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Surface observation of nickel-plated iron single crystals deformed at 77 K
SURFACE OBSERVATION SINGLE CRYSTALS
OF NICKEL-PLATED IRON DEFORMED AT 77 K
S. KOBAYASHI
and M. MESH11
Department of Materials Science and Engineering Materials
Research
Center.
The Technological
Institute.
Northwestern
and University.
Evanston.
IL. L’.S..A
Abstract-The surface morphologC of nickel-plated iron single crystals deformed at 77 K has heen investigated to identify the mechanism of surface film softening. Two types of striation were found to form on the specimen surfaces. i.e. cracks approximately perpendicular to the tensile axis on the edge-faces and slip-like lines on the screw-faces. The direction of these lines deviated from the traces of the primary slip planes. Specimens which were electroplated on only one of the edge-faces exhibited a clear correspondence between the cracks on the plated face and the slip steps on the unplated face. Both the cracks and the slip steps were irregularly jogged. The lines connecting the corresponding points on the two faces were parallel to the primary slip direction. The observations indicate that dislocation loops are generated near the cracks below the stress level for screw dislocation motion. As the edge component of these loops can move substantially at the low stress level. the generation of a large number of dislocation loops results in macroscopic deformation. The observed angle of deviation between the direction of the slip-like lines and the trace of the primary slip plane on the screw-face is consistent with this model. Risumh-On a Ctudii la morphologie de la surface de monocristaux de fer nickel& et diform.3 it 77 K afin d-identifier le mecanisme responsable de I’adoucissement par la couche superficielle. On a observ.6 deux types de rayures sur la surface de I’&hantillon: des fissures approximativement paralliles B I’axe de traction sur les faces coin et des lignes analogues aux lignes de glissement sur les faces vis. On observait des diviations de ces lignes par rapport aux traces des plans de glissement primaires. On a mls en ividence. sur des Cchantillons polis 6lectrolytiquement sur une seule face coin. une correspondance ttroite entre les fissures de la face plaqute et les marches de glissement sur la face non plaquke. Les fissures et les marches de glissement prisentaient toutes deux des crans irreguliers. Les lignes joignant les points correspondants des deux faces itaient parall&les g la direction de glissement primaire. Nos observations montrent la formation de boucles de dislocations au voisinage des fissures pour une contramte infkrieure j la valeur ntcessaire pour deplacer les dislocations vis. La composante coin de ces boucles pouvant se dkplacer d’une facon notable sous faihle contrainte. la production d‘un grand nomhre de boucles de dislocations conduit h une d&formation macroscopique. L’angle de dPviation qu’on observe entre la direction des lignes analogues aux lignes de glissement et la trace du plan de gllssement primaire sur la face vis. est en accord avec ce modele. Zusammenfassung-Urn den Mechanismus der Entfestigung durch Oherfliichenschichten zu hestimmen. wurde die OhertfHchenmorphologie nickelplattierter. bei 77 K verformter Eiseneinkristalle untersucht. Die Entstehung zweier Streifentypen wurde an der ProbenobertXiche beobachtet. d.h. Risse ungefiihr senkrecht zur Zugachse an den StirnflPchen und gleitstufenlhnliche Linien an den ScitcnfGchen. Dir Richtung dirser Linien with von der Spur der Hauptgleitehene ab. Prohen. die nur an einer dcr StirnRBchen elektroplattiert waren. weigten einem deutlichen Zusammenhang zwischen Rissen an der plattlerten Fltiche und den Gleltstufen an der unplattierten FlBchc. Sowohl Risse als such Gleitstufcn enthielten unregelmlBige Spriinge. Die Verbindungslinien rwischen zwei sich auf den gegeniiherliegenden Mantelfliichen entsprechenden Punkten wuren parallel zur primsren Gleitrlchtung. Die Beobachtungen deuten darauf hin. daf3 in der Nihe der Risse Versetzungsschleifen unterhalh der Spannung fiir Schrauhcnvcrsetzungsbewegung erzeugt werden. Da sich die Stufenkomponente dieser Schlcifcn bei einer niedrigen Spannung merklich bewegen kann. fiihrt die Bildung einer grof3cn Anzahl von Versetzungsschlelfen zu einer makroskopischen Verformung. Dcr heobachtete Winkcl zwischen dcr Richtung gleltstufenartiger Limen und der Spur der primiren Gleitchene an dcr Seitenlliiche 1st mlt diesem Model1 vertraglich.
1. INTRODUffION The low temperature deformation behavior of b.c.c. metals is characterized by several interesting phenomena including alloy softening [I. 21 and irradiation softening [j-5]. These softening phenomena are directly related to the large temperature dependence of the yield stress of b.c.c. metals at low temperatures.
A number of explanations have been presented for these observations and are still being argued. Recently, a new kind of softening has been reported in Nb and Ta [6] and in Fe [7]. i.e. softening due to surface films such as anodic oxide films on Nb and Ta single crystals and electroplated Ni films on Fe single crystals.‘These films are found to lower the yield stress at temperatures such as 77 K.
1515
KOBAYASHI and MESHII:
1516
I
t
SURFACE OBSERVATION ,
600
(77.K)
COlp3l
=
0
i
5 Tanrile
*
I5
IO Strain
60
(Xl
Fig. I. Stress-strain curves for control and Ni-plated iron single crystals deformed at 77 K. The’ inset indicates the tensile axis of specimens in the unit stereographic triangle.
The surface film softening effect is illustrated by the stress-strain curves shown in Fig. 1. Surface films cause a decrease in yield stress and an increase in uniform elongation. Serration is generally observed in the initial part of the stress-strain curve. The softening effect observed is directly caused by the surface film since the effect can be either eliminated or generated by removing or adding the surface film. The stress level suddenly increases when the surface film is removed from a Ni-plated specimen after a small amount of deformation, or conversely, the stress level can be lowered by N&plating the control specimen after a small amount of deformation [S]. Surface observation of Ni-plated iron single crystals [7] revealed that many cracks were formed in the surface film during serration, indicating a close relation between crack formation and serration. At the same time, striations resembling slip lines appeared on different faces. The objective of this investigation is to examine the surface morphology of Ni-plated iron single crystals deformed at 77 K where surface film softening is prevalent, Analysis of the results should provide key information to identify the mechanism of the surface film softening. 2. EXPERIMENTAL
PROCEDURE
Tensile specimens with a tensile axis 15’ from [I IO] on the [lOO]-[I IO] great circle were cut from large (001)[ t lo] iron single crystal sheets (inset, Fig. 1).The shouldered specimens had a gage Length of approximately 4.5 mm and a cross section of approximately 1.2 x 0.7 mm. The chemical analysis of impurities in the as-grown crystal was as follows: C: 0.002. Si: 0.001. Mn: 0.002. P: 0.001. S: 0.002. Ni: 0.005. Co: 0.01, Cu: 0.001. Al: 0.001 (wt.?,). After cutting, the specimens were chemically polished in a H202 + 5% HF solution and subsequently annealed in a ZrH2 purification system at 85O’C for 48 h. All specimens were stored in liquid nitrogen until tested. Thin Ni films were deposited by electroplating in a Watts bath at 1.5 A/dm2 and 3O’C. The bath consisted of NiS04.6H20 215 g/l. NiClz.6HZ0 3Og/l and H,BO, 15 g/l. Electron diffraction patterns indi-
OF DEFORMED
NICKEL-PLATED
IRON
cated that the Ni films deposited on the iron (001) surface were f.c.c. and had a preferred orientation of : 110;. Grains as large as 1000 A were mixed with grains as small as 100 A. Using the scanning electron microscope. the thickness of the Ni films was found to be ~c 4000& Tensile tests were performed on an Instron machine at 77 K at a nominal strain rate of 2 x 10-4s-‘. Stresses and strains are indicated in tensile stress and tensile strain. The Schmid factor for the (lOl)[lli] and (lOi)[lll] slip systems is 0.483. After the tensile test the specimen surface was examined with a Nomarski interference microscope and a scanning electron microscope. 3, O~ERYATION OF SURFACE MORPHOLOGY Figure 2 illustrates the relation among the tensile direction, specimen surfaces. slip planes and slip directions. The broader top (bottom) face is (001) and the primary slip directions [1 ii] and [I 11) are 13.1’ from the narrower side faces. Optical micrographs of slip lines observed on the control specimens are shown in Fig. 3. As small strains do not produce any visible markings on the surfaces, micrographs taken from the necked region of a specimen deformed 14”; are shown here to illustrate slip lines on the control specimens. The slip traces observed on the top face are wavy. as shown in Fig. 3(a). The average direction of these slip traces corresponds to the trace of (101) and (lOi) which is 60” from the tensile axis. The micrograph of the side face (Fig. 3b) shows two sets of fairly straight lines. These micrographs indicate that two slip systems, (lOl)[l IT] and (lOi)[ll I]. operate predominantly in the control specimens. The deformation morphology of the Ni-plated specimens was quite different from that of the control specimens. Coarse lines approximately perpendicular to the tensile axis appeared on the top face (edge face) during serration. as shown in Fig. 4(a). These lines are jogged. As shown in Fig. 5, the scanning electron microscope showed clearly that these lines were cracks in the surface film. The striations observed on the side faces (screw faces) are straight and appear like slip lines, as shown in Fig. 4(b). The development of the surface morphology during deformation is shown schematically in Fig. 6. At the cloimrll A.
Fig. 2. Schematic illustratjon of specimen geometry indicating tensile axis, specimen faces, primary slip planes and primary slip directions.
KOBAYASHI
and
MESHII:
SURFACE
OBSERVATION
4
(a)
Top
Fig. 3. Optical
1.
OF
Top
(b)
face
*
Side
T. A.
N
1517
face 14”, at 77 K.
,2OOgm,
)
(b)
face micrographs showing surface structure (a) Top face; (b) side face. Tensile
IRON
200pm,
micrographs showing surface structure of control specimen deformed (a) Top face; (b) side face. Tensile axis is indicated by arrow.
T. A.
Fig. 4. Optical
NICKEL-PLATED
A.
4
(a)
DEFORMED
Side
of Ni-plated specimen deformed axis is indicated by arrow.
face I”,;, at 77 K
very early stage of serration. a bundle of cracks and slip-like lines appears only on the top and one of the side faces respectively (Fig. 6a). Then a new bun-
dle of cracks and slip-like lines forms on the bottom and other side faces as shown in Fig. 6(b). These bun-
,
IOJm
Fig. 5. Scanning electron micrograph illustrating a crack on top face of Ni-plated specimen deformed 2.59, at 77 K. Tensile axis is indicated by arrow.
dles of surface cracks on both top and bottom faces are interconnected by the coarse slip-like lines on both side faces. The number of crack bundles increases with deformation, keeping the distance between individual bundles nearly constant (Fig. 6~). Furthermore. these bundles of cracks on the top face are always interconnected with those on the bottom face by slip-like lines on the side faces. The surface morphology at this stage is characterized by a striped pattern of cracks and a zig-zag pattern of slip-like lines (Fig. 6~). Further deformation increases the number of cracks filling the spaces between the bundles so that the coarse cracks cover the top and bottom faces entirely, as shown in Fig. 6(d). Careful examination of the side faces revealed that
1518
KOBAYASHI and MESHII:
SURFACE OBSERVATION
T.A.
f. A.
OF DEFORMED
NICKEL-PLATED
IRON
T. A.
T.A.
t
lo)
(bf
fc)
fdl
Fig. 6. Sequence of surface marking formation in a Ni-plated specimen. the direction of the slip-like lines deviated from the {lOI} traces. On the side faces, the two slip planes, (101) and (lOi), should intersect each other with an angle of 81.8” (Fig. 2). But the observed angle was 70.3 + 1.2”. This deviation was also confirmed by using twinning traces as a reference direction in specimens where twinning occurred. All measurements were done at small strains (< Z”/,) to minimize the error due to lattice rotation. This observation can be explained by the model proposed in the next section. 4. MODEL FOR THE FORMATION OF SURFACE MORPHOLOGY The essentials of the model are that a large number of small dislocation loops are generated near the surface cracks below the macroscopic yield stress of the iron substrate and that only the edge component of these dislocations is mobile. The dislocation loops generated from the top face expand to the bottom face and make a new set of cracks. Since the specimens are oriented for duplex slip, dislocations are generated at these new cracks on the other primary slip system. The manner in which the slip propagates in the present case can be likened to the reflection of light by a set of two parallel mirrors. Therefore this slip propagation results in the striped pattern on the top and bottom faces and the zig-zag pattern on the side faces as shown in Fig 6(c). As the crack lines are not parallel to the slip plane traces on the top face (Fig, 7) each dislocation loop generated near a crack expands on different (101) or (IOi) planes. Since only edge disl~ations are subs~ntially mobile at the low stress level, the dislocation loops are elongated along the Burgers vectors. The slip-like lines observed on the side faces are the loci of the ends of these dislocation loops and should deviate from the traces of f 101) slip planes. The calculated angle between these two sets of slip-like lines is 72.4”, which is in good agreement with the observed value of 70.3 + 1.2”. This model is substantiated by several other experimental observations. As mentioned before, each bundle of surface cracks on the top and bottom faces is linked by the slip-like lines on both side faces. If the disl~tion sources were near the center of the specimen they would have to be in a line perpendicular to the tensile axis in
order to explain the configuration of surface cracks. Furthermore, several sets of sources would have to be located at such a distance that dislocations coming from two different Sets of sources would meet just at the surface to make the zig-zag patterns on the side faces and the striped patterns on the top and bottom faces (Fig. 6~). These situations, however, seem to be unrealistic and the proposition that dislocations are generated near the surface cracks appears most acceptable. In order to examine further the proposed model, specimens were electroplated with nickel only on the top face and were deformed slightly at 77 K. The softening effect was also confirmed in these specimens upon defo~ation. Figure 8(a) shows that slip markings appeared on the bottom face which was not covered with Ni film. The jogged appearance of the slip markings is noted. The direction of these slip markings was again roughly perpendicular to the tensile axis. Furthermore, an examination of the Niplated top face revealed that the ~st~bution of cracks was nearly identical to these slip markings on the bottom face (Fig. 8b). It was also noted that the line connecting two corresponding points on these two patterns was parallel to one of the two primary slip directions. Figure 9 gives a magnified view of a small area marked A in Fig. 8. Both secondary electron images and Y-modulation displays clearly indicate that the striations on the plated face are cracks and those on the unplated face are slip steps.
>
T.A./
/
Slip Plana
Fig. 7. Schematic illustration of formation of a slip-like line and the geometric relation with a crack line and the slip plane.
KOBAYASHI and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IRON
(a) Unplated bottom face
(b) Piated top
1519
face
Fig. 8. Scanning electron micrographs of surface structure of a one-face-plated specimen deformed 2.5”,, at 77 K. Note that the specimen was tilted and rotated 45” for the maximum contrast. (a) Slip markings on unplated bottom face; (b) cracks on plated top face.
This observation further substantiates the model proposed. The fact that the slip morphology observed on the unplated face was drastically altered by the Ni film on the opposite face indicates that the site of dislocation generation is at or near the film. The configuration of the slip pattern, such as shown in Fig. 8(a), also illustrates the distribution of sites of dislocation generation in detail. In addition. the exclusive motion of the edge component is again supported in this observation. A set of matching patterns of cracks was also observed on Ni-plated top and bottom faces. An
exampfe of three matching patterns is shown in Fig. 10. Figure lO(b) was taken from the top face and Figs. IO(a) and (c) were taken from the bottom face. Figure 10(d) schematically illustrates the relative position of each pattern and a possible propagation sequence. Although the patterns are not exactly the same, the itching among them is evident. Reference points for matching are indicated by arrows on the micrographs. The observation clearly supports the slip propagation process proposed in Fig. 6 and makes the possibility of dislocation generation sites other than along the cracks unlikely.
KOBAYASHI and MESHII:
SURFACE OBSERVATION
OF DEFORMED
NICKEL-PLATED
IRON
Fig; 4. Magnified images of the area marked A in Fig. 8. faf Secondary electron image of unplated bottom frtce; {b) secondary electron &age of plated top Face; (cf ~-rn~d~l~t~~n display of unpiated bottom face; (d) I’-modulatibn display of plated top face.
5. DISCUSSION A number of observations support tl;e contention that the rnoh~~~tyof edge dislocations is greater than that of screw dislocations in b.c.c. metals at ‘low temperatures [g-16]. Therefore, the continuous generation af ZJ large number of edge dislocations is the key element for the surface film softening. In the conare readily trol specimens, edge dislocations exhausted and can ~ont~but~ onty to the microst~~n. The macroscopic yielding takes place only when the stress becomes sufficiently high for screw dislocations to move substantially. On the other hand, in Niplated specimens, edge dislocations are continuously generated near the cracks and the strain rate imposed can be maintained by the motion of the edge dislocations; i.e., macrostrain occurs by the motion of edge dislocations at a lower stress than the yield stress of the control specimen. The lowest yield stress observed (- 26OMPa) in the present investigation is still higker than the stress level at which edge dislocations are known to move irreversibly (C 100 MPa) [14-lb]. This difference in stress levels indicates that the generation of disioca-
tion loops requires a stress significantly higher than the critical stress for edge dislocation motion.’ Actually, small stress drops were observed occasionally at a stress between 100 and 2ilOMPa on the stress-strain curves. The plastic strain corresponding to this stress drop is very small. The frequency of the stress drops increased somewhat with strtss until the macroscopic yield stress was reached at which point the frequency suddenly increased and the continual stress drops caused the serrated stress-strain relation. The argument presented here indicates that the macroscopic yield stress observed in Ni-plated iron single crystals is controlled by the crack formation in the Ni film instead of by the dislocation motion. Therefore if the cracks can be formed at a lower stress under a suitable condition to generate dislocations, the yield stress can be as low as the stress for the edge dislocation motion. The low resolved shear stress of 30 - 40 MPa was reported in oxide-coated Nb single crystals at 77 K El?]. The critical stress for the crack formation which generates a suiI%ent number of dislocation loops may depend on more than ane factor. The strength of the surface film is
~UB~~~SHI
and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IROhi
1521
T. A. Ic
(c)
c
(d)
Fig. IO. Optical micrographs of a Ni-plated specimen deformed O.lP; at 77 K, (a)*(b) and (c) were taken from different areas iilustrated in (d). The similarity of the crack pattern indicates the manner of slip p~~pa~at~~~(see text).
certainly important. The residual tensiIe stress in Ni film can facilitate the crack formation. The number and geometry of stress concentrators where the cracks initiate must also be considered. The elastic moduli of the film with respect to those of the substrate may also influence the dislocation generation. It is suggested that the microplastic strain of the substrate increases the tensile stress in the surface film; therefore the crack formation would start at a lower stress level. The attainment of the lowest yield stress by the combination of prestrain and surface film [17.18] can be explained in this manner. Cracks are likely to be initiated at the corners where interlaminar shear stress is maximum [19.20]. if crack propagation occurs only by virtue of the bsittle nature of the Ni-film, cracks wouid propagate on both the top and side faces. The cracks were, however, observed only on the top and bottom faces. to which the primary slip directions inclined sharply. Slip-like lines. instead of cracks, form on the faces (side faces in this case) which are nearly parallel to the slip. directions. Reversing the surface geometry between the top
and side faces, cracks were found to form only on the side faces [1X]. This observation indicates that the interaction between substrate and surface film is essential for the crack formation, although the manner of propagation may be affected by the mechanical property of the film and its adherence to the substrate [2l]. Once a crack is nucleated, a number of dislocation loops are generated near the crack tip, which form a slip step on the substrate surface if they are edge d~s~~a~ons but not if they are screw dislocations. The surface film cracks more easily under the stress normal to the film than under the stress lying in its plane [22]. Therefore cracks propagate on the edge-face where the normal component of the slip vector is large. The crack propagation, therefore, consists of a chain reaction, namely, crack forrnationdislocation generation-surface step-further cracking. In discussing the surface film softening, it is suggested that the plastic deformation during serration occurs by the motion of edge dislocations. Each crack line produces a substantial plastic deformation in a
I522
KOBAYASHI and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IRON
small region. The extent of this plastic deformation can be estimated from the slip displacement at the slip markings on the unplated bottom face of the specimen whose top face was Ni-plated (Fig. 8a). The displacement ranged from loo0 to 5OOOA.The average ratio of the plastic strain of the specimen to the number of the slip markings (or cracks) yields approximately 5 x lo-’ as the plastic strain per slip step (or crack). If this plastic strain occurs exclusively by the motion of the edge dislocations, the’displacement should be about 32OOA on the top (edge) face. Good agreement between this value and the measured slip displacement supports the motion of edge dislocations. The surface film softening phenomenon in Niplated iron single crystals was investigated using single crystal specimens oriented for duplex slip. The model developed here, however, can be applied to single crystals of other orientations. A similar observation was made in specimens with the tensile axis in the center of the unit stereographic triangle [18). The coarse structure of the cracks and slip-like lines observed in this study facilitated the morphological investigation. The coarseness of the morphology is not essential for the proposed model to be operational. A larger number of finer cracks (and finer slip steps) should produce a similar softening effect if they generate a sufficient number of dislocation loops. 6. SUMMARY The surface morphology of deformed specimens was investigated to elucidate why the electroplated Ni film reduced the yield stress of iron single crystals at 77 K. The findings of this investigation can be summarized as follows:
of dislocations took place near the cracks on the plated face and only the edge component of these dislocations moved .to form the slip steps on the opposite, unplated, face. The configuration of the slip steps was nearly identical to the crack configuration on the plated face. The line connecting the corresponding points was parallel to the primary slip direction. 6. The surface film softening is caused by the generation of many edge dislocations below the macroscopic yield stress of the substrate. The crack formation in the surface film controls the stress for the dislocation generation. Acknowledgements-The authors would like to thank Dr. Tomoyuki Takeuchi of the National Institute for Metals, Tokyo, for providing iron single crystal sheets, Dr. Kenichi Kojima for discussion of the results, and,Professor J. R. Weertman and Mr. D. J. Quesnel for reading this manuscript. This research is supported by the U.S. Energy Research and Development Administration.
REFERENCES 1. J. W. Christian, Proc. 2nd Inc. Co@ Strength of Metals and Alloys, p. 31. American Society for Metals (1970). 2. W. C. Leslie, Metail. Trans. 3, 5 (1972). 3. A. Sato and M. Meshii, Scripm Met. 8, 851 (1974); Proc. Int. Conf Fundamental Aspects of Radiation Damuge in Metals, p. 984. Gatlinburg (1975). 4. P. Groh, F. Vanoni and P. Moser, Defects and Defect Clusters in B.C.C. Metals and Their Alloys, p. 19
(1973). 5. K. Kitajima, H. Abe, S. Takamura and S. Okuda, Proc. Int. Conf in Metals,
6. 7.
8.
1. Two types of striation appeared on the specimen surfaces: cracks nearly perpendicular to the tensile axis and sliplike lines which deviated from the traces of the primary slip planes IlOl}. 2. Cracks were observed on the faces where the primary slip directions had large normal components (edge-faces) and the sliplike lines were formed on the faces nearly parallel to the slip directions (screwfaces). 3. The plastic deformation resulted from the formation and propagation of the cracks and the slip-like lines. The cracks and the slip-like lines were interconnected. 4. A bundle of cracks formed on one of the edgefaces; then cracks of a similar configuration often appeared on the opposite edge-face along with the appearance of sliplike lines on the screw-faces. This projection of cracks from one face to another occurred in the direction of the primary slip vectors. Since there were two primary slip vectors (duplex slip orientation), the projection was repeated like the reflection of light by a set of two parallel mirrors. 5. The deformation morphology in one-face-plated specimens demonstrated clearly that the generation
9. 10.
Fundamental
Aspects
of Radiation
Damage
p. 977. Gatlinburg (1975). V. K. Sethi and R. Gibala, Scripta Met. 9, 527 (1975). K. Kojima, S. Kobayashi and M. Meshii, Scripta Met. 10, 347 (1976). S. Kobayashi, K. Kojima and M. Meshii, Proc. 2nd Int. Conf: Mechanical Behavior of Materials, p. 78. American Society for Metals (1976). V. V’tek, Crystal Lattice Defects 5, 1 (1974). H. s’aka, K. Noda and T. Imura, Crystal Lattice Defects
4, 45 (1973).
11. A. S. Keh, W. A. Spitzig and Y. Nakada, Phil. Mag. 23, 829 (1971). 12. D. S. Tomalin and C. J. McMahon, Jr., Proc. 2nd Int. Conf: Strength of Metals and Alloys, p. 134. American
Society for Metals (1970). 13. A. P. L. Turner and T. Vreeland, Jr., Acta Met. 18, 1225 (1970). 14. H. D. Solomon and C. J. McMahon, Work Hardening, p. 309. Gordon & Breach, New York (1968). 15. C. J. McMahon. Microolasticitv. v. 121. Interscience.
New York (1968). ’ _. 16. A. Sato and M. Meshii, Phys. Status Solidi, (A) 28, 561 (1975). 17. V. K. Sethi and R. Gibala, Surface Eficrs in Crystal Plasticity, p. 599. Noordhoff, Lkyden rl977). _ 18. K. Koiima and M. Meshii. Phvs. Status Solidi (A) %, 39., 491 (1477). 19. R. B. Pipes and N. J. Pagano, J. camp. Mater. 4, 538 (1970). 20. S. Tang and A. Levy, J. camp. Mater. 9, 42 ,(1975). 21. T. Evans and D. R. Schwarzenberger, Phil. Msg. 4, .
889 (1957). 22. F. R. Lipsett and R. King, Proc.
608 (1957).
Phys. Sot.
(B) 70,
OF NICKEL-PLATED IRON DEFORMED AT 77 K
S. KOBAYASHI
and M. MESH11
Department of Materials Science and Engineering Materials
Research
Center.
The Technological
Institute.
Northwestern
and University.
Evanston.
IL. L’.S..A
Abstract-The surface morphologC of nickel-plated iron single crystals deformed at 77 K has heen investigated to identify the mechanism of surface film softening. Two types of striation were found to form on the specimen surfaces. i.e. cracks approximately perpendicular to the tensile axis on the edge-faces and slip-like lines on the screw-faces. The direction of these lines deviated from the traces of the primary slip planes. Specimens which were electroplated on only one of the edge-faces exhibited a clear correspondence between the cracks on the plated face and the slip steps on the unplated face. Both the cracks and the slip steps were irregularly jogged. The lines connecting the corresponding points on the two faces were parallel to the primary slip direction. The observations indicate that dislocation loops are generated near the cracks below the stress level for screw dislocation motion. As the edge component of these loops can move substantially at the low stress level. the generation of a large number of dislocation loops results in macroscopic deformation. The observed angle of deviation between the direction of the slip-like lines and the trace of the primary slip plane on the screw-face is consistent with this model. Risumh-On a Ctudii la morphologie de la surface de monocristaux de fer nickel& et diform.3 it 77 K afin d-identifier le mecanisme responsable de I’adoucissement par la couche superficielle. On a observ.6 deux types de rayures sur la surface de I’&hantillon: des fissures approximativement paralliles B I’axe de traction sur les faces coin et des lignes analogues aux lignes de glissement sur les faces vis. On observait des diviations de ces lignes par rapport aux traces des plans de glissement primaires. On a mls en ividence. sur des Cchantillons polis 6lectrolytiquement sur une seule face coin. une correspondance ttroite entre les fissures de la face plaqute et les marches de glissement sur la face non plaquke. Les fissures et les marches de glissement prisentaient toutes deux des crans irreguliers. Les lignes joignant les points correspondants des deux faces itaient parall&les g la direction de glissement primaire. Nos observations montrent la formation de boucles de dislocations au voisinage des fissures pour une contramte infkrieure j la valeur ntcessaire pour deplacer les dislocations vis. La composante coin de ces boucles pouvant se dkplacer d’une facon notable sous faihle contrainte. la production d‘un grand nomhre de boucles de dislocations conduit h une d&formation macroscopique. L’angle de dPviation qu’on observe entre la direction des lignes analogues aux lignes de glissement et la trace du plan de gllssement primaire sur la face vis. est en accord avec ce modele. Zusammenfassung-Urn den Mechanismus der Entfestigung durch Oherfliichenschichten zu hestimmen. wurde die OhertfHchenmorphologie nickelplattierter. bei 77 K verformter Eiseneinkristalle untersucht. Die Entstehung zweier Streifentypen wurde an der ProbenobertXiche beobachtet. d.h. Risse ungefiihr senkrecht zur Zugachse an den StirnflPchen und gleitstufenlhnliche Linien an den ScitcnfGchen. Dir Richtung dirser Linien with von der Spur der Hauptgleitehene ab. Prohen. die nur an einer dcr StirnRBchen elektroplattiert waren. weigten einem deutlichen Zusammenhang zwischen Rissen an der plattlerten Fltiche und den Gleltstufen an der unplattierten FlBchc. Sowohl Risse als such Gleitstufcn enthielten unregelmlBige Spriinge. Die Verbindungslinien rwischen zwei sich auf den gegeniiherliegenden Mantelfliichen entsprechenden Punkten wuren parallel zur primsren Gleitrlchtung. Die Beobachtungen deuten darauf hin. daf3 in der Nihe der Risse Versetzungsschleifen unterhalh der Spannung fiir Schrauhcnvcrsetzungsbewegung erzeugt werden. Da sich die Stufenkomponente dieser Schlcifcn bei einer niedrigen Spannung merklich bewegen kann. fiihrt die Bildung einer grof3cn Anzahl von Versetzungsschlelfen zu einer makroskopischen Verformung. Dcr heobachtete Winkcl zwischen dcr Richtung gleltstufenartiger Limen und der Spur der primiren Gleitchene an dcr Seitenlliiche 1st mlt diesem Model1 vertraglich.
1. INTRODUffION The low temperature deformation behavior of b.c.c. metals is characterized by several interesting phenomena including alloy softening [I. 21 and irradiation softening [j-5]. These softening phenomena are directly related to the large temperature dependence of the yield stress of b.c.c. metals at low temperatures.
A number of explanations have been presented for these observations and are still being argued. Recently, a new kind of softening has been reported in Nb and Ta [6] and in Fe [7]. i.e. softening due to surface films such as anodic oxide films on Nb and Ta single crystals and electroplated Ni films on Fe single crystals.‘These films are found to lower the yield stress at temperatures such as 77 K.
1515
KOBAYASHI and MESHII:
1516
I
t
SURFACE OBSERVATION ,
600
(77.K)
COlp3l
=
0
i
5 Tanrile
*
I5
IO Strain
60
(Xl
Fig. I. Stress-strain curves for control and Ni-plated iron single crystals deformed at 77 K. The’ inset indicates the tensile axis of specimens in the unit stereographic triangle.
The surface film softening effect is illustrated by the stress-strain curves shown in Fig. 1. Surface films cause a decrease in yield stress and an increase in uniform elongation. Serration is generally observed in the initial part of the stress-strain curve. The softening effect observed is directly caused by the surface film since the effect can be either eliminated or generated by removing or adding the surface film. The stress level suddenly increases when the surface film is removed from a Ni-plated specimen after a small amount of deformation, or conversely, the stress level can be lowered by N&plating the control specimen after a small amount of deformation [S]. Surface observation of Ni-plated iron single crystals [7] revealed that many cracks were formed in the surface film during serration, indicating a close relation between crack formation and serration. At the same time, striations resembling slip lines appeared on different faces. The objective of this investigation is to examine the surface morphology of Ni-plated iron single crystals deformed at 77 K where surface film softening is prevalent, Analysis of the results should provide key information to identify the mechanism of the surface film softening. 2. EXPERIMENTAL
PROCEDURE
Tensile specimens with a tensile axis 15’ from [I IO] on the [lOO]-[I IO] great circle were cut from large (001)[ t lo] iron single crystal sheets (inset, Fig. 1).The shouldered specimens had a gage Length of approximately 4.5 mm and a cross section of approximately 1.2 x 0.7 mm. The chemical analysis of impurities in the as-grown crystal was as follows: C: 0.002. Si: 0.001. Mn: 0.002. P: 0.001. S: 0.002. Ni: 0.005. Co: 0.01, Cu: 0.001. Al: 0.001 (wt.?,). After cutting, the specimens were chemically polished in a H202 + 5% HF solution and subsequently annealed in a ZrH2 purification system at 85O’C for 48 h. All specimens were stored in liquid nitrogen until tested. Thin Ni films were deposited by electroplating in a Watts bath at 1.5 A/dm2 and 3O’C. The bath consisted of NiS04.6H20 215 g/l. NiClz.6HZ0 3Og/l and H,BO, 15 g/l. Electron diffraction patterns indi-
OF DEFORMED
NICKEL-PLATED
IRON
cated that the Ni films deposited on the iron (001) surface were f.c.c. and had a preferred orientation of : 110;. Grains as large as 1000 A were mixed with grains as small as 100 A. Using the scanning electron microscope. the thickness of the Ni films was found to be ~c 4000& Tensile tests were performed on an Instron machine at 77 K at a nominal strain rate of 2 x 10-4s-‘. Stresses and strains are indicated in tensile stress and tensile strain. The Schmid factor for the (lOl)[lli] and (lOi)[lll] slip systems is 0.483. After the tensile test the specimen surface was examined with a Nomarski interference microscope and a scanning electron microscope. 3, O~ERYATION OF SURFACE MORPHOLOGY Figure 2 illustrates the relation among the tensile direction, specimen surfaces. slip planes and slip directions. The broader top (bottom) face is (001) and the primary slip directions [1 ii] and [I 11) are 13.1’ from the narrower side faces. Optical micrographs of slip lines observed on the control specimens are shown in Fig. 3. As small strains do not produce any visible markings on the surfaces, micrographs taken from the necked region of a specimen deformed 14”; are shown here to illustrate slip lines on the control specimens. The slip traces observed on the top face are wavy. as shown in Fig. 3(a). The average direction of these slip traces corresponds to the trace of (101) and (lOi) which is 60” from the tensile axis. The micrograph of the side face (Fig. 3b) shows two sets of fairly straight lines. These micrographs indicate that two slip systems, (lOl)[l IT] and (lOi)[ll I]. operate predominantly in the control specimens. The deformation morphology of the Ni-plated specimens was quite different from that of the control specimens. Coarse lines approximately perpendicular to the tensile axis appeared on the top face (edge face) during serration. as shown in Fig. 4(a). These lines are jogged. As shown in Fig. 5, the scanning electron microscope showed clearly that these lines were cracks in the surface film. The striations observed on the side faces (screw faces) are straight and appear like slip lines, as shown in Fig. 4(b). The development of the surface morphology during deformation is shown schematically in Fig. 6. At the cloimrll A.
Fig. 2. Schematic illustratjon of specimen geometry indicating tensile axis, specimen faces, primary slip planes and primary slip directions.
KOBAYASHI
and
MESHII:
SURFACE
OBSERVATION
4
(a)
Top
Fig. 3. Optical
1.
OF
Top
(b)
face
*
Side
T. A.
N
1517
face 14”, at 77 K.
,2OOgm,
)
(b)
face micrographs showing surface structure (a) Top face; (b) side face. Tensile
IRON
200pm,
micrographs showing surface structure of control specimen deformed (a) Top face; (b) side face. Tensile axis is indicated by arrow.
T. A.
Fig. 4. Optical
NICKEL-PLATED
A.
4
(a)
DEFORMED
Side
of Ni-plated specimen deformed axis is indicated by arrow.
face I”,;, at 77 K
very early stage of serration. a bundle of cracks and slip-like lines appears only on the top and one of the side faces respectively (Fig. 6a). Then a new bun-
dle of cracks and slip-like lines forms on the bottom and other side faces as shown in Fig. 6(b). These bun-
,
IOJm
Fig. 5. Scanning electron micrograph illustrating a crack on top face of Ni-plated specimen deformed 2.59, at 77 K. Tensile axis is indicated by arrow.
dles of surface cracks on both top and bottom faces are interconnected by the coarse slip-like lines on both side faces. The number of crack bundles increases with deformation, keeping the distance between individual bundles nearly constant (Fig. 6~). Furthermore. these bundles of cracks on the top face are always interconnected with those on the bottom face by slip-like lines on the side faces. The surface morphology at this stage is characterized by a striped pattern of cracks and a zig-zag pattern of slip-like lines (Fig. 6~). Further deformation increases the number of cracks filling the spaces between the bundles so that the coarse cracks cover the top and bottom faces entirely, as shown in Fig. 6(d). Careful examination of the side faces revealed that
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KOBAYASHI and MESHII:
SURFACE OBSERVATION
T.A.
f. A.
OF DEFORMED
NICKEL-PLATED
IRON
T. A.
T.A.
t
lo)
(bf
fc)
fdl
Fig. 6. Sequence of surface marking formation in a Ni-plated specimen. the direction of the slip-like lines deviated from the {lOI} traces. On the side faces, the two slip planes, (101) and (lOi), should intersect each other with an angle of 81.8” (Fig. 2). But the observed angle was 70.3 + 1.2”. This deviation was also confirmed by using twinning traces as a reference direction in specimens where twinning occurred. All measurements were done at small strains (< Z”/,) to minimize the error due to lattice rotation. This observation can be explained by the model proposed in the next section. 4. MODEL FOR THE FORMATION OF SURFACE MORPHOLOGY The essentials of the model are that a large number of small dislocation loops are generated near the surface cracks below the macroscopic yield stress of the iron substrate and that only the edge component of these dislocations is mobile. The dislocation loops generated from the top face expand to the bottom face and make a new set of cracks. Since the specimens are oriented for duplex slip, dislocations are generated at these new cracks on the other primary slip system. The manner in which the slip propagates in the present case can be likened to the reflection of light by a set of two parallel mirrors. Therefore this slip propagation results in the striped pattern on the top and bottom faces and the zig-zag pattern on the side faces as shown in Fig 6(c). As the crack lines are not parallel to the slip plane traces on the top face (Fig, 7) each dislocation loop generated near a crack expands on different (101) or (IOi) planes. Since only edge disl~ations are subs~ntially mobile at the low stress level, the dislocation loops are elongated along the Burgers vectors. The slip-like lines observed on the side faces are the loci of the ends of these dislocation loops and should deviate from the traces of f 101) slip planes. The calculated angle between these two sets of slip-like lines is 72.4”, which is in good agreement with the observed value of 70.3 + 1.2”. This model is substantiated by several other experimental observations. As mentioned before, each bundle of surface cracks on the top and bottom faces is linked by the slip-like lines on both side faces. If the disl~tion sources were near the center of the specimen they would have to be in a line perpendicular to the tensile axis in
order to explain the configuration of surface cracks. Furthermore, several sets of sources would have to be located at such a distance that dislocations coming from two different Sets of sources would meet just at the surface to make the zig-zag patterns on the side faces and the striped patterns on the top and bottom faces (Fig. 6~). These situations, however, seem to be unrealistic and the proposition that dislocations are generated near the surface cracks appears most acceptable. In order to examine further the proposed model, specimens were electroplated with nickel only on the top face and were deformed slightly at 77 K. The softening effect was also confirmed in these specimens upon defo~ation. Figure 8(a) shows that slip markings appeared on the bottom face which was not covered with Ni film. The jogged appearance of the slip markings is noted. The direction of these slip markings was again roughly perpendicular to the tensile axis. Furthermore, an examination of the Niplated top face revealed that the ~st~bution of cracks was nearly identical to these slip markings on the bottom face (Fig. 8b). It was also noted that the line connecting two corresponding points on these two patterns was parallel to one of the two primary slip directions. Figure 9 gives a magnified view of a small area marked A in Fig. 8. Both secondary electron images and Y-modulation displays clearly indicate that the striations on the plated face are cracks and those on the unplated face are slip steps.
>
T.A./
/
Slip Plana
Fig. 7. Schematic illustration of formation of a slip-like line and the geometric relation with a crack line and the slip plane.
KOBAYASHI and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IRON
(a) Unplated bottom face
(b) Piated top
1519
face
Fig. 8. Scanning electron micrographs of surface structure of a one-face-plated specimen deformed 2.5”,, at 77 K. Note that the specimen was tilted and rotated 45” for the maximum contrast. (a) Slip markings on unplated bottom face; (b) cracks on plated top face.
This observation further substantiates the model proposed. The fact that the slip morphology observed on the unplated face was drastically altered by the Ni film on the opposite face indicates that the site of dislocation generation is at or near the film. The configuration of the slip pattern, such as shown in Fig. 8(a), also illustrates the distribution of sites of dislocation generation in detail. In addition. the exclusive motion of the edge component is again supported in this observation. A set of matching patterns of cracks was also observed on Ni-plated top and bottom faces. An
exampfe of three matching patterns is shown in Fig. 10. Figure lO(b) was taken from the top face and Figs. IO(a) and (c) were taken from the bottom face. Figure 10(d) schematically illustrates the relative position of each pattern and a possible propagation sequence. Although the patterns are not exactly the same, the itching among them is evident. Reference points for matching are indicated by arrows on the micrographs. The observation clearly supports the slip propagation process proposed in Fig. 6 and makes the possibility of dislocation generation sites other than along the cracks unlikely.
KOBAYASHI and MESHII:
SURFACE OBSERVATION
OF DEFORMED
NICKEL-PLATED
IRON
Fig; 4. Magnified images of the area marked A in Fig. 8. faf Secondary electron image of unplated bottom frtce; {b) secondary electron &age of plated top Face; (cf ~-rn~d~l~t~~n display of unpiated bottom face; (d) I’-modulatibn display of plated top face.
5. DISCUSSION A number of observations support tl;e contention that the rnoh~~~tyof edge dislocations is greater than that of screw dislocations in b.c.c. metals at ‘low temperatures [g-16]. Therefore, the continuous generation af ZJ large number of edge dislocations is the key element for the surface film softening. In the conare readily trol specimens, edge dislocations exhausted and can ~ont~but~ onty to the microst~~n. The macroscopic yielding takes place only when the stress becomes sufficiently high for screw dislocations to move substantially. On the other hand, in Niplated specimens, edge dislocations are continuously generated near the cracks and the strain rate imposed can be maintained by the motion of the edge dislocations; i.e., macrostrain occurs by the motion of edge dislocations at a lower stress than the yield stress of the control specimen. The lowest yield stress observed (- 26OMPa) in the present investigation is still higker than the stress level at which edge dislocations are known to move irreversibly (C 100 MPa) [14-lb]. This difference in stress levels indicates that the generation of disioca-
tion loops requires a stress significantly higher than the critical stress for edge dislocation motion.’ Actually, small stress drops were observed occasionally at a stress between 100 and 2ilOMPa on the stress-strain curves. The plastic strain corresponding to this stress drop is very small. The frequency of the stress drops increased somewhat with strtss until the macroscopic yield stress was reached at which point the frequency suddenly increased and the continual stress drops caused the serrated stress-strain relation. The argument presented here indicates that the macroscopic yield stress observed in Ni-plated iron single crystals is controlled by the crack formation in the Ni film instead of by the dislocation motion. Therefore if the cracks can be formed at a lower stress under a suitable condition to generate dislocations, the yield stress can be as low as the stress for the edge dislocation motion. The low resolved shear stress of 30 - 40 MPa was reported in oxide-coated Nb single crystals at 77 K El?]. The critical stress for the crack formation which generates a suiI%ent number of dislocation loops may depend on more than ane factor. The strength of the surface film is
~UB~~~SHI
and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IROhi
1521
T. A. Ic
(c)
c
(d)
Fig. IO. Optical micrographs of a Ni-plated specimen deformed O.lP; at 77 K, (a)*(b) and (c) were taken from different areas iilustrated in (d). The similarity of the crack pattern indicates the manner of slip p~~pa~at~~~(see text).
certainly important. The residual tensiIe stress in Ni film can facilitate the crack formation. The number and geometry of stress concentrators where the cracks initiate must also be considered. The elastic moduli of the film with respect to those of the substrate may also influence the dislocation generation. It is suggested that the microplastic strain of the substrate increases the tensile stress in the surface film; therefore the crack formation would start at a lower stress level. The attainment of the lowest yield stress by the combination of prestrain and surface film [17.18] can be explained in this manner. Cracks are likely to be initiated at the corners where interlaminar shear stress is maximum [19.20]. if crack propagation occurs only by virtue of the bsittle nature of the Ni-film, cracks wouid propagate on both the top and side faces. The cracks were, however, observed only on the top and bottom faces. to which the primary slip directions inclined sharply. Slip-like lines. instead of cracks, form on the faces (side faces in this case) which are nearly parallel to the slip. directions. Reversing the surface geometry between the top
and side faces, cracks were found to form only on the side faces [1X]. This observation indicates that the interaction between substrate and surface film is essential for the crack formation, although the manner of propagation may be affected by the mechanical property of the film and its adherence to the substrate [2l]. Once a crack is nucleated, a number of dislocation loops are generated near the crack tip, which form a slip step on the substrate surface if they are edge d~s~~a~ons but not if they are screw dislocations. The surface film cracks more easily under the stress normal to the film than under the stress lying in its plane [22]. Therefore cracks propagate on the edge-face where the normal component of the slip vector is large. The crack propagation, therefore, consists of a chain reaction, namely, crack forrnationdislocation generation-surface step-further cracking. In discussing the surface film softening, it is suggested that the plastic deformation during serration occurs by the motion of edge dislocations. Each crack line produces a substantial plastic deformation in a
I522
KOBAYASHI and MESHII:
SURFACE OBSERVATION OF DEFORMED NICKEL-PLATED IRON
small region. The extent of this plastic deformation can be estimated from the slip displacement at the slip markings on the unplated bottom face of the specimen whose top face was Ni-plated (Fig. 8a). The displacement ranged from loo0 to 5OOOA.The average ratio of the plastic strain of the specimen to the number of the slip markings (or cracks) yields approximately 5 x lo-’ as the plastic strain per slip step (or crack). If this plastic strain occurs exclusively by the motion of the edge dislocations, the’displacement should be about 32OOA on the top (edge) face. Good agreement between this value and the measured slip displacement supports the motion of edge dislocations. The surface film softening phenomenon in Niplated iron single crystals was investigated using single crystal specimens oriented for duplex slip. The model developed here, however, can be applied to single crystals of other orientations. A similar observation was made in specimens with the tensile axis in the center of the unit stereographic triangle [18). The coarse structure of the cracks and slip-like lines observed in this study facilitated the morphological investigation. The coarseness of the morphology is not essential for the proposed model to be operational. A larger number of finer cracks (and finer slip steps) should produce a similar softening effect if they generate a sufficient number of dislocation loops. 6. SUMMARY The surface morphology of deformed specimens was investigated to elucidate why the electroplated Ni film reduced the yield stress of iron single crystals at 77 K. The findings of this investigation can be summarized as follows:
of dislocations took place near the cracks on the plated face and only the edge component of these dislocations moved .to form the slip steps on the opposite, unplated, face. The configuration of the slip steps was nearly identical to the crack configuration on the plated face. The line connecting the corresponding points was parallel to the primary slip direction. 6. The surface film softening is caused by the generation of many edge dislocations below the macroscopic yield stress of the substrate. The crack formation in the surface film controls the stress for the dislocation generation. Acknowledgements-The authors would like to thank Dr. Tomoyuki Takeuchi of the National Institute for Metals, Tokyo, for providing iron single crystal sheets, Dr. Kenichi Kojima for discussion of the results, and,Professor J. R. Weertman and Mr. D. J. Quesnel for reading this manuscript. This research is supported by the U.S. Energy Research and Development Administration.
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(1973). 5. K. Kitajima, H. Abe, S. Takamura and S. Okuda, Proc. Int. Conf in Metals,
6. 7.
8.
1. Two types of striation appeared on the specimen surfaces: cracks nearly perpendicular to the tensile axis and sliplike lines which deviated from the traces of the primary slip planes IlOl}. 2. Cracks were observed on the faces where the primary slip directions had large normal components (edge-faces) and the sliplike lines were formed on the faces nearly parallel to the slip directions (screwfaces). 3. The plastic deformation resulted from the formation and propagation of the cracks and the slip-like lines. The cracks and the slip-like lines were interconnected. 4. A bundle of cracks formed on one of the edgefaces; then cracks of a similar configuration often appeared on the opposite edge-face along with the appearance of sliplike lines on the screw-faces. This projection of cracks from one face to another occurred in the direction of the primary slip vectors. Since there were two primary slip vectors (duplex slip orientation), the projection was repeated like the reflection of light by a set of two parallel mirrors. 5. The deformation morphology in one-face-plated specimens demonstrated clearly that the generation
9. 10.
Fundamental
Aspects
of Radiation
Damage
p. 977. Gatlinburg (1975). V. K. Sethi and R. Gibala, Scripta Met. 9, 527 (1975). K. Kojima, S. Kobayashi and M. Meshii, Scripta Met. 10, 347 (1976). S. Kobayashi, K. Kojima and M. Meshii, Proc. 2nd Int. Conf: Mechanical Behavior of Materials, p. 78. American Society for Metals (1976). V. V’tek, Crystal Lattice Defects 5, 1 (1974). H. s’aka, K. Noda and T. Imura, Crystal Lattice Defects
4, 45 (1973).
11. A. S. Keh, W. A. Spitzig and Y. Nakada, Phil. Mag. 23, 829 (1971). 12. D. S. Tomalin and C. J. McMahon, Jr., Proc. 2nd Int. Conf: Strength of Metals and Alloys, p. 134. American
Society for Metals (1970). 13. A. P. L. Turner and T. Vreeland, Jr., Acta Met. 18, 1225 (1970). 14. H. D. Solomon and C. J. McMahon, Work Hardening, p. 309. Gordon & Breach, New York (1968). 15. C. J. McMahon. Microolasticitv. v. 121. Interscience.
New York (1968). ’ _. 16. A. Sato and M. Meshii, Phys. Status Solidi, (A) 28, 561 (1975). 17. V. K. Sethi and R. Gibala, Surface Eficrs in Crystal Plasticity, p. 599. Noordhoff, Lkyden rl977). _ 18. K. Koiima and M. Meshii. Phvs. Status Solidi (A) %, 39., 491 (1477). 19. R. B. Pipes and N. J. Pagano, J. camp. Mater. 4, 538 (1970). 20. S. Tang and A. Levy, J. camp. Mater. 9, 42 ,(1975). 21. T. Evans and D. R. Schwarzenberger, Phil. Msg. 4, .
889 (1957). 22. F. R. Lipsett and R. King, Proc.
608 (1957).
Phys. Sot.
(B) 70,