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The nucleation of hydrides in a Zr-2.5 wt% Nb alloy
160
Journal
THE NUCLEATION
OF HYDRIDES
of Nuclear
Materials 126 ( 1Y84) 160 169 North-Holland. Amsterdam
IN A Zr-2.5 wt% Nb ALLOY
V. PEROVIC Metallurgy Sectron, Ontarro Hydra Research Laboratones, 800 K~pirng Avenue, Toronto. Cunudu, M8Z 5S4
and G.C. WEATHERLY Department of Metallurgy and Materials Scrence. Unrversrty of Toronto, Toronto, Canada. MS Received
2 March
1984; accepted
IA4
10 May 1984
The pr~ipltation of hydride plates in a Zr-2.5 wtl Nb alloy ts shown to be senstttve to the prtor heat treatment of the ahoy For heat treatments that lead to a faceted a//? two phase mtcrostructure. the a-j3 interface is characterized by an eprtaxtal dislocation array and steps with assoctated stram fields. For this structure, the nucleation of hydrides IS controlled by the defect structure of the interface. On annealmg the a--/3 structures below the monotectotd temperature, the retarned p phase ts unstable, decomposing first to /3, and w and ultimately to a and fiNb. At the intermedtate stage, t.e. wtth a &/w two phase structure. hydride precipitation takes the form of stacks of small hydride plates confined to channels rn the ,f3 iattrce between the w partrcfes. For both microst~ctural conditions, the preferred sate for hydride nucleation appears to he that which can most effectively accommodate the strains associated with hydrtde prectpttatton. Stmilarities m the precipttatton behavtour m a-P Zr alloys and Ti alloys are discussed.
1. Introduction
tation.
The precipitation of zirconium hydride in zirconium and its alloys usually leads to marked embrittlement of the metal, both at room temperature and at temperatures up to 3OO’C which are of interest in nuclear reactor service conditions [1,2]. The hydride precipitates have a characteristic acicular or plate morphology. which is often referred to as a “cornflake” structure. We have shown that this morphology corresponds on a microscopic scale to stacks of hydride plates formed by repeated nucleation and growth of plates which often share a common habit plane 131.The Individual plates in a stack appear to grow by a displacive or martensrtic transformation [4,5], with the stress field of a larger parent hydride plate helping to nucleate a smaller daughter hydride by a sympathetic nucleation mechanism, As the strain field of an individual hydride plate has both a shear and dilational component, this leads to the formation of offset stacks which have been observed experimentally [3,5]. The nucleation behaviour of hydrides must be determined in part by the difficulties of accommodating the volume and shear strains associated with precrpi-
in solid solution before preciprtation. As hydrogen dissolved in solid solution dilates the zirconium lattice it will be attracted to any defect or interface where the dilation can be partrally or wholly accommodated. The partial molar volume of hydrogen in a cu-Zr has recently been measured by MacEwen using neutron diffraction [6]. The value reported by MacEwen, - 1700 mm3/mole. is somewhat larger than the partial molar volume of hydrogen in the hydride phase, - 1300 mm3/mole, but agrees well with recent data for cubic metals and hcp titanium [7,8]. A further complicating factor in the hydride nucleation behaviour is the composition (and prior thermomechanical treatment) of the alloy. For example the pressure tube alloy Zr-2.5 wt% Nb, used in the present study, can, under certain conditions, contain up to 10% of a retained p-Zr phase with a bee structure. As hydrogen is much more soluble in the bee than hcp form of Zr, a greater solubiiity of H might be antrcipated in these two phase alloys. However the terminal solid solubilities of H in pure Zr, Zircaloy and Zr-2.5 Nb do not vary significantly over the temperature range from 100 to 400°C suggesting that any such effect is t~bution
0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
A second
consideration
of hydrogen
is the non-uniform
dis-
V. Pet&c,
161
G. C. Weatherly / Hydrides in a Zr - 2.5 wf 5%Nb allqy
negligible in these alloys [l]. In this paper we present results on hydride precipitation in a two phase a-/3 Zr-Nb alloy, which show that the nucleation site depends on the prior heat treatment of the alloy. The nucleation behaviour is determined by the site in the microstructure where the most effective relief of the strains associated with precipitation can be achieved.
2. Experimental procedure The starting material was a Zr-2.5 wt% Nb pressure tube alloy containing - 1000 ppm 0 and 40-70 ppm N impurities. Samples were taken from pressure subes which were either as-extruded at 850°C and air-cooled to room temperature or as-extruded, cold-worked - 40% and stress relieved at 400 *C for periods up to 24 h (24 h at 400 o C is the standard heat treatment for pressure tube alloys used in the CANDU system). Some samples were given a further heat treatment at temperatures that ranged from SOO°C to 850 *C to develop a more equiaxed two phase a-j3 grain structure. The as-extruded and cold-worked pressure tube al- lo-15 ppm H. This is considerably in loys contained excess of the room temperature solid solubility of H, which is reported to be less than 1 ppm [1,2], so that hydride precipitation could be studied in these alloys without further additions of H. For some of the vacuum heat-treated samples, the hydrogen lost during the heat treatment had to be replaced by a gas treatment in a hydrogen atmosphere at 400 o C, followed by slow cooling to room temperature. This gave a H content in the range of 60-100 ppm. Thin foil TEM studies were used to characterize the precipitation of the hydrides. As recent studies in Ti alloys [9] have suggested that hydrogen can be inadvertently introduced into the foil by el~tropo~s~ng, precautions were taken to ensure that the effects we observed were characteristic of bulk samples rather than an artefact of sample preparation. The most convincing evidence of this came from optical metallography which showed similar patterns of precipitation in bulk samples and thin foils. (In these examples, the bulk sample had been prepared by standard metallographic procedures without electropolishing so no H could be introduced during sample preparation - see e.g. fig. 6.)
As-extruded material or alloys slowly cooled from 750 o C to room temperature contained a two phase a-8
structure. The (Y phase is cph Zr, a = 3.23 A, c = 5.15 A; the fl phase is retained bzr, containing - 20 wt% Nb, with a bee structure, a = 3.53 A. The orientation relationship between the two phases is Pitsch-Schrader [3] i.e. (10iO),/)(110)8, [l~lO],~~[OOl],. The close similarity in the atomic arrangements of the hcp and bee crystals for this orientation relations~p has been discussed by Kelly and Groves [lo], and the matrix describing the transformation from one crystal type to the other is given (in the notation adopted by Kelly and Groves) by &‘--I=
-0.085 [
+0.116 -
+ 0.03
1
relative to axes [OliO], [ZllO] and [OOOl] in the a-Zr lattice. This matrix forms the basis for a discussion of the structure of the interface between the two phases [ll]. (We shall show later that there is a direct relationship between the nature of the interface and its ability to act as a nucleation site for hydride precipitation.) Two important defects are observed at the interface which could play a role in hydride nucleation. The first is an array of [OOOC] dislocations, accommodating the 3% misfit between the (0002) planes in azr and the (110) planes in pzr (fig. 1). The density of these dislocations varies with the orientation of the interface plane separating the two phases. Other arrays of epitaxial
0.5
pm
Fig. 1. Arrays of misfit dislocations at the interface between a and retained pzl in Zr-2.5 Nb, annealed for 1 day at 820 ‘C, furnace cooled to 650 o C and helium quenched.
V. Perourc, G.C. Weaiherly / Hydrzdes in a Zr- 2.5 wt B Nh allq
162
dislocations accommodating the misfit in the [OliO] and [2110] directions might be present (these dislocations could have lattice translation vectors or could be vectors of the appropriate DSC lattice [ll] but if so, they are below the resolution of the electronmicroscope techniques used in this study). The second defect observed at the interface is a ledge structure (fig. 2). Although pure steps or ledges without a strain field can be present at interfaces [ll], at the majority of the steps a strain field was observed (see fig. 2). The strain field may arise from an array of DSC dislocations as discussed by Balluffi et al. [ll] or could be associated with the residual elastic strains required to bring the a-Zr and /3-Zr lattices into high planar co-incidence configuration [12,13]. On air cooling from 75O’C or on annealing at 400 or 500’ C, the pzr phase is unstable and can decompose either athermally or isothermally according to the reactions [14]. P ZI + w + /I, (at temperatures
below
- 450 o C)
misfit between the (0002)” and (llO),g planes.) The w phase has a hexagonal structure, the lattice parameters of this phase also being dependent on the heat treatment. After the same treatment of 40 h at 4OO”C, the w-phase parameters were reported to be u = 5.035 A, c = 3.13 A [14]. The equilibrium phase, ph,,. developed after prolonged heat treatment, contains - 85 wt% Nb, with a lattice parameter close to that of pure Nb, viz u = 3.34 A. Two marked microstructural changes accompany these phase transformations. The regular dislocation arrays observed at the a/Pz, interface (fig. 1) are no longer seen, and the interface changes from being faceted with steps to an irregular morphology with pronounced perturbations. The second change is the precipitation and growth of a high volume fraction of w particles (see fig. 3) within the p phase. The orientation relationship found by electron diffraction between the /I, and w phases is that commonly reported for this precipitation reaction,
orPZr+a+PINb+P,-+a+PL,, (at temperatures
above 450 o C)
The & phase becomes partially enriched in Nb and after annealing for 40 h at 400’ C, the lattice parameter of this bee phase has decreased from 3.53 A to 3.47 A. (This corresponds to an increase from 3% to 5% in the
Fig. 2. As fig. 1, showing steps at the a-Bzr associated strain fields (arrowed).
interface
with
The stress free transformation strain describing the structural change /3, + w is a nearly uniform dilation. Taking the values for the lattice parameters quoted
Fig. 3. Cold worked pressure tube alloy (as extruded + 30% cold work, annealed for 24 h/4CO°C). Longitudinal section showing the breakup of the retained pzr phase into w + /I,: no epitaxial dislocations arc seen at the interface between a and 8,.
163
V. Perovic, G. C. Weatherly / Hydrides in a Zr - 2.5 wt % Nb alloy
directions lying in above *, we find that in the (llO), the expansion is 38, while in the orthogonal (111)/J,> [llllLSr direction, the expansion is 4%. The w particles will be in a state of compression, while the surrounding j3, lattice will be in tension. 2.2. Hydride 2.2.1.
precipitation
In a-Pz,
microstructures
For these structures, hydride nucleation is observed at the a-j3 interface. At the earliest stage of the precipitation, a series of small plates or needles (< 10 nm in size) are found decorating the steps at the interface (fig. 4). These plates are often stacked in arrays, similar to those observed in coarser intragranularly nucleated hydrides [3]. The hydrides in fig. 4 are too small to permit a positive identification of their crystal structure ( y or S hydride), but larger hydrides (fig. 5) were identified as S(ZrH, s) with an approximate (lll),]](OOOl),, [liO],]([llZO],orientation relationship [3]. On continued growth the hydrides nucleated at the a-B interface with a common habit plane and orientation relationship develop into either a striated or monolithic plate (see fig. 5). In a previous study we suggested that where a monolithic plate formed, the habit plane of the plate (taken to be that defined by the final shape of the hydride - fig. 5b) contradicted that expected from considerations of the martensitic nature of the transformation [3]. The observations of figs. 4 and Sa, which represent an earlier stage in the nucleation and growth sequence, show that the final morphology (fig. 5b) is simply a consequence of the growth and coalescence of a number of hydride plates sharing a common orientation relationship. The hydride plates in fig. 5a have a habit plane close to the basal plane, as predicted from martensite theory for plates with a (lll),]](OOOl),, [liO],]][ll~O], orientation relationship [4]. 2.2.2. In a-p-o microstructures We noted earlier that in this heat-treated condition, the smooth regular a--/? interface has started to break-up as the w phase develops. The interface between the a and /? phases is no longer a preferential site for hydride nucleation. The pattern of precipitation for this microstructure is shown in figs. 6 and 7. Fig. 6 compares the results of an optical and electron microscopy examination of the same structure. In fig. 6a, the two phase microstructure of a coarse-grained (Y-/I alloy containing
Fig. 4. Dark field micrograph from hydride diffraction spot showing arrays of small hydride plates decorating the steps at the o//3=, interface. (The sample was heat treated for 1.2 h/750 o C and furnace cooled to room temperature.)
less than 1 ppm H is shown. After the addition of - 80 ppm H by treatment at 400°C, followed by slow cooling to room temperature, the /3/w regions appear umformly dark on examination in the optical microscope (fig. 6b). (Note that the polishing and etching treatments for the two samples shown in figs. 6a and b were identical.) On examination in the TEM the P/U grains are found to contain arrays of hydride plates (fig. 6~). A clearer indication of the distribution of the three phases (/I,, u and hydride) is given in fig. 7. By using dark field techniques to identify the different phases, we find that the hydride plates are arranged in stacks filling the channels between the o cuboids produced by transformation of the retained Pzr. The diffraction pattern (fig. 7d) and its analysis (fig. 7e) indicate that there are at least three phases present (&, o and hydride), and confirms the orientation relationship between the j3 and w phases noted above. A number of diffraction patterns from different zone axes of the retained bee & phase were examined, and from these it was deduced that the hydride phase is the y hydride (ZrH) with an approximate orientation relationship. (111),11(112)&
* The values found experimentally
by electron diffraction agreed with these figures, within the accuracy ( + :%) of the parallel beam electron diffraction technique.
PO11,Ilwol P, Positive identification
of the y hydride
was made by
164
V. Perouic, G.C. Wearherty / hydrides in a Zr - 2.5 wt 5%Nb al&
interfaces: (a) Bright field, dark field pair showing arrays of hydride plates that share a Fig. 5. Hydride precipitation at a/bzr common orientation relationship with the azr lattice, and have nucleated at the a/jSzr interface. (h) Dark field micrograph showing a monolithic hydride plate at the a/B=, interface. (Heat treatment as fig. 4.)
the observation of superlattice reflections, which are not found with the S hydride phase, ZrH,,s [4]. The same factors that have been found to control the nucleation and growth of hydride stacks in pure Zr and a/PNb Zr ahoys [3,5] appear to be playing a role in these a/&/o microstructures. A close examination of many of the large hydride plates running along the
channels between the w cuboids shows that they are composed of many smaller plates offset in stacks in the manner previously documented [3] - see fig. 8. 2.2.3. In CI-/~,~~structures The +-PNb microstructures are the equilibrium structures expected for these alloys after prolonged heat
V. Perovic, G.C. Weather4
Fig. 6. (a) Optical micrograph of coarse grained Zr-2.5 microstructure after loading with hydrogen at 400 *C ( colour. (Samples etched in a solution of 45 ml lactic acid, from hydride diffraction spot showing arrays of hydride
/
Hydrides in a Zr - 2.5 wt % Nb alloy
Nb alloys, containing - 80 ppm H) showing
less than 1 ppm H (heat treated as fig. 1). (b) Same that the retained p phase not etches a uniform black
45 ml nitric acid and 5 ml hydrofluoric plates within the retained p phase.
treatment at temperatures below the monotectoid (610 *C). Hydride precipitation in these microstructures has been discussed elsewhere 131. Heterogeneous nucleation was again observed, with hydride plates nucleated preferentially at the cx-_PNb phase boundary or at OL--01 grain boundaries.
acid.) (c) TEM dark field micrograph
3. Discussion The total free energy change nucleation of a hydride is described AG=A(AG,)+~ys+C(~:,)*+Eint+u,,~~CN,.
accompanying the by the equation
166
V. Perooics G. C. Weatherly / Hydrides in a Zr - 2.5 wt % Nh alloy
The first three terms in this expression account for the free energy change in the absence of any stress field. A, B and C will depend on the shape of the nucleus and the elastic constants of the matrix and hydride, AC, is a volume free energy change, y, a surface energy term and 0,; is a stress free transformation strain describing the unconstr~ned shape change as the hydride forms from the matrix. The iast two terms account for the interaction with a stress field (external or internal). When the hydrogen is in solid solution, the interaction
energy between the hydrostatic stress field CJ,, and a single H atom is given by o,,pu (ii, = 1700 mm’/mole) and we assume that a concentration Cn, of hydrogen is lost from solid solution in forming the hydride (C,,, e 1). The term Einr describes the interaction between the strain field of the hydride and an external or internal stress field. In a previous analysis of this problem 13.41 we assumed that the correct form for e:, was given by
V. Perovic, G.C. Weatherly / Hydrides in a Zr- 2.5 wt % Nb allo)
0.
2y3 x
0
2iifl
*
00
167
1137
\
00 0
0:
0
0
0
l /j REFLECTIONS
>olifl i iiT
0
0
0
0
0
0
0
0
\
e
w
0’
0
HYDRIDE
REFLECTIONS
0
o REFLECTIONS
X
DOUBLE
DIFFRACTION
Fig. 7. The distribution of hydrides and w-phase particles in a partially decomposed microstructure (pressure tube alloy, annealed for 1 day at 400 OC and furnace cooled.) (a) bright field micrograph. (b) dark field using w reflection, g = (lOil)w. (c) dark field using hydride reflection, R = (113)y, (d) diffraction pattern showing the orientation relationship between 8, and w phases discussed in the text, (e) indexing of pattern shown in fig. 7d. Two variants of the hydride contribute to the pattern, which is further complicated by double
ET,=
diffraction
effects and reflections
00
0
I 0 0
s/2 0
1
A - 0.17 for the precipitation
with a surface
of 6 hydride in a-Zr [4]. This implicitly assumes that the shape change accompanying hydride precipitation is that characteristic of a martensitic transformation, i.e. a shear of s in the habit plane of the plate and a dilation A normal to the habit plane. For large hydride plates there is considerable experimental support for this assumption [4], and the formation of hydride stacks is also in accord with this shape change [3,5]. However, in order to account for this shape change for 6 hydride it is necessary to invoke one or more lattice invariant shears after the pure lattice strain step of the transformation. We have no way of determining whether these lattice invariant shears occur as the hydride plate is formed (and hence should be considered as part of the nucleation event), or whether they occur at a later stage during growth of the hydride to relieve the strains associated with the pure lattice strain. Thus we cannot exclude the possibility that at the nucleation stage, the appropriate value for the shape change would be the pure lattice strain. For 6 hydride precipitating in a-Zr this corresponds closely to a uniform dilation and simple shear [15], and CT, would be given approximately by with
s - 0.35,
A s/2
associated
oxide film.
with again s - 0.35. The equivalent value of E: for y-hydride precipitation in the j3, phase (bee, a = 3.47 A) is not known, but based on the lattice parameters and crystal structures of the two phases, a volume expansion of - 20% and shear (to account for the change from a body-centred cubic (8) to face-centred tetragonal (y) (crystal structure) must be present. It is evident that irrespective of the precise details of the components of EL, in all cases a large shear and local volume change accompany precipitation. Heterogeneous rather than homogeneous nucleation is anticipated under these circumstances. The experimental results presented in an earlier section show that the heterogeneous nucleation site varies with the heat treatment of the alloy. In the a-B=, structures, the dislocation arrays at the interface (i.e. the epitaxial dislocations and the virtual or DSC dislocation arrays at steps) give sites where the H content is higher (due to the u,,c;I interaction term discussed above) and where hydrides can preferentially form. The behaviour of the alloy in this heat-treated condition is very similar to that discussed by Banejee and Arunachalam in Ti alloys [16]. They showed that the mode of hydride precipitation in a-P Ti alloys can be explained by the partial accom-
168
V. Perouic, G. C. Weatherly / Hydrides in a Zr - 2.5 wt %, Nh ullo~
0.2
pm
-j
mechanisms advanced by Banerjee and Arunachalam can explain the results of this part of the study. The region of tensile strain at the core of the epitaxial dislocations or ledges helps to relieve the 17% volume misfit of the 6 hydride, while the steps could also accommodate the shear component of the transformation [16]. The decomposition of the retained pzr phase. although initially resulting only in a small reduction in the lattice parameter of the bee phase, has a marked effect on the interface. The boundary develops pronounced perturbations (fig. 3) and all evidence of epitaxial dislocations and of steps with strain fields disappear. This is rather surprising because the orientation relationship between the a and /? phases is unchanged and the lattice parameter of /3 only decreases by 2% on annealing at 400 ’ C. Nevertheless, the interface behaves as though the interfacial energy were now isotropic, and there are no appreciable strain fields at the interface to assist in nucleation. Although the interfacial strain fields have decreased, there will be an appreciable strain within the p,, grains as the w precipitates form, which can assist in hydride nucleation. The mean strains within the w particles and the /3, matrix are given by [17] (c(,>~=
(1 -f)(~:,),
(Qp=f(c7,>
+f(r?,>.
and
-f(fF,>,.
where f is the volume fraction of w formed, (CT,) is the strain tensor describing the precipitation of o from /I, and (c,‘;), is the constrained strain in the particles. (ET,) and (E:), are related by +:;)I
Fig. 8. (a) Distribution of hydride plates in coarse-graincd Zr-2.5 Nb (produced by annealing at 750 ‘C, furnace cooling and heating for 3 h/400 o C). Each plate is composed of stacks of smaller plates or laths (arrowed). (b) Schematic diagram illustrating the distribution of hydride plates in channels bctween the o particles. A single variant of the hydride is observed within any one channel.
modation of the strain field of the precipitate at the interface. Although there are minor differences in the crystallography of the two alloys (a, /? have a Burgers orientation relationship and the hydride that forms is the y hydride in the Ti alloy [16]), we believe that the
= +T,>
where a is an accommodation factor < 1 which can be derived from expressions given by Eshelby [18]. Using the values for E: for the p recipitation of w in /3. and an accommodation factor of 2/3 [18] (as the o particles are nearly equiaxed), the mean tensile strain in the /3 matrix is given roughly by 0.01 f. This strain could help to accommodate the small hydride plates. Note that the 0 particles themselves are under compression and hence they would not be an energetically favoutable site for nucleation. An alternative explanation for the formation of hydride stacks between the w particles could be heterogeneous nucleation assisted by defects * at the O/P interface. The high volume fraction of GJ phase * These
defects could form to relieve the volume strains accompanying the precipitation of w and changes in the [I lattice parameter.
V. Perouic, G. C. Weatherly / Hydrides rn a Zr - 2.5 wt % Nb alloy
(giving particle overlap in the image as the sample was tilted) and the high density of hydride plates prevented any detailed analysis of the o/p-interface. The common features associated with precipitation of fee hydride phase in LY-P microstructures in both Ti and Zr alloys has already been noted. A further comparison with precipitation in /3 phase Ti alloys can be made. Morgan and Hammond [19] reported that an fee phase was formed during ageing of a complex /3-Ti alloy at temperatures between 500°C and 600’ C. The diffraction evidence suggested that this phase was crystallographically identical to the interface phase in Ti alloys, which was later shown to be Ti hydride [7]. When this result is considered together with the evidence presented here of hydrides nucleated within the j3 grains as the p phase decomposes it seems likely that the phase observed by Morgan and Hammond was a hydride [19]. The diffraction effects described by Morgan and Hammond were identical to those found in this study, e.g. fig. 7d.
4. Summary The pattern of precipitation of hydrides in a twophase a-/3 zirconium alloy (Zr-2.5 Nb) is sensitive to the heat treatment of the alloy. Interphase precipitation controlled by defects at the a-P interface is observed in samples where the /3 phase has not started to decompose appreciably. On decomposition of the retained fi phase (to 8, and w), hydride precipitation is found to occur as arrays of hydride plates in /? between the o phase particles.
Acknowledgement The authors are grateful to Ontario Hydro Research Division and NSERC (Canada) for their support of this work, and to M. Koch for technical assistance.
169
References [l] D.O. Northwood and U. Kosasih, Intern. Met. Rev. 28 (1983) 92. [2] C.F. Ells, J. Nucl. Mater. 28 (1968) 129. [3] V. Perovic, G.C. Weatherly and C.J. Simpson, Acta Metall. 31 (1983) 1381. [4] G.C. Weatherly, Acta Metall. 29 (1981) 501. [5] V. Perovic, G.C. Weatherly and C.J. Simpson, Scripta Metall. 15 (1982) 409. [6] S.R. MacEwen, Chalk River Nuclear Laboratories. AECL private communication (1984). (7) B. Baranowski, S. Majchrzak and T.B. Flanagan, J. Phys. F, 1 (1971) 258. [8] J.L. Waisman, G. Sines and L.B. Robinson, Met. Trans. 4 (1973) 291. and J.C. Williams, Scripta Metall. 17 (1983) 191 D. Banqee 1125. and Crystal UOI A. Kelly and G.W. Groves, Crystallography Defects (Longman, 1970). [ill R.W. Balluffi, A. Brokman and A H. King, Acta Metall. 30 (1982) 1453. WI W.M. Stobbs and G.R. Purdy. Acta Metall. 26 (1978) 1069. Institute Phys., Conf. Ser. No. 61, 447, 1131 G.C. Weatherly, EMAG, Cambridge (1981). P41 R.F. Hehemann, Can. Metall. Q. 11 (1972) 201. u51 G.J.C. Carpenter, J. Nucl. Mater. 48 (1973) 264. Acta Metall. 29 (1981) WI D. BanerJee and V.S. Arunachalam, 1685. P71 L.M. Brown and D.R. Clarke, Acta Metall. 23 (1975) 82. P81 J.D. Eshelby, Progr. Solid Mech. 2 (1961) 89. Proc. Fourth Intern. P91 G.C. Morgan and C. Hammond, Conf. on Titamum, Kyoto. Japan, 2 (1980) 1443.
Journal
THE NUCLEATION
OF HYDRIDES
of Nuclear
Materials 126 ( 1Y84) 160 169 North-Holland. Amsterdam
IN A Zr-2.5 wt% Nb ALLOY
V. PEROVIC Metallurgy Sectron, Ontarro Hydra Research Laboratones, 800 K~pirng Avenue, Toronto. Cunudu, M8Z 5S4
and G.C. WEATHERLY Department of Metallurgy and Materials Scrence. Unrversrty of Toronto, Toronto, Canada. MS Received
2 March
1984; accepted
IA4
10 May 1984
The pr~ipltation of hydride plates in a Zr-2.5 wtl Nb alloy ts shown to be senstttve to the prtor heat treatment of the ahoy For heat treatments that lead to a faceted a//? two phase mtcrostructure. the a-j3 interface is characterized by an eprtaxtal dislocation array and steps with assoctated stram fields. For this structure, the nucleation of hydrides IS controlled by the defect structure of the interface. On annealmg the a--/3 structures below the monotectotd temperature, the retarned p phase ts unstable, decomposing first to /3, and w and ultimately to a and fiNb. At the intermedtate stage, t.e. wtth a &/w two phase structure. hydride precipitation takes the form of stacks of small hydride plates confined to channels rn the ,f3 iattrce between the w partrcfes. For both microst~ctural conditions, the preferred sate for hydride nucleation appears to he that which can most effectively accommodate the strains associated with hydrtde prectpttatton. Stmilarities m the precipttatton behavtour m a-P Zr alloys and Ti alloys are discussed.
1. Introduction
tation.
The precipitation of zirconium hydride in zirconium and its alloys usually leads to marked embrittlement of the metal, both at room temperature and at temperatures up to 3OO’C which are of interest in nuclear reactor service conditions [1,2]. The hydride precipitates have a characteristic acicular or plate morphology. which is often referred to as a “cornflake” structure. We have shown that this morphology corresponds on a microscopic scale to stacks of hydride plates formed by repeated nucleation and growth of plates which often share a common habit plane 131.The Individual plates in a stack appear to grow by a displacive or martensrtic transformation [4,5], with the stress field of a larger parent hydride plate helping to nucleate a smaller daughter hydride by a sympathetic nucleation mechanism, As the strain field of an individual hydride plate has both a shear and dilational component, this leads to the formation of offset stacks which have been observed experimentally [3,5]. The nucleation behaviour of hydrides must be determined in part by the difficulties of accommodating the volume and shear strains associated with precrpi-
in solid solution before preciprtation. As hydrogen dissolved in solid solution dilates the zirconium lattice it will be attracted to any defect or interface where the dilation can be partrally or wholly accommodated. The partial molar volume of hydrogen in a cu-Zr has recently been measured by MacEwen using neutron diffraction [6]. The value reported by MacEwen, - 1700 mm3/mole. is somewhat larger than the partial molar volume of hydrogen in the hydride phase, - 1300 mm3/mole, but agrees well with recent data for cubic metals and hcp titanium [7,8]. A further complicating factor in the hydride nucleation behaviour is the composition (and prior thermomechanical treatment) of the alloy. For example the pressure tube alloy Zr-2.5 wt% Nb, used in the present study, can, under certain conditions, contain up to 10% of a retained p-Zr phase with a bee structure. As hydrogen is much more soluble in the bee than hcp form of Zr, a greater solubiiity of H might be antrcipated in these two phase alloys. However the terminal solid solubilities of H in pure Zr, Zircaloy and Zr-2.5 Nb do not vary significantly over the temperature range from 100 to 400°C suggesting that any such effect is t~bution
0022-3115/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
A second
consideration
of hydrogen
is the non-uniform
dis-
V. Pet&c,
161
G. C. Weatherly / Hydrides in a Zr - 2.5 wf 5%Nb allqy
negligible in these alloys [l]. In this paper we present results on hydride precipitation in a two phase a-/3 Zr-Nb alloy, which show that the nucleation site depends on the prior heat treatment of the alloy. The nucleation behaviour is determined by the site in the microstructure where the most effective relief of the strains associated with precipitation can be achieved.
2. Experimental procedure The starting material was a Zr-2.5 wt% Nb pressure tube alloy containing - 1000 ppm 0 and 40-70 ppm N impurities. Samples were taken from pressure subes which were either as-extruded at 850°C and air-cooled to room temperature or as-extruded, cold-worked - 40% and stress relieved at 400 *C for periods up to 24 h (24 h at 400 o C is the standard heat treatment for pressure tube alloys used in the CANDU system). Some samples were given a further heat treatment at temperatures that ranged from SOO°C to 850 *C to develop a more equiaxed two phase a-j3 grain structure. The as-extruded and cold-worked pressure tube al- lo-15 ppm H. This is considerably in loys contained excess of the room temperature solid solubility of H, which is reported to be less than 1 ppm [1,2], so that hydride precipitation could be studied in these alloys without further additions of H. For some of the vacuum heat-treated samples, the hydrogen lost during the heat treatment had to be replaced by a gas treatment in a hydrogen atmosphere at 400 o C, followed by slow cooling to room temperature. This gave a H content in the range of 60-100 ppm. Thin foil TEM studies were used to characterize the precipitation of the hydrides. As recent studies in Ti alloys [9] have suggested that hydrogen can be inadvertently introduced into the foil by el~tropo~s~ng, precautions were taken to ensure that the effects we observed were characteristic of bulk samples rather than an artefact of sample preparation. The most convincing evidence of this came from optical metallography which showed similar patterns of precipitation in bulk samples and thin foils. (In these examples, the bulk sample had been prepared by standard metallographic procedures without electropolishing so no H could be introduced during sample preparation - see e.g. fig. 6.)
As-extruded material or alloys slowly cooled from 750 o C to room temperature contained a two phase a-8
structure. The (Y phase is cph Zr, a = 3.23 A, c = 5.15 A; the fl phase is retained bzr, containing - 20 wt% Nb, with a bee structure, a = 3.53 A. The orientation relationship between the two phases is Pitsch-Schrader [3] i.e. (10iO),/)(110)8, [l~lO],~~[OOl],. The close similarity in the atomic arrangements of the hcp and bee crystals for this orientation relations~p has been discussed by Kelly and Groves [lo], and the matrix describing the transformation from one crystal type to the other is given (in the notation adopted by Kelly and Groves) by &‘--I=
-0.085 [
+0.116 -
+ 0.03
1
relative to axes [OliO], [ZllO] and [OOOl] in the a-Zr lattice. This matrix forms the basis for a discussion of the structure of the interface between the two phases [ll]. (We shall show later that there is a direct relationship between the nature of the interface and its ability to act as a nucleation site for hydride precipitation.) Two important defects are observed at the interface which could play a role in hydride nucleation. The first is an array of [OOOC] dislocations, accommodating the 3% misfit between the (0002) planes in azr and the (110) planes in pzr (fig. 1). The density of these dislocations varies with the orientation of the interface plane separating the two phases. Other arrays of epitaxial
0.5
pm
Fig. 1. Arrays of misfit dislocations at the interface between a and retained pzl in Zr-2.5 Nb, annealed for 1 day at 820 ‘C, furnace cooled to 650 o C and helium quenched.
V. Perourc, G.C. Weaiherly / Hydrzdes in a Zr- 2.5 wt B Nh allq
162
dislocations accommodating the misfit in the [OliO] and [2110] directions might be present (these dislocations could have lattice translation vectors or could be vectors of the appropriate DSC lattice [ll] but if so, they are below the resolution of the electronmicroscope techniques used in this study). The second defect observed at the interface is a ledge structure (fig. 2). Although pure steps or ledges without a strain field can be present at interfaces [ll], at the majority of the steps a strain field was observed (see fig. 2). The strain field may arise from an array of DSC dislocations as discussed by Balluffi et al. [ll] or could be associated with the residual elastic strains required to bring the a-Zr and /3-Zr lattices into high planar co-incidence configuration [12,13]. On air cooling from 75O’C or on annealing at 400 or 500’ C, the pzr phase is unstable and can decompose either athermally or isothermally according to the reactions [14]. P ZI + w + /I, (at temperatures
below
- 450 o C)
misfit between the (0002)” and (llO),g planes.) The w phase has a hexagonal structure, the lattice parameters of this phase also being dependent on the heat treatment. After the same treatment of 40 h at 4OO”C, the w-phase parameters were reported to be u = 5.035 A, c = 3.13 A [14]. The equilibrium phase, ph,,. developed after prolonged heat treatment, contains - 85 wt% Nb, with a lattice parameter close to that of pure Nb, viz u = 3.34 A. Two marked microstructural changes accompany these phase transformations. The regular dislocation arrays observed at the a/Pz, interface (fig. 1) are no longer seen, and the interface changes from being faceted with steps to an irregular morphology with pronounced perturbations. The second change is the precipitation and growth of a high volume fraction of w particles (see fig. 3) within the p phase. The orientation relationship found by electron diffraction between the /I, and w phases is that commonly reported for this precipitation reaction,
orPZr+a+PINb+P,-+a+PL,, (at temperatures
above 450 o C)
The & phase becomes partially enriched in Nb and after annealing for 40 h at 400’ C, the lattice parameter of this bee phase has decreased from 3.53 A to 3.47 A. (This corresponds to an increase from 3% to 5% in the
Fig. 2. As fig. 1, showing steps at the a-Bzr associated strain fields (arrowed).
interface
with
The stress free transformation strain describing the structural change /3, + w is a nearly uniform dilation. Taking the values for the lattice parameters quoted
Fig. 3. Cold worked pressure tube alloy (as extruded + 30% cold work, annealed for 24 h/4CO°C). Longitudinal section showing the breakup of the retained pzr phase into w + /I,: no epitaxial dislocations arc seen at the interface between a and 8,.
163
V. Perovic, G. C. Weatherly / Hydrides in a Zr - 2.5 wt % Nb alloy
directions lying in above *, we find that in the (llO), the expansion is 38, while in the orthogonal (111)/J,> [llllLSr direction, the expansion is 4%. The w particles will be in a state of compression, while the surrounding j3, lattice will be in tension. 2.2. Hydride 2.2.1.
precipitation
In a-Pz,
microstructures
For these structures, hydride nucleation is observed at the a-j3 interface. At the earliest stage of the precipitation, a series of small plates or needles (< 10 nm in size) are found decorating the steps at the interface (fig. 4). These plates are often stacked in arrays, similar to those observed in coarser intragranularly nucleated hydrides [3]. The hydrides in fig. 4 are too small to permit a positive identification of their crystal structure ( y or S hydride), but larger hydrides (fig. 5) were identified as S(ZrH, s) with an approximate (lll),]](OOOl),, [liO],]([llZO],orientation relationship [3]. On continued growth the hydrides nucleated at the a-B interface with a common habit plane and orientation relationship develop into either a striated or monolithic plate (see fig. 5). In a previous study we suggested that where a monolithic plate formed, the habit plane of the plate (taken to be that defined by the final shape of the hydride - fig. 5b) contradicted that expected from considerations of the martensitic nature of the transformation [3]. The observations of figs. 4 and Sa, which represent an earlier stage in the nucleation and growth sequence, show that the final morphology (fig. 5b) is simply a consequence of the growth and coalescence of a number of hydride plates sharing a common orientation relationship. The hydride plates in fig. 5a have a habit plane close to the basal plane, as predicted from martensite theory for plates with a (lll),]](OOOl),, [liO],]][ll~O], orientation relationship [4]. 2.2.2. In a-p-o microstructures We noted earlier that in this heat-treated condition, the smooth regular a--/? interface has started to break-up as the w phase develops. The interface between the a and /? phases is no longer a preferential site for hydride nucleation. The pattern of precipitation for this microstructure is shown in figs. 6 and 7. Fig. 6 compares the results of an optical and electron microscopy examination of the same structure. In fig. 6a, the two phase microstructure of a coarse-grained (Y-/I alloy containing
Fig. 4. Dark field micrograph from hydride diffraction spot showing arrays of small hydride plates decorating the steps at the o//3=, interface. (The sample was heat treated for 1.2 h/750 o C and furnace cooled to room temperature.)
less than 1 ppm H is shown. After the addition of - 80 ppm H by treatment at 400°C, followed by slow cooling to room temperature, the /3/w regions appear umformly dark on examination in the optical microscope (fig. 6b). (Note that the polishing and etching treatments for the two samples shown in figs. 6a and b were identical.) On examination in the TEM the P/U grains are found to contain arrays of hydride plates (fig. 6~). A clearer indication of the distribution of the three phases (/I,, u and hydride) is given in fig. 7. By using dark field techniques to identify the different phases, we find that the hydride plates are arranged in stacks filling the channels between the o cuboids produced by transformation of the retained Pzr. The diffraction pattern (fig. 7d) and its analysis (fig. 7e) indicate that there are at least three phases present (&, o and hydride), and confirms the orientation relationship between the j3 and w phases noted above. A number of diffraction patterns from different zone axes of the retained bee & phase were examined, and from these it was deduced that the hydride phase is the y hydride (ZrH) with an approximate orientation relationship. (111),11(112)&
* The values found experimentally
by electron diffraction agreed with these figures, within the accuracy ( + :%) of the parallel beam electron diffraction technique.
PO11,Ilwol P, Positive identification
of the y hydride
was made by
164
V. Perouic, G.C. Wearherty / hydrides in a Zr - 2.5 wt 5%Nb al&
interfaces: (a) Bright field, dark field pair showing arrays of hydride plates that share a Fig. 5. Hydride precipitation at a/bzr common orientation relationship with the azr lattice, and have nucleated at the a/jSzr interface. (h) Dark field micrograph showing a monolithic hydride plate at the a/B=, interface. (Heat treatment as fig. 4.)
the observation of superlattice reflections, which are not found with the S hydride phase, ZrH,,s [4]. The same factors that have been found to control the nucleation and growth of hydride stacks in pure Zr and a/PNb Zr ahoys [3,5] appear to be playing a role in these a/&/o microstructures. A close examination of many of the large hydride plates running along the
channels between the w cuboids shows that they are composed of many smaller plates offset in stacks in the manner previously documented [3] - see fig. 8. 2.2.3. In CI-/~,~~structures The +-PNb microstructures are the equilibrium structures expected for these alloys after prolonged heat
V. Perovic, G.C. Weather4
Fig. 6. (a) Optical micrograph of coarse grained Zr-2.5 microstructure after loading with hydrogen at 400 *C ( colour. (Samples etched in a solution of 45 ml lactic acid, from hydride diffraction spot showing arrays of hydride
/
Hydrides in a Zr - 2.5 wt % Nb alloy
Nb alloys, containing - 80 ppm H) showing
less than 1 ppm H (heat treated as fig. 1). (b) Same that the retained p phase not etches a uniform black
45 ml nitric acid and 5 ml hydrofluoric plates within the retained p phase.
treatment at temperatures below the monotectoid (610 *C). Hydride precipitation in these microstructures has been discussed elsewhere 131. Heterogeneous nucleation was again observed, with hydride plates nucleated preferentially at the cx-_PNb phase boundary or at OL--01 grain boundaries.
acid.) (c) TEM dark field micrograph
3. Discussion The total free energy change nucleation of a hydride is described AG=A(AG,)+~ys+C(~:,)*+Eint+u,,~~CN,.
accompanying the by the equation
166
V. Perooics G. C. Weatherly / Hydrides in a Zr - 2.5 wt % Nh alloy
The first three terms in this expression account for the free energy change in the absence of any stress field. A, B and C will depend on the shape of the nucleus and the elastic constants of the matrix and hydride, AC, is a volume free energy change, y, a surface energy term and 0,; is a stress free transformation strain describing the unconstr~ned shape change as the hydride forms from the matrix. The iast two terms account for the interaction with a stress field (external or internal). When the hydrogen is in solid solution, the interaction
energy between the hydrostatic stress field CJ,, and a single H atom is given by o,,pu (ii, = 1700 mm’/mole) and we assume that a concentration Cn, of hydrogen is lost from solid solution in forming the hydride (C,,, e 1). The term Einr describes the interaction between the strain field of the hydride and an external or internal stress field. In a previous analysis of this problem 13.41 we assumed that the correct form for e:, was given by
V. Perovic, G.C. Weatherly / Hydrides in a Zr- 2.5 wt % Nb allo)
0.
2y3 x
0
2iifl
*
00
167
1137
\
00 0
0:
0
0
0
l /j REFLECTIONS
>olifl i iiT
0
0
0
0
0
0
0
0
\
e
w
0’
0
HYDRIDE
REFLECTIONS
0
o REFLECTIONS
X
DOUBLE
DIFFRACTION
Fig. 7. The distribution of hydrides and w-phase particles in a partially decomposed microstructure (pressure tube alloy, annealed for 1 day at 400 OC and furnace cooled.) (a) bright field micrograph. (b) dark field using w reflection, g = (lOil)w. (c) dark field using hydride reflection, R = (113)y, (d) diffraction pattern showing the orientation relationship between 8, and w phases discussed in the text, (e) indexing of pattern shown in fig. 7d. Two variants of the hydride contribute to the pattern, which is further complicated by double
ET,=
diffraction
effects and reflections
00
0
I 0 0
s/2 0
1
A - 0.17 for the precipitation
with a surface
of 6 hydride in a-Zr [4]. This implicitly assumes that the shape change accompanying hydride precipitation is that characteristic of a martensitic transformation, i.e. a shear of s in the habit plane of the plate and a dilation A normal to the habit plane. For large hydride plates there is considerable experimental support for this assumption [4], and the formation of hydride stacks is also in accord with this shape change [3,5]. However, in order to account for this shape change for 6 hydride it is necessary to invoke one or more lattice invariant shears after the pure lattice strain step of the transformation. We have no way of determining whether these lattice invariant shears occur as the hydride plate is formed (and hence should be considered as part of the nucleation event), or whether they occur at a later stage during growth of the hydride to relieve the strains associated with the pure lattice strain. Thus we cannot exclude the possibility that at the nucleation stage, the appropriate value for the shape change would be the pure lattice strain. For 6 hydride precipitating in a-Zr this corresponds closely to a uniform dilation and simple shear [15], and CT, would be given approximately by with
s - 0.35,
A s/2
associated
oxide film.
with again s - 0.35. The equivalent value of E: for y-hydride precipitation in the j3, phase (bee, a = 3.47 A) is not known, but based on the lattice parameters and crystal structures of the two phases, a volume expansion of - 20% and shear (to account for the change from a body-centred cubic (8) to face-centred tetragonal (y) (crystal structure) must be present. It is evident that irrespective of the precise details of the components of EL, in all cases a large shear and local volume change accompany precipitation. Heterogeneous rather than homogeneous nucleation is anticipated under these circumstances. The experimental results presented in an earlier section show that the heterogeneous nucleation site varies with the heat treatment of the alloy. In the a-B=, structures, the dislocation arrays at the interface (i.e. the epitaxial dislocations and the virtual or DSC dislocation arrays at steps) give sites where the H content is higher (due to the u,,c;I interaction term discussed above) and where hydrides can preferentially form. The behaviour of the alloy in this heat-treated condition is very similar to that discussed by Banejee and Arunachalam in Ti alloys [16]. They showed that the mode of hydride precipitation in a-P Ti alloys can be explained by the partial accom-
168
V. Perouic, G. C. Weatherly / Hydrides in a Zr - 2.5 wt %, Nh ullo~
0.2
pm
-j
mechanisms advanced by Banerjee and Arunachalam can explain the results of this part of the study. The region of tensile strain at the core of the epitaxial dislocations or ledges helps to relieve the 17% volume misfit of the 6 hydride, while the steps could also accommodate the shear component of the transformation [16]. The decomposition of the retained pzr phase. although initially resulting only in a small reduction in the lattice parameter of the bee phase, has a marked effect on the interface. The boundary develops pronounced perturbations (fig. 3) and all evidence of epitaxial dislocations and of steps with strain fields disappear. This is rather surprising because the orientation relationship between the a and /? phases is unchanged and the lattice parameter of /3 only decreases by 2% on annealing at 400 ’ C. Nevertheless, the interface behaves as though the interfacial energy were now isotropic, and there are no appreciable strain fields at the interface to assist in nucleation. Although the interfacial strain fields have decreased, there will be an appreciable strain within the p,, grains as the w precipitates form, which can assist in hydride nucleation. The mean strains within the w particles and the /3, matrix are given by [17] (c(,>~=
(1 -f)(~:,),
(Qp=f(c7,>
+f(r?,>.
and
-f(fF,>,.
where f is the volume fraction of w formed, (CT,) is the strain tensor describing the precipitation of o from /I, and (c,‘;), is the constrained strain in the particles. (ET,) and (E:), are related by +:;)I
Fig. 8. (a) Distribution of hydride plates in coarse-graincd Zr-2.5 Nb (produced by annealing at 750 ‘C, furnace cooling and heating for 3 h/400 o C). Each plate is composed of stacks of smaller plates or laths (arrowed). (b) Schematic diagram illustrating the distribution of hydride plates in channels bctween the o particles. A single variant of the hydride is observed within any one channel.
modation of the strain field of the precipitate at the interface. Although there are minor differences in the crystallography of the two alloys (a, /? have a Burgers orientation relationship and the hydride that forms is the y hydride in the Ti alloy [16]), we believe that the
= +T,>
where a is an accommodation factor < 1 which can be derived from expressions given by Eshelby [18]. Using the values for E: for the p recipitation of w in /3. and an accommodation factor of 2/3 [18] (as the o particles are nearly equiaxed), the mean tensile strain in the /3 matrix is given roughly by 0.01 f. This strain could help to accommodate the small hydride plates. Note that the 0 particles themselves are under compression and hence they would not be an energetically favoutable site for nucleation. An alternative explanation for the formation of hydride stacks between the w particles could be heterogeneous nucleation assisted by defects * at the O/P interface. The high volume fraction of GJ phase * These
defects could form to relieve the volume strains accompanying the precipitation of w and changes in the [I lattice parameter.
V. Perouic, G. C. Weatherly / Hydrides rn a Zr - 2.5 wt % Nb alloy
(giving particle overlap in the image as the sample was tilted) and the high density of hydride plates prevented any detailed analysis of the o/p-interface. The common features associated with precipitation of fee hydride phase in LY-P microstructures in both Ti and Zr alloys has already been noted. A further comparison with precipitation in /3 phase Ti alloys can be made. Morgan and Hammond [19] reported that an fee phase was formed during ageing of a complex /3-Ti alloy at temperatures between 500°C and 600’ C. The diffraction evidence suggested that this phase was crystallographically identical to the interface phase in Ti alloys, which was later shown to be Ti hydride [7]. When this result is considered together with the evidence presented here of hydrides nucleated within the j3 grains as the p phase decomposes it seems likely that the phase observed by Morgan and Hammond was a hydride [19]. The diffraction effects described by Morgan and Hammond were identical to those found in this study, e.g. fig. 7d.
4. Summary The pattern of precipitation of hydrides in a twophase a-/3 zirconium alloy (Zr-2.5 Nb) is sensitive to the heat treatment of the alloy. Interphase precipitation controlled by defects at the a-P interface is observed in samples where the /3 phase has not started to decompose appreciably. On decomposition of the retained fi phase (to 8, and w), hydride precipitation is found to occur as arrays of hydride plates in /? between the o phase particles.
Acknowledgement The authors are grateful to Ontario Hydro Research Division and NSERC (Canada) for their support of this work, and to M. Koch for technical assistance.
169
References [l] D.O. Northwood and U. Kosasih, Intern. Met. Rev. 28 (1983) 92. [2] C.F. Ells, J. Nucl. Mater. 28 (1968) 129. [3] V. Perovic, G.C. Weatherly and C.J. Simpson, Acta Metall. 31 (1983) 1381. [4] G.C. Weatherly, Acta Metall. 29 (1981) 501. [5] V. Perovic, G.C. Weatherly and C.J. Simpson, Scripta Metall. 15 (1982) 409. [6] S.R. MacEwen, Chalk River Nuclear Laboratories. AECL private communication (1984). (7) B. Baranowski, S. Majchrzak and T.B. Flanagan, J. Phys. F, 1 (1971) 258. [8] J.L. Waisman, G. Sines and L.B. Robinson, Met. Trans. 4 (1973) 291. and J.C. Williams, Scripta Metall. 17 (1983) 191 D. Banqee 1125. and Crystal UOI A. Kelly and G.W. Groves, Crystallography Defects (Longman, 1970). [ill R.W. Balluffi, A. Brokman and A H. King, Acta Metall. 30 (1982) 1453. WI W.M. Stobbs and G.R. Purdy. Acta Metall. 26 (1978) 1069. Institute Phys., Conf. Ser. No. 61, 447, 1131 G.C. Weatherly, EMAG, Cambridge (1981). P41 R.F. Hehemann, Can. Metall. Q. 11 (1972) 201. u51 G.J.C. Carpenter, J. Nucl. Mater. 48 (1973) 264. Acta Metall. 29 (1981) WI D. BanerJee and V.S. Arunachalam, 1685. P71 L.M. Brown and D.R. Clarke, Acta Metall. 23 (1975) 82. P81 J.D. Eshelby, Progr. Solid Mech. 2 (1961) 89. Proc. Fourth Intern. P91 G.C. Morgan and C. Hammond, Conf. on Titamum, Kyoto. Japan, 2 (1980) 1443.