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THE PLASTICITY OF PURE NIOBIUM SINGLECRYSTALS

M. Duesbery, R. Foxall, P. Hirsch

To cite this version:M. Duesbery, R. Foxall, P. Hirsch. THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS.Journal de Physique Colloques, 1966, 27 (C3), pp.C3-193-C3-204. �10.1051/jphyscol:1966325�. �jpa-00213135�

JOURNAL DE PHYSIQUE Colloque C 3, supplkment au no 7-8, Tome 27, juilbet-aodt 1966, page C 3-193

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS

M. S. DUESBERY, R. A. FOXALL and P. B. HIRSCH

Cavendish Laboratory, University of Cambridge.

R6sumb. - On ktudie la dkformation de monocristaux de niobium purifiks par recuit dans l'ultra-vide. Les courbes tension-dkformation montrent trois degrks de durcissement analogues B ceux de cristaux c. f. c. Les premiers stades de la dkformation sont caractkrisks par des lignes de glissement ondulkes sur la face supkrieure et des lignes de glissement droites sur la face latkrale. Les glissements se situent dans les plans { 011 ) ou { 121 ), suivant I'orientation du cristal.

L'influence de l'orientation sur les plans de glissement effectifs montre que les tensions critiques de cisaillement sont diffkrentes pour les plans { 01 1 } et { 121 }, et que ces dernikres dkpendent du sens du glissement. L'asymktrie de glissement suivant les plans { 121 ) peut s'expliquer par la triple disso- ciation de dislocations vis.

Ce processus de dissociation explique aussi les grandes forces de frottement de reseau, leur variation avec la tempQature et l'allongement de boucles de glissement suivant la direction du vecteur de Burgers.

Abstract. - The deformation of single crystals of niobium purified by annealing in ultra-high vacua is studied. The stress-strain curves have 3 stages of hardening similar to those of f. c. c. crystals. The early stages of deformation are characterised by wavy slip lines on the top face and straight slip lines on the side face. Slip takes place on {011 ) or { 121 ) planes, depending on the orientation of the crystal. The results of the orientation dependence of the operating slip planes show that the critical resolved shear stresses for slip on (01 1) planes and on { 121 ) planes differ from each other, and that the latter depends on the sense of slip. The asymmetry of slip on { 121 ] planes can be explained in terms of the 3-fold dissociation of screw dislocations. This mode of dissoc~ation also explains the large lattice friction stress, its temperature dependence, and the elongation of glide loops along the Burgers vector direction.

1. Introduction. - Recent studies have revealed single crystals of niobium are purified by annealing in that, under suitable conditions of purity, orientation, ultra-high vacua, and the effect of this treatment on temperature and strain-rate, the shear stress-shear the mechanical properties is investigated. The depen- strain curves of several body-centred cubic metals are dence of the operating slip plane on orientation, basically similar to the three-stage hardening curves sense of application of stress, temperature and purity characteristic of face-centred cubic metals and alloys. has also been studied. This effect has so far been noted for niobium i itch ell et a1 1963 ; Votava 1964 ; Taylor and Christian, 1965), for tantalum (Mitchell et a1 1963 ; Thomas 1965 ; Mitchell and Spitzig 1966), for iron (Keh 1965) and for molybdenum (Thomas 1965).

The tendency to three-stage hardening is also observed in the work on iron by Jaoul and Gonzales (1961). However, there are several outstanding diffe- rences between the deformation characteristics of the two classes of crystal, particularly the relatively high flow stress of b. c. c. metals, its strong dependence on temperature and purity, the relative ease of cross-slip and the related problem concerning the difficulty of defining the slip plane.

In this paper experiments are reported in which

2. The effect of purity on the stress-strain curve.

2.1 . EXPERIMENTAL PROCEDURE AND RESULTS. - For this investigation, two standards of purity have been used : 1) crystals produced and purified by zone melting only and 2) crystals produced by zone- melting with further purification by ultra-high vacuum annealing, a technique due to Taylor and Christian (1965).

The single crystals were grown by electron beam zone-melting (Calverley et a1 1957) from 118 in. dia- meter rods of electron-beam melted niobium supplied by Murex Ltd. Crystals produced by zone melting only were given three passes from top to bottom at speeds of 5, 2 and 1 mm/mn respectively, the final

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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1966325

C 3 - 194 M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

pass being made in a vacuum better than 5 X 10-6 Torr. Tensile specimens, 2.5 cm long and 2 mm dia. were obtained by spark cutting and spark-lathing, using a final polishing treatment to remove spark damage. Figure l a illustrates the shear stress-shear strain curve obtained using this method of purifica- tion. Crystals produced for annealing were grown by 1 pass at 5 mm/mn. No spark-lathing was necessary in specimen preparation.

The ultra-high vacuum apparatus used for the annea- ling was a Varian VT-102 unit capable of a base pressure of 2 X 10-'l Torr, comprising a sorption forepump, a 250 litre sec-' sputter ion pump and a titanium sublimation pump. Annealing was effected by A. C. resistance heating. In general, the single crystal rods were held at about 2350 O C (96 % Tm OK) in a vacuum better than lOU9 Torr from a base pres- sure of the order of 5 X 10-'' Torr. Pressures were measured by a hot-filament nude ionization gauge within the chamber. In all cases, the anneal was ter- minated by melting.

All tests relevant to this section were carried out in tension at 295 OK on an Instron Floor Model machine at a standard strain rate of 1.3 X 10-4 sec-'. In each case the operative slip plane was determined by four-trace analysis and the shear stress-shear strain

curves were computed for the appropriate system using the methods described by Mitchell et a1 (1963).

TEMPERATURE E 2 9 5 - K

/

0 0 2 0 4 06 0.8 1.0

SHEAR STRAIN

FIG. l. - Shear stress-shear strain curves (a) for crystal puri- fied by zone-melting only (b) for crystal annealed for 24 hours.

Figure 2 illustrates the effect of annealing time on the stress-strain curve ; the curve for the unannealed crystal is included for comparison. Anneals inexcess of 8 hours consisted of 2 annealing runs. The first effects

SHEAR STRAIN

FIG. 2. - Shear stress-shear strain curves as a function of annealing time.

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS C 3 - 195

are the removal of the region of easy glide apparent in a strain rate of 4.4 X 10-5 sec-', where G is the the curve for the un-annealed crystal and a rapid shear modulus. This value is modified to about G1500 decrease in the initial flow stress. Thereafter the initial for the standard conditions used in this work. This parabolic region, stage 0, is almost removed. The iength of easy glide passes through a maximum, with an accompanied minimum in the work hardening rate. The length of the transition region decreases. The work hardening rate in stage 11 steadily increases and the stress at the onset of stage I11 steadily decreases, both to constant values.

Figure 1 illustrates a comparison between the stress- strain curve obtained for niobium purified by zone- melting only (Fig. la) and that for niobium annealed for 24 hours (Fig. lb).

2.2. DISCUSSION. - The marked improvement of the deformation characteristics achieved during the prolonged annealing treatment (Fig. 2) is due both to increasing purity and decreasing dislocation density. Taylor and Christian, using a very similar technique report that the initial dislocation density is reduced from about 5 X 106 cm-2 to about 5 X 10' cm-'. A detailed explanation of the manner in which the 3-stage hardening curve is improved in terms of the separate effects is rather difficult at present.

The work hardening rate in stage I1 is of particular interest in the 3-stage hardening curve. Mitchell et a1 (1963) reported that this was equal to about G1600 for

FIG. 3. - Straight slip lines on side face during stage I. 0.05 tensile X 160 straight slip

FIG. 4. - Bands of secondary slip on side face during stage 11. X 110, 0.40 tensile.

C 3 - 196 M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

value is also obtained with the 5-2-1 programme. bands become coarser, and begin to break out of the During annealing the rate increases from G1700 for the bands across the neighbouring primary structure un-annealed crystal to G1400 for a crystal annealed (Fig. 4, centre). This behaviour continues until in late for more than twelve hours. This value is very similar stage I1 the side faces show a fairly uniform diffuse to the value of G1300 obtained in f. c. c. metals. structure of interlocking primary and conjugate slip

The stress at the onset of stage 111, z,,,, is also sensitive to purity and reduces steadily during annea- ling. The final value is a factor of 2 below that obtai- ned by Mitchell et a1 (1963).

Finally, figure 1 clearly illustrates the development of the 3-stages of hardening as a result of ultra-high vacuum annealing. It is interesting to note that the changes of the stress-strain curve reported here are closely analogous to the effects obtained by reducing the alloy content in a face-centred cubic alloy system ; namely a reduction of the initial flow stress, z,, ,, the length of easy glide and the transition region, and an increase in the work-hardening rate in stages I and 11.

3. Nature of the slip lines as a function of defor- mation.

3.1. OBSERVATIONS. - Niobium single crystals purified by zone-.melting only were spark-machined to a square cross-section with one pair of faces almost parallel to the operative slip direction. This pair of faces will be referred to subsequently as the side faces, and the pair at right-angles to these as the top faces. Thus the slip lines on the side face are caused by dislocations with near screw character coming through the surface and trace the path of edge dislocations ; the slip lines on the top face are formed by edges, and trace the path of the screws, The slip lines were obser- ved using the Nomarski interference contrast techni- que. This method showed up slip lines which are virtually invisible under normal illumination condi- tions.

The orientation used is in the centre of the stan- dard triangle ; slip on (01 1) is expected and observed. It is convenient to deal first with the side faces. During stages 0 and I of the deformation, straight slip bands extending right across the face are observed (Fig. 3). As the crystal is deformed into the transition region, discrete narrow bands of conjugate slip begin to develop (Fig. 4). These bands are typically from 20 - 160 y wide, and extend over the whole width of the face. The secondary slip occurs predominantly on the (132) conjugate system, indicating that the more highly stressed (011) conjugate system has been overshot D.

During the transition the conjugate bands increase in number, until the whole crystal is fairly uniformly covered. During stage I1 the number of bands remains roughly constant, but the individual slip lines in the

FIG. 5. - Breakthrough of secondary slip on side face during late stage IT. X 160, 0.50 tensile.

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS C 3 - 197

FIG. 6. - Breakthrough of secondary slip on side face during stage I11 (oblique illumination) X 100, 0.60 tensile.

lines (Fig. 5). The side faces in stage I11 are shown in (Fig. 6) , which was taken using oblique illumination only. The conjugate slip has become more active, but the general picture remains much the same as in late stage 11.

In contrast to the straight slip lines on the side faces, the slip lines on the top face are much shorter and wavy in character. In stage 0 of the deformation the slip lines are long and only slightly wavy (Fig. 7a). However, the slip lines change character sharply on deformation into stage I (Fig. 7b), and develop into a tightly packed network of very short wavy lines. During stage I this structure remains constant in density, but the step height increases.

The photographs in figures 8 and 9 taken with obli- que illumination only, show the development of the slip line structure on the top face during the transition and stages I1 and 111. During the transition, extremely coarse cc hills )) and (( valleys )) develop on the top face. Correlation of these (( hills )I with the side face structure indicates that the (( hills )) are formed where the primary slip is unrestricted and that the valleys correspond to the bands of conjugate slip. No such bands of conjugate slip are observed on the top face, but the wavy structure would make any such bands very difficult to see.

During the late transition (Fig. 8b) and in stage I1 (Fig. 9a), long, coarse traces of the conjugate slip

a - 0,05 tensile b - 0,15 tensile FIG. 7. -Wavy slip on top face (a) during stage 0, and (b) during stage I.

C 3 - 198 M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

a - 0.30 tensile b - 0.40 tensile

FIG. 8. -Wavy slip on top face during the transition stage (oblique illumination).

a - 0.45 tensile b - 0.50 tensile

FIG. 9. -Wavy slip on top face (a) during stage 11, and (b) during stage I11 (oblique illumination).

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS C 3 - 199

system are observed. These are relatively straight, and interact with the primary hills to give a zigzag appearance to the slip lines.

Finally, in stage I11 (Fig. 9b) the conjugate activity increases and the top face structure becomes a uniform network of primary and conjugate slip.

Preliminary observations suggest that the nature of the slip lines on crystals of niobium purified by ultra high vacuum annealing after zone melting is rather similar to that of the unannealed crystals ; however, the bands of secondary slip tend to be fewer in number and wider.

3.2 DISCUSSION. - The appearance of bands of secondary slip in stage I1 suggests that the high work- hardening rate characteristic of this stage is due to elastic interactions with secondary dislocations, just as in the case of f. c. c. crystals. Dislocations with different Burgers vectors can interact strongly, as for example in the reaction.

Electron microscope observations of the disloca- tion structures in different hardening stages are in progress. Preliminary observations in stage I show bands of multipoles, somewhat similar to the irregular bands in copper single crystals (Steeds 1966). By analogy with the f. c. C. case the density of secondary dislocations in stage I1 is expected to be high, and primary screw dislocations may be prevented from mutual annihilation by the presence of clouds of secondary dislocations. The significance of the onset of stage 111 is not yet understood.

The long slip lines on the side face, and the short slip lines on the top face suggest that edges travel much further than the screws, and the slip bands are probably formed by the cross-slip mechanism, just as observed by Low and Guard (1959) in FeSi crystals and confirmed by Low and Turkalo (1962).

4. Operating slip planes.

4.1. EXPERIMENTAL RESULTS. - The slip planes of specimens deformed in tension were determined by a combination of optical and X-ray methods. The inclination of the slip traces to the tensile axis was measured at four points around the circumference of the crystals, and the results were combined with a Laue back-reflection determination of the orientation. Due to the wavy nature of the slip lines, measurements were made only on relatively long and straight traces. The independent measurements in each set were

found to be consistent with a definite slip plane, within the estimated experimental accuracy of , 1+0.

The slip direction of specimens deformed in tension and the slip planes of specimens deformed in compres- sion were determined by plotting the changes in orien- tation of the stress axis during deformation.

Figure 10 shows the reference triangle used (shaded triangle). The upper part of the triangle has been reversed in order that the same slip direction, i. e. [ l i l ] , operates over the whole of the triangle. Orientations in the upper part of the triangle differ from those in the lower part in that the sense of slip is reversed ; the sense of slip in tension for the upper orientations is crystallographically identical with the slip sense in compression for the lower orientations, and vice versa.

When studying the slip plane it is sufficient to define the orientation by means of the angle X (Fig. 10) between the [011] axis and the pole of the plane containing [l1 l] with the maximum resolved shear stress. Thus all orientations lie within the range - 300 X + 300. The slip plane will be defined by the angle cp (Fig. 10) between its pole and the 101 l ] axis.

Slip pla~e

211 [~iil

I1011

FIG. 10. - Stereographic projection of standard triangle.

Specimens were prepared by vacuum annealing for 12 hours in the manner previously described. These crystals were observed to slip on ( 110 } and ( 112 } planes only.

The results are plotted as a function of orientation in figure 1 1 and are superimposed on standard trian- gles in figure 12. Figure l la and 12a show the calcu- lated variation, assuming that slip takes place on the plane of the above type that bears the greatest resol- ved shear stress, and that the critical resolved shear stress on each plane is the same. Figures I lb and 12b represent the observed variation for crystals deformed in tension. The theoretical boundaries B

M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

FIG. 11. - Orientation dependence of the slip plane (a) theoretical (b) in tension and (c) in compression.

and C in figures l l a have been displaced to B' and C' respectively, in figure l lb.

These displacements indicate that the critical resol- ved shear stress on (121), (011) and (112) planes in tension, z(t), are related by

(0.942 ) 0.003) zlzl(t) = zoll(t) =

= (1.055 i- 0.008) ql2(t) .

FIG. 12. - Stereographic projections of orientation depen- dence of the slip plane, (a) theoretical (b) in tension and (c) in compression.

Figures l l c and 12c show the observed variation for crystals deformed in compression. The theoretical boundaries at B and C in figure 1 l a have now been displaced to B" and C" in figure l lc. These displa- cements indicate the relation in compression for the critical resolved shear stresses z(c)

(1.138 $. 0.006) zlZ1(~) = zOl1(c) =

= (1.00 + 0.05) zi12(c) .

Now assuming that z,, ,(t) = zoll(c), since the dis- placements in opposite senses on the (011) plane are related by a 1800 rotation about [Oll], these results suggest that

and

Crystallographically slip on (121) in tension is equiva- lent to slip on (T12) in compression, and vice versa. Hence, on the simplest model we would expect the two ratios given above to be equal. The difference in the values of the two ratios can be explained by assuming an orientation dependence of the critical

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS

(0) COMPRESSION (b) TENSION

FIG. 13. - Orientation dependence of the flow stress (gms . mm-2) at a shear strain of 10-4 (a) in compression and (b) in tension.

resolved shear stresses for slip on (121) or (011) planes. Figure 13 shows the experimentally determined orientation dependence of the critical resolved shear stress measured at a shear strain of 10-4, both for tension and compression. This stress tends to increase towards the corners and edges of the triangle, particu- larly towards the [001] corner. The way in which an orientation dependence of the critical resolved shear stress can reconcile the experimental results can be seen from the following argument. Since the bounda- ries between the slip systems occur at different orien- tations in the triangle, the assumption zO1 , ( t ) = z O l 1 (c) is no longer valid. We shall therefore consider the ratios

t o l l ( c ) - 1.138 e O 1 l ( t ) 1.055 and - - ;a = 7121(~)

which should be equal in the absence of an orientation dependence, and the pair of ratios

z011(t) - = 0.942 and = 1.00 7121(f) z i1 2 ( C )

which should similarly be equal. For simplicity we shall assume that the critical resolved shear stresses can be written in the form

where z ( ~ ) is an orientation dependent term which is the same for all slip systems. Then

and

Now the (112) plane operates at the top of the triangle in tension, and the (121) plane at the bottom of the triangle in compression ; therefore in accordance with the observed orientation dependence

z(x1) > ~ ( ~ 2 1

(see Fig. 13). Also, since z ( ~ ) is positive and

it follows that

zbi i ( t ) l~' i12( t ) 7611(~) /7 '121(~) > 1 ;

according to the crystallographic ,argument given above these last two ratios should also be equal. Using these facts it follows that

In a similar manner it can be shown that

again in agreement with observation, although in

'bn(t) < 1 and the effect of r(x) is to increase this case 7121(f)

the ratio ZO"0 towards the top of the triangle. z i 1 2 ( ~ )

C 3 - 202 M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

Although the observed ratios can be explained qualitatively in this way, to make the equations consistent quantitatively the orientation dependent term z ( ~ ) has to differ somewhat for the different slip systems in tension and compression.

If the differences between the critical resolved shear stress on (01 1 ) and { 1121, and the asymmetry for {l 12) slip in tension and compression are due primarily to differences in the lattice friction stresses, we expect the differences to be very much greater at lower tem- peratures where the magnitude of the lattice friction stress is known to be large. Preliminary experiments a t temperatures down to 175 OK have confirmed that the ratios z,, ,(t)/ziI2(t) and z12 ,(t)/zol ,(t) increase with decreasing temperature. Measurements show that at 175 OK, z121(t)/zol,(t) > 1.16, and thus slip in the " hard direction " on (112) planes does not occur for any orientation, the boundary between slip on (121) and (01 1) in tension being displaced out of the standard triangle.

A similar asymmetry for slip in Fe-Si crystals has been reported by S6stik and Zgrubovh (1965) although in this case the slip plane is not a low-index crystal- lographic plane, but is close to the plane of maximum resolved shear stress.

4.2 DISCUSSION. - The experimental results indi- cate that there is an asymmetry in the critical resolved shear stress for { 112) slip. This can be explained by considering the dissociation of dislocations on { 112) planes. A dislocation with Burgers vector + a [ l i l ] can dissociate according to the reaction

with a stacking fault between the two partials. The dissociation takes place in such a way that the a [l111 dislocation produces the twinning shear ; the fault is atomistically equivalent to a layer of twin three { 112 ) layers thick. Further dissociation of the 3 a[lT1] dislocation into two 4 a[lTl] partials results in the formation of a high energy fault in which the nearest neighbour atoms on adjacent { 112 ) planes are very close, and the packing is not of the b. c. c. type. However, a + a [ l i l ] screw dislocation can dissociate on three intersecting ( 112) planes (Fig. 14a) according to the reaction

all the faults being of the low energy twin type. (Hirsch 1960, Mitchell, Foxall and Hirsch 1963, Sleeswyk 1963). In order to move such a dislocation on a ( 112 ) plane it is necessary to constrict it, or a high energy

lslip plane

FIG. 14. - Dissociation of a screw dislocation on ( 112 ) planes and constriction under an applied stress.

fault must be formed, and the stress required in either case may be large and account for the high lattice friction stress in b. c. c. metals, at least as far as screws are concerned. Thus it has been shown that on the constriction mechanism for reasonable values of the stacking fault energy the lattice friction stress at the absolute zero can attain values -- G/100, where G is the shear modulus (Mitchell, Foxall and Hirsch 1963). Sleeswyk (1963) pointed out that the symme- trical dissociation on three planes is unstable relative to the configuration shown in figure 14b, where dissociation takes place on two planes only, with the third partial lying at their intersection. Again, this dislocation can only move if a constriction is produced, or if the stress is high enough for a high energy fault to be formed.

The movement of such a dislocation will now be considered in more detail. There are only two distinct low energy configurations for the dissociation (Fig. 14 c) which need be considered in this argument, and these two have opposite Burgers vectors. Under the in- fluence of an applied stress into the plane of the figure (Fig. 14d), the partial dislocations at C in figure 14c will constrict into the slip plane ; the two disloca- tions will then move in opposite directions. It is possi- ble, of course, for the partial at B to glide before the dislocation is fully constricted. In this case, however a high energy fault is formed on the slip plane between B and C, and the stress must be high enough to pro- duce this high energy fault. Consideration of the crystallography of the dislocation shows that slip in this sense, whether by the constriction mechanism or by forming the high energy fault, produces a compression for orientations in the lower part of the standard triangle. When a stress is applied in the

THE PLASTICITY OF PURE NIOBIUM SINGLE CRYSTALS C 3 - 203

opposite sense (i. e. out of the plane of the figure), movement of the dislocation appears to be much more difficult, since it seems to involve the formation of either two high energy faults, or one high energy fault and one constriction before the dislocation acquires a glissile configuration. The crystallography of this situation shows that slip in this hard direction corres- ponds to tension for orientation in the lower part of the standard triangle.

The asymmetry of the dissociation of screw dislo- cations therefore leads to the prediction that

and the crystallographically equivalent relation

in accordance with the experimental observations. The possibility of an asymmetry in the lattice

friction stress for movement of edge dislocations in opposite senses cannot be ruled out. If the lattice fric- tion forces resisting the movement of the partials +a [ l i l ] and & a [ l i l ] are F, and F2 respectively, it is easy to show by a virtual work argument that the shear stress, 2, to move the dislocation (Burgers vector b) as a whole is determined by the total friction force F = F, i- F2, i. e.

Since the atom displacements involved in moving the dislocation in opposite senses are crystallogra- phically equivalent, F, and F, would be expected to be the same and there would therefore be no asym- metry. However, the dislocation configuration would be somewhat different for slip in the two senses. A simple calculation using isotropic elasticity shows that

where G is the shear modulus, v Poisson's ratio, bl b2 the Burgers vectors of the two partials, do the equili- brium separation in the absence of stress and friction forces, d, the separation of the two partials in the presence of the stress and friction forces. The positive and negative signs correspond to motion of the dislo- cations in opposite senses ; the positive sign applies when the larger partial 3 a[l%l] is leading, the nega- tive sign when the twinning partial 4 a [ l i l ] is leading. Experimentally, the latter sense of slip corresponds to the " soft " direction, the former to the " hard "

direction. Clearly, if F , > 2 F, the dislocation will be more constricted for movement in the hard direction than in the soft direction. If the narrowing of the ribbon leads to an increase in F, and/or F,, the stress required to move the dislocation in the hard direction would be greater, as observed experimentally. How- ever, it is not at all clear whether the necessary condi- tion on the frictional forces is satisfied, or whether the frictional forces would be changed in the correct sense. Thus, while the possibility of an asymmetry in the movement of the edges cannot be ruled out, it is not possible to predict at this stage whether it would exist at all or what its sense would be. On the other hand, the movement of the dissociated screws will result in an asymmetry of the observed sense.

The mechanism proposed here gives qualitative explanations for a number of facts as follows :

1. The large lattice friction stress in niobium and other b. c. c. metals is likely to be due to the difficulty in moving dissociated screws ; the large temperature dependence will be due to the need for changing the dislocation into a glissile configuration by forming constrictions or high energy faults (Hirsch 1960, Mitchell, Foxall and Hirsch 1963).

2. The nature of the slip lines in niobium suggests that edges move much more easily than screws, a fact observed directly in Fe-Si crystals by Low and Guard (1959). The screw dislocation dissociation mechanism would explain this observation and the existence of long lengths of screw dislocations.

3. The same mechanism also explains the exis- tence of an asymmetry in the critical resolved shear stress for slip on { 112) planes, and its sense.

This mechanism however does not explain slip on { 110 ) planes. Various mechanisms for dissociation on { 110 ) planes have been suggested ; Crussard (1961) and Cohen, Hinton, Lay and Sass (1962) have sugges- ted the dissociation (on a (1iO) plane)

while Kroupa (1963) and Kroupa and Vitek (1964) have shown that a screw can dissociate on three { 110) planes according to the reaction

Another mode of dissociation is due to Wasilewski (1965), in which the dislocation dissociates into

a[l l l ] partials on a { 110 ) plane ; a 3-fold disso- ciation of screws into + a[l l l ] dislocations on 3 { 110 ) planes is also possible on this scheme. None of these

C 3 - 204 M. S. DUESBERY, R. A. FOXALL AND P. B. HIRSCH

modes of dissociation predicts any asymmetry, and so far there is no experimental evidence for any asymmetry for slip on { l l0 ) planes.

The reasons for the occurrence of { 110 ) and { 1 12 ) slip under different conditions are not yet clear. The explanation may well lie in the possible dissociation of dislocations in a composite manner on { 110 ) and { 112) planes, and this possibility must be explored further.

5. Conclusions.

1. Purification of niobium single crystals by annealing in ultra-high vacuum reduces the critical resolved shear stress to 600 g.mm-2 at 295 OK, at a strain-rate of 1.3 X 10-4 sec-'.

2. The stress-strain curves of these crystals have 3 stages of hardening similar to those of face centred cubic metals.

3. The slip lines in the early stages of deformation are wavy on the top face and straight on the side face suggesting that the edge dislocations travel much further than the screws, and that slip bands are formed by the double cross-slip mechanism.

4. Stage I1 of the stress-strain curve is characte- rised by the appearance of bands of secondary slip, rather similar to the case for f. c. c. crystals. The rapid hardening rate is likely to be due to interactions bet- ween primary and secondary dislocations.

5. Slip occurs either on (011 ) or ( 121 ) planes depending on the orientation of the crystal.

6 . The results on the orientation dependence of the operating slip planes show that the critical resolved shear-stress on (01 l), (121) in tension, and (121) in compression are all different from each other.

7. These results indicate that the lattice friction stresses for these modes of slip differ from each other and that there is also an orientation dependent contri- bution to the flow stress.

8. The asymmetry for slip on (121) planes is explained in terms of the 3-fold dissociation of screw dislocations.

9. This mode of dissociation also explains qualita- tively the large friction stress, its temperature depen- dence, and the elongation of glide loops along the Burgers vector direction.

Acknowledgments. - Our thanks are due to Pro- fessor Sir Nevill Mott, F. R. S., for the provision of laboratory facilities, and to Dr. J. W. Christian, Dr. G. Taylor and Mr. K. Bowen, Metallurgy Depart- ment, University of Oxford, and to members of the Metal Physics Group of the Cavendish Laboratory, Cambridge, for helpful discussions. This work has been supported by the National Physical Laboratory, and one of us (R. A. F.) also acknowledges the receipt of a maintenance grant from S. R. C.

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