Stacking fault energy measurements in some austenitic stainless steels

Stacking fault energy measurements in some austenitic stainless steels


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I. P. JOhiS


and M. H. LORE’ITO

Department of Physical Metallurgy and Science of Materials. CTniversity of Birmingham, Birmingham Bl5 171, England (Received

6 May 1977)

Abstract-Weak beam electron microscopy has been used to image a variety of faulted defects in a range of austenitic stainless steels. The observations have shown that the most reliable value of stacking-fault energy 7. can be obtained from measurements of the separation of partial dislocations in isolated dislocations. The values of stacking fault energy derived from extended nodes show a very large scatter and the significance of the different values of 7 derived from the various faulted defects is discussed in terms of the influence of temperature on stacking fault energy and of solute impedance effects. The sensitivity of stacking fault energy of these stainless steels to Cr and Ni content is assessed. R&m&-On a observe par la technique de la microscopic electronique avec un faisceau faiblement excite differents dtfauts d’empilement dans des aciers inoxydables austenitiques. Nos observations ont montrb que la valeur la plus sfire de l’inergie de defaut d’empilement 7 est obtenue en mesurant la separation des dislocations partielles sur des dislocations isolees. Les valeurs de l’energie de dtfaut d’empilement que l’on obtient a partir des noeuds dissocies prisentent une grande dispersion; I’on discute les differences dans les valeurs de p obtenues a partir de divers dcfauts en fonction de l’influence de la temperature sur 1energie de defaut d’empilement et des effets dimptdance du solute. Nous avons confirm6 la sensibiliti de l’energie de difaut d’empilement aux teneurs en Cr et en Ni de ces aciers austenitiques. Zusammenfassung-In einer Reihe austenitischer rostfreier Stable wurde eine Vielzahl von Stapelfehlerdefekten mittels Schwachstrahlelektronenmikroskopie (‘weak beam’) abgebildet. Die Beobachtungen zeigten, daB der zuverhissigste Wert fur die Stapelfehlerenergie y aus Slessungen des Abstandes der Teilversetzungen isolierter Versetzungen erhalten werden kann. Werte fur die Stapelfehlerenergie. die aus ausgedehnten Knoten abgeleitet wurden, weisen eine starke Streuung auf. Die Bedeutung der verschiedenen, aus unterschiedlichen Stapelfehlerdefekten ermittelten y-Werte wird anhand des Einflusses der Temperatur auf die Stapelfehlerenergie und anhand von Impedanzeffekten der Ldsungsatome diskutiert. Die Abhlngigkeit der Stapelfehlerenergie dieser rostfreien Stlhle von Cr- und Ni-Gehalt wird abgeschatzt.


The w.b. technique has been used by several authors for the examination of partial dislocation spacings in single dissociated dislocations in materials of high 7. as described by Cockayne et al. [3,4] and Howie and Basinski[5]. Results have been reported on Cu + 10at.x Al by Cockayne et al. [4]. on Si by Ray and Cockayne [q, on Cu by Stobbs and Sworn [7], on Au by Jenkins[8], on Ge by Haussermann and Schaumburg [9], and on Ge and Si by Gomez er al. [lo]. Recent experiments which are relevant to the accuracy of this method include those of Carter and Ray [l l] who have shown, with w.b. microscopy, that constrictions observed in dissociated dislocations in copper alloys were due to jogs, and those of Hazzledine er al. [12] who explained the observation of nonparallel dissociated dislocations in Cu-10 at.% Al in terms of foil surface effects. Morton and Forwood (1973) observing [13] bright field images of dislocation dipoles in nickel foils, estimated 7 using image simulation techniques and calculated equilibrium diagrams describing the configura-

Several direct methods for determining the stackingfault energies, y, of f.c.c. metals have been suggested. ‘Direct’ methods are here taken to mean those involving the measurement of the equilibrium configuration of a small group of partial dislocations, wherein the force exerted on the dislocations by the stacking fault is balanced by dislocation-dislocation strain field interactions (see Ref. 1 for a review). Methods involving the size-distribution of stacking fault tetrahedra or faulted dipoles are thus excluded The high resolution dark-field technique of weak-beam (w.b.) microscopy (see Ref. 2 for the principles and practice of w.b. microscopy), has obvious applications for improving the accuracy of these direct methods and extending their ranges to higher 7 alloys. *Now at Chalfont Technological Centre, British Aluminium Company Ltd., Gerrards Cross, Buckinghamshire, England. 39





tional coordinates of dipoles which were dissociated into their Shockley pairs. There have been no such studies in the literature of dissociated dipoles using w.b. microscopy. The paper describes the application of the w.b. technique to the examination of faulted lattice defect configurations in a range of austenitic stainless steels (f.c.c. Fe-G-Ni alloys). The influence of Cr and Ni on the value of 7 in stainless steels is also examined

form-that is, divided by any linear dimension of the ensemble. Following Morton and Forwood [13] we choose the inter-glide plane separation (see Fig. I). The stacking fault energy is thereby multiplied by this quantity. Because of the symmetry of the arrangement, it is sufficient to specify two contigurational coordinates _K, and x2 which are delined in Fig. 1. The coordinates at equilibrium are determined by minimising the energy in two dimensional cotigurational space. This is particularly easy in this case since both the gradient and Hessian have analytic forms 2. EXPERIMENTAL PROCEDURE (once the sextic, or equivalent, has been solved nu2.1 Specimen preparation merically). Five casts of Fe-Cr-Ni alloys were prepared with In all cases surface relaxation effects were ignored. Scattering factors were taken from Doyle and the compositions as shown in Table 1. High purity iron, ferro-chrome and ferro-nickel were used as Turner [ZO]. Absorption coefficients were obtained by matching experimental and computed bend contours, starting materials. The alloys were induction melted under argon and homogenized for 12 h at 12OO”C, and elastic constants were those measured by Salmutter and Stangler [23]. also under argon. The casts were reduced by rolling with intermediate anneals, to strip 20.5 mm thick. 2.3 fificroxopy Four thermo-mechanical treatments were applied: The specimens in the form of 3 mm diameter discs (a) Vacuum-annealed at 1050°C and slow cooled, (b) As in (a) followed by light deformation at room were jet thinned using an electrolyte of 3% perchloric acid, 35% butoxyethanol and 62% ethanol. They were temperature, (c) As in (b) followed by annealing for 24 h at 3oO”C, examined in a Philips E1M300 microscope. The w.b. diffraction conditions used were those (d) As in (b) followed by annealing for 3 h at 700’C. recommended by Cockayne [Z], i.e. 2.2 Computing (i) Ia.1 2 .2 nm-’ Single many-beam defect profiles were calculated (ii) Iwl = l&.5,1 &j using the differential equation formulation [ 143 of (iii) no other reflections (systematic or non-systematic) strongly excited, where s, is the deviation parameter Howie and Whelan (1961). Many-beam images and groups of profiles at different dislocation depths were, and &, is the extinction distance for the retlection g. Measurements of w.b. image-peak separations were however, calculated by regarding the strain field as made from the photographic negatives using a microan assemblage of stacking faults [15], and then multiplying the scattering matrices together. With the lat- densitometer and the radii of w.b. images of three-fold nodes were measured from magnified positives. All ter method one ‘integration’ through the general&d measurements were corrected for angular distortions foil thickness [16] is sufficient, whereas with the in the planes of the images. former, n integrations are required, where n is the number of beams. x2 P The dislocation strain fields were calculated assumx1 =* ing linear anistropic elasticity using the matrix formux*-x2 lation of Bamett and Lothe [17], which was a develx* =y opment of earlier treatments by Stroh [18] and Esh-. cc elby et al. [19]. This formulation was also used to calculate the equilibrium diagrams for the dissociated dipoles. Because dislocation stresses are homogeneous Fig. 1. Schematic drawing of a, dissociated dipole, illustratin x and y (z along the dislocation) the absolute caring the symmetry coordinates x1 and x2. The dislocations point out of the page, along the z axis. tesian coordinates may be expressed in ‘reduced

Table 1. Alloy compositions


CC wt.%

Ni wt.%

C wt.%

Si wt.%

Mn wt.%

MO wt.%

26122 21122 21124 16122 16/14

25.85 21.00 21.10 16.21 16.20

21.07 22.00 13.80 20.77 14.00

0.08 0.07 0.08 0.08 0.08

0.02 0.02 0.02 0.02 0.02

Other elements <0.002%, balance Fe.






3.1 Isolated dissociated


Me&ured w.b. image pe& separations for dissociated f (110) dislocations fd,,) were corrected for image shifts (i.e. displacement of the w.b. image peaks irom the positions of the actual partial dislocation cores) using the approach of Cockayne et al. [3]. This simplitied approach is convenient when examining large numbers of dislocation images. Its validity in the ease of elastically anisotropic austenitic stainless steels was confirmed by many-beam calculations of defects for a number of chosen cases. These showed that the image shifts from the dislocation cores are often large (e.g. 1 1.4 nm for an edge dislocation with d = j.Onm (where d is the true partial separation)) but the differences between d and-dQ,,, are very nuch less since the shifts of each partial image peak are in the same direction. There are strong depth dependencies of image peak intensities and also depth dependencies of dub%.The values of dDbJpredicted by this correction agree closely (to 0.1 or 0.2 nmj. with the anisotropic calculations. for the diffraction conditions used here. at foil depths where the image peaks are both strong. At a depth &‘3 greater or less than this. the calculated images and profiles generally show one of the peaks to be very weak and to have moved in towards the other. stronger peak, by about O.rlnm. The lvcak peak (typically about twice the background intensity) would generally be invisible experimentally and on this basis it was concluded that this correction procedure was adequate for estimating d-values from the experimental w.b. dislocation images.

3.3 Dissociated dipoles Again, the true lateral separations between the dislocations were required this time in several beam directions since the separation between the glide planes must also be determined. The image shifts were expected to be more significant in this case because they would be in opposite directions for the two dislocations. In fact the calculated image shifts were much smaller than for the isolated dislocations, being generally below 0.5 nm. This is presumably because the strain fields of the two dislocations tend to cancel. For the same reason the w.b. peaks were weaker than for the corresponding isolated dislocations. Such corrections were considered negligible in comparison to the waviness of the dislocation images (see Fig. 9). .ti attractive way to determine much of the defect geometry initially seemed to be to define that beam direction where the two inner partials were occluded. Unfortunately this was the one case where the image shifts were substantial. In addition the angle over which occlusion occurred was greater than that suggested by the single partial image half-width and the inter-glide plane separation. and the range of occlusion was asymmetric about the true position. Thus, in the event, occlusion was used to provide an initial





guess at the defect geometry, and the lateral separations measured in various beam directions were then used to refine this estimate.




The degree of dissociation of the dislocations was found to be dependent on the thermal and mechani4 treatments as well as on the type of distocotion configuration. The results obtained for each thermomechanical treatment are discussed. There vv-asno sigr&cant qualitative difference between the various alloys. In section (5) the derivation of ; from the various measurements is discussed. 3.1 Anttenlrd nr 105OC and s!ow-cooled The annealed specimens had low dislocation densities, and as expected many of the dislocations were in hexagonal networks. None of the long dislocations in these networks was found to be dissociated although some of the nodes were measurably dissociated in the 21,!14 and 162-t alloys. Typical bright field and w.b. micrographs of such undisscxiated dislocations are shown in Fig. 1. Some dissociated dislocations were however observed but these dissociated dislocations were always associated with obvious slip traces as can be seen from the example shown in Fig_ 3. It thus seemed likely that these dissociated dislocations had been introduced during or after the thinning process. When these dislocations were steeply inchned they took up equilibrium line directions qualitatively similar to those observed by Hazzledine zr al. (19751. although the partial pairs were more nearly parallel in this case. A few nodes were observed. Thex w2i2 extended to a very small extent in the 21 ;I4 and 16..14 alloys only. No extrinsic$ntrinsic fault pairs were seen. The only dipoles observed in the alloy-s which had been annealed at 105O’C were lying in slip bands and the foil surface slip traces indicated that they had been produced after the heat treatment. Examples~can be seen in Fig. 4. w.b. microscopy show& that these dipoles were dissociated into their Shxkley .pairs. The dipole partial dislocation w.b. images tended to be wavy and constricted at discrete points and the spacing of the Shockley pairs increased or decreased near the foil surfaces, in a similar manner to the iso lated dissociated disiocations but on a slightly exaggerated scale. 4.2 Treattwnt perntirre

(a) + light defortwtion

at roonl ten:-

All the dislocations were dissociated and contained many constrictions. Some of these ClGGi~ originate from dislocation intersections, since the constrictions define the trace of another slip plane. The influence of the jogs on the separation of the partisis does nor in fact extend v-cry far as can be seen in Fig. 5 where the partial images are non-paraliel for or& -2Onrz

ALiSTENLTIC STAINLESS STEELS prohbIy different in origin from that obsmcd by Clarebrough [?I]. The dislocations away from the tangles were not affected in this way and were suitable for measurements of d+ The number of nodes observed after this treatment was far greater than in the slowly cooled specimens although many of the nodes were again asymmetric. Some symmetrical nodes were* however observed (cf. Fig. 7). Like the symmetric node in the lightly deformed specimen (see 4.2) the nodes observed in these specimens were more extended than those in the as-annealed specimens, although there was a wide scatter in the results. The nodes shown in Fig. 8 appear to be close to equilibrium since the shapes of the edge node labelled A and the screw node IabelIed B are in very good agreement with the shapes computed for such nodes by Brown and Tholen [22}. The only intrinsic-extrinsic FdUk pairs observed in specimens annealed to 3OO’C were in regions which were too thick for w.b. microscopy. The 3OO’C anneal produced some dissociated dipoles which were isolated from dislocation tangles and which appeared to be in near-equilibrium configurations. An example is shown in Fig. 9. The exaggerated waviness of the partials and the curvature of one of the partials near the foil surfaces. as mentioned in sections 3.2 and 4.1. can be clearly seen in Fig. 9. 4.4 Trean~rrt

Fig. 2. Bright field and weali beam electron micrographs of dislocations in the 16-t-I alloy after annealing at 105O’C and slow cooling. The electron beam direction was near (I I I] and the operative reflection 022 was used in

the bright field microgaph (a) and for the weak beam micrograph (b) 066 was set at a positive deviation from the Bqg condition. (Since the grown-in dislocations are probably moved during deformation. they* could not be distinguished experimentally from the fresh dislocations and will not be considered separately hereafter) Extended nodes, fault pairs and dissociated dipofes were observed but virtually all the dislocations were shown to be heavily jogged and were in non-equilibrium configurations. For example the shapes of the nodes were clearly dominated by constrictions associated with the jogs and only one symmetrical node was observed. The extension of this was much greater than those observed in the annealed specimens.

The single dislocations were again all dissociated. The most obvious effect of annealing at 300°C was observed to be the formation of wide areas of stacking-fault, where the d&cations were in tangles. A typical area is shown in Fig. 6. This effect was assumed to be the result of internal stresses and was

(b) + 3 h arrtrenI at 7OO’C

After this anneal the dislocation density was reduced from that in the 3OO’C annealed specimens. Some of the dislocations were constricted, often over only part of their length. Many long relatively isolated dislocations were dissociated (apart from lengths near constrictions) and the separation of the partials was uniform over long segments as shown in Fig. 10. Except for the highest 7 alloys, the threefold nodes were al1 extended but only by small extensions similar to those observed in the IOWC annealed specimens and only two symmetrical nodes were found which were sufficiently dissociated to allow measurements Of 7. No extrinsic-intrinsic fault pairs were observed after this heat treatment. Similarly no dipoles were observed except where they had obviously been introduced after the heat treatment as discussed in Section


OF 7

These measurements will be d&u& under the headings of the different defects from which ;’ can be derived 5.1 isolated dislocations L&,,.was determined from long isolated away from constrictions ‘in all specimens as-deformed specimens which contained dislocations. The results are presented in

dislocations (except the no suitable Table 2 and

Fig. 3. \Veak beam micrograph of the 16,‘14 alloy showing dissociated dislocations introduced after the heat treatment. Imaged with g = 0% with G6 set at a positive deviation from the Brag condition and with the electron beam direction near [I 121.

Fig. 4. Weak beam micrograph of the 1614 alloy showing dislocation dipoles in a slip trace. Imaged with g = 022 with a positive deviation on &6.

Fig. 5. Weak beam micrographs of dislocations showing localised constrictions in the 21’14 alloy after deformation at room temperature. Imaged with g = 202 with 606 set positive of Bragg,. Electron beam direction near [01 I].

Fig. 6. Weak beam micrograph showing Gde areas of stackinv fault in the 16i14 alloy after a recovery treatment at 3oO’C. Imaged with g = O-20with 0 10 0 set po&e of Brag. Electron beam direction near [loll.






Fig. 7. Weak beam micrograph showing a z>mmetrical extended node in the ‘l/l4 alloy after a recovery treatment at 300’C. lmagcd with g = 111 with 555 set positive ol Bragg. Electron beam direction near [I I I].

the experimental points as xT+ 0. i.e. for screw disloin Fig. Il. In the figure the values of d are plotted cations. which could not be reproduced by assuming as a function of zT, the character of the i; 1 lo> dislocadifferent elastic constants. A similar deviation has tion. The error bars show the experimental scatter been reported and discussed by Stobbs and Sworn [7] along each dislocation since thsse were considerably greater than the measurement errors. It can be seen in Cu and Gomez et nl. [lo] for Si. Values of ;: calculated from the dissociation of edge that the values of rf show a relatively small scatter although it will be recalled that some disIocations in dislocations are shown in Table 2 and indicate a scatter of only about f20”,d. annealed specimens showed no visible dissociation. These have not been included. The curves drawn in Fig. I1 represent equilibrium curves of d against zT. Values of ; calculated from the measurements on for various assumed values of ;: computed using aninodes are shown in Table 3 and it is clear that where sotropic elasticity theory with elastic constants taken a sufficient number of symmetrical nodes has been from Salmutter and Stangler [23]. It appears that observed there is a large scatter in the results for each there is a systematic deviation of curves from

F_ig.8. Weak beam micropraph showing a screw node (on (1 t i)) at B and an [email protected] node at .A (on { I1 It) in the 16 t-i alloy after a recovery treatment at 3Do”C. Imaged with g = 111 with +&i positive of Bragg. Electron beam direction near [ t12].



T&e were mely observed. and then only in parts of the specimens too thick for w.b. microscopy. No determination of 7 was therefore possible.

5 4 Dipoles 7 was deduced by determining the defect configuration as described in Section 3.2 and then plotting the results on an equilibrium diagram for the relevant dislocation character. Three dipoles in the 21/14 ahoy were investigated in detail. The results are presented in Figs. f2(aj-(cj. The first dipole in Fig. I2 was evidently nowhere near equilibrium. 7 was deterfrom mined the other two dipoles as -23 -+ 1 erg;cm’ and 12 & 4erg~cm’ respectively.

6. DiSCUSSION There are two aspects to this work. The first concerns the practical problem of determining ‘/ in substitutional solid solutions. The second involves the variation of 7 with Cr and Xi contents ‘and with temperature. in austentic stainless steels. These will be taken separately. 6.1 The determination qf ;’ in substitutiorlal solid solurims

Fig. 9. Weak beam micrographs of a dissociated di in the 21: 14 ahoy after a recovery treatment at 30 Imaged in (a) with g = 220 with 660 positive- of Btagg. in (b) with g = 020 with 0 10 0 positive of Bragg and in (c) with g = 020 with 0 10 0 positive _of Bragg. The electron beam directions were close to [IIZ], [OOI] and [lOi].


Annealing the stainless steels at high temperatures (> 7oO’C) evidently tends to constrict all the defects examined. There were basic differences between the behaviours of the different types of defect after the various heat treatments. The isolated dislocations were either completely constricted, or the partials were at their equilibrium separation. The fraction of dislocation line that was constricted increased with annealing temperature. The nodes, on the other hand, were never completely constricted, except in the highest ;’ alloys, after the high temperature anneals. They showed a wider spread in the degree of extension for any particular heat treatment, and generally yielded a value of 7 greater than that obtained from the isolated dislocations. Dipoles also showed a range of configurations for any particufar heat treatment, although an insufficient length of dipolar dislocation was examined to say whether the partials were completely constricted at any stage. The explanation of these observations is suggested to be as follows_. p rises markedly with temperature (this will be sub&ntiated further in Section 6.2). As a result, at high temperatures isolated dislocations will tend to be compIetely constricted but nodes, for which the equilibrium splitting is larger will not be completely constricted_ On cooling to room temperature 7 decreases but solute impedance forces (which cannot

alloy for any one heat treatment

and there is in a ddition a signiCcant difference between the radii of ncsdes in specimens annealed to different temperatures.

be easily


at lower


become significant and act against the elastic forces which attempt to maintain the defects in equilibrium. As equilibrium is approached the elastic forces on partial dislocations in isolated dislocations are larger






Fig. 10. Weak beam micrograph of dissociated isolated dislocations in the 16 71 alloy after annealing at 3X-C. Imaged with g = O?l with 066 set positive of Bragg. Electron beam direction near [I I lj.

in nodes. Thus at low temperatures. where solute impedance forces become more significant. the nodes are less likely to be in equilibrium and the departure from equilibrium is likely to bs variable since solute impedance effects will vary locztlly. Thus in annealed specimens the extension of nodes will tend to show a scatter between the high and low temperature equilibria but the degree of dissociation of isolated dislocations wiIl either be close to the low temperature equilibrium value or they will remain constricted if the nucleation of pa&Is was unable to occur during cooling. The dipoles are believed to show a spread in implied 7, not simply because of lower restorative forces on the individual partials. but because of the low restorative force betkveen positive and negative total disIocations. It is therefore concluded that in alloys where solute impedance tjrces are important, ;’ is best determined by examination of isolated dislocations. This concluthan the forces on partial dislocations

sion may be tentatively extended to pure metals. Although there are no solute impedance forces, jogs still occur. and the present investigation has shown that the more complicated defects, such as nodes and dipoles, are considerably more sensitive to jogs than isolated dislocations. where the partial separation is perturbed only _ 30nm either side of the jog. Attempts have been made to measure the equilibrium configurations of dissociated dipoles using computed. strong, two-beam images [ 13.31. Such images are very sensitive to the finer details of the configurations and. on the face of it. are an attractive altemative to w.b. studies. since the w.b. peaks are weak for dipole partials. During the course of this work. when computing strong beam images of dipoles. it became clear that these images were more sensitive to the number of beams employed than b%-ereimages of isolated dislocations (whether these were dissociated or not). This is perhaps not surprising. since in a single disIocation image the strong two-beam in-

Table 2. 7 and d, (edge) values from Fig. 1 I

-_ 16










10 dlnml

28mJm-* :33 :36













16 I 1L

12 10 dhml




LO 50 oL(degI





Fig. 11. Measured widths (corrected for image shifts) of dissociated dislocations as a function of character angle, z, of the total dislocation (a) 21/24 alloy, (b) 16/14 alloy, (c) 16/22 alloy, (d) X/22 alloy. (e) 26/22 alloy. The full lines represent equilibrium curves calculated using anisotropic elasticity theon-. of d and x for assumed values of stacking fault energy, 7.

teraction comes from the long range part of the strain field, whereas the higher order Bloch wave transitions occur in the more strained crystal closer to the dislocation core. b a dipole, the long range part of the strain field tends to cancel and a large part of the image intensity comes from the extended core region of the dipole. Because of the uncertainty associated with many bean absorption parameters, and the greater sensitivity of the matching technique to inelastic image contributions, the w.b. technique, where feasible, is considered preferable. It is still possible that there is a region where the w.b. peaks are not resolvable, but the partial separations still have a detectable effect on the strong beam images. In this

region, of course, the interpretation of any determined core structure poses considerable difEculties 6.2 The variation of y with temperature and composition The suggestion in Section 6.1, that 7 of austenitic stainless steels increases markedly with increasing temperature, has been made before. Latanison and Ruff measured [25] the variation in diameter of threefold nodes in two Fe-O-Ni alloys over the range 25-325°C using in situ heating of the electron microscope specimens. Both reversible and irreversible effects were observed in cyclic heatineooling experiments. Node sizes were observed to decrease with increasing temperature but the irreversible component




Table 3. Inscribed node radii W, and y estimates from nearly symmetrical nodes







Annealed 105O’C Annealed 1050°C Recovered 700°C Recovered 3CO’C Recovered 300°C Recovered 300°C Recovered 3OOC As deformed

39 32 34 42 13 26 36

74 * 15 82 + 15 85 + 15 256 + 10 122 + 20 145 +_ 20 174 * 20 None symmetrical

50 * 45 * 44k6 16 f 31 * 27 + 23 2

1 3 3 2

Annealed 105O’C Recovered 700°C Recovered 700°C Recovered 300°C Recovered 300°C Recovered 300°C As deformed

35 30 28 38 15 85

71 + 15 79 + 15 65 & 20 229 k 30 235 + 30 163 + 15 None symmetrical

52 k 47 * 55 + 18 k 18 + 25 *

8 7 10 3 3 2

Annealed 1050°C Recovered 700°C Recovered 3OO’C Recovered 300°C As deformed


Annealed 105O’C Recovered 700°C Recovered 300°C Recovered 300°C Recovered 300°C Recovered 300°C As deformed


7 (mJm_‘)


Annealed 1050°C Recovered 700°C Recovered 300°C Recovered 300°C As deformed

30 17 46

5 15 19 28

22 12 36

None extended 80+ 15 120 + 20 84+ 15 None symmetrical None extended None extended 87 2 10 79 + 10 76 + 15 69 f 15 None symmetrical None extended None extended 84 f 10 72 + 15 162 + 10

1-o. IXd. c

06. -1.5



i’(d,) (mJm_‘)

7 6 18 f 4

23 2 5

47 + 7 32 + 3 45 f 6


42 k 4 4625 48 + 7 53 f. 7

33 2 5

35 +5 44*4 50 + 8 25 * 2


%$0 (X,1 05



Fig. 12. (a)-(c) Equilibrium diagram for three dissociated dipoles in the 21/14 alloy. The &shed lines represent equilibrium curves of X, vs x a over the y range determined for the 21/14 alloy (see Fig. 1 and Table 2). The experimentally determined values of 7 are shown as shaded areas which indicate the measurement errors. For full explanation see text.




is removed after the first heating to elevated temperature. The authors suggested that the large reversible changes are due to the variation of 7 with temperature. The smaller irreversible effect was thought to arise from increased solute impedance forces on partial dislocations at the elevated temperatures. The temperature and apparent effects on 7 were far less than in the present work, but followed the same general trend. The alloys used in this work are all within the range of metastable austenitic stainless steels, i.e. although the annealed alloys are all f.c.c. at room temperature, the thermodynamically stable phase is b.c.c. Thus one cannot argue simply that 7 is directly related to the stability of the f.c.c. phase with respect to the h.c.p. phase. Several workers (e.g. Fujita and Ueda [26]) have suggested that martensitic transformation of the metastable f.c.c. phase, by refrigeration or deformation, occurs via an h.c.p. phase. The final product is predominantly b.c.c. Since the f.c.c. phase becomes increasingly stable against martensitic transformation induced by deformation, as the temperature is raised (e.g. Reed and Gunter [273), one may infer that the f.c.c. phase does increase in thermodynamic stability relative to the h.c.p. phase. This would be consistent with the suggestion that 7 of the austenitic Fe-Cr-Ni alloys increases with temperature. Similarly, the change in 7 with Ni content (Table 2) appears to be consistent with the change in the tendency to transform martensitically. An increase in Ni content for a fixed Cr content decreases the value of M, and increases 7 as expected, since Ni stabilises the f.c.c. structure in stainless steels. However the influence of Cr content on M, cannot be used as a measure of 7. Since Cr is a b.c.c. stabiliser and the stability (against a martensitic transformation) will depend on the relative stability of f.c.c. and c.p.h. phases only if the transformation to b.c.c. martensite involves the h.c.p. phase. The complex effect of Cr on y will not then be reflected in changes in M, Considerable effort has been expended in the past in measuring y of austenitic stainless steels, the great majority of the determinations being from node-curvature measurements. The published results up to 1969 have been reviewed by Neff et al. [ZS] and more recent measurements have been made by Latanison and Ruff [25] and Lecroisey and Pineau [29]. There is a very wide scatter in the published values of ‘J. This may have been due to one or more of the following factors, (1) the large variation in the diameters of nodes of similar character at room temperature due to solute impedance forces as discussed above, (2) variations in the purity of the alloys used (several of the determinations used commercial grades of stainless steels), (3) variations in the assumed elastic constants and methods of calculation of 7. The values of 7 reported here, determined from the widths of extended isolated dislocations, agree with the previously published results on the quahtative effects of Cr and Ni content but are generally lower,




especially for the three high Ni steels where the 7 values appear to be about 207; lower. The higher values previously reported in the literature are undoubtedly a result of the sensitivity of nodes to solute impedance effects, discussed above. The especial sensitivity at high y are as expected since systematic errors from using strong bright field rather than w.b. imaging will be more significant at smaller partial separations. Acknowledgements-We would like to acknowledge Professor R. E. Smallman for his interest in this work and for the provision of laboratory facilities. C. C. Bampton and I. P. Jones would like to acknowledge financial support from S.R.C. in the form of a research studentship and feilowship respectively. Support from S.R.C. under grant B/RG/1624 is also gratefully acknowledged.

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