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Grain boundary cohesion and fracture in ordered intermetallics
Scripta METALLURGICA et MATERIALIA
Vol. 25, pp. 1259-1264, 1991 Printed in the U.S.A.
Pergamon Press plc
VIEWPOINT SET No. 17
GRAIN BOUNDARY COHF,SION AND FRACTURE IN ORDERED IN'rERMETALLICS E. P. George,* C.L. White,t and J. A. Horton* * Metals md Ceramics Division, Oak Ridge National Laborato~, Oak Ridge, TN 37831-6093. 1"Depmlmentof Metanurgical and Materials Engineering, Michigan TeclmologicalUniversity, HoughtonM149931. (Received April 8, 1991)
Grain boundaries (GBs) in conventional metals do not normally constitute a serious source of weakness, so that when brittle intergranular fracture does occur, it is usually the result of ex~insic factors, like hostile environments, or harmful impurities. In contrast, GBs in sever~ high-purity intermemlllcs that fracture intergranularly are actually quite clean and free of impurities [1-7]. They are therefore considered to be inlrinsically brittle. Polycrystslline Ni3AI is perhaps the most extensively studied of such inlrinslcally brittle intermetallic alloys. As is well known now, the brittleness of Ni3A1 can be overcome by small additions of boron [1,8,9]. Fig. 1 schematically shows relationships among the various mechanisms that have been proposed to explain the so-called boron effect. In this paper we take the position that the available experimental evidence supports a mechanism based on increased GB cohesion [1]. According to this view, boron alters GB chemistry (and possibly also GB structure), thereby increasing GB cohesive energy and suength. Increased GB cohesion not only suppresses crack nucleation but, by increasing crack-tip plastic deformation and blunting, also suppresses crack propagation. These effects are so pronounced in B-doped Ni3AI that ductility is dramatically increased and the alloy fractures transgranularly.
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FIG 1 Schematicdiagramshowingthe possible r.lationships among the vari ous mechanisms proposed for the boron effect. (The dashed line indicates possible relationship lhat has not yet been formulated in detail in the literature.)
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Ductll:mlk~
An akernativemechanism based on enhanced sliptransferacrossOBs [10-13] has also been proposed. According to this view, boron disorders the GB region, thereby increasing GB dislocation mobility [14], the number of available dislocation reactions at the OBs [ 15], or both. These effects arc suggested to result in enhanced slip transfer across GBs. Unlike the cohesion argument, slip transfer has been discussed mainly as it relates to GB crack nucleation: when dislocations pile up at GBs, the stress concentration at the head of the pile-up can nucleate cracks if it is not effectively dissip~_t~'d by slip in the adjacent grain. However, crack propagation rather than nucleation appears to be the critical step in both B-free and B-doped Ni3Ah Using sharply notched bend bars tested in 3-point bending at a constant displacement rate, Khadlcikm- et Id [16] showed that catastrophic fracture did not accompany crack initiation in Ni3AI; rather, the plot of load vs crack opening displacement was indicative of stable crack growth. If nucleation is not the critical step, then ductility must depend on the ease of crack propagation, which in turn depends on the competition between GB decobeslon and crack-tip plasticity [17,18]. As discussed 1259 0030-9748/91 $3.00
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below, improved GB cohesion will improve ductility by directly affecting both of these competing processes, whereas the influence of enhanced slip transfer is linked with only the latter (see dashed line in Fig. 1). The approach we have taken in this paper is to outline the evidence supporting the cohesion argument, and cite observations not satisfactorily explained by the slip transfer arLmmeut. Because of length limitations, not all the relevant literature can be cited, nor can all elements of the issue be presented in detail Specifically, the thermodynamics of interracial separation, and the plastic deformation behavior near the tips of nearly brittle GB cracks will be described only very generally, and the interested reader is refen'ed to the cited references for derailed treatments. Effect of Boron on Grain Boundary Cohesion Our understanding of GB cohesion, and the effects of GB segregants, has its origins in the Griffith model for brittle crack propagation as medified to account for the energetic contribution of the GBs [see, e.g., Ref. 19]: ~sd -- 2Ys - ~'#b,
(1)
where ~d is the ideal work of fracture, and Ysand Yfb are the surface and GB energies, respectively. Early investigators recognized that segregation will alter ~b and Ys(and thus ~ ) . But, because Gibbsian thermodynamics predicts that equilibrium segregation will deoregse both 7s and ~,~/,, the net effect on 7'~din Eq. (1) remained unclear. Evainafion of the effect of segregation on Ysis further complica3ed by the fact that the amount of segregant inherited by the new surfaces after fracture will generally be the amount present on the GBs prior to fracture, and not the equilibrium level for those surfaces. Gibbslan interfacial thfmlodypamies was first rigorously applied to the problem of rapid (i.e. nonequilibrium) separation of a segregated GB by Rice [20], who showed that the expmimentaUy observed segregation behavior of embrittling elements (namely, that they segregate even more strongly to free surfaces than to GBs) is qualitatively consistent with predictions of the modified Griffith theory (a detailed discussion is given in Ref. 21). Based on his analysis, Rice predicted that if a GB segregant was observed to segregate less strongly to free surfaces than to GBs, it should be beneficial to GB cohesion. At the time of that prediction, no such segregation behavior had ever been ~ and its occurrence was considered unlikely. It is quite remarkable, the~.fore, that detailed surface ..~.d GB segreg.ation studies of B-doped Ni3AI [1,22,23], as well as less extenstve studies of B-dop.e.d Ni3(S,,Ti) [7] have mnce shown that boron does not segregate mxongiy to free surfaces, whereas R segregates qmte strongly to GBs. This behavior is in sharp contrast to that of embrittling elements like sulfur, and indicates that boron, unlike embrittling segregants, should increase the ideal work of separation (7hi) of the GBs. The Linkage Between Cohesion and Plastic Deformation The Griffith model fails to account for the plastic deformation that almost always accompanies GB fracture in metals. Attempts to measure the actual work of separation (Ta,u) during GB fracture inevitably indicate values significantly larger than ?'at- Likewise, the effect of segregation on 7act is generally too large to be explained solely by interracial t b e n n o d ~ [24]. Discrepancies between Tact and Ysd are generally attributed to the plastic work, Yd' associa_te4with GB crack propagation:
Yact= Y~ + Ypt = 2 ~ - y~,+ Ypt.
(2)
The large magnitude of Y,!relative to ?'uihas occasionally been used to argue that ?',a is irrelevant to the fracture process, and that the true role of GB segregants is to fundamentally alter the nature of plastic deformation near the affected GBs, thereby altering 7D/independently of any effect on Y~d- However, although ?~dis generally small compared to ~,p/, the latter quunti[y is strongly dependent on the cohesive strength (Crmax)of the boundary [17,18], which in Run is directly related to ~d. (¢Ymazis the maximum local stress that can be sustained by atoms at the GB
without inevemible seperation.) separation tzl) ¢m've mr revermble separation ot a L,ts. While me Rice analysis makes sound predictions regarding the effects of segregants on ~,a, one must make the further assumption that the shape of the o-A curve is not drasticaliy altered by the segregation process in order to make the additional conclusion that Omaxscales with the Tut. In other words, if boron is expected to increase Y/d(based on the Rice analysis), then depellding on how it affects the shape of the ~-A curve, it may also increase Crmar Recent ~ analyses based on first-principles calculations as well as more empirical .approaches [25-27] have concluded that boron does in fact enhance the cohesive su'ength of Ni3AI m so, at least in this system, eYmaxreally does appear to scale with the ~,a. Further evidence for increased GB cohesion resulting from boron segregation in Ni3AI comes from the work of Kbadklkar et al. [28], who used finite element stress analysis to determine the stress to initiate GB separation i. a double notched tensile specimen, and found that B-doped Ni3A] always required higher stresses than undoped alloys. (Because of inhomogeneities
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in microplauicity, the stresses determined in their experiments do not yield values that arc numerically equal to Omav but they do reflect the strength of OBs rather than the ovemli plasticity of the polycrystslline aggregate.) Accouling to the cohesive suength argument then, ~ increases the maximum stress that the GB crack tip can withstand. But it is this local stress that is also the driving force for plastic deformation near the crack tip. Therefore, changes in 7'~dor os~w even though these terms are small, can result in large changes in the amount of plastic deformation accompanying crack propagation. According to this view, ~d (or more accura~ly Omax)acts as a valve [19], controlling the magnitude of the (generaUy) much larger 7~ term. T h i s relatively old concept, dating back to at least the work of McLean [29], is quite different from the view that segregation directly affects the plastic deformation behavier near the GBs independently of any effect on cohesive strength. Effect of Boron on Slin Transfer Across Grain Boundaries Experimental evidence for enhanced sfip transfer comes mainly from HaU-Petch type analyses of the grainsize dependance of yield strength, in which the Hall-Perch slope (/~) of B-doped Ni3AI is found to be lower than that of undoped powder-metallurgy Ni3AI [10,11]. This result has been interpreted to mean that boron enhances slip wansfer in Nifd. There are some problems with this interpremtiou, however. For example, there are indications that processing variables, impurities and alloy chemistry affect k3, independently of any boron effect. Thus, ky for arc-melted I~.tAl is very s ~ . [~m~msl~2f~R * Refs. 30,31],.wheats/~ for.NiAl produced by powder me talmrgyisverystrouglypositivetu.3ZMt-am ,tter.~Zl. Atso, me~appearstoeenocte~coneinfion~tweenme magnitude of k? and the propensity for intergranular fracture: B-free NiAI (both the arc melted and PM varieties mentioned ahoge) fractmes predominantly intergranularly, whereas B-doped NiA1 ,~ol~e almost flat, Ref. 31) and Zr-doped NiAI (slope almost flat for grain sizes larger than 16 lan, and 1.01 MPa m / 2 for smaller grain sizes, Ref. 33) fracture transgranuisrly. These results indicate that there are many possible factors which can affect/~ and that it is not a straightforward matter to make the connection between k.y,or its dependence on chemical composition, and fracture behavior. Beyond the diff~-uities in interpreting k.v,the exact mechanism by which boron might facilitate sfip transfer at GBs also remains unclear. Schulson et al. [14] suggested that boron facilitates slip transfer by enhancing GB dislocation mobility. Isolated TEM observations of dislocations moving in GBs of B-doped Ni3A1 have been reported in support of this view [12]. On the other hand, Bond et al. [34] have reported that plastic deformation can initiate abruptly in grains adjacent to impinging slip bands without observable motion of dislocations within the Benriched GBs. These latter observations were interpreted [34] to mean that, rather than facilitating slip transfer, boron actually enhances the cohesive strength of the GBs (although the possibility that boron reduced the stresses required to operate dislocation sources in the GB could not be ruled out). The only direct measurements of GB dislocation mobifities are those of Swiatnicki and Grabski [35] who concluded that boron actually decreases dislocation mobilifies in Ni3AI. They studied the spreading kinetics of lattice dislocations injected by plastic deformation into GBs in B-free and B-doped Ni3AI, and showed that the mobilities of GB dislocations in both alloys are negligible at room temperature; at higher temperatures (>300°C), the dislocations in the B-doped alloy actually have lower mobilities than those in the B-free alloy. These latter results suggest that if, indeed, boron facilitates slip transfer across (;Be, it is by some mechanism other than increased GB dislocation mobility. B~-~-Induced GB Disorder and its Role in EnhancinE Slio Transfer King and You [15] showed that a greater number of dislocation reactions arc possible at compositionaUy disordered GBs than at those that have perfect chemical ord~. Tbey s u g a r , therefme, that if boron led to local disorderin~ at the GBs, it might facilitate slip franker. Unfemmately, it ts quite tricky to directly image GB structures by high-resolution TEM (or any other technique), and there is cummtly evidence both for [36] and against [37,38] the existence of a very thin (<2 tun) disordered region at the GBs. A detailed discussion of these conflicting results is beyond the scope of this paper and is the subject of other papers in this viewpoint set. Because GBs are difficult to image directly, there have been several attempts to obtain indin~t evidence of disorder, all of which depend on evaluations of GB cbemisWy. Sieloff et al. [39,40] and Baker et al. [41] reported that whereas GBs in B-free Ni3A1 had the bulk composition, GBs in B-doped Ni3AI were Ni-era'iched (by as much as 6-7 at.% relative to the bulk), suggesting cosegregation of B and Ni, leading to B - ~ disorder. However, their results may have been influenced by rapid solidification and insufficient statistics, respectively, and may not be generally applicable to Ni3AI alloys. To overcome some of these deficiencies, G e m ~ et al. [42] used Auger electron specumcopy to analyze a large number of GBs in tlmilady processed (arc-melted and xeerysmllized) undoped and B-doped Ni3AI. They showed that GBs in both B-free and B-doped Ni3A ! (24 at.% AI) arc slightly Ni-cnriched relative to the holk--but by about the sang amount (Le., there was no iMkafion that boron attracted excess nickel to the GBs). These results suggest that GBs in both undoped and B-doped Ni3AI (24 at.% AI) are prohahly disordered, but there is no indication that boron dram~*/c~tly increases the amount of ~ . It must be Ixinted out that any uncertainty regarding the ~ of disordered regions near GBs is limited to relatively thin (<2 nm) layers. Recently, however, Baker and Schulson [43] have ~-ported the presence of rela-
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tively thick (-20 nm) disordered layers (or phases) on all the GBs of powder-processed, B-doped Ni3Al, but only on some of the GBs of undoped Ni3A1. If this were a general fealure of Ni3Al alloys, it would imply that boron improves ductility by promoting the formation of thick disordered layers on all the GBs of Ni3Al. However, early work by Liu et al. [ 1], and also recent reconfn'mations by Horton and Liu [44,45], showed that such a thick disordered layer is not present in arc-melted and rccrystallized B-doped Ni~AI (24 at.% A1), which is nevertheless extremely ductile. (Note that the detection of a 20 nm thick layer is a relauveiy suaightforward matter in conventional TEM, and not subject to the kind of uncertainties associated with the detection of the much thinner disordered regions mentioned earlier.) It is not entirely clear why the powder-processed material has this disordered phase on its GBs whe~as the arc-melted material does not [44]. Regardless, the imlx~nant conclusion to be drawn is that, since the arc-melted and well-recrystallized alloy of Liu et aL [1] shows very good ductility, the presence of a thick disordered layer is definitely not necessary for B-induced docfilization. A f'mal point to note is that thick disordered GB layers by themselves (i.e., in the absence of boron) do not ducfilize Ni3AI as effectively as does boron by itself (i.e., in the absence of thick disordered GB phases). Hanada et al. [46] showed that relatively thick layers of a Ni-rich fcc phase form on the boundaries of undoped Ni3AI when it is sufficiently Ni-rich (Ni-22.5 at.% Al). Presun~biy, ff the presence of GB disorder is important in promoting ductility, this alloy should be quite ductile. In fact, however, it exhibited only limited ductilities (-7 and 15% for grain sizes of 15 and 65 ~ respectively), compared to the extensive ductilities (>50~) obtainable in B-doped alloys that do not contain any thick GB phase [1]. The limited results of Hanada et aL .~.pesr also to beinconsistent with the slip transfer mechanism: If the ductility of undoped Ni3AI is limited by its ability to transmit slip at the the GBs, one would normally argue that the longer slip bands possible in larger grain size material should result in higher slress concenlrafions at the grain boundaries and, therefore, lower ductilities. However, Hanada et al. observed quite the opposite effect: in both stoichiometric and substoichiometric undoped Ni3AI, ductility incr..eased significantly with increasing grain size rather than with decreasing grain size. (No second phase was reported m the stoichiomelric alloy, so the grain size effect cannot be explained by arguing that larger grain sizes simply allow greater GB coverage by a fixed volume fraction of the second phase.) Other Svsterns in which Beneficial Sem-e~ant~ Have Been Identified The B2-slrucmred NiAI alloy is similar to the L12-structured Ni3AI alloy, in that it..~acture,s in a predominantly intergranular manner with limited tensile ductility[4,47]: .Like ~1~.., xts m ~ . ~ .ular brittleness ts not related to nnpurity segregation at the GBs, and appears to be mmnstc [4]. Microalloymg with boron is able to suppress this intergranular fracture, and Auger analysis has confirmed that boron does indeed segregate to the GBs [4,48]. The grain size dependence of the yield strength of undoped, arc-meited NiAI indicates an almost fiat HallPetchslo.pe [30,31]: If one uses the .u.'sditional in.terpret~'.on of ky, .~s."...~gges.ts that th.• GBs "mundoped~.NiAI are not ertecuve onstactes to slip thruster ~tween grams, ana met~ore mmmtco snp transter ~s prommy not me reason behind the GB brittleness of undoped NiAI (although, as we pointed out earlier, there are problems in interpreting and relating it to fracutre behavior.) One is therefore left to conclude that.the intri~ic.in.tergranular brittleness of 1 is a result of poor GB cohesion, and that the beneficial effect of boron Is related to its mlprovement of that cohesion. Of course, weak GBs are only part of the problem in NiAI, because single cry.s.tals, are also brittle. Therefore, even after boron strengthens the GBs and suppresses intergranular fracture, ductility is not gready improved, because the next most brittle fracture mode (transgranular cleavage) intervenes before extensive plastic deformation can occur. Intermetallic alloys are not unique, either in their tendency to exhibit intrinsic intergranular britdeness, or in their ability to be made ductile by beneficial segregants. Morris and coworkers [49,50] have shown that both Fe12Mn and Fe-30Mn (wt.%) alloys exhibit intrinsic GB brittleness, and that these alloys can be ductilized by the addition of boron, which segregates to the GBs. White et al. [51] observed a similar effect when boron was added to a Pt-30Rh-8W (wt.%) alloy. Both the Fe-30Mn and the Pt-Rh-W alloys are disordered fcc solid solutions, while the Fe-12Mn alloy is a mixture of a bcc solid solution and two martensitic phases (bcc and hexagonal). Liu and coworkers [52] have shown that the inlrinsic intcrgranular brittleness (at elevated temperatures and high strain rates) of fcc iridium alloys can be overcome by the addition of small amounts of thorium, which by segregating to the GBs [53], suppresses intergranular fracture, and dramatically improves ductility'. This is a rather diverse group of disordered alloys in which the beneficial effect of GB dopants cannot be explained by the disordering mechanism proposed for Ni3AI. Arguments based on GB cohesion, on the other hand, are appealing because they are applicable to both ordered and disordered alloys. Clearly, surface segregation and Hall-Perch studies need to be performed on these d i ~ systems to test the generality of the proposed mechanisms of ductility improvcment.
Although segregation experiments do not directly measure Ytd, their interpretation is fairly soundly based in classical thermodynamics. And, from such a viewpoint, there is strong evidence to indicate that GB cohesion is enhanced as a result of boron segregation in Ni3Al. As we pointed out earlier, segregation is usually detrimental to
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ductility, causing rather than preventing GB fracture. Most systems for which segregants have been directly observed at GBS, and for which surface segregation behavior is known, support the Rice prediction that cmbrinling GB segregants will segregate even more sm~ngiy to free surfaces than to GBs. The only known cases showing the reverse behavior are boron in Ni3A1 [1,22,23] and Ni3(Si,Ti) [7]: in both cases, boron segregates quite strong.ly to GBs but not to free surfaces. Before this unusual segregation behavior was discovered, Rice had predicted mat elements which show such behavior would increase GB cohesion and, indeed, boron has since been found to suppress GB fracture and improve ductility in both Ni3A1 and Ni3(Si,Ti). The unusual segregation behavior in these systems, the unusual (beneficial) effect of that segregation, and the correspondence of these two anomalies with Rice's treaUnent of GB cohesion seem to be much more than a coincidence. Furthermore, the segregation behavior of sulfur, an element known to be detrimental to the ductility of Ni3A1 [54] [and probably Ni3(Si,Ti)), is also consistent with the Rice prediction: in both of these alloys, sulfur segregates much more strongly to free surfaces than to GBs [1,7,22,23]. Theoretical evidence also indicates that boron increases the cohesive strength ( O'ma~) of Ni3Al GBs. The actual magnitude of that increase is expected to depend on the detailed structure and compomtion of the GB, which in turn is expected to depend on the alloy composition, among other factors. Thus, for example, as the composition of Ni3AI deviates from st~ichiometry, the GBs arc expected to deviate even more from stoichiometry [55]. The reason for this is that deviations from s~oichiometry are accommodated in Ni3A! by anti-site defects, which are energetically favored to be located near GBs rather than in the bulk [55], resulting in excess Ni (or AI) at the GBS, and consequently some local dismder. And, indeed, Auger analysis of GBs in Ni-rich Ni3A1 (24% AI) has confirmed that the GBs are even more Ni-enriched [42]. Similarly, boron also segregates at the GBs [1], so that the GBs are significandy B-enriched (and therefore of a different composition) compared to the bulk. Both these factors, namely the Ni and B enrichments at the GBs (of Ni-rich alloys), are expected to affect area r And, indeed, embedded-atom calculations [27] indicate that the cohesive strength of a (210) symmetrical [100] flit boundary in Ni3AI is increased by both Ni and B segregation individually, and even more when they occur simultaneously. These calculations also agree with the experimental observation that boron is most beneficial in Ni-rich alloys (especially Ni-24% A1) in which the GBs are Ni- and B-enriched, and not very beneficial in Al-rich alloys (Ni-25.2% AI) in which the GBs are not Ni-enriched and only slightly B=enriched [1,42]. Suramarv and Conclusions In summary, there is indirect experimental evidence (based on the unusual segregation behavior of boron), as well as direct theoretical evidence, to support the notion that boron increases GB cohesion in Ni3AI. Whether that is enough m account for the dramatic ductilizing effect of boron is still unclear, although it is worth remembering that embrittling impurities can have similarly large effects on fracture mode and ductility (in the opposite direction) through changes principally in the interfacial energies. There is also indirect evidence (based on the lowering of the Hall-Perch slope by boron) to suppc~ the notion that boron facilitates slip wansfer across GBs. However, as discussed in the text, there are factors other than the presence of boron which could affect the magnitude of the HallPerch slope, makl,g its interpretation uncertain. Even ff boron really does facilitate slip u'ansfer, the details of exactly how this happens are still unclear. Of the two mechanisms suggested so far, the one which suggests that boron facilitates slip uan~er by increasing the mobility of GB dislocations appears to have been discounted recently by TE_MeL~ul]~ nts. The second, that boron facilitates slip wansfer by disordering ~ GB region, is still the subject ot c o n __~,~rabledebate because of the difficulties involved in interpreting high-resolution images of GBs in these materials. However, it is clear that the uncertainty is limited to very thin (< 2 rim) disordered regions, and not thick (-20 nm) disordered layers which are plainly not needed to obtain B-induced ductilization. F'mally, GB cohesion arguments have the advantage that they are applicable to both beneficial and harmful segregants, in both ordered and disordered alloys. Slip u'ansfer arguments based on GB disordering, on the other hand, have trouble explaining segregant effects in disordered alloys.
We thank C.T. Liu, W.C. Oliver, M. H. Yon, and C.G. McKamey for useful discussions. This research was sponsored at ORNL by the Division of Materials Sciences, U.$. DeparUnent of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc., and at Michigan Technological University by NSF Grant No. DMR-8922824. References 1. 2. 3. 4. 5.
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Horton, Acta Metall. 34, 1395 (1986). 15. A.H. King and M.H. Yoo, in High-Temperature Ordered lntermetailic Alloys !I, eds. N.S. Stoloff et al. (Materials Research Society, Pi~burgh, PA, 1987), Vol. 81, p. 99. 16. P.S. ~ k R r , J.D. Rigrtey, J.J. Lewarldowski, and K.Ve.dtlla,in High-Temperature Ordered Inter-metallic Alloys Ill, eds. C.T. Liu, et aL (Materials Research Society, Pittsburgh, PA, 1989), Vol. 133, p. 523. 17. C.J. McMahon, Jr. and V. Vitek, Acta Metall. 27, 509 (1979); M.L. Jokl, V. Vitek, and C.J. McMahon, Jr., Acta Metall. 28, 1479 (1980). 18. H. ~ m g , A.H. King, and R. Thompson, J. Mater. Res. 6, 314 (1991). 19. J.R. Rice and J.-S. Wang, Mater. Sci. Engr. AI07, 23 (1989). 20. J.R. Rice, in The Effect of Hydrogen on the Behavior of Metals (AIME, New York, 1976), p. 455; 21. J.P. I-Iirtharid J.R. Rice, Metall. Trans. IIA, 1501 (1980). 22. C.L. White, R.A. Padgett, C.T. Liu, and S.M. Yalisove, Scripta Metall. 18, 1417 (1984). 23. C.L. White, C.T. Lie, and R.A. Padgett, Acta Metall. 36, 2229 (1988). 24. R.G. Thompson, C.L. White, J.J. Well ~ D.S. Eab'ton,Metall. Trans. 12A, 1339 (1981). 25. G.S. Painter and F.W. Averill, Phys. Rev. Lett. $& 234 (1987). 26. M.E. Eberb.art and D.D. Vvedinaky, Phys. Rev. Lett. 58, 61 (1987). 27. S.P. Chen, A.F. Voter, R.C. Albers, A.M. Boring, and P.J. Hay, Scripta Metall. 23, 217 (1989). 28. P.S. Khadkikar, J.J.I..¢wandowski, arid K. VfX[tlla,Metall. Trans. 20A, 1247 (1987). 29. D. McLean, Grain Boundaries in Metals (Oxford UniversityPress, London, 1957), p. 299. 30. P. Nagpal and I. Baker, Scripta Metall. 24, 2381 (1990). 31. EJ~.George, J.J. Liao, and C.T. Liu, Oak Ridge National Laboratory, unpublished research (1990). 32. R.D. Noebe, R.R. Bowman,C.L. Cullers, and S.V. Raj, to be published in High-Temperature urderedlntermetaUic Alloys IV, eds. J.O. Sfiegleret aL (Materials Research Society, Piuslmrgh, PA, 1991), VoL 213. 33. M.V. Zelles, R.D. Noebe, and I.E. Locci, in $rd Annual HITEMP Review, NASA CP-10051, 1990, p. 21-1. 34. G.M. Bond, LM. Robertson, and H.K. Bimbatun, J. Mater. Res. 2, 436 (1987). 35. W.A. Swiamicki and M.W. Grabski, Acta Metall. 37, 13ff7(1989). 36. R.A.D. Mackenzie md S.L. Sass, Scripta Metall. 22, 1807 (1988). 37. M.J. Mills, Scripta Metall. 23, 2061 (1989). 38. J.E. Ko.m~waki, Scripta MetaU. 23, 1219 (1989). 39. D.D. Sieloff, S.S. Brenner,and M.G. Burke, in High-Temperature Ordered lntermetallic Alloys II, eds. N.S. Stoloffet al. (Materials Research Society, Pittrdmrgh,PA, 1987), Vol. 81, p. 87. Al 40. D.D. Sieloff, S.S. Bremler,and Hua Ming-Jian, in High-Temperature Ordered Intermetallic IoysII1, eds. C.T. Liu, et al. (MaterialsResearch Society, Pittsburgh, PA, 1989), Vol. 133, p. 155. 41. I. Baker, E.M. Schulson, and J.R. Michael, Philos. Mag. B57, 379 (1988). 42. E.P. George, C.T. Liu, and R.A. PadgelL Scripta Metall. 23, 979 (1989). 43. I. Baker and E.M. Schulson, Scripta MetalL 23, 1883 (1989). 44. J.A. Horton and C.T. Liu, Scripta MetalL 24, 1251 (1990). 45. J.A. Horton and C.T. Liu, to be published in High.Temperature Orderedlntermetallic Alloys IV, eds. J.O. Sfiegler et al. (MaterialsResearch Society, Pittsburgh, PA, 1991), Vol. 213. 46. S.Hanada, S.Watanabe, and O.Izumi, J. Mater. Sci. 21, 203 (1985). 47. ICH. Hal-mand K.Vedula, Scripta MetalL 23, 7 (1989). 48. E.P. George, C.T. Liu, and J.J. Liao, in Alloy Phase Stability and Design, eds. G.M. Stocks et al. (Materials Research Society, Pittslmrgh, PA, 1990), Vol 186, in press. 49. S.K. Hwang and J.W. Morris, Jr., Metall. Trans. I1A, 1197 (1980). 50. M.J. Strum, S.K. Hwang, and J.W. Morris, Jr., in inI~acial Strl~tlo'e, Properties and Design, eds. M.H. Yoo et al. (Materials Research Society, Pittsimrgh,PA, 1989), Vol. 122, p. 467. 51. C.L. White, J.R. Keiser, and D.N. Braaki, Metall. Trans. 12A, 1485 (1981). 52. C.T. Liu, H.Inouye, and C.A. Schaflhauser, Metall. Trans. 12A, 993 (1981). 53. C.L. White, R.E. Ciausin8, and L. Heatherly, MetalL Trine. 10A, 683 (1979). 54. C.L. White and D.F. Stein, Metall. Trans. 9A, 13 (1978). 55. StephenM. Foiles, in High-Temperature Ordered Intermetallic Alloys I1, eds. N.S. Stoloff et al. (MaterialsResearch Society, pittsburgh, PA, 1987), Vol. 81, p. 51.
Vol. 25, pp. 1259-1264, 1991 Printed in the U.S.A.
Pergamon Press plc
VIEWPOINT SET No. 17
GRAIN BOUNDARY COHF,SION AND FRACTURE IN ORDERED IN'rERMETALLICS E. P. George,* C.L. White,t and J. A. Horton* * Metals md Ceramics Division, Oak Ridge National Laborato~, Oak Ridge, TN 37831-6093. 1"Depmlmentof Metanurgical and Materials Engineering, Michigan TeclmologicalUniversity, HoughtonM149931. (Received April 8, 1991)
Grain boundaries (GBs) in conventional metals do not normally constitute a serious source of weakness, so that when brittle intergranular fracture does occur, it is usually the result of ex~insic factors, like hostile environments, or harmful impurities. In contrast, GBs in sever~ high-purity intermemlllcs that fracture intergranularly are actually quite clean and free of impurities [1-7]. They are therefore considered to be inlrinsically brittle. Polycrystslline Ni3AI is perhaps the most extensively studied of such inlrinslcally brittle intermetallic alloys. As is well known now, the brittleness of Ni3A1 can be overcome by small additions of boron [1,8,9]. Fig. 1 schematically shows relationships among the various mechanisms that have been proposed to explain the so-called boron effect. In this paper we take the position that the available experimental evidence supports a mechanism based on increased GB cohesion [1]. According to this view, boron alters GB chemistry (and possibly also GB structure), thereby increasing GB cohesive energy and suength. Increased GB cohesion not only suppresses crack nucleation but, by increasing crack-tip plastic deformation and blunting, also suppresses crack propagation. These effects are so pronounced in B-doped Ni3AI that ductility is dramatically increased and the alloy fractures transgranularly.
3 .
.
.
.
.
.
.
.
|
-
,,--
FIG 1 Schematicdiagramshowingthe possible r.lationships among the vari ous mechanisms proposed for the boron effect. (The dashed line indicates possible relationship lhat has not yet been formulated in detail in the literature.)
~
a,m~,xs.¢~
.
v"l
(~W_~) [
.
)
Ductll:mlk~
An akernativemechanism based on enhanced sliptransferacrossOBs [10-13] has also been proposed. According to this view, boron disorders the GB region, thereby increasing GB dislocation mobility [14], the number of available dislocation reactions at the OBs [ 15], or both. These effects arc suggested to result in enhanced slip transfer across GBs. Unlike the cohesion argument, slip transfer has been discussed mainly as it relates to GB crack nucleation: when dislocations pile up at GBs, the stress concentration at the head of the pile-up can nucleate cracks if it is not effectively dissip~_t~'d by slip in the adjacent grain. However, crack propagation rather than nucleation appears to be the critical step in both B-free and B-doped Ni3Ah Using sharply notched bend bars tested in 3-point bending at a constant displacement rate, Khadlcikm- et Id [16] showed that catastrophic fracture did not accompany crack initiation in Ni3AI; rather, the plot of load vs crack opening displacement was indicative of stable crack growth. If nucleation is not the critical step, then ductility must depend on the ease of crack propagation, which in turn depends on the competition between GB decobeslon and crack-tip plasticity [17,18]. As discussed 1259 0030-9748/91 $3.00
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below, improved GB cohesion will improve ductility by directly affecting both of these competing processes, whereas the influence of enhanced slip transfer is linked with only the latter (see dashed line in Fig. 1). The approach we have taken in this paper is to outline the evidence supporting the cohesion argument, and cite observations not satisfactorily explained by the slip transfer arLmmeut. Because of length limitations, not all the relevant literature can be cited, nor can all elements of the issue be presented in detail Specifically, the thermodynamics of interracial separation, and the plastic deformation behavior near the tips of nearly brittle GB cracks will be described only very generally, and the interested reader is refen'ed to the cited references for derailed treatments. Effect of Boron on Grain Boundary Cohesion Our understanding of GB cohesion, and the effects of GB segregants, has its origins in the Griffith model for brittle crack propagation as medified to account for the energetic contribution of the GBs [see, e.g., Ref. 19]: ~sd -- 2Ys - ~'#b,
(1)
where ~d is the ideal work of fracture, and Ysand Yfb are the surface and GB energies, respectively. Early investigators recognized that segregation will alter ~b and Ys(and thus ~ ) . But, because Gibbsian thermodynamics predicts that equilibrium segregation will deoregse both 7s and ~,~/,, the net effect on 7'~din Eq. (1) remained unclear. Evainafion of the effect of segregation on Ysis further complica3ed by the fact that the amount of segregant inherited by the new surfaces after fracture will generally be the amount present on the GBs prior to fracture, and not the equilibrium level for those surfaces. Gibbslan interfacial thfmlodypamies was first rigorously applied to the problem of rapid (i.e. nonequilibrium) separation of a segregated GB by Rice [20], who showed that the expmimentaUy observed segregation behavior of embrittling elements (namely, that they segregate even more strongly to free surfaces than to GBs) is qualitatively consistent with predictions of the modified Griffith theory (a detailed discussion is given in Ref. 21). Based on his analysis, Rice predicted that if a GB segregant was observed to segregate less strongly to free surfaces than to GBs, it should be beneficial to GB cohesion. At the time of that prediction, no such segregation behavior had ever been ~ and its occurrence was considered unlikely. It is quite remarkable, the~.fore, that detailed surface ..~.d GB segreg.ation studies of B-doped Ni3AI [1,22,23], as well as less extenstve studies of B-dop.e.d Ni3(S,,Ti) [7] have mnce shown that boron does not segregate mxongiy to free surfaces, whereas R segregates qmte strongly to GBs. This behavior is in sharp contrast to that of embrittling elements like sulfur, and indicates that boron, unlike embrittling segregants, should increase the ideal work of separation (7hi) of the GBs. The Linkage Between Cohesion and Plastic Deformation The Griffith model fails to account for the plastic deformation that almost always accompanies GB fracture in metals. Attempts to measure the actual work of separation (Ta,u) during GB fracture inevitably indicate values significantly larger than ?'at- Likewise, the effect of segregation on 7act is generally too large to be explained solely by interracial t b e n n o d ~ [24]. Discrepancies between Tact and Ysd are generally attributed to the plastic work, Yd' associa_te4with GB crack propagation:
Yact= Y~ + Ypt = 2 ~ - y~,+ Ypt.
(2)
The large magnitude of Y,!relative to ?'uihas occasionally been used to argue that ?',a is irrelevant to the fracture process, and that the true role of GB segregants is to fundamentally alter the nature of plastic deformation near the affected GBs, thereby altering 7D/independently of any effect on Y~d- However, although ?~dis generally small compared to ~,p/, the latter quunti[y is strongly dependent on the cohesive strength (Crmax)of the boundary [17,18], which in Run is directly related to ~d. (¢Ymazis the maximum local stress that can be sustained by atoms at the GB
without inevemible seperation.) separation tzl) ¢m've mr revermble separation ot a L,ts. While me Rice analysis makes sound predictions regarding the effects of segregants on ~,a, one must make the further assumption that the shape of the o-A curve is not drasticaliy altered by the segregation process in order to make the additional conclusion that Omaxscales with the Tut. In other words, if boron is expected to increase Y/d(based on the Rice analysis), then depellding on how it affects the shape of the ~-A curve, it may also increase Crmar Recent ~ analyses based on first-principles calculations as well as more empirical .approaches [25-27] have concluded that boron does in fact enhance the cohesive su'ength of Ni3AI m so, at least in this system, eYmaxreally does appear to scale with the ~,a. Further evidence for increased GB cohesion resulting from boron segregation in Ni3AI comes from the work of Kbadklkar et al. [28], who used finite element stress analysis to determine the stress to initiate GB separation i. a double notched tensile specimen, and found that B-doped Ni3A] always required higher stresses than undoped alloys. (Because of inhomogeneities
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in microplauicity, the stresses determined in their experiments do not yield values that arc numerically equal to Omav but they do reflect the strength of OBs rather than the ovemli plasticity of the polycrystslline aggregate.) Accouling to the cohesive suength argument then, ~ increases the maximum stress that the GB crack tip can withstand. But it is this local stress that is also the driving force for plastic deformation near the crack tip. Therefore, changes in 7'~dor os~w even though these terms are small, can result in large changes in the amount of plastic deformation accompanying crack propagation. According to this view, ~d (or more accura~ly Omax)acts as a valve [19], controlling the magnitude of the (generaUy) much larger 7~ term. T h i s relatively old concept, dating back to at least the work of McLean [29], is quite different from the view that segregation directly affects the plastic deformation behavier near the GBs independently of any effect on cohesive strength. Effect of Boron on Slin Transfer Across Grain Boundaries Experimental evidence for enhanced sfip transfer comes mainly from HaU-Petch type analyses of the grainsize dependance of yield strength, in which the Hall-Perch slope (/~) of B-doped Ni3AI is found to be lower than that of undoped powder-metallurgy Ni3AI [10,11]. This result has been interpreted to mean that boron enhances slip wansfer in Nifd. There are some problems with this interpremtiou, however. For example, there are indications that processing variables, impurities and alloy chemistry affect k3, independently of any boron effect. Thus, ky for arc-melted I~.tAl is very s ~ . [~m~msl~2f~R * Refs. 30,31],.wheats/~ for.NiAl produced by powder me talmrgyisverystrouglypositivetu.3ZMt-am ,tter.~Zl. Atso, me~appearstoeenocte~coneinfion~tweenme magnitude of k? and the propensity for intergranular fracture: B-free NiAI (both the arc melted and PM varieties mentioned ahoge) fractmes predominantly intergranularly, whereas B-doped NiA1 ,~ol~e almost flat, Ref. 31) and Zr-doped NiAI (slope almost flat for grain sizes larger than 16 lan, and 1.01 MPa m / 2 for smaller grain sizes, Ref. 33) fracture transgranuisrly. These results indicate that there are many possible factors which can affect/~ and that it is not a straightforward matter to make the connection between k.y,or its dependence on chemical composition, and fracture behavior. Beyond the diff~-uities in interpreting k.v,the exact mechanism by which boron might facilitate sfip transfer at GBs also remains unclear. Schulson et al. [14] suggested that boron facilitates slip transfer by enhancing GB dislocation mobility. Isolated TEM observations of dislocations moving in GBs of B-doped Ni3A1 have been reported in support of this view [12]. On the other hand, Bond et al. [34] have reported that plastic deformation can initiate abruptly in grains adjacent to impinging slip bands without observable motion of dislocations within the Benriched GBs. These latter observations were interpreted [34] to mean that, rather than facilitating slip transfer, boron actually enhances the cohesive strength of the GBs (although the possibility that boron reduced the stresses required to operate dislocation sources in the GB could not be ruled out). The only direct measurements of GB dislocation mobifities are those of Swiatnicki and Grabski [35] who concluded that boron actually decreases dislocation mobilifies in Ni3AI. They studied the spreading kinetics of lattice dislocations injected by plastic deformation into GBs in B-free and B-doped Ni3AI, and showed that the mobilities of GB dislocations in both alloys are negligible at room temperature; at higher temperatures (>300°C), the dislocations in the B-doped alloy actually have lower mobilities than those in the B-free alloy. These latter results suggest that if, indeed, boron facilitates slip transfer across (;Be, it is by some mechanism other than increased GB dislocation mobility. B~-~-Induced GB Disorder and its Role in EnhancinE Slio Transfer King and You [15] showed that a greater number of dislocation reactions arc possible at compositionaUy disordered GBs than at those that have perfect chemical ord~. Tbey s u g a r , therefme, that if boron led to local disorderin~ at the GBs, it might facilitate slip franker. Unfemmately, it ts quite tricky to directly image GB structures by high-resolution TEM (or any other technique), and there is cummtly evidence both for [36] and against [37,38] the existence of a very thin (<2 tun) disordered region at the GBs. A detailed discussion of these conflicting results is beyond the scope of this paper and is the subject of other papers in this viewpoint set. Because GBs are difficult to image directly, there have been several attempts to obtain indin~t evidence of disorder, all of which depend on evaluations of GB cbemisWy. Sieloff et al. [39,40] and Baker et al. [41] reported that whereas GBs in B-free Ni3A1 had the bulk composition, GBs in B-doped Ni3AI were Ni-era'iched (by as much as 6-7 at.% relative to the bulk), suggesting cosegregation of B and Ni, leading to B - ~ disorder. However, their results may have been influenced by rapid solidification and insufficient statistics, respectively, and may not be generally applicable to Ni3AI alloys. To overcome some of these deficiencies, G e m ~ et al. [42] used Auger electron specumcopy to analyze a large number of GBs in tlmilady processed (arc-melted and xeerysmllized) undoped and B-doped Ni3AI. They showed that GBs in both B-free and B-doped Ni3A ! (24 at.% AI) arc slightly Ni-cnriched relative to the holk--but by about the sang amount (Le., there was no iMkafion that boron attracted excess nickel to the GBs). These results suggest that GBs in both undoped and B-doped Ni3AI (24 at.% AI) are prohahly disordered, but there is no indication that boron dram~*/c~tly increases the amount of ~ . It must be Ixinted out that any uncertainty regarding the ~ of disordered regions near GBs is limited to relatively thin (<2 nm) layers. Recently, however, Baker and Schulson [43] have ~-ported the presence of rela-
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tively thick (-20 nm) disordered layers (or phases) on all the GBs of powder-processed, B-doped Ni3Al, but only on some of the GBs of undoped Ni3A1. If this were a general fealure of Ni3Al alloys, it would imply that boron improves ductility by promoting the formation of thick disordered layers on all the GBs of Ni3Al. However, early work by Liu et al. [ 1], and also recent reconfn'mations by Horton and Liu [44,45], showed that such a thick disordered layer is not present in arc-melted and rccrystallized B-doped Ni~AI (24 at.% A1), which is nevertheless extremely ductile. (Note that the detection of a 20 nm thick layer is a relauveiy suaightforward matter in conventional TEM, and not subject to the kind of uncertainties associated with the detection of the much thinner disordered regions mentioned earlier.) It is not entirely clear why the powder-processed material has this disordered phase on its GBs whe~as the arc-melted material does not [44]. Regardless, the imlx~nant conclusion to be drawn is that, since the arc-melted and well-recrystallized alloy of Liu et aL [1] shows very good ductility, the presence of a thick disordered layer is definitely not necessary for B-induced docfilization. A f'mal point to note is that thick disordered GB layers by themselves (i.e., in the absence of boron) do not ducfilize Ni3AI as effectively as does boron by itself (i.e., in the absence of thick disordered GB phases). Hanada et al. [46] showed that relatively thick layers of a Ni-rich fcc phase form on the boundaries of undoped Ni3AI when it is sufficiently Ni-rich (Ni-22.5 at.% Al). Presun~biy, ff the presence of GB disorder is important in promoting ductility, this alloy should be quite ductile. In fact, however, it exhibited only limited ductilities (-7 and 15% for grain sizes of 15 and 65 ~ respectively), compared to the extensive ductilities (>50~) obtainable in B-doped alloys that do not contain any thick GB phase [1]. The limited results of Hanada et aL .~.pesr also to beinconsistent with the slip transfer mechanism: If the ductility of undoped Ni3AI is limited by its ability to transmit slip at the the GBs, one would normally argue that the longer slip bands possible in larger grain size material should result in higher slress concenlrafions at the grain boundaries and, therefore, lower ductilities. However, Hanada et al. observed quite the opposite effect: in both stoichiometric and substoichiometric undoped Ni3AI, ductility incr..eased significantly with increasing grain size rather than with decreasing grain size. (No second phase was reported m the stoichiomelric alloy, so the grain size effect cannot be explained by arguing that larger grain sizes simply allow greater GB coverage by a fixed volume fraction of the second phase.) Other Svsterns in which Beneficial Sem-e~ant~ Have Been Identified The B2-slrucmred NiAI alloy is similar to the L12-structured Ni3AI alloy, in that it..~acture,s in a predominantly intergranular manner with limited tensile ductility[4,47]: .Like ~1~.., xts m ~ . ~ .ular brittleness ts not related to nnpurity segregation at the GBs, and appears to be mmnstc [4]. Microalloymg with boron is able to suppress this intergranular fracture, and Auger analysis has confirmed that boron does indeed segregate to the GBs [4,48]. The grain size dependence of the yield strength of undoped, arc-meited NiAI indicates an almost fiat HallPetchslo.pe [30,31]: If one uses the .u.'sditional in.terpret~'.on of ky, .~s."...~gges.ts that th.• GBs "mundoped~.NiAI are not ertecuve onstactes to slip thruster ~tween grams, ana met~ore mmmtco snp transter ~s prommy not me reason behind the GB brittleness of undoped NiAI (although, as we pointed out earlier, there are problems in interpreting and relating it to fracutre behavior.) One is therefore left to conclude that.the intri~ic.in.tergranular brittleness of 1 is a result of poor GB cohesion, and that the beneficial effect of boron Is related to its mlprovement of that cohesion. Of course, weak GBs are only part of the problem in NiAI, because single cry.s.tals, are also brittle. Therefore, even after boron strengthens the GBs and suppresses intergranular fracture, ductility is not gready improved, because the next most brittle fracture mode (transgranular cleavage) intervenes before extensive plastic deformation can occur. Intermetallic alloys are not unique, either in their tendency to exhibit intrinsic intergranular britdeness, or in their ability to be made ductile by beneficial segregants. Morris and coworkers [49,50] have shown that both Fe12Mn and Fe-30Mn (wt.%) alloys exhibit intrinsic GB brittleness, and that these alloys can be ductilized by the addition of boron, which segregates to the GBs. White et al. [51] observed a similar effect when boron was added to a Pt-30Rh-8W (wt.%) alloy. Both the Fe-30Mn and the Pt-Rh-W alloys are disordered fcc solid solutions, while the Fe-12Mn alloy is a mixture of a bcc solid solution and two martensitic phases (bcc and hexagonal). Liu and coworkers [52] have shown that the inlrinsic intcrgranular brittleness (at elevated temperatures and high strain rates) of fcc iridium alloys can be overcome by the addition of small amounts of thorium, which by segregating to the GBs [53], suppresses intergranular fracture, and dramatically improves ductility'. This is a rather diverse group of disordered alloys in which the beneficial effect of GB dopants cannot be explained by the disordering mechanism proposed for Ni3AI. Arguments based on GB cohesion, on the other hand, are appealing because they are applicable to both ordered and disordered alloys. Clearly, surface segregation and Hall-Perch studies need to be performed on these d i ~ systems to test the generality of the proposed mechanisms of ductility improvcment.
Although segregation experiments do not directly measure Ytd, their interpretation is fairly soundly based in classical thermodynamics. And, from such a viewpoint, there is strong evidence to indicate that GB cohesion is enhanced as a result of boron segregation in Ni3Al. As we pointed out earlier, segregation is usually detrimental to
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ductility, causing rather than preventing GB fracture. Most systems for which segregants have been directly observed at GBS, and for which surface segregation behavior is known, support the Rice prediction that cmbrinling GB segregants will segregate even more sm~ngiy to free surfaces than to GBs. The only known cases showing the reverse behavior are boron in Ni3A1 [1,22,23] and Ni3(Si,Ti) [7]: in both cases, boron segregates quite strong.ly to GBs but not to free surfaces. Before this unusual segregation behavior was discovered, Rice had predicted mat elements which show such behavior would increase GB cohesion and, indeed, boron has since been found to suppress GB fracture and improve ductility in both Ni3A1 and Ni3(Si,Ti). The unusual segregation behavior in these systems, the unusual (beneficial) effect of that segregation, and the correspondence of these two anomalies with Rice's treaUnent of GB cohesion seem to be much more than a coincidence. Furthermore, the segregation behavior of sulfur, an element known to be detrimental to the ductility of Ni3A1 [54] [and probably Ni3(Si,Ti)), is also consistent with the Rice prediction: in both of these alloys, sulfur segregates much more strongly to free surfaces than to GBs [1,7,22,23]. Theoretical evidence also indicates that boron increases the cohesive strength ( O'ma~) of Ni3Al GBs. The actual magnitude of that increase is expected to depend on the detailed structure and compomtion of the GB, which in turn is expected to depend on the alloy composition, among other factors. Thus, for example, as the composition of Ni3AI deviates from st~ichiometry, the GBs arc expected to deviate even more from stoichiometry [55]. The reason for this is that deviations from s~oichiometry are accommodated in Ni3A! by anti-site defects, which are energetically favored to be located near GBs rather than in the bulk [55], resulting in excess Ni (or AI) at the GBS, and consequently some local dismder. And, indeed, Auger analysis of GBs in Ni-rich Ni3A1 (24% AI) has confirmed that the GBs are even more Ni-enriched [42]. Similarly, boron also segregates at the GBs [1], so that the GBs are significandy B-enriched (and therefore of a different composition) compared to the bulk. Both these factors, namely the Ni and B enrichments at the GBs (of Ni-rich alloys), are expected to affect area r And, indeed, embedded-atom calculations [27] indicate that the cohesive strength of a (210) symmetrical [100] flit boundary in Ni3AI is increased by both Ni and B segregation individually, and even more when they occur simultaneously. These calculations also agree with the experimental observation that boron is most beneficial in Ni-rich alloys (especially Ni-24% A1) in which the GBs are Ni- and B-enriched, and not very beneficial in Al-rich alloys (Ni-25.2% AI) in which the GBs are not Ni-enriched and only slightly B=enriched [1,42]. Suramarv and Conclusions In summary, there is indirect experimental evidence (based on the unusual segregation behavior of boron), as well as direct theoretical evidence, to support the notion that boron increases GB cohesion in Ni3AI. Whether that is enough m account for the dramatic ductilizing effect of boron is still unclear, although it is worth remembering that embrittling impurities can have similarly large effects on fracture mode and ductility (in the opposite direction) through changes principally in the interfacial energies. There is also indirect evidence (based on the lowering of the Hall-Perch slope by boron) to suppc~ the notion that boron facilitates slip wansfer across GBs. However, as discussed in the text, there are factors other than the presence of boron which could affect the magnitude of the HallPerch slope, makl,g its interpretation uncertain. Even ff boron really does facilitate slip u'ansfer, the details of exactly how this happens are still unclear. Of the two mechanisms suggested so far, the one which suggests that boron facilitates slip uan~er by increasing the mobility of GB dislocations appears to have been discounted recently by TE_MeL~ul]~ nts. The second, that boron facilitates slip wansfer by disordering ~ GB region, is still the subject ot c o n __~,~rabledebate because of the difficulties involved in interpreting high-resolution images of GBs in these materials. However, it is clear that the uncertainty is limited to very thin (< 2 rim) disordered regions, and not thick (-20 nm) disordered layers which are plainly not needed to obtain B-induced ductilization. F'mally, GB cohesion arguments have the advantage that they are applicable to both beneficial and harmful segregants, in both ordered and disordered alloys. Slip u'ansfer arguments based on GB disordering, on the other hand, have trouble explaining segregant effects in disordered alloys.
We thank C.T. Liu, W.C. Oliver, M. H. Yon, and C.G. McKamey for useful discussions. This research was sponsored at ORNL by the Division of Materials Sciences, U.$. DeparUnent of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc., and at Michigan Technological University by NSF Grant No. DMR-8922824. References 1. 2. 3. 4. 5.
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