint a and burn-up F. Their role will now be discussed in the light of the pattern established for the in-pile kinetics. 3.1. The range of fuel working temperatures To make the discussion more specific the operating temperatures of the sodium-bonded FBR metal fuels have been taken from EBR II irradiations [7]. The ranges of working temperatures for the ceramic fuels have been based on the design and operation data given in Table 2. These temperature ranges have been plotted together with the common scale T/T, valid for all three types of fuel in Fig. 4. For the helium-bonded ceramic fuels two working ranges are indicated labelled A and C. “A” pertains to the temperatures at the beginning of the irradiation when the fuel-clad gap is still open and “C” to the situation after gap closure, i.e. for the bum-up range 3
590 TABLE 2 Pin design parameters Fuel
Na-(U + ~Fs)~
Na-(U + 1OPu + 15Zr)b
Na-MXC
He-MX=
Outer clad diameter Da
4.42
5.22
8.70
8.70
0.30 0.25 1.65 0
0.5 0.28 1.83 0
0.50 0.3 3.55 5
0.50 0.1 3.75 15
75 28 -
75 33 -
Hot
Hot
80 480 750 Cool
80 ~80 750 Hot and cool
(mm)
Clad thickness d (mm) Radial gap Sa (mm) Pellet radius a0 (mm) Fabrication porosity (%) Smear density (%) Linear rating (kW m-r) ~coolatlt (X) Fuel operational concept
aRef. 7, numbers in weight per cent. bRef. 8, numbers in weight per cent. CConditions at maximum rating. e]TKl
U
lTlKl
MC
[TlKl
MN
I
0.50-702.5
0301L2l.5
1780
A
1915
1
1
Fig. 4. Comparison of the in-pile operation temperatures of the three dense fuels o-U based alloys, nitride, carbide on the common temperature scale 0 = T/T,. L, sodiumbonded ceramic fuels; A, helium-bonded fuels at start of irradiation; C, helium-bonded fuels for F z 3 at.%.
First the sodium-bonded metallic and ceramic fuels will be compared. The metal fuels operate exclusively in the temperature range 8 > 0.5 and the ceramic fuels in the range 0.3 < 8 < 0.5. Hence the metal fuels operate in a “hot fuel” and the ceramic fuels in a “cool fuel” pin concept in spite of the fact that both are sodium-bonded. The consequences of this difference are straight forward. The “hot” metallic fuel swells quickly in a radial direction, displaces the sodium bond and starts to make contact with the clad. Contact
591
is complete at 2 - 3 at.% burn-up. The gap volume is redistributed as coarse porosity within the fuel, allowing gas release to occur. Strong release exists where the fuel structure contains porosity of at least 20%, see Fig. 5. The “cool” ceramic fuel, however, swells very slowly and only starts to make contact with the cladding after 11 at.% bum-up in spite of severe pellet fracturing, see Fig. 6. If the linear rating in sodium-bonded ceramic fuels exceeds 100 kW m-i, however, the “cool fuel” pin concept is no longer applicable. For the helium-bonded ceramic fuel the temperature-bum-up history is more complicated, see Fig. 7. After a short period A in the temperature range 8 5 0.5 the fuel temperatures drop to values where at least half
0
50 FUEL
.VOLUME
INCREASE,
100 X
Fig. 5. Relation between irradiation-induced porosity and integral gas release in metallic fuels (Fs, fissium): local release starts at values of 5% to 10% irradiation induced (grain boundary) porosity (from ref. 9).
(a)
(b)
Fig. 6. Comparison of sodium-bonded and helium-bonded carbide pin cross sections. In the case of sodium-bonding up to 11 at.% no firm fuel clad mechanical interaction (FCMI) exists for linear rating x < 100 kW m-l : (a) sodium-bonded MC at 6.8 at.%; (b) helium-bonded MC at 5 at.%.
0
10
1
2
3
6%
5
F.9.
Fig. 7. Temperature-burn-up history of a helium-bonded carbide pellet. The burn-up periods A, B and Care indicated (schematic representation); Tst indicates thermal stability limit of the initial fuel porosity,
of the total fuel volume operates at 8 < 0.5 and only the inner part at 0 > 0.5 (Fig. 6(b)), bum-up range C in Fig. 7. By matching the thermal stability limit of the as-fabricated fuel with the initial operating temperatures, one can combine the advantages of the “hot fuel concept” with that of the “cool fuel” in the helium-bonding pin concept. The porosity in the central fuel zone is increased by transporting gap volume towards the centre, enhancing there during period A, the porosity for gas release taking place later during period C. The outer fuel ring in contact with the clad remains “cool” during period C and the swelling is partly accommodated by the fabrication porosity under the action of the clad restraint. 3.2. Smear density p and clad restraint cr The actual heavy atom density in a dense FBR-fuel pin represents a compromise between “as high as possible” and “reasonably low” to provide the space for the accommodation of swelling. The smear densities given in Table 1 are at present regarded as feasible for target burn-ups greater than 12 at.%. In the two current pin concepts with dense fuels, the sodiumbonded alloy fuel and the helium-bonded ceramic fuels, the fuels make firm contact with the clad after about 3 at.% bum-up, and then the clad is stressed by the swelling fuel over the largest part of its in-pile time. Therefore, the technological key problem with all dense fuels is to keep the FCMI within tolerable limits with regard to clad integrity and pin geometry until the target bum-up is attained. Hence a basic understanding of FCMI is required with the in-pile mechanisms in fuel and clad being of equal importance. Their quantitative description (and basic understanding) should be sufficiently precise to enable reactor engineers to predict, i.e. to calculate, the change in clad diameter AD/D, as a function of bum-up until end of life
593
(EOL) with an error of +O.l%. This is a formidable problem which has not yet been solved satisfactorily. Consequently the development of a new fuel for optimized pin performance still has to take place by a procedure of trial and error in fabrication and irradiation supported by detailed P.I.E. and modelling. The better the basic mechanisms are known the quicker one can hope to reach the goal. As regards the clad performance the clad strain AD/D,-, is composed roughly of a stress sensitive part due to irradiation creep and a stress insensitive part due to void swelling. In Fig. 8 the clad strains of three pin designs are compared. The helium-bonded carbide and the sodium-bonded metal fuel pins show higher clad strains because in both cases severe FCMI operates for F > 3 at.%. However, in the sodium-bonded carbide fuel pin which usually has no FCMI up to 11 at.% burn-up the clad deformation occurs only through void swelling and is hence considerably less. I
I
AD/Dl%l
L.’
a
b , 3-
0, 0
2
L
6
0
10
12
1L --)
Flo/oI
Fig. 8. Clad deformation (316 type steel) in thre pin concepts: curve a, sodium-bonded metal fuel with FCMI [7]; curve b, helium-bonded carbide fuel with FCMI [lo]; curve c, sodium-bonded carbide fuel without FCMI [ 111.
4. Free swelling and swelling under restraint The strong in-pile restructuring during the first 3 at.% burn-up leads in both the sodium-bonded alloys and the helium-bonded ceramics to three structural zones with distinct in-pile properties, see Figs. 9(a) and 9(b). These determine the swelling behaviour of the fuels until EOL. The properties of the porous centre zone in the two fuel cross sections are equivalent. They provide high gas release and are mechanically “soft”, i.e. they are expected to contribute little to FCMI. The origin and the properties of the two outer zones are different: (a) because alloys and ceramics operate in different temperature ranges
(a)
(b)
Fig. 9. Formation of structural zones in dense FBR fuels: (a) alloy U-15 wt.% Pu-12 wt.% Zr, zone boundaries are defined by alloy phase transitions, see Table 1, F = 2.4 at.% [8]; (b) helium-bonded carbide after 5 at.% burn-up, the zone boundaries were determined by the radial variations of swelling ~2 (see Table 3). porosity and retained xenon (by electron probe microanalysis). 8 > 0.5 and 8 < 0.5 and (b) the alloys consist of metallic multiphase systems with strongly anisotropic crystal structures whereas the ceramic fuels have primarily one cubic phase. Consequently the details of the relevant swelling mechanisms will differ in the two cases. Nevertheless, basic aspects of the fission gas behaviour are common as will be shown in this section. In the late 1950s and in the 1960s the nucleation and growth of fission gas bubbles was studied at low burn-up in metal fuels. In dense ceramic fuels these phenomena were studied only recently at higher burn-ups, 2 to 11 at.% [5, 11 - 171. In principle fission damage is the same in all dense fuels since the fission spikes have practically the same properties in metals and dense ceramics. Thus the low burn-up results obtained on metal fuels are also applicable to carbides and nitrides with the exception of the “irradiation growth mechanism” which is a particular property of fuel alloys based on a-u.
4.1. The irradiation growth effect in metal fuels Metallic thermal reactor fuels (adjusted a-U) alloys containing e.g. 500 to 1200 ppm Al, or metals such as molybdenum, cerium or tin as well as low and highly alloyed FBR fuels (U + 5 wt.% Fs, U + 15 wt.% Pu + 10 wt.% Zr) show a swelling behaviour which is largely or partly complicated by the irradiation growth of the anisotropic crystal structure of the cx-U phase [4, 181, and in part of the phase originating from the U-Pu system. Irradiation growth produces strong local anisotropic deformations of the cy grains and results in local stress concentrations which induce plastic deformation (formation of dislocation networks) and produce microcracks and cavities. Up to 8 = 0.48 this mechanism absorbs all fission rate created lattice vacan-
p3
pza
Pl
PO
p3a
p3
PZ
Ca SO.5 >5
04)
Single atomsb 2 - 40 40 - 450
170 - lo3
en So.5 57
220 56 >15
little
50 - 80 2-4 -15
of
Gt 1
Gas content gl(%
/Jl
(%I
Swellinga
(51) (<4)
C -1015 - 10r4
Bubble densities N1 (cm-j)
<170 5170
Single atomsb 2 -30 30 - 350
Bubble sizes e (ml
All quantities Ni, ~11and gi are primarily a function of burn-up F and temperature 7’. aUpper limits correspond to F = 12 at.%. b Atomic volume a.
III
PO
IV
Pl
Population
Zone
Structural zones and bubble populations (free swelling)
TABLE 3
grain boundary porosity
Transition P*“p? at curve 7$(F) defines zone boundary IV/III under conditions of free swelling
Transition P3-+P$ within zone IV on curve e(F)
Intragranular bubbles Heterogeneous nucleation
Remarks
596
ties at low burn-up and consequently prevents the formation of fission gas bubbles. Coarse porosity (break away swellings is formed at temperatures 0.49 < 6 G 0.59 by interaction between the mechanisms of fission gas precipitation and irradiation growth and leads to extremely high rates of swelling, These can, however, be limited by clad restraint, see below. The details of this interaction depend sensitively on the alloying and heat treatment of the fuels, operating temperature and mechanical restraint. No general theory of the phenomena exists. Proposed mechanisms for the “break away swelling” in pure and adjusted o-U are as follows. (i) Local tensile hydrostatic stresses are formed on bubbles as a result of the growth mechanism [ 191. (ii) Bubble sweeping and coalescence occur by the recovery of the dense dislocation substructure as a result of previous irradiation growth in a defined temperature range. This can be largely avoided by anchoring the dislocation tangles with precipitates of UAlz [ 201. (iii) Bubble growth occurs as a result of the decrease in the surface energy ys in eqn. (1) owing to contamination of the bubble surface with fission product atoms [Zl]. This is still an open problem which also applies to ceramic dense fuels. (iv) For the FBR fuel alloys an interpretation by “microtears” 1221 appears to be appropriate [ 8,231. Obviously more detailed investigations using a combination of density measurements, SEM, replica electron microscopy (REM) and especially TEM with a high voltage electron microscope are required as used for “adjusted o-U” [20, 241 to evaluate the mechanisms qu~titatively in the other alloy fuels. Earlier TEM investigations with 100 keV electrons of relatively low penetrating power required very thin foils (30 - 50 nm, corresponding to the size of the larger bubbles and precipitates). Because of the defectsurface interaction these specimens were not representative of the bulk situation, e.g. refs. 25, 26. Thicker specimens (100 to 200 nm) transparent to 1000 keV electrons are practically free of surface effects and are expected to show the interaction between bubbles and dislocations, precipitates and grain and twin boundaries in a representative way [ 241. The high porosity introduced into the metallic FBR fuels by the irradiation growth effect has, however, turned out to be favourable. If sufficient space for swelling is provided the high porosity permits a strong fission gas release since the fuel operates at 0 > 0.5 and further swelling can be limited by clad restraint. 4.2. Bubble nucleation and growth at low burn-up (F d 0.5 at.%) and i? > 0.5 Despite their experimental limitations the early TEM investigations [25, 261 provided the basis for establishing the bubble nucleation mechanisms. At very low burn-up thin specimens showed very little irradiation damage and were free of stresses from the growth effect. Under these conditions the critical gas atom concentration C* required for bubble nucleation
597
was found to be about C* = lOi crne3 and the nucleation mechanism to be homogeneous with bubble densities N = 1016 cme3 at 8 x 0.49 and lower values, 10ls to 1013 cm3, at increasing temperatures for 8 > 0.5 [25, 261. Similar values were found later also in carbide and nitride fuels at burn-up values greater than about 3 at.%. On the basis of theoretical homogeneous nucleation models [27 - 291 it is difficult to define the size of the stable nucleus to which the classical diffusion-based growth law can be applied. Therefore phenomenological models were used for the estimation *of the bubble density N which lead to relations N2 - G/D, or at least show G ID, to be the leading term if fission gas resolution is taken into account [ 30,311. An investigation of the swelling performance of cubic y-U around 0 = 0.75 and y-stabilized uranium alloys containing zirconium, niobium or molybdenum and an alloy U-18 wt.% Pu-14 wt.% MO at 0.52 < 8 > 0.73 showed very high rates of swelling (with the exception of a U-14 wt.% MO alloy), in spite of the complete absence of cracks and growth effects [32]. This demonstrated that in general the irradiation of cubic alloys at 8 > 0.5 also leads to high rates of swelling. The fission gas bubbles attained diameters of several microns and linked together where they were largest. Post-irradiation annealing of irradiated metallic fuels under various pressures [26, 331 has demonstrated that the fission gas bubbles were in fact in equilibrium with the surface tension of the matrix according to eqn. (l), i.e. fission gas swelling can be reduced by external perssure (clad restraint u). Irradiation of certain uranium-base alloys under hydrostatic pressure also showed that the swelling effects associated with the growth process, can be reduced; 40 bar diminished the break away swelling between 430 and 550 “C!by a factor of 2 [34]. 4.3. Swelling burn-up 4.3.1.
performance
of ceramic
dense
fuels
at 8 2 0.5
up
to high
Survey The high rates of swelling encountered in metal fuels initiated the interest in ceramic fuels at the beginning of the 1960s. As regards dense fuels (carbides, nitrides), mainly helium-bonded mixed carbides with linear rating between 49 and 70 kW m-l and densities around 95% were irradiated at first in thermal and fast reactors [35 - 371 with stainless steel and niobium cladding. All countries with FBR projects had started prograrnmes on fabrication, property measurements and irradiation of carbide and to a lesser degree nitride fuels. Since each project developed its own fuel and pin design with the related irradiation conditions these technological developments [38, 391 yielded relatively limited information which could be employed for a systematic analysis of the basic swelling mechanisms. Theoretical models to describe carbide swelling were thus mainly based on the previous information from metal fuels and on theoretical studies on nucleation and bubble growth, bubble interaction with fission spikes (borrowed from oxide experiments), dislocations and grain boundaries and on bubble migration [28, 40, 411. A severe deficiency resulted from the fact that no reliable
598
fission gas diffusion data were available and the interpretation of gas release measurements from carbides and other nuclear fuels was not unambiguous
r421.
A systematic analysis of the swelling mechanisms was started around 1974 at the Institute for Transuranium Elements. During the first phase the out-of-pile and in-pile restructuring and the fission gas swelling were analysed by optical microscopy and REM in MC, MCN and MN fuels irradiated at high linear power (x - 130 kWm_l). Severe interaction between fission gas swelling and in-pile restructuring was observed [12, 131. The varying temperature history in the helium-bonded fuels and the limited burn-up (mainly not more than 4 at.%) precluded the establishment of a clear picture valid over a larger burn-up range. However, the existence of two temperature ranges for fission gas swelling with a rather well-defined transition temperature from low to high swelling was identified and good correlations between out-of-pile self-diffusion measurements and in-pile restructuring was found
v41.
It took considerable work by detailed post irradiation analysis (especially by REM, SEM and TEM and local gas analyses by electron probe microanalysis (EPMA)) on a variety of fuels irradiated under different conditions before a quantitative picture of the fission gas swelling in dense ceramic fuels started to emerge. Further detailed analyses are still required on heliumbonded carbides and nitrides at high burn-up and from technologically relevant pin designs before this picture is complete. Transient fuel and pin performance especially after higher burn-up will be another topic of future basic and technological research. The following picture of the swelling in dense ceramic fuels should be seen in relation to the temperature dependence of the fission gas diffusion and the fuel operating temperatures in Figs. 3 and 4 and their anticipated modifications with increasing burn-ups.
4.3.2. Low burn-up range (F < 0.5 at.%) At the start of irradiation homogeneous bubble nucleation exists giving rise to one bubble population with strong temperature dependence of the bubble density N(T) (at 8 = 0.35, N = lOi’ cme3 and at 8 = 0.6, N = lOi’ cmd3) and of the bubble growth rate.
High burn-up range (2 < F < 12 at.%) In this range fission gas swelling develops into a complex pattern which is conveniently separated into free swelling (sodium-bonded carbide and nitride, see Fig. 4) and swelling under restraint (helium-bonded fuels). For the basic understanding of fission gas swelling it is essential to recognize that with increasing burn-up an increasing interaction exists between fission gas kinetics and fission damage (lattice damage and fission product atom) as indicated formally by eqn. (3). 4.3.3.
599
4.3.3.1. Free swelling at temperatures 8 < 0.5 (sodium-bonded MC and MN). After about 2 at.% bum-up and at 0.35 < 8 Q 0.5 two distinct bubble populations start to develop, Pi and P2 (see Table 3), of which P, grows systematically with increasing burn-up and contains of the order of 15% of the fission gas created and makes the main contribution to the low temperature swelling. A third population P3 of grain boundary bubbles appears first near e = 0.5. The important property of P, and P, is that these populations possess bum-up dependent transition temperatures T:(F) and T:(F) above which they grow faster and hence produce higher rates of swelling (T:(F) < T:(F)). In Fig. 10 the relation T:(F) has been plotted on the reduced temperature scale 8 of Figs. 3 and 4 for carbide and nitride. As is expected, the two curves coincide at low burn-up but then start to diverge because of the different fission product solubilities in the two fuels. Two questions arise: (i) what makes some bubbles grow faster, i.e. what produces the separation between bubble population P, and P,? and (ii) what is the reason for the existence of the transition curves T:(T) and T:(T)? Before detailed microstructural investigation by TEM and SEM became available the two questions were answered in the following way [ 151. (i) The small bubbles of population PI were supposed to be very mobile in the matrix and perform a Brownian motion. This leads to bubble coalescence and formation of the bubbles of P,. New bubbles of P, are continuously nucleated and P, and P2 are thus in a continuous dynamic equilibrium. (ii) Below the curve c(F) the bubbles of P, become overpressurized because of the lack of vacancies and if the pressure is high enough the surrounding matrix yields by thermally activated creep, the bubbles expand and this produces the higher rate of swelling at (TJ) > (!Z?$F).However, the analyses of TEM and SEM micrographs [ 5, 161 provide new evidence on the processes occuring at a submicroscopic scale over a large bum-up range. (i) The bubbles of population P, are found to be exclusively associated with the density of the irradiation-induced dislocation and fine-scale needle-
1 0
e
2
L
6
8
10
FI%l
Fig. 10. Transition temperature-burn-up relation Z’?(F) for MC and MN plotted on a common reduced temperature scale. Note that the two curves diverge with increasing burn-up owing to different solubilities for the rare earth fission products.
600
like precipitation networks with bubble densities N = 1 - 4 X 10” cmP3. Hence bubbles in the size range 3 to 25 nm are stationary. Pi is not affected by the transition curve T:(F). The population of larger bubbles Pz develops independently from P, on preferential growth sites like dislocation nodes, larger precipitates or by the growing together of closely spaced smaller bubbles. (ii) As the radial position corresponding to the temperature T: is passed in a pellet cross section (analysed on a fracture surface by SEM) the most significant feature of the microstructure is the appearance of “elongated bubbles” where two or even three bubbles have touched and grown together, see Fig. 11. These elongated geometries become more spherical at higher temperatures. In fact these features exist already below T:(F) even for bubbles with 10 nm size, but their density is insignificant. Hence the increase in the rate of swelling when crossing the curve T,*(F) is associated with the increase in size and density of the “elongated” or “dumbell” bubbles.
Fig. 11. Scanning electron micrograph-of a transgranular fracture surface from a sodiumbonded carbide at F = 11.8 at.%. Position for T > T?(F).The large fraction of elongated fission gas bubbles should be noted.
4.3.3.2. Swelling under restraint (helium-bonded MC and MN), 8 5 0.5. In the helium-bonded ceramic fuels two additional effects occur. (i) As indicated in Figs. 4 and 7 a large part or all of the fuel operates initially for a short period at 8 > 0.5, but later mainly at 8 < 0.5. This will affect the nucleation of fission gas bubbles and solid fission product precipitates at F < 2 at.%. (ii) Helium-bonded fuels have about 15% fabrication porosity and are subjected to clad restraint u for F > 3 at.%. The essential in-pile mechanism under these conditions is the accommodation of the swelling contributions M from the solid fission products and
601
the three bubble populations by the fabrication porosity PO in the outer part of the fuel adjacent to the clad. The driving force is provided by the clad restraint u. The problem has been treated theoretically by Ronchi [ 151. Its solution requires a computer code. A somewhat crude, approximate treatment, however, sufficient for many practical purposes is given by the relation [ 171 A(F, T, u) = M(F, T, a) - P,[l
- exp{-ko(F
- Fn)}]
(4)
where A is the “local swelling” and k is a parameter which depends on the mechanical properties of the fuel matrix. Since the temperature range over which this equation applies is 0.34 < 8 < 0.5 thermally activated creep cannot be involved. The magnitude of k can be estimated from post-irradiation analysis. A theoretical expression for k can be obtained from a hotpressing model [43] into which the creep rate of the matrix enters. However, experimental values of irradiation creep measured in carbide fuels [44, 451 and extrapolated to 100% density are too low by a factor of, at least, 10. It appears that the situation may be better described by a hot-pressing model based on the diffusion of lattice vacancies [46].
5. Summary and Conclusions 5.1. Main basic mechanisms
contributing
to swelling are as follows:
(1) atomic diffusion of fission product atoms by isms, (2) ingrowth of a dislocation network (10” to 10” (3) ingrowth of solid fission product precipitates, (4) development of intragranular gas bubbles, (5) development of intergranular bubbles and open There is strong interaction between (2), (3) and (4), (3) and (5). 5.2. 2
Mechanisms
operating
vacancy jump mechancm cmd3) [ 51,
porosity. at 8 > 0.5 also between
in the three main pin concepts
outlined
in Table
“Hot” fuel (sodium-bonded alloys, no fabrication porosity) - The initial 25% gap volume is transformed rapidly into fuel porosity (mainly in the fuel centre) creating open porosity for high gas release. Fuel swelling is limited by FCMI. It appears that the swelling mechanism in the outer fuel zone has not yet been investigated in detail. “Cool” fuel (sodium-bonded MX fuels, < 5% fabrication porosity) Swelling is kept very low, provided the sodium-bond remains sound. The initial gap volume (about 15%) is slowly used up. FCMI starts around 12%, gas release is low [ 111. “Hot/cool” fuel (helium-bonded MX fuels, fabrication porosity about 15%) -The initial gap volume is transformed rapidly into fuel porosity (centre zone) and crack volume (outer fuel ring). FCMI (clad restraint)
602
directs part of the low temperature fabrication porosity.
swelling in the outer
fuel ring into the
5.3. Fission gas kinetics In the helium- and sodium-bonded dense ceramic fuels, swelling at temperatures 0 < 0.5 is of great technical importance. In the range 0.35 < 8 < 0.5 the rate of swelling is governed by the slow thermally activated migration of the fission gas atoms, i.e. the slow growth of a rather high density of gas bubbles. The mechanism is based on the fission-rate-induced concentration of lattice vacancies. Above a bum-up dependent transition temperature 8:(F) the rate of swelling increases, with 0:(F) S 0.5. The low temperature gradients in dense fuels together with the strong interaction between bubbles, dislocations and solid fission product precipitates makes bubble migration unlikely to play an important role in swelling and gas release during steady state irradiations. As a consequence of these complex interactions further detailed investigation of dense LMFBR fuels at high bum-up are required before the basic laws of swelling under these conditions can be quantified.
Acknowledgments The author acknowledges numerous discussions and the provision of unpublished results from his colleagues, especially Drs. M. Coquerelle, I. L. F. Ray and C. Ronchi. He thanks Dr. L. C. Walters for providing Fig. 9(a).
References 1 A. Seeger, Proc. 2nd UN Conf. on Peaceful Uses of Atomic Energy, Geneva, 1958, Vol. 6, United Nations, Geneva, 1958, p. 250. 2 J. A. Brinkman, J. Appl. Phys., 25 (1954) 961. 3 H. Blank, Eur. Appl. Res. Rep., Nucl. Sci. Technol. Sect., 1 (1979) 307. 4 S. F. Pugh, Prog. Nucl. Energ., Ser. 5, 1 (1956) 662. 5 I. L. F. Ray and H. Blank, J. Nucl. Muter., 124 (1984) 159. 6 U. Benedict, Thermodynamics of Nuclear Materials, 1979, Vol. 1, IAEA, Vienna, 1979, p. 453. 7 R. E. Einziger and B. R. Seidel, Nuci. Technol., 50 (1980) 25. 8 L. C. Walters, B. R. Seidel and J. H. Kittel, Nucl. Technol., 65 (1984) 179. 9 L. C. Walters and J. H. Kittel, Nucl. Technol., 48 (1980) 273. 10 P. J. Levine, U. P. Nayak and A. Boltax, Proc. 7th Znt. Conf. on SMiRT,Chicago, 1983, Vol. C, North Holland, Amsterdam, 1983, p. 161. 11 M. Colin, M. Coquerelle, J. L. F. Ray, C. Ronchi, C. T. Walker and H. Blank, Nucl. Technol., 63 (1983) 442. 12 C. Ronchi and C. Sari, J. Nucl. Mater., 58 (1975) 140. 13 C. Ronchi, I. L. F. Ray, H. Thiele and J. van de Laar, J. Nucl. Mater., 74 (1978) 193. 14 Hj. Matzke and C. Ronchi, Advanced LMFBR Fuels. In J. Leary and J. H. Kittel (eds.), ANS 1977, ERDA 4455, p. 218.
603 15 C. Ronchi, J. Nucl. Mater., 84 (1979) 55. 16 I. L. F. Ray and H. Blank, ENC ‘86, Geneva, June 1 - 6, 1986, Topic VI, part 2. 17 H. Blank, F. Caligara, M. Coquerelle and C. ,Ronchi, Modelling of swelling and fuelclad contact pressure in a “real-structure” framework. IAEA Specialist’s Meet. on Theoretical Modelling of LMFBR Fuel Pin Behaviour, May 28 -June 1, 1979, Paper 26. 18 S. H. Paine and J. H. Kittel, Proc. Znt. Conf. on Peaceful Uses of Atomic Energy, Geneva, 1955, Vol. 7, United Nations, New York, 1956, p. 445. 19 J. W. Harrison, J. Nucl. Mater., 23 (1967) 139. 20 B. Hudson, J. Codd and G. A. Burras, Acta Metall., 23 (1975) 101. 21 P. Blanchard,J. Nucl. Mater., 26 (1968) 241. 22 C. L. Angerman and G. R. Caskey,J. Nucl. Mater., 13 (1964) 182. 23 D. R. O’Boyle, ANL-7417, 20, 1967. 24 C. Baker and B. Hudson, Znt. Conf. on Physical Metallurgy of Reactor Fuel Elements, CEGB, Berkeley, September 2 - 7, 1973, paper 40. 25 B. Hudson, J. Nucl. Mater., 22,(1967) 121. 26 J. Lehman, P. Paoli and N. Azam, J. Nucl. Mater., 27 (1968) 285. 27 G. W. Greenwood, A. J. E. Foreman and D. E. Rimmer, J. Nucl. Mater., 1 (1959) 305. 28 B. L. Eyre and R. Bullough, J. Nucl. Muter., 26 (1968) 249. 29 D. R. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, 1976, NTIS, US Dept. of Commerce, Springfield, VA. 30 J. W. Harrison, J. Nucl. Muter., 31 (1969) 327. 31 H. Blank, F. Caligara and I. L. F. Ray, Spec. Meet. on Fuel Element Performonce Computer Modelling, Blackpool, March 1980, IAEA-ZW GFPT/7, 1980, p. 76. 32 G. W. Greenwood, AERE-Rep.-3468, 1960. 33 B. Hudson, J. Nucl. Muter., 27(1968) 54. 34 J. Lehmann, P. Pavoli and N. Azam, J. Nucl. Muter., 26 (1968) 238. 35 B. T. Bradbury, B. R. T. Frost and J. R. Findlay, in Plutonium 1965, Chapman and Hall, London, 1967, p. 949. 36 A. Stroasser, J. Cihi, S. Horwitz and R. Martin, in Plutonium 1965, Chapman and Hall, London, 1967, p. 979. 37 J. P. Mustelier, in Plutonium 1965, Chapman and Hall, London, 1967, p. 1006. 38 R. Farmakes (ed.), Proc. Conf on Fust Reactor Fuel Element Technology, New Orleans, 1971, American Nuclear Society, 1971. 39 J. Leary and J. H. Kittel (eds.), Proc. Topical Meet. on Advanced LMFBR Fuels, Tuscan, 1977, ANS-ERDA 4455. 40 J. W. Harrison, J. Nucl. Muter., 30 (1965) 319. 41 P. Prajoto, A. R. Wazzan and D. Okrent, Nucl. Eng. Design, 48 (1978) 461. 42 Hj. Matzke, Science of Advanced LMFBR Fuels, North Holland, Amsterdam, 1985, Chapter 9. 43 D. S. Wilkinson and M. F. Ashby, Acta Metall., 23 (1975) 1277. 44 I. Miiller-Lyda and W. Dienst, J. Nucl. Muter., 90 (1980) 232. 45 W. Dienst, J. Nucl. Muter., 124 (1984) 153. 46 R. L. Coble, J. Appl. Phys., 41 (1970) 4798.
Metals, 121 (1986)
583
583 - 603
BASIC ASPECTS OF SWELLING IN DENSE LIQUID METAL FAST BREEDER REACTOR FUELS* H. BLANK
Commission of the European Communities Joint Research Centre, Karkruhe Establishment, European Institute for Transuranium Elements, Postfach 2340, D-7500 Karlsruhe (F.R.G.)
Summary The basic aspects of swelling in dense liquid metal fast breeder reactor fuels, alloys, carbides and nitrides, are analysed as functions of burn-up by use of a common reduced temperature scale. In addition to temperature and burn-up, swelling depends on stress and the composition and as-fabricated structure of the fuel. Therefore the technological boundary conditions, as defined by pin design and operation parameters, have to be respected in order to limit the analysis. This leads to the concepts of “hot” fuels, “cool” fuels as well as free swelling and swelling under restraint. With increasing bum-up the in-pile kinetics responsible for swelling are affected by the ingrowth of fission damage and the increasing concentration of fission products. The resulting phenomena are not yet well understood and represent a field of present and future research.
1. Introduction In contrast with the oxide fuels currently employed, swelling in dense liquid metal fast breeder reactor (LMFBR) fuels is a phenomenon which, if its implications are not properly taken care of, limits useful pin life. The technological requirements of the LMFBR fuel cycle provide the framework within which the swelling properties of dense fuels have to be determined. The present situation for fast reactors is characterized by the need to optimize the fuel cycle. This need also defines the boundary conditions on the choice of a particular fuel and for which the swelling problems have to be solved with regard to a high target burn-up. The boundary conditions may differ between different countries. At present three candidate fuels, metallic fuels, carbides and nitrides, exist whose swelling properties will be discussed from a basic point of view.
*Paper
presented
0022-5088/86/$3.50
at Actinides
85, Aix en Provence, 0 Elsevier
September Sequoia/Printed
2
- 6, 1985. in The Netherlands
584 TABLE 1 Properties of dense fuels Fuel ff-U
U+15Pu+lOZr
MN
MC
18.95
14.13
13.53
12.95
75 14.2
75 10.6
80 10.8
80 10.36
1405
1426
3050
2700
940 1045 -
-
-
-
about 910 about 935
-
-
Thermal conductivity (W cm-‘K-l ) 400 - 800 “C 800 - 1200 “C
0.18 - 0.25
-
-
-
-
0.17 - 0.22
0.17 - 0.22
Minimum rate of swelling (e 4 0.35) So% (at.%)-’
about 3
about 1.5
1.6 + 0.2
Heavy metal densities Theoretical density (g cmp3) Smear densitya (%) (g cmp3) Melting temperature
(K)
Transformation temperatures a-+P P+r a+b+{+a+{+y cr+{++y
Vurrent
(K)
pin design.
Some of the relevant properties of these fuels are summarized in Table 1. In spite of the large differences between their melting points it is possible to understand the relevant swelling mechanisms on a common basis. This is outlined in Section 2. In Section 3 their in-pile operating conditions are described, and in Section 4 the basic aspects of swelling in the three fuels are discussed in more detail.
2. Basic aspects of swelling - a survey 2.1. Lattice damage The first step in the understanding of the in-pile kinetics for a nuclear fuel is to know the fission damage to the fuel lattice. Basically it is the same regardless whether the fuel is metallic or ceramic, especially since all fuels regarded here possess metallic thermal and electrical conductivity. In each fission event one heavy atom (U,Pu) is fissioned and most of the energy of about 200 MeV is imparted as kinetic energy to the two fission fragments and the two to three fission neutrons. When the two fragments come to rest in the fuel matrix (after straight paths of 6 to 10 pm in length)
585
about 95% of their kinetic energy has been transformed into heat, increasing the fuel temperature locally, and the remainder into lattice damage by the formation of Frenkel pairs (lattice vacancies and interstiti~s~. These are mostly distributed in clusters on the branches of defect cascades. Owing to geometric effects in the fuel lattice the clusters are enriched in vacancies because the interstitials are transported further away by focused collisions [l, 21. For each fission event a volume uf of crystal (uf = lo-l7 cm3) is damaged in this way. Depending on the local temperature this damage will either remain, or anneal out quickly before the same volume is affected by another fission spike [3]. Since the lifetime of the interstitials is much shorter than that of the vacancies at low temperatures a mean fission rate induced vacancy concentration C,*(F, T,S)is reached which depends on the fission rate k, the temperature 2’ and the density S of appropriate sinks. These vacancies are available for interaction with the fission product atoms (solid and gaseous) or for supporting anisotropic irradiation growth as in the case of o-U [4]. Most of the interstitials and a proportion of the vacancies precipitate initially into small dislocation loops. These loops grow until they interact and form a dislocation network as shown in Fig. 1. 2.2. Behaviour of fission product atoms The second consequence of nuclear fission in an operating fuel is the increasing concentration of fission product atoms which in most cases are not soluble in the fuel matrix and tend to form precipitates. If these precipitates are solid their space requirements and hence their contribution to swelling is relatively low and cannot be changed. However, about 25% of the fission product atoms are rare gases (xenon, krypton) and precipitate as gas bubbles. These require additional space depending on the bubble size, temperature and pressure. The relation between bubble radius r and gas pressure p is
p=2y, r
+(J
Ts = 1000
erg cm-2
(1)
where ys is the surface energy of the fuel and u is a possible hydrostatic stress in the surrounding matrix which may be positive or negative depending on the fuel type and technologicat conditions. The connection between the gas pressure p in the bubble and the temperature is given by the equation of state of the gas. This may be approximated by a (modified) van der Waals equation in the case of bubbles with radii r < 0.2 pm and by the ideal gas law for larger ones. At very low fuel temperatures, i.e. T/T& 0.35where T, is the melting temperature, all fission product atoms remain more or less in dynamic solution in the fuel matrix (or form only extremely small precipitates at higher burn-up). Under these conditions the rate of fuel swelling is the lowest possible. Values of these lower bounds So for the rate of swelling are given in Table 1.
586
(a)
(b) Fig. 1. Lattice damage in a carbide fuel at 3.5 at.% burn-up as observed by transmission electron microscopy (TEM) showing dislocations, several types of precipitates and fission gas bubbles: (a) specimen tilted for dislocation contrast; (b) tilted for bubble contrast
[51.
After, for example, a bum-up of 12 at.% the fuel contains 12% more atoms compared with the initial metal (sub)lattice of which 21% are now impurity atoms, i.e. in addition to the volume increase the fuel has also drastically changed its overall composition.
587
2.3. Point defect kinetics in dense fuels and a common temperature scale From a fundamental point of view both the intrinsic lattice defects, vacancies and interstitials, and the extrinsic ones, the fission fragment atoms, represent a variety of point defect species i. These migrate in the fuel lattice according to their specific mobilities determined by their diffusion coefficients Di. The directions of motion are dictated by the local forces Fi = grad /Ji, where /Li is the chemical potential of species i which may in general contain chemical, thermal and mechanical contributions. Depending on their size, fission fragment atoms will combine with one or several lattice vacancies and correspondingly will migrate by either a simple or a more complex vacancy mechanism. The latter case is certainly true for the fission gas atoms xenon and krypton and for caesium. Hence the intrinsic lattice vacancies, either provided at low temperatures by the fission damage with a concentration C: or existing at high temperatures in the thermal equilibrium concentration C,, play a fundamental role in the kinetics of fuel swelling and in-pile restructuring. In order to compare the mobility of vacancies and impurity atoms between different substances it is convenient to use a common temperature scale by writing for each substance 8 = T/T,. The underlying concept is that the kinetic situation in different crystaIline substances is practically the same at the same fraction 8 of the absolute melting temperatures. This reduced temperature scale is generally valid for substances of simple crystal structures as in the present cases where it applies to the metal (sub)lattice of each fuel. It can be divided into three ranges. (a) 8 < 0.35. Thermally activated migration of vacancies is practically non-existent. Atoms are stochastically moved by high energy atomic collisions with a fission rate induced diffusion coefficient D* = lo-l8 cm* s-l and no biased point defect migration is possible. This implies that no precipitation of the fission products occurs and fission gas bubbles do not form [3]. The rate of swelling is given by So in Table 1. (b) 0.35 L 19< 0.5. Vacancies introduced into the lattice by quenching, plastic deformation or irradiation are mobile with a thermally activated vacancy diffusion coefficient D, = fa2v0 exp(-ML/RT) ,UYL is the migration energy of a metal vacancy in the lattice, f is the correlation factor, a the next neighbour distance and v. the frequency factor. Fission fragment atoms i sitting on a lattice position or in a vacancy cluster, e.g. xenon, krypton, caesium, may acquire additional mobile vacancies from the irradiation-induced concentration C,* and their diffusion coefficient Di in this temperature range becomes Di = AiEi(T)C:D,
= Di, exp(-&i/RT)
588
Aj and Ei are an entropy factor and an interaction energy term which depend on the details of the migration mechanism and on the interaction energy between vacancies and impurity atoms. These details are not known. However, at low impurity concentrations the factor E,(T) probably will not change the term AH& of eqn. (2) very much and the temperature dependence of Di will not differ very much from that of D,. Hence in the range 0.35 ,< 8 2 0.5 fission product atoms may migrate by a biased thermally activated vacancy mechanism with an activation energy similar to AH&. The in-pile kinetics are “‘slow” with a moderate temperature dependence. However, this picture will change with increasing concentrations of fission product atoms. As regards the fission gas, bubbles are nucleated in this temperature range with high densities and grow slowly. Consequently the rate of swelling is low. Gas release is negligible unless special release paths (e.g. open porosity) are built into the fuel in the fabrication process. Even then the rate of gas release is relatively low. (c) e > 0.5 In this temperature range the vacancy diffusion coefficient D, of eqn. (2) becomes very large and irradiation-induced vacancies anneal out very quickly. But thermal activation is now sufficiently strong to create a thermal equilibrium concentration C, = exp(-AHfVIkT) which replaces C,*. All diffusion coefficients Di are now faster with activation energies Qi near that of the lattice self-diffusion given by AH,’ + AH;. The in-pile kinetics are “fast” with a strong temperature dependence. Fission gas bubbles are nucleated with low densities and grow rapidly within the grains and on the grain boundaries. The rate of swelling is high. Grain boundary bubbles coalesce and form channels from which the fission gas can escape, see Fig. 2. Hence high swelling is accompanied by high gas release. The approximate temperature variation of the single gas atom diffusion coefficient D, in the three temperature ranges is plotted in the Arrhenius diagram in Fig. 3. The abscissa has the scale l/0 thus the diagram should in principle be valid for all nuclear fuels. It must, however, be regarded as a With increasing burn-up the situation rather qualitative representation. becomes more complex due to vacancy-impurity and impurity-impurity interactions and the diffusion coefficients Di will change in the ranges (b) and (c). Depending on the type and amount of fission product atoms going into solution in the matrix the pattern of Fig. 3 is expected to change slowly with increasing bum-up. For example, the difference in the solubility of the rare earth elements between carbide and nitride causes differences in the lattice parameter changes with burn-up. The lattice parameter of MC shrinks with increasing bum-up whereas that of MN remains practically constant [6]. Consequently differences in the development of the fission gas kinetics are to be expected as well. In addition solid fission product atoms may contaminate the surface of the fission gas bubbles and change the surface energy yS.
589
-e;l 0.6 -10
10
It
0.5
0.L
Tm
0.35
Dg lcm2/s1
Fig. 2. Grain boundary porosity in a helium-bonded carbide fuel at about 0.6 of a pellet radius at 5 at.%, Scanning electron micrograph of a fracture surface. Fig. 3. The approximate temperature dependence of the fission gas single atom diffusion coefficient D, in nuclear fuels. Arrhenius diagram with a common reduced temperature scale l/6 = T,/T valid at low burn-up (F Q 1 at.%). This pattern is expected to change noticeably with increasing bum-up. Three temperature ranges can be recognized: 6 > 0.5, 0.35 < 0 Q 0.5 and 0 < 0.35.
3. The technological boundary conditions for swelling The technological boundary conditions are fixed by three groups of parameters: (i) the initial fuel composition and structure which result from the specific fabrication procedure of each fuel; (ii) the pin concept and the detailed pin design; (iii) the operation conditions in the reactor. These technological factors determine the main parameters responsible for the swelling performance of a fuel, namely fuel temperature T, smear density /sof the fuel in a pin cross section, fuel-cladding restraint a and burn-up F. Their role will now be discussed in the light of the pattern established for the in-pile kinetics. 3.1. The range of fuel working temperatures To make the discussion more specific the operating temperatures of the sodium-bonded FBR metal fuels have been taken from EBR II irradiations [7]. The ranges of working temperatures for the ceramic fuels have been based on the design and operation data given in Table 2. These temperature ranges have been plotted together with the common scale T/T, valid for all three types of fuel in Fig. 4. For the helium-bonded ceramic fuels two working ranges are indicated labelled A and C. “A” pertains to the temperatures at the beginning of the irradiation when the fuel-clad gap is still open and “C” to the situation after gap closure, i.e. for the bum-up range 3
590 TABLE 2 Pin design parameters Fuel
Na-(U + ~Fs)~
Na-(U + 1OPu + 15Zr)b
Na-MXC
He-MX=
Outer clad diameter Da
4.42
5.22
8.70
8.70
0.30 0.25 1.65 0
0.5 0.28 1.83 0
0.50 0.3 3.55 5
0.50 0.1 3.75 15
75 28 -
75 33 -
Hot
Hot
80 480 750 Cool
80 ~80 750 Hot and cool
(mm)
Clad thickness d (mm) Radial gap Sa (mm) Pellet radius a0 (mm) Fabrication porosity (%) Smear density (%) Linear rating (kW m-r) ~coolatlt (X) Fuel operational concept
aRef. 7, numbers in weight per cent. bRef. 8, numbers in weight per cent. CConditions at maximum rating. e]TKl
U
lTlKl
MC
[TlKl
MN
I
0.50-702.5
0301L2l.5
1780
A
1915
1
1
Fig. 4. Comparison of the in-pile operation temperatures of the three dense fuels o-U based alloys, nitride, carbide on the common temperature scale 0 = T/T,. L, sodiumbonded ceramic fuels; A, helium-bonded fuels at start of irradiation; C, helium-bonded fuels for F z 3 at.%.
First the sodium-bonded metallic and ceramic fuels will be compared. The metal fuels operate exclusively in the temperature range 8 > 0.5 and the ceramic fuels in the range 0.3 < 8 < 0.5. Hence the metal fuels operate in a “hot fuel” and the ceramic fuels in a “cool fuel” pin concept in spite of the fact that both are sodium-bonded. The consequences of this difference are straight forward. The “hot” metallic fuel swells quickly in a radial direction, displaces the sodium bond and starts to make contact with the clad. Contact
591
is complete at 2 - 3 at.% burn-up. The gap volume is redistributed as coarse porosity within the fuel, allowing gas release to occur. Strong release exists where the fuel structure contains porosity of at least 20%, see Fig. 5. The “cool” ceramic fuel, however, swells very slowly and only starts to make contact with the cladding after 11 at.% bum-up in spite of severe pellet fracturing, see Fig. 6. If the linear rating in sodium-bonded ceramic fuels exceeds 100 kW m-i, however, the “cool fuel” pin concept is no longer applicable. For the helium-bonded ceramic fuel the temperature-bum-up history is more complicated, see Fig. 7. After a short period A in the temperature range 8 5 0.5 the fuel temperatures drop to values where at least half
0
50 FUEL
.VOLUME
INCREASE,
100 X
Fig. 5. Relation between irradiation-induced porosity and integral gas release in metallic fuels (Fs, fissium): local release starts at values of 5% to 10% irradiation induced (grain boundary) porosity (from ref. 9).
(a)
(b)
Fig. 6. Comparison of sodium-bonded and helium-bonded carbide pin cross sections. In the case of sodium-bonding up to 11 at.% no firm fuel clad mechanical interaction (FCMI) exists for linear rating x < 100 kW m-l : (a) sodium-bonded MC at 6.8 at.%; (b) helium-bonded MC at 5 at.%.
0
10
1
2
3
6%
5
F.9.
Fig. 7. Temperature-burn-up history of a helium-bonded carbide pellet. The burn-up periods A, B and Care indicated (schematic representation); Tst indicates thermal stability limit of the initial fuel porosity,
of the total fuel volume operates at 8 < 0.5 and only the inner part at 0 > 0.5 (Fig. 6(b)), bum-up range C in Fig. 7. By matching the thermal stability limit of the as-fabricated fuel with the initial operating temperatures, one can combine the advantages of the “hot fuel concept” with that of the “cool fuel” in the helium-bonding pin concept. The porosity in the central fuel zone is increased by transporting gap volume towards the centre, enhancing there during period A, the porosity for gas release taking place later during period C. The outer fuel ring in contact with the clad remains “cool” during period C and the swelling is partly accommodated by the fabrication porosity under the action of the clad restraint. 3.2. Smear density p and clad restraint cr The actual heavy atom density in a dense FBR-fuel pin represents a compromise between “as high as possible” and “reasonably low” to provide the space for the accommodation of swelling. The smear densities given in Table 1 are at present regarded as feasible for target burn-ups greater than 12 at.%. In the two current pin concepts with dense fuels, the sodiumbonded alloy fuel and the helium-bonded ceramic fuels, the fuels make firm contact with the clad after about 3 at.% bum-up, and then the clad is stressed by the swelling fuel over the largest part of its in-pile time. Therefore, the technological key problem with all dense fuels is to keep the FCMI within tolerable limits with regard to clad integrity and pin geometry until the target bum-up is attained. Hence a basic understanding of FCMI is required with the in-pile mechanisms in fuel and clad being of equal importance. Their quantitative description (and basic understanding) should be sufficiently precise to enable reactor engineers to predict, i.e. to calculate, the change in clad diameter AD/D, as a function of bum-up until end of life
593
(EOL) with an error of +O.l%. This is a formidable problem which has not yet been solved satisfactorily. Consequently the development of a new fuel for optimized pin performance still has to take place by a procedure of trial and error in fabrication and irradiation supported by detailed P.I.E. and modelling. The better the basic mechanisms are known the quicker one can hope to reach the goal. As regards the clad performance the clad strain AD/D,-, is composed roughly of a stress sensitive part due to irradiation creep and a stress insensitive part due to void swelling. In Fig. 8 the clad strains of three pin designs are compared. The helium-bonded carbide and the sodium-bonded metal fuel pins show higher clad strains because in both cases severe FCMI operates for F > 3 at.%. However, in the sodium-bonded carbide fuel pin which usually has no FCMI up to 11 at.% burn-up the clad deformation occurs only through void swelling and is hence considerably less. I
I
AD/Dl%l
L.’
a
b , 3-
0, 0
2
L
6
0
10
12
1L --)
Flo/oI
Fig. 8. Clad deformation (316 type steel) in thre pin concepts: curve a, sodium-bonded metal fuel with FCMI [7]; curve b, helium-bonded carbide fuel with FCMI [lo]; curve c, sodium-bonded carbide fuel without FCMI [ 111.
4. Free swelling and swelling under restraint The strong in-pile restructuring during the first 3 at.% burn-up leads in both the sodium-bonded alloys and the helium-bonded ceramics to three structural zones with distinct in-pile properties, see Figs. 9(a) and 9(b). These determine the swelling behaviour of the fuels until EOL. The properties of the porous centre zone in the two fuel cross sections are equivalent. They provide high gas release and are mechanically “soft”, i.e. they are expected to contribute little to FCMI. The origin and the properties of the two outer zones are different: (a) because alloys and ceramics operate in different temperature ranges
(a)
(b)
Fig. 9. Formation of structural zones in dense FBR fuels: (a) alloy U-15 wt.% Pu-12 wt.% Zr, zone boundaries are defined by alloy phase transitions, see Table 1, F = 2.4 at.% [8]; (b) helium-bonded carbide after 5 at.% burn-up, the zone boundaries were determined by the radial variations of swelling ~2 (see Table 3). porosity and retained xenon (by electron probe microanalysis). 8 > 0.5 and 8 < 0.5 and (b) the alloys consist of metallic multiphase systems with strongly anisotropic crystal structures whereas the ceramic fuels have primarily one cubic phase. Consequently the details of the relevant swelling mechanisms will differ in the two cases. Nevertheless, basic aspects of the fission gas behaviour are common as will be shown in this section. In the late 1950s and in the 1960s the nucleation and growth of fission gas bubbles was studied at low burn-up in metal fuels. In dense ceramic fuels these phenomena were studied only recently at higher burn-ups, 2 to 11 at.% [5, 11 - 171. In principle fission damage is the same in all dense fuels since the fission spikes have practically the same properties in metals and dense ceramics. Thus the low burn-up results obtained on metal fuels are also applicable to carbides and nitrides with the exception of the “irradiation growth mechanism” which is a particular property of fuel alloys based on a-u.
4.1. The irradiation growth effect in metal fuels Metallic thermal reactor fuels (adjusted a-U) alloys containing e.g. 500 to 1200 ppm Al, or metals such as molybdenum, cerium or tin as well as low and highly alloyed FBR fuels (U + 5 wt.% Fs, U + 15 wt.% Pu + 10 wt.% Zr) show a swelling behaviour which is largely or partly complicated by the irradiation growth of the anisotropic crystal structure of the cx-U phase [4, 181, and in part of the phase originating from the U-Pu system. Irradiation growth produces strong local anisotropic deformations of the cy grains and results in local stress concentrations which induce plastic deformation (formation of dislocation networks) and produce microcracks and cavities. Up to 8 = 0.48 this mechanism absorbs all fission rate created lattice vacan-
p3
pza
Pl
PO
p3a
p3
PZ
Ca SO.5 >5
04)
Single atomsb 2 - 40 40 - 450
170 - lo3
en So.5 57
220 56 >15
little
50 - 80 2-4 -15
of
Gt 1
Gas content gl(%
/Jl
(%I
Swellinga
(51) (<4)
C -1015 - 10r4
Bubble densities N1 (cm-j)
<170 5170
Single atomsb 2 -30 30 - 350
Bubble sizes e (ml
All quantities Ni, ~11and gi are primarily a function of burn-up F and temperature 7’. aUpper limits correspond to F = 12 at.%. b Atomic volume a.
III
PO
IV
Pl
Population
Zone
Structural zones and bubble populations (free swelling)
TABLE 3
grain boundary porosity
Transition P*“p? at curve 7$(F) defines zone boundary IV/III under conditions of free swelling
Transition P3-+P$ within zone IV on curve e(F)
Intragranular bubbles Heterogeneous nucleation
Remarks
596
ties at low burn-up and consequently prevents the formation of fission gas bubbles. Coarse porosity (break away swellings is formed at temperatures 0.49 < 6 G 0.59 by interaction between the mechanisms of fission gas precipitation and irradiation growth and leads to extremely high rates of swelling, These can, however, be limited by clad restraint, see below. The details of this interaction depend sensitively on the alloying and heat treatment of the fuels, operating temperature and mechanical restraint. No general theory of the phenomena exists. Proposed mechanisms for the “break away swelling” in pure and adjusted o-U are as follows. (i) Local tensile hydrostatic stresses are formed on bubbles as a result of the growth mechanism [ 191. (ii) Bubble sweeping and coalescence occur by the recovery of the dense dislocation substructure as a result of previous irradiation growth in a defined temperature range. This can be largely avoided by anchoring the dislocation tangles with precipitates of UAlz [ 201. (iii) Bubble growth occurs as a result of the decrease in the surface energy ys in eqn. (1) owing to contamination of the bubble surface with fission product atoms [Zl]. This is still an open problem which also applies to ceramic dense fuels. (iv) For the FBR fuel alloys an interpretation by “microtears” 1221 appears to be appropriate [ 8,231. Obviously more detailed investigations using a combination of density measurements, SEM, replica electron microscopy (REM) and especially TEM with a high voltage electron microscope are required as used for “adjusted o-U” [20, 241 to evaluate the mechanisms qu~titatively in the other alloy fuels. Earlier TEM investigations with 100 keV electrons of relatively low penetrating power required very thin foils (30 - 50 nm, corresponding to the size of the larger bubbles and precipitates). Because of the defectsurface interaction these specimens were not representative of the bulk situation, e.g. refs. 25, 26. Thicker specimens (100 to 200 nm) transparent to 1000 keV electrons are practically free of surface effects and are expected to show the interaction between bubbles and dislocations, precipitates and grain and twin boundaries in a representative way [ 241. The high porosity introduced into the metallic FBR fuels by the irradiation growth effect has, however, turned out to be favourable. If sufficient space for swelling is provided the high porosity permits a strong fission gas release since the fuel operates at 0 > 0.5 and further swelling can be limited by clad restraint. 4.2. Bubble nucleation and growth at low burn-up (F d 0.5 at.%) and i? > 0.5 Despite their experimental limitations the early TEM investigations [25, 261 provided the basis for establishing the bubble nucleation mechanisms. At very low burn-up thin specimens showed very little irradiation damage and were free of stresses from the growth effect. Under these conditions the critical gas atom concentration C* required for bubble nucleation
597
was found to be about C* = lOi crne3 and the nucleation mechanism to be homogeneous with bubble densities N = 1016 cme3 at 8 x 0.49 and lower values, 10ls to 1013 cm3, at increasing temperatures for 8 > 0.5 [25, 261. Similar values were found later also in carbide and nitride fuels at burn-up values greater than about 3 at.%. On the basis of theoretical homogeneous nucleation models [27 - 291 it is difficult to define the size of the stable nucleus to which the classical diffusion-based growth law can be applied. Therefore phenomenological models were used for the estimation *of the bubble density N which lead to relations N2 - G/D, or at least show G ID, to be the leading term if fission gas resolution is taken into account [ 30,311. An investigation of the swelling performance of cubic y-U around 0 = 0.75 and y-stabilized uranium alloys containing zirconium, niobium or molybdenum and an alloy U-18 wt.% Pu-14 wt.% MO at 0.52 < 8 > 0.73 showed very high rates of swelling (with the exception of a U-14 wt.% MO alloy), in spite of the complete absence of cracks and growth effects [32]. This demonstrated that in general the irradiation of cubic alloys at 8 > 0.5 also leads to high rates of swelling. The fission gas bubbles attained diameters of several microns and linked together where they were largest. Post-irradiation annealing of irradiated metallic fuels under various pressures [26, 331 has demonstrated that the fission gas bubbles were in fact in equilibrium with the surface tension of the matrix according to eqn. (l), i.e. fission gas swelling can be reduced by external perssure (clad restraint u). Irradiation of certain uranium-base alloys under hydrostatic pressure also showed that the swelling effects associated with the growth process, can be reduced; 40 bar diminished the break away swelling between 430 and 550 “C!by a factor of 2 [34]. 4.3. Swelling burn-up 4.3.1.
performance
of ceramic
dense
fuels
at 8 2 0.5
up
to high
Survey The high rates of swelling encountered in metal fuels initiated the interest in ceramic fuels at the beginning of the 1960s. As regards dense fuels (carbides, nitrides), mainly helium-bonded mixed carbides with linear rating between 49 and 70 kW m-l and densities around 95% were irradiated at first in thermal and fast reactors [35 - 371 with stainless steel and niobium cladding. All countries with FBR projects had started prograrnmes on fabrication, property measurements and irradiation of carbide and to a lesser degree nitride fuels. Since each project developed its own fuel and pin design with the related irradiation conditions these technological developments [38, 391 yielded relatively limited information which could be employed for a systematic analysis of the basic swelling mechanisms. Theoretical models to describe carbide swelling were thus mainly based on the previous information from metal fuels and on theoretical studies on nucleation and bubble growth, bubble interaction with fission spikes (borrowed from oxide experiments), dislocations and grain boundaries and on bubble migration [28, 40, 411. A severe deficiency resulted from the fact that no reliable
598
fission gas diffusion data were available and the interpretation of gas release measurements from carbides and other nuclear fuels was not unambiguous
r421.
A systematic analysis of the swelling mechanisms was started around 1974 at the Institute for Transuranium Elements. During the first phase the out-of-pile and in-pile restructuring and the fission gas swelling were analysed by optical microscopy and REM in MC, MCN and MN fuels irradiated at high linear power (x - 130 kWm_l). Severe interaction between fission gas swelling and in-pile restructuring was observed [12, 131. The varying temperature history in the helium-bonded fuels and the limited burn-up (mainly not more than 4 at.%) precluded the establishment of a clear picture valid over a larger burn-up range. However, the existence of two temperature ranges for fission gas swelling with a rather well-defined transition temperature from low to high swelling was identified and good correlations between out-of-pile self-diffusion measurements and in-pile restructuring was found
v41.
It took considerable work by detailed post irradiation analysis (especially by REM, SEM and TEM and local gas analyses by electron probe microanalysis (EPMA)) on a variety of fuels irradiated under different conditions before a quantitative picture of the fission gas swelling in dense ceramic fuels started to emerge. Further detailed analyses are still required on heliumbonded carbides and nitrides at high burn-up and from technologically relevant pin designs before this picture is complete. Transient fuel and pin performance especially after higher burn-up will be another topic of future basic and technological research. The following picture of the swelling in dense ceramic fuels should be seen in relation to the temperature dependence of the fission gas diffusion and the fuel operating temperatures in Figs. 3 and 4 and their anticipated modifications with increasing burn-ups.
4.3.2. Low burn-up range (F < 0.5 at.%) At the start of irradiation homogeneous bubble nucleation exists giving rise to one bubble population with strong temperature dependence of the bubble density N(T) (at 8 = 0.35, N = lOi’ cme3 and at 8 = 0.6, N = lOi’ cmd3) and of the bubble growth rate.
High burn-up range (2 < F < 12 at.%) In this range fission gas swelling develops into a complex pattern which is conveniently separated into free swelling (sodium-bonded carbide and nitride, see Fig. 4) and swelling under restraint (helium-bonded fuels). For the basic understanding of fission gas swelling it is essential to recognize that with increasing burn-up an increasing interaction exists between fission gas kinetics and fission damage (lattice damage and fission product atom) as indicated formally by eqn. (3). 4.3.3.
599
4.3.3.1. Free swelling at temperatures 8 < 0.5 (sodium-bonded MC and MN). After about 2 at.% bum-up and at 0.35 < 8 Q 0.5 two distinct bubble populations start to develop, Pi and P2 (see Table 3), of which P, grows systematically with increasing burn-up and contains of the order of 15% of the fission gas created and makes the main contribution to the low temperature swelling. A third population P3 of grain boundary bubbles appears first near e = 0.5. The important property of P, and P, is that these populations possess bum-up dependent transition temperatures T:(F) and T:(F) above which they grow faster and hence produce higher rates of swelling (T:(F) < T:(F)). In Fig. 10 the relation T:(F) has been plotted on the reduced temperature scale 8 of Figs. 3 and 4 for carbide and nitride. As is expected, the two curves coincide at low burn-up but then start to diverge because of the different fission product solubilities in the two fuels. Two questions arise: (i) what makes some bubbles grow faster, i.e. what produces the separation between bubble population P, and P,? and (ii) what is the reason for the existence of the transition curves T:(T) and T:(T)? Before detailed microstructural investigation by TEM and SEM became available the two questions were answered in the following way [ 151. (i) The small bubbles of population PI were supposed to be very mobile in the matrix and perform a Brownian motion. This leads to bubble coalescence and formation of the bubbles of P,. New bubbles of P, are continuously nucleated and P, and P2 are thus in a continuous dynamic equilibrium. (ii) Below the curve c(F) the bubbles of P, become overpressurized because of the lack of vacancies and if the pressure is high enough the surrounding matrix yields by thermally activated creep, the bubbles expand and this produces the higher rate of swelling at (TJ) > (!Z?$F).However, the analyses of TEM and SEM micrographs [ 5, 161 provide new evidence on the processes occuring at a submicroscopic scale over a large bum-up range. (i) The bubbles of population P, are found to be exclusively associated with the density of the irradiation-induced dislocation and fine-scale needle-
1 0
e
2
L
6
8
10
FI%l
Fig. 10. Transition temperature-burn-up relation Z’?(F) for MC and MN plotted on a common reduced temperature scale. Note that the two curves diverge with increasing burn-up owing to different solubilities for the rare earth fission products.
600
like precipitation networks with bubble densities N = 1 - 4 X 10” cmP3. Hence bubbles in the size range 3 to 25 nm are stationary. Pi is not affected by the transition curve T:(F). The population of larger bubbles Pz develops independently from P, on preferential growth sites like dislocation nodes, larger precipitates or by the growing together of closely spaced smaller bubbles. (ii) As the radial position corresponding to the temperature T: is passed in a pellet cross section (analysed on a fracture surface by SEM) the most significant feature of the microstructure is the appearance of “elongated bubbles” where two or even three bubbles have touched and grown together, see Fig. 11. These elongated geometries become more spherical at higher temperatures. In fact these features exist already below T:(F) even for bubbles with 10 nm size, but their density is insignificant. Hence the increase in the rate of swelling when crossing the curve T,*(F) is associated with the increase in size and density of the “elongated” or “dumbell” bubbles.
Fig. 11. Scanning electron micrograph-of a transgranular fracture surface from a sodiumbonded carbide at F = 11.8 at.%. Position for T > T?(F).The large fraction of elongated fission gas bubbles should be noted.
4.3.3.2. Swelling under restraint (helium-bonded MC and MN), 8 5 0.5. In the helium-bonded ceramic fuels two additional effects occur. (i) As indicated in Figs. 4 and 7 a large part or all of the fuel operates initially for a short period at 8 > 0.5, but later mainly at 8 < 0.5. This will affect the nucleation of fission gas bubbles and solid fission product precipitates at F < 2 at.%. (ii) Helium-bonded fuels have about 15% fabrication porosity and are subjected to clad restraint u for F > 3 at.%. The essential in-pile mechanism under these conditions is the accommodation of the swelling contributions M from the solid fission products and
601
the three bubble populations by the fabrication porosity PO in the outer part of the fuel adjacent to the clad. The driving force is provided by the clad restraint u. The problem has been treated theoretically by Ronchi [ 151. Its solution requires a computer code. A somewhat crude, approximate treatment, however, sufficient for many practical purposes is given by the relation [ 171 A(F, T, u) = M(F, T, a) - P,[l
- exp{-ko(F
- Fn)}]
(4)
where A is the “local swelling” and k is a parameter which depends on the mechanical properties of the fuel matrix. Since the temperature range over which this equation applies is 0.34 < 8 < 0.5 thermally activated creep cannot be involved. The magnitude of k can be estimated from post-irradiation analysis. A theoretical expression for k can be obtained from a hotpressing model [43] into which the creep rate of the matrix enters. However, experimental values of irradiation creep measured in carbide fuels [44, 451 and extrapolated to 100% density are too low by a factor of, at least, 10. It appears that the situation may be better described by a hot-pressing model based on the diffusion of lattice vacancies [46].
5. Summary and Conclusions 5.1. Main basic mechanisms
contributing
to swelling are as follows:
(1) atomic diffusion of fission product atoms by isms, (2) ingrowth of a dislocation network (10” to 10” (3) ingrowth of solid fission product precipitates, (4) development of intragranular gas bubbles, (5) development of intergranular bubbles and open There is strong interaction between (2), (3) and (4), (3) and (5). 5.2. 2
Mechanisms
operating
vacancy jump mechancm cmd3) [ 51,
porosity. at 8 > 0.5 also between
in the three main pin concepts
outlined
in Table
“Hot” fuel (sodium-bonded alloys, no fabrication porosity) - The initial 25% gap volume is transformed rapidly into fuel porosity (mainly in the fuel centre) creating open porosity for high gas release. Fuel swelling is limited by FCMI. It appears that the swelling mechanism in the outer fuel zone has not yet been investigated in detail. “Cool” fuel (sodium-bonded MX fuels, < 5% fabrication porosity) Swelling is kept very low, provided the sodium-bond remains sound. The initial gap volume (about 15%) is slowly used up. FCMI starts around 12%, gas release is low [ 111. “Hot/cool” fuel (helium-bonded MX fuels, fabrication porosity about 15%) -The initial gap volume is transformed rapidly into fuel porosity (centre zone) and crack volume (outer fuel ring). FCMI (clad restraint)
602
directs part of the low temperature fabrication porosity.
swelling in the outer
fuel ring into the
5.3. Fission gas kinetics In the helium- and sodium-bonded dense ceramic fuels, swelling at temperatures 0 < 0.5 is of great technical importance. In the range 0.35 < 8 < 0.5 the rate of swelling is governed by the slow thermally activated migration of the fission gas atoms, i.e. the slow growth of a rather high density of gas bubbles. The mechanism is based on the fission-rate-induced concentration of lattice vacancies. Above a bum-up dependent transition temperature 8:(F) the rate of swelling increases, with 0:(F) S 0.5. The low temperature gradients in dense fuels together with the strong interaction between bubbles, dislocations and solid fission product precipitates makes bubble migration unlikely to play an important role in swelling and gas release during steady state irradiations. As a consequence of these complex interactions further detailed investigation of dense LMFBR fuels at high bum-up are required before the basic laws of swelling under these conditions can be quantified.
Acknowledgments The author acknowledges numerous discussions and the provision of unpublished results from his colleagues, especially Drs. M. Coquerelle, I. L. F. Ray and C. Ronchi. He thanks Dr. L. C. Walters for providing Fig. 9(a).
References 1 A. Seeger, Proc. 2nd UN Conf. on Peaceful Uses of Atomic Energy, Geneva, 1958, Vol. 6, United Nations, Geneva, 1958, p. 250. 2 J. A. Brinkman, J. Appl. Phys., 25 (1954) 961. 3 H. Blank, Eur. Appl. Res. Rep., Nucl. Sci. Technol. Sect., 1 (1979) 307. 4 S. F. Pugh, Prog. Nucl. Energ., Ser. 5, 1 (1956) 662. 5 I. L. F. Ray and H. Blank, J. Nucl. Muter., 124 (1984) 159. 6 U. Benedict, Thermodynamics of Nuclear Materials, 1979, Vol. 1, IAEA, Vienna, 1979, p. 453. 7 R. E. Einziger and B. R. Seidel, Nuci. Technol., 50 (1980) 25. 8 L. C. Walters, B. R. Seidel and J. H. Kittel, Nucl. Technol., 65 (1984) 179. 9 L. C. Walters and J. H. Kittel, Nucl. Technol., 48 (1980) 273. 10 P. J. Levine, U. P. Nayak and A. Boltax, Proc. 7th Znt. Conf. on SMiRT,Chicago, 1983, Vol. C, North Holland, Amsterdam, 1983, p. 161. 11 M. Colin, M. Coquerelle, J. L. F. Ray, C. Ronchi, C. T. Walker and H. Blank, Nucl. Technol., 63 (1983) 442. 12 C. Ronchi and C. Sari, J. Nucl. Mater., 58 (1975) 140. 13 C. Ronchi, I. L. F. Ray, H. Thiele and J. van de Laar, J. Nucl. Mater., 74 (1978) 193. 14 Hj. Matzke and C. Ronchi, Advanced LMFBR Fuels. In J. Leary and J. H. Kittel (eds.), ANS 1977, ERDA 4455, p. 218.
603 15 C. Ronchi, J. Nucl. Mater., 84 (1979) 55. 16 I. L. F. Ray and H. Blank, ENC ‘86, Geneva, June 1 - 6, 1986, Topic VI, part 2. 17 H. Blank, F. Caligara, M. Coquerelle and C. ,Ronchi, Modelling of swelling and fuelclad contact pressure in a “real-structure” framework. IAEA Specialist’s Meet. on Theoretical Modelling of LMFBR Fuel Pin Behaviour, May 28 -June 1, 1979, Paper 26. 18 S. H. Paine and J. H. Kittel, Proc. Znt. Conf. on Peaceful Uses of Atomic Energy, Geneva, 1955, Vol. 7, United Nations, New York, 1956, p. 445. 19 J. W. Harrison, J. Nucl. Mater., 23 (1967) 139. 20 B. Hudson, J. Codd and G. A. Burras, Acta Metall., 23 (1975) 101. 21 P. Blanchard,J. Nucl. Mater., 26 (1968) 241. 22 C. L. Angerman and G. R. Caskey,J. Nucl. Mater., 13 (1964) 182. 23 D. R. O’Boyle, ANL-7417, 20, 1967. 24 C. Baker and B. Hudson, Znt. Conf. on Physical Metallurgy of Reactor Fuel Elements, CEGB, Berkeley, September 2 - 7, 1973, paper 40. 25 B. Hudson, J. Nucl. Mater., 22,(1967) 121. 26 J. Lehman, P. Paoli and N. Azam, J. Nucl. Mater., 27 (1968) 285. 27 G. W. Greenwood, A. J. E. Foreman and D. E. Rimmer, J. Nucl. Mater., 1 (1959) 305. 28 B. L. Eyre and R. Bullough, J. Nucl. Muter., 26 (1968) 249. 29 D. R. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, 1976, NTIS, US Dept. of Commerce, Springfield, VA. 30 J. W. Harrison, J. Nucl. Muter., 31 (1969) 327. 31 H. Blank, F. Caligara and I. L. F. Ray, Spec. Meet. on Fuel Element Performonce Computer Modelling, Blackpool, March 1980, IAEA-ZW GFPT/7, 1980, p. 76. 32 G. W. Greenwood, AERE-Rep.-3468, 1960. 33 B. Hudson, J. Nucl. Muter., 27(1968) 54. 34 J. Lehmann, P. Pavoli and N. Azam, J. Nucl. Muter., 26 (1968) 238. 35 B. T. Bradbury, B. R. T. Frost and J. R. Findlay, in Plutonium 1965, Chapman and Hall, London, 1967, p. 949. 36 A. Stroasser, J. Cihi, S. Horwitz and R. Martin, in Plutonium 1965, Chapman and Hall, London, 1967, p. 979. 37 J. P. Mustelier, in Plutonium 1965, Chapman and Hall, London, 1967, p. 1006. 38 R. Farmakes (ed.), Proc. Conf on Fust Reactor Fuel Element Technology, New Orleans, 1971, American Nuclear Society, 1971. 39 J. Leary and J. H. Kittel (eds.), Proc. Topical Meet. on Advanced LMFBR Fuels, Tuscan, 1977, ANS-ERDA 4455. 40 J. W. Harrison, J. Nucl. Muter., 30 (1965) 319. 41 P. Prajoto, A. R. Wazzan and D. Okrent, Nucl. Eng. Design, 48 (1978) 461. 42 Hj. Matzke, Science of Advanced LMFBR Fuels, North Holland, Amsterdam, 1985, Chapter 9. 43 D. S. Wilkinson and M. F. Ashby, Acta Metall., 23 (1975) 1277. 44 I. Miiller-Lyda and W. Dienst, J. Nucl. Muter., 90 (1980) 232. 45 W. Dienst, J. Nucl. Muter., 124 (1984) 153. 46 R. L. Coble, J. Appl. Phys., 41 (1970) 4798.