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On grain boundary dissociation during diffusion (and stress) induced grain boundary migration
S c r i p t a METALLURGICA e t MATERIALIA
Vol.
25, pp. 1 0 2 3 - 1 0 2 8 , 1991 P r i n t e d in t h e U.S.A.
ON GRAIN BOUNDARY DISSOCIATION DURING DIFFUSION BOUNDARY MIGRATION
Pergamon P r e s s p l c All rights reserved
(AND STRESS)
INDUCED GRAIN
S. A. Hackney Department of Metallurgical Engineering Michigan Technologlcal University Houghton, MI 49931 (Received January
29, 1991)
Introduction Grain boundary dissociation is a term used to describe the separation of a single grain boundary into two (or more) new boundaries. Grain boundary dissociation during dlffnsion induced grain boundary migration (DIGM) has been observed by a number of different investigators, Including (1-3). Usually, grain boundary dissociation is attributed to a thermodynamic instability in the grain boundary energy/misorlentatlon space (4). However, when energy terms other than grain boundary energy, such as strain energy, are also reduced by dissociation, these factors must be considered as contributing to or causing the dissociation phenomena. The purpose of this note is to examine the microscopic nature of the contact angles that dissociated boundary segments make with undlssociated boundary segments in grain boundaries which have undergone DIGM. If local equilibrium exists at these grain boundary intersections, this study will reveal information about the nature of the driving force for grain boundary dissociation during DIGM. Evidence will then be presented which suggests that an applied stress can result in grain boundary mlgratlon and dissociation in a manner analogous to that observed during DIGM. Experimental
Procedure
The experimental techniques used to study DIGM in Cu-Zn by transmission electron microscopy have been described elsewhere (5). The Cu-Zn samples discussed here were electropolished from both sides for one second and then from one side until perforation occurred. Experimental techniques employed to study grain boundary migration in thermally stressed A1 are discussed in (6). Semiquantltative EDS was used to examine migration regions for solute enrichment. Experimental Results It has been observed in a previous study (1) using these experlmental conditions that twin formation by dissociation can occur at the point of initiation of DIGM. Most dissociation phenomena observed in this laboratory involve the twin boundary as one of the product boundaries and this is to be expected on the basis of boundary energy versus misorientatlon which has a low energy cusp for the coherent twin interface. However, grain boundary dissociation does not always lead to twin boundary formation, as shown in Fig. 1. A low angle (~2" [110] twist boundary) (Fig. lb) grain boundary has been formed by dissociation -1.5 x 10 -4 cm from the point of DIGM initiation (7)(dislocation wall at 0). A triple Junction is isolated in the inset. Shown in Fig. 2 is twin formation by dissociation Just after DIGM initiation. The original position of the grain boundary is indicated by the dlslocatlon wall which is thought to form as migration is initiated (7). The twin boundary occurs 1 x 10 -5 cm from the dislocation wall and is shown to have an incoherent step. The final position of the grain boundary is also indicated.
1025 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
1024
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
The dissoclated/undissoclated grain boundary trlple Junction is isolated in the inset. The experlmental results on thermal stress induced grain boundary mlgratlon/dlssoclatlon are shown in Fig. 3. This specimen was thermally cycled four times to a maximum thermocouple reading of 350°C. The grain boundary pores were observed to have occurred on the first temperature cycle and mark the original position of the boundary. The dislocation wall between the migrated grain boundary and the original position formed when dislocations left in the wake of the migrating grain boundary rearranged to a stable configuration. This reorganization process has not occurred on the right hand side of Fig. 3a. The left hand side, however, shows an organized dislocation wall which forms a well defined trlple Junction with the high angle boundary. As shown, the dislocation wall can be described approximately as a 2" [100] twist boundary. Discussion Cahn (4) has discussed grain boundary dissociation in a general thermodynamic context. A grain boundary is unstable with respect to dissociation when it is possible to form two (or more) new grain boundaries from the orlglnal (while still conserving the orlglnal mlsorlentation) with a reduction in the system free energy. The grain boundaries that have been studied here were presumed to be stable against dissociation prior to the introduction of zinc by diffusion or application of thermal stress because of the ample high temperature anneal. The introduction of zinc probably leads to changes of the grain boundary free energy/misorlentation curve. It is possible that this may result in the grain boundary becoming unstable with respect to dissociation. Another possibility which might result in grain boundary free energy driven dissociation results from the nonequlllbrlum nature of the alloying process. Concentration gradients of zinc result in lattice parameter gradients which can produce dislocations. When a grain boundary moves through the concentration gradient induced dlslocatlon field, as shown in Fig. 4, the absorption of dlslocatlons by the grain boundary can change the mlsorientatlon and/or the structure of the grain boundary. The possibility exists that the angle of misorlentatlon may change to a value at which the grain boundary is unstable with respect to dissociation. Similar arguments can be applied to the thermally stressed A1, where it is clear in Fig. 3 that numerous dislocations have moved in the vicinity of the grain boundary (note the dislocation tracks in the lower grain). These causes of grain boundary dissociation would be associated with grain boundary free energy driven dissociation. For Isotropic boundaries, the necessary condition for the observation of grain boundary free energy driven dissociation for Isotropic boundaries is that ~13 > ¥Ia + ¥~' where ¥ is the grain boundary free energy and the subscripts 13, 12, and 23 refer to the orlglnal grain boundary prior to dlssociatlon and the two new boundaries after dissociation, respectively. This indicates that the contact angle between 13, 12, and 23 would be zero or undefined. This is the normal condition for "wetting" and this analogy led Cahn (4) to treat boundary free energy driven grain boundary dissociation as a form of wetting. The important implication here is that non-zero contact angles between the dissociated and undlssoclated segments of the grain boundary (assuming local equilibrium of boundary tensions) would indicate that dissociation is not being driven by a reduction in boundary energy. When a highly anisotroplc boundary is involved, as in Figure 2, the situation is slightly more complicated. To be lore specific, if an Isotroplc boundary of area A dissociates into another parallel Isotropic boundary and a nonparallel anlsotroplc boundary with a normal fixed by large torque terms, the thermodynamic criteria for the observation of dissociation becomes
Vol. 25, No. 5
GRAIN BOUNDARY DISSOCIATION
1025
A¥13 > A¥12 + (~23A/cose) (1) where ~23 refers to the anisotropic boundary and e is the angle between the anlsotropic and the isotropic boundaries. The thermodynamic state of the trlple Junction for this case can be elucldated by the examination of the ~P shadow plot [8].
The magnitude ~13 is equivalent to I~31, ¥12 is I~12[ and
¥23/C0S~ is l~3maxl where ~ is the angle between the ~~ vector and the 23 grain boundary normal.
Having defined these terms, the following expression
may be considered:
An equality in equation (2) would refer to the limlting condition for equilibrium when the three ~p vectors are parallel to one another on the shadow plot.
For the llmiting case being considered here, the angle ¢ would
be equal to the angle 8 (the boundaries would be aligned so that the ~P are parallel) and equation (2) can be related dlrectly to equation (1) . This implies that a net driving force for dissociation occurs only when the inequality holds in equation (2) and the triple junction is undefined in terms of thermodynamic criteria, even when one boundary is highly anlsotroplc. Based on the non-zero, well defined, contact angles found in Figs. 1, 2, and 3, it is likely that grain boundary dissociation during DIGM and also during stress induced grain boundary migration is not driven by a reduction in grain boundary free energy. It is therefore necessary to consider other possible driving forces. Read and Shockley (9) were the first to consider that grain boundary migration and grain boundary dissociation might occur as a result of applied stress. They hypothesized that a general grain boundary will migrate in a specific way to relieve stress. They also proposed that the dislocation structure of a grain boundary might "pull apart" (dissociate) under an applied stress. Experimental results at elevated temperature (6, 10, 11) would tend to support the general contentions of Read and Shockley. Grain boundary dissociation of an isotroplc boundary of area A into parallel Isotroplc boundaries in a volume of materlal under applied stress may be observed if ~ 3 A > ~12A + ~23A + AW (3) where AW is the change in strain energy which occurs as a result of the dissociation process. If AW is less than zero, as implied by Read and Shockley, then grain boundary dissociation may occur even though ¥13 < ¥12 ÷ ¥23"
This means it is possible for grain boundary dissociation to occur with
a non-zero contact angle, as is observed in this study. Conclusions Experimental results reveal that grain boundary migration and dissociation may be driven by thermal stress or by diffusion of a second element. Consideration of the observed microscopic nature of dissociation trlple Junctions and assuming local equilibrium, it is apparent that the dissociation process is not being driven by a reduction of boundary free energy. Based on the work of Read and Shockley, it has been proposed that a reduction in strain energy is the cause of the grain boundary dissociation observed in this study. Acknowledqments The author would llke to thank Professor A. H. King for a reading of the manuscript. This work was supported by DOE grant DE FG02 87ER45315.
1026
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
References 1,
2. 3,
4. 5. 6. 7,
8. 9.
10. 11.
S. A. Hackney, Scripta Metal1., 22, 1255 (1988). C.R.M. Grovenor, D. A. Smith, and M. J. Gorlnge, Thin Solid Films, 74, 269 (1980). F. S. Chen and A. H. King, Scripta Met., 20, 1401 (1986). J. W. Cahn, J. de Physique, ~, 393, C6-19~--(1982). S. A. Hackney, Scripta Metal1., 20, 937 (1986). T. Lillo, M. R. Pllchta, and S. A. Hackney, Ultramicroscopy, 29, 257 (1989). S. A. Hackney, Scripta Metal1., 20, 1385 (1986). D. W. Hoffman and J. W. Cahn, Surf. Sci., 31, 368 (1972). W. T. Read and W. Shockley, A Symposium on-~he Plastic Deformation of Crystalline Solids, Mellon Institute, p. 137 (1950). S. A. Hackney and T. Lillo, Scripta Met., 24, 1653 (1990). T. Lillo, S. A. Hackney, and M. R. Plichta, accepted to Ultramicroscopy.
urlng close up of triple Junction between dissociated and undissociated grain boundaries.
VOl. 25, No. 5
GRAIN BOUNDARY DISSOCIATION
Fig. lb.
1027
Misorientatlon across low angle dissociation product.
Fig. 2. Grain boundary dissociated to give twin (TW) during DIGM. The triple Junction is isolated in the inset.
1028
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
Fig. 3. Grain boundary dissociation in A1 under applied stress. Insets show misorientation across dissociated
Fig. 4. Grain boundary undergoing DIGM in misfit dislocation field. Dislocation free grain is enriched in Zn relatlve to grain with high dislocation density.
Vol.
25, pp. 1 0 2 3 - 1 0 2 8 , 1991 P r i n t e d in t h e U.S.A.
ON GRAIN BOUNDARY DISSOCIATION DURING DIFFUSION BOUNDARY MIGRATION
Pergamon P r e s s p l c All rights reserved
(AND STRESS)
INDUCED GRAIN
S. A. Hackney Department of Metallurgical Engineering Michigan Technologlcal University Houghton, MI 49931 (Received January
29, 1991)
Introduction Grain boundary dissociation is a term used to describe the separation of a single grain boundary into two (or more) new boundaries. Grain boundary dissociation during dlffnsion induced grain boundary migration (DIGM) has been observed by a number of different investigators, Including (1-3). Usually, grain boundary dissociation is attributed to a thermodynamic instability in the grain boundary energy/misorlentatlon space (4). However, when energy terms other than grain boundary energy, such as strain energy, are also reduced by dissociation, these factors must be considered as contributing to or causing the dissociation phenomena. The purpose of this note is to examine the microscopic nature of the contact angles that dissociated boundary segments make with undlssociated boundary segments in grain boundaries which have undergone DIGM. If local equilibrium exists at these grain boundary intersections, this study will reveal information about the nature of the driving force for grain boundary dissociation during DIGM. Evidence will then be presented which suggests that an applied stress can result in grain boundary mlgratlon and dissociation in a manner analogous to that observed during DIGM. Experimental
Procedure
The experimental techniques used to study DIGM in Cu-Zn by transmission electron microscopy have been described elsewhere (5). The Cu-Zn samples discussed here were electropolished from both sides for one second and then from one side until perforation occurred. Experimental techniques employed to study grain boundary migration in thermally stressed A1 are discussed in (6). Semiquantltative EDS was used to examine migration regions for solute enrichment. Experimental Results It has been observed in a previous study (1) using these experlmental conditions that twin formation by dissociation can occur at the point of initiation of DIGM. Most dissociation phenomena observed in this laboratory involve the twin boundary as one of the product boundaries and this is to be expected on the basis of boundary energy versus misorientatlon which has a low energy cusp for the coherent twin interface. However, grain boundary dissociation does not always lead to twin boundary formation, as shown in Fig. 1. A low angle (~2" [110] twist boundary) (Fig. lb) grain boundary has been formed by dissociation -1.5 x 10 -4 cm from the point of DIGM initiation (7)(dislocation wall at 0). A triple Junction is isolated in the inset. Shown in Fig. 2 is twin formation by dissociation Just after DIGM initiation. The original position of the grain boundary is indicated by the dlslocatlon wall which is thought to form as migration is initiated (7). The twin boundary occurs 1 x 10 -5 cm from the dislocation wall and is shown to have an incoherent step. The final position of the grain boundary is also indicated.
1025 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
1024
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
The dissoclated/undissoclated grain boundary trlple Junction is isolated in the inset. The experlmental results on thermal stress induced grain boundary mlgratlon/dlssoclatlon are shown in Fig. 3. This specimen was thermally cycled four times to a maximum thermocouple reading of 350°C. The grain boundary pores were observed to have occurred on the first temperature cycle and mark the original position of the boundary. The dislocation wall between the migrated grain boundary and the original position formed when dislocations left in the wake of the migrating grain boundary rearranged to a stable configuration. This reorganization process has not occurred on the right hand side of Fig. 3a. The left hand side, however, shows an organized dislocation wall which forms a well defined trlple Junction with the high angle boundary. As shown, the dislocation wall can be described approximately as a 2" [100] twist boundary. Discussion Cahn (4) has discussed grain boundary dissociation in a general thermodynamic context. A grain boundary is unstable with respect to dissociation when it is possible to form two (or more) new grain boundaries from the orlglnal (while still conserving the orlglnal mlsorlentation) with a reduction in the system free energy. The grain boundaries that have been studied here were presumed to be stable against dissociation prior to the introduction of zinc by diffusion or application of thermal stress because of the ample high temperature anneal. The introduction of zinc probably leads to changes of the grain boundary free energy/misorlentation curve. It is possible that this may result in the grain boundary becoming unstable with respect to dissociation. Another possibility which might result in grain boundary free energy driven dissociation results from the nonequlllbrlum nature of the alloying process. Concentration gradients of zinc result in lattice parameter gradients which can produce dislocations. When a grain boundary moves through the concentration gradient induced dlslocatlon field, as shown in Fig. 4, the absorption of dlslocatlons by the grain boundary can change the mlsorientatlon and/or the structure of the grain boundary. The possibility exists that the angle of misorlentatlon may change to a value at which the grain boundary is unstable with respect to dissociation. Similar arguments can be applied to the thermally stressed A1, where it is clear in Fig. 3 that numerous dislocations have moved in the vicinity of the grain boundary (note the dislocation tracks in the lower grain). These causes of grain boundary dissociation would be associated with grain boundary free energy driven dissociation. For Isotropic boundaries, the necessary condition for the observation of grain boundary free energy driven dissociation for Isotropic boundaries is that ~13 > ¥Ia + ¥~' where ¥ is the grain boundary free energy and the subscripts 13, 12, and 23 refer to the orlglnal grain boundary prior to dlssociatlon and the two new boundaries after dissociation, respectively. This indicates that the contact angle between 13, 12, and 23 would be zero or undefined. This is the normal condition for "wetting" and this analogy led Cahn (4) to treat boundary free energy driven grain boundary dissociation as a form of wetting. The important implication here is that non-zero contact angles between the dissociated and undlssoclated segments of the grain boundary (assuming local equilibrium of boundary tensions) would indicate that dissociation is not being driven by a reduction in boundary energy. When a highly anisotroplc boundary is involved, as in Figure 2, the situation is slightly more complicated. To be lore specific, if an Isotroplc boundary of area A dissociates into another parallel Isotropic boundary and a nonparallel anlsotroplc boundary with a normal fixed by large torque terms, the thermodynamic criteria for the observation of dissociation becomes
Vol. 25, No. 5
GRAIN BOUNDARY DISSOCIATION
1025
A¥13 > A¥12 + (~23A/cose) (1) where ~23 refers to the anisotropic boundary and e is the angle between the anlsotropic and the isotropic boundaries. The thermodynamic state of the trlple Junction for this case can be elucldated by the examination of the ~P shadow plot [8].
The magnitude ~13 is equivalent to I~31, ¥12 is I~12[ and
¥23/C0S~ is l~3maxl where ~ is the angle between the ~~ vector and the 23 grain boundary normal.
Having defined these terms, the following expression
may be considered:
An equality in equation (2) would refer to the limlting condition for equilibrium when the three ~p vectors are parallel to one another on the shadow plot.
For the llmiting case being considered here, the angle ¢ would
be equal to the angle 8 (the boundaries would be aligned so that the ~P are parallel) and equation (2) can be related dlrectly to equation (1) . This implies that a net driving force for dissociation occurs only when the inequality holds in equation (2) and the triple junction is undefined in terms of thermodynamic criteria, even when one boundary is highly anlsotroplc. Based on the non-zero, well defined, contact angles found in Figs. 1, 2, and 3, it is likely that grain boundary dissociation during DIGM and also during stress induced grain boundary migration is not driven by a reduction in grain boundary free energy. It is therefore necessary to consider other possible driving forces. Read and Shockley (9) were the first to consider that grain boundary migration and grain boundary dissociation might occur as a result of applied stress. They hypothesized that a general grain boundary will migrate in a specific way to relieve stress. They also proposed that the dislocation structure of a grain boundary might "pull apart" (dissociate) under an applied stress. Experimental results at elevated temperature (6, 10, 11) would tend to support the general contentions of Read and Shockley. Grain boundary dissociation of an isotroplc boundary of area A into parallel Isotroplc boundaries in a volume of materlal under applied stress may be observed if ~ 3 A > ~12A + ~23A + AW (3) where AW is the change in strain energy which occurs as a result of the dissociation process. If AW is less than zero, as implied by Read and Shockley, then grain boundary dissociation may occur even though ¥13 < ¥12 ÷ ¥23"
This means it is possible for grain boundary dissociation to occur with
a non-zero contact angle, as is observed in this study. Conclusions Experimental results reveal that grain boundary migration and dissociation may be driven by thermal stress or by diffusion of a second element. Consideration of the observed microscopic nature of dissociation trlple Junctions and assuming local equilibrium, it is apparent that the dissociation process is not being driven by a reduction of boundary free energy. Based on the work of Read and Shockley, it has been proposed that a reduction in strain energy is the cause of the grain boundary dissociation observed in this study. Acknowledqments The author would llke to thank Professor A. H. King for a reading of the manuscript. This work was supported by DOE grant DE FG02 87ER45315.
1026
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
References 1,
2. 3,
4. 5. 6. 7,
8. 9.
10. 11.
S. A. Hackney, Scripta Metal1., 22, 1255 (1988). C.R.M. Grovenor, D. A. Smith, and M. J. Gorlnge, Thin Solid Films, 74, 269 (1980). F. S. Chen and A. H. King, Scripta Met., 20, 1401 (1986). J. W. Cahn, J. de Physique, ~, 393, C6-19~--(1982). S. A. Hackney, Scripta Metal1., 20, 937 (1986). T. Lillo, M. R. Pllchta, and S. A. Hackney, Ultramicroscopy, 29, 257 (1989). S. A. Hackney, Scripta Metal1., 20, 1385 (1986). D. W. Hoffman and J. W. Cahn, Surf. Sci., 31, 368 (1972). W. T. Read and W. Shockley, A Symposium on-~he Plastic Deformation of Crystalline Solids, Mellon Institute, p. 137 (1950). S. A. Hackney and T. Lillo, Scripta Met., 24, 1653 (1990). T. Lillo, S. A. Hackney, and M. R. Plichta, accepted to Ultramicroscopy.
urlng close up of triple Junction between dissociated and undissociated grain boundaries.
VOl. 25, No. 5
GRAIN BOUNDARY DISSOCIATION
Fig. lb.
1027
Misorientatlon across low angle dissociation product.
Fig. 2. Grain boundary dissociated to give twin (TW) during DIGM. The triple Junction is isolated in the inset.
1028
GRAIN BOUNDARY DISSOCIATION
Vol. 25, No. 5
Fig. 3. Grain boundary dissociation in A1 under applied stress. Insets show misorientation across dissociated
Fig. 4. Grain boundary undergoing DIGM in misfit dislocation field. Dislocation free grain is enriched in Zn relatlve to grain with high dislocation density.