grain boundary migration initiated by diffusion

SOLID STATE PHYSICS

GRAIN BOUNDARY MIGRATION INITIATED BY DIFFUSION

A. D. Korotaev and Yu. I. Pochivalov UDC 531.724'539.219.3

A review is presented of work related to two new processes which arise in crystalline materials when impurities diffuse along grain boundaries from the surface of the material: diffusion-initiated grain boundary migration and recrystallization. We analyze the conditions under which DIGM occurs, the kinetics of the process, its driving forces, and also the changes in the grain fine structure and the near-grain regions, as well as the nucleation of new grains on the migrating boundaries, caused by an uncompensated impurity atom flux. We consider the mechanisms for DIGM. It is shown that not one of the mechanisms proposed to describe DIGM is capable of explaining all the experimentally observed properties of grain boundary migration under DIGM conditions. We note that changes in the grain boundary structure caused by the impurity atoms diffusing along it are due to diverse grain-boundary processes, which have important technological implications.

It is well-known [i-6] that grain boundaries play a determining role in the macroscopic properties of solids, especially polycrystalline metals and alloys. Therefore, there is a natural deep interest among metal physics researchers in the structure, thermodynamic properties, and phase composition of grain boundaries, as well as a continually increasing number of original works and monographs devoted to these questions [5-10]. It is of ~ ut- most importance that the structure and properties of grain boundaries may be altered significantly as a result of external influences and, thus, it may be possible to use these processes to influence the actual structure of polycrystalline materials. We note in this connection, for example, reports of nonequilibrium [6, 11-13] or excited [14] grain boundary states associated with the pinning of lattice dislocations by them during deformation or boundary migration during recrystallization.

It was suggested in [15] that activated grain boundary states may arise in the presence of directional uncompensated impurity atom fluxes.

It should be noted that the greatly enhanced diffusion rate along grain boundaries (by several orders of magnitude) in comparison with crystals is a long-established and well- studied fact [i, 2, 6, i0]. However, until recently attention was not focused on the fact that there is every reason to anticipate significant changes in the state of a boundary in the presence of grain boundary diffusion currents of foreign atoms, since large internal stresses arise in the diffusion zone (including those resulting from osmotic pressure [5]), along with changes in the point defect concentrations (the Kirkendall grain boundary effect [16]), lattice dislocations are generated [17], together with, possibly, grain boundary dislocations, etc. When diffusing impurity atom fluxes are present a number of new phenomena are observed, including activated sintering [19, 20], activated recrystallization [21-23], diffusion-induced grain boundary migration [16, 18, 24-50], recrystallization [30], etc.~

Of these phenomena, at the present time diffusion-induced grain boundary migration ~here- after referred to as DIGM) is the one which is the most completely and thoroughly stud~ed.

Unfortunately, in the domestic literature there are only isolated discussions of this problem [15, 51, 52, 55, 90], and there have not yet been any full reviews of the DIGM phenomenon (such a review was written in 1987 by King, in the Western literature [18])~. In addition, the physical processes which control DIGM are of primary importance in activated sintering and recrystallization phenomena [19-23], in activated grain boundary slippage [15, 51, 52], the stages of subcritical fracture growth during solid metal embrittlement [56],

V. D. Kuznetsov Physicotechnical Institute, Tomsk State University, Siberia. Trans- lated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34-57, May, 1992. Orig- inal article submitted February ii, 1992.

1064-8887/92/3505-0425512.50 © 1992 Plenum Publishing Corporation 425

structural superplasticity [54], etc. Therefore, it is most pertinent and important to analyze the fundamental systematics and the physical processes of the DIGM phenomenon. The present review addresses this problem.

The name given to this phenomenon, DIGM, comes from [25, 26], although it was first independently observed in [24, 91]. Using x-ray diffraction for a study of the diffusion pair Cr-W after an anneal at 1525 K, den Broeder [24] observed an alloy of 85% W and 15% Cr in addition to pure W, with no data which indicated formation of intermediate compositions. Metallographic and microanalysis demonstrated that the grain boundaries migrated in the tungsten diffusion zone, and alloys of the composition indicated above were observed only in regions swept out by the migrating boundaries. It was proposed that the nucleation and diffusion growth mechanism for the new phase (the alloy of 85% W and 15% Cr) at the migrating boundaries was analogous to the well-known mechanism for discontinuous decomposition in the sense of the development of grain boundary diffusion and the cooperative reac- tions of phase formation and grain boundary migration which it causes. Between the time of this observation to the present the phenomenon of DIGM has been observed in more than 30 systems, including metals [24-48], semiconductors [49], and ceramic materials [50]. The basic experimental systematics which govern the development of DIGM were formulated in the work of Balluffi and Cahn [16].

i. The phenomenon is observed in various diffusing metal pairs (alloys) during mixing (alloying) or as the concentration of the diffusing element in the original alloy is reduced when there is a positive or negative deviation from the ideal free energy of mixing.

2. The DIGM effect is observed only in the presence of a diffusion current of the dis- solved element along the grain boundaries and is not observed in the absence of such a current.

3. As a rule, the migrating grain front exhibits a stepwise composition change, so that this boundary is also a surface separating an enriched (or depleted) region, with respect to the diffusing element, in comparison with the original matrix. It is true, as will be shown below, that there are a number of systems and conditions in which strong diffusional saturation of this element is observed in the lattice regions in front of the migrating boundary [30-32, 47].

4. The temperature regime characteristically required for the appearance of DIGM is a region where the diffusional mobility of the doping element in the lattice is low, while its diffusi0nal transport in the grain boundaries is rather strong. In subsequent work, especially that carried out at the Siberian Physicotechnical Institute [51, 57], it has been shown that the DIGM phenomenon is observed only under the conditions of B I grain boundary diffusion, by the classification of Harrison [53]. We shall discuss this point in more detail in the section devoted to the forces which drive DIGM.

5. Balluffi and Cahn [16] and Cahn et al. [26] observed DIGM only for high angle boundaries and did not observe it for gains with small angle mismatch (~15°), the structure of which corresponds to the presence of a series of discrete lattice dislocations. There is very limited experimental data on the influence of the structure of high angle boundaries on their mobility (rate of migration) during DIGM. In particular, it has been noted [52-63] that DIGM may be realized in symmetric and asymmetric tilt boundaries, including special ones with a reciprocal density of coincident vertices E = 5, while it is not observed for boundaries of coherent twins (~ = 3) [62].

6. In the majority of the systems studied the origin of the boundary migration takes place with local "swelling" of the boundary (Fig. la) and its subsequent migration in the same direction. The spatial distribution and direction of generation of the displacements at different points on the original boundary is nearly random. The depth of the boundary migration zone (and, consequently, that of the zone where the composition of the sample is changed), the distance D in Fig. 2b, may be microns during strong DIGM, so that in rather thin films (hundreds of angstroms) a nearly homogeneous boundary migration takes place over the entire transverse dimension of the sample (Fig. 2a). In later work, an oscillatory boundary migration was observed [24, 47, 48, 63].

7. There is a resulting flux of atoms along the migrating boundary (the difference between the fluxes of dopant atoms and the atoms of the matrix), which causes the overall quantity of material in the diffusion zone to increase (during mixing) or to decrease

426

Original position of~ grain boundary

T/

-j-

-_i ~ Doping

zone

\ \ !I / !

b~

d t

Fig. i Fig. 2

Fig. i. Schematic of grain boundary migration during DIGM: a) individual boundary [16]; b) close to a triple junction.

Fig. 2. Schematic of the formation of a doped (or undoped) zone after boundary migration in thin (a) and thick (b) samples [16].

(when dopant atoms leave the original alloy). Correspondingly, a change in the volume of the material takes ]place in this zone, with the formation of internal compressive or tensile stresses normal to the migrating boundary. The appearance of such stresses leads to a lowering of the observed rate of boundary migration during DIGM [29], while the presence of the resulting flux of atoms along the boundary in substitutional alloys causes a reverse flow of vacancies, which may provide the physical mechanism for the boundary migration [16]. We note, though, that since DIGM has been observed under conditions of a diffusion flux of interstitial impurities along the boundaries [41-45], such a mechanism must not be general to all cases where the phenomenon appears.

At present it has become clear that the phenomenon under discussion is very important, firstly due to the undoubted influence of the processes which take place during DIGM on the effects of structural superplasticity [6, 15, 54], subcritical fracture growth in solid- metal embrittlement [15, 56], discontinuous decomposition [57], etc. Secondly, it is important in connection with the well-known ideas [6, 8, 15, 58-60] having to do with the production of an actiwLted grain boundary state by some influence on its structure. There is reason to suppose that an activated grain boundary state may arise when directional unequal impurity atom fluxes occur along grain boundaries.

In particular, this idea is supported by the data of [25, 27, 61] on the unusually high diffusional mobility on migrating boundaries in comparison with stationary ones, the data of [34, 63, 64] on the dissociation of boundaries during DIGM, etc. Consequently, as first noted in [15], the phenomenon of DIGM may be related to the transition of grain boundaries into an activated state. Correspondingly, in this case it is necessary to carry out an extremely careful anaIysis of this factor for the case of activated recrystallization as well. Naturally, in the present discussion we will not restrict ourselves to the most general experimentally observed features of DIGM, as presented above, but rather we shall consider ~ in turn the most important physical principles of this phenomenon.

i. KINETICS OF DIFFUSION-INITIATED GRAIN BOUNDARY MIGRATION

From the very beginning of the studies of the phenomenon of DIGM a unique morphology was observed in the migrating boundaries. In fact, many of the original boundaries migrate without change in shape, that is, the entire boundary migrates at nearly the same rate [25 27, 47, 48]. Anotherportion of the original boundaries develop into separated portions, migrating in different directions [25, 27, 34, 47, 48]. In particular, a dominant migration of grain boundaries close to triple junctions (Fig. ib) has been observed [34, 38, 65]~, while in other works [47, 48], in contrast, the speed and distance of migration in the central region of a boundary were observed to be larger than in regions close to grain junctions. Finally, a certain fraction of the grains do not participate in the migration at all.

427

2"2# 213 ~17 E5 Z29E29 7.5 ZI7 ZI3 ~25 £ , ~tm

3O

20

lO

0

I l ~ t

iN I

\

~0 20 30

Ii i ^ I & l

I , I " A,

/tO EO 60 70 8, deg

Fig. 3. Migration distance I for tilt boundaries in copper, annealed in zinc vapor for various lengths of time [66]: V) 3 h; a) 6 h; o) 12 h; and A) 24h; e is the boundary tilt angle.

Naturally, it was initially proposed that the latter fact is related to the properties of the boundary structure, primarily the angle mismatch at the boundary. Electron microscopic study of the migration of tilted boundaries in Au-Ag with a <iii> axis of rotation in thin foils [62] demonstrated that, indeed, the special boundary Z = 3 did not migrate, while all the other special boundaries (Z = 5, 7, 18, 19) exhibit a migration rate which is close to that found for boundaries with arbitrary orientation. Migration of the specially oriented Z = 5 boundary, with a misorientation angle close to the <i00> axis, was observed in Cu-Au [26]. It is interesting that, although until recently it was thought [16, 26, 63] that the phenomenon of DIGM was not observed for small angle boundaries, in [50] this migration was observed in a ceramic (calcite bicrystals). Thus, the phenomenon of DIGM has now been observed for the majority of boundaries, including special and small angle boundaries, with the exception of the special type Z = 3. This is supported by the data of [48], where very rare cases of coherent twin boundary migration were found under conditions of a high rate of DIGM for general boundaries and for incoherent twin boundaries. Nevertheless, it is anticipated theoretically (as a consequence of the low diffusion mobility of impurity atoms along special boundaries, the low density of grain boundary dislocations, etc.) that DIGM should take place to a lesser degree on special boundaries than on general ones.

Direct support for this prediction was obtained in [66] in a systematic study of the influence of misorientation near the <i00> axis on the rate of DIGM for symmetric tilt boundaries in copper bicrystals. When zinc was diffused out of the gas phase from the surface of the bicrystal, normal to the misorientation axis of the grains, during annealing at 673 K, a clear dependence of the boundary migration rate on misorientation was observed (Fig. 3). Namely, DIGM was not observed for small angle boundaries, and boundaries close to special misorientation angles of Z = 5, 17, and 25 exhibited low migration rates. It is interesting that boundaries with the minimal rate of migration included faceted boundaries, while for boundaries of a general type twin formation during migration was characteristic. Chen and King [66] remark that a definite explanation has not been obtained for the observed dependence of the migration rate on the experimental conditions. It is possible that the fundamental reason for the lowered mobility of boundaries under these conditions is a low rate of diffusion and, consequently, a lower diffusion flux of atoms along the boundaries of these special types. Undoubtedly, though, a definitive resolution of these questions of the dependence of the migration rate during DIGM on structure will require special experiments.

A large amount of experimental data has shown [27, 47, 48, 60-65] that the rate of migration v for boundaries during DIGM does not remain constant. First of all, discontinuous (jump-like) boundary movement has been observed, first in metallographic studies, from the weak traces of intermediate boundary positions (with less etching than the final positions or immobile boundaries) [27, 47, 48, 64, 65], and then in in situ electron microscope studies [63]. It is most interesting that at the points where the boundaries stop (as in their initial positions) there remain entangled dislocations with a high dislocation density [63, 64].

Thus, the DIGM speed v decreases with time, which apparently suggests changes in the boundary structure, in particular facetization [65, 66], adsorption of impurities on it,

and an accumulation of other factors which slow the rate of migration. As a result, the

428

boundaries are stationary for a significant portion of the overall migration time, while during the motion between stopping points the rate of migration reaches values v ~ 1 ~m/min

It has been suggested [63, 64] that diffusion of an impurity atom flux along an immobile boundary causes its free energy to increase sufficiently that dissociation (splitting) of the boundary into high and low mobility components occurs. The latter appears either as the formation of dislocations with small misorientation angles (<5 ° ) [47, 48, 63, 67] or as coherent twin boundaries [34, 38, 63, 64]. Meyrick et al. [64] even introduced the idea of "diffusion initiatedboundary dissociation," thus emphasizing the importance of grain boundary diffusion currents in establishing the energetic requirements for boundary splitting. We remind the reader that the change in the free energy due to alloying during DIGM significantly exceeds that due to boundary dissociation.

Secondly, for prolonged annealing times a cessation of boundary migration under DIGM conditions has been observed [27, 47, 48, 65]. Moreover, in a number of works [27, 48, 64, 65] an oscillatory migration has been found, that is a reversal of the migration direction. Since the fundamental reason for DIGM is a composition difference between the original grain and the region surrounding the migrating boundary (this will be considered in more detail below in our discussion of the driving force of the migration), it is natural to suppose that the migration is suppressed due to changes in the grain composition in front of the migrating boundary due to bulk diffusion. However, theoretical estimates [32, 47, 50] and curves of the alloy composition variation in front of migrating boundaries [35] have shown that the cessation of the DIGM process occurs despite the presence of a step-like concentration profile at the boundaries, that is under conditions where bulk diffusion is absent.

Another possible reason for cessation of DIGM may be a change in the structure of the boundaries, as perhaps indicated by their facetization during migration [47, 62, 65, 67]. It appears that the normals to the facets, as a rule, deviate only by degrees from low index crystallographic axes. Thus, in [67] it was found for the Cu-Zn system that the facet planes close to {iii} and {ii0} in grains which grow during DIGM also have high index grains into which the boundary migrates. For the Cu-Ni system, the planes of facets were close to {020} and {220} for one of the grains [47]. It is just this fact, according to [65], which explains the reduction in v, until the DIGM process ceases. However, Pan and Balluffi [62] did not observe any influence of facetization on the maximum boundary movement during DIGM. An interesting kinetic structural property of boundaries which move during DIGM, the presence of a high density of step defects, was observed in [47, 67]. Unfortunately, it has not been possible definitively to assign a role of these defects in the migration kinetics.

Den Broeder and Nakahara [30] have proposed that the reduction in v to zero is due to the influence of stresses in the surface and subsurface layers, caused by volume changes brought about by the change in the composition behind the migrating boundaries. Indeed, in the presence of a resultant grain boundary diffusion flux of atoms (for example, as a consequence of diffusion coefficient for the impurity atoms diffusing from the surface which is larger than that for the atoms of the majority element) there must be an increase in the overall number of atoms in the diffusion layer and a change in the lattice parameter in this layer. All of this indicates a change in the volume (the dimensions) of the diffusion zone and, correspondingly, the development of high compressive stresses normal to the migrating boundary. Due to t]~e inhomogeneous distribution of the impurity atoms diffusing from the surface, the increase in volume, as well as the stresses which arise, are also inhomogeneous. In particular, during the formation of compressive stresses in the diffusion zone tensile stresses arise in the sublayer.

Experimentally, during diffusion saturation of iron by zinc from the gas phase surface structures have been observed close to boundaries in the form of mounds [68]. This indicates an increase in the overall number of atoms and the lattice parameter in the diffusion zone. As a result it was observed [68, 69] that when DIGM processes are active in thin (~40 ~m) foils with uniform migration of the grain boundaries across the thickness of the foil, DIGM is completely suppressed in samples with thickness &h = 7 mm. Yu and Shewmon [68] and She~- mon and Yu [69] note that it is possible that the high unrelaxed compressive stresses in the diffusion zone reduce somewhat the diffusion rate for impurity atoms from the surface, and that the grain boundary fluxes of atoms of different kinds equalize, so that the resulting grain boundary atomic fluxes disappear and the DIGM process is correspondingly suppressed~

429

-~,~

6,0 i i t i , i

8.0 ~oo. tO~, , t ' - '

Fig. 4. Arrhenius curves for the DIGM migration rate [47]: i) 60 min anneal; 2) 8 min anneal.

TABLE i. Activation Ener- gies Qv for Diffusion- Initiated Grain Boundary Migration in Various Sys- tems

Diffusion[ Qv, 1 Source pair k J/mole

Fe--Zn 287,0 [27] Fe--Zn 269,0 [47] Cu--Ni 64,3 -77,1 [30] Cu--Ni 158,7 [62] Au--Ag 33,0 [68]

One of the most important characteristics of the diffusion kinetics of solid state processes, including DIGM processes, is the activation energy. Naturally, therefore, measure- ments of this quantity on the basis of the temperature dependence of the boundary migration speed v have been performed by many workers [27, 30, 47, 62, 68]. Indeed, over a wide range of temperatures (for example [47], 823 to 1173 K, Fig. 4) a linear dependence is found for logv on I/T, indicating that the migration mechanism does not change over this range of study. Analogous results have been obtained in [27, 30, 62, 68]. The activation energies Qv obtained for DIGM in various alloys are shown in Table i.

To begin with, we should note that the value of Qv has been determined in a rather small number of works, and a correspondingly small number of diffusion pairs (metallic systems). Moreover, the experimental values obtained by different workers for one and the same system are different. Thus, for the Fe-Zn system, the value of Qv (Table I) is close to that for bulk diffusion (Q = 240 kJ/mole [27]), exceeding by almost a factor of two the grain boundary diffusion activation energy (Qb = 155-187 kJ/mole [28]). For the Cu-Ni system in [30] the value of Qv (see Table i) is close to the activation energy for grain boundary diffusion, while that found in [47] is lower by a factor of two. Analogous data were obtained in [62] for the Au-Ag system, where the activation energy for DIGM is about half the activation energy for grain boundary diffusion of silver in gold (Qb ~ 64.0 kJ/mole [47, 62]).

Therefore, although the phenomenology of DIGM is defined by the atomic grain boundary diffusion fluxes from an external source and by alloy formation in the material as a result of retention of migrating boundaries in the bulk of the material, it is not possible to relate the processes which control DIGM to a concrete mechanism.

It appears to us that it would be useful with regard to this question to use the ideas about grain boundary fluxes as a factor, but including the intrinsic mechanisms for boundary migration. In various metallic systems, boundaries which differ as to type and impurity diffusion conditions may exhibit intrinsic activation energies or may be significantly different. In support of this idea we note the data discussed above as to the cessation of DIGM processes at long annealing times under conditions where the diffusion fluxes are retained at the boundaries and in the absence of noticeable impurity diffusion in the near-boundary

430

region. We note also that there is data which, in several systems (for example, for diffusion of Ag in copper [69]), indicates the absence of DIGM in the presence of grain boundary diffusion. Finally, we note especially the discrete (discontinuous) nature of the boundary migration during DIGM, with the subsequent splitting of the boundaries which takes place as they stop, as a necessary condition for subsequent movement [38, 48, 63, 64]. All of these observations demonstrate the presence of independent processes which control the grain boundary migration rate. It will be absolutely necessary to carry out special study of the questions considered above, using a variety of approaches, in order to elucidate the nature of DIGM: study of the DIGM activation energy, electron-microscopic study of the boundary structure in various stages of migration, and elucidation of the composition and str~cture of the sub-boundary regions. It is necessary as well to obtain the numerical values of the DIGM activation energy in a wide variety of metallic systems.

2. CHANGES IN ALLOY COMPOSITION DURING DIFFUSION-INITIATED GRAIN BOUNDARY MIGRATION

Measurement of the composition ahead of and behind a migrating boundary is an important question for the elucidation of the nature and driving forces of DIGM. Thus, even in the early reports [24-27, 62], a composition asymmetry was noted and, consequently, there is a chemical driving force for the boundary migration even when a random motion occurs in the presence of a grain boundary diffusion impurity atom flux. Indeed, a step change in the composition in the vicinity of a grain, swept out during DIGM and bounded by the starting and final position of the migrating boundary, has been observed by x-ray analysis [24], and then by local microanalysis [26-28, 30, 31, 35, 47, 48, 62, 63, 65]. It has been proposed that the composition of the grain ahead of a migrating boundary remains constant, so that the relation

v > D_~ k (iO

was considered [64, 65] as a necessary condition for the appearance of DIGM (D v is the bulk diffusion coefficient and % is the interatomic distance). Therefore, local measurement of the composition immediately ahead of and behind a migrating boundary is very important. Elec- tron microprobe analysis is widely used to accomplish this [30, 31, 35, 65] with a spatial resolution in the analyzed region of about 1 ~m, and, to a lesser degree, analytical electron microscopy has been employed on thin foils with a spatial resolution better than 50 nm [26, 47, 48, 62, 63]. Microprobe analysis makes it possible to determine the overall composition of an alloy with a high accuracy in the region of a migrating boundary, while the analytic electron microscopy method provides a means for constructing the distribution of the impurities diffusing along the boundary at various distances behind and ahead of the migrating boundary with high spatial resolution. Using analytical electron microscopy various types of distributions of the diffusing impurity have been observed [26, 47, 48, 62] behind the migrating boundary. Thus, in [26, 47, 62, 63] a monotonic decrease in the impurity concentration has been observed from the initial position of the migrating boundary in the direction of its final position (Fig. 5a); in [47, 48] a maximum in the concentration was located in the middle of this region (Fig. 5b, d); and when oscillating boundary movement was observed [48] there was a nonmonotonic dependence of the impurity concentration (Fig. 5c) on the coordinate in the vicinity of the migrating boundary. The final position of the boundary in this case (Fig. 5c) may be within the region, while in the ffrst two cases a step increase in the impurity concentration is observed at the points corresponding to the initial and final boundary positions.

In addition, in [27, 30, 32, 48] where DIGM was observed at high temperatures, a smooth concentration profile was observed (Fig. 5d) at the initial and final positions of the migrating boundary, indicating the presence of significant bulk diffusion ahead of such a boundary. Under these conditions the relationship (i) is not satisfied. Estimates of the value of Dv/v in [9, ii, 26] using the experimental values of the boundary migration rates and the bulk diffusion coefficients D v also showed (Tables 2 and 3) that at high temperatures the DIGM processes take place under the conditions Dr/% > v.

Analogous data on the values of Dv/v > % during high temperature DIGM has also been obtained in [27, 30]. Thus, DIGM processes take place actively both in the absence and in the presence of bulk diffusion of the impurity atoms in the region of the matrix grain lying near the migrating boundary. The distance by which the bulk diffusion penetrates that grain due to bulk diffusion is ten or more interatomic distances (Tables 2 and 3).

431

• /2

0

[ Matrix I b!GM 1 I Matrix I Direc- tion of "

Initial I boundaryl 20 grain

"boundary mlgra- Final grair -position I tlon I boundary

'~ ~ ~--I I position

Di, loca-it; ill

f~

f2

fo

8

6

O

Matrix I,DIG~ Matrix

:nitial IFinal ~rain " I Igrain boundar~ position I L bOundary |position

b

! 3 £, ~m

98

O

cl

,t 4 8 12 £, ~m

ro ¢J

Matrzx I.DIGM . Matrix •

llnitial ~grain boun, [daryposi- l tion

d

Final l / '% t grain [ t \ bound-'~ I ] ary po-',]

I ,I

0 2 ~ i, ~ , ~Jm

Fig. 5. Variation of the dopant concentration behind a boundary undergoing DIGM: a) a boundary which is a dislocation wall [47]; b) an isolated dislocation remains at the original position of the boundary [47]; c) the boundary oscillates during migration [48]; and the final position is indicated by the dashed line; and d) variation of the concentration for high annealing temperatures.

Quantitatively, the effects of alloy formation in the DIGM process, in particular close to the surface of the interface between a diffusing pair (or close to the surface of the sample in DIGM under conditions of impurity saturation from the gas phase [25, 26, 39, 47, 65, 66, 69]), are most significant. Thus, in [27, 50] it was shown that the concentration of the impurities diffusing during DIGM close to the surface reaches the solubility limit in the matrix. In addition, in [35] the Zn concentration in the surface layer of iron (the matrix) for T = 723 to 823 K exceeded the solubility limit for this element by some 2-7%.

As the penetration depth for the migrating boundary increases, the concentration of the diffusing element in the region of the grain behind it decreases significantly. Thus, when DIGM takes place under conditions of copper saturation by zinc from the gas phase, the content of the latter in the surface layer, CZn, at 753 K was about 22 at. %, while at a depth of 35 ~m it was 2 at. %. For 673 K the surface value was 28 at. % and that at a depth of 28 ~m was about 2 at. %.

In [25, 27], using the theory of Cahn [70], for comparatively thin samples, in which the boundaries normal to the surface migrate over their entire length during DIGM under impurity saturation conditions from both surfaces, the authors calculated the concentration profile of the impurity with depth. According to [70],

c (z) = ch (z l/~o/O~ ~} co ch (zo ] , r ~ ) ' ( 2 )

where c 0 and c(z) are the impurity concentrations at the surface and at a distance z from the surface; z 0 is the half-thickness of the sample; v 0 is the boundary migration rate during DIGM from the surface; D b is the diffusion coefficient for the impurities along the boundary; 6 is the diffusion width of the latter; and the coordinate axis z is directed along the diffusion direction along the boundary.

The impurity distribution behind a migrating boundary calculated from the relation (2) as a function of sample thickness agrees well with experiment. Indeed, the values

kq9

TABLE 2. Estimates of the Penetration Distance Dv/v for Bulk Diffusion of Impurity Atoms Ahead of a Boundary Migrating by DIGM [32]

~trix ]elementDiffusing I T,K Time, h Iv, pm/secID, m2/sec [ D~/v,m Ag Cu 673 408 42d:4 8.10 - ~ 6.10 -9

773 ' 008 18__+4 6- 10 -18 3,3.10 -r

Ag Pd 673 216 5--+0,7 3.10 -2~ 6.10 -l l

773 144 8-4-1,0 9-10 -2° 1-10 -s

Au Ni 873 75 23-+3. 1. '10 ~16 4,3- I0 -g

Au Pd 773 144 ' 26-1-7 3-10 -Is 1,1.10 -g

Cu Mn 673 2,116 8-I-,I 5- I0 -m O. I0 -9

773 144 30+-12 4- I0 -Is 1,3- I0 - r

Cu Pd 673 216 4--I-0,7 3.10 -m 7,5. I0 -it

Pt Pd 773 408 2-+0,8 I- lO - ~ 5. I0 -12

1073 48 58-+I I I . I0 -{s 2. I0 -8

TABLE 3. Estimates of the Penetration Distance Dv/v Using the Bulk Diffusion of Nickel in a Copper Matrix in Front of a Migrating Boundary [47]

T, I< [ D~,m2 /sec ! v , m / s e c ( D~/v, m Note

823 2,05- iiO -m 3,9.10 -ll 5,2.10 -11 <L

873 1,79- lO -m 6,8- 10 -11 2,6-10 -I° ~ ,

923 •,24- 10 -19 1,1.1,0 -~° 1,1.10 -9 --3.

973 7,03. I0 -is 1,66- 10 -9 4,1- 10 -9 .>~, 1023 3,3.10 -18 2,5.10 -1° 1,3.10 -8 >~,

1073 1,39. I0 -'7 3,59.10 -1° 3,9.10 -8 > L

1123 5,1- 10 -17 4,15.10 -9 1,0- 10 -7 >>%

1173 1,65. 110 -16 5,9-10 -~ 2,5.10 -r >>L

calculated from (2) for the impurity concentration at the surface for sample thicknesses of 30-40 ~m exceed the values in the middle of the sample by a factor of 3-5.

Using the experimentally determined values of c(z) and v 0 in the relation (2), Hill- ert and Purdy [25] and Li and Hillert [27] found the value of Db6. These values turn out to be 3-4 orders of magnitude larger than the corresponding values for a stationary boundary. It is noted also [48] that the concentration of the diffusing impurities at a stationary boundary is significantly lower than at a migrating one. All of this suggests a significant change in the structure and properties of migrating boundaries, in particular a transition of them to an excited dynamic state under the conditions for DIGM [15]. One of the pieces of experimental evidence for a change in the boundary structure during DIGM is the observation of many step defects (ledges) in it [47, 67].

The data presented above definitively demonstrate the existence of difference in the chemical composition of the material ahead of and behind the migrating boundary, and this difference is, in the final analysis, the fundamental reason for DIGM. In a certain sense, the phenomenon of DI~ may be regarded as a kinetic mechanism for alloy formation under conditions of low diffusion mobility of the dopant element in the bulk of the grains, while the intrinsic change in the composition behind the migrating boundaries, apparently, is the driving force of DIGM. However, there is sufficiently reliable experimental data which does not fit into this explanation, and suggests a need to search for new structural mechanisms for DIGM and to analyze the driving forces of this process.

433

3. DRIVING FORCES AND MECHANISMS FOR DIFFUSION-INITIATED GRAIN BOUNDARY MIGRATION

A thermodynamic analysis of the force balance for a boundary during its migration, with formation of a composition asymmetry in the surrounding grains, leads [71] to the following relationship for the driving forces

AOm=vV~- -oV~ , (3/ M d z .

whore M and v are the mobility and rate of migration for the boundaries, respectively; V m is the molar volume of the alloy; o is the surface energy of the boundary; z is the coordinate along the direction of the boundary; and e is the angle between the local normal to the boundary and the direction of macroscopic boundary motion. For a planar boundary or for the case of its migration without change in shape, de/dz = 0, so that

AOm ,-.vVm_ (4) M

In [25-27, 30] the Gibbs free energy was taken as the driving force, AGm, which acts on a boundary migrating with a change in composition. As is well-known, there are various ways in which chemical forces can be dissipated (in particular in processes of grain boundary diffusion), but in [25-27] these were not considered. The value of AG m is calculated under the assumption of a subregular solid solution [25]

AG~ = ( I - - c o ) [ e T l n l - c ° -+-(A 3 -3B) (co ~ - - c ' ) - - 48 (c] - - c3)] q- L l r - - c J

c

where c o and c are the impurity concentrations in the original matrix and in the region behind the migrating boundary, respectively; and A and B are constants or, in the general case, using the idea of an ideal (entropic) AGme = RT inc for an original value of c o = 0 and a nonideal AGmn = RT in~ component of the chemical energy

(5)

aG~ = R T ( l n c + In ~). ( 6 )

For the Fe-Zn system, using the known values of the thermodynamic constants and the experimentally determined values c o = 0 and c = 0.06, we obtain from (5) the value AG m = (259-367) kJ/mole. Using the known values of V m the value AG m ~ (108-109 ) J/m 3 was esti- mated in [25-27]. These values exceed significantly the capillary forces (surface tension) for the minimal radius of curvature of the boundary (rmin). Thus, in [67] the value obtained was rmi n = 90 nm. For a value ~ = 1J/m 2 (for example, for nickel y = 0.87 J/m 2 [47]) the capillary forces are P ~ ¥/rmi n = 107 J/m 3, so that indeed AG m > P. In [27] an ideal solid solution model (y = i) was used to analyze the experimental data for alloy formation under DIGM conditions, where since c ~ 1 the relation (6) was put in the form

AG~ = RTIn c ~. RTc. ( 7 )

In essence, it was thus assumed that the driving force is the ideal (entropic) component of the chemical energy and this approximation was subsumed in subsequent works. It was remarked in [26], incidentally, that for aging alloys with limited solubility in~ > 0 and, consequently, if AG m is considered as a driving force in the matrix, then the value determined here has just the entropic component of the chemical energy for alloy formation. Under this approximation, Li and Hillert [27] succeeded in describing fully the observed experimental systematics of the development of DIGM in the Fe-Zn system.

However, in the first place, as was remarked in [26], in this picture there is no mechanism by which the reduction in the free energy, brought about by the increase in the entropy of mixing, would provide a driving force for boundary migration. Secondly, above we have already noted that at high temperatures DIGM takes place under conditions such that alloy formation takes place strongly ahead of the migrating boundary by bulk impurity diffusion from the boundary. This should remove the driving force for the migration considered above. Thirdly, from this understanding of the driving forces for the migration it is not possible to explain the DIGM process when the concentration of the element diffusing from

434

the boundary is reduced beyond the migrating boundary (dezincification in the Fe-Zn system [25, 27], and others), the observation of oscillating boundary movement [25, 27], etc. Fourthly, quantitatively similar values of the change in the entropic component of the free energy analogous to those found above are achieved in grain boundary diffusion of isotope atoms from the matrix, but DIGM is not observed in this case [26, 30].

All of these facts demonstrate the impossibility of using the idea of the chemical Gibbs energy as the driving force for DIGM in the general case and stimulate a search for aIter- native ideas.

Hillert [71] has considered a driving force for DIGM due to bulk diffusion of impurities in front of the migrating boundary• It is noted that if the composition is changed from c I to c 2 in a rather thin layer (the diffusion zone) close to the boundary, there ap- pear elastic distortions of the lattice, with an energy density given by

- - (e= - c , ) ~, ~ s~ ' I - -

where E is the modulus of elasticity for the grain under consideration; > is the Poisson coefficient; and q:=~/a.da/dc=dlna/dc is the relative change in the lattice parameter a as the alloy concentration c is changed• Correspondingly, as shown in [71], the increase in the free energy due to the change in composition and the appearance of elastic stresses in the grain ahead of the boundary is

~o~ = E V ~ (c~ - c , ) ~. ( 9 ) 1--p

This increase AG v now represents the driving force for DIGM. It is true, as is clear from the above discussion, that as a driving force AG v may be considered only under the condition Dv/v ~ ~, where ~ is the interatomic distance in the direction of boundary migration. Using experimental data for the Cu-Ni [47] and Cu-Zn [67] systems, we may estimate the numerical values of AG v and compare them with the surface tension P for the experimentally observed curvatur~ of the boundaries migrating under the conditions for DIGM in these systems• We find that in the Cu-Ni system, 2.8"103 J/m 3 ~ kG v ~ 7.3"103 J/m s , while the value of P is about 1.7-i0 s J/m 3. Thus, the ratio is P/AG v = 23-60 and, consequently, the driving force caused by coherent stresses is greatly insufficient to explain the migration of a boundary with the curvature experimentally observed during DIGM. For the system Cu-Zn it was also found [67] that the value of AG v is more than an order of magnitude lower than that required to overcome the surface tension of the boundary for the experimentally observed curvature. A similar conclusion has been obtained by Li and Hillert [27]• We note, incidentally, that in general consideration of AG v as the driving force in DIGM is allowed only when Dv/v> ~, while this phenomenon is widely observed for Dv/v < ~.

Nevertheless, in many works, including recent ones, the possibility of an important role played by elastic distortion in the grain ahead of the boundaries migrating during DIGM has not been excluded. Additional evidence for a certain role of this factor in the DIGM phenomenon is provided by the data of [72-76] on chemically initiated migration of liquid films in refractory metals. This phenomenon is closely related to the known effects of activated sintering, that is, the sharp drop in the sintering rate of W and Mo powder when a liquid phase is present in the system (typically nickel, iron, palladium, etc). It appears r~ .:~ t,~-,oJ that the presence of a liquid layer on the grain boundaries or the powder particles in such systems (Mo-Ni, W-N±, W-Fe, W-Pd, etc.) leads to an intense migration of this liquid grain boundary layer. In this case, beyond the migrating liquid film a grain of a refractory ~±±uy, ..... of the type Mo + ~,"~ W + Fe, etc., is grown, corresponding to the equilibrimi~ solubility of the metal in the liquid layer• Thus, the phenomenon is

w±Ga in the .... phase, but the rate of ............... process perfectly analogous to .... ±nuuceu ~O±iu U L t e ±lqU±u

uamuumat~u is de~ur±u~d well on the basis of a driving force ......... from (9). In paruic ±dr, in the systems Mo-Ni and W-N± the rate of this process increases paL abo±lua±±y ............ as a function of the nickel concentration beyond the migrating layer. It also seems that the possibility of doping the liquid layer makes ±L ......... pumSlu±e L/a-r~n 76] to realize a pLauL±ca± uunuru± oveE the migration rate of .... Lne liquid film in accord with that expected from (4) ....... wuen we consider t ~ ~ _ ~ ~,_ ~ _., ~-,_ , _ ~ <92 as the driving force Thus, in r~,~ t l~j an a±xoy of 9u4 with Ni, wnxutt .au • l'IO I U

. . . . . . a I __ n ~ d L ~ been first fired in the presence of a ±±qu~u phase, was Lepe~teu±y ' .... ~ to the same tern- 1 ~ _ . . ] J . _A _1__1 ] 1_ . - f & l _ z _ perature, T = ,ul'~w'J K with doping from a ±±qu±u ItlCgUl flmnl .... W±Ln~- iron. As a result ol Ultl3

doping an increase in the migration rate was observed, and the grains growing from the

435

I

a~,L

O,Z

CFe , at. % Z

i

2 * E ,10 ~ 6x

Fig. 6 Fig. 7

I 2

//

R

Fig. 6. Liquid layer migration rate as a function of iron concentra- - uo.eLe.t tion UFe and ............ uli~ deformation 6 in the system Mo-Ni-Fe [74].

Fig. 7. Schematic of boundary movement during initiation of DIGM [37].

migrating film had the composition Mo + 1.46% Ni + 1.15% Fe, while the original composition of the grains after the activated sintering was Mo + 1.46% Ni. As the Fe content in the melt was changed, the composition of the growing grains changed as well, so the value of q in the relation (9) is changed in the following manner:

I aa , , I aa . . . . . c~i)-~--- - - (c~o-cL), (io)

o aCNl LcN' ~ a OCFe

where CNi ° and CFe ° are the contents of Ni and Fe in the original grain, and CNi I and CFe l are the contents of the same elements in the grains growing behind the migrating liquid film doped with iron by liquid induced migration. From the value of q obtained we can use (9) to construct the dependence of the migration rate for the liquid film (Fig. 6). It is apparent that the data obtained are close to the prediction of (9) for a parabolic curve of v(q). Analogously it was observed in [76] that the migration rate in liquid induced migration was reduced in the Mo-Ni system when the liquid film was doped with tungsten, there was a change in the rate in this same system upon doping of the liquid phase with cobalt and tin [75], etc. It is most significant that according to (9), when q = 0 no migration of the liquid film will be observed [72-76]. It is interesting that in [74-76], along with migration of the liquid film, a migration of the boundaries was observed where the liquid phase was absent, that is, the DIGM process was observed. It is characteristic that the DIGM process is suppressed for compositions of the grain boundary phase corresponding to q = O.

From the entire discussion above it also follows that until now there has been no definitive resolution of the question as to the usefulness of the coherent deformation energy in the diffusion zone ahead of the migrating boundaries as the driving forces for the DIGM processes. The more so since an intense local plastic deformation was observed in [67, 77] immediately ahead of the boundary, possibly as a result of the production of dislocations at this boundary, in which a grain boundary diffusion current of atoms arises. Naturally a relaxation of the elastic stresses in the diffusion zone is associated with the local plastic deformation.

An interesting model for the driving force of the DIGM process was proposed in [37], where the grain boundary is considered as a thin layer of thickness t, bounded by the surfaces 1 and 2, with a liquid-like (amorphous) structure (Fig. 7). In this layer, therefore, the atoms diffusing along the boundary have a high mobility and form a highly con- centrated solid solution. A displacement of one of the surfaces from the surface by 6x, with the corresponding change in curvature, causes a change in the surface energy which is given by

AG~= 27V~ 2~V~,~__ __ 2 ~ V ~ x R + ~ x R R 2 '

(il)

436

where y is the specific surface energy for the surfaces 1 and 2. The change in the free energy is again obtained for the grain boundary layer as a result of the formation of a solid solution

_ [ao I tax ao, = t S / / t "

The general change in the free energy for a displacement of surface I is

12)

AG, = (a G + AG, ) = + \ac )r

An a n a l o g o u s a n a l y s i s f o r a d i s p l a c e m e n t o f s u r f a c e 2 by 6x g i v e s

13)

AO~ = 2~Vm + AOc, 14) R~

where AGc i s t h e change in t h e f r e e e n e r g y due t o t h e t r a n s f o r m a t i o n f rom t h e amorphous g r a i n b o u n d a r y p h a s e t o t h e c r y s t a l l i n e one . The o v e r a l l v a l u e f o r t h e f r e e e n e r g y in t h e m i g r a t i o n o f t h e b o u n d a r y t h e n p r o v i d e s a d r i v i n g f o r c e f o r t h e m i g r a t i o n :

AGF~AGI@AGi.

I t i s s i g n i f i c a n t f o r t h i s model t h a t , f i r s t l y , t h e d r i v i n g f o r c e depends on t h e s u r f a c e bounda ry e n e r g y ¥, so t h a t i t p r e d i c t s a low d r i v i n g f o r c e f o r DIGN f o r s p e c i a l b o u n d a r i e s . Second , as t h e b o u n d a r y c u r v a t u r e i n c r e a s e s i t p r e d i c t s an i n c r e a s e in t h e d r i v i n g f o r c e o f t h e m i g r a t i o n . T h i r d , t h e l a t t e r i s p r o p o r t i o n a l t o ( 3 G / S c ) ' c , and t h i s may e x p l a i n t h e s i g n i f i c a n t d e p e n d e n c e o f t h e m i g r a t i o n s p e e d on t h e d e g r e e t o which t h e b o u n d a r y i s s a t u r a t e d w i t h i m p u r i t i e s . Us ing a c t u a l d a t a in (13) and ( 1 4 ) , f o r t h e s y s t e m Ag-Cu, Chaki [37] e s t i m a t e s t h e o r e t i c a l l y v = 1 5 ' 1 0 -z2 m / s e e f o r T = 673 K, where t h e e x p e r i m e n t a l v a l u e i s [32] v = (12 ± 4 ) ' 1 0 - zz m / s e e . However , d e s p i t e t h e s a t i s f a c t o r y a g r e e m e n t w i t h t h e d a t a p r e s e n t e d , i t i s d o u b t f u l w h e t h e r t h e model o f [37] i s p r o m i s i n g , p r i m a r i l y due t o t h e p h y s i c a l l y i n c o r r e c t b a s i c i d e a as t o t h e s t r u c t u r e o f t h e b o u n d a r y as an amorphous l a y e r o f t h i c k n e s s t . From t h e v i e w p o i n t o f modern d a t a [6 , 8] such an i d e a does n o t c o r - r e s p o n d t o t h e r e a l s t r u c t u r e o f a h i g h a n g l e b o u n d a r y .

It is important that even when the question as to the nature of the driving forces for DIGM is resolved the problem of elucidating the physical mechanism for the realization of this process will remain: that is, the mechanism for the structural (atomic) details of boundary migration.

In fact, the only mechanism for DIGM is still that of Cahn and Balluffi [16], namely a cllmb of grain boundary dislocations caused by a resultant flux of point defects (vacancies) due to a directional grain boundary flux of atoms. The latter is caused directly by the difference diffusion coefficients for the impurity atoms and the original matrix and, consequently, represents the Kirkendall grain boundary effect. Balluffi and Cahn [16] as- sume that the local gradient of the chemical potential of the grain boundary vacancies may be viewed as the driving force for a climb of grain boundary dislocations and, therefore, for grain boundary steps (Fig. 8), bound to these dislocations. The corresponding Cahn- Balluffi equation has the form

bd bd b,/~ DB DA

c~ = ~ - , (15) 1 + 5f/ d - I

where c B is the atomic concentration of the impurity atoms B in the vicinity of the migrating boundary; b n is the component of the Burgers vector for the grain boundary dislocation normal to the boundary; $ is the height of a step on the boundary, bound to a grain boundary dislocation; and DBbd and DA bd are the coefficients of boundary diffusion for the impurities and the matrix, respectively.

Unfortunately the mechanism of Cahn and Balluffi has not yet found experimental support, although the evidence of a climb of grain boundary dislocations during migration was obtained in [78], and the presence of steps on boundaries undergoing DIGM was observed by Liu et al. [47] and Hackneyet al. [67]. However, such steps may be due as well to lattice dislocations intersecting the boundary or may be a kinetic feature of the migrating boundaries.

437

Crystal i

Grain boundary Diane Crystal 2

DSC of the lattice

a o b

Fig. 8. Climb of grain boundary dislocations at a symmetric tilt boundary in a simple cubic structure [16]: a) original structure; b) grain boundary dislocation after climb by vacancy annihilation (here b is the Burgers vector and % is the width of the boundary).

It is necessary to note as well a number of known experimental facts which do not agree with the Cahn-Balluffi mechanism. First, there is the observation of the DIGM phenomenon during grain boundary diffusion of interstitial impurities [41-45]. Second, is the observation [72-76] of the liquid-induced migration, analogous to DIGM, in which the migrating boundary takes the form of a liquid layer, to which the dislocation migration mechanism is inapplicable. Third, is the fact that the Cahn-Balluffi mechanism does not predict the nucleation of new grains during DIGM and the peculiarities of the change in their structure, in particular the splitting of boundaries during migration, etc. Therefore, the Cahn-Bal- luffi mechanism cannot be regarded as generally accepted, and, consequently, the question as to the migration mechanism initiated by grain boundary diffusion, remains to be eluci- dated. The ideas proposed in [15] about the transition of the boundary into a special excited state during DIGM or the ideas in [52, 56] on the formation of osmotic pressure on the boundary under DIGM conditions do not solve the problems either. The idea of osmotic pressure as the driving force DIGM is directly incompatible with the data presented above as to the existence of DIGM under conditions where bulk diffusion ahead of the migrating boundary is both absent and strongly present. The latter, in particular, demonstrates that the B l regime of Harrison [53] is not satisfied.

Thus, although as discussed above a number of kinetic and thermodynamic models have been developed for DIGM, many experimentally observed systematics of this phenomenon have not been satisfactorily explained, and a generally accepted model has not yet been found.

4. DIFFUSION-INDUCED RECRYSTALLIZATION

An interesting phenomenon which takes place simultaneously with DIGM, and was first observed in [27, 30], is diffusion-induced recrystallization: that is, a process whereby new grains of an alloy are formed on a boundary as it undergoes migration. Corresponding- ly, the surface of samples saturated with a diffusing element from the gas phase exhibits [27] a fine-grain polycrystalline l~yer. Den Broder and Nakahara [3] concluded that the nucleation of new grains on the original boundaries of the surface layer and on the DIGM front is also the result of unequal grain boundary diffusion currents for the impurity atoms and the matrix, therefore the observed phenomenon is regarded as diffusion-induced recrystallization. Subsequently this phenomenon was observed [30, 38, 39, 44, 47, 48, 63, 77] not only during diffusion saturation from the gas phase but also in diffusion of pairs of various metals [30, 47, 63, 77, 79], where the growth of the nuclei of new grains in essence is the DIGM process with the appearance of new boundaries. However, in regions of diffusion-induced recrystallization the concentration of the diffusing impurities always exceeds significantly that in the regime of DIGM. Thus, den Broeder et al. [79] observed that in diffusion-induced recrystallization regions when grain boundary diffusion of aluminum in copper takes place, the A1 concentration is CAl = I0 at. %, while that for DIGM is CAl = 5 at. %. Analogous data were obtained in [30], where once again the concentration of the diffusing impurity in diffusion-induced recrystallization exceeded

438

a

IGM

~ ~ . _ W///,LV~////,~,:. c

Fig. 9. Schematic of the formation of new grains under diffusion-induced recrystallization conditions [64]: I and II are the orientations of. the original grains; III and IV are the nuclei of the new grains. DIR denotes diffusion-induced recrystallization.

Fig. i0. Generation of dislocations by a migrating grain boundary during diffusion of nickel in molybdenum.

that for DIGM by a factor of two. In [47, 48, 63, 77, 79] this same conclusion was reached indirectly, from the fact that the diffusion-induced recrystallization zone is restricted to a surface layer of a diffusion metal pair. Interesting features of grain growth during diffusion-induced recrystallization were found in [64]. First, the new grains do not grow in the direction of migration of the original boundary on which they grow, but they grow in the opposite direction (Fig. 9a). Second, the new grains form along the original boundaries, one part of which grows into one of the accompanying grains, while the other part grows into a neighboring grain (Fig. 9b). The nuclei which grow in each grain have a single crystallographic orientation, which does not coincide with the orientation of the original grains (Fig. 9b), so that when they meet the growing grains coagulate and three boundaries are observed in the diffusion-induced recrystallization region (Fig. 9c) between grains of different orientation.

Considering the totality of the systematics described above for the development of DIGM and the structural effects which accompany this phenomenon, we naturally expect a stronger driving force for the development of diffusion-induced recrystallization, since the nucleation of new grains is related to the appearance of additional boundaries in comparison with DIGM. Qualitatively, this circumstance explains the fact that diffusion- induced recrystallization is observed only in surface layers with a high concentration of the impurities diffusing from an external source along the boundaries. However, it remains unclear, although extremely interesting, as to what the mechanism is for the nucleation of new grains. In this connection it will be necessary to return again to a discussion of the structural features of the region near the boundaries which form during DIGM. First of all, due to the change in the lattice parameter as the composition changes at the boundary of the grain (and close to the boundary when v < Dv/X) , as well as the difference in the partial coefficients of the grain boundary diffusion for the impurity atoms and the majority atoms of the alloy and, as a consequence, the increase in the number of atoms in the diffusion layer, internal stresses arise [30, 69, 80], the relaxation of which occurs via the generation of dislocation in the region near the boundary [67, 77, 80] (Fig. i0).

439

a

b

Fig. ii. Schematic for the splitting of a boundary and the creation of a grain at a triple junction under diffusion- induced recrystallization conditions [34].

Fig. 12. Nucleation of new grains in the presence of a grain boundary flux of nickel atoms in molybdenum.

Experimentally these dislocation formations (walls) are observed close to the migrating boundaries [25, 34, 36, 47, 62, 67, 77, 80] and in a number of reports [25, 48, 62] have been considered as a factor in the accommodation of the grain region behind the migrating boundaries with different composition or as a consequence of the relaxation of osmotic pressure [57]. However, it cannot be excluded that it is just this deformation of the region near the boundaries which causes the appearance of nuclei of new grains during DIGM which serve as centers for recrystallization [81, 82]. In particular, this suggestion has been made in [34, 77].

In addition, a high density of microtwins is characteristic of the grains which grow during DIGM [38, 44, 48, 62-64], nucleating on the migrating boundary. Lopez [38] has proposed that the nucleation of microtwins is also a consequence of the high stresses which are created in the diffusion layer by the migrating boundary, especially in twisted portions of the boundary. It is in just these regions where we might expect high local stresses and, possibly, the crystallographic orientations necessary for nucleation of microtwins.

Ideas distinctly different from those discussed above with regard to the nucleation mechanism for grains during diffusion-induced recrystallization were discussed in [63, 64]. It was proposed there-that the most probable mechanism for such nucleation is a splitting (dissociation) of the original boundary into a low mobility one of a special type and a high mobility one, which, due to the migration under conditions for DIGM, causes growth of a new grain. We recall that the idea of splitting during the stationary period of a boundary during DIGM with formation of small angle dislocation braids (walls) was first proposed in [63]. It was assumed in this case that the splitting of the dislocation walls causes transformation of the boundary into a highly mobile configuration (in particular, as we represent it, as a consequence of the "emission" into the dislocation braid of the impurities which accumulate at the boundary during migration). In subsequent work, the ideas discussed in [63] were used in [47, 48, 67]. However, Meyrick et al. [63] considered the splitting of the boundary with formation of a Z = 3 twin and a high mobility component to be a more effective means of splitting in comparison with formation of a small angle dislocation braid. In support of this idea, data has been presented in [83, 84] on the splitting of boundaries with formation of special boundaries of the type Z = 3 under conditions typical of recrystallization as a mechanism for formation of annealing twins.

440

Since when boundaries split under DIGM conditions the change in the free energy as a result of alloy formation, as a rule, significantly exceeds the increase in energy due to the formation of E = 3 twin boundaries, this splitting becomes most probable. In this connection in [63, 64], the possibility of existence of diffusion-induced dissociation (splitting) of the boundaries under DIGM conditions was put forward. Thus, the splitting of the boundaries may be viewed as a mechanism for the nucleation of new grains on the original boundaries under DIGM conditions. In this scheme the properties of the crystallographic orientation of the newly nucleated grains found in [64] may be understood (Fig. 9b, c), since the low mobility segment of the boundary must be of the special type ~ = 3.

Apparently, direct evidence of the splitting of boundaries was obtained in [34] from electron microscopic study under conditions where copper was saturated by zinc from the vapor phase during DIGM processes at triple grain junctions. Firstly, in this case the nucleation of a new grain was observed in the absence of nucleation at the boundaries (as also in [25, 47, 48, 67], there is a dislocation braid, or wall, in the original position types among the grains A and B (Fig. lla), and the boundaries AD and BD between the original grains A and B and the nucleating one at the triple junction, D, showed that the original boundary AB was a sum of a twin boundary plus a twist through an angle of 7 ° near the [133] axis. The boundaries AD and DB are correspondingly twin and twist boundaries (Fig. llb). Thus, as the grain D nucleates at the AB boundary, it splits and, moreover, forms the boundary DC.

The nucleation of new grains when a flux of Ni atoms is present in molybdenum is~ easily observed in electron microscopic study of thin foils (Fig. 12).

Hackney [34] suggests that the dominance of new grain nucleation at triple grain junctions is due to the intense plastic deformation in the junction region as DIGM begins. The deformation of this region is much larger than in a typical grain, since in the junction, in essence, there are three diffusion currents, arising on the individual boundaries and, consequently, the stresses associated with the gradient of the impurity concentration are significantly larger. Moreover, due to the structural features of such a junction, the generation of dislocations is significantly enhanced [85-87] in comparison with the typical boundary. The idea that the processes are more intense at triple junctions, including dislocation generation processes, is indicated by a very interesting cycle of experimental studies [88, 89, 92-98]. The above discussion suggests that we might expect significant anomalies in the behavior of triple junctions under dynamic DIGM conditions. Undoubtedly, it would be of interest to study these questions, in particular, by electron microscope methods in thin films.

We note, in particular, that in contrast to [92-98], large mechanical stresses may arise at triple junctions under DIGM conditions, due primarily to the change in composition and also due to osmotic pressure. Therefore, close to triple junctions we may expect strong plastic deformation and, possibly, the appearance of new boundaries due to a junction dis- clination mechanism.

In conclusion, in this brief review of the DIGM phenomenon and some of the processes which accompany it we emphasize that due to the increased entropy of mixing, the driving forces for the kinetic grain boundary processes are apparently similar in magnitude to the largest ones known for grain boundary phenomena in metals. And the structural changes at the boundaries due to impurity atom diffusion currents on the grain boundaries significantly increases their mobility, and causes the appearance of various grain boundary processes which have important applied implications. Among these processes we note grain boundary slippage and the corresponding enhancement of the Kobol creep, as well as the phenomena of superplasticity, subcritical fracture growth during hardening of metals, and activating sintering, among others.

LITERATURE CITED

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Moscow (1975). 3. V.E. Panin, V. A. Likhachev, and Yu. V. Grinyaev, Structural Deformation Levels in

Solids [in Russian], Nauka, Novosibirsk (1985). 4. V.E. Panin, Yu. V. Grinyaev, V. I. Danilov, L. B. Zuev, et al., Structural Levels

of Plastic Deformation and Fracture [in Russian], Nauka, Novosibirsk (1990).

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5. B. S. Bokshtein, Ch. V. Kopetskii, and L. S. Shvindlerman, Thermodynamics and Kinet- ics of Grain Boundaries in Metals [in Russian], Metallurgiya, Moscow (1986).

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