Influence of Fe substitutions on the deformation behavior and fault energies of Ni3Ge–Fe3Ge L12 intermetallic alloys

Acta mater. 49 (2001) 1725–1736 www.elsevier.com/locate/actamat

INFLUENCE OF Fe SUBSTITUTIONS ON THE DEFORMATION BEHAVIOR AND FAULT ENERGIES OF Ni3Ge–Fe3Ge L12 INTERMETALLIC ALLOYS T. J. BALK†, MUKUL KUMAR‡ and K. J. HEMKER§ Departments of Mechanical Engineering and Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218-2686, USA ( Received 28 December 2000; accepted 14 February 2001 )

Abstract—Ni3Ge exhibits a yield strength anomaly, whereas the yield strength of Fe3Ge shows a normal decline with temperature, and there is a gradual transition from anomalous to normal behavior as Fe content increases. A dramatic strengthening for 77 K deformation has also been noted to occur in these alloys as a result of increasing Fe content. The combined use of transmission electron microscopy (TEM) and image simulations has facilitated identification of the operative deformation mechanisms and allowed for a quantitative measure of superdislocation dissociations. A transition from octahedral glide and Kear–Wilsdorf locking to cube glide of superdislocations has been observed to coincide with an increase in either deformation temperature or Fe content. The low-temperature strengthening has been correlated with enhanced cross-slip, which is aided by a significant lowering of the cube-plane antiphase boundary energy with increasing Fe content. It is proposed that the strengthening and the transition to cube glide are promoted by an increase in the complex stacking fault energy, which enhances both cross-slip and cube-plane mobility.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Transmission electron microscopy (TEM); Dislocations (mobility); Intermetallic compounds; Mechanical properties (plastic); Image simulation

1. INTRODUCTION

The anomalous increase of flow strength with increasing temperature exhibited by many L12 intermetallic compounds has attracted considerable attention in the literature. The deformation mechanism responsible for the yield strength anomaly is well documented, see for example [1]. The anomaly is associated with the thermally activated formation of Kear–Wilsdorf (KW) locks [2]; the process involves cross-slip of screw-oriented superdislocations from a {111} octahedral plane, where they are mobile, to a {010} cube cross-slip plane, where they are subjected to high friction stresses. The dissociation of a superdislocation in the L12-ordered crystal structure results in the formation of an antiphase boundary (APB) bounded by two similar 1/2具110典 superpartials, and further subdissociation of the superpartial results in a complex

† Present address: Max-Planck-Institut fu¨r Metallforschung, Stuttgart, Germany. ‡ Present address: Lawrence Livermore National Laboratory, University of California, 7000 East Avenue, L-356, Livermore, CA 94550 USA. § To whom all correspondence should be addressed. Tel.: +1-410-516-4489; Fax: +1-410-516-7254 E-mail address: [email protected] (K. J. Hemker)

stacking fault (CSF) bounded by dissimilar Shockley partials. The planarity of the dissociated core geometry, and, in particular, the widths of the APB and the CSF that are governed by the respective fault energies, have a profound effect on the dislocation mobility and, consequently, the gross deformation behavior [1]. There are several L12 alloys that do not exhibit the anomalous yield stress behavior. In order to study the transition from anomalous to normal mechanical behavior of L12 intermetallics, the model system (NixFe1⫺x)3Ge was chosen. This system is pseudobinary and has been reported to exhibit complete solid solubility if the Ge content is held constant at 25 at% and Fe is substituted for Ni as the composition varies from Ni3Ge to Fe3Ge [3]. The L12 compounds Ni3Ge and Fe3Ge show dramatically different mechanical behavior. Ni3Ge has been reported to have a strong anomaly [3], whereas Fe3Ge shows a more normal decrease of yield strength with increasing temperature [3, 4]. Moreover, Suzuki et al. [3] have reported that the temperature dependence of flow strength changes from anomalous to normal as the Fe content is increased, and this has also been corroborated by the current authors [5, 6]. The dislocation structures have been described for binary Ni3Ge [7] and Fe3Ge [8],

1359-6454/01/$20.00  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 0 9 7 - 0

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but the microstructural observations of this transition in the ternary alloys have not been documented. This study of the dislocation configurations that are characteristic of the Ni3Ge–Fe3Ge model system has been undertaken to determine the effect of Fe content on the fault energies and consequently on the yielding behavior of these alloys. Thus, it focuses on the characteristics of superdislocations in the context of the attendant fault energies and the influence they exert on microscopic deformation and macroscopic behavior. Specifically, the faults that govern the dissociation of dislocation cores will be investigated through experimental measurement of the dissociation widths and calculation of the fault energies within the framework of anisotropic elasticity. 2. EXPERIMENTAL METHODOLOGY

Alloys with the following nominal compositions were prepared for this study: Ni3Ge, Ni60Fe15Ge25, Ni50Fe25Ge25, Ni43Fe32Ge25, Ni20Fe55Ge25 and Fe3Ge. Details of the preparation of the polycrystalline master ingots have been given elsewhere [5]. Samples of each alloy were analyzed chemically using inductively coupled plasma spectrometry, and test results verified that compositions were within 0.2 at% of nominal composition except for Ni43Fe32Ge25, which was found to contain 44.5 at% Ni and 30.5 at% Fe. In the case of Fe3Ge, an extended heat treatment of 2 weeks at 1200 K, followed by 7 weeks at 873 K and then 4 weeks at 773 K, was required to produce the L12 crystal structure. Shorter heating times resulted in either the D019 crystal structure or the L12 phase with a microstructure dominated by stacking faults that remained from the D019 to L12 phase transformation. Following heat treatment, light microscopy observations of etched samples revealed equiaxed grains that ranged in size from 100 µm to 250 µm for the Fe-containing alloys, while Ni3Ge was found to exhibit a columnar grain structure with grain sizes up to 1 mm×1 mm×5 mm. Compression samples (10 mm in length and 4 mm square crosssection) were cut by electro-discharge machining, polished through 1200 grit grinding papers and deformed, at temperatures ranging from 77 K to 900 K, to 1–5% plastic strain at an average strain rate of 10⫺4 s⫺1. The deformed samples were sectioned at an angle of 45° to the compression axis and subsequently electropolished in a solution of 6% perchloric acid, 34% 2-butoxyethanol and 60% methanol at 15–20 V and ⫺40°C using a Struers Tenupol apparatus. The foils were examined in a Philips EM420 transmission electron microscope (TEM) at an accelerating voltage of 120 kV (weak-beam observations), as well as in a Philips CM300 TEM at 300 kV (high-resolution observations). Weak-beam image simulations were carried out using CUFOUR [9], which is a many-beam simulation program incorporating anisotropic elasticity, in order to account for the image shifts inherent in weak-

beam imaging of narrowly dissociated dislocations. The effects of convergence were not included, although intensity profiles of all simulated images were averaged over the length of the dislocations, to account for thickness oscillations. Five fundamental diffracted beams in the systematic row of the operating reflection and the transmitted beam were considered in all cases. Extinction distances and absorption coefficients for the relevant beams for the different alloy compositions were calculated using the program EMS developed by Stadelmann [10] and the scattering factors reported by Weickenmeier and Kohl [11]. High-resolution TEM observations were compared with simulated images of superdislocation cores. Atom supercells were made using CREATOR, a program written by S. M. Foiles and M. S. Daw, that uses anisotropic elasticity to determine the shifts in atom positions that result from the presence of one or more dislocations. Image simulations of the supercells were performed using EMS [10], and each simulated image was compared with the experimental image by overlaying a plot of the simulated peak positions. 3. OBSERVATIONS

3.1. Mechanical testing Samples of all six Ni3Ge–Fe3Ge alloys were deformed in compression to approximately 1% and 5% plastic strain, over a temperature range of 77 K to 900 K. For each test, the 0.2% offset flow stress (nominally the yield strength) was obtained from the true stress–true strain curves. The results are presented in Fig. 1, which shows the temperature dependence of yield strength for anomalous alloys [Fig. 1(a)] and for those alloys that exhibit no anomaly [Fig. 1(b)]. Ni3Ge, Ni60Fe15Ge25 and Ni50Fe25Ge25 all exhibited a flow stress anomaly, although the rate of anomalous strengthening decreased with increasing Fe content. The anomalous temperature range of Ni50Fe25Ge25 was significantly reduced, and the anomalous behavior was not observed in Ni43Fe32Ge25, Ni20Fe55Ge25 or Fe3Ge. In these ternary alloys, the flow stress dropped between 77 and 300 K, remained level up to 600 K, and dropped again at higher temperatures. In fact, all ternary alloys showed a sharp drop in flow stress above 600 K, regardless of the behavior that was exhibited at lower temperatures. Elevated-temperature data are not available for Ni3Ge and Fe3Ge because the specimens exhibited severe grain-boundary cracking above ambient temperatures. In general, these results indicate that a gradual transition, from anomalous to normal behavior, occurs as the Fe content increases, in agreement with the earlier findings of Suzuki et al. [3]. In addition to the gradual disappearance of anomalous behavior that is evident in Fig. 1, the strength was seen to increase markedly with Fe content for deformation at 77 K. The increase was greatest for

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Fig. 2. True stress–true strain curves showing the compressive deformation behavior of all six alloys at 77 K.

Fig. 1. Temperature dependence of 0.2% offset flow stress for (a) anomalous alloys and (b) alloys that do not exhibit a flow stress anomaly. The anomalous behavior decreases gradually with increasing Fe content, and disappears completely with the presence of 32 at% Fe. For all alloys, the flow stress drops with increasing temperature above 600 K; this is the peak for anomalous alloys, as well as the end of the plateau for Ni43Fe32Ge25 and Ni20Fe55Ge25.

the initial additions of Fe, as can be seen in Fig. 2, which contains the true stress–true strain curves for deformation of all six alloys at 77 K. As shown in Fig. 2, Fe3Ge showed only limited ductility and cracked consistently at less than 0.5% plastic strain. Nevertheless, the strengthening effects measured at 77 K were determined to be significantly larger than are normally attributed to solid-solution strengthening. 3.2. Deformation microstructures The following TEM investigations were conducted on large-grained polycrystalline samples compressed to 1% strain in order to better understand the change in yielding behavior as a function of Fe content and

temperature. A dramatic difference was observed in the room-temperature deformation microstructures of binary Ni3Ge [Fig. 3(a)], an alloy containing 32 at% Fe [Fig. 3(b)] and binary Fe3Ge [Fig. 3(c)]. Straight, screw-character 具110典 superdislocations, as seen in Fig. 3(a), dominated the microstructure in binary Ni3Ge. Tilting experiments determined that they were in the KW-locked configuration with the APB lying on the cube cross-slip plane. Numerous superdislocation dipoles (SD) were observed, and in some cases fringe contrast could be discerned between widely spaced dislocations that were isolated from other dislocations. In contrast, ambient-temperature compressive deformation of an Fe-rich (32 at% Fe) alloy produced a microstructure consisting of curved 具110典 superdislocations with random line orientations [Fig. 3(b)]. From stereographic trace analysis, it was determined that the superdislocations were gliding on the cube plane. The deformation microstructure of Fe3Ge was unique amongst the alloys examined in this study in that there was no evidence that octahedral glide or cross-slip had occurred. The superdislocations after room-temperature deformation [Fig. 3(c)] had Burgers vectors of the type 具110典, were found to lie exclusively on the cube plane and were oriented in a “cube-edge” configuration, similar to that reported by Ngan et al. [8]. Closer inspection of the dislocations in Fig. 3(c) indicates that one set of segments is very straight and exactly oriented along a 具100典 direction that is 45° from the Burgers vector, while the second set is slightly curved and only loosely aligned along a second 具100典 direction. Moreover, the straight segments in different dislocations appear to be lined up along the same 具100典 trace. These findings, coupled with the observation of separate but parallel dislocations that appear to trail behind the straight segments, suggest that the cube-edge morphology results from interaction with a second slip system on an orthogonal {100} type plane. Nevertheless, no screw-oriented dislocations were observed in the Fe3Ge microstructures.

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Fig. 4. Microstructure of Ni3Ge deformed at 77 K. Although the dominant microstructural feature is an array of straight superdislocations with the screw orientation, there is a significant fraction of mixed-orientation superdislocations that were gliding on the octahedral planes. g = [2¯ 02] and B = [111].

Fig. 3. A comparison of the room-temperature deformation microstructures in (a) Ni3Ge, characterized by straight, screworiented superdislocations, (b) Ni43Fe32Ge25, characterized by curved superdislocations with random line orientation, and (c) Fe3Ge, characterized by cube-edge oriented superdislocations on the cube plane. g = [022] in all micrographs; B⬇[1¯ 1¯ 1] in (a), while B⬇[100] for (b) and (c). Parts (a) and (b) are reprinted from Balk et al. [5], with permission of Elsevier Science.

Similar to the room-temperature experiments, deformation of Ni3Ge at 77 K also produced a microstructure that was dominated by straight, screw-oriented superdislocations, but with a significant fraction of superdislocations of mixed orientation that were gliding on the octahedral planes, as in Fig. 4. The measured spacing between the lines that correspond to superpartials in the pure edge orientation on the octahedral plane was determined to be 5.5±0.2 nm, and is recorded in Table 1. The CSF spacing could not be determined because the individual Shockley partials of the dissociated superpartial were not resolved, even in the edge orientation. (A third line of intensity, which is quite faint and can barely be

discerned in the inset of Fig. 4, was conclusively determined from image simulations to be an imaging artefact.) The spacing of APB-dissociated 30° kinks was measured to be 3.5±0.2 nm on the octahedral plane. The spacing between the superpartials that were aligned along the screw orientation was also measured, and the observed width of the APB is 3.8±0.4 nm on the cube plane. Detailed tilting experiments were performed to determine the APB plane when the superpartials were in the screw orientation, as illustrated in Fig. 5. Judging from the fact that the apparent APB width decreases as the thin foil is tilted from the cube-plane normal to the octahedral-plane normal, it can be concluded that the APB is lying on the cube plane, indicating the formation of a complete KW lock. The projected lengths and curvature of the dislocation lines themselves also confirm that the superpartials are lying on the cube plane. In particular, compare the curvature of the mixed segment of the dissociated superdislocation in Fig. 5(a) with the projected image of the same dislocation in Fig. 5(b). The apparent shortening of the segment upon tilting from the cube to the octahedral-plane normal indicates that the segment lies on the cube plane. With 15 at% Fe present, the dislocations in the Ni60Fe15Ge25 specimens deformed at 77 K, although still generally screw-oriented with a high degree of KW locking, showed localized bowing on the cube plane, as seen in Fig. 6(a). In this example, three families of dislocations have been activated, each consisting primarily of screw-oriented superdislocations. The observed increase in flow stress, when compared with binary Ni3Ge, suggests that cross-slip locking occurs more frequently in this alloy. Higher-magnification weak-beam images, as for example Fig. 6(b),

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Table 1. Dissociation distances and antiphase boundary energies in the Ni3Ge–Fe3Ge system as a function of alloy composition and temperature. The observed widths have been corrected for image shifts within the framework of anisotropic elasticity Alloy composition (temperature)

Ni75Ge25 (77 K) Ni75Ge25 (300 K) Ni60Fe15Ge25 (77 K) Ni60Fe15Ge25 (600 K) Ni50Fe25Ge25 (300 K) Ni43Fe32Ge25 (77 K) Ni43Fe32Ge25 (300 K) Ni20Fe55Ge25 (77 K) Fe75Ge25 (300 K)

Fault plane

{001} {111} {111} {001} {001} {001} {111} {111} {001} {001} {001} {001} {001} {111} {001} {001} {001} {001} {001}

Line orientation

0° (screw) 90° (edge) 30° 45° 0° (screw) 0° (screw) 90° (edge) 60° 90° (edge) 0° (screw) 90° (edge) 0° (screw) 0° (screw) 90° (edge) 90° (edge) 0° (screw) 30° 45° 75°

dmeasured (nm)

3.8±0.4 5.5±0.2 3.5±0.2 4.2±0.2 3.7±0.5 5.0±0.2 5.3±0.3 4.1±0.3 8.9±0.3 6.2±0.2 8.2±0.2 5.7±0.3 5.8±0.3 6.8±0.3 12.9±0.4 6.0±0.2 8.5±0.4 9.9±0.4 12.2±0.4

dcorrected (nm)

2.7±0.1 3.6±0.3 2.7±0.2 3.7±0.2 2.7±0.2 3.8±0.1 3.8±0.5 3.4±0.3 8.2±0.2 5.5±0.3 7.1±0.1 4.2±0.4 5.4±0.3 4.2±0.2 9.0±0.3 5.6±0.3 8.0±0.5 9.3±0.4 11.3±0.5

Antiphase boundary energy (mJ/m2)

gmeasured

gcorrected

212±22 220±8 259±15 261±13 219±29 154±6 223±13 264±20 141±5 124±4 151±7 132±7 127±5 168±7 95±3 114±5 99±5 99±4 91±3

296±11 339±29 337±25 292±12 297±22 202±6 315±41 320±28 153±4 140±7 172±5 180±17 132±8 272±13 137±4 121±6 106±6 106±5 98±4

Fig. 5. Detailed tilting experiment, performed to determine the plane of dissociation of the APB in Ni3Ge. (a) B苲[001] and (b) B苲[111]. These images were taken with a (g, 3.3g) weakbeam condition, using g = [2¯ 20] and a deviation parameter of 0.24 nm⫺1. As the foil is tilted from the cube-plane normal to the octahedral-plane normal, the width of the APB decreases, indicating that it is dissociated on the cube plane.

Fig. 6. (a) Observation of the dislocation structure in Ni60Fe15Ge25 after deformation at 77 K. Although the dislocations are generally aligned along the screw orientation, with a high degree of KW locking, they show considerable localized bowing on the cube plane. In this micrograph, three families of superdislocations are present, each with a different Burgers vector. (b) Higher-magnification, weak-beam micrograph used to measure the dissociation width on the cube plane, which is considerably larger than in Ni3Ge. g = [2¯ 02] and B⬇[010].

revealed nominally screw-oriented superdislocations with wider dissociation widths on the cube plane (dobs = 5.0±0.2 nm) than those observed in binary Ni3Ge. The uncorrected dissociation widths of edge superdislocations (5.3±0.3 nm) on the octahedral planes, however, did not appear to change when compared with what is observed for Ni3Ge, within the range of uncertainty. At a higher temperature (600 K), where the peak in the flow stress occurs for this alloy, there was evidence only of cube glide of

smoothly curved and widely dissociated 具110典 superdislocations of mixed character, as seen in Fig. 7. With polycrystalline samples, it was not possible to conclusively determine whether this represented glide on the primary cube plane or if it was a manifestation of the advanced stages of the cross-slip process with transfer and activation of dislocations from the octahedral to the cube cross-slip plane, as has been reported for the intermediate-temperature creep of Ni3Al [12].

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Fig. 7. Microstructure of Ni60Fe15Ge25 deformed at 600 K, the peak temperature of the flow stress anomaly. Only smoothly curved and widely dissociated superdislocations of mixed character, that had undergone cube glide, were observed. g = [2¯ 02] and B⬇[010].

Figure 8 is a micrograph from Ni50Fe25Ge25 deformed at room temperature. In many of the grains, including this one, it was observed that the average orientation of dislocations was in the screw direction, but the KW-locked segments can be seen bowing out on the cube cross-slip plane. The presence of switchover kinks and the absence of octahedral-plane macrokinks on KW-locked superdislocations suggest that double cross-slip processes are inactive at this test temperature. Several edge-oriented dipoles can also be observed in the microstructure, though not at the same locations as the kinks. These observations are very similar to those of the microstructure that develops in Ni43Fe32Ge25 during deformation at 77 K,

Fig. 8. Room-temperature deformation microstructure of Ni50Fe25Ge25. The average orientation of superdislocations is in the screw direction, but the KW-locked segments can clearly be seen bowing out on the cube cross-slip plane. g = [2¯ 02] and B⬇[010]. Figure reprinted from Balk et al. [5], with permission of Elsevier Science.

as shown in Fig. 9(a). Considerable localized crossslip activity is inferred from the microstructure, where numerous switch-over kinks (SK) and mixed-character dipoles (D) are observed along the dislocation line with the average screw orientation, as shown in the close-up micrograph of Fig. 9(b). In a few instances loops were observed, as for example in Fig. 9(a), where the mixed- and edge-character segments were gliding on the octahedral plane, though the APB was found to be on the cube plane for segments in the average screw line orientation with dobs = 5.8±0.3 nm. For the edge superdislocation segment, the width of the APB on the octahedral plane was measured to be 6.8±0.3 nm, which is only marginally wider than what was measured in the Ni3Ge and Ni60Fe15Ge25 alloys after 77 K deformation. In general, the measured changes in APB width on the cube plane were more significant than the changes on the octahedral plane. An even stronger indication of the increase in cubeplane mobility is given in Figs 3(b) and 10, which are representative of the room-temperature deformation microstructure in the majority of grains in Ni50Fe25Ge25 samples (Fig. 10) and in all grains in Ni43Fe32Ge25 samples deformed at 300 K [Fig. 3(b)]. Here, mixed dislocations dominate the microstructure along with numerous dipoles, thus indicating unim-

Fig. 9. 77 K deformation of Ni43Fe32Ge25. (a) The microstructure is similar to that in Fig. 8, with KW-locked superdislocation segments beginning to bow on the cube cross-slip plane. (b) Close-up micrograph revealing the presence of switch-over kinks (SK) and mixed-character dipoles (D). In both micrographs, g = [2¯ 02] and B⬇[010].

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Fig. 10. Many grains of Ni50Fe25Ge25 deformed at room temperature have the microstructure shown here. Mixed dislocations dominate, along with numerous dipoles, indicating unimpeded slip on the cube plane and providing evidence for the increase in cube-plane mobility with increasing Fe content. g = [2¯ 02] and B⬇[010]. Figure reprinted from Balk et al. [5], with permission of Elsevier Science.

peded slip on the cube plane. Cusps along the dislocation line can also be observed and are quite possibly due to local segmentation along the “cube-edge” (具100典) directions or APB tube formation, as suggested by Ngan et al. [8]. Tilting experiments have shown that the superdislocations are APB-dissociated on the cube plane and that cube glide has replaced octahedral glide as the dominant deformation mechanism. The deformation microstructure of Ni20Fe55Ge25 at 77 K is shown in Fig. 11. The vast majority of superdislocations were found to lie on the cube plane in the form of dipoles that ranged in character from screw to edge. The large population of mixed-character superdislocations suggests that cube glide is relatively easy at 77 K and that all characters are equally mobile. Measurements of the superpartial dissociation width were carried out on single superdislocations that were not part of a dipole, as for example with a screw segment that was observed to be dissociated by 6.0±0.2 nm. Although similar to Ni50Fe25Ge25 (300 K), Ni43Fe32Ge25 (300 K) and Ni20Fe55Ge25 (77 K), in that deformation was dominated by cube glide, Fe3Ge was unique amongst the alloys in this study in that there was no evidence that octahedral glide or cross-slip had occurred. The superdislocations observed in the room-temperature deformation microstructure of Fe3Ge were all found to exist in stepped configurations, similar to the “cube-edge” structure reported by Ngan et al. [8]. As shown in Fig. 3(c), the segments were oriented along alternating directions. The short, parallel segments were aligned exactly along a 具100典 direction at 45° to the Burgers vector, while the longer connecting segments ranged in character. Unlike the Ni-containing alloys, however, no screworiented superdislocations were observed. Figure 12 shows one of the “cube-edge” superdislocations from

Fig. 11. Superdislocation dipoles dominate the deformation microstructure of Ni20Fe55Ge25 at 77 K. (a) The two superdislocations in this screw dipole are closely coupled along the entire length of the dislocation. (b) Loops were also observed, where the dipole ranged in character from screw to edge. g = [2¯ 02] and B⬇[010].

Fig. 12. A superdislocation characteristic of the deformation microstructure of Fe3Ge at 300 K. No evidence of octahedral glide nor of KW locking was observed. The superdislocations all lay on the cube plane, in stepped “cube-edge” configurations where neighboring segments were aligned along alternating 具100典 directions. This cube-edge structure also existed on a smaller length scale, at the junctions between longer dislocation segments. g = [022] and B⬇[100].

which measurements of the dissociation width were obtained. Measurement of the 45° segment yielded an APB width of 9.9±0.4 nm, while the 75° segment yielded a width of 12.2±0.4 nm. The cube-edge orientation exists on two length scales; the longer segments range in length from 200 nm to 1 µm, while junctions of these longer segments often form cube-edge structures with step lengths of 50 nm or smaller, as shown in the inset of Fig. 12.

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In an attempt to resolve the splitting of superpartial dislocations, weak-beam TEM was performed at conditions that might permit observation of the very narrow dissociation of the CSF. However, even when imaging along a beam direction near the octahedralplane normal under extreme weak-beam conditions, no sub-dissociation of the superpartials could be discerned. This lack of CSF splitting held true for all of the superdislocations observed in this study, from screw to edge character. It has thus been inferred that the CSF width is smaller than 1–1.5 nm, which is the experimental limit of resolution of the weak-beam technique. Due to the inability to image CSF dissociations using weak-beam TEM, high-resolution transmission electron microscopy (HRTEM) was employed to view directly the arrangement of atomic columns in and around the superdislocation core. A beam direction of [110] was used to allow the observation of superdislocations with 具110典 Burgers vector and 0° or 60° character. An HRTEM micrograph of a 60° superdislocation in Ni3Ge is shown in Fig. 13, where the edge component of the dislocation is apparent in the two extra half-planes of atoms that can be seen in the upper portion of the figure. The distance between the extra half-planes was measured to be 14 interatomic spacings (14×a0/4[112]), or 3.1 nm, which agrees with the weak-beam observations to within 10%. In order to determine the fault widths in this dissociated superdislocation, a series of image simulations was generated for dislocation supercells with varying APB and CSF widths. Each simulated image was compared with the experimental image by overlaying a plot of the simulated peak positions, represented by crosses, as illustrated in Fig. 13. By com-

Fig. 13. High-resolution electron micrograph of a 60° superdislocation in Ni3Ge. The edge component is evident in the two extra half-planes of atoms that lie in the upper half of the figure. Overlaid on the experimental image is a plot of the peak positions from an HRTEM image simulation that corresponds to a 60° superdislocation with CSF width of 1.0 nm. Through comparison with image simulations, the CSF dissociation width has been determined to be between 0.5 and 1.0 nm.

paring the degree to which each supercell matched the experimentally observed atom positions, e.g., across the APB plane and around each superpartial, it was determined that the width of the CSF in Ni3Ge is between 0.5 and 1.0 nm. Since the sum of APB width and CSF width was held constant throughout the simulations, in order to match the measured distance between extra half-planes, the width of the APB thus varied between 2.1 and 2.6 nm.

4. CALCULATION OF FAULT ENERGIES

The precise determination of fault energies is of intrinsic value towards modeling the anomalous flow stress behavior, as it allows determination of the forces that govern cross-slip. The reduction in APB energy on the cube plane relative to the octahedral plane provides the thermodynamic driving force for cross-slip, while the magnitude of the CSF energy controls both the frequency of cross-slip and the mobility of superdislocations on the cube plane. It should be noted, however, that the experimental observations do not directly bring forward the equilibrium width of the planar fault and it is necessary to correct for image shifts. These effects are particularly acute during weak-beam imaging of narrowly dissociated superdislocations in ordered lattices with magnitudes of Burgers vectors larger than those encountered in normal face-centered cubic (fcc) solid solutions, due to substantial overlapping of the strain fields of the individual partial dislocations. Image simulations were carried out to determine the true dissociation distances in the manner described by Hemker and Mills [13]. In the particular case of Ni3Ge–Fe3Ge alloys, the elastic constants for binary Ni3Ge have been both experimentally measured [14] and predicted from first-principles calculations [15]. Experimental values for the Fe-containing alloys are not available, but the stiffness matrix for Fe3Ge has been predicted by Mryasov and Freeman. The elastic constants for the intermediate compositions were approximated using the rule-of-mixtures approach, i.e., individual elastic constants were obtained from linear interpolation, based on Fe content. These values are listed in Table 2. The results obtained from image simulations and matching are given in Table 1, where the experimentally measured and corrected values for the APB dissociation widths have been compiled for the six alloys studied. Where possible, several line orientations were analyzed to obtain a consistent measure of the APB energy. The typical scatter in the data is of the order of 5–10%, with somewhat higher uncertainty in measurement of APB widths for the octahedral plane. This arises, in particular, in those instances where the dislocations are strongly curved and when the dissociation distance is very small. The dissociation width as determined from HRTEM was also used to calculate fault energies for Ni3Ge, yielding an APB

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Table 2. Effect of elastic and APB energy anisotropy on the driving force for cross-slip of screw superdislocations from octahedral to cube planes under zero-stress conditions. Values for APB energies are taken from Table 1. Elastic constants for the intermediate compositions are derived using rule-of-mixtures calculations from the measured values for Ni3Ge [14] and calculated values for Fe3Ge [15]

Alloy composition

Elastic anisotropy, A = 2c44/(c11⫺c12), a = (A + 2)/A√3

Elastic constants, c11, c12, c44 (GPa)

Ni75Ge25 [14] Ni75Ge25 [15] Ni60Fe15Ge25 Ni50Fe25Ge25 Ni43Fe32Ge25 Ni20Fe55Ge25 Fe75Ge25 [15]

263, 271, 248, 238, 231, 209, 189,

143, 144, 139, 136, 134, 128, 123,

103 102 103 102 102 102 102

1.72, 1.61, 1.89, 2.00, 2.10, 2.52, 3.09,

energy of 368 to 385 mJ/m2, and a CSF energy of 386 to 595 mJ/m2. The APB energies were calculated by treating the superpartials as individual dislocations and balancing the repulsive force between the superpartials, as calculated using anisotropic elasticity [16, 17], with the surface tension associated with the planar fault. The APB energies calculated using the corrected dissociation distances show much better agreement than the energies associated with the as-observed values. This point can be illustrated by considering an example of image matching that unifies observations made using variable diffraction conditions and dislocation characters; see Table 3. The observed APB widths vary with both foil orientation and dislocation character, and the APB energies calculated using these observed values span a wide range (219–390 mJ/m2). This variation is related to three factors: (1) the elastic interaction forces change with dislocation character, which results in increasing separation as the character of the dislocation becomes more strongly edge-oriented; (2) the projection of the image from a tilted foil; and (3) image shifts associated with the overlapping strain field of the partial dislocations. Calculating the APB energies with anisotropic elasticity accounts for the first effect, but not for the last two. However, image simulations, as calculated using CUFOUR, naturally account for and correct these latter two effects. The trends in the corrected APB widths indicate that the APB energy for the {001} planes is significantly lowered as a result of increasing Fe content. The cube-plane energy decreases from a value of about 295 mJ/m2 to about 105 mJ/m2 as Fe com-

1.25 1.30 1.19 1.15 1.13 1.04 0.95

APB anisotropy, z = g111/g001

Cross-slip force, Fc = g001[(z⫺a)/a] (mJ/m2)

1.15±0.16 1.15±0.16 1.59±0.19 – 2.01±0.17 – –

⫺60.7–+15.1 ⫺69.6–+2.3 +36.8–+99.9 – +86.6–+128.1 – –

pletely replaces Ni, with a dramatic drop of about 95 mJ/m2 seen for the alloy with 15 at% Fe as compared with the value for Ni3Ge. As a point of contrast, the octahedral-plane APB energy decreases from approximately 335 mJ/m2 to 270 mJ/m2 as the Fe concentration rises to 32 at%, with only a marginal decrease of about 20 mJ/m2 seen for the alloy containing 15 at% Fe. It is possible to obtain a measure of the driving forces represented by the changes in both the APB energies and elastic anisotropy [18]. Since the elastic anisotropy changes only marginally from 0 at% Fe to 32 at% Fe, the value of the parameter “a”, which is defined in Table 2 and reflects the elastic anisotropy [19, 20], also changes only gradually as the Fe content is increased. However, the parameter, “z”, the ratio of APB energies on the octahedral to cube planes and a measure of the APB energy anisotropy [19, 20], almost doubles in value. As a consequence, we can observe the considerable influence that the APB anisotropy exerts on the cross-slip driving force (Fc), which increases dramatically with increasing Fe content. It can be inferred from the initially negative driving force that thermal activation is required for the cross-slip process to occur in Ni3Ge, but is likely unnecessary in the Fe-containing alloys. 5. DISCUSSION

5.1. Loss of anomaly with increasing Fe content In the Ni3Ge–Fe3Ge system, the observed transition from anomalous to normal temperature dependence of yield strength with increasing Fe content is

Table 3. Description of a tilting experiment for Ni3Ge deformed at room temperature. Observed APB widths vary with beam direction and dislocation character, and energies calculated from these measurements show a large amount of scatter. However, upon correction of the observed dissociation widths using image simulation, the calculated APB energies converge and show good agreement between different dislocation segments Beam direction

Line orientation

Experimental observations dobs (nm)

苲[001] 苲[111] 苲[001] 苲[111]

45° 45° 0° (screw) 0° (screw)

4.2 2.8 3.7 2.2

gAPB (mJ/m2) 261 390 219 343

Image simulations dinput (nm) 3.7 3.7 2.7 2.7

gAPB (mJ/m2) 292 292 297 297

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BALK et al.: DEFORMATION OF INTERMETALLICS

effected by an increase in low-temperature strength, rather than a decrease in high-temperature strength, see Fig. 1. This finding, which is in agreement with the data of Suzuki et al. [3] and a previous comment of Veyssie`re and Saada [21], suggests that the change in behavior is not related to a loss of the underlying cause of the yield strength anomaly but rather to a prominent increase in low-temperature strength. The observed fourfold increase in strength that is realized as Fe is substituted for Ni is much larger than is normally attributed to solid-solution strengthening. A more likely origin appears to be the effect that changes in dislocation core geometry have on the mobility of the dislocations that carry deformation in these alloys. The dramatic increase in low-temperature strength that was measured in this study suggests that Fe promotes cross-slip locking, which is consistent with the TEM observations that, at 77 K, the formation of KW locks is more prevalent in the Fe-containing alloys with higher Fe content. As dislocation loops expand in anomalous L12 alloys, cross-slip locking events are thought to give rise to straight screw-oriented segments on the cube cross-slip plane that are interrupted by mixed-character kinks on the primary octahedral plane. These kinks can be of two types: simple or switch-over, depending on two distinct formation mechanisms [22, 23]. The formation of such kinks has been described as a signature of the dynamic by-passing of KW locks that is observed with increasing temperature in the anomalous regime [24]. Simple and switch-over kinks have both been observed in this study and examples are shown in Figs 4, 8 and 9. In this way, subtle observations of the deformation microstructure also indicate that, with increasing Fe content, there is an increasing instability of octahedral glide and an increasing propensity for cube cross-slip at low temperatures. 5.2. Evidence for cube glide The TEM observations indicate that, as the Fe content changes from 0 at% to 32 at% and beyond, the post-mortem microstructure changes from screw dislocations locked in the KW configuration after octahedral glide, to localized bowing and expansion of these “locks” on the cube cross-slip plane, to mixedcharacter superdislocations undergoing extensive cube glide. There is a general shift of the transition to cube glide towards lower temperatures as Fe content increases; cube glide is observed at 600 K in Ni60Fe15Ge25, but appears at room temperature in Ni50Fe25Ge25 and at 77 K in Ni20Fe55Ge25. These instances were observed to coincide with the end of anomalous yield strength regimes (Ni60Fe15Ge25 and Ni50Fe25Ge25), or with the absence of an anomalous region altogether (Ni20Fe55Ge25). The observation of cube glide at 77 K indicates that the lattice friction to cube glide is overcome at lower temperatures than is typically observed in alloys with the L12 crystal structure. The lattice fric-

tion experienced by superdislocations on the cube plane results from the dislocation core geometry. The APB may dissociate on either {111} or {010} planes, but it is important to note that the CSF, which is bounded by dissimilar Shockley partials, can only dissociate on {111} octahedral planes. For this reason, the CSF dissociation results in an out-of-cube-plane extension of each superpartial dislocation, and requires that a Peierls-like frictional stress be overcome in order for cube glide to occur. Higher temperatures naturally increase dislocation mobility by assisting the constriction of CSF-dissociated superpartials and helping the dislocations overcome the frictional resistance to cube glide, as has been reported for the intermediate-temperature creep [12] and elevated-temperature in situ straining [25–28] of Ni3Al. The fact that relatively few superdislocations were found in the screw orientation in Fig. 3(b) (Ni43Fe32Ge25) and Fig. 10 (Ni50Fe25Ge25) suggests that, at room temperature, the extent of the CSF dissociation in these alloys is insufficient to pose an effective barrier to the motion of dislocations that have cross-slipped from the octahedral to the cube plane. Moreover, the observations that Fe3Ge exhibits a strong temperature dependence is consistent with the existence of a Peierls-like stress that must be overcome by thermally activated processes. In this way, the experimental results and observations of cube glide suggest that the extent of CSF dissociation decreases with increasing Fe content. 5.3. Fault energies and the role of dislocation core geometry The observations of enhanced cross-slip locking that are outlined above can be associated with the dramatic increase in the driving force for cross-slip, which is evidenced by the sharp drop in the cubeplane APB energy, see Table 1. The data in Table 2, which were calculated using the methodology of Saada and Veyssie`re [19, 20], clearly indicate that the cross-slip force rises with an increase in Fe content in these alloys. It is, however, important to note that the APB energy anisotropy is not the only factor that governs the cross-slip process. It has been argued, first by Paidar et al. [29] and more recently by Hemker and Mills [13], Dimiduk et al. [30], Baluc and Scha¨ ublin [31] and Karnthaler et al. [32], that the CSF dissociation plays a key role in determining the rate of cross-slip, because the kinetics of the crossslip process is governed by the activation barrier to the recombination of the Shockley partials that constitute the leading superpartial. It has been shown that the addition of boron to Ni3Al causes the CSF energy to increase, which in turn narrows the CSF dissociation and enhances the cross-slip process, thereby leading to an increase in macroscopic strength [13]. A similar increase in CSF energy with increasing Fe content would agree with the observations made in the current study. A higher CSF energy would allow easier constriction of the

BALK et al.: DEFORMATION OF INTERMETALLICS

leading superpartial dislocation and thus result in enhanced cross-slip, thereby increasing the low-temperature strength. A higher CSF energy would also decrease the out-of-cube-plane extension of superdislocations lying on the cube plane, thereby decreasing friction and increasing cube-plane mobility. Attempts to measure the CSF energy as a function of Fe content with weak-beam TEM observations were thwarted by the fact that the dissociation distances were below the resolution limit (苲1.5 nm) of the weak-beam dark-field technique. Comparison of HRTEM observations of a dissociated 60° superdislocation in Ni3Ge with HRTEM image simulations (Fig. 13) yielded an estimated CSF width of 0.5–1.0 nm, which is in accordance with the inability to image the CSF dissociation using weak-beam TEM. The total fault width observed in HRTEM was found to be within 10% of the corrected weak-beam observations for Ni3Ge. HRTEM observations of the CSF dissociation in Fe3Ge were precluded by the preferential alignment of superdislocations along 具100典 type directions. Moreover, the suggestion that the CSF dissociation in the Fe-containing alloys is smaller than the 0.5–1.0 nm that was observed for Ni3Ge indicates that quantitative experimental measures of this dissociation will be hard to come by and points to the need for first-principles or atomistic calculations of the superdislocation core structure in Fe3Ge. 6. SUMMARY AND CONCLUSIONS

The temperature dependence of yield strength and the underlying changes in deformation microstructure and dislocation core structure have been investigated in the model pseudo-binary Ni3Ge–Fe3Ge system. The results of this study can be summarized as follows. 1. The transition from anomalous to normal temperature dependence of yield strength with increasing Fe content has been verified, with the disappearance of the anomaly occurring between 25 at% and 32 at% Fe. 2. For deformation at 77 K, the 0.2% offset yield strength increases dramatically with Fe content, exhibiting a fourfold increase as Ni is completely replaced by Fe. 3. At 77 K, the deformation microstructures of all alloys but Fe3Ge point to the inhibition of octahedral glide by the formation of KW locks, which suggests that the high degree of strengthening at 77 K is related to enhanced cross-slip locking of superdislocations. 4. The APB energy on the octahedral plane has been measured to decrease only slightly with Fe additions, while the cube-plane APB energy has been observed to drop significantly. These findings indicate that the thermodynamic driving force for cube cross-slip increases dramatically with Fe content.

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5. A shift in deformation mechanisms, from octahedral glide and KW locking to cube glide of mixed-character superdislocations, has been observed with increases in either temperature or Fe content. 6. The onset of cube glide, and the increase in cubeplane mobility, both of which are brought about by Fe additions, appear to be related to changes in CSF energy. An increase in CSF energy with rising Fe content would be consistent with both the observed increase in cube-plane mobility and the dramatic strengthening that was measured at 77 K. 7. The CSF width in Ni3Ge has been determined to be between 0.5 and 1.0 nm. The proposed increase in CSF energy with Fe content appears to preclude experimental measurement of the CSF dissociation in high Fe-containing alloys, thus providing an ideal application for first-principles or atomistic calculations of the dislocation core structure. Acknowledgements—This work was supported by the US Air Force Office of Scientific Research (#F49620-95-1-0280) and the NSF-NYI program (#DMR-9457964). The Electron Microscopy Center at Johns Hopkins University has been generously supported by the NSF (#EAR-9512438) and the W. M. Keck Foundation. The authors also wish to thank Dr D. M. Dimiduk of Wright-Patterson Air Force Base for help in alloy preparation for this study. Partial support for MK received under the auspices of the Department of Energy and Lawrence Livermore National Laboratory (University of California) through contract #W-7405-Eng-48 is gratefully acknowledged.

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