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Twinning and accommodation kinking in zinc
TWINNING
AND ACCOMMODATION
KINKING
IN ZINC*
A. J. W. MOORE? The traces of twins and their accompanying accommodation kinks in cleavage surfaces of zinc single crystals were examined by interferometry and by optical and reflection electron microscopy. They were compared with metallographic sections cut normal to the twin trace. The results suggest that changes of shape of the twin beneath the surface determine the number and distribution of the accommodation kinks lying parallel to the twin trace. A growth history of the twin is described which conforms to these observations. The tip of the twin inside the metal may be markedly blunted giving rise to considerable internal stress. MACLES
ET KINKING
D’ACCOMMODATION
DANS
LE ZINC
Les traces des macles et des Kinkings d’accommodation sur la surface de clivage de monocristaux de zinc sont ttudiees par interferometrie et par microscopies optique et electronique. Elles sont comparees aux coupes metallographiques perpendiculaires a la trace de la macle. Les resultats indiquent que les changements de forme de la macle au-dessous de la surface determinent le nombre et la repartition des Kinkings d’accommodation. Un mode de croissance des macles, conforme B ces observations, est decrit. La pointe de la macle a l’interieur du metal donne naissance a l’importantes contraintes internes. DIE
ENTSTEHUNG
VON
ZWILLINGEN
UND
AKKOMODATIONS-KINKS
IN ZINK.
Die Spuren von Zwillingen und die sie beglsitenden Akkomodations-Kinks auf Spaltflachen von Zink Einkristallen wurden interferometrisch und durch optische und elektronenreflektions-mikroskopische Methoden untersucht. Sie wurden mit metallographschen Proben, die senkrecht zur Zwillingsebene entnommen worden waren, verglichen. Die Ergebnisse lassen die Vermutung zu, dass die Veranderungen in der Gestalt des Zwillings unter der Oberflache die Anzahl und die Verteilung der zu den Zwillingsspuren parallel liegenden Akkomodations-Kinks bestimmen. Ein mit diesen Beobachtungen iibereinstimmender Wachstumsablauf der Zwillingsbildung wird beschrieben. Die im Metal1 liegende Spitze des Zwillings kann auffallend abgestumpft sein und so zu betrachtlichen inneren Spannungen Anlass geben.
The phenomena of kinking and twinning in zinc are readily studied on faces of single crystals cleaved on the basal plane. Since this plane contains the only definitely established slip directions, the examination is not complicated by deformation due to simple slip. The traces of twins appear on cleavage faces in three directions mutually at 120” (parallel to the axial directions) and are the result of a shear of about 0.14 (So) on the 1012 planes. Although the atom movements are rather more complex* many of the larger scale effects of twinning can be interpreted in terms of a simple shear which causes a change of slope of 3”58’ on the basal plane, thus making the twin visible on cleavage faces. 0rowan2 and Hess and Barrett3 showed that cadmium and zinc can deform plastically by a mechanism involving a sudden bend or kink in the basal plane. The bend planes are perpendicular to the basal planes and produce sets of kinks which are either parallel to, or normal to, the u-axes and which are hence first- and second-order prismatic planes respectively. The concept of kinking has made it possible to explain how the shear strain due to twinning may be accommodated in the lattice when the twin is not propagated right through the crystal. Jillson pictured the process as a simple first-order kink parallel to the
twin trace on the cleavage plane as shown in Fig. 1. When the twin trace on a cleavage plane is lenticular in shape, Pratt and Pugh5 have shown that. the strain at the end of the twin is accommodated by a kink at right angle to the twin trace and crossing it at its tip. Moore6 and Holden’ have measured the angle of the first-order accommodation kink by independent methods which show that the principal kink, when fully developed, does not appear to bend the lattice by more than about 45’-50’. The angles and dimensions of a kink are of particular interest because they are a measure of the changes of shape of the twin beneath the surface. It has been shown5s6 that the same twin may have other first-order accommodation kinks parallel to the principal kink and lying between it and the twin. These have been termed
* Received July 6, 19.54; in revised form October 6, 1954. t Research Laboratory on the Physics and Chemistry of Surfaces, Department of Physical Chemistry, Cambridge, England, and now at Division of Tribophysics, C.S.I.R.O., Melbourne, Australia. ACTA
METALLURGICA,
VOL.
3, MARCH
1955
FIGURE 1. 163
164
ACTA
c
METALLURGICA,
FIGURE2.
secondary kinks in this paper. Further examples are described and compared with metallographic sections of the same twins and their possible importance in the development of the twin is discussed. EXPERIMENTAL
Preparation
and Cleavage Specimens
of Single
Crystal
Single crystals about 15 cm long and 1 cm square cross section were grown by the method of Bridgmans from 99.998 per cent Zn (Imperial Smelting Corporation Crown Special Zinc) in graphite moulds shaped to give the pointed crystal shown in Fig. 2, under a vacuum of 1O-3 mm Hg. Crystals oriented with the specimen axis in the basal plane and the face A (Fig. 2) making an angle of 10” or less with the basal plane were selected and specimens 1 cm ‘long parted off by cutting with hydrochloric acid. The faces (A and B) approximately parallel to the basal plane were soldered to the brass holders of a small tensile testing machine and cleaved by application of tensile stress approximately normal to the basal plane. For the sectioning experiments another set of zinc crystals were made from 99.999 per cent Zn (Imperial Smelting Corporation Special High Purity Zinc) in round Pyrex glass moulds sealed in vucuo. Crystals were selected with the basal plane approximately perpendicular to the longitudinal axis and specimens a few millimeters thick were parted from these while at liquid air temperature by cleaving with a knife. The cleavage features on these surfaces appeared to be identical with those produced by cleavage in tension. Twins with traces in directions suitable for sectioning were produced by bending the crystal over a 6-mm diameter rod after cleavage. Techniques
of Examination
On the cleaved zinc surface, features such as kinks and twins can be detected only by methods sensitive to very small changes of tilt of the surface, and with the Vickers Projection Microscope the best results were obtained with the 33 mm lens and the plane glass illuminator. The use of such a low-aperture lens restricted the magnification used. For greater resolution, both in the plane of the specimen surface and in a direction normal to it, the technique of reflection electron microscopy as applied by Menterg was used. This method is very sensitive to small changes of slope, particularly when the change occurs about an axis
VOL.
3,
1955
approximately perpendicular to the plane of incidence of the electron beam. Owing to the oblique angle of observation (lo”- 13’), the image is greatly foreshortened and a scale is given on each picture showing the magnifications in the plane of the surface in the direction of the beam, and normal to the beam. For measuring changes of slbpe, both a needle-type profilometer (Talysurf) and multiple-beam interferometry were used. For the latter, pieces of selected microscope slide about 2 mm square, partially silvered to give about 2.5per cent reflection in order to match the reflectivity of the zinc, were used as reference flats and the specimens were observed using an illuminating system as described by Tolansky.‘O Prior to sectioning the cleavage surfaces in a direction normal to the cleavage plane and to the twin trace, the crystal was given a heavy electrodeposit of zinc and cold-mounted in plastic. The desired section was exposed by grinding under water on a 150-grade carborundum paper followed by the finer grades and subsequently diamond-polished using the technique of Samuels.” Finally, the specimen was electropolished in a phosphoric acid-alcohol bath12 until all deformation due to grinding was removed. These specimens were examined in a Bausch and Lomb Metallograph under polarized light. The section was identified by means of diverging scratches drawn on the cleavage surface before plating. Angle measurements from the sections are only approximate since if slip occurs, the shear parallel to the basal plane would have the effect of changing the angle between planes which coincided with the original twin plane and the original basal plane. If the shear is inhomogeneous the twin may appear curved. RESULTS
AND DISCUSSION
When partial cleavage occurs on a basal plane other than that on which the crystal actually parts, bending strain in parts of the crystal may cause twinning. A twin formed in this way and accompanied by marked accommodation kinking, was extensively studied both by interferometry and reflection electron microscopy. (i) The angular relationships between a huin and its Kink: Figure 3 shows the multiple-beam interference fringes across the twin and its accommodation. The angle between the surface of the accommodation region and the undeformed surface (7 in Fig. l), measured at selected points along the twin, is shown in Fig. 4. It varies between 40’ and 17’ and decreases progressively towards the thin end of the twin. On the same graph the width of the twin (ZD)and the width of the accommodation (W) are plotted. If it is assumed that the lattice relationships for the twin and its accommodation kink have the simple geometrical pattern shown in Fig. 1, then since angles (Yand ,8 are known from the lattice constants of zinc, the angle between the sides of the twin in the body of the metal (angle X in Fig. 1) can
FIG. 3. Interference fringes across the end of a twin and its accommodation kmk. FIG. 5. Reflection electron micrograph of twin with an accommodation kink (shown by arrows) half-way across the accommodation region. FIG. 11. The tip of the twin shown in FIG. 7 at higher magnification (polarised light).
be expressed in terms of w and W by tanX=
0.465411 0.9976-0.4987R’
where R=
This expression holds for the two conditions where the twin plane is the side of the twin nearest to, and furthest from, the accommodation kink. This angle appears to fall from a value of about 4” to
about zero at the end of the twin. Twin and kink systems already illustrated in the literature can be similarly measured and they give approximate values for X of 4”50’ 7 and about 5o.6 The an& X can also be expressed in terms of the angle (y) of the principal kink tanX=
6.711 7.199+0.9976
cot7
166
ACTA
METALLURGICA,
:::-_~~~
0
Z
-2
Q
I F E 15r $
“?J’” OFK’NK 0
0.5WIDTH
0
>
tit_ 0.5 DISTAKiE
OF TWIN
I
I I .o 1.5 FRClYlTIP OFTWIN (mm)
FIGURE4.
? .5 Z 2 -0.05
&
-0.025
g
23
5
VOL.
3,
1955
and from this it appears that the value of 0’45’ which has been suggested for the maximum angle for the principal kink of a simple twin in zinc corresponds to an angle of X of 4’40’. (ii) The relationship between the shape of a twin and its kinks: In Fig. 3 the contour lines across the accommodation zone are not straight, showing that near the twin the slope of the cleavage plane is reduced. The same phenomenon, which indicates the presence of one or more secondary kinks between the principal kink and the twin, has also been shown by using a needle-type surface profilometer.6 The secondary kinks may be either in the same or the opposite sense to the principal kink increasing or reducing the slope of the basal plane respectively. Figure 5 is an electron micrograph showing another example of the latter type. It is a portion of the twin and its accommodation kink at a point about 0.4
6b
FIGS. 6 and 7. Comparisons between the traces of twin kink systems on the cleavage plane, with the corresponding sections. The sections are taken with polarised light. FIG. 12. Reflection electron micrograph showing how the accommodation kink becomes indefmite near the end of the twin. The patches of corrosion near the end of the twin may be seen also in FIG. 3 as grey patches which interrupt the interference fringes.
MOORE:
TWINNING
AND
ACCOMMODATION
mm from its tip, and a change in slope can be observed about half-way across the accommodation region, The intensity of the reflected electrons from the different regions shows that the secondary kink is in the opposite sense to the primary kink. Examples of the former type of secondary accommodation are shown in the optical photomicrographs in Figs. 6a and 7a where the tones of the different regions indicate that the accommodation slope is greater nearer the twin. Talysurf records across the same regions gave the traces shown in Fig, 8. The principal kink in Fig. 8a is about. 40’ and applies to the twin shown in Fig. 6. For Fig. 8b it is about 50’ and corresponds to the twin in Fig. 7, and in both cases there is a marked increase near the edge of the twin. In all cases of accommodation studied, a smooth bend was never observed but always an abrupt kink. Equation (2) indicates that an increase in the angle between the sides of the twin should be accompanied by an increase in the angle of the accommodation kink. Thus, where there is more than one kink the angle between the sides of the twin should vary to correspond with the different kinks. This relationship was investigated by cutting sections normal to the basal plane and to the twin trace on the basal plane. Figures 6b and 7b are sections of the twins shown in Figs. 6a and 7a and show clearly the slope of the cleavage plane due to the twinning shear, and the accommodation kink. The side of the twin furthest from the accommodation kink appears to consist of three regions of different slope: (a) Near the surface the two sides of the twin are nearly parallel. (b) Towards the middle of the twin the sides converge sharply, (c) Furthest from the surface the sides converge more gently. Sections of several twins have been observed and the majority have shown only slopes (a) and (c). Photographs of these taken normal to the cleavage plane showed a secondary kink of sense opposite to that of the principal kink. This produced a region of low accommodation angle near the twin which corresponded to slope (a) on the twin. On the other hand some sections of twins (i.e. Figs. 6 and 7) showed slopes (a), (b), and (c) and in the few cases where these could be compared with photographs normal to the cleavage plane it appeared that the only secondary kink present was in the same sense as the principal kink. This corresponded to slope (b). The fact that a further secondary kink corresponding to slope (a) was absent appears to be
2p. 4*P FIGURE
8.
KINKING
IN
ZINC
167
FIGURE9.
related to the extent that the twin had grown. This is discussed later. Figure 9 shows diag~mmatically how the accommodation kinks may correspond to changes in the shape of the twin, Features giving rise to both of the above types of kink are included and they all may be summarised as follows : 1. The bend plane (Fd) of the principal accommodation kink is a plane normal to the basal plane and lies close to the tip (B) of the twin. 2. Other secondary accommodation kinks with bend planes GJ, NK may occur between the principal kink and the twin. If they are of the opposite sense to the principal kink and reduce the accommodation angle to nearly zero (i.e., with kink Li, c?) then there is a corresponding region of the twin where its opposite sides converge more sharply (L?$). The former type appears to be common to almost all twin kink systems, but the latter type has been observed only in certain cases. 3. The twin boundary (AB) nearer to the accommodation kink is shown in the sections normal to the basal plane to be straighter than the boundary further from the accommodation kink. Since the two boundaries are not parallel they cannot both contain the twinning plane. It is probable, therefore, that the straighter boundary is the true twinning plane, while the boundary (CDEB) further from the accommodation consists of a number of fine steps each consisting of a short length of true twinning plane. At any point, the length of the steps relative to their height is determined by the angle between the two sides of the twin, (iii) The gm.e& of a twits: It is possible to speculate on a scheme for various stages of growth of the twin, which will conform to the final shape shown in Fig. 9. A simple explanation which fits the general facts is as follows : Consider a very small parallel-sided twin AB (Fig.
ACTA
168
I=
METALLURGICA,
D
lb)
7 L
(cl
L
I
FIGURE 10.
10a) with an accommodation kink at C and with length equal to the steps referred to in 3 above. The twin grows by the production of an adjacent parallel twin DE of the same thickness as AB but two step lengths long (Fig. lob). The kink moves outwards to its new position at EF. Further growth (Fig. 10~) proceeds by the production of additional twinned regions each a step-length longer than the previous one, the kink moving to its new position each time. A continuation of this process gives a situation similar to Jillson’s conception of the simple twin and kink system shown in Fig. 1. Since a kink is analogous to a boundary between mosaic blocks, it may be pictured as a row of dislocations of the same sign (e.g., Cottrell13). If 45’ is taken as a typical value of the accommodation kink angle, this corresponds to about one excess dislocation in the kink for every 75 atomic layers. If 5” is taken as a typical angle between the sides of the twin, then the correspond-
VOL.
3, 195.5
ing ratio of step-length to step-height is about 11. The excess dislocations could possibly arise as the twin grows and if n are assumed to arise from each new step, then the step-length would be (&2X75)/11 = 9n atomic layers (approximately). Thus, unless n is very large, which is unlikely, there is no possibility of the steps being visible. For convenience, the dislocations have been drawn with n= 1. This scheme of growth would also conform to the observation of Pratt and PughI that as the twin grows wider under increasing stress, the accommodation region also becomes correspondingly wider. The production of secondary kinks could be similar to the process shown as Fig. 10d and 10e. The twin is initially in the condition of 1Oc with a density D, of positive dislocations along the kink. For the case where the secondary kink is in opposite sense to the principal kink, the secondary kink starts to form at the point where the increase in length of the twin for successive stages of growth becomes less, i.e., the ratio of steplength to step-height is reduced (Fig. 10d). If the dislocations forming the kink arise from the successive stages of growth, then the density DZ of dislocations along the new length of kink will be greater than D1. It would appear that a kink having two different densities of dislocations along its length cannot move sideways. Instead, it splits into two kinks, one of density Dz, which becomes the principal kink and moves sideways as the twin grows, and one of density D1-Dz, which is fixed at the point where the twin growth changes and so becomes the secondary kink. Since D1-02 is negative-i.e., an excess of negative dislocations is presentthe secondary kink is of opposite sense to the principal kink. The additional positive dislocations needed to extend the principal kink to the surface of the zinc could be extracted from the region of the secondary kink, leaving an excess of negative dislocations to line up and form the kink. In crystals where there is no secondary kink to correspond to the nearly parallelsided portion of the twin (Figs. 6 and 7), it is possible that the kink has been absorbed by the twin growing past it. Where the principal and secondary kinks are in the same sense, the secondary kink starts to form by a similar mechanism at the point where there is a greater increase in length of the twin for successive stages of growth (Fig. 10e). Dl-Dz is now positive and the moving principal kink extracts only some of the excess dislocations from the fixed secondary kink. This process does not assume any particular mechanism for the formation of the small unit steps. If they should arise from a series of twinning dislocations passing down the twin plane as described by Thompson and MillardI for cadmium, then it is possible that the step-height would be the thickness of twin produced by one dislocation. The changes in the length of the steps would arise from variations in the difference between the internal stress in the zinc and the amount of stress
MOORE:
TWINNING
AND
ACCOMMODATION
which has been relieved by the growth of the twin. Such variations arise from the changes in the rate of deformation and the probability that a much greater stress is needed to initiate a twin than is required to cause it to grow.ls When the sections of the tips of the twins are highly magnified (Fig. 11) they appear to be rounded or even flattened. The metal beyond the tip of the twin appears to have an abrupt and coherent boundary with the twin which has undergone a shear of 0.14. In addition, the principal accommodation kink commences from a point slightly beyond the tip of the twin. These anomalies are strong evidence of considerable internal stress around the twin. At the end of the twin trace on the basal plane, the very small change of angle in the accommodation is only just detectable even in the electron microscope. Figure 12 shows the cleavage surface at the end of the same twin shown in Fig. 3. The accommodation kink, which is seen clearly on the left-hand side at A, becomes rapidly ill-defined and has disappeared altogether at the tip of the twin B. Again, this is probably determined by the elastic stresses arising from the fact that at the end of the twin, twinned material which has been sheared must be separated from untwinned material by planes other than twin planes. It is thus clear that the internal stresses set up during twinning have to be considered more seriously than hitherto. CONCLUSIONS
1. Between the principal accommodation kink and the twin there may be secondary kinks. No kinks appear to be more than 40-50’ when fully developed and the secondary kinks may be in the same or in opposite sense to the principal kink. 2. Sections of twins have shown that, in the side of the twin furthest from the accommodation kink, there
KINKING
IN
ZINC
169
are changes of shape corresponding to the pattern of the kinks, and from this, speculation may be made about the mode of growth of the twin. 3. The tip of the twin in the body of the metal is markedly rounded, indicating considerable internal stress. ACKNOWLEDGMENTS
This paper describes work done jointly between the Research Laboratory on the Physics and Chemistry of Surfaces, Department of Physical Chemistry, Cambridge, and the Division of Tribophysics, C.S.I.R.O., Melbourne, Australia. I thank Dr. F. P. Bowden, F.R.S., and Dr. W. Boas for their interest and encouragement and Dr. J. W. Menter for helpful collaboration, particularly with the electron microscopy. Acknowledgement is also made to the Ministry of Supply (Air) for a grant to the Cambridge Laboratory. REFERENCES 1. C. H. Mathewson and A. J. Phillips, Proc. Inst. Met. Div., Amer. Inst. Min. (Metall.) Engrs. (1927), p. 143. 2. E. Orowan, Nature 149, 643 (1942). 3. J. B. Hess and C. S. Barrett, Trans. Amer. Inst. Min. (Metall.) Engrs. 185, 599 (1949). 4. D. C. Tillson, Trans. Amer. Inst. Min. (Metall.) Engrs. 188, 1009 (i950). ’ 5. P. L. Pratt and S. F. Pugh, J. Inst. Metals 80, 6.53 (1952). 6. A. J. W. Moore, Proc. Phys. Sot. B55, 956 (1952). J. Holden, Phil. Mag. 43, 976 (1952). Proc. Amer. Acad. Arts and Sciences 60,305 :: P. W. Bridgman, _ $f9W6)Menter J. Inst Metals 81 163 (1952). Beam ‘Zlttwferdmetry (Clarendon, 1:: S. Tolansky,’ Mdtiile Oxford, 1948). 11. ._ L. E. Samuels, J. Inst. Metals 81, 471 (1953). 12. P. A. Jacquet, Metaux Corrosion Usure 19, 71 (1944). 13. A. H. Cottrell. Proves in Metal Physics Z (Butterworths, London, 1949); p. 93. 14. P. L. Pratt and S. F. Pugh, Acta Met. 1, 218 (1953). 15. N. Thompson and D. J. Millard, Phil. Mag. 43,422 (1952). 16. R. L. Bell and ‘R. W. Cahn, Acta Met. 1, 752 (1953).
AND ACCOMMODATION
KINKING
IN ZINC*
A. J. W. MOORE? The traces of twins and their accompanying accommodation kinks in cleavage surfaces of zinc single crystals were examined by interferometry and by optical and reflection electron microscopy. They were compared with metallographic sections cut normal to the twin trace. The results suggest that changes of shape of the twin beneath the surface determine the number and distribution of the accommodation kinks lying parallel to the twin trace. A growth history of the twin is described which conforms to these observations. The tip of the twin inside the metal may be markedly blunted giving rise to considerable internal stress. MACLES
ET KINKING
D’ACCOMMODATION
DANS
LE ZINC
Les traces des macles et des Kinkings d’accommodation sur la surface de clivage de monocristaux de zinc sont ttudiees par interferometrie et par microscopies optique et electronique. Elles sont comparees aux coupes metallographiques perpendiculaires a la trace de la macle. Les resultats indiquent que les changements de forme de la macle au-dessous de la surface determinent le nombre et la repartition des Kinkings d’accommodation. Un mode de croissance des macles, conforme B ces observations, est decrit. La pointe de la macle a l’interieur du metal donne naissance a l’importantes contraintes internes. DIE
ENTSTEHUNG
VON
ZWILLINGEN
UND
AKKOMODATIONS-KINKS
IN ZINK.
Die Spuren von Zwillingen und die sie beglsitenden Akkomodations-Kinks auf Spaltflachen von Zink Einkristallen wurden interferometrisch und durch optische und elektronenreflektions-mikroskopische Methoden untersucht. Sie wurden mit metallographschen Proben, die senkrecht zur Zwillingsebene entnommen worden waren, verglichen. Die Ergebnisse lassen die Vermutung zu, dass die Veranderungen in der Gestalt des Zwillings unter der Oberflache die Anzahl und die Verteilung der zu den Zwillingsspuren parallel liegenden Akkomodations-Kinks bestimmen. Ein mit diesen Beobachtungen iibereinstimmender Wachstumsablauf der Zwillingsbildung wird beschrieben. Die im Metal1 liegende Spitze des Zwillings kann auffallend abgestumpft sein und so zu betrachtlichen inneren Spannungen Anlass geben.
The phenomena of kinking and twinning in zinc are readily studied on faces of single crystals cleaved on the basal plane. Since this plane contains the only definitely established slip directions, the examination is not complicated by deformation due to simple slip. The traces of twins appear on cleavage faces in three directions mutually at 120” (parallel to the axial directions) and are the result of a shear of about 0.14 (So) on the 1012 planes. Although the atom movements are rather more complex* many of the larger scale effects of twinning can be interpreted in terms of a simple shear which causes a change of slope of 3”58’ on the basal plane, thus making the twin visible on cleavage faces. 0rowan2 and Hess and Barrett3 showed that cadmium and zinc can deform plastically by a mechanism involving a sudden bend or kink in the basal plane. The bend planes are perpendicular to the basal planes and produce sets of kinks which are either parallel to, or normal to, the u-axes and which are hence first- and second-order prismatic planes respectively. The concept of kinking has made it possible to explain how the shear strain due to twinning may be accommodated in the lattice when the twin is not propagated right through the crystal. Jillson pictured the process as a simple first-order kink parallel to the
twin trace on the cleavage plane as shown in Fig. 1. When the twin trace on a cleavage plane is lenticular in shape, Pratt and Pugh5 have shown that. the strain at the end of the twin is accommodated by a kink at right angle to the twin trace and crossing it at its tip. Moore6 and Holden’ have measured the angle of the first-order accommodation kink by independent methods which show that the principal kink, when fully developed, does not appear to bend the lattice by more than about 45’-50’. The angles and dimensions of a kink are of particular interest because they are a measure of the changes of shape of the twin beneath the surface. It has been shown5s6 that the same twin may have other first-order accommodation kinks parallel to the principal kink and lying between it and the twin. These have been termed
* Received July 6, 19.54; in revised form October 6, 1954. t Research Laboratory on the Physics and Chemistry of Surfaces, Department of Physical Chemistry, Cambridge, England, and now at Division of Tribophysics, C.S.I.R.O., Melbourne, Australia. ACTA
METALLURGICA,
VOL.
3, MARCH
1955
FIGURE 1. 163
164
ACTA
c
METALLURGICA,
FIGURE2.
secondary kinks in this paper. Further examples are described and compared with metallographic sections of the same twins and their possible importance in the development of the twin is discussed. EXPERIMENTAL
Preparation
and Cleavage Specimens
of Single
Crystal
Single crystals about 15 cm long and 1 cm square cross section were grown by the method of Bridgmans from 99.998 per cent Zn (Imperial Smelting Corporation Crown Special Zinc) in graphite moulds shaped to give the pointed crystal shown in Fig. 2, under a vacuum of 1O-3 mm Hg. Crystals oriented with the specimen axis in the basal plane and the face A (Fig. 2) making an angle of 10” or less with the basal plane were selected and specimens 1 cm ‘long parted off by cutting with hydrochloric acid. The faces (A and B) approximately parallel to the basal plane were soldered to the brass holders of a small tensile testing machine and cleaved by application of tensile stress approximately normal to the basal plane. For the sectioning experiments another set of zinc crystals were made from 99.999 per cent Zn (Imperial Smelting Corporation Special High Purity Zinc) in round Pyrex glass moulds sealed in vucuo. Crystals were selected with the basal plane approximately perpendicular to the longitudinal axis and specimens a few millimeters thick were parted from these while at liquid air temperature by cleaving with a knife. The cleavage features on these surfaces appeared to be identical with those produced by cleavage in tension. Twins with traces in directions suitable for sectioning were produced by bending the crystal over a 6-mm diameter rod after cleavage. Techniques
of Examination
On the cleaved zinc surface, features such as kinks and twins can be detected only by methods sensitive to very small changes of tilt of the surface, and with the Vickers Projection Microscope the best results were obtained with the 33 mm lens and the plane glass illuminator. The use of such a low-aperture lens restricted the magnification used. For greater resolution, both in the plane of the specimen surface and in a direction normal to it, the technique of reflection electron microscopy as applied by Menterg was used. This method is very sensitive to small changes of slope, particularly when the change occurs about an axis
VOL.
3,
1955
approximately perpendicular to the plane of incidence of the electron beam. Owing to the oblique angle of observation (lo”- 13’), the image is greatly foreshortened and a scale is given on each picture showing the magnifications in the plane of the surface in the direction of the beam, and normal to the beam. For measuring changes of slbpe, both a needle-type profilometer (Talysurf) and multiple-beam interferometry were used. For the latter, pieces of selected microscope slide about 2 mm square, partially silvered to give about 2.5per cent reflection in order to match the reflectivity of the zinc, were used as reference flats and the specimens were observed using an illuminating system as described by Tolansky.‘O Prior to sectioning the cleavage surfaces in a direction normal to the cleavage plane and to the twin trace, the crystal was given a heavy electrodeposit of zinc and cold-mounted in plastic. The desired section was exposed by grinding under water on a 150-grade carborundum paper followed by the finer grades and subsequently diamond-polished using the technique of Samuels.” Finally, the specimen was electropolished in a phosphoric acid-alcohol bath12 until all deformation due to grinding was removed. These specimens were examined in a Bausch and Lomb Metallograph under polarized light. The section was identified by means of diverging scratches drawn on the cleavage surface before plating. Angle measurements from the sections are only approximate since if slip occurs, the shear parallel to the basal plane would have the effect of changing the angle between planes which coincided with the original twin plane and the original basal plane. If the shear is inhomogeneous the twin may appear curved. RESULTS
AND DISCUSSION
When partial cleavage occurs on a basal plane other than that on which the crystal actually parts, bending strain in parts of the crystal may cause twinning. A twin formed in this way and accompanied by marked accommodation kinking, was extensively studied both by interferometry and reflection electron microscopy. (i) The angular relationships between a huin and its Kink: Figure 3 shows the multiple-beam interference fringes across the twin and its accommodation. The angle between the surface of the accommodation region and the undeformed surface (7 in Fig. l), measured at selected points along the twin, is shown in Fig. 4. It varies between 40’ and 17’ and decreases progressively towards the thin end of the twin. On the same graph the width of the twin (ZD)and the width of the accommodation (W) are plotted. If it is assumed that the lattice relationships for the twin and its accommodation kink have the simple geometrical pattern shown in Fig. 1, then since angles (Yand ,8 are known from the lattice constants of zinc, the angle between the sides of the twin in the body of the metal (angle X in Fig. 1) can
FIG. 3. Interference fringes across the end of a twin and its accommodation kmk. FIG. 5. Reflection electron micrograph of twin with an accommodation kink (shown by arrows) half-way across the accommodation region. FIG. 11. The tip of the twin shown in FIG. 7 at higher magnification (polarised light).
be expressed in terms of w and W by tanX=
0.465411 0.9976-0.4987R’
where R=
This expression holds for the two conditions where the twin plane is the side of the twin nearest to, and furthest from, the accommodation kink. This angle appears to fall from a value of about 4” to
about zero at the end of the twin. Twin and kink systems already illustrated in the literature can be similarly measured and they give approximate values for X of 4”50’ 7 and about 5o.6 The an& X can also be expressed in terms of the angle (y) of the principal kink tanX=
6.711 7.199+0.9976
cot7
166
ACTA
METALLURGICA,
:::-_~~~
0
Z
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Q
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“?J’” OFK’NK 0
0.5WIDTH
0
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tit_ 0.5 DISTAKiE
OF TWIN
I
I I .o 1.5 FRClYlTIP OFTWIN (mm)
FIGURE4.
? .5 Z 2 -0.05
&
-0.025
g
23
5
VOL.
3,
1955
and from this it appears that the value of 0’45’ which has been suggested for the maximum angle for the principal kink of a simple twin in zinc corresponds to an angle of X of 4’40’. (ii) The relationship between the shape of a twin and its kinks: In Fig. 3 the contour lines across the accommodation zone are not straight, showing that near the twin the slope of the cleavage plane is reduced. The same phenomenon, which indicates the presence of one or more secondary kinks between the principal kink and the twin, has also been shown by using a needle-type surface profilometer.6 The secondary kinks may be either in the same or the opposite sense to the principal kink increasing or reducing the slope of the basal plane respectively. Figure 5 is an electron micrograph showing another example of the latter type. It is a portion of the twin and its accommodation kink at a point about 0.4
6b
FIGS. 6 and 7. Comparisons between the traces of twin kink systems on the cleavage plane, with the corresponding sections. The sections are taken with polarised light. FIG. 12. Reflection electron micrograph showing how the accommodation kink becomes indefmite near the end of the twin. The patches of corrosion near the end of the twin may be seen also in FIG. 3 as grey patches which interrupt the interference fringes.
MOORE:
TWINNING
AND
ACCOMMODATION
mm from its tip, and a change in slope can be observed about half-way across the accommodation region, The intensity of the reflected electrons from the different regions shows that the secondary kink is in the opposite sense to the primary kink. Examples of the former type of secondary accommodation are shown in the optical photomicrographs in Figs. 6a and 7a where the tones of the different regions indicate that the accommodation slope is greater nearer the twin. Talysurf records across the same regions gave the traces shown in Fig, 8. The principal kink in Fig. 8a is about. 40’ and applies to the twin shown in Fig. 6. For Fig. 8b it is about 50’ and corresponds to the twin in Fig. 7, and in both cases there is a marked increase near the edge of the twin. In all cases of accommodation studied, a smooth bend was never observed but always an abrupt kink. Equation (2) indicates that an increase in the angle between the sides of the twin should be accompanied by an increase in the angle of the accommodation kink. Thus, where there is more than one kink the angle between the sides of the twin should vary to correspond with the different kinks. This relationship was investigated by cutting sections normal to the basal plane and to the twin trace on the basal plane. Figures 6b and 7b are sections of the twins shown in Figs. 6a and 7a and show clearly the slope of the cleavage plane due to the twinning shear, and the accommodation kink. The side of the twin furthest from the accommodation kink appears to consist of three regions of different slope: (a) Near the surface the two sides of the twin are nearly parallel. (b) Towards the middle of the twin the sides converge sharply, (c) Furthest from the surface the sides converge more gently. Sections of several twins have been observed and the majority have shown only slopes (a) and (c). Photographs of these taken normal to the cleavage plane showed a secondary kink of sense opposite to that of the principal kink. This produced a region of low accommodation angle near the twin which corresponded to slope (a) on the twin. On the other hand some sections of twins (i.e. Figs. 6 and 7) showed slopes (a), (b), and (c) and in the few cases where these could be compared with photographs normal to the cleavage plane it appeared that the only secondary kink present was in the same sense as the principal kink. This corresponded to slope (b). The fact that a further secondary kink corresponding to slope (a) was absent appears to be
2p. 4*P FIGURE
8.
KINKING
IN
ZINC
167
FIGURE9.
related to the extent that the twin had grown. This is discussed later. Figure 9 shows diag~mmatically how the accommodation kinks may correspond to changes in the shape of the twin, Features giving rise to both of the above types of kink are included and they all may be summarised as follows : 1. The bend plane (Fd) of the principal accommodation kink is a plane normal to the basal plane and lies close to the tip (B) of the twin. 2. Other secondary accommodation kinks with bend planes GJ, NK may occur between the principal kink and the twin. If they are of the opposite sense to the principal kink and reduce the accommodation angle to nearly zero (i.e., with kink Li, c
ACTA
168
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METALLURGICA,
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7 L
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L
I
FIGURE 10.
10a) with an accommodation kink at C and with length equal to the steps referred to in 3 above. The twin grows by the production of an adjacent parallel twin DE of the same thickness as AB but two step lengths long (Fig. lob). The kink moves outwards to its new position at EF. Further growth (Fig. 10~) proceeds by the production of additional twinned regions each a step-length longer than the previous one, the kink moving to its new position each time. A continuation of this process gives a situation similar to Jillson’s conception of the simple twin and kink system shown in Fig. 1. Since a kink is analogous to a boundary between mosaic blocks, it may be pictured as a row of dislocations of the same sign (e.g., Cottrell13). If 45’ is taken as a typical value of the accommodation kink angle, this corresponds to about one excess dislocation in the kink for every 75 atomic layers. If 5” is taken as a typical angle between the sides of the twin, then the correspond-
VOL.
3, 195.5
ing ratio of step-length to step-height is about 11. The excess dislocations could possibly arise as the twin grows and if n are assumed to arise from each new step, then the step-length would be (&2X75)/11 = 9n atomic layers (approximately). Thus, unless n is very large, which is unlikely, there is no possibility of the steps being visible. For convenience, the dislocations have been drawn with n= 1. This scheme of growth would also conform to the observation of Pratt and PughI that as the twin grows wider under increasing stress, the accommodation region also becomes correspondingly wider. The production of secondary kinks could be similar to the process shown as Fig. 10d and 10e. The twin is initially in the condition of 1Oc with a density D, of positive dislocations along the kink. For the case where the secondary kink is in opposite sense to the principal kink, the secondary kink starts to form at the point where the increase in length of the twin for successive stages of growth becomes less, i.e., the ratio of steplength to step-height is reduced (Fig. 10d). If the dislocations forming the kink arise from the successive stages of growth, then the density DZ of dislocations along the new length of kink will be greater than D1. It would appear that a kink having two different densities of dislocations along its length cannot move sideways. Instead, it splits into two kinks, one of density Dz, which becomes the principal kink and moves sideways as the twin grows, and one of density D1-Dz, which is fixed at the point where the twin growth changes and so becomes the secondary kink. Since D1-02 is negative-i.e., an excess of negative dislocations is presentthe secondary kink is of opposite sense to the principal kink. The additional positive dislocations needed to extend the principal kink to the surface of the zinc could be extracted from the region of the secondary kink, leaving an excess of negative dislocations to line up and form the kink. In crystals where there is no secondary kink to correspond to the nearly parallelsided portion of the twin (Figs. 6 and 7), it is possible that the kink has been absorbed by the twin growing past it. Where the principal and secondary kinks are in the same sense, the secondary kink starts to form by a similar mechanism at the point where there is a greater increase in length of the twin for successive stages of growth (Fig. 10e). Dl-Dz is now positive and the moving principal kink extracts only some of the excess dislocations from the fixed secondary kink. This process does not assume any particular mechanism for the formation of the small unit steps. If they should arise from a series of twinning dislocations passing down the twin plane as described by Thompson and MillardI for cadmium, then it is possible that the step-height would be the thickness of twin produced by one dislocation. The changes in the length of the steps would arise from variations in the difference between the internal stress in the zinc and the amount of stress
MOORE:
TWINNING
AND
ACCOMMODATION
which has been relieved by the growth of the twin. Such variations arise from the changes in the rate of deformation and the probability that a much greater stress is needed to initiate a twin than is required to cause it to grow.ls When the sections of the tips of the twins are highly magnified (Fig. 11) they appear to be rounded or even flattened. The metal beyond the tip of the twin appears to have an abrupt and coherent boundary with the twin which has undergone a shear of 0.14. In addition, the principal accommodation kink commences from a point slightly beyond the tip of the twin. These anomalies are strong evidence of considerable internal stress around the twin. At the end of the twin trace on the basal plane, the very small change of angle in the accommodation is only just detectable even in the electron microscope. Figure 12 shows the cleavage surface at the end of the same twin shown in Fig. 3. The accommodation kink, which is seen clearly on the left-hand side at A, becomes rapidly ill-defined and has disappeared altogether at the tip of the twin B. Again, this is probably determined by the elastic stresses arising from the fact that at the end of the twin, twinned material which has been sheared must be separated from untwinned material by planes other than twin planes. It is thus clear that the internal stresses set up during twinning have to be considered more seriously than hitherto. CONCLUSIONS
1. Between the principal accommodation kink and the twin there may be secondary kinks. No kinks appear to be more than 40-50’ when fully developed and the secondary kinks may be in the same or in opposite sense to the principal kink. 2. Sections of twins have shown that, in the side of the twin furthest from the accommodation kink, there
KINKING
IN
ZINC
169
are changes of shape corresponding to the pattern of the kinks, and from this, speculation may be made about the mode of growth of the twin. 3. The tip of the twin in the body of the metal is markedly rounded, indicating considerable internal stress. ACKNOWLEDGMENTS
This paper describes work done jointly between the Research Laboratory on the Physics and Chemistry of Surfaces, Department of Physical Chemistry, Cambridge, and the Division of Tribophysics, C.S.I.R.O., Melbourne, Australia. I thank Dr. F. P. Bowden, F.R.S., and Dr. W. Boas for their interest and encouragement and Dr. J. W. Menter for helpful collaboration, particularly with the electron microscopy. Acknowledgement is also made to the Ministry of Supply (Air) for a grant to the Cambridge Laboratory. REFERENCES 1. C. H. Mathewson and A. J. Phillips, Proc. Inst. Met. Div., Amer. Inst. Min. (Metall.) Engrs. (1927), p. 143. 2. E. Orowan, Nature 149, 643 (1942). 3. J. B. Hess and C. S. Barrett, Trans. Amer. Inst. Min. (Metall.) Engrs. 185, 599 (1949). 4. D. C. Tillson, Trans. Amer. Inst. Min. (Metall.) Engrs. 188, 1009 (i950). ’ 5. P. L. Pratt and S. F. Pugh, J. Inst. Metals 80, 6.53 (1952). 6. A. J. W. Moore, Proc. Phys. Sot. B55, 956 (1952). J. Holden, Phil. Mag. 43, 976 (1952). Proc. Amer. Acad. Arts and Sciences 60,305 :: P. W. Bridgman, _ $f9W6)Menter J. Inst Metals 81 163 (1952). Beam ‘Zlttwferdmetry (Clarendon, 1:: S. Tolansky,’ Mdtiile Oxford, 1948). 11. ._ L. E. Samuels, J. Inst. Metals 81, 471 (1953). 12. P. A. Jacquet, Metaux Corrosion Usure 19, 71 (1944). 13. A. H. Cottrell. Proves in Metal Physics Z (Butterworths, London, 1949); p. 93. 14. P. L. Pratt and S. F. Pugh, Acta Met. 1, 218 (1953). 15. N. Thompson and D. J. Millard, Phil. Mag. 43,422 (1952). 16. R. L. Bell and ‘R. W. Cahn, Acta Met. 1, 752 (1953).