4.01.3.1.1 Irradiation growth: Macroscopic behavior

One of the most specific macroscopic effects of irra­diation on materials is the dimensional change with­out applied stress. In the case of zirconium alloys, it is known that under neutron irradiation, a zirconium single crystal undergoes an elongation along the (a)

axis and a shortening along the (c) axis without significant volume evolution. Thorough reviews of this phenomenon have been given.72,150,159-163 It is observed that the elongation along the (а) axis is rapid at the beginning of the irradiation and slows down until reaching a low stationary growth rate (Figure 18). The growth strain remains small (<0.02%) and saturates at fluences less than 5 x 1024 nm~2.161,164 Eventually, at higher fluence a growth breakaway (increase of the growth rate) occurs for the annealed zirconium single crystal.161

Since the deformation of the polycrystalline clad­ding is the result of the growth of all the grains, texture has a major influence on the growth of the polycrystalline material. A weakly textured product made of zirconium alloy, with Kearns factors close to fd~ 0.33 along the three directions, such as p-quenched zirconium alloys165,166 as reviewed by Fidleris,150 exhibits a very low growth. The Kearns factor fd is the resolved fraction of basal poles along the direction d. On the other hand, strongly textured products, with most grains orientated with (c) axis along one given macroscopic direction (high Kearns factor, fd> 0.5), exhibit a negative growth in this direction and a positive growth in the direction with low Kearns factor fd< 0.2). In the case of highly textured products such as cold-worked tubing, in SRA or RXA metallurgical state, a large majority of the grains exhibit their (c) axis close to the radial direction ((c) axes oriented in the (r, в) plane with an
angle between 20° and 45° to the radial direction, the Kearns factor along the radial direction being f ~ 0.6). The directions (1120) or (1010) are along the rolling direction (low Kearns factor along the rolling, or axial direction fa ~ 0.1-0.16.167,168) Due to this strong texture, an elongation of the tube along

the rolling direction is observed159,169,168 as well as a

decrease of the thickness as shown on rolled sheet,159 the strain along the diameter of the tube remaining low.153 In the case of pressure tube for Canadian deuterium uranium (CANDU) reactors, made of cold-worked Zr-2.5Nb, since the (c) axes are mainly along the transverse direction (f ~ 0.3, fa ~ 0.05, f ~ 0.6, respectively for radial, axial, and transverse Kearns factors), the irradiation growth leads to an increase of the length in the axial direction and a decrease of the diameter.163

As for the zirconium single crystal, textured RXA Zy-4 or Zy-2 products, for instance, in the form of tubing, exhibit first a rapid elongation along the roll­ing direction, and then a decrease in the growth rate, reaching a low stationary growth rate.159 It can be noticed that the stationary growth strain of the polycrystal is higher than that for the Zr single crys — tal.161 This demonstrates the role of the grain bound­aries on the growth mechanisms. For higher fluence, higher than 3-5 x 1025 nm~2, a growth breakaway is observed, yielding a high growth rate.

It is reported150,160,166 that for polycrystalline zir­conium alloys, the grain size affects the growth rate

of RXA zirconium alloys during the initial growth transient at 553 K, the growth rate increasing when the grain size decreases. On the other hand, the stationary growth is not affected by the grain size. This phenomenon is also observed for Zircaloy-2.159 Ibrahim and Holt170 and Holt171 have also suggested that the grain shape, especially in the case of Zr-2.5% Nb material, can play a role on the growth behavior.

It is shown that for cold-worked materials (e > 10%) the growth rate increases as the cold work­ing increases150,159,160 (Figure 19). For the extreme case of SRA zirconium alloys, which could undergo up to 80% cold working followed by a SRA treat­ment, the growth rate is so high that the stationary growth rate is not observed, and from the beginning of the irradiation, the growth rate is comparable to the growth rate measured for RXA zirconium alloys after the breakaway growth. Several authors, as reviewed by Fidleris etal.159 and Holt,72 have clearly correlated the increase of the growth rate with the increase of the dislocation density due to the cold working. This also proves the importance of the ini­tial dislocations network in the growth mechanisms.

Several authors have studied the effect ofthe impu­rity and alloying elements on the growth rate and especially on the growth acceleration. At 280 °C, for a high-purity zirconium single crystal obtained by the melting zone method, no growth breakaway is observed. On the other hand, for a lower purity zirco­nium single crystal obtained by using the iodine puri­fication method161 the breakaway growth is observed.

Similarly, for polycrystalline RXA zirconium alloys, irradiated at elevated temperature (390-430 °C), the growth rate is higher than that of pure zirconium.73,160 It is particularly noticed by Griffiths eta/.73 that RXA zirconium alloys exhibit accelerated growth contrary to pure zirconium. It is believed that minor elements (Fe, Cr), and especially iron, play a major role on the breakaway.54,160 On the other hand, it appears that the tin content, in solid solution, has no effect on the stationary growth rate at high temperatures (280 °C)150,160 but that the niobium leads to a reduced growth rate compared to RXA Zy-4.168

The irradiation temperature has a complex influ­ence on the growth behavior72,150 (Figure 20). For SRA zirconium alloys, it is shown that the growth rate increases as the temperature increases. On the other hand, for RXA zirconium alloys the prebreakaway growth rate has a very low temperature sensitivity, the growth rate increasing very slowly with increasing temperature. A growth peak is even observed around 570 K, the growth rate decreasing rapidly above 620 K. However, for postbreakaway growth, the tempera­ture sensitivity is high, as high as for SRA zirconium alloys.150 It is also shown that the breakaway fluence decreases with increase in the temperature.72

4.01.3.1.2 Irradiation growth: Mechanisms

The mechanisms proposed in the literature in order to explain the growth under irradiation of zirconium and its alloys have progressively evolved as the obser­vations of the microstructure have progressed.

Temperature (K) 700 600 500 400 350 Figure 20 Generalized representation of the temperature dependence of irradiation growth of Zircaloy. Adapted from Fidleris, V. J. Nucl. Mater. 1988, 159, 22-42.

1/T(K)

Several comprehensive reviews of these mechanisms have been given,44’46’72’163 and a nice history of the various mechanisms for irradiation growth of zirco­nium alloys is provided by Holt.162 Some of these mechanisms are not compatible with all the observa­tions. For instance, the fact that both vacancy and interstitial (a) loops are present in the polycrystalline material, as described in the first part, shows that the model proposed by Buckley172 described in Northwood173 and Holt162 for the growth of zirconium alloys is not correct.

The most promising model that gives the best agreement with the observations is the model based on the DAD, first proposed by Woo and Gosele174 and described in detail by Woo.44 This last model is based on the assumption that the diffusion of SIAs is anisotropic, the vacancy diffusion anisotropy being low. Indeed, as reported in the first part of this chap­ter, several authors28,33,34,175 have shown, using atom­istic simulations, that the mobility of the SIAs is higher in the basal plane than along the (c) axis and that the vacancy diffusion is only slightly anisotropic.

The growth mechanism proposed by Woo44 is the most convincing model, since every feature of the growth phenomenon is understood in its frame unlike in the previous models. According to this mechanism, during the first stage of the irradiation of RXA zirconium alloys, with low initial dislocation density, the grain boundaries are the dominant sinks.

(a) (b) (c)

Figure 21 (a-c) The three phases of growth of

recrystallized zirconium alloys. (d) Growth mechanisms of stress relieved zirconium alloys.

Due to the rapid mobility of SIAs in the basal plane, the grain boundaries perpendicular to the basal plane are preferential sinks for SIAs. In contrast, grain boundaries parallel to the basal plane constitute preferential sinks for vacancies. This leads to a fast initial growth of polycrystalline zirconium alloys, in agreement with the model first proposed by Ball176 (Figure 21 (a)). This mechanism explains why the initial growth transient is sensitive to the grain size.

As the irradiation dose increases, the (a) loop density increases and the (a) loops become the dom­inant sink for point defects. In the absence of (c) component dislocation (as is the case in RXA zirco­nium alloys), calculations of DAD-induced bias
show that linear (a) type dislocations parallel to the (c) axis are preferential SIA sinks while (a) type loops are relatively neutral and may receive a net flow of either interstitials or vacancies, depending on the sink situation in their neighborhood. This explains why both interstitial and vacancy (a) type loops can be observed. This also explains why in the neigh­borhood of prismatic grain boundaries, or surfaces, which experience a net influx of SIAs, there will be a higher vacancy supersaturation leading to a predom­inance of vacancy loops towards interstitial loops as shown by Griffiths.46 It has to be pointed out that the simultaneous growth of interstitial and vacancy (a) type loops in the prismatic plane does not induce strain of the crystal although they are the dominant sinks (Figure 21 (b)). This explains the low station­ary growth rate observed.

For irradiation doses higher than 5 x 1025 nm~2, vacancy (c) component dislocation loops in the basal plane are observed in RXA zirconium alloys (Figure 21 (c)). The origin of the nucleation of (c) component loops remains unclear. Nevertheless, it has been shown, as described previously, that it is favored by the iron dissolution in the matrix coming from the precipitates.57,73,75,76 The appearance of (c) component defects has been clearly correlated to the breakaway growth71 (Figure 22). The fact that these vacancy (c) component basal loops are able to grow in zirconium alloys, whereas it is the (a) prismatic loops that are the most stable, is easily explained in the frame of the DAD model. Indeed, it can be shown that it is due to the DAD that vacancies are elimi­nated preferentially on the (c) component loops and on the grain boundaries parallel to the basal plane. The SIAs are eliminated on (a) type dislocations
and grain boundaries parallel to the prismatic plane. This partitioning of the point defects on these differ­ent sinks leads to the growth of the vacancy (c) component loops and therefore to the accelerated growth of RXA zirconium alloys. However, as pointed out by Griffiths et a/.,73 although there is a clear correlation between the occurrence of the breakaway and the appearance of (c) loops, the strain induced by the loops observed is much lower than the growth strain measured.

The fast and continuous growth of cold-worked or SRA zirconium alloys can also be easily explained by this model. Indeed, since in these materials the (c + a) line dislocations are already present before irradiation, under irradiation, the vacancies are prefer­entially eliminated on the dislocations with (c + a)

Burgers vector in the basal plane,72,162,163 leading to

the climb of these dislocations. On the other hand, the SIAs are eliminated on (a) type dislocations, leading to the climb of these dislocations. This parti­tioning of point defects therefore leads to the fast and continuous growth of cold-worked or SRA zirco­nium alloys (Figure 21 (d)). Here the growth created by the point-defect flux to the grain boundaries is relatively unimportant because they are not dominat­ing sinks. Irradiation growth under such circumstances is thus not sensitive to the grain size or shape.177

It has also been discussed by several authors, espe­cially by Holt,162 that due to the polycrystalline nature of the material, the growth strain of the indi­vidual grains can induce strain incompatibilities between adjacent grains that exhibit different orien­tations. Intergranular stresses can then result from these strain incompatibilities, leading to a local irradiation creep of individual grains even without

	G2	D2 D1
Many <c> component dislocations
Some <c> component dislocations
0.05

9

macroscopic applied stress on the material. This phe­nomenon can also affect the growth behavior of the polycrystalline material. It has also been shown that the intergranular stresses resulting from a deformation prior to irradiation can lead to a complex transient growth behavior at the beginning of the irradiation due to intergranular stress relaxation.162,178