Cell structures in copper single crystals deformed in the [001] and [111] axes

Scripta

METALLURGICA

V o l . 14, pp. 1 8 3 - 1 8 8 , 1 9 8 0 P r i n t e d in the U . S . A .

P e r g a m o n P r e s s Ltd. All rights reserved.

CELL STRUCTURES IN COPPER SINGLE CRYSTALS DEFORMED IN THE [001] AND [iii] AXES Yozo Kawasaki and Tomoyuki Takeuchi National Research Institute for Metals Nakameguro Meguro-ku, Tokyo 153 (Received i.

October

2,

1979)

Introduction

Observations of the dislocation distribution in deformed copper singl4 crystals oriented for single glide showed that the cell structures developed approximately parallel to the active slip plane and the orientation of the plane cell walls deviated 2-3 degrees from the sllp plane (1,2). Close examinations of cell structures in deformed [415] and [112] copper crystals(3,4) showed that cell walls were on planes rotated around the <1127 axis on the active slip plane. The rotation angle in the [415] crystal was 3 degrees and that in the [112] crystal decreased from 15 to 7 degrees with the increase in the flow stress, and the slip llne lengths could be correlated with the cell structures(4). In the deformed [001] copper crystals, it was found by Druuen and Salmoto(5) and by GSttler (6) that the cell walls did not lie on any slip planes and the shape of individual cells in thin foils was spherical and the cell structure was isotropic in the deformed crystals. In deformed [iii] copper crystals, Ambrosi, GSttler, and Schwink(7) reported that the cell structures were analogous to those of the [001] crystals. Recently, in deformed [001] and [iii] copper single crystals, Ambrosi and Schwink(8) found that the slip line lengths were inversely proportional to the shear stress. The orientation dependence of the work-hardening behaviour of copper single crystals showed that the work-hardening characteristlces of the crystals near the [001] axls(9) were qualitatively different from those near the [iii] axis(10). This difference has been also observed in the fact that the flow stress response to the change in strain rate during deformation of the [001] crystal showed stepwise response, but the response in the other crystals showed transient phenomena(ll). In the present report, the three dimensional cell structures are observed in the [001] and [iii] copper crystals deformed at various temperatures by transmission electron microscopy, the slip distances estimated from the cell structures are compared with the slip llne lengths measured by Ambrosi and Schwlnk(8). 2.

Experimental Procedure

3 Test specimens, 2xSx45 mm , were cut from cylindrical (25 m m diameter) single crystals grown from high purlty(99.999 %) electrolytic copper by a Bridgman method. The [001] and the [iii] crystals used in the present observation were those extended in the previous experiments (9,10). The two side surfaces of the [001] crystals were the {i00) planes and the broad and the side surfaces of the [iii] crystals were the (121) and the (i01) planes, respectively. The axes of the specimens were within one degree from the ideal orientations respectively. The observations of cell structures were made in the specimens deformed until fracture in the range between -195 °C and 600 °C. Thin slices of 0.34 mm thick were cut from the deformed specimens by a multi-wire saw along low index crystallographic planes, and finally electropollshed. The foils were examined in a Shimadzu SMH-5B electron microscope operated at 500 kV. 3.

Results

Stress-strain curves The stress-strain curves of the [001](9) and [iii](i0) crystals deformed at various temperatures are shown in Fig. i and 2, respectively. The [001] crystals had no linear hardening

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FIG. i Stress-strain curves of the [001] crystals at various temperatures.

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FIG. 2 Stress-strain curves of the [iii] crystals at various temperatures.

stage even at low temperature, and they had no coarse slip line pattern on the surfaces of the deformed crystals, which appears on the crystals with the tensile axes deviated from the [001] axis by a few degrees. The [iii] crystals had linear hardening reglon at low temperature. The serrated flow at -195 °C meant twinning deformation and the cell structure of this specimen was not observed. The specimens of the both orientations fractured inside or near the grip part, and all the thin foils for electron microscopy were cut from the uniform part of the specimens. The [001] crystals As a typical example showing three dimensional features of the cell structure, the dislocation structures in the specimen deformed at 200 °C were shown in Fig. 3, (a) in the (001) foil perpendicular to the tensile axis and (b) in the (i00) foil parallel to the tensile axis. In the (001) cross-sectlon each cell had approximately a circular shape, but a close examination shows that many of cell walls lie approximately on the (ii0) and (ii0) planes. In the FIG. 3 Dislocation structures in the [001] crystal, deformed at 200 °C, (a) observed in the (001) foil and (b) in the (i00) foil. 19 ~ .

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FIG. 4 Dislocation structure in the [001] crystal, deformed at -195 °C, observed in the (001) foil.

FIG. 5 Average diameters of the cells observed in the (001) foils, in the [001] crystals deform ed at various temperatures, plotted against shear stress in a logarithmic scale.

(i00) side plane, the shape of each cell was elongated along the tensile axis. The cell structure in the (001) plane of the [001] crystals deformed at -195 °C is shown in Fig. 4. The cell structures in the [ill]Crystals were similar at all temperatures below 600 =C. At 600 =C, some recrystallized grains were observed among very coarse cell structures. The size of individual cells in the (001) foils was measured by GSttler's method(5). The diameter of about i00 cells were counted in several micrographs and the average values at various temperature are plotted against resolved shear stress in Fig. 5. As seen from Fig. 3(a) and Fig. 4, the ratio of the maximum to minimum diameter of the cells in the (001) foils was about i0. The average cell diameter was inversely proportional to the shear stress. GSttler(5) observed the average cell diameter in the (iii) foils of the [001] crystals which were deformed to various stresses at room temperature, and his result is shown in Fig.5 by a dashed line for comparison. The [iii] crystals Three dimensional cell structures in the [iii] crystals deformed at 200 °C are shown in Fig. 61 (a) in the (iii) foil perpendicular to the tensile axis, (b) in the ([2[) foil and (c) in the (I01) foil parallel to the tensile axis. Many cell walls were formed in pairs, similar to those in the deformed [112] copper crystals(3). Although the cell walls in the (iii) foll had a complicated feature, the cell walls in the (121) and (i01) foils showed that most of the cell walls had nearly plane shape,which is different from the cell structure in the [001] crystal. The cell structure in the (i01) foll cut from the specimen deformed at -90 °C is shown in Fig.7. The three dimensional cell structures in the [iii] crystals were similar at all temperatures below 600 °C. The crystallographic planes of cell walls in the Jill] crystals were estimated from the electron micrographs of cell structures in the specimens deformed at various temperatures. The result of this analysis is shown in Fig. 8, schematically. The (ili), (ill), and (11i) planes are the active slip planes in the [iii] crystals and B, C, and D are the corresponding cellwalls, respectively. The cell walls B in the (iii) foll of Fig. 6(a) were observed nearly along the trace of the slip plane[i01](horlzontal) and in the (i01) foil of Fig. 6(c) deviated by about 25 degrees from the [121] direction, the trace of the slip plane. The cell walls C and D in the (i2i) foil of Fig.6~b) deviated by about 29 degrees from the traces of the slip planes, respectively, and in the (i01) foil of Fig.6(c) deviated by about 14 degrees from the trace of the slip plane [i01]. The planes of cell walls were determined by two-surface analysis, and the results are as follows. The cell wall B was on a plane rotated by about 25 degrees from the (iii) plane around the [lOi] axis in the anti-clockwise direction, as shown in Fig. 8. The cell wall C was on a plane rotated by about 25 degrees from the (ill) plane around the [i12! axis in anti -clockwise directlnn and D by about 25 degrees from the (ill) plane around the [211] axis in

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FIG. 6 Dislocation structures in the [iii] crystal deformed at 200 °C, (a) observed in the (iii) foil, (b) in the (i2i) foil and (c) in the (i01) foil. the clockwise direction. The rotation angles of cell walls in the crystals until fracture were almost independent of deformation temperature. Average spacings between the cell walls were counted on the electron micrographs of the (i0i) foils. The closely spaced pair cell-walls were counted as one wall. One family of the layered cell walls corresponds to B and the other to C and D in Fig. 8(c). The average spacings on the (I01) foils for both families are plotted in Fig. 9 as a function of the shear stress. Both spacings(d) were on approximately the same line and they were inversely proportional to the shear stress(T). The relation was expressed by the equation d=78/T, where d is in ~m and T is in MN/m 2. The dashed line shown for comparison was the result observed on the one family of the plane cell walls in the (ii0) foil of the [112] copper crystals extended to various stresses at room temperature(3). FIG. 7 4. Discussion Dislocation structure in the [iii] crystal deThe [001] crystals formed at -90°C, observed in the (lOl) foil. The specimen surfaces of the [001] crystals

Vol.

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No.

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FIG. 8 Geometrical relationships between the cell walls and the corresponding active slip plane in the [Iii] crystals.

FIG. 9 Average spacings of cell walls in the (i01) foils of the [iii] crystals deformed at various temperatures, plotted against the shear stress in logarithmic scale.

after deformation nad a fine wavy pattern(12-14) (or cloth-like structure(6)). On the crystals whose tensile axes were deviated a few degrees from the [001] axis, coarse bands of slip-line clusters appear in the fine wavy pattern(9). Two kinds of slip mechanism co-existed in these crystals. The wave length of the wavy pattern on the [001] crystals increased at high deformation temperatures and it was approximately inversely proportional to the stress. The wave length, however, was about i0 times larger than the average cell diameter shown in Fig. 5. This indicates that the wavy pattern on the specimen surface does not correspond to the size of individual cells but they correspond to the periodical distribution of the regions of fine cells in the inhomogeneous distribution of cells with various sizes. GSttler(5) observed that the dislocations of all the active slip systems distribute uniformly in the cell walls. The (ii0) and (if0) planes on which the cell walls preferentially develop are on the symmetrical orientations with respect to the four active slip vectors. The cell structure in the deformed [001] crystals satisfies the four-fold rotational symmetry relation around the [001] tensile axis. The cell structure in the [001] crystal elongated in the [001] direction, and was different from the layered cell structures which were formed nearly in the active slip planes in the [415] and [112] crystals. The slip distance of dislocations in the [001] crystal can not be estimated in the same way as in the [415] and [112] crystals(4). The cell sizes in the (001) foils of the [001] crystal were about six times as large as the slip line lengths measured by Ambrosi and Schwink(8). Dislocations in the [001] crystal penetrate many cell walls during deformation. The

[iii] crystals The cell structures observed in the [ill] crystal were similar to the layered cell structures in the [415] and [112] crystals. If it is assumed that the primary dislocations freely pass through the cell walls of the other systems and are stopped only by the cell walls of the primary system, the slip distance of the primary dislocations is estimated from the spacing and the deviation angle of the cell walls, as in the case of the [415] and [112] crystals(4). The slip distances for the cell walls C, D on the (121) plane are Lc,D=l.05d/tan29°=l.89d=156/T, where 1.05d is the spacing of the cell walls C, D on the (12~) plane and the relation d=78/T is used. The slip distance was inversely proportional to the shear stress. Ambrosi and Schwink (8) found that the slip line lengths(L) were inversely proportional to the shear stress(T) and the relations were L=I27/T at 295 K and L=I57/T at 77 K, where L i s ~ m and T is in MN/m 2. The agreement between the calculated slip distance and the observed slip line lengths was satisfac-

188

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STRUCTURES

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FIG. i0 Projection of the slip-system octahedron to the [iii] tensile direction. The [121]-type combination of the sllp systems is C5, D4, CI, and DI. The [212]-type is B4, Bb, Cl,and DI.

IN C O P P E R

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tory. Therefore, the primary dislocations in the [iii] crystal are stopped by the cell walls of the primary sllp system. The slip systems of the [iii] crystal are illustrated by a slip system octahedron in Fig. i0. The slip systems with the first and the second Schmid factors of the crystals with the tensile axis on the [121] side on the [121]-[111]-[212] line of the stereographic projection are C5, D4, and CI, DI, respectively, and this combination of the slip systems is called the [121] -type(9). The slip systems with the first and the second Schmid factors in the crystals on the [212] side are B4, Bb, and CI, DI, respectively, and this combination is called the [212]-type(9). In the case of the crystal with the ideal [iii] tensile axis, the cross -sectional shape changed in the similar figure with elongation(9). This indicates that the [121]- and [212]-types of the slip system combinations worked equally.

In the present observation of the [iii] crystals, three kinds of the cell walls were observed as shown by B, C, and O in Fig. 8. The crystallographic planes of the cell walls were not symmetrical with respect to the [iii] tensile axis. The cell walls B correspond to the [212]-type of the slip -system combination and the cell walls C and D to the [121]-type. The observed cell structures in the [iii] crystals do not have three-fold rotational sygmetry relation, hut have a mirror image symmetry relation on the plane normal to the direction 2 in Fig. i0. Deviation of cell walls from the slip plane Cell walls in deformed copper crystals except the [001] crystals had plane shape. The deviation angle of the cell wall plane from the slip plane increased with increasing multiplicity of the combination of the active slip systems. This multiplicity means the increase in the number of the active Burgers vectors of the secondary dislocations, which penetrate the cell walls and also compose the dislocation tangles in the cell walls. The deviation angle was about 3 degrees in the [415](4), about i0 degrees in the [112] crystals(4), and about 25 degrees in the [iii] crystals. The plane of the cell walls always rotated in such a way that the plane normal approachs to the tensile axis under deformation. The [001] crystals had the cell walls preferentially on the symmetry plane of a pair of the conjugate slip plane, and the angle between the cell walls and the slip plane is 35 degrees, hut the rotation relation of the cell walls is opposite to that of the other crystals. In the combination of the active systems, the [001] crystals have two pairs of the sllp vectors which are perpendicular each other. Such a combination of the active sllp vectors (90 degree-type) is absent in the other cystals. The [001]-type combination of the sllp systems and corresponding dislocation arrangements in the cell walls are expected to produce a dislocation reaction which is essentially different from that in the cell walls of the other crystal orientation. References i. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12. 13. 14.

J. D. Y. Y. E. G. P. P. T. T. T. W. J. T.

W. Steeds, Proc. Roy. Soc. London A 292, 343 (1966). M. Moon and W. H. Robinson, Can. J. Phys. 45, 1017 (1967). Kawasaki, J. Phys. Soc. Japan 36, 142 (1974). Kawasaki, Japan. J. appl. Phys. 18, 1429 (1979). GSttler, Phil. Mag. 28, 1057 (1973). Van Druuen and S. Salmoto, Acta metall. 19, 213 (1971). Ambrosi, E. G~ttler, and Ch. Schwlnk, Script metall. 8, 1093 (1974). Amhrosi and Ch. Schwink, Script metal1. 12, 303 (1978). Takeuchl, J. Phys. Soc. Japan 40, 741 (1976). Takeuchi, J. Phys. Soc. Japan 41, 490 (1976). Takeuchl, J. Phys. Soc. Japan 41, 1943 (1976). Vorbrugg, H. Ch. Goetting, and Ch. Schwink, Phys. Status Solidi (b) 46, 275 (1971). Diehl, Z. Metallkde 47, 331 (1956). Takeuchi, Japan. Inst. Metals 16, 629 (1975).