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Transmission electron microscopy investigations of ordered Zr3Al
JOURNAL OF NUCLEAR MATERIALS 50 (1974) 139-154.
0 NORTH-HOLLAND PUBLISHING COMPANY
TRANSMISSION ELECTRON MICROSCOPY INVESTIGATIONS OF ORDERER Zr+l L.M. HOWE, M. RAINVILLE
and E.M. SCHULSON
Chalk River Nuclear Laboratories, Atomic Energy of CanadaLiinited, Chalk River, Ontario, Canada Received 31 August 1973 ZrsAl is an ordered fee alloy of the Lla type. The ordered phase appears to be very stable thermally as it has not been possible to disorder ZrsAf by quenching. It is possible, however, to disorder ZrsAl by irradiation. In deformed ZrsAl the superlattice dislocations were observed to be extended, i.e. they consisted of intrinsic stacking faults on (Ill) bounded by partial dislocations. The total Burgers vector is of the type (110) and the superlattice dislocations have dissociated as follows: (1 lO)-*f(211)+ f(l2b. During high-temperature annealing of the deformed material, dislocation networks were produced in which all of the dislocation nodes were extended; hence intrinsic and extrinsic stacking faults must alternate at the nodes. Weak beam images were obtained of long and relatively straight dislocation lines in annealed ZrsAl in order to obtain information on the equilibrium width of the extended dislocations. ZrsAl est un alliage ordon& cubique $ faces cent&es du type Liz. La phase ordonn& semble &tre tr& stable thermiquement puisqu’il n’a pas &e possible d’obtenir Zrs Al d&ordonnd par trempe, 11est possible cependant de dhsordonner ZrsAl par irradiation. Dans l’alliage d&ordonne ZrsAl les dislocations de surstructure apparaissent Btendues, c’est-adire qu’elles sont constituees par des difauts d’empllement intrindques sur les plans { 1111 limit& par des dislocations partielles. Le vecteur de Burgers total est du type (110) et les dislocations de surstructure sont dissocibs comme suit: (110)+$(21l)+f(121). Durant le recuit a haute temp&ature du materiau d6formi des reseaux de dislocations sont form& dans lequeis tous les noeuds de dislocations sont &endus, Par suite, les defauts d’empilement intrinsiques et extrinseques doivect alterner aux noeuds. Des images, sous faible faisceau, de dislocations longues et relativement droites ont 6t6 obtenues dam Zrs Al recuit afin d’obtenir des informations sur la largeur d’iquilibre des dislocations dtendues. ZrsAl kristallisiert als kfz. Ordnungsphase im Lla-Typ und scheint thermisch sehr stabil zu sein, weil die ungeordnete ZrsAlStruktur durch Abschrecken bisher nicht hergestetlt werden konnte. Es ist jedoch. moglich, die ungeordnete Struktur durch Bestrahlung zu erzeugen. In verformtem ZrsAl nehmen die Versetzungen in der Uberstrukturphase zu, sie bestehen aus eigenfehlgeordneten Stapelfehlern auf den {ill}-Ebenen, die durch Teilversetzungen gebunden sind. Der gesamte Burgers-Vektor ist vom Typ (llO>, die Ve~etzun~n in der ~be~t~kt~ di~o~~emn,~rn~ss (110) -+&2111+ i(12i). Wound der W&mebehandlung des verformten Materials bei hohen Temperaturen entstehen Versetzungsnetzwerke, in denen alle Versetzungsverzweigungen zunehmen; somit miissen die eigen- und fremdfehlgeordneten Stapelfehler an den Verzweigungen abwechseln. Es wurden schwache Bilder von langen und relativ geraden Versetzungslinien in wiirmebehandeltem Zrs Al gewonnen, aus denen Auskunft iiber die Gieichgewichtsbreite der verkingerten Versetzungen erhalten wurde.
1. Introduction The possibility of using ordered alloys (or intermetallic compounds) as material for fuel sheaths or pressure tubes in nuclear power reactors is presently being explored. Of the various alloys which satisfy the criteria of low therms-neutron capture cross section (Xu, G 0.01 cm2/ cm3) and high melting temperature (7’, > lOOO”C), Zr3Al was selected as the material for an initial study. Experiments by Schulson [I], on unirradiated material, indicate that the alloys which
are based on the Zr,Al phase generally have better tensile properties than the currently developed Zr alloys which are based on the o-Zr phase. Furthermore, oxidation experiments [I] indicate that the corrosion rates for selected, near-stoichiometric alloys are not catastrophically high as are the rates for dilute Zr-Al alloys, but appear to be comparable to those for Zircaloy-2. Consequently, more detailed investigations have been initiated on ZrgAl based alloys. In the present study transmission electron-microscope observations were made primarily to investigate the nature of the dislo-
L.M. Howe et al., Ordered Lr3Al
130
Table 1 Alloy composition and phase content. Alloy composition
Apprcximate
phase content (%)
(wt% Al)
Zr 3Al
a(Zr)
ZrzAl
6.5 8.8 9.5
65 65 45
35 12 10
23 45
(2) 9.5 wt% Al material was def’ormed in tension at room temperature (3) 6.5 wt% Al material was quenched from either 900 or 950°C directly into water held at 0°C‘. 2..?. Electron microscopy
cation structure produced during the deformation of ordered ZrgAl as no previous electron-microscope studies on this material have been reported. In addition, information was obtained on the thermal and irradiation stability of the ordered Zr,Al phase.
2. Experimental details 2.1. Alloy preparation The alloys were prepared by Canadian Westinghouse Co. Ltd. by melting together reactor grade zirconium sponge and aluminum wire (99.6% purity) in vacuum on a water-cooled copper block using the arc-melting technique with a non-consumable, thoriated tungsten electrode. The compositions of the alloys used in this investigation were 6.5, 8.8 and 9.5 wt%’ Al. 2.2. Transformation The Zr,Al phase forms via the two peritectoid actions:
re-
Zr t Zr,A13 -+ 3 Zr,Al,
(1)
Zr,Al
(2)
+ Zr + Zr,Al.
Reaction (1) occurs at temperatures below z 1250°C and reaction (2) occurs below e 975°C [2]. To form the Zr,Al matrix the alloys were rolled at = 1050°C and then transformed in vacuum at 900°C. The approximate phase content of the three alloys is listed in table 1. The 900°C annealing treatment yielded Zr,Al in a highly ordered state and with a low dislocation density. Some of the material was left in the annealed condition and the following operations were performed on the remainder: (1) 6.5 and 8.8 wt% Al material was reduced from l-5% by rolling at room temperature
Discs 2.3 mm in diameter were produced by a combination of sparkcutting, sparkplaning and chemical polishing operations. Specimens suitable for transmission electron microscopy were obtained from these discs by jet electropolishing using a cooled electrolyte consisting of 57~ perchloric acid and 95%’ ethanol. The observations were made with a Siemens Elmlskop 101 electron microscope operated at 100 kV with pointed filaments and thin-film, self-cleaning objective apertures. In order to achieve the desirable diffraction conditions the specimen was tilted using the high-resolution tilting and rotating cartridge made by Siemens for the Elmiskop 101. All dark field images were obtained by beam tilting to preserve maximum contrast and resolution
3. Results aad discussion 3.1. The ordered Zr3Al phase Diffraction patterns from Zr,Al grains in annealed specimens from all three alloys revealed the presence of both fundamental and superlattice spots characteristic of an ordered fee alloy of the L 12 type; an example of which is given in fig. la. This is in agreement with the X-ray diffraction results of Keeler and Mallery [3] and Pb;tzschke and Schubert [4] who report that Zr3Al has the Ll, structure with the lattice parameter a = 4.372 and 4.374 a respectively. In the perfectly ordered case, the Al atoms all occupy the corners of the unit cell and the Zr atoms arc at the face centers. Samples were taken from the 6.5 wt% Al alloy which was quenched from 900°C. As shown by the electron diffraction pattern in fig. I b both fundamental and superlattice spots are still present. In fact. the superlattice spots were observed to be as intense in the quenched material as in the annealed material. An identical result was obtained with material quenched from 950°C which is in the p(Zr) + Zr,Al region of the phase diagram. Quenching from much higher tem-
141
L.M. Howe et al., Ordered ZrsAl
Fig. 2. Electron diffraction patterns (neat [ 1121 zone) from the same ZrsAl grain taken before (a) and after (b) bombardment with 1 MeV electrons to a displacement density of 0.7 dpa. As a result of the bombardment the intensity of the superlattice spots has been greatly reduced. vated temperatures quenching.
Although
and then order very rapidly this latter
ruled out at the present
possibility
time, it is considered
during
cannot rather
be un-
likely.
Fig. 1. Electron diffraction patterns from ZrsAl showing both fundamental and superlattice spots characteristic of an ordered fee alloy of the Liz type. (a) annealed material - near [Oil] zone, (b) material quenched from 900°C - near (0111 zone. peratures
was not possible
as Zr,Al
transforms
above
975°C. It thus appears that Zr,Al remains an ordered phase throughout the temperature range in which it is stable. The alternative is that the alloys disorder at ele-
It is possible, however, to disorder Zr,Al by irradiation. Fig. 2, for example, shows electron diffraction patterns taken from the same area of a Zr3Al foil initially (a) and after bombardment (b), in the high-voltage electron microscope at Harwell, with 1 MeV electrons to a displacement density of 0.7 displacements per atom (dpa). As a result of the bombardment the intensity of the superlattice spots is greatly reduced. Observations from other areas of the foil confirmed these observations and showed, in addition, that at 1.6 dpa the superlattice intensity is very weak and at 2.5 and 3.3 dpa the superlattice spots have virtually disappeared. The dpa values were calculated assuming a displacement threshold energy of 25 eV. A more detailed investigation of the effect of irradiation on
142
L.M. Howe et al., Ordered Zr,Al
Zr,Al is presently underway and will form the basis of a separate study; hence this aspect of the work will not be discussed further here. 3.2. Planar defects in annealed and in quenched Zr3141 In annealed as well as in quenched material a low density of planar defects was present in the Zr,Al grains. These planar defects were in contrast for botl fundamental and superlattice reflections; and hence are not antiphase domain boundaries. In fact, there were no antiphase domain boundaries in any of the annealed or quenched material which indicates that the Zr,Al is present in a highly ordered state. The diffraction patterns from regions with these defects revealed only Zr3Al reflections so the defects are not precipitates of a second phase. In some instances these Fig. 3. Planar defect forming a closed system in the interior of a Zr 3Al grain in an annealed Zr-8.8 wt% Al alloy. Visibility criteria indicate that regions A and B represent stacking faults on (111) and (171) respectively. In the other regions the faults are not on { 111) and in some cases do not appear to be confined to any particular plane. Bright field (b.f.) image taken near [ 1 lo] zone.
Fig. 4. Planar defect terminating on agrain boundary in a Zr-6.5 wt% Al alloy quenched from 950°C. Bf. image taken near [OOl] zone.
L.&i. Howe et al., Ordered ZrsAl
143
Fig. 5. Same defects as in fig. 4 shown imaged in dark field (d.f.) under various diffraction conditions. The foil was oriented near the [OOl] zone for (a) and (b) and near the [ 1121 zone for (c) to (f). Diffraction contrast analysis indicates that regions A and B represent intrinsic stacking faults on (111) and (111) respectively. However the regions C,D, E and F are not stacking faults on any (111).
planar defects formed a closed system in the interior of a grain (fig. 3) whereas in others they formed an interconnecting system terminating on a grain boun-
dary (fig. 4). At the moment the origin as well as the detailed nature of these planar defects is not fully understood.
144
L.M. Howe et al., Ordered %r3Al
Table 2 Visibility
g
critieria
for the stacking
01modulo 2n (R = $[lli]
faults in fig. 5
Expt. OLmodule 2n 0bserv.a) (R = k[ 1i 1] (system A)
Expt. observ.“’ (system B) V
111 0
I.V.
$r
200
37l
V
$7t
V
020
&i
V
ST
V
220
$I
V
0
I.V.
220
0
I.V
#n
V
13i
#n
V
0
I.V.
131
0
I.V.
$n
V
311
0
I.v.
0
I.V.
331
$77
V
&I
V
331
&l
V
&
V
042
0
I.V.
0
I.V.
a) V - visible (in contrast):
I.V. ~ invisible
(out of contrast).
Consider, for example the contrast features of the planar defect in figs. 4 and 5. The image of a stacking fault is characterized by the value of the phase angle 01 = 27rgR whereg is the reciprocal lattice vector for the operating reflection and R is the displacement vector of the fault. For the fundamental reflections in the fee lattice, (Y= 3 nrr, where n = 0, Itl, +2, etc. depending on the indices of the Bragg reflection. It is customary to refer to c~modulo 2n(-n < 01< + rr) in which case the possible values of (Yare 0, 53 rr modulo 2n; the stacking fault being out of contrast for the former value and in contrast for the latter value. From the observed visibility conditions for the defects, as summarized in table 2, it appears that regions A and B of the defect are stacking faults on (11 i) and (li 1) respectively. However, a similar analysis shows that in regions such as C, D, E and F the planar defects are not stacking faults on (111) or (i 11); a conclusion also confirmed by considering the expected position of the traces of these planes on the foil surface. Also, in some of these regions the fault does not appear to be confined to any particular plane. In fee materials stacking faults are generally classified as intrinsic or extrinsic. An intrinsic fault is caused by motion of a Shockley partial dislocation (involving shear on one plane only), or by condensation of vacancies (i.e. by removal of a plane of atoms). An extrinsic fault is caused by the motion of a Shockley
partial dislocation involving shear on two adjacent planes, or by condensation of interstitial atoms (i.e. by insertion of a close-packed plane of atoms). The nature of the stacking fault can be determined by observing the sense (light or dark) of the edge fringe in bright and dark field images [ 5, 61, which also gives the sense of sloping of the stacking fault, or by exam ining the properties of the edge fringe in the dark field image alone [7]. This analysis can be used in cases where the foil is sufficiently thick for absorption effects to be important as witnessed by the symmetrical nature of the bright field image and the asymmetrical nature of the dark field image. Consider the properties of the edge fringe of the stacking faults on ( 111) and ( 1i 1) for the planar defect shown in fig. 5. Orienting the dark field images so that the diffraction vectorg points to the right of the line of intersection of the fault plane with the foil plane, it is observed that the fringe at the right is bright for 1200) reflections (class A) and is dark for (11 I) and { 220} reflections (class B). As shown by Gevers et al. [7], this is the contrast expected from an intrinsic stacking fault. It is believed that these planar defects are possibly formed during the transformation of Zr,Al from the other phases. Density measurements [8] indicate that a significant volume contraction occurs during the peritectoidal formation of Zr,Al. This may result in a fairly high vacancy concentration in some regions of the Zr,Al grains with the subsequent collapse and formation of vacancy-type defects in these regions. The fact that the analyzed faults on { 11 l} were intrinsic lends some support to this view. 3.3. Dislocations and stacking faults in deformed Zr#l In the fee superlattice Ll,, the dislocations can be coupled together as pairs (i.e. superlattice dislocations) in such a manner that when they move through the lattice order is restored. For the close-packed { 1113 planes in the superlattice, the slip vector 2BA is of the type (1 10) which is exactly twice that in an ordinary fee lattice. Some possible dissociation schemes for glissile dislocations in the Ll, structure are as follows (see for example, Marcinkowski et al. [9] and Oblak and Kear [lo]): Scheme (1):
2BA =
-BA (i% +6A)
+
BA (% +6Ai’
L.M, Howe et al., Ordered Zr3AI
145
Fig. 6. ZrsAl grain in a Zr-8.8
wt% Al alloy which was deformed 5% by rolling at room temperature. At this level of deformation appreciable interaction has occurred amongst the extended superlattice dislocations on the various (111) glide planes. B.f. image taken near [ 1121 zone.
where &! is a perfect dislocation of type i(110) and a and fi are partial dislocations of type i(l12). In this scheme, pairs of $
2BA =
B% (~+~+%)+(%+%+&
-
where 2B6 and 26A are partial dislocations of type 4 (112). In this scheme pairs of 3 (112) dislocations are coupled together by a stacking fault. Also, each $(112) dislocation may itself dissociate into three Shockley partial dislocations (i.e. %? + m + fi) coupled by a complex fault. In ordered CusAu [9] and Ni3Mn [ 1 l] scheme (1) is the observed mode of deformation. Evidence
for scheme (2) occurring under certain deformation conditions has been found in the ordered Ni3(A1,Ti)y’ phase [lo] and in Ni3Ga [ 121. Figs. 6-8 show the type of structure which was found to be characteristic of the Zr3Al grains in all of the deformed Zr-Al alloys. The structure consists of planar faults on { Ill} bounded by partial dislocations (i.e. extended dislocations); faults on planes other than { 111) were not observed. These faults were visible for both fundamental and superlattice reflections and thus are not antiphase domain boundaries. Detailed contrast analysis of the faults has shown that they are stacking faults which are visible for (Y= 2ng. R = +in modulo 2n and invisible for (Y= 0; hence they can be characterized by a displacement vector R = $(l 11) (or equivalently by R = 4(112) or 4 (112)). The nature of the stacking faults was determined using the methods previously outlined. The analysis was performed on material from all three alloys which
Fig. 7. Extended superlattice dislocations on (i 11) in a ZrsAl grain of a Zr -6.5 wt% Al alloy which was deformed I’S by roilmg at room temperature. The stacking faults are intrinsic (see (a) and (d)). The elecv;n micrographs (a), (d) and (f) are normal d.K A-‘. For (a), (b) and Cc) the zone axis was near images whereas (b), (c) and (e) are d.f. weak beam images taken with s = 2 X 10 [Ol l] and for (d), (e) and (f) near [ 1121. The partial dislocations A and S lie along [ 1 lOI* (where p denote\ the projection ot [ 1 IO] on to the foil surface).
L.M. Howe et al., Ordered Zr3Al
147
Fig. 8. Extended superlattice dislocations on (ill) in a Zr3Al grain of a Zr-6.5 wt% Al alloy which was deformed 1% by rolling - at room temperature. Dark field images are shown for the following diffraction conditions: (a) g = 1 il, s > 0, (b) g = 111, s > 0 and (c)g = li 1, s < 0. The partial dislocation D is out of contrast in (a) but in contrast for (b) and (c). Zone axis near [Oil].
had been deformed at room temperature. Approximately 100 stacking faults were examined using (11 l}, (220) and {ZOO}reflections and all of the stacking faults were found to be intrinsic. Examples of this behaviour are shown in fig. 7.
The determination of the Burgers vector of the partial dislocations bounding the intrinsic stacking faults will now be considered. The normal criterion for invisibility of partial dislocations is g * b = 0, 4 [ 131. Also, Silcock and Tunstall [ 141 have shown
L.M. Howe et al., Ordered &AI
148
that for s > 0 a partial is visible wheng* b = + 3 but not when g. b = -3. In figs. 7 and 8, the extended dislocations have a (T 11) glide plane as confirmed by the invisibility of the stacking faults for ( 131): (022), (311) and (31i) reflections. The values ofg*b for undissociated and dissociated superlattice dislocations on (iI 1) are listed in table 3 for the operating reflections used in the analysis. The partial dislocations A in fig. 7 are out of contrast for the (022) and (131) reflections whereas the partial dislocation B is out of contrast for the (3il) reflection. This is consistentwithb=$[211] andb=$[12i] forAandB respectively. This is confirmed by the fact that for the (2%) and ( 111) reflections dislocations A and B are not simultaneously out of contrast which they would havebeenifb=$[211] andi[l2i] fortheng*b= +f for one partial and -4 for the other. Similarly it can be shown that b= 3 [li2] for dislocation C in fig. 7. Partial dislocation D in fig. 8 has b = 4 [1211as it is out of contrast for the (37 1) reflection (g.6 = 0) and for the (1 il) reflection when s > 0 (g-b = --3) but is in contrast for the ( 111) reflection (g* b = + 3) and for the (111) reflection when s < 0. As illustrated in fig. 7, dark field weak beam images were found to be very useful in determining the Burgers vectors of the partial dislocations. Further details on the weak beam imaging technique will be discussed subsequently. The superlattice dislocations AB and AC in fig. 7 have, therefore dissociated as follows:
in agreement with proposed scheme (2) where the antrphase boundary energy is large relative to the stacking fault energy. However, even under weak beam imaging conditions possible further dissociation of each 4 (1 12) dislocation into three Shockley partial dislocations could not be resolved. Many of the partial dislocations bounding the stacking faults were noted to be quite straight and were found to be parallel to (110) (see fig. 7). Similar behaviour has been reported by Oblak and Kear [ 1 I ] for the superlattice dislocations in the Ni,(Al,Ti) y’ phase. Their proposed reason for the alignment is that a f(112) partial dislocation may then be able to dissociate into a Shockley partial and a normal perfect dislocation and thus enable the latter to cross-slip onto the cube plane. In fig. 7 for example, the partials A and B may tend to dissociate as follows: 5]211]
-+f[li2]
+$[iLo]
(A).
i(12iJ
+t[llz]
+& [IlO]
(B).
when they lie along [ 1 IO] ) thus permitting the 4 [ 1 IO] dislocations to cross-slip onto (001) as the antiphase boundary energy is a minimum for { 100) in the Ll, structure. Evidence fd‘r this cross-slip actually occurring was not found in this investigation. However-. it is planned to study this aspect further, particularly in alloys deformed at elevated temperatures. 3.4. Dislocation networks
[IlO]
-4
[211] +$ [121]
(AB) 1
[lOI]
-4
[211] t$ [Ii?]
(AC) .
Table 3 Values of g-b for dislocations on (ill). \-pmp-mmm ‘1,?I [llO]
!L/
(iii)
~-[Oil]
_~_
,r;P,,
$[211]
4[12il
S[lT2]
0
3
(lil)
0
2
2
-3
(200)
2
0
2
3 4
3
3
(220)
0
2
2
3
_~3
(022)
2
-4
m-2
0
2
4 -2
(202)
2
-2
0
5
4
-3
4
2
0
0
2
4
(151) (3111)
2
-2 2
--2
4
-3 5
2
(311)
2
2
4
2
; 0
(311)
4
-~2
2
2
2
5 7 0
Dislocation networks were formed in ordered Zr,Al which was deformed at room temperature and then annealed at 850-900°C. Examples of these are shown in figs. 9 and 10. A detailed analysis was performed of the dislocations comprising the networks; both in the vicinity of the nodes where the partial dislocations were extended and in regions away from the nodes where the dislocations were not extended to any appreciable extent. For the latter dislocations, besides using the g- b = 0 visibility criterion, a comparison was made of the general features of the experimental images with the theoretical image profiles which have been obtained by other investigators for undissociated dislocations (see Hirsch et al. [5]) This analysis also confirmed the presence of superlattice dislocations as well as the dissociation scheme (2) outlined above. In the fee lattice it can be shown that a stable net-
L.M. Howe et al., Ordered Zr&
149
Fig. 9. Dislocation network in a Zr&l grain from a Zr-6.5 wt% Al alloy which was deformed at room temperature and then annealed at 900°C. Note that all of the dislocation nodes are extended. Bright field image taken near (0131 zone.
work will consist of alternating extended and contracted nodes if the stacking faults are all of the same kind i.e. either all are intrinsic or all are extrinsic. If all of the dislocation nodes are extended, as was observed for the networks in Zr,Al (see figs. 9 and lo), then intrinsic and extrinsic stacking faults must alternate, as illustrated in fig. 11. In early observations on deformed fee metals, mainly intrinsic stacking faults were observed which suggested that either the energy of an extrinsic stacking fault greatly exceeded that of an intrinsic stacking fault or that some mechanistic barrier existed which tended to prevent dissociation into extrinsic faults. However, extrinsic stacking faults were subsequently observed in fee metals [ 16-181. Furthermore, experimental measurements [ 181 as well as more detailed theoretical treatments (for discussion, see Hirth and Lothe [ 191) indicate that the intrinsic and extrinsic stacking fault energies should be nearly equal. Hirth and Lothe [ 191 suggest that the formation of pairs of partials that bound an extrinsic stack-
ing fault is kinetically more difficult than the formation of the single partials bounding an intrinsic fault due to the higher core energies of the partial dislocations in the former case. In ordered Zr,Al extrinsic and intrinsic stacking faults were present in dislocation nodes formed during high-temperature annealing but only intrinsic stacking faults were produced during deformation at room temperature. Also, stacking fault energy measurements indicate that the energies of intrinsic and extrinsic stacking faults are similar in Zr,Al (to be discussed in subsect. 3.5). Hence for Zr,Al it would appear that either: (1) there is definitely a mechanistic barrier to the formation of extrinsic stacking faults at room temperature whereas at significantly higher temperatures the additional thermal activation energy available for overcoming the barrier enables both intrinsic and extrinsic stacking faults to form, or (2) it becomes kinetically more feasible for an extrin-
150
L.M. Howe et al., Ordered Zrg Al
Fig. 10. Screw dislocation network in a ZrsAl grain showing extended dislocation nodes (same material as in fig. 9). B.f. images (a) and (b) taken nea [ 1121 zone and (e) and (f) taken near [ 1141 zone. D.F.w.b. images (c) and (d) taken near [OOl] and [ 1121 zone respectively. With reference to fig. 11, the following diffraction conditions qply for the above electron micrographs: (a) g&=OforA’B’= [ilo], (b)g.b=OforB’C’=- - [loi],(c)g~b=OforA’C’=[011],(d)g~6=OforC’6’=j[ii2],(e)g~b=O for B’S’ = 4[2ii], (f)g.b = 0 for A’s’ = 3[121].
151
L.M. Howe et al., Ordered Zr&
8’
Fig. 11. Schematic drawing of the network in fig. 10 with the regions in the vicinity of the nodes being expanded for clarity. Thompson’s notation [ 151 used except that primes have been put on the letters to signify that the dislocations being considered are superlattice dislocations and their associated partial dislocations. Note that intrinsic and extrinsic stacking faults alternate at the nodes. The Burgersvectors of the dislocations are as follows: A’B’ = [ilO], B’C’ = [lOi], A’C’ = [Oil], C’S’ = $[fi2], B’s’ = +[2ii], andA’6’=i[iZi].
sic stacking fault to be produced under conditions where there is more time available for the dissociation and movement of partial dislocations such as occurs during the formation of dislocation networks during the annealing of cold-worked material It is planned to investigate this further by determining the nature of the stacking faults formed as a function of the deformation temperature. 3.5. Determination
of the equlibrium separation of
partial dislocations and estimation of the stacking fault energy
Cockayne et al. [20] have developed a method for
fairly accurately determining the position of a dislocation line using images formed by diffracted beams which appear weak in the diffraction pattern. The principle of the method is to set the crystal at an orientation a long way from the Bragg reflecting condition, so that the beam is only weakly excited in the perfect region of a crystal whereas along a dislocation line the local region of high strain close to the core can bend the lattice planes into the reflecting condition. If this occurs over sufficient depth in the crystal a relatively strong, narrow peak is produced in the image close to the dislocation core. The condition for such a peak is s,+d/dz(g-
R)=O
152
L.M. Howe et al., Ordered Zr41
(a) Fig. 12. Weak beam images showing $1 =2x10-zA-‘.
the dissociation
of superlat tice ddislocations
at a turning point of d/dz @*I?), where R is the displacement produced by the dislocation, sg is the deviation parameter giving the distance of the reciprocal lattice point g from the reflecting sphere and z is a coordinate in the beam direction. The above criterion for the image peak position is an approximation, the accuracy of which depends upon the nature of the strain field and $1. For images of dislocations in which detail >25 A is required, the criterion is satisfactory provided that lsgl > 2 X 10e2 8-l. Using the weak beam technique the separation of partial dislocations has been measured in G-Al alloys [21], silicon [22], gold 1231) copper 124,251 and the separation of superlattice dislocations in Fe-AI alloys [26,27] and NiAl
1281. Weak beam images were obtained of fairly long and relatively straight dislocations in deformed and partially annealed Zr,Al using {220} reflections and with 1~~1 in the region 1.6 X lop2 to 2.3 X 1O-2 8-l. This corresponded to taking the weak beam images ing with the reflection ng satisfied where n was not necessarily integral but varied over the range 3 to 4. The exact value of lssl for a weak beam image was obtained from the position of the Kikuchi line in the selected area diffraction pattern. measurements of the separation
in Zr,Al
into partial
distocations.
I:or (a) and (b 1:
Aobs of the partial dislocations were obtained for dislocations where g was parallel to b in which case both partial dislocations were visible and in good contrast I as shown in fig. 12. The measurements were made at many points along the dislocation line and Aobs is the mean value of these measurements for those regions of the dislocation line which were at the same orientation. The Burgers vectors of the dislocations were determined by setting up strong two-beam diffraction conditions and noting the refections for which the dislocations were either in or out of contrast. Following the method outlined by Cockayne 1291. the true separation A between the partial dislocations was caIculated from the observed separation Aobs. The values of A obtained are plotted in fig. 13 as a function of the angle /3 between the line direction and the Burgers vector. The majority of the examined dislocations were closer to the screw orientation than to the edge orientation; hence the preponderance of points in fig. 13 at low 0 values. A value for the stacking fault energy y can be obtained by comparing theoretical curves of the partial dislocation width as a function of orientation for various values of-y with the experimental data. An accur. ate determination of the stacking fault energy by this
the relationship between the radius of curvature p and the stacking fault energy y can be expressed as:
method requires sufficient information of the elastic constants in the material in order to perform a calculation using anisotropic elasticity theory. Unfortunately, at present, insufficient information is available for Zr,Al. An estimate of the stacking fault energy can be obtained, however, from isotropic elasticity theory; in particular, using the relationship [ 191
x
+ (0.,04(~)+
0 SCREW
IO
20
I
I
30
ORIENTATION
VO OF
o.24(&)cos20)log10P,e;
where b, is the magnitude of the Burgers vector of the partial dislocation, (Yis the angle between b, and the tangent to the dislocation line at the nodal point, and E is a core parameter usually taken as equal to b,. The radius of curvature was measured at 12 nodes in a symmetrical network of screw orientation and the stacking fault energy was determined using the above relationship. The measurements for the the two different types of nodes (i.e. encompassing either an intrinsic I or an extrinsic E stacking fault) were initially treated separately and showed that -rr X YE as the two values were within 2 erg*cmp2 of one another which is well within the experimental uncertainty of the measurements. The calculated value of the stacking fault energy obtained by averaging all of the measurements was 81 + 5 erg.cmF2.
where b is the magnitude of the total Burgers vector of the disloqation, /J is the shear modulus and v is Poisson’s ratio. Based on the measurements of Schulson and Turner [30], p = 4.9 X 1011 dyn*cmm2 (49 GN*m-2) and u = 0.34. As shown in fig. 13, the experimental points fall in a band between the theoretical curves (shown dotted) plotted for y = 70 erg*cm-2 and y = 90 erg*cmW2. An estimate of the stacking fault energy can also be obtained from measurements of the radius of curvature of extended nodes in dislocation networks. According to the analysis of Brown and Thiilen [ 3 11, based upon the approximation of isotropic elasticity, I
cos 2o
@;
* = pb2(2 - v) 8ny( 1 - V) (
I
= 0.27 - 0.08 &
I
I
50
60
OISLOCATION
LINE
I
I
70
80
I/??
90 EOGE
Fig. 13. A plot of partial dislocation separation A as a function of orientation of the dislocation line. Experimentally determined values are plotted as open circles and the theoretical curves corresponding to y = 70 and 90 erg - cme2 are shown dotted.
154
L.M. Howe et al., Ordered h3Al
4. Conclusions ( 1) Zr,Abis an orderec’ fee alloy of the Ll, type which appears to be very stable thermally as it has not been possible to disorder Zr,Al by quenching. It is possible, however, to disorder Zr,Al by irradiation, (2) Planar defects, which possibly form during the transformation of Zr,Al from other phases, were present in annealed and in quenched Zr,Al. (3) In Zr3Al the superlattice dislocations are extended (i.e. they consist of an intrinsic stacking fault bounded by partial dislocations). The dissociation of the superlattice dislocation (b = (110)) occurs as follows:
(4) During high-temperature annealing of deformed material dislocation networks were produced in which all of the dislocation nodes were extended. In order for Such a network to be stable in a fee lattice intrinsic and extrinsic stacking faults must alternate at the nodes. (5) The stacking fault energy in Zr,Al was estimated to be 70-90 erg-cm-*.
Acknowledgements The advice and technical assistance provided by J.F. Watters in electropolishing Zr,Al in the initial stages of the program is gratefully acknowledged. We are also grateful to G.J.C. Carpenter for performing the electron bombardment experiments in the highvoltage electron microscope at Harwell.
References [1] E.M. Schulson, [2] D.J. McPherson 46 (1954) 354, [3] J.H. Keeler and 394.
J. Nucl. Mater. 50 (1974) 127. and M. Hansen, T.A.S.M. (Met. Trans.) 374. J.H. Mallery, Trans. AIME 203 (1955)
[4] M. PGtzschke and K. Schuberl, Z. Metallk. 53 (1967) 541; [S] P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashleq and M.J. Whelan, Electron Microscopy of Thin Crystals (Butterworths, London, 1965) pp. !56- 194, 222 275 [6] A. Art, R. Gevers and S. Amelinckx, Phys. Stat. So!. 3 (1963) 697. 171 R. Cevers, A. Art and S. Amelinckx. Phyc. Stat. Sol. .:
(1963) 1563. E.M. Schulson, private commumcation. M.J. Marcinkowski, N. Brown and R.M. Fisher, Acra Met. 9 (1961) 129. J.M. Oblak and B.H. Kear, Electron Microscopy and Structure of Materials (University of California Press. Berkeley, 1971) p. 566. 1111 M.J. Marcinkowski and D.S. Miller, Phil. Mag. 6 (1961 i 871. [I21 S. Takeuchi and E. Kuramoto, Acta Met 21 (1973) 415 [I31 A. Howie and M.J. Whelan, Proc. Roy. Sot. A267 (1962) 206. 1141 J.M. Silcock and W.J. Tunstall, Phil. Mag. 10 ( 1964) 361. I151 N. Thompson, Proc. Phys. Sot. Land. B 66 (1953) 481. [I61 M.H. Loretto, Phil. Mag. 10 (1964) 467; 12 (1965) 125. [I71 P.R. Swarm, Acta Met. 14 (1966) 76. [ISI P.C.J. Gallagher, Phys. Stat. Soiidi 16 (1966) 95. [I91 J.P. Hirth and J. Lothe, Theory of Dislocations (McGrawHill, New York, 1968) pp. 288.-333. 1201 D.J.H. Cockayne, I.L.F. Ray and M.J. Whelan, Phxl. Mag. 20 (1969) 1265. [*II D.J.H. Cockayne, I.L.!:. Ray and M.J. Whelan, Septrgmc (‘ongrks International de Microscopic I’lectroniquc, (irenoble, Vol. 2 (1970) p. 321. 1221 1.L.F. Ray and D.J.H. Cockaync, Proi. Roy Sot. I.ond. A 325 (1971)
543.
~231 M.L. Jenkins, Phil. Mag. 26 (1972) 747. 1241 W.M. Stobbs and C.H. Sworn, Phil. Mag. 24 (1972) 136.5. ~51 D.J.H. Cockayne, M.L. Jenkins and 1.L.F. Ray, Phil. Msg. 24 (1972)
1383.
1261 1.L.F. Ray, R.C. Crawford
and D.J.H. Cockayne. Phil. Mag. 21 (1970) 1027. v71 R.C. Crawford, I.L.F. Ray and D.J.H. Cockaync, PhII. Mag. 27 (1973) 1. 12x1 R.C. Campany, M.H. Loretto and R.E. Smallman, Re ported at a symposium on Weak Beams held at the Fifth European Congress on Electron Microscopy. liniversity (11’Manchester (1972) to be published. r*91 D.J.H. Cockayne, D. Phil. Thesis, Oxford University II 970). [301 L.M. Schulson and R.B. Turner, Private communication. [311 L.M. Brown and A.R. ThGlen. Disc. Faraday Sot. 38 (1964)
35.
0 NORTH-HOLLAND PUBLISHING COMPANY
TRANSMISSION ELECTRON MICROSCOPY INVESTIGATIONS OF ORDERER Zr+l L.M. HOWE, M. RAINVILLE
and E.M. SCHULSON
Chalk River Nuclear Laboratories, Atomic Energy of CanadaLiinited, Chalk River, Ontario, Canada Received 31 August 1973 ZrsAl is an ordered fee alloy of the Lla type. The ordered phase appears to be very stable thermally as it has not been possible to disorder ZrsAf by quenching. It is possible, however, to disorder ZrsAl by irradiation. In deformed ZrsAl the superlattice dislocations were observed to be extended, i.e. they consisted of intrinsic stacking faults on (Ill) bounded by partial dislocations. The total Burgers vector is of the type (110) and the superlattice dislocations have dissociated as follows: (1 lO)-*f(211)+ f(l2b. During high-temperature annealing of the deformed material, dislocation networks were produced in which all of the dislocation nodes were extended; hence intrinsic and extrinsic stacking faults must alternate at the nodes. Weak beam images were obtained of long and relatively straight dislocation lines in annealed ZrsAl in order to obtain information on the equilibrium width of the extended dislocations. ZrsAl est un alliage ordon& cubique $ faces cent&es du type Liz. La phase ordonn& semble &tre tr& stable thermiquement puisqu’il n’a pas &e possible d’obtenir Zrs Al d&ordonnd par trempe, 11est possible cependant de dhsordonner ZrsAl par irradiation. Dans l’alliage d&ordonne ZrsAl les dislocations de surstructure apparaissent Btendues, c’est-adire qu’elles sont constituees par des difauts d’empllement intrindques sur les plans { 1111 limit& par des dislocations partielles. Le vecteur de Burgers total est du type (110) et les dislocations de surstructure sont dissocibs comme suit: (110)+$(21l)+f(121). Durant le recuit a haute temp&ature du materiau d6formi des reseaux de dislocations sont form& dans lequeis tous les noeuds de dislocations sont &endus, Par suite, les defauts d’empilement intrinsiques et extrinseques doivect alterner aux noeuds. Des images, sous faible faisceau, de dislocations longues et relativement droites ont 6t6 obtenues dam Zrs Al recuit afin d’obtenir des informations sur la largeur d’iquilibre des dislocations dtendues. ZrsAl kristallisiert als kfz. Ordnungsphase im Lla-Typ und scheint thermisch sehr stabil zu sein, weil die ungeordnete ZrsAlStruktur durch Abschrecken bisher nicht hergestetlt werden konnte. Es ist jedoch. moglich, die ungeordnete Struktur durch Bestrahlung zu erzeugen. In verformtem ZrsAl nehmen die Versetzungen in der Uberstrukturphase zu, sie bestehen aus eigenfehlgeordneten Stapelfehlern auf den {ill}-Ebenen, die durch Teilversetzungen gebunden sind. Der gesamte Burgers-Vektor ist vom Typ (llO>, die Ve~etzun~n in der ~be~t~kt~ di~o~~emn,~rn~ss (110) -+&2111+ i(12i). Wound der W&mebehandlung des verformten Materials bei hohen Temperaturen entstehen Versetzungsnetzwerke, in denen alle Versetzungsverzweigungen zunehmen; somit miissen die eigen- und fremdfehlgeordneten Stapelfehler an den Verzweigungen abwechseln. Es wurden schwache Bilder von langen und relativ geraden Versetzungslinien in wiirmebehandeltem Zrs Al gewonnen, aus denen Auskunft iiber die Gieichgewichtsbreite der verkingerten Versetzungen erhalten wurde.
1. Introduction The possibility of using ordered alloys (or intermetallic compounds) as material for fuel sheaths or pressure tubes in nuclear power reactors is presently being explored. Of the various alloys which satisfy the criteria of low therms-neutron capture cross section (Xu, G 0.01 cm2/ cm3) and high melting temperature (7’, > lOOO”C), Zr3Al was selected as the material for an initial study. Experiments by Schulson [I], on unirradiated material, indicate that the alloys which
are based on the Zr,Al phase generally have better tensile properties than the currently developed Zr alloys which are based on the o-Zr phase. Furthermore, oxidation experiments [I] indicate that the corrosion rates for selected, near-stoichiometric alloys are not catastrophically high as are the rates for dilute Zr-Al alloys, but appear to be comparable to those for Zircaloy-2. Consequently, more detailed investigations have been initiated on ZrgAl based alloys. In the present study transmission electron-microscope observations were made primarily to investigate the nature of the dislo-
L.M. Howe et al., Ordered Lr3Al
130
Table 1 Alloy composition and phase content. Alloy composition
Apprcximate
phase content (%)
(wt% Al)
Zr 3Al
a(Zr)
ZrzAl
6.5 8.8 9.5
65 65 45
35 12 10
23 45
(2) 9.5 wt% Al material was def’ormed in tension at room temperature (3) 6.5 wt% Al material was quenched from either 900 or 950°C directly into water held at 0°C‘. 2..?. Electron microscopy
cation structure produced during the deformation of ordered ZrgAl as no previous electron-microscope studies on this material have been reported. In addition, information was obtained on the thermal and irradiation stability of the ordered Zr,Al phase.
2. Experimental details 2.1. Alloy preparation The alloys were prepared by Canadian Westinghouse Co. Ltd. by melting together reactor grade zirconium sponge and aluminum wire (99.6% purity) in vacuum on a water-cooled copper block using the arc-melting technique with a non-consumable, thoriated tungsten electrode. The compositions of the alloys used in this investigation were 6.5, 8.8 and 9.5 wt%’ Al. 2.2. Transformation The Zr,Al phase forms via the two peritectoid actions:
re-
Zr t Zr,A13 -+ 3 Zr,Al,
(1)
Zr,Al
(2)
+ Zr + Zr,Al.
Reaction (1) occurs at temperatures below z 1250°C and reaction (2) occurs below e 975°C [2]. To form the Zr,Al matrix the alloys were rolled at = 1050°C and then transformed in vacuum at 900°C. The approximate phase content of the three alloys is listed in table 1. The 900°C annealing treatment yielded Zr,Al in a highly ordered state and with a low dislocation density. Some of the material was left in the annealed condition and the following operations were performed on the remainder: (1) 6.5 and 8.8 wt% Al material was reduced from l-5% by rolling at room temperature
Discs 2.3 mm in diameter were produced by a combination of sparkcutting, sparkplaning and chemical polishing operations. Specimens suitable for transmission electron microscopy were obtained from these discs by jet electropolishing using a cooled electrolyte consisting of 57~ perchloric acid and 95%’ ethanol. The observations were made with a Siemens Elmlskop 101 electron microscope operated at 100 kV with pointed filaments and thin-film, self-cleaning objective apertures. In order to achieve the desirable diffraction conditions the specimen was tilted using the high-resolution tilting and rotating cartridge made by Siemens for the Elmiskop 101. All dark field images were obtained by beam tilting to preserve maximum contrast and resolution
3. Results aad discussion 3.1. The ordered Zr3Al phase Diffraction patterns from Zr,Al grains in annealed specimens from all three alloys revealed the presence of both fundamental and superlattice spots characteristic of an ordered fee alloy of the L 12 type; an example of which is given in fig. la. This is in agreement with the X-ray diffraction results of Keeler and Mallery [3] and Pb;tzschke and Schubert [4] who report that Zr3Al has the Ll, structure with the lattice parameter a = 4.372 and 4.374 a respectively. In the perfectly ordered case, the Al atoms all occupy the corners of the unit cell and the Zr atoms arc at the face centers. Samples were taken from the 6.5 wt% Al alloy which was quenched from 900°C. As shown by the electron diffraction pattern in fig. I b both fundamental and superlattice spots are still present. In fact. the superlattice spots were observed to be as intense in the quenched material as in the annealed material. An identical result was obtained with material quenched from 950°C which is in the p(Zr) + Zr,Al region of the phase diagram. Quenching from much higher tem-
141
L.M. Howe et al., Ordered ZrsAl
Fig. 2. Electron diffraction patterns (neat [ 1121 zone) from the same ZrsAl grain taken before (a) and after (b) bombardment with 1 MeV electrons to a displacement density of 0.7 dpa. As a result of the bombardment the intensity of the superlattice spots has been greatly reduced. vated temperatures quenching.
Although
and then order very rapidly this latter
ruled out at the present
possibility
time, it is considered
during
cannot rather
be un-
likely.
Fig. 1. Electron diffraction patterns from ZrsAl showing both fundamental and superlattice spots characteristic of an ordered fee alloy of the Liz type. (a) annealed material - near [Oil] zone, (b) material quenched from 900°C - near (0111 zone. peratures
was not possible
as Zr,Al
transforms
above
975°C. It thus appears that Zr,Al remains an ordered phase throughout the temperature range in which it is stable. The alternative is that the alloys disorder at ele-
It is possible, however, to disorder Zr,Al by irradiation. Fig. 2, for example, shows electron diffraction patterns taken from the same area of a Zr3Al foil initially (a) and after bombardment (b), in the high-voltage electron microscope at Harwell, with 1 MeV electrons to a displacement density of 0.7 displacements per atom (dpa). As a result of the bombardment the intensity of the superlattice spots is greatly reduced. Observations from other areas of the foil confirmed these observations and showed, in addition, that at 1.6 dpa the superlattice intensity is very weak and at 2.5 and 3.3 dpa the superlattice spots have virtually disappeared. The dpa values were calculated assuming a displacement threshold energy of 25 eV. A more detailed investigation of the effect of irradiation on
142
L.M. Howe et al., Ordered Zr,Al
Zr,Al is presently underway and will form the basis of a separate study; hence this aspect of the work will not be discussed further here. 3.2. Planar defects in annealed and in quenched Zr3141 In annealed as well as in quenched material a low density of planar defects was present in the Zr,Al grains. These planar defects were in contrast for botl fundamental and superlattice reflections; and hence are not antiphase domain boundaries. In fact, there were no antiphase domain boundaries in any of the annealed or quenched material which indicates that the Zr,Al is present in a highly ordered state. The diffraction patterns from regions with these defects revealed only Zr3Al reflections so the defects are not precipitates of a second phase. In some instances these Fig. 3. Planar defect forming a closed system in the interior of a Zr 3Al grain in an annealed Zr-8.8 wt% Al alloy. Visibility criteria indicate that regions A and B represent stacking faults on (111) and (171) respectively. In the other regions the faults are not on { 111) and in some cases do not appear to be confined to any particular plane. Bright field (b.f.) image taken near [ 1 lo] zone.
Fig. 4. Planar defect terminating on agrain boundary in a Zr-6.5 wt% Al alloy quenched from 950°C. Bf. image taken near [OOl] zone.
L.&i. Howe et al., Ordered ZrsAl
143
Fig. 5. Same defects as in fig. 4 shown imaged in dark field (d.f.) under various diffraction conditions. The foil was oriented near the [OOl] zone for (a) and (b) and near the [ 1121 zone for (c) to (f). Diffraction contrast analysis indicates that regions A and B represent intrinsic stacking faults on (111) and (111) respectively. However the regions C,D, E and F are not stacking faults on any (111).
planar defects formed a closed system in the interior of a grain (fig. 3) whereas in others they formed an interconnecting system terminating on a grain boun-
dary (fig. 4). At the moment the origin as well as the detailed nature of these planar defects is not fully understood.
144
L.M. Howe et al., Ordered %r3Al
Table 2 Visibility
g
critieria
for the stacking
01modulo 2n (R = $[lli]
faults in fig. 5
Expt. OLmodule 2n 0bserv.a) (R = k[ 1i 1] (system A)
Expt. observ.“’ (system B) V
111 0
I.V.
$r
200
37l
V
$7t
V
020
&i
V
ST
V
220
$I
V
0
I.V.
220
0
I.V
#n
V
13i
#n
V
0
I.V.
131
0
I.V.
$n
V
311
0
I.v.
0
I.V.
331
$77
V
&I
V
331
&l
V
&
V
042
0
I.V.
0
I.V.
a) V - visible (in contrast):
I.V. ~ invisible
(out of contrast).
Consider, for example the contrast features of the planar defect in figs. 4 and 5. The image of a stacking fault is characterized by the value of the phase angle 01 = 27rgR whereg is the reciprocal lattice vector for the operating reflection and R is the displacement vector of the fault. For the fundamental reflections in the fee lattice, (Y= 3 nrr, where n = 0, Itl, +2, etc. depending on the indices of the Bragg reflection. It is customary to refer to c~modulo 2n(-n < 01< + rr) in which case the possible values of (Yare 0, 53 rr modulo 2n; the stacking fault being out of contrast for the former value and in contrast for the latter value. From the observed visibility conditions for the defects, as summarized in table 2, it appears that regions A and B of the defect are stacking faults on (11 i) and (li 1) respectively. However, a similar analysis shows that in regions such as C, D, E and F the planar defects are not stacking faults on (111) or (i 11); a conclusion also confirmed by considering the expected position of the traces of these planes on the foil surface. Also, in some of these regions the fault does not appear to be confined to any particular plane. In fee materials stacking faults are generally classified as intrinsic or extrinsic. An intrinsic fault is caused by motion of a Shockley partial dislocation (involving shear on one plane only), or by condensation of vacancies (i.e. by removal of a plane of atoms). An extrinsic fault is caused by the motion of a Shockley
partial dislocation involving shear on two adjacent planes, or by condensation of interstitial atoms (i.e. by insertion of a close-packed plane of atoms). The nature of the stacking fault can be determined by observing the sense (light or dark) of the edge fringe in bright and dark field images [ 5, 61, which also gives the sense of sloping of the stacking fault, or by exam ining the properties of the edge fringe in the dark field image alone [7]. This analysis can be used in cases where the foil is sufficiently thick for absorption effects to be important as witnessed by the symmetrical nature of the bright field image and the asymmetrical nature of the dark field image. Consider the properties of the edge fringe of the stacking faults on ( 111) and ( 1i 1) for the planar defect shown in fig. 5. Orienting the dark field images so that the diffraction vectorg points to the right of the line of intersection of the fault plane with the foil plane, it is observed that the fringe at the right is bright for 1200) reflections (class A) and is dark for (11 I) and { 220} reflections (class B). As shown by Gevers et al. [7], this is the contrast expected from an intrinsic stacking fault. It is believed that these planar defects are possibly formed during the transformation of Zr,Al from the other phases. Density measurements [8] indicate that a significant volume contraction occurs during the peritectoidal formation of Zr,Al. This may result in a fairly high vacancy concentration in some regions of the Zr,Al grains with the subsequent collapse and formation of vacancy-type defects in these regions. The fact that the analyzed faults on { 11 l} were intrinsic lends some support to this view. 3.3. Dislocations and stacking faults in deformed Zr#l In the fee superlattice Ll,, the dislocations can be coupled together as pairs (i.e. superlattice dislocations) in such a manner that when they move through the lattice order is restored. For the close-packed { 1113 planes in the superlattice, the slip vector 2BA is of the type (1 10) which is exactly twice that in an ordinary fee lattice. Some possible dissociation schemes for glissile dislocations in the Ll, structure are as follows (see for example, Marcinkowski et al. [9] and Oblak and Kear [lo]): Scheme (1):
2BA =
-BA (i% +6A)
+
BA (% +6Ai’
L.M, Howe et al., Ordered Zr3AI
145
Fig. 6. ZrsAl grain in a Zr-8.8
wt% Al alloy which was deformed 5% by rolling at room temperature. At this level of deformation appreciable interaction has occurred amongst the extended superlattice dislocations on the various (111) glide planes. B.f. image taken near [ 1121 zone.
where &! is a perfect dislocation of type i(110) and a and fi are partial dislocations of type i(l12). In this scheme, pairs of $
2BA =
B% (~+~+%)+(%+%+&
-
where 2B6 and 26A are partial dislocations of type 4 (112). In this scheme pairs of 3 (112) dislocations are coupled together by a stacking fault. Also, each $(112) dislocation may itself dissociate into three Shockley partial dislocations (i.e. %? + m + fi) coupled by a complex fault. In ordered CusAu [9] and Ni3Mn [ 1 l] scheme (1) is the observed mode of deformation. Evidence
for scheme (2) occurring under certain deformation conditions has been found in the ordered Ni3(A1,Ti)y’ phase [lo] and in Ni3Ga [ 121. Figs. 6-8 show the type of structure which was found to be characteristic of the Zr3Al grains in all of the deformed Zr-Al alloys. The structure consists of planar faults on { Ill} bounded by partial dislocations (i.e. extended dislocations); faults on planes other than { 111) were not observed. These faults were visible for both fundamental and superlattice reflections and thus are not antiphase domain boundaries. Detailed contrast analysis of the faults has shown that they are stacking faults which are visible for (Y= 2ng. R = +in modulo 2n and invisible for (Y= 0; hence they can be characterized by a displacement vector R = $(l 11) (or equivalently by R = 4(112) or 4 (112)). The nature of the stacking faults was determined using the methods previously outlined. The analysis was performed on material from all three alloys which
Fig. 7. Extended superlattice dislocations on (i 11) in a ZrsAl grain of a Zr -6.5 wt% Al alloy which was deformed I’S by roilmg at room temperature. The stacking faults are intrinsic (see (a) and (d)). The elecv;n micrographs (a), (d) and (f) are normal d.K A-‘. For (a), (b) and Cc) the zone axis was near images whereas (b), (c) and (e) are d.f. weak beam images taken with s = 2 X 10 [Ol l] and for (d), (e) and (f) near [ 1121. The partial dislocations A and S lie along [ 1 lOI* (where p denote\ the projection ot [ 1 IO] on to the foil surface).
L.M. Howe et al., Ordered Zr3Al
147
Fig. 8. Extended superlattice dislocations on (ill) in a Zr3Al grain of a Zr-6.5 wt% Al alloy which was deformed 1% by rolling - at room temperature. Dark field images are shown for the following diffraction conditions: (a) g = 1 il, s > 0, (b) g = 111, s > 0 and (c)g = li 1, s < 0. The partial dislocation D is out of contrast in (a) but in contrast for (b) and (c). Zone axis near [Oil].
had been deformed at room temperature. Approximately 100 stacking faults were examined using (11 l}, (220) and {ZOO}reflections and all of the stacking faults were found to be intrinsic. Examples of this behaviour are shown in fig. 7.
The determination of the Burgers vector of the partial dislocations bounding the intrinsic stacking faults will now be considered. The normal criterion for invisibility of partial dislocations is g * b = 0, 4 [ 131. Also, Silcock and Tunstall [ 141 have shown
L.M. Howe et al., Ordered &AI
148
that for s > 0 a partial is visible wheng* b = + 3 but not when g. b = -3. In figs. 7 and 8, the extended dislocations have a (T 11) glide plane as confirmed by the invisibility of the stacking faults for ( 131): (022), (311) and (31i) reflections. The values ofg*b for undissociated and dissociated superlattice dislocations on (iI 1) are listed in table 3 for the operating reflections used in the analysis. The partial dislocations A in fig. 7 are out of contrast for the (022) and (131) reflections whereas the partial dislocation B is out of contrast for the (3il) reflection. This is consistentwithb=$[211] andb=$[12i] forAandB respectively. This is confirmed by the fact that for the (2%) and ( 111) reflections dislocations A and B are not simultaneously out of contrast which they would havebeenifb=$[211] andi[l2i] fortheng*b= +f for one partial and -4 for the other. Similarly it can be shown that b= 3 [li2] for dislocation C in fig. 7. Partial dislocation D in fig. 8 has b = 4 [1211as it is out of contrast for the (37 1) reflection (g.6 = 0) and for the (1 il) reflection when s > 0 (g-b = --3) but is in contrast for the ( 111) reflection (g* b = + 3) and for the (111) reflection when s < 0. As illustrated in fig. 7, dark field weak beam images were found to be very useful in determining the Burgers vectors of the partial dislocations. Further details on the weak beam imaging technique will be discussed subsequently. The superlattice dislocations AB and AC in fig. 7 have, therefore dissociated as follows:
in agreement with proposed scheme (2) where the antrphase boundary energy is large relative to the stacking fault energy. However, even under weak beam imaging conditions possible further dissociation of each 4 (1 12) dislocation into three Shockley partial dislocations could not be resolved. Many of the partial dislocations bounding the stacking faults were noted to be quite straight and were found to be parallel to (110) (see fig. 7). Similar behaviour has been reported by Oblak and Kear [ 1 I ] for the superlattice dislocations in the Ni,(Al,Ti) y’ phase. Their proposed reason for the alignment is that a f(112) partial dislocation may then be able to dissociate into a Shockley partial and a normal perfect dislocation and thus enable the latter to cross-slip onto the cube plane. In fig. 7 for example, the partials A and B may tend to dissociate as follows: 5]211]
-+f[li2]
+$[iLo]
(A).
i(12iJ
+t[llz]
+& [IlO]
(B).
when they lie along [ 1 IO] ) thus permitting the 4 [ 1 IO] dislocations to cross-slip onto (001) as the antiphase boundary energy is a minimum for { 100) in the Ll, structure. Evidence fd‘r this cross-slip actually occurring was not found in this investigation. However-. it is planned to study this aspect further, particularly in alloys deformed at elevated temperatures. 3.4. Dislocation networks
[IlO]
-4
[211] +$ [121]
(AB) 1
[lOI]
-4
[211] t$ [Ii?]
(AC) .
Table 3 Values of g-b for dislocations on (ill). \-pmp-mmm ‘1,?I [llO]
!L/
(iii)
~-[Oil]
_~_
,r;P,,
$[211]
4[12il
S[lT2]
0
3
(lil)
0
2
2
-3
(200)
2
0
2
3 4
3
3
(220)
0
2
2
3
_~3
(022)
2
-4
m-2
0
2
4 -2
(202)
2
-2
0
5
4
-3
4
2
0
0
2
4
(151) (3111)
2
-2 2
--2
4
-3 5
2
(311)
2
2
4
2
; 0
(311)
4
-~2
2
2
2
5 7 0
Dislocation networks were formed in ordered Zr,Al which was deformed at room temperature and then annealed at 850-900°C. Examples of these are shown in figs. 9 and 10. A detailed analysis was performed of the dislocations comprising the networks; both in the vicinity of the nodes where the partial dislocations were extended and in regions away from the nodes where the dislocations were not extended to any appreciable extent. For the latter dislocations, besides using the g- b = 0 visibility criterion, a comparison was made of the general features of the experimental images with the theoretical image profiles which have been obtained by other investigators for undissociated dislocations (see Hirsch et al. [5]) This analysis also confirmed the presence of superlattice dislocations as well as the dissociation scheme (2) outlined above. In the fee lattice it can be shown that a stable net-
L.M. Howe et al., Ordered Zr&
149
Fig. 9. Dislocation network in a Zr&l grain from a Zr-6.5 wt% Al alloy which was deformed at room temperature and then annealed at 900°C. Note that all of the dislocation nodes are extended. Bright field image taken near (0131 zone.
work will consist of alternating extended and contracted nodes if the stacking faults are all of the same kind i.e. either all are intrinsic or all are extrinsic. If all of the dislocation nodes are extended, as was observed for the networks in Zr,Al (see figs. 9 and lo), then intrinsic and extrinsic stacking faults must alternate, as illustrated in fig. 11. In early observations on deformed fee metals, mainly intrinsic stacking faults were observed which suggested that either the energy of an extrinsic stacking fault greatly exceeded that of an intrinsic stacking fault or that some mechanistic barrier existed which tended to prevent dissociation into extrinsic faults. However, extrinsic stacking faults were subsequently observed in fee metals [ 16-181. Furthermore, experimental measurements [ 181 as well as more detailed theoretical treatments (for discussion, see Hirth and Lothe [ 191) indicate that the intrinsic and extrinsic stacking fault energies should be nearly equal. Hirth and Lothe [ 191 suggest that the formation of pairs of partials that bound an extrinsic stack-
ing fault is kinetically more difficult than the formation of the single partials bounding an intrinsic fault due to the higher core energies of the partial dislocations in the former case. In ordered Zr,Al extrinsic and intrinsic stacking faults were present in dislocation nodes formed during high-temperature annealing but only intrinsic stacking faults were produced during deformation at room temperature. Also, stacking fault energy measurements indicate that the energies of intrinsic and extrinsic stacking faults are similar in Zr,Al (to be discussed in subsect. 3.5). Hence for Zr,Al it would appear that either: (1) there is definitely a mechanistic barrier to the formation of extrinsic stacking faults at room temperature whereas at significantly higher temperatures the additional thermal activation energy available for overcoming the barrier enables both intrinsic and extrinsic stacking faults to form, or (2) it becomes kinetically more feasible for an extrin-
150
L.M. Howe et al., Ordered Zrg Al
Fig. 10. Screw dislocation network in a ZrsAl grain showing extended dislocation nodes (same material as in fig. 9). B.f. images (a) and (b) taken nea [ 1121 zone and (e) and (f) taken near [ 1141 zone. D.F.w.b. images (c) and (d) taken near [OOl] and [ 1121 zone respectively. With reference to fig. 11, the following diffraction conditions qply for the above electron micrographs: (a) g&=OforA’B’= [ilo], (b)g.b=OforB’C’=- - [loi],(c)g~b=OforA’C’=[011],(d)g~6=OforC’6’=j[ii2],(e)g~b=O for B’S’ = 4[2ii], (f)g.b = 0 for A’s’ = 3[121].
151
L.M. Howe et al., Ordered Zr&
8’
Fig. 11. Schematic drawing of the network in fig. 10 with the regions in the vicinity of the nodes being expanded for clarity. Thompson’s notation [ 151 used except that primes have been put on the letters to signify that the dislocations being considered are superlattice dislocations and their associated partial dislocations. Note that intrinsic and extrinsic stacking faults alternate at the nodes. The Burgersvectors of the dislocations are as follows: A’B’ = [ilO], B’C’ = [lOi], A’C’ = [Oil], C’S’ = $[fi2], B’s’ = +[2ii], andA’6’=i[iZi].
sic stacking fault to be produced under conditions where there is more time available for the dissociation and movement of partial dislocations such as occurs during the formation of dislocation networks during the annealing of cold-worked material It is planned to investigate this further by determining the nature of the stacking faults formed as a function of the deformation temperature. 3.5. Determination
of the equlibrium separation of
partial dislocations and estimation of the stacking fault energy
Cockayne et al. [20] have developed a method for
fairly accurately determining the position of a dislocation line using images formed by diffracted beams which appear weak in the diffraction pattern. The principle of the method is to set the crystal at an orientation a long way from the Bragg reflecting condition, so that the beam is only weakly excited in the perfect region of a crystal whereas along a dislocation line the local region of high strain close to the core can bend the lattice planes into the reflecting condition. If this occurs over sufficient depth in the crystal a relatively strong, narrow peak is produced in the image close to the dislocation core. The condition for such a peak is s,+d/dz(g-
R)=O
152
L.M. Howe et al., Ordered Zr41
(a) Fig. 12. Weak beam images showing $1 =2x10-zA-‘.
the dissociation
of superlat tice ddislocations
at a turning point of d/dz @*I?), where R is the displacement produced by the dislocation, sg is the deviation parameter giving the distance of the reciprocal lattice point g from the reflecting sphere and z is a coordinate in the beam direction. The above criterion for the image peak position is an approximation, the accuracy of which depends upon the nature of the strain field and $1. For images of dislocations in which detail >25 A is required, the criterion is satisfactory provided that lsgl > 2 X 10e2 8-l. Using the weak beam technique the separation of partial dislocations has been measured in G-Al alloys [21], silicon [22], gold 1231) copper 124,251 and the separation of superlattice dislocations in Fe-AI alloys [26,27] and NiAl
1281. Weak beam images were obtained of fairly long and relatively straight dislocations in deformed and partially annealed Zr,Al using {220} reflections and with 1~~1 in the region 1.6 X lop2 to 2.3 X 1O-2 8-l. This corresponded to taking the weak beam images ing with the reflection ng satisfied where n was not necessarily integral but varied over the range 3 to 4. The exact value of lssl for a weak beam image was obtained from the position of the Kikuchi line in the selected area diffraction pattern. measurements of the separation
in Zr,Al
into partial
distocations.
I:or (a) and (b 1:
Aobs of the partial dislocations were obtained for dislocations where g was parallel to b in which case both partial dislocations were visible and in good contrast I as shown in fig. 12. The measurements were made at many points along the dislocation line and Aobs is the mean value of these measurements for those regions of the dislocation line which were at the same orientation. The Burgers vectors of the dislocations were determined by setting up strong two-beam diffraction conditions and noting the refections for which the dislocations were either in or out of contrast. Following the method outlined by Cockayne 1291. the true separation A between the partial dislocations was caIculated from the observed separation Aobs. The values of A obtained are plotted in fig. 13 as a function of the angle /3 between the line direction and the Burgers vector. The majority of the examined dislocations were closer to the screw orientation than to the edge orientation; hence the preponderance of points in fig. 13 at low 0 values. A value for the stacking fault energy y can be obtained by comparing theoretical curves of the partial dislocation width as a function of orientation for various values of-y with the experimental data. An accur. ate determination of the stacking fault energy by this
the relationship between the radius of curvature p and the stacking fault energy y can be expressed as:
method requires sufficient information of the elastic constants in the material in order to perform a calculation using anisotropic elasticity theory. Unfortunately, at present, insufficient information is available for Zr,Al. An estimate of the stacking fault energy can be obtained, however, from isotropic elasticity theory; in particular, using the relationship [ 191
x
+ (0.,04(~)+
0 SCREW
IO
20
I
I
30
ORIENTATION
VO OF
o.24(&)cos20)log10P,e;
where b, is the magnitude of the Burgers vector of the partial dislocation, (Yis the angle between b, and the tangent to the dislocation line at the nodal point, and E is a core parameter usually taken as equal to b,. The radius of curvature was measured at 12 nodes in a symmetrical network of screw orientation and the stacking fault energy was determined using the above relationship. The measurements for the the two different types of nodes (i.e. encompassing either an intrinsic I or an extrinsic E stacking fault) were initially treated separately and showed that -rr X YE as the two values were within 2 erg*cmp2 of one another which is well within the experimental uncertainty of the measurements. The calculated value of the stacking fault energy obtained by averaging all of the measurements was 81 + 5 erg.cmF2.
where b is the magnitude of the total Burgers vector of the disloqation, /J is the shear modulus and v is Poisson’s ratio. Based on the measurements of Schulson and Turner [30], p = 4.9 X 1011 dyn*cmm2 (49 GN*m-2) and u = 0.34. As shown in fig. 13, the experimental points fall in a band between the theoretical curves (shown dotted) plotted for y = 70 erg*cm-2 and y = 90 erg*cmW2. An estimate of the stacking fault energy can also be obtained from measurements of the radius of curvature of extended nodes in dislocation networks. According to the analysis of Brown and Thiilen [ 3 11, based upon the approximation of isotropic elasticity, I
cos 2o
@;
* = pb2(2 - v) 8ny( 1 - V) (
I
= 0.27 - 0.08 &
I
I
50
60
OISLOCATION
LINE
I
I
70
80
I/??
90 EOGE
Fig. 13. A plot of partial dislocation separation A as a function of orientation of the dislocation line. Experimentally determined values are plotted as open circles and the theoretical curves corresponding to y = 70 and 90 erg - cme2 are shown dotted.
154
L.M. Howe et al., Ordered h3Al
4. Conclusions ( 1) Zr,Abis an orderec’ fee alloy of the Ll, type which appears to be very stable thermally as it has not been possible to disorder Zr,Al by quenching. It is possible, however, to disorder Zr,Al by irradiation, (2) Planar defects, which possibly form during the transformation of Zr,Al from other phases, were present in annealed and in quenched Zr,Al. (3) In Zr3Al the superlattice dislocations are extended (i.e. they consist of an intrinsic stacking fault bounded by partial dislocations). The dissociation of the superlattice dislocation (b = (110)) occurs as follows:
(4) During high-temperature annealing of deformed material dislocation networks were produced in which all of the dislocation nodes were extended. In order for Such a network to be stable in a fee lattice intrinsic and extrinsic stacking faults must alternate at the nodes. (5) The stacking fault energy in Zr,Al was estimated to be 70-90 erg-cm-*.
Acknowledgements The advice and technical assistance provided by J.F. Watters in electropolishing Zr,Al in the initial stages of the program is gratefully acknowledged. We are also grateful to G.J.C. Carpenter for performing the electron bombardment experiments in the highvoltage electron microscope at Harwell.
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J. Nucl. Mater. 50 (1974) 127. and M. Hansen, T.A.S.M. (Met. Trans.) 374. J.H. Mallery, Trans. AIME 203 (1955)
[4] M. PGtzschke and K. Schuberl, Z. Metallk. 53 (1967) 541; [S] P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashleq and M.J. Whelan, Electron Microscopy of Thin Crystals (Butterworths, London, 1965) pp. !56- 194, 222 275 [6] A. Art, R. Gevers and S. Amelinckx, Phys. Stat. So!. 3 (1963) 697. 171 R. Cevers, A. Art and S. Amelinckx. Phyc. Stat. Sol. .:
(1963) 1563. E.M. Schulson, private commumcation. M.J. Marcinkowski, N. Brown and R.M. Fisher, Acra Met. 9 (1961) 129. J.M. Oblak and B.H. Kear, Electron Microscopy and Structure of Materials (University of California Press. Berkeley, 1971) p. 566. 1111 M.J. Marcinkowski and D.S. Miller, Phil. Mag. 6 (1961 i 871. [I21 S. Takeuchi and E. Kuramoto, Acta Met 21 (1973) 415 [I31 A. Howie and M.J. Whelan, Proc. Roy. Sot. A267 (1962) 206. 1141 J.M. Silcock and W.J. Tunstall, Phil. Mag. 10 ( 1964) 361. I151 N. Thompson, Proc. Phys. Sot. Land. B 66 (1953) 481. [I61 M.H. Loretto, Phil. Mag. 10 (1964) 467; 12 (1965) 125. [I71 P.R. Swarm, Acta Met. 14 (1966) 76. [ISI P.C.J. Gallagher, Phys. Stat. Soiidi 16 (1966) 95. [I91 J.P. Hirth and J. Lothe, Theory of Dislocations (McGrawHill, New York, 1968) pp. 288.-333. 1201 D.J.H. Cockayne, I.L.F. Ray and M.J. Whelan, Phxl. Mag. 20 (1969) 1265. [*II D.J.H. Cockayne, I.L.!:. Ray and M.J. Whelan, Septrgmc (‘ongrks International de Microscopic I’lectroniquc, (irenoble, Vol. 2 (1970) p. 321. 1221 1.L.F. Ray and D.J.H. Cockaync, Proi. Roy Sot. I.ond. A 325 (1971)
543.
~231 M.L. Jenkins, Phil. Mag. 26 (1972) 747. 1241 W.M. Stobbs and C.H. Sworn, Phil. Mag. 24 (1972) 136.5. ~51 D.J.H. Cockayne, M.L. Jenkins and 1.L.F. Ray, Phil. Msg. 24 (1972)
1383.
1261 1.L.F. Ray, R.C. Crawford
and D.J.H. Cockayne. Phil. Mag. 21 (1970) 1027. v71 R.C. Crawford, I.L.F. Ray and D.J.H. Cockaync, PhII. Mag. 27 (1973) 1. 12x1 R.C. Campany, M.H. Loretto and R.E. Smallman, Re ported at a symposium on Weak Beams held at the Fifth European Congress on Electron Microscopy. liniversity (11’Manchester (1972) to be published. r*91 D.J.H. Cockayne, D. Phil. Thesis, Oxford University II 970). [301 L.M. Schulson and R.B. Turner, Private communication. [311 L.M. Brown and A.R. ThGlen. Disc. Faraday Sot. 38 (1964)
35.