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Dislocation substructure in single crystals of hexagonal Ag-Al oriented for prismatic slip
DISLOCATION
SUBSTRUCTURE IN SINGLE CRYSTALS OF HEXAGONAL A&-Al ORIENTED FOR PRISMATIC SLIP* P. R. OKAMOTOf
and G. THOMAS?
Single crystals of hexagonal Ag-33 at.% Al oriented for prismatic slip were strained in tension at various temperatures between 77’K and 500°K. Surface slip lines were examined by optical microscopy and the dislocation substructure was studied by transmission electron microscopy as a function of temperature and strain. Below 400°K all crystals deform by repeated yielding. The dislocation substructure consists of broad slip bands containing a high density of perfect, nonbasal-vacancy loops and clusters of helical dislocations aligned along the traces of prismatic planes. Above 400°K repeated yielding is not observed and t,he dislocation distribution is uniform. A correlation is found between the surface slip lines, the load drops in the stress-strain curves and the internal slip bands. The formation of loops in slip bands provide an explanation for the anomalous behavior of the critical resolved shear stress reported in earlier investigations of this alloy. SOUS-STRUCTURE DE DISLOCATIONS HEXAGONAL ORIENTES POUR
DANS DES MONOCRISTAUX DE Ag-Al LE GLISSEMENT PRISMATIQUE
Des monocristaux de Ag-33 at. y0 Al hexagonal orient& pour le glissement prismatique sont soumis a une deformation de traction a diverses temperatures comprises entre 77°K et 500°K. Les lignes de glissement en surface sont examin& en microscopic optique et la sous-structure de dislocations est etudiee en microscopic Blectroniquepar transmission en fonction de la temperature et de ia deformation. En-dessous de 400’K tons les oristaux se di?formenten presentant le phenomene de crochet de traction &p&e. La sous-structure de dislocations oonsiste en de larges bandes de glissement contenant nne forte densite de boucles de laeunes parfaites non sit&es dans le plan de base et des amas de dislocations en h&ice align&s le long des traces des plans prismatiques. Au-dessus de 400”K, on n’observe pas 1%phenomene de crochet de traction rep&e et la distribution de dislocations est uniforme. On trouve une correlation entre les lignes de glissement en surface, 18schutes de charge dans les courbes contrainte-deformation, et les bandes de glissement internea. La formation de boucles dans les bandes de glissement fournit une explication du comportement anormal de la eission critique reduite indiqut; par des recherches anterieures snr cet alliage. VERSETZUNGSSTRUKTUR IN EINKRISTALLINEN HEXAGONALEN AG-Al-KRISTALLEN IN ORIENTIERUNGEN FUR PRISMATISCHE GLEITUNG Einkristalle aus hexagonalem Ag-33 At.-% Al, orientiert ftir prismatisohe.Abgleitung, wurden bei verschiedenen Temperaturen zwischen 77°K und 500°K zugverformt. Oberfliichengleitlinien wurden lichtmikroskopisoh untersucht sowie die Versetzungsstruktur mittles Durchstrahlung im Elektronenmikroskop in Abhangigkeit von Temperatur und Dehnung. Unterhalb 400°K verformen sich alle Kristalle durch wiederholtes F&Ben. Die Versetzungsstruktur besteht aus breiten Gleitb&ndern mit einer hogen Diohte idealer, Niehtb~is-~erstellen.ringen und Agglomeraten van Spiralv8~etz~gen entlang der Spur von prismatisehen Ebenen. Oberhalb 400°K wird wi~erholtes FlieBen nicht beobachtet, und die Versetzungsve~eilung ist einheitlich. Es wird ein Zusammonhang gefnnden zwischen den Obe~~chengleitlinien, dem Lastabfall in der Verfestigungskurve und den inneren Gleitlinien. Die Bildung von Versetzungsringen in Gleitbandern gestattet eine Erklarnng des anomalen Verhaltens der kritischen Schubspannung, welches in friiheren -4rbeiten fiir diese Legierung gefunden wurde.
1. INTRODUCTION
In recent years much effort has been directed towards a better understanding of the mechanical properties of the 5 intermediate phases of the noble metals. These phases are solid solutions which have the hexagonal close packed structure and generally occur after the primary u solid solutions in the phase diagrams. Interest in the 6 phases centers not only on their unusually high strength but also on their potentialities for studying the effects introduced by a * Received November 25, 1966; revised January 19, 1967. t Inorganic Materials Research Division, Lawrence Radiation Laboratory and Department, of Mineral Technology, College of Engineering, University of California, Berkeley, California. ACTA METALLURGICA,
VOL. IS, AUGUST
1967
change in crystal structure and higher solute concentrations on the various strengthening mechanisms developed for the Msolid solutions.(l) In many respects the 5 Ag-33 at. y. Al alloy and the (12lO)(liOO) mode of slip is an ideal system for study from both an experimental and theoretical point of view. For example, since dislocations gliding on prismatic planes are not expected to be dissociat,ed and in view of the similarity of t,he effective volumes for silver and aluminum atoms, possible ambiguities in interpretation arising from Suzuki and Cottrell looking will be minimized. Furthermore, most 5 phases are stable over a wide composition range and form from the melt by a
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peritectic reaction. As a rule the two conditions lead to severe segregation problems when growing single crystals from the melt. However, in the 5 AgAl phase, the liquidus and solidus have practically the same solute composition, namely 33 at.% aluminum. consequently, single crystals of Ag-33 at. y0 Al can be grown with very uniform composition. In spite of the current interest in the 5 phases, transmission electron microscopy observations similar to those in deformed u solid solutions have not been reported. The purpose of this investigation was to carry out such observations on single crystals of the l-Ag-33 at. % Al phase. In particular, the dislocation distribution produced during first order prismatic slip has beenstudiedas a functionof temperature andstrain. Previous work on this alloy by Mote et aZ.@) showed that three rate controlling mechanisms can operate depending on test temperature. Their results together with the present data are shown in Fig. 1. Over region T the critical resolved shear stress (crss) decreases rapidly with temperature. More recent work by Rosen et aZ.f3) has suggested that prismatic slip in this region is controlled by the nucleation and growth of kinks in dislocations lying in Peierls potential troughs. Over region II the crss is independent of temperature and the strain rat.econtrolling mechanism has been ascribed to the destruction of short, range order(4) by the Fisher mechanism. Finally, over region III, slip is again controlled by a thermally activated mechanism and the crss for prismatic slip drops below that for basal slip. A satisfactory theory for region III has not yet been established. However, on the basis of the work by Howard et aZ.(b)the controlling mechanism has been tentatively ascribed to a diffusion controlled local disordering in the immediate vicinity of the dislocation.
0
100
200
300
400 T
500
600
700
800
fKl
Fra. 1. Effect of temperature on the critical resolved shear stress for prismatic and basal slip (after Mote’s)). Squares indicate values obtained during the present investigcttion.
VOL. TABLE
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1967
1. Chemical composition in weight peroent
Mark
Top
Middle
Bottom
Ag Mg cu Ca Ni Cr
88.95 0.001* 0.002
88.89 0.001 0.003 0.001* o-001* 0.001 0.002 B&l
88.92 0.001 0.002
z
o*&* 0.001 0.002 Bal
0.001+ 0.001 0.002 Ral
* Indicates less than
In spite of the thorough investigation on the nature of prismatic slip, there remains one anomalous experimental fact which has not been explained. In an attempt to ascertain whether disordering resulting from plastic deformation could be detected by a decrease in the crss in region II, Mote et aZ.@) prestrained their specimens at 77°K. After reloading and restraining in tension at 300”K, the crss was always identical with that obtained for well annealed crystals. This somewhat surprising result is inconsistent with the Fisher mechanism and implies either the absence of short range order or that very strong barriers to dislocations are formed on active slip planes forcing further slip to occur in undeformed regions of the crystal. Since X-ray diffraction data(*) on the degree of order in this system has confirmed the existence of short range order, barriers of some form should exist. One of the objects of this investigation was to look for such barriers. 2. EXPERIMENTAL
TECHNIQUES
Single crystal prismatic bars having the composition Ag-33 at.% Al and oriented such that the (1210) direction and the normal to the {liOO} plane were at 45 f 2’ to the tensile axis were grown by the techniques previously described by Mote et aZ.t2) Sections of the prismatic bar were then used as seed crystals from which single crystal strips with dimensions 10 x g x 0.025 in. were grown under argon. Finally, tensilespecimenswithdimensions2.25 x 8 x 0.025in. were spark cut from the single crystal strips. In order to remove the effects of spark cutting, the specimens were given a 15-min anneal at 900% then etched in a 40% nitric acid solution and finally electropolished to produce a smooth surface. After back reflection Laue X-ray photographs had been taken to confirm the initial orientation, the specimens were strained on an Instron Tensile Machine. The chemical analysis of the alloys used are given in Table 1. Special grips were designed to hold the specimen rigidly in place by two slide rods which screw into the upper grip and slide into the lower grip where they
OKAMOTO
AND
THOMAS:
DISLOCATION
could be clamped by set screws, The entire grip unit is then rigid and may be transferred to the tensile apparatus without introducing deformation prior to straining. High temperature tests were conducted with the specimen immersed in a constant tem~rature bath consisting of a molten mixture of sodium nitrate and sodium nitrite. Low temperature baths were either liquid nitrogen or liquid nitrogen-ethyl alcohol mixtures. Unless otherwise stated, all specimens were deformed at an unresolved strain rate of 1O-2 per min. Immediately after straining, the slip lines on the specimen were examined on a Zeiss Metallographic Microscope. Thin foils were then made by the window technique using the following electrolyte : Potassium Cyanide Sodium Hydroxide Silver Cyanide Potassium Carbonate Distilled Water
SUBSTRUCTURE
;
IN
HEXAGONBL
Ag-Al
1327
30 -
: \ 25r” - 202 E 3 152 2 IO(R ~~
(a)
77*K 2lO*K
ic1
300*u
i
400EK 500*K
r-
3.0 g 1.5 g 0.5 g 0.3 g 100 g
The polishing was carried out at temperatures slightly above the freezing temperature of the electrolyte ( -5°C). Optimum polishing conditions were obtained when using a potential of 3 V and a current density of 0.02 A/cm2. All transmission electron microscopy observations were made with a Siemens Elmiskop electron microscope operated at 100 kV and equipped with a Gatan double tilting stage. Some limi~tions are imposed on the ex~~ments due to problems arising from the electropolishing techniques. Most of the electrolytes tested during this investigation failed to polish surfaces which deviated more than 10 degrees from the basal plane. The electrolyte finally chosen was only of limited success in t,his regard. Consequently, most of the tensile specimens were so oriented that the large face was parallel to the basal plane. Although this particular orientation ensured a zero shear stress on the basal plane, it prevented a study of the dislocation dist‘ribution in all but (0001) sections. Moreover, in view of the particular symmetry of the (0001) orientation and the great many possible slip systems which can operate in h.e.p. crystals, unambiguous Burgers vector determinations are impossible to achieve with the available low order reflections. The reflections necessary for an unambiguous Burgers vector analysis are usually of higher order and are accessible only when the foil is in higher index orientations. Therefore, a preliminary study was made of the reciprocal space in the vicinity of the [OOOl] reciprocal lattice section in order to gain the necessary familiarity of the regions eon~ining these high index poles. The result of the preliminary investigation
FIG. 2. (a) Effect of test temperature on the form of tensile CLWV~R;(b) effect of unresolved strain rate on the form of the tensile curve et 300°K. q, = 10-z per min (schematic).
was the construction of a fully indexed [OOOl]Kikuchi map described elsewhere. w The map contains the poles of all the non-basal Burgers vectors commonly observed in h.e.p. crystals and provides, at a glance, all the reflections necessary for an unambiguous Burgers vector determination which lie within 20 degrees of the [OOOI]orientation. Since tilting experiments were controlled by following the Kikuchi bands, the foil orientation was known at all times. The c/a ratio was determined from the Kikuchi patterns and was observed to be 1.58. This value is consistent with that expected for the composition of the alloy (Table 1). 3. EXPERIMENTAL
RESULTS
3.1 ~~~~~-$~YU~~ GUrZteS Tensile tests were conducted at five different temperatures: 77’K, 210”K, 300”K, 4OO*K and 500°K. Figure 2 shows the temperature dependence of typical tensile curves. Repeated yielding was observed at all temperatures except at 500°K. All crystals, which deformed by repeated yielding, exhibited a pronounced initial yield drop followed by a series of smaller drops occurring more or less at a constant average stress level. No apparent plastic flow was observed prior to the initial yield. At 500°K plastic flow became more uniform and a small amount of plastic flow occurred before the load reached its maximum value.
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For comparative purposes the upper and lower critical resolved shear stresses were calculated for the most favorably oriented (l~lO}~l~OO~ slip system. The lower yield was arbitrarily taken to be t,he bottom of the initial yield drop. The values are in good agreement with those of Mote et uZ.(~) and have been plotted on the curve taken from their work (see Fig. 1). The repeated yielding phenomenon ~haracte~sti~ of dynamic strain aging has now been observed in single crystals of many f.c.c. and b.c.c. solid solutions of the noble metals. However, the only reported example of repeated yielding in single crystals of the [ phases has been that of Thorntonc7) who observed the effect in (J-13.5 at,.% Ge and CS-16.5 at.% Ge. He found that, depending on both temperature and strain rate, repeated yielding can be replaced by homogeneous yielding. Repeated yielding has also been observed in polycrystalline Ag-33 at. y0 Al@) but not in single crystals of the alloy. In the case of polycryst~lline Ag-33 at. y0 Al, the ~m~rature dependence of the yield stress paralleled that for prismatic slip in single crystals. However, the strain rate and temperature dependence of the repeated yielding was not investigated. Therefore, in order to obtain such information, specimens were deformed at 77”K, 210°K and 300°K at four different unresolved st,rain rates from 10 $ to 1O-2 8, where &, = 10m2per min. Except for the case at 77°K and 10 i, where fracture occurred almost immediately, repeated yielding was observed for all strain rates. Although the load drops increased somewhat at the highest strain rate, t.he only apparent change was due to the reduction in time scale, i.e. the load peaks appeared closer together with increasing strain rate. An example of the effect at 300°K is shown schematically in Fig. 2(b). The lack of dependence of repeated yielding on temperature and strain rate indicates that dynamical strain aging effects do not play an important role. The result is consistent with the small Cottrell locking effect expected for this alloy. 3.2 S&n line patterns Visual observations during the tensile tests showed that each load drop was associated with the appearance of a slip cluster across the gage section of the specimen. The initial clusters always occurred near one of the grips but they were soon followed by others at various points along the gage sections. The surface under observation was parallel to t.he basal plane, and, therefore, contained the primary (1210) slip direction. Consequently, the initial clusters were very faint and were observable only when viewed from certain critical angles.
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With increasing total strain,* a gradual transition occurred from a random formation of slip clusters to a preferential formation near already existzing ones, similar to slip band growth. This stage continued until the entire gage section was nearly covered by wide bands of slip clusters. Further slip beyond this stage apparently concentrates in one of the wide slip bands causing the specimen to begin literally slipping apart resulting in very large offsets at the edges of the specimen. [See Fig. 3(a).] Secondary slip lines usually make their appearance at this time. Tensile tests conducted at temperatures other than 300°K required the use of constant temperature baths so that visual observations could not be made during actual straining. However, metallographi~ examinations conducted immediately aft,er the test showed that crystals deformed at 210°K and 400’K had slip trace patterns which were very similar to those obtained at 300°K. Figures 3(a), (b), (c) and (d) are typical slip trace patterns after 35% strain at various temperatures. Specimens deformed at 500°K did not exhibit the coarse slip markings characteristic of repeated yielding. The slip traoes were instead rather diffuse and somewhat wavy. Specimens deformed at 77°K were not examined optically but were electropolished immediateIy after straining in order to minimize possible recovery effects. 3.3 The e#ect of temperature on the dislocation
distri-
bution
The dislocation density in as grown crystals was too low to be measured accurately. Most of the areas examined showed only a few isolated dislocations but occasionally twist boundaries were observed. The upper limit of the dislocation density in as grown cr.ystals was estimated to be approximately lO*/cm2. Figures 4-S are typical examples of the dislocation substructure in crystals strained 35% at various temperatures in regions I and II. Throughout this temperature range, the substructure consists of well defined slip bands and clusters of helical dislocations aligned along traces of the prismatic planes, i.e. along (l%O) directions. All slip bands contain loops which at 77*K are so small and dense that, as seen in Fig. 4, individual loops are not resolved. However, the loops and the helical nature of dislocations become readily apparent under strain contrast conditions. For example, Fig. 5 shows a higher magni~cation, dark field micrograph of an edge of the slip band in Fig. 4. In the vicinity of A, where the deviation from the Bragg condition is negative, the loops and the helical * Refers to unresolved strains crtlculated by assuming homogeneous deformation.
OKAMOTO
AND
THOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
(b)
(4 FIG. 3. Typical surface slip line p&terns on [OOOl]surfaces ofcrystsls &rained 35% at: (a) T = 300°K, note large offsets at the edge of the specimen; (b) T = 300°K; (c) T = 210“K; (cl) T = 400°K.
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FIG. 4. Slip bands in an [OOOl]foil strained 35% at 77’K. Each bend contains a high density of unresolved loops. Note offsets on primary slip baad and the clustering of helices between bands. Arrows represent 2 ,u.
dislooationr:; near the top foil surface produce strong strain cant r&St.(@) As can be seen, the diameter of the loops and helioes are of the same order of mag~tude- -a feature which was observed throughout regions I aknd II. Another common feature is the apparent I&ring of helices within a cluster, for example at B. Very frequently such pairs exhibited the abrupt change in background contrast oharacteristic of dip moles. Further evidence that the elusters
consist primarily of helical dipoles is prov id ed by the change in pair-spacing which occurred UPC 3n reversing the operating reflection and by the facii t)hat pairs were frequently observed in the process of pinching off rows of loops. One of the most striking features of . crystals strained in regions I and II is the re:markable similarity between the transmission elec tn 3n micrographs of the slip bands and the surfa ce slip line
OKAMOTO
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FIG. 5. Dark field micrograph of an edge of a slip band in Fig. 4. Note black-white strain contrast images of loops and helices near A and pairing of helices at B.
patterns.
The
similarity
is especially
clear
when
comparing Fig. 6(a) with the surface markings of the same specimen shown in Fig. 3(c). Both micrographs show
the
large
(l2lO){liOO}
that the surface load
in the
offsets
suffered
by
slip bands and provide slip lines which
stress-strain
curves
the
primary
strong evidence
accompanied are direct
each mani-
festations of the internal slip bands. A glance at Figs. 4-8 shows that over regions I and II, the changes in the dislocation distribution with increasing temperature is primarily one of scale only. The average spacing between slip bands tends to increase at higher temperatures while the relative number of helical dislocations
between bands tend to
decrease.
For example,
at 77”K,
the primary
slip
bands in Fig. 4 are very closely spaced and tend t’o appear as a single broad band. Also the number of clusters of helices is very high and as seen near t’he top left corner of Fig. 4, they tend to be evenly spaced. At 210”K, Fig. 6(a) clearly shows an apparent increase in the interband spacing along with a noticeable decrease in the number of helices between slip bands. Also the average size of the loops has increased to the point where they can be resolved individually as black dots. At 300”K, Fig. 7 shows that the interband regions are almost free of helical clusters while the loops have grown large enough to be resolved as double-arc 10ops.(~s) Figure 7 also shows another
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FIG. 7. Slip bands in an [OOOl] foil strained 35%
feature
of the slip bands.
arrays of steeply
inclined
edge of each band.
These
are the coplanar
dislocations
seen near the
Since the foil orientation
of Fig. 7
SUBSTRUCTURE
at 300°K.
IS
Note high density of double-arc
repeated
yielding
distribution in Fig. 9.
Ag-AI
HEXAGONAL
is not observed.
1333
loops.
The dislocation
in such cryst,als is always uniform as eeen
is very near [OOOl], the array consists predominantly of edge dislocations
gliding
on {liOO}
planes.
Such
3.4 The eSfect of strain on the dislocation distribution
coplanar arrays are never observed among the clusters of helical dislocations. At 400”K, the loops still
strains slip lines tend to cluster around
cluster in well defined
but as seen in Fig. 8,
ones.
for helices to be found
electron micrographs
bands,
there is an increasing tendency
It was mentioned
in Section 3.2 that at higher total pre-existing
The same effect is observed in the transmission of slip bands.
For example,
at
in the same region as the loops rather than in between
210”K,
bands. Also the diameters have greatly increased.
The dislocation distribution in crystals strained at temperatures above region II reflect the radical change in the mechanical behavior observed at lower temperatures. In addition to the rapid decrease in the crss,
50% strain respectively, clearly shows a widening of the slip bands and a decrease in the interband spacing with increasing strain. Figures 7 and 10(a) show a similar change at 300°K. The effect of increasing strain therefore appears to have the same effect as a decrease in the deformation temperature since both
the crystals deform homogeneously
tend to increase the density of slip bands and helices.
of the loops
and helices
in the sense that
Figs. 6(a) and (b) corresponding
to 35%
and
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Fra. 8. Slip band in 8x1[OOOl]foil strained 35% at 400°K.
3.5 Burgersvector de~r~~~~ons Figure 10(a) shows a slip band in au [OOOl] foil with all loops in contrast for g(2iiO). Figure 10(b) shows the loops out of contrast for g(ZOZ0). Since the loops do not vanish with the other two equivalent (2200) reflections their Burgers vector must be one of --the following : j[1210], &[1213] or @Y&3]. The above ambiguity can be eliminated with a minimum of tilting by use of Kikuchi maps.@) Such maps provide one of the most effective means of controlling the tilting of’ the foil and therefore, allow preselected orientations and reflections to be obtained very rapidly. The 12021) Kikuchi bands were selected to eliminate the above ambiguity since, with respect to the [OOOl] orientation, they are the nearest of the low order Kikuchi bands which pass through the (1120) but not through the (1123) zone axes. Such contrast experiment@) have shown that all dislocations,
15,
1967
Note mingling of loops and heliees.
including the loops, have Burgers vectors of the form &(llzO). In fact, except for the loops, all dislocations in a cluster or slip band aligned along a particular (1120) direction always have the corresponding &(1120) Burgers vector. On the other hand, the loops have a unique g(l%O) Burgers vector in the sense that it is the same for all loops regardless of the particular (1120) direction of the band in which they form. For example, Fig. 1l(a) shows two interesting slip bands whose loops vanish in Fig. 11(b) for g(2021). Therefore, loops -- in both bands have the same Burgers vector e.g. 15[1210] while other dislocations have Burgers vectors corresponding to the (1120) direction of their respective slip band. Some loops do not vanish with the vast majority, for example those at A. However such loops have been pinched off from screw dipoles and have the same Burgers vector as the parent dislocation.
OKAMOTO
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THOMAS:
DISLOCATION
SUBSTRUCTURE
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Ag-Al
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FI:o. 9. Typical disloca,tion distnibution in [OOOl]foil strained 36i”/c at 500°K. Note absence of slip band structure
3.6 Dislocation
distribution with slip bands
Since most of the foils examined in this report were in or very near the [OOOl] orientation, the (liO0) slip planes are viewed edge on. Consequently, it is difficult to obtain an accurate picture of the spatial distribution of dislocations in the slip bands. However, when the loops are out of contrast the grosser features of the distribution becomes apparent. Figure IO(b) shows that many dislocations are in the form of coplanar arrays mentioned earlier or in clusters of heavily eusped screw dislocations. A slip band containing multiple arrays is shown in Figs. 12(a) and (b). The dislocations in a given array appear to bow out between cusps in the same direction and indicate that the arrays consist of dislocations of the same sign. Since most of the dislocations have a large edge component, the cusps were probably formed by dislocationloop interactions. Since the foil orientation of Figs. 10 and 12 is very near [OOOI],the projected width of some of the arrays is too large for dislocations to be gliding on (liOO> planes. However, since the arrays cut the foil surfaces along (1210) directions their glide plane must be of the form {IOT I}. The glide plane is thought to be the {lOIll plane since this assumption leads to reasonable estimates for the foil thickness, i.e., in the range of 3500 A4500 A. Finally, it is of interest to note that the arrays of
steeply inclined dislocations observed in slip bands are never seen among the clusters of helical dislocations. Therefore, the large offsets produced by slip bands but not by the clusters (see Figs. 4 and 6) must be a direct result of the passage of thousands of dislocations comprising an array. However, the fact that helices are also observed in slip bands strongly suggests that the cluster of helices act as nuclei for slip bands. In order to obtain a view of the dislocation distribution in non-[00011 foils and to ensure that the peculiar distribution of loops and helioes is not a function of specimen shape, several crystals having the tensile orientation shown in Fig. 13(c) were also pulled in tension. Figure 13(a) is an example of the slip lines observed on the large face of a specimen strained 20% at 300°K and shows that cross slip onto the basal plane occurs very frequently. This feature was not observed in the surface markings of Fig. 3 since there the basal plane itself was the surface under observation. In foils taken from the large face of the specimen, screw dislocations gliding on the primary (liO0) slip planes will appear as short segments aligned along traces of the basal plane while pure edge dislocations will appear as very long dislocations lying along the [OOOl] direction. Unfo~unately, very few crystals with this orientation were successfully polished due to the limitations of the electropolishing solution
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SUBSTRUCTURE
IN
HEXAGONAL
Ag--Al
1337
FICJ.11. Intersecting slip bands in a foil strained 35% at 21O’K: (a) all loops in contrast; (b) loops in both slip bands out of contrast ; (c) part of Kikuchi map indicating orientation and reflections for (a) end (b).
described in Section 2. Nevertheless, typical of the limited area examined, Fig. 13(b) shows most of the expected features. For example, helical dislocations now appear as short segments aligned along traces of the basal planes and tend to cluster into bands along the projected widths of the primary (liO0)planes. The clustering effect is also observed for the loops, although not as well defined as in the case of [OOOI]
foils Also noticeably absent is the array of edge dislocations commonly observed in the slip bands in [OOOl]foils. However, this is not too surprising since the orientation of Fig. 13(c) is ideal for an edge dislocation to escape from the foil surface. This is not likely to happen in an [OOOl] foil since the geometry makes it impossible for an edge dislocation to escape at the foil edge. In any case, aside from the
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FIG. 12, Slip bands in an [OOOl]foil strained 45% at 210’K: (ta)loops in contrast; (b) wkh loops out of coplanar mrraysof heavily cusped dislocations.
absence of the edge dislocations, the distribution is consistent, with those observed on [OOOl] foils and is thus independent of the specimen shape. 3.7 Xrntureof the prismatic
hops
The nature of the loops, i.e., whether vacancy or interstitial, was determined by the usual tilting methodsol) Defining s the deviation parameter as positive when the Kikuchi line lies outside the diffraction spot of the operating reflection, the image of the loop will lie outside the actual loop position when the product (S - 6)s is positive and vice versa. The inclination of the loop plane is determined by noting the change in size after large angle tilting under constant diffraction conditions. Figure 14(a), (b) and (c) are a series of micrographs of the same loop band shown in Fig. 10. The corresponding reflections and orientations are shown in Fig. 14(d). In Fig. 10(b) the loops vanish for g(2020) so that the loops have the Burgers vector b = j--[1210]. Figure 14(a) and (b) show that the loops are in outside contrast for g(2110) and inside for g(2iTo), respectively. Since 8 is positive for all micrographs, the Burgers vector b of the loops must have the direction as indicated in Fig. 14.
contrastshowing
In order to determine the inclination of the loop plane relative to the electron beam, the foil was tilted as shown in Fig. 14(d) about 15” along the (2IiO) Kikuchi band to reach the [Oil43 orientation. As shown in Figs. 14(b) and (c), practically all the loops have increased in size. The sense of tilt indicat’ed. in Figs. 14(c) and (d) shows that the loops lie on nonbasal planes. Therefore, the sense of inclination of the loops and the contrast experiments of Fig. 14 show that all loops are vacancy loops. In most cases, loops observed in specimens deformed at temperatures lower than 3QO’K were less than about 200 A dia., and are thus too small for the above techniques to be of value in determining their nature. In principle, it should be possible to uniquely determine the nature of small loops by strain contrast techniques.02Ja) However, when viewed under strain contrast conditions, the high density of loops within a slip band appear as a jumble of complex images. In many instances, it was possible to change the sense of the black-white image relative to the operating reflection for a given loop by changing any of a number of diffraction conditions. Consequently, it was not possible to determine uniquely the nature of loops in any of the slip bands observed at lower temperatures.
OKAMOTO
AND
THOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1339
TENSILE AXIS
FIG. 13. (a) Surface slip lines on an irrational face of a crystal strained 20% at 300°K; (b) dislocation distribution of Primary {llOO} slip plane is inclined about specimen in (a). Note helices and loops and absence of edge dislocations. 50" to the foil surface; (c) orientation of the tensile specimen shown in (a) end (b).
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(0)
(4 FIU. 14. Same ax-e&as in Fig. 10 showing loops for; (a) (gb)s > 0; (b) (gb)a < 0 and (c) after tilting approximately 15”. Note loops increase in size; (d) portion of the Kikuchi map mdicating the orientations and reflections and the direction of tilt.
OKAMOTO
AND THOMAS:
DISLOCATION
The difficulties of such experiments are discussed in detail elsewhere. Some small loops were observed between slip bands. By contrast experiments, these were shown to exist only at the top surface of the foil and are, therefore, due to ~lish~ng and/or ion bombardment and are not related to the deformation process.os) 4. DISCUSSION
4.1 dletastable arrangements The principle features to be discussed are the broad slip bands containing a high density of perfect prismatic loops and the long alusters of helical dislocations which are characteristic distributions in specimens deformed in regions I and II (see Fig. 1). The clusters of long helical dislocations have been shown to consist primarily of helical dipoles. Presumably they were initially screw dipoles which later transformed into he&es by climb, thereby losing most of their screw character. Such clusters of screw dipoles could be formed by the operation of sources on neighboring glide planes.04) If the distance between glide planes is y,,, then the screw part of the loops emitted by the sources will be unable to pass each other unless the applied stress exceeds ,ub/&ry,,. However, nearby screw dislocations of opposite sign tend to annihilate one another by cross slip. Whether such an event occurs depends critically on the distance ~parating the two dislocations and the crss of the cross slip plane. For the case of two screw dislocations of opposite sign gliding on neighboring prismatic planes, y0 apart, the force of attraction reaches a maximum when both lie on the same basal plane. Assuming that the screw dislocations are not extended, cross slip will occur only if the attractive stress wpb/2ny, exceeds the crss for basal slip. If we use for Ag-33 at.% Al the values 7s =I 7 x lo8 dyn/cm2 (see Fig. l), p = 2.89 x 10n dyn/cma(s) and b = 2.87 x lo-* cm, then cross slip will not occur unless y0 is less than about 200 A. The measured ~paration distance of most screw dipoles was found to lie between 500 and 200 A. As expected, dipoles having separations on the order of 200 A were usually those in the process of pinching off loops. See, for example, the dipoles at A in Figs. 11(a) and 12(a). Consequently, screw dipoles need not always annihilate and if many sources operate over a small volume of crystal, clustering of screw dislocations can occur with the probability that most of the dislocations will be paired off as dipoles.04) However, as pointed out by both Lio5) and Hazzledine,(16) two or more screw dipoles are not stable and would tend to repel each other unless held in place by a large friction
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1341
stress. Therefore the consistent observations of such metestable clusters over a wide temperature range is in accord with the conclusions of Rosen et a?.,@) that prismatic slip in Ag-33 at. % Al is controlled by the Peierls mechanism. Moreover, the fact that clusters are observed over both regions I and If suggests that the Peierls stress is still appreciable at room temperature. Thus, there appears to be some justification in the assumption made by Dorn and Rajnako’) in their theory of the Peierls mechanism, that the Peierls stress decreases only about linearly with increasing temperature. Although this assumption is inoonsistent with the Kuhlman-Wilsdorf ‘“uncertainty concept ” ,(la) it now appears to have a strong basis in fact.
The necessary barriers to slip proposed by Mote et aI.t2) have now been identified, namely the high density of loops within the slip bands. Theoretical calculations of Kroupa and Hirsch(lg) have shown that loops can be very effective barriers to glide dislocations; and the direct observations of Pricec20) have shown that in cadmium, a high density of loops can sufficiently harden a slip band so as to cause further slip to occur in undeformed regions of a crystal. Therefore, the fact that prestrain does not reduce the crss for prismatic slip in region II, is no longer an effective argument against the Fisher meohanism.(21) Since the alloy under investigation is known to be short range orderedt4) the Fisher mechanism@r) provides a natural explanation for the repeated yielding observed over regions I and II. Much of the work in disordering the crystal in the vicinity of the slip plane will be done by the first few dislocations. Therefore, the initial series of loops emitted by neighboring sources, which give rise to t#he long clusters of screw dislocations, could very well be responsible for the initial disordering. Further slip could then proceed in the same region at much lower stresses. Consequently, areas containing clusters represent “weak” regions in the crystal where further slip will most likely occur. Since the stress needed to produce the initial disordering is large, further slip will occur in bursts giving rise to a load drop and localized regions of intense slip, namely, the broad slip bands. Furthermore, such intense slip bursts are not blocked by usual barriers such as subgrain boundaries. (See for example Fig. 15.) The sequence of slip described above is consistent with the observation that large offsets as seen, for example, in Figs. 4 and 6, are produced by the broad slip bands, but not by the clusters of long screw
1342
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1967
Fm. 16. Slip band in an [OOOlJpenetrating a subgrain boundary.
OKAMOTO
AND
THOMAS:
DISLOCATION
dislocations. Such offsets must have been produced by the passage of many thousands of dislocations all of the same sign. Remnants of such dislocations were always observed in slip bands in the form of coplanar arrays of steeply inclined dislocations and, thus, provide direct evidence for the slip burst phenomenon. Furthermore, such arrays not only have the same Burgers vector as the clusters which precede it, but were also observed to be gliding on the {lOiO} plane or on one of its cross slip planes of the form {lOi Z}. Therefore, the sequence of slip also satisfies the conditions for maximum instability proposed by Washburn and Murty(22) to explain the repeated yielding phenomenon in pure copper .cz3)
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1343
et aZ.(26) the vacancy concentration produced during
such load drops is given approximately by C, N 1O-3 E. For a total strain of 35 %, the vacancy concentration is about 3 x 10e4. We can easily calculate the vacancy concentration needed to produce the high density of loops in a slip band from the equation : c, where
rrr%n
r = average loop radius b = Burgers vector of the loop n = average loop density.
If we take as an example the slip band of Fig. 16 corresponding to E = 35 ‘A, and assume a foil thick4.3 Formation of loops and he&es ness of 4500 A, we obtain a loop density on the order The vacancies required to account for the loops and of 1015loops/cm3. This value is a lower limit since only regions where loops were actually countable were helices are probably formed during plastic deformation used in its evaluation. The average loop radius was (<500”K) by any one or more of the many theoretical found to be 125 A. Therefore, using the values mechanisms described in the literature. However, then C,N2 x 10”’ since Ag-33 at. ‘A Al is an intermediate phase, one n - 1015, r N 125A, b-3& which is on the same order of magnitude predicted must also consider the possibility of vacancies from resistivity experiments. originating from a defect lattice. Since the observed vacancy concentration is on the It is well known, for example, that beyond certain order obtained from relatively fast quenching expericritical compositions many intermediate phases form ments, the vacancy condensation mechanism appears vacancy concentrations well in excess of their thermal to be an attractive one for explaining the presence of equilibrium value. On the basis of the theoretical the observed loops and helices. However, several work of Jones,lz4) the critical composition in [-AgAl, facts strongly suggest that the loops were not formed if it exists at all, should occur at Ag-31 at. % Al. by this mechanism. First of all, one would expect However, the lattice parameter measurements of Massalski and Cockayne(25) show that a sudden the condensation mechanism to produce basal loops having one of the following Burgers vectors: [OOOI], increase in the c/a ratio occurs at this composition Q[OOOl]or &(2023). In contrast to this, the loops have and continues to increase as the aluminum rich phase boundary is approached. Such a change would not be been shown to be non-basal and their Burgers vector expected if a defect lattice forms beyond the “critical” determined to be of the form &(1210). Secondly, composition of Ag-31 at. o/o Al. Furthermore, if one except for sign, all the loops have the same Burgers were to assume that a defect lattice formed in spite vector in both the primary and secondary slip bands. of the increase in c/a, then in order to maintain the Loops forming by a condensation of point defects critical electron concentration per unit cell up to the would not be expected to favor a single Burgers vector over its two equivalent ones unless the resolved shear composition Ag-33 at.% Al, a minimum vacancy concentration on the order of 10e2 is required. Since stress in a given band favors in some way the observed this concentration is about 100 times larger than the Burgers vector. However, it would then be difficult maximum theoretical concentration existing at the to explain why the loops have the same Burgers vector in both the primary and secondary slip bands. melting temperature for most metals, we can conclude Another possible explanation is that the loops were that the vacancies in Ag-33 at. % Al do not originate generated from the helices in the following manner. from a defect lattice. Once a cluster of screw dipoles “weakens” the crystal On the other hand, experiments have shown that sufficiently to trigger a slip burst the point defects an unusually large number of point defects are created in specimens which deform by repeated yielding.(26s27) which are generated can be absorbed by the screw dislocations thus transforming the clusters into In these experiments, the rate of creation of vacancies helical dipoles. If the original separation of the screw is determined by measuring the decay rate of resistivity dipoles was sufficiently small, the corresponding transients associated with load drops in crystals helical dipole could interact to produce loops. The deforming by repeated yielding. According to Blewitt
ACTA
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1967
FIG. 16. Slip band in an [OOOl]foil strained 35% at 300°K.
hypothesis
that
the
clusters
of helices
act
as the
nuclei for the band of loops would not only explain
heat to raise the temperature
in the slip bands.
course
an absolute
bulk
diffusion
why the number of slip bands and clusters of helices
since Weertman(2sj
per unit area increase in the same sense with temper-
helices
ature and strain but also why the diameter
locations
loops
and helices
are always
of the
of the same order of
magnitude. However,
the preceding explanation is unsatisfacFirst of all, the transformation
is not
Of
necessity
and de Wit(2s) have shown that
can be generated
from
initially
at very low temperatures
However,
their
important
here since it predicts that helices will form
preferentially
mechanism
straight dis-
by pipe diffusion.
from
is not
dislocations
believed
to
predominantly
be in
tory on several points.
edge rather than screw character
of screw to helical dislocations requires diffusion of vacancies generated by plastic deformation. Since
observations show exactly the reverse. Secondly, if loops were generated from helical dipoles then they should have the same Burgers vector as the parent
loops and helices were observed in crystals strained at temperatures where bulk diffusion is negligible it seems improbable that such a transformation can occur during each load drop in the stress-strain curve unless the intense localized slip generates sufficient
while experimental
dipole which is clearly not the case for the vast majority of the loops observed in the slip bands. is
Although the mechanism of formation of the loops not clearly understood, their presence must
OKAMOTO
AND
THOMAS:
DISLOCATION
undoubtedly cause severe work hardening of the slip bands and therefore provides an explanation for the anomalous behavior of the critical resolved shear stress for prismatic slip reported by Mote et a2.(21 5. CONCLUSIONS
Single crystals of hexagonal Ag-33 at. % Al oriented for prismatic slip deformed by repeated yielding in regions I and II. In this temperature range the dislocation distribution is characterized by : (a) broad slip bands containing a high density of perfect, non-basal vacancy loops and (b) clusters of long helical dislocations. Both the slip bands and clusters lie along (1210) directions. 2. Except for the loops, all dislocations in slip bands lying parallel to a particular (l%O) direction have the corresponding +(l??lO) Burgers vector. On the other hand, the loops have a unique &I210> Burgers vector in the sense that it is the same for all loops regardless of the particular (l%O) slip band in which they are formed. 3. For a constant total strain, the effect of increasing temperature is to increase the average spacing between slip bands. An increase in total strain produces the same effect as a decrease in the deformation temperature. 4. The high density of loops serve as barriers to glide dislocations proposed by Mote et al.@) to explain the anomalous behavior in the critical resolved shear stress for prismatic slip. 5. Beyond region II, the repeated yielding effect is not observed and the dislocations are uniformly distributed. 1.
ACKNOWLEDGMENTS
This research was conducted as part of the activities of the Inorganic Materials Research Division of the Lawrence Radiation Laboratory of the University of California, Berkeley, and was done under the auspices of the U.S. Atomie Energy Commission. The authors express their appreciation of this eontinued suppofi
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1345
of their research. One of us (P. R. Okamoto) is grateful to the National Science Foundation for the award of a Traineeship. We wish to thank Professor J. E. Dorn for valuable discussions. REFERENCES 1. P. A. FLIXX,Strengthening M~han~~~~ in Sol&%, p. 17. A.S.M. (1962). 2. J. D. MOTE, K. TANAKA and J. E. DORN, Trams. Met. Sot. AIME 221, 856 (1961). 3. A. ROSEN, J. D. MOTE and J. E. DORN, Trans. filet. Sot. AIME 230. 1070 (1964). 4. J. P. NE&ANN, &ta set. 10, 984 (1962). 5. E. HOWARD, W. BARMORE,J. D. MOTE and J. E. DORN, Trans. Met. Sot. AlAlE 227, 1061 (1963). 6. P. R. OKAMOTO, E. LEVINE and G. THOMAS,J. appl. Phys. 33, 289 (1967). 7. P. H. TEO&NTON, Phil. Mag. 3, 2013 (1963). 8. K. TANAKA and J. D. MOTE, UCRL-9992 (1961). 9. W. L. BELL and G. THOMAS, Phys. Status Solidi 12, 843 (1965). 10. G. THOMASand W. BELL, to be published in The PTOC. Ho?~o~~u Co@. on Lattice Defects 1965. 11. D. J. MAZEY, R. S.BARNES and A. HOWIE, Phil. Mug. 7, 1861(1962). For review seeG. THO~~AS,Thin Films,p. 227. A.S.M. (1964). 12. M. F. ASHBY and L. M. BROWN, Phil. Msg. 8,1063,1649 (1963). 13. W. L. BELL, D. M. MAHER and G. TEOMAS, Report Harwell Consultants Symposium on the Nature of Small Defect Clusters,Vol. 2, p. 314. H.M.S.O. (1966). 14. P. B. HIRSCE and J. S. LALLY, Phil. Mag. 12,595 (1965). 15. J. C. M. IA,&&ASS. Faraday Sot. 38, 123 (1964). 16. P. M. HAZZLEDINE,Discuss. Faraday Sot. Q8, 184 (1964). 17. J. E. DORN and S. RAJNAK, Trans. Met. Sot. AIME 230, 1052 (1964). 18. D. KURLMAN-W~LSDOR~,Phya. Rec. 120,773 (1960). 19‘ F. KROUPA andP. B. HIRSCH,Discuss. Faruday Sot. 33,4S 119641. 20. k. B.‘PRxz, ~l~tro~ M~ro~~py and St~e~th of Cry&& edited by G, THOMAS and J. WASKBUR~, D. * 41. Interscience (i963). 21. J. C. FISHER, Acta Met. 2, 9 (1954). J. WASHBURNand G. MURTY, J. appl. Phys. 87,266 (1966). Z: Z. S. BASIN~KI and P. J. JACKSON,Phys. Status Solidi 9, so5 (1965). 24. H. JONES, Proc. R. Sot. A147, 396 (1934). 26. T. B. MASSALSKI and B. COCKAYNE, Acta Met. 7, 762 (1959). 26. T. H. BLEWITT,R. P. COLTMAN and J. K. REDMAN, Report of The 1954 Conference on Defecta in Crystalline Solids, p. 369. Ph_m. Sot., London (1953). 27. J. M. ANDERSONand A. F. BROWN, Phys. Stats Solidi 12, 309 (1965). J. WEEBTMAN, Tram. Met. Sot. AIM&’ QQ7,1439 (1963). z: R. DEWIT, Fans. Met. Sot. AIME QQ7, 1443 (1963).
SUBSTRUCTURE IN SINGLE CRYSTALS OF HEXAGONAL A&-Al ORIENTED FOR PRISMATIC SLIP* P. R. OKAMOTOf
and G. THOMAS?
Single crystals of hexagonal Ag-33 at.% Al oriented for prismatic slip were strained in tension at various temperatures between 77’K and 500°K. Surface slip lines were examined by optical microscopy and the dislocation substructure was studied by transmission electron microscopy as a function of temperature and strain. Below 400°K all crystals deform by repeated yielding. The dislocation substructure consists of broad slip bands containing a high density of perfect, nonbasal-vacancy loops and clusters of helical dislocations aligned along the traces of prismatic planes. Above 400°K repeated yielding is not observed and t,he dislocation distribution is uniform. A correlation is found between the surface slip lines, the load drops in the stress-strain curves and the internal slip bands. The formation of loops in slip bands provide an explanation for the anomalous behavior of the critical resolved shear stress reported in earlier investigations of this alloy. SOUS-STRUCTURE DE DISLOCATIONS HEXAGONAL ORIENTES POUR
DANS DES MONOCRISTAUX DE Ag-Al LE GLISSEMENT PRISMATIQUE
Des monocristaux de Ag-33 at. y0 Al hexagonal orient& pour le glissement prismatique sont soumis a une deformation de traction a diverses temperatures comprises entre 77°K et 500°K. Les lignes de glissement en surface sont examin& en microscopic optique et la sous-structure de dislocations est etudiee en microscopic Blectroniquepar transmission en fonction de la temperature et de ia deformation. En-dessous de 400’K tons les oristaux se di?formenten presentant le phenomene de crochet de traction &p&e. La sous-structure de dislocations oonsiste en de larges bandes de glissement contenant nne forte densite de boucles de laeunes parfaites non sit&es dans le plan de base et des amas de dislocations en h&ice align&s le long des traces des plans prismatiques. Au-dessus de 400”K, on n’observe pas 1%phenomene de crochet de traction rep&e et la distribution de dislocations est uniforme. On trouve une correlation entre les lignes de glissement en surface, 18schutes de charge dans les courbes contrainte-deformation, et les bandes de glissement internea. La formation de boucles dans les bandes de glissement fournit une explication du comportement anormal de la eission critique reduite indiqut; par des recherches anterieures snr cet alliage. VERSETZUNGSSTRUKTUR IN EINKRISTALLINEN HEXAGONALEN AG-Al-KRISTALLEN IN ORIENTIERUNGEN FUR PRISMATISCHE GLEITUNG Einkristalle aus hexagonalem Ag-33 At.-% Al, orientiert ftir prismatisohe.Abgleitung, wurden bei verschiedenen Temperaturen zwischen 77°K und 500°K zugverformt. Oberfliichengleitlinien wurden lichtmikroskopisoh untersucht sowie die Versetzungsstruktur mittles Durchstrahlung im Elektronenmikroskop in Abhangigkeit von Temperatur und Dehnung. Unterhalb 400°K verformen sich alle Kristalle durch wiederholtes F&Ben. Die Versetzungsstruktur besteht aus breiten Gleitb&ndern mit einer hogen Diohte idealer, Niehtb~is-~erstellen.ringen und Agglomeraten van Spiralv8~etz~gen entlang der Spur von prismatisehen Ebenen. Oberhalb 400°K wird wi~erholtes FlieBen nicht beobachtet, und die Versetzungsve~eilung ist einheitlich. Es wird ein Zusammonhang gefnnden zwischen den Obe~~chengleitlinien, dem Lastabfall in der Verfestigungskurve und den inneren Gleitlinien. Die Bildung von Versetzungsringen in Gleitbandern gestattet eine Erklarnng des anomalen Verhaltens der kritischen Schubspannung, welches in friiheren -4rbeiten fiir diese Legierung gefunden wurde.
1. INTRODUCTION
In recent years much effort has been directed towards a better understanding of the mechanical properties of the 5 intermediate phases of the noble metals. These phases are solid solutions which have the hexagonal close packed structure and generally occur after the primary u solid solutions in the phase diagrams. Interest in the 6 phases centers not only on their unusually high strength but also on their potentialities for studying the effects introduced by a * Received November 25, 1966; revised January 19, 1967. t Inorganic Materials Research Division, Lawrence Radiation Laboratory and Department, of Mineral Technology, College of Engineering, University of California, Berkeley, California. ACTA METALLURGICA,
VOL. IS, AUGUST
1967
change in crystal structure and higher solute concentrations on the various strengthening mechanisms developed for the Msolid solutions.(l) In many respects the 5 Ag-33 at. y. Al alloy and the (12lO)(liOO) mode of slip is an ideal system for study from both an experimental and theoretical point of view. For example, since dislocations gliding on prismatic planes are not expected to be dissociat,ed and in view of the similarity of t,he effective volumes for silver and aluminum atoms, possible ambiguities in interpretation arising from Suzuki and Cottrell looking will be minimized. Furthermore, most 5 phases are stable over a wide composition range and form from the melt by a
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peritectic reaction. As a rule the two conditions lead to severe segregation problems when growing single crystals from the melt. However, in the 5 AgAl phase, the liquidus and solidus have practically the same solute composition, namely 33 at.% aluminum. consequently, single crystals of Ag-33 at. y0 Al can be grown with very uniform composition. In spite of the current interest in the 5 phases, transmission electron microscopy observations similar to those in deformed u solid solutions have not been reported. The purpose of this investigation was to carry out such observations on single crystals of the l-Ag-33 at. % Al phase. In particular, the dislocation distribution produced during first order prismatic slip has beenstudiedas a functionof temperature andstrain. Previous work on this alloy by Mote et aZ.@) showed that three rate controlling mechanisms can operate depending on test temperature. Their results together with the present data are shown in Fig. 1. Over region T the critical resolved shear stress (crss) decreases rapidly with temperature. More recent work by Rosen et aZ.f3) has suggested that prismatic slip in this region is controlled by the nucleation and growth of kinks in dislocations lying in Peierls potential troughs. Over region II the crss is independent of temperature and the strain rat.econtrolling mechanism has been ascribed to the destruction of short, range order(4) by the Fisher mechanism. Finally, over region III, slip is again controlled by a thermally activated mechanism and the crss for prismatic slip drops below that for basal slip. A satisfactory theory for region III has not yet been established. However, on the basis of the work by Howard et aZ.(b)the controlling mechanism has been tentatively ascribed to a diffusion controlled local disordering in the immediate vicinity of the dislocation.
0
100
200
300
400 T
500
600
700
800
fKl
Fra. 1. Effect of temperature on the critical resolved shear stress for prismatic and basal slip (after Mote’s)). Squares indicate values obtained during the present investigcttion.
VOL. TABLE
15,
1967
1. Chemical composition in weight peroent
Mark
Top
Middle
Bottom
Ag Mg cu Ca Ni Cr
88.95 0.001* 0.002
88.89 0.001 0.003 0.001* o-001* 0.001 0.002 B&l
88.92 0.001 0.002
z
o*&* 0.001 0.002 Bal
0.001+ 0.001 0.002 Ral
* Indicates less than
In spite of the thorough investigation on the nature of prismatic slip, there remains one anomalous experimental fact which has not been explained. In an attempt to ascertain whether disordering resulting from plastic deformation could be detected by a decrease in the crss in region II, Mote et aZ.@) prestrained their specimens at 77°K. After reloading and restraining in tension at 300”K, the crss was always identical with that obtained for well annealed crystals. This somewhat surprising result is inconsistent with the Fisher mechanism and implies either the absence of short range order or that very strong barriers to dislocations are formed on active slip planes forcing further slip to occur in undeformed regions of the crystal. Since X-ray diffraction data(*) on the degree of order in this system has confirmed the existence of short range order, barriers of some form should exist. One of the objects of this investigation was to look for such barriers. 2. EXPERIMENTAL
TECHNIQUES
Single crystal prismatic bars having the composition Ag-33 at.% Al and oriented such that the (1210) direction and the normal to the {liOO} plane were at 45 f 2’ to the tensile axis were grown by the techniques previously described by Mote et aZ.t2) Sections of the prismatic bar were then used as seed crystals from which single crystal strips with dimensions 10 x g x 0.025 in. were grown under argon. Finally, tensilespecimenswithdimensions2.25 x 8 x 0.025in. were spark cut from the single crystal strips. In order to remove the effects of spark cutting, the specimens were given a 15-min anneal at 900% then etched in a 40% nitric acid solution and finally electropolished to produce a smooth surface. After back reflection Laue X-ray photographs had been taken to confirm the initial orientation, the specimens were strained on an Instron Tensile Machine. The chemical analysis of the alloys used are given in Table 1. Special grips were designed to hold the specimen rigidly in place by two slide rods which screw into the upper grip and slide into the lower grip where they
OKAMOTO
AND
THOMAS:
DISLOCATION
could be clamped by set screws, The entire grip unit is then rigid and may be transferred to the tensile apparatus without introducing deformation prior to straining. High temperature tests were conducted with the specimen immersed in a constant tem~rature bath consisting of a molten mixture of sodium nitrate and sodium nitrite. Low temperature baths were either liquid nitrogen or liquid nitrogen-ethyl alcohol mixtures. Unless otherwise stated, all specimens were deformed at an unresolved strain rate of 1O-2 per min. Immediately after straining, the slip lines on the specimen were examined on a Zeiss Metallographic Microscope. Thin foils were then made by the window technique using the following electrolyte : Potassium Cyanide Sodium Hydroxide Silver Cyanide Potassium Carbonate Distilled Water
SUBSTRUCTURE
;
IN
HEXAGONBL
Ag-Al
1327
30 -
: \ 25r” - 202 E 3 152 2 IO(R ~~
(a)
77*K 2lO*K
ic1
300*u
i
400EK 500*K
r-
3.0 g 1.5 g 0.5 g 0.3 g 100 g
The polishing was carried out at temperatures slightly above the freezing temperature of the electrolyte ( -5°C). Optimum polishing conditions were obtained when using a potential of 3 V and a current density of 0.02 A/cm2. All transmission electron microscopy observations were made with a Siemens Elmiskop electron microscope operated at 100 kV and equipped with a Gatan double tilting stage. Some limi~tions are imposed on the ex~~ments due to problems arising from the electropolishing techniques. Most of the electrolytes tested during this investigation failed to polish surfaces which deviated more than 10 degrees from the basal plane. The electrolyte finally chosen was only of limited success in t,his regard. Consequently, most of the tensile specimens were so oriented that the large face was parallel to the basal plane. Although this particular orientation ensured a zero shear stress on the basal plane, it prevented a study of the dislocation dist‘ribution in all but (0001) sections. Moreover, in view of the particular symmetry of the (0001) orientation and the great many possible slip systems which can operate in h.e.p. crystals, unambiguous Burgers vector determinations are impossible to achieve with the available low order reflections. The reflections necessary for an unambiguous Burgers vector analysis are usually of higher order and are accessible only when the foil is in higher index orientations. Therefore, a preliminary study was made of the reciprocal space in the vicinity of the [OOOl] reciprocal lattice section in order to gain the necessary familiarity of the regions eon~ining these high index poles. The result of the preliminary investigation
FIG. 2. (a) Effect of test temperature on the form of tensile CLWV~R;(b) effect of unresolved strain rate on the form of the tensile curve et 300°K. q, = 10-z per min (schematic).
was the construction of a fully indexed [OOOl]Kikuchi map described elsewhere. w The map contains the poles of all the non-basal Burgers vectors commonly observed in h.e.p. crystals and provides, at a glance, all the reflections necessary for an unambiguous Burgers vector determination which lie within 20 degrees of the [OOOI]orientation. Since tilting experiments were controlled by following the Kikuchi bands, the foil orientation was known at all times. The c/a ratio was determined from the Kikuchi patterns and was observed to be 1.58. This value is consistent with that expected for the composition of the alloy (Table 1). 3. EXPERIMENTAL
RESULTS
3.1 ~~~~~-$~YU~~ GUrZteS Tensile tests were conducted at five different temperatures: 77’K, 210”K, 300”K, 4OO*K and 500°K. Figure 2 shows the temperature dependence of typical tensile curves. Repeated yielding was observed at all temperatures except at 500°K. All crystals, which deformed by repeated yielding, exhibited a pronounced initial yield drop followed by a series of smaller drops occurring more or less at a constant average stress level. No apparent plastic flow was observed prior to the initial yield. At 500°K plastic flow became more uniform and a small amount of plastic flow occurred before the load reached its maximum value.
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ACTA
METALLURGICA,
For comparative purposes the upper and lower critical resolved shear stresses were calculated for the most favorably oriented (l~lO}~l~OO~ slip system. The lower yield was arbitrarily taken to be t,he bottom of the initial yield drop. The values are in good agreement with those of Mote et uZ.(~) and have been plotted on the curve taken from their work (see Fig. 1). The repeated yielding phenomenon ~haracte~sti~ of dynamic strain aging has now been observed in single crystals of many f.c.c. and b.c.c. solid solutions of the noble metals. However, the only reported example of repeated yielding in single crystals of the [ phases has been that of Thorntonc7) who observed the effect in (J-13.5 at,.% Ge and CS-16.5 at.% Ge. He found that, depending on both temperature and strain rate, repeated yielding can be replaced by homogeneous yielding. Repeated yielding has also been observed in polycrystalline Ag-33 at. y0 Al@) but not in single crystals of the alloy. In the case of polycryst~lline Ag-33 at. y0 Al, the ~m~rature dependence of the yield stress paralleled that for prismatic slip in single crystals. However, the strain rate and temperature dependence of the repeated yielding was not investigated. Therefore, in order to obtain such information, specimens were deformed at 77”K, 210°K and 300°K at four different unresolved st,rain rates from 10 $ to 1O-2 8, where &, = 10m2per min. Except for the case at 77°K and 10 i, where fracture occurred almost immediately, repeated yielding was observed for all strain rates. Although the load drops increased somewhat at the highest strain rate, t.he only apparent change was due to the reduction in time scale, i.e. the load peaks appeared closer together with increasing strain rate. An example of the effect at 300°K is shown schematically in Fig. 2(b). The lack of dependence of repeated yielding on temperature and strain rate indicates that dynamical strain aging effects do not play an important role. The result is consistent with the small Cottrell locking effect expected for this alloy. 3.2 S&n line patterns Visual observations during the tensile tests showed that each load drop was associated with the appearance of a slip cluster across the gage section of the specimen. The initial clusters always occurred near one of the grips but they were soon followed by others at various points along the gage sections. The surface under observation was parallel to t.he basal plane, and, therefore, contained the primary (1210) slip direction. Consequently, the initial clusters were very faint and were observable only when viewed from certain critical angles.
VOL.
15,
1967
With increasing total strain,* a gradual transition occurred from a random formation of slip clusters to a preferential formation near already existzing ones, similar to slip band growth. This stage continued until the entire gage section was nearly covered by wide bands of slip clusters. Further slip beyond this stage apparently concentrates in one of the wide slip bands causing the specimen to begin literally slipping apart resulting in very large offsets at the edges of the specimen. [See Fig. 3(a).] Secondary slip lines usually make their appearance at this time. Tensile tests conducted at temperatures other than 300°K required the use of constant temperature baths so that visual observations could not be made during actual straining. However, metallographi~ examinations conducted immediately aft,er the test showed that crystals deformed at 210°K and 400’K had slip trace patterns which were very similar to those obtained at 300°K. Figures 3(a), (b), (c) and (d) are typical slip trace patterns after 35% strain at various temperatures. Specimens deformed at 500°K did not exhibit the coarse slip markings characteristic of repeated yielding. The slip traoes were instead rather diffuse and somewhat wavy. Specimens deformed at 77°K were not examined optically but were electropolished immediateIy after straining in order to minimize possible recovery effects. 3.3 The e#ect of temperature on the dislocation
distri-
bution
The dislocation density in as grown crystals was too low to be measured accurately. Most of the areas examined showed only a few isolated dislocations but occasionally twist boundaries were observed. The upper limit of the dislocation density in as grown cr.ystals was estimated to be approximately lO*/cm2. Figures 4-S are typical examples of the dislocation substructure in crystals strained 35% at various temperatures in regions I and II. Throughout this temperature range, the substructure consists of well defined slip bands and clusters of helical dislocations aligned along traces of the prismatic planes, i.e. along (l%O) directions. All slip bands contain loops which at 77*K are so small and dense that, as seen in Fig. 4, individual loops are not resolved. However, the loops and the helical nature of dislocations become readily apparent under strain contrast conditions. For example, Fig. 5 shows a higher magni~cation, dark field micrograph of an edge of the slip band in Fig. 4. In the vicinity of A, where the deviation from the Bragg condition is negative, the loops and the helical * Refers to unresolved strains crtlculated by assuming homogeneous deformation.
OKAMOTO
AND
THOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
(b)
(4 FIG. 3. Typical surface slip line p&terns on [OOOl]surfaces ofcrystsls &rained 35% at: (a) T = 300°K, note large offsets at the edge of the specimen; (b) T = 300°K; (c) T = 210“K; (cl) T = 400°K.
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ACTA
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FIG. 4. Slip bands in an [OOOl]foil strained 35% at 77’K. Each bend contains a high density of unresolved loops. Note offsets on primary slip baad and the clustering of helices between bands. Arrows represent 2 ,u.
dislooationr:; near the top foil surface produce strong strain cant r&St.(@) As can be seen, the diameter of the loops and helioes are of the same order of mag~tude- -a feature which was observed throughout regions I aknd II. Another common feature is the apparent I&ring of helices within a cluster, for example at B. Very frequently such pairs exhibited the abrupt change in background contrast oharacteristic of dip moles. Further evidence that the elusters
consist primarily of helical dipoles is prov id ed by the change in pair-spacing which occurred UPC 3n reversing the operating reflection and by the facii t)hat pairs were frequently observed in the process of pinching off rows of loops. One of the most striking features of . crystals strained in regions I and II is the re:markable similarity between the transmission elec tn 3n micrographs of the slip bands and the surfa ce slip line
OKAMOTO
AND
THOMAS:
DISLOCSTION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1331
FIG. 5. Dark field micrograph of an edge of a slip band in Fig. 4. Note black-white strain contrast images of loops and helices near A and pairing of helices at B.
patterns.
The
similarity
is especially
clear
when
comparing Fig. 6(a) with the surface markings of the same specimen shown in Fig. 3(c). Both micrographs show
the
large
(l2lO){liOO}
that the surface load
in the
offsets
suffered
by
slip bands and provide slip lines which
stress-strain
curves
the
primary
strong evidence
accompanied are direct
each mani-
festations of the internal slip bands. A glance at Figs. 4-8 shows that over regions I and II, the changes in the dislocation distribution with increasing temperature is primarily one of scale only. The average spacing between slip bands tends to increase at higher temperatures while the relative number of helical dislocations
between bands tend to
decrease.
For example,
at 77”K,
the primary
slip
bands in Fig. 4 are very closely spaced and tend t’o appear as a single broad band. Also the number of clusters of helices is very high and as seen near t’he top left corner of Fig. 4, they tend to be evenly spaced. At 210”K, Fig. 6(a) clearly shows an apparent increase in the interband spacing along with a noticeable decrease in the number of helices between slip bands. Also the average size of the loops has increased to the point where they can be resolved individually as black dots. At 300”K, Fig. 7 shows that the interband regions are almost free of helical clusters while the loops have grown large enough to be resolved as double-arc 10ops.(~s) Figure 7 also shows another
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1965
OKAMOTO
AND
THOMAS:
DISLOCATION
FIG. 7. Slip bands in an [OOOl] foil strained 35%
feature
of the slip bands.
arrays of steeply
inclined
edge of each band.
These
are the coplanar
dislocations
seen near the
Since the foil orientation
of Fig. 7
SUBSTRUCTURE
at 300°K.
IS
Note high density of double-arc
repeated
yielding
distribution in Fig. 9.
Ag-AI
HEXAGONAL
is not observed.
1333
loops.
The dislocation
in such cryst,als is always uniform as eeen
is very near [OOOl], the array consists predominantly of edge dislocations
gliding
on {liOO}
planes.
Such
3.4 The eSfect of strain on the dislocation distribution
coplanar arrays are never observed among the clusters of helical dislocations. At 400”K, the loops still
strains slip lines tend to cluster around
cluster in well defined
but as seen in Fig. 8,
ones.
for helices to be found
electron micrographs
bands,
there is an increasing tendency
It was mentioned
in Section 3.2 that at higher total pre-existing
The same effect is observed in the transmission of slip bands.
For example,
at
in the same region as the loops rather than in between
210”K,
bands. Also the diameters have greatly increased.
The dislocation distribution in crystals strained at temperatures above region II reflect the radical change in the mechanical behavior observed at lower temperatures. In addition to the rapid decrease in the crss,
50% strain respectively, clearly shows a widening of the slip bands and a decrease in the interband spacing with increasing strain. Figures 7 and 10(a) show a similar change at 300°K. The effect of increasing strain therefore appears to have the same effect as a decrease in the deformation temperature since both
the crystals deform homogeneously
tend to increase the density of slip bands and helices.
of the loops
and helices
in the sense that
Figs. 6(a) and (b) corresponding
to 35%
and
ACTA
1334
~ETALLU~~ICA,
VOL.
Fra. 8. Slip band in 8x1[OOOl]foil strained 35% at 400°K.
3.5 Burgersvector de~r~~~~ons Figure 10(a) shows a slip band in au [OOOl] foil with all loops in contrast for g(2iiO). Figure 10(b) shows the loops out of contrast for g(ZOZ0). Since the loops do not vanish with the other two equivalent (2200) reflections their Burgers vector must be one of --the following : j[1210], &[1213] or @Y&3]. The above ambiguity can be eliminated with a minimum of tilting by use of Kikuchi maps.@) Such maps provide one of the most effective means of controlling the tilting of’ the foil and therefore, allow preselected orientations and reflections to be obtained very rapidly. The 12021) Kikuchi bands were selected to eliminate the above ambiguity since, with respect to the [OOOl] orientation, they are the nearest of the low order Kikuchi bands which pass through the (1120) but not through the (1123) zone axes. Such contrast experiment@) have shown that all dislocations,
15,
1967
Note mingling of loops and heliees.
including the loops, have Burgers vectors of the form &(llzO). In fact, except for the loops, all dislocations in a cluster or slip band aligned along a particular (1120) direction always have the corresponding &(1120) Burgers vector. On the other hand, the loops have a unique g(l%O) Burgers vector in the sense that it is the same for all loops regardless of the particular (1120) direction of the band in which they form. For example, Fig. 1l(a) shows two interesting slip bands whose loops vanish in Fig. 11(b) for g(2021). Therefore, loops -- in both bands have the same Burgers vector e.g. 15[1210] while other dislocations have Burgers vectors corresponding to the (1120) direction of their respective slip band. Some loops do not vanish with the vast majority, for example those at A. However such loops have been pinched off from screw dipoles and have the same Burgers vector as the parent dislocation.
OKAMOTO
AND
THOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1335
FI:o. 9. Typical disloca,tion distnibution in [OOOl]foil strained 36i”/c at 500°K. Note absence of slip band structure
3.6 Dislocation
distribution with slip bands
Since most of the foils examined in this report were in or very near the [OOOl] orientation, the (liO0) slip planes are viewed edge on. Consequently, it is difficult to obtain an accurate picture of the spatial distribution of dislocations in the slip bands. However, when the loops are out of contrast the grosser features of the distribution becomes apparent. Figure IO(b) shows that many dislocations are in the form of coplanar arrays mentioned earlier or in clusters of heavily eusped screw dislocations. A slip band containing multiple arrays is shown in Figs. 12(a) and (b). The dislocations in a given array appear to bow out between cusps in the same direction and indicate that the arrays consist of dislocations of the same sign. Since most of the dislocations have a large edge component, the cusps were probably formed by dislocationloop interactions. Since the foil orientation of Figs. 10 and 12 is very near [OOOI],the projected width of some of the arrays is too large for dislocations to be gliding on (liOO> planes. However, since the arrays cut the foil surfaces along (1210) directions their glide plane must be of the form {IOT I}. The glide plane is thought to be the {lOIll plane since this assumption leads to reasonable estimates for the foil thickness, i.e., in the range of 3500 A4500 A. Finally, it is of interest to note that the arrays of
steeply inclined dislocations observed in slip bands are never seen among the clusters of helical dislocations. Therefore, the large offsets produced by slip bands but not by the clusters (see Figs. 4 and 6) must be a direct result of the passage of thousands of dislocations comprising an array. However, the fact that helices are also observed in slip bands strongly suggests that the cluster of helices act as nuclei for slip bands. In order to obtain a view of the dislocation distribution in non-[00011 foils and to ensure that the peculiar distribution of loops and helioes is not a function of specimen shape, several crystals having the tensile orientation shown in Fig. 13(c) were also pulled in tension. Figure 13(a) is an example of the slip lines observed on the large face of a specimen strained 20% at 300°K and shows that cross slip onto the basal plane occurs very frequently. This feature was not observed in the surface markings of Fig. 3 since there the basal plane itself was the surface under observation. In foils taken from the large face of the specimen, screw dislocations gliding on the primary (liO0) slip planes will appear as short segments aligned along traces of the basal plane while pure edge dislocations will appear as very long dislocations lying along the [OOOl] direction. Unfo~unately, very few crystals with this orientation were successfully polished due to the limitations of the electropolishing solution
1336
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METALLURGICA,
VOL.
15,
1967
OKAMOTO
AND
TIIOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag--Al
1337
FICJ.11. Intersecting slip bands in a foil strained 35% at 21O’K: (a) all loops in contrast; (b) loops in both slip bands out of contrast ; (c) part of Kikuchi map indicating orientation and reflections for (a) end (b).
described in Section 2. Nevertheless, typical of the limited area examined, Fig. 13(b) shows most of the expected features. For example, helical dislocations now appear as short segments aligned along traces of the basal planes and tend to cluster into bands along the projected widths of the primary (liO0)planes. The clustering effect is also observed for the loops, although not as well defined as in the case of [OOOI]
foils Also noticeably absent is the array of edge dislocations commonly observed in the slip bands in [OOOl]foils. However, this is not too surprising since the orientation of Fig. 13(c) is ideal for an edge dislocation to escape from the foil surface. This is not likely to happen in an [OOOl] foil since the geometry makes it impossible for an edge dislocation to escape at the foil edge. In any case, aside from the
ACTA
1338
METALLURGICA,
(4
VOL.
15,
196’7
(bf
FIG. 12, Slip bands in an [OOOl]foil strained 45% at 210’K: (ta)loops in contrast; (b) wkh loops out of coplanar mrraysof heavily cusped dislocations.
absence of the edge dislocations, the distribution is consistent, with those observed on [OOOl] foils and is thus independent of the specimen shape. 3.7 Xrntureof the prismatic
hops
The nature of the loops, i.e., whether vacancy or interstitial, was determined by the usual tilting methodsol) Defining s the deviation parameter as positive when the Kikuchi line lies outside the diffraction spot of the operating reflection, the image of the loop will lie outside the actual loop position when the product (S - 6)s is positive and vice versa. The inclination of the loop plane is determined by noting the change in size after large angle tilting under constant diffraction conditions. Figure 14(a), (b) and (c) are a series of micrographs of the same loop band shown in Fig. 10. The corresponding reflections and orientations are shown in Fig. 14(d). In Fig. 10(b) the loops vanish for g(2020) so that the loops have the Burgers vector b = j--[1210]. Figure 14(a) and (b) show that the loops are in outside contrast for g(2110) and inside for g(2iTo), respectively. Since 8 is positive for all micrographs, the Burgers vector b of the loops must have the direction as indicated in Fig. 14.
contrastshowing
In order to determine the inclination of the loop plane relative to the electron beam, the foil was tilted as shown in Fig. 14(d) about 15” along the (2IiO) Kikuchi band to reach the [Oil43 orientation. As shown in Figs. 14(b) and (c), practically all the loops have increased in size. The sense of tilt indicat’ed. in Figs. 14(c) and (d) shows that the loops lie on nonbasal planes. Therefore, the sense of inclination of the loops and the contrast experiments of Fig. 14 show that all loops are vacancy loops. In most cases, loops observed in specimens deformed at temperatures lower than 3QO’K were less than about 200 A dia., and are thus too small for the above techniques to be of value in determining their nature. In principle, it should be possible to uniquely determine the nature of small loops by strain contrast techniques.02Ja) However, when viewed under strain contrast conditions, the high density of loops within a slip band appear as a jumble of complex images. In many instances, it was possible to change the sense of the black-white image relative to the operating reflection for a given loop by changing any of a number of diffraction conditions. Consequently, it was not possible to determine uniquely the nature of loops in any of the slip bands observed at lower temperatures.
OKAMOTO
AND
THOMAS:
DISLOCATION
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1339
TENSILE AXIS
FIG. 13. (a) Surface slip lines on an irrational face of a crystal strained 20% at 300°K; (b) dislocation distribution of Primary {llOO} slip plane is inclined about specimen in (a). Note helices and loops and absence of edge dislocations. 50" to the foil surface; (c) orientation of the tensile specimen shown in (a) end (b).
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VOL.
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1967
(0)
(4 FIU. 14. Same ax-e&as in Fig. 10 showing loops for; (a) (gb)s > 0; (b) (gb)a < 0 and (c) after tilting approximately 15”. Note loops increase in size; (d) portion of the Kikuchi map mdicating the orientations and reflections and the direction of tilt.
OKAMOTO
AND THOMAS:
DISLOCATION
The difficulties of such experiments are discussed in detail elsewhere. Some small loops were observed between slip bands. By contrast experiments, these were shown to exist only at the top surface of the foil and are, therefore, due to ~lish~ng and/or ion bombardment and are not related to the deformation process.os) 4. DISCUSSION
4.1 dletastable arrangements The principle features to be discussed are the broad slip bands containing a high density of perfect prismatic loops and the long alusters of helical dislocations which are characteristic distributions in specimens deformed in regions I and II (see Fig. 1). The clusters of long helical dislocations have been shown to consist primarily of helical dipoles. Presumably they were initially screw dipoles which later transformed into he&es by climb, thereby losing most of their screw character. Such clusters of screw dipoles could be formed by the operation of sources on neighboring glide planes.04) If the distance between glide planes is y,,, then the screw part of the loops emitted by the sources will be unable to pass each other unless the applied stress exceeds ,ub/&ry,,. However, nearby screw dislocations of opposite sign tend to annihilate one another by cross slip. Whether such an event occurs depends critically on the distance ~parating the two dislocations and the crss of the cross slip plane. For the case of two screw dislocations of opposite sign gliding on neighboring prismatic planes, y0 apart, the force of attraction reaches a maximum when both lie on the same basal plane. Assuming that the screw dislocations are not extended, cross slip will occur only if the attractive stress wpb/2ny, exceeds the crss for basal slip. If we use for Ag-33 at.% Al the values 7s =I 7 x lo8 dyn/cm2 (see Fig. l), p = 2.89 x 10n dyn/cma(s) and b = 2.87 x lo-* cm, then cross slip will not occur unless y0 is less than about 200 A. The measured ~paration distance of most screw dipoles was found to lie between 500 and 200 A. As expected, dipoles having separations on the order of 200 A were usually those in the process of pinching off loops. See, for example, the dipoles at A in Figs. 11(a) and 12(a). Consequently, screw dipoles need not always annihilate and if many sources operate over a small volume of crystal, clustering of screw dislocations can occur with the probability that most of the dislocations will be paired off as dipoles.04) However, as pointed out by both Lio5) and Hazzledine,(16) two or more screw dipoles are not stable and would tend to repel each other unless held in place by a large friction
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1341
stress. Therefore the consistent observations of such metestable clusters over a wide temperature range is in accord with the conclusions of Rosen et a?.,@) that prismatic slip in Ag-33 at. % Al is controlled by the Peierls mechanism. Moreover, the fact that clusters are observed over both regions I and If suggests that the Peierls stress is still appreciable at room temperature. Thus, there appears to be some justification in the assumption made by Dorn and Rajnako’) in their theory of the Peierls mechanism, that the Peierls stress decreases only about linearly with increasing temperature. Although this assumption is inoonsistent with the Kuhlman-Wilsdorf ‘“uncertainty concept ” ,(la) it now appears to have a strong basis in fact.
The necessary barriers to slip proposed by Mote et aI.t2) have now been identified, namely the high density of loops within the slip bands. Theoretical calculations of Kroupa and Hirsch(lg) have shown that loops can be very effective barriers to glide dislocations; and the direct observations of Pricec20) have shown that in cadmium, a high density of loops can sufficiently harden a slip band so as to cause further slip to occur in undeformed regions of a crystal. Therefore, the fact that prestrain does not reduce the crss for prismatic slip in region II, is no longer an effective argument against the Fisher meohanism.(21) Since the alloy under investigation is known to be short range orderedt4) the Fisher mechanism@r) provides a natural explanation for the repeated yielding observed over regions I and II. Much of the work in disordering the crystal in the vicinity of the slip plane will be done by the first few dislocations. Therefore, the initial series of loops emitted by neighboring sources, which give rise to t#he long clusters of screw dislocations, could very well be responsible for the initial disordering. Further slip could then proceed in the same region at much lower stresses. Consequently, areas containing clusters represent “weak” regions in the crystal where further slip will most likely occur. Since the stress needed to produce the initial disordering is large, further slip will occur in bursts giving rise to a load drop and localized regions of intense slip, namely, the broad slip bands. Furthermore, such intense slip bursts are not blocked by usual barriers such as subgrain boundaries. (See for example Fig. 15.) The sequence of slip described above is consistent with the observation that large offsets as seen, for example, in Figs. 4 and 6, are produced by the broad slip bands, but not by the clusters of long screw
1342
ACTA
METALLURGICA,
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1967
Fm. 16. Slip band in an [OOOlJpenetrating a subgrain boundary.
OKAMOTO
AND
THOMAS:
DISLOCATION
dislocations. Such offsets must have been produced by the passage of many thousands of dislocations all of the same sign. Remnants of such dislocations were always observed in slip bands in the form of coplanar arrays of steeply inclined dislocations and, thus, provide direct evidence for the slip burst phenomenon. Furthermore, such arrays not only have the same Burgers vector as the clusters which precede it, but were also observed to be gliding on the {lOiO} plane or on one of its cross slip planes of the form {lOi Z}. Therefore, the sequence of slip also satisfies the conditions for maximum instability proposed by Washburn and Murty(22) to explain the repeated yielding phenomenon in pure copper .cz3)
SUBSTRUCTURE
IN
HEXAGONAL
Ag-Al
1343
et aZ.(26) the vacancy concentration produced during
such load drops is given approximately by C, N 1O-3 E. For a total strain of 35 %, the vacancy concentration is about 3 x 10e4. We can easily calculate the vacancy concentration needed to produce the high density of loops in a slip band from the equation : c, where
rrr%n
r = average loop radius b = Burgers vector of the loop n = average loop density.
If we take as an example the slip band of Fig. 16 corresponding to E = 35 ‘A, and assume a foil thick4.3 Formation of loops and he&es ness of 4500 A, we obtain a loop density on the order The vacancies required to account for the loops and of 1015loops/cm3. This value is a lower limit since only regions where loops were actually countable were helices are probably formed during plastic deformation used in its evaluation. The average loop radius was (<500”K) by any one or more of the many theoretical found to be 125 A. Therefore, using the values mechanisms described in the literature. However, then C,N2 x 10”’ since Ag-33 at. ‘A Al is an intermediate phase, one n - 1015, r N 125A, b-3& which is on the same order of magnitude predicted must also consider the possibility of vacancies from resistivity experiments. originating from a defect lattice. Since the observed vacancy concentration is on the It is well known, for example, that beyond certain order obtained from relatively fast quenching expericritical compositions many intermediate phases form ments, the vacancy condensation mechanism appears vacancy concentrations well in excess of their thermal to be an attractive one for explaining the presence of equilibrium value. On the basis of the theoretical the observed loops and helices. However, several work of Jones,lz4) the critical composition in [-AgAl, facts strongly suggest that the loops were not formed if it exists at all, should occur at Ag-31 at. % Al. by this mechanism. First of all, one would expect However, the lattice parameter measurements of Massalski and Cockayne(25) show that a sudden the condensation mechanism to produce basal loops having one of the following Burgers vectors: [OOOI], increase in the c/a ratio occurs at this composition Q[OOOl]or &(2023). In contrast to this, the loops have and continues to increase as the aluminum rich phase boundary is approached. Such a change would not be been shown to be non-basal and their Burgers vector expected if a defect lattice forms beyond the “critical” determined to be of the form &(1210). Secondly, composition of Ag-31 at. o/o Al. Furthermore, if one except for sign, all the loops have the same Burgers were to assume that a defect lattice formed in spite vector in both the primary and secondary slip bands. of the increase in c/a, then in order to maintain the Loops forming by a condensation of point defects critical electron concentration per unit cell up to the would not be expected to favor a single Burgers vector over its two equivalent ones unless the resolved shear composition Ag-33 at.% Al, a minimum vacancy concentration on the order of 10e2 is required. Since stress in a given band favors in some way the observed this concentration is about 100 times larger than the Burgers vector. However, it would then be difficult maximum theoretical concentration existing at the to explain why the loops have the same Burgers vector in both the primary and secondary slip bands. melting temperature for most metals, we can conclude Another possible explanation is that the loops were that the vacancies in Ag-33 at. % Al do not originate generated from the helices in the following manner. from a defect lattice. Once a cluster of screw dipoles “weakens” the crystal On the other hand, experiments have shown that sufficiently to trigger a slip burst the point defects an unusually large number of point defects are created in specimens which deform by repeated yielding.(26s27) which are generated can be absorbed by the screw dislocations thus transforming the clusters into In these experiments, the rate of creation of vacancies helical dipoles. If the original separation of the screw is determined by measuring the decay rate of resistivity dipoles was sufficiently small, the corresponding transients associated with load drops in crystals helical dipole could interact to produce loops. The deforming by repeated yielding. According to Blewitt
ACTA
1344
METALLURGICA,
VOL.
15,
1967
FIG. 16. Slip band in an [OOOl]foil strained 35% at 300°K.
hypothesis
that
the
clusters
of helices
act
as the
nuclei for the band of loops would not only explain
heat to raise the temperature
in the slip bands.
course
an absolute
bulk
diffusion
why the number of slip bands and clusters of helices
since Weertman(2sj
per unit area increase in the same sense with temper-
helices
ature and strain but also why the diameter
locations
loops
and helices
are always
of the
of the same order of
magnitude. However,
the preceding explanation is unsatisfacFirst of all, the transformation
is not
Of
necessity
and de Wit(2s) have shown that
can be generated
from
initially
at very low temperatures
However,
their
important
here since it predicts that helices will form
preferentially
mechanism
straight dis-
by pipe diffusion.
from
is not
dislocations
believed
to
predominantly
be in
tory on several points.
edge rather than screw character
of screw to helical dislocations requires diffusion of vacancies generated by plastic deformation. Since
observations show exactly the reverse. Secondly, if loops were generated from helical dipoles then they should have the same Burgers vector as the parent
loops and helices were observed in crystals strained at temperatures where bulk diffusion is negligible it seems improbable that such a transformation can occur during each load drop in the stress-strain curve unless the intense localized slip generates sufficient
while experimental
dipole which is clearly not the case for the vast majority of the loops observed in the slip bands. is
Although the mechanism of formation of the loops not clearly understood, their presence must
OKAMOTO
AND
THOMAS:
DISLOCATION
undoubtedly cause severe work hardening of the slip bands and therefore provides an explanation for the anomalous behavior of the critical resolved shear stress for prismatic slip reported by Mote et a2.(21 5. CONCLUSIONS
Single crystals of hexagonal Ag-33 at. % Al oriented for prismatic slip deformed by repeated yielding in regions I and II. In this temperature range the dislocation distribution is characterized by : (a) broad slip bands containing a high density of perfect, non-basal vacancy loops and (b) clusters of long helical dislocations. Both the slip bands and clusters lie along (1210) directions. 2. Except for the loops, all dislocations in slip bands lying parallel to a particular (l%O) direction have the corresponding +(l??lO) Burgers vector. On the other hand, the loops have a unique &I210> Burgers vector in the sense that it is the same for all loops regardless of the particular (l%O) slip band in which they are formed. 3. For a constant total strain, the effect of increasing temperature is to increase the average spacing between slip bands. An increase in total strain produces the same effect as a decrease in the deformation temperature. 4. The high density of loops serve as barriers to glide dislocations proposed by Mote et al.@) to explain the anomalous behavior in the critical resolved shear stress for prismatic slip. 5. Beyond region II, the repeated yielding effect is not observed and the dislocations are uniformly distributed. 1.
ACKNOWLEDGMENTS
This research was conducted as part of the activities of the Inorganic Materials Research Division of the Lawrence Radiation Laboratory of the University of California, Berkeley, and was done under the auspices of the U.S. Atomie Energy Commission. The authors express their appreciation of this eontinued suppofi
SUBSTRUCTURE
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of their research. One of us (P. R. Okamoto) is grateful to the National Science Foundation for the award of a Traineeship. We wish to thank Professor J. E. Dorn for valuable discussions. REFERENCES 1. P. A. FLIXX,Strengthening M~han~~~~ in Sol&%, p. 17. A.S.M. (1962). 2. J. D. MOTE, K. TANAKA and J. E. DORN, Trams. Met. Sot. AIME 221, 856 (1961). 3. A. ROSEN, J. D. MOTE and J. E. DORN, Trans. filet. Sot. AIME 230. 1070 (1964). 4. J. P. NE&ANN, &ta set. 10, 984 (1962). 5. E. HOWARD, W. BARMORE,J. D. MOTE and J. E. DORN, Trans. Met. Sot. AlAlE 227, 1061 (1963). 6. P. R. OKAMOTO, E. LEVINE and G. THOMAS,J. appl. Phys. 33, 289 (1967). 7. P. H. TEO&NTON, Phil. Mag. 3, 2013 (1963). 8. K. TANAKA and J. D. MOTE, UCRL-9992 (1961). 9. W. L. BELL and G. THOMAS, Phys. Status Solidi 12, 843 (1965). 10. G. THOMASand W. BELL, to be published in The PTOC. Ho?~o~~u Co@. on Lattice Defects 1965. 11. D. J. MAZEY, R. S.BARNES and A. HOWIE, Phil. Mug. 7, 1861(1962). For review seeG. THO~~AS,Thin Films,p. 227. A.S.M. (1964). 12. M. F. ASHBY and L. M. BROWN, Phil. Msg. 8,1063,1649 (1963). 13. W. L. BELL, D. M. MAHER and G. TEOMAS, Report Harwell Consultants Symposium on the Nature of Small Defect Clusters,Vol. 2, p. 314. H.M.S.O. (1966). 14. P. B. HIRSCE and J. S. LALLY, Phil. Mag. 12,595 (1965). 15. J. C. M. IA,&&ASS. Faraday Sot. 38, 123 (1964). 16. P. M. HAZZLEDINE,Discuss. Faraday Sot. Q8, 184 (1964). 17. J. E. DORN and S. RAJNAK, Trans. Met. Sot. AIME 230, 1052 (1964). 18. D. KURLMAN-W~LSDOR~,Phya. Rec. 120,773 (1960). 19‘ F. KROUPA andP. B. HIRSCH,Discuss. Faruday Sot. 33,4S 119641. 20. k. B.‘PRxz, ~l~tro~ M~ro~~py and St~e~th of Cry&& edited by G, THOMAS and J. WASKBUR~, D. * 41. Interscience (i963). 21. J. C. FISHER, Acta Met. 2, 9 (1954). J. WASHBURNand G. MURTY, J. appl. Phys. 87,266 (1966). Z: Z. S. BASIN~KI and P. J. JACKSON,Phys. Status Solidi 9, so5 (1965). 24. H. JONES, Proc. R. Sot. A147, 396 (1934). 26. T. B. MASSALSKI and B. COCKAYNE, Acta Met. 7, 762 (1959). 26. T. H. BLEWITT,R. P. COLTMAN and J. K. REDMAN, Report of The 1954 Conference on Defecta in Crystalline Solids, p. 369. Ph_m. Sot., London (1953). 27. J. M. ANDERSONand A. F. BROWN, Phys. Stats Solidi 12, 309 (1965). J. WEEBTMAN, Tram. Met. Sot. AIM&’ QQ7,1439 (1963). z: R. DEWIT, Fans. Met. Sot. AIME QQ7, 1443 (1963).