discontinuous reactions in solids - prof. s. k. pabi publications/67...professor manna and professor...

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Discontinuous reactions in solidsI. Manna, S. K. Pabi, and W. Gust

chemical diffusionR gas constantDiscontinuous reactions are solid state moving

RF reaction frontboundary phase transitions characterised by adiscontinuous or abrupt change in orientation and s segregation factorcomposition between the matrix phases in the sdyn dynamic segregation factorreactant and product aggregate across the sdDb grain boundary chemical diffusion triplemigrating boundary or reaction front that provides producta short circuit path of diffusion. The reactions (sdDb )0 pre-exponential factor of grain boundaryinclude discontinuous precipitation, discontinuous

chemical diffusion triple productcoarsening, discontinuous dissolution, andt timediffusion induced grain boundary migration. All

T temperaturethese reactions may account for a substantialTcr lowest (or minimum) temperature of DDchange in microstructure, composition, andTDP highest temperature for DPmaterial properties, and hence, deserve adequate

scientific attention for a better understanding. The TS solidus temperaturepresent review provides a comprehensive Tsv solvus temperaturediscussion on the current status of understanding Tv(max) temperature corresponding to maximumabout nucleation and growth mechanisms, genesis RF velocityand driving force, product morphology and v reaction front velocitydistribution, kinetic growth models, and related

Vm molar volumeexperimental techniques, and above all, thew maximum colony widthunresolved questions concerning thesew∞ random width of a discontinuousdiscontinuous reactions. In addition, exhaustive

precipitation colonylists have been provided to document thew: ∞ average width of 30–40 w∞ valuesimportant literature on the concerned subjects,

whenever possible. Finally, a particular emphasis xav metastable composition of ahas been placed on analysing the recent findings xe equilibrium composition of aabout dynamic behaviour of grain boundaries, x

a~

metastable composition of a~

after DDscope of determination of Arrhenius parameters at T3by kinetic analysis, and orientation/structural x

bequilibrium composition of b

dependence of boundary migration and diffusion.x0 initial composition of a0IMR/350a solute depleted matrix phase

© 2001 IoM Communications Ltd and ASM International. a~

supersaturated inhomogeneous a afterProfessor Manna and Professor Pabi are in the Department

DDof Metallurgical and Materials Engineering, Indian Institutea0 supersaturated matrix phaseof Technology, Kharagpur (WB), India, and Professor Gust

is in the Institut fur Metallkunde, University of Stuttgart, b precipitate phaseStuttgart, Germany. c specific energy of a/b interfaces

d width of random grain boundary; anintermetallic phase in Cu–In system

DGcDIGM Gibbs chemical energy change in DIGMList of selected symbols andDGDP Gibbs energy change in DPabbreviations DGc,eDP Gibbs chemical energy change in DP in

C Cahn parameter case of equilibriumCP continuous precipitation DGDC Gibbs energy change in DCD volume diffusion coefficient DGcDP Gibbs chemical energy change in DP

Db grain boundary chemical diffusion DGcDP Gibbs interfacial energy change in DPcoefficient DGcDC Gibbs chemical energy change in DC

DC discontinuous coarsening DGcDC Gibbs interfacial energy change in DCDCI DC at same temperature as that for DP DGI Gibbs energy change for

DCII DC at temperature other than that for initiation/nucleation of DPDP DT Tsv−T

DD discontinuous dissolution l or lDP true interlamellar or interrod spacingDIGM diffusion induced grain boundary l∞ random value of interlamellar spacing in

migration DPDIR diffusion induced recrystallisation lDC interlamellar spacing in DCDP discontinuous precipitation lDP interlamellar spacing in DPM grain boundary mobilityP fraction of chemical free energy Introductionconsumed in DP

A binary supersaturated solid solution a0 may relieveQ activation energy for volume diffusionQb activation energy for grain boundary its thermodynamic metastability through a solid state

ISSN 0950–6608 International Materials Reviews 2001 Vol. 46 No. 2 53

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54 Manna et al. Discontinuous reactions in solids

energy (e.g. recrystallisation), reduction in interfacialarea (e.g. grain growth), or metastability of the crystalstructure of the matrix (e.g. massive transformation).On the other hand, chemical driving force plays acrucial role for both types of moving boundary reac-tion resulting into a two-phase aggregate, i.e. invariantand discontinuous reactions. The discontinuous andinvariant reactions are characterised by an identicalreaction mechanism and product morphology, and adiscontinuous or abrupt change in compositionand/or orientation between the matrices in the reac-tant and product phases across the moving boundarythat acts as the reaction front. However, the reactantand product matrices in a discontinuous reactionshare identical crystal structure, whereas the sameanalogy is not valid in an invariant reaction. Thepresent review is devoted exclusively to discontinuousreactions as inclusion of invariant reactions in itspurview obviously would either exceed the prescribedlength or deny sufficient scope to present an objective

1 Schematic binary phase diagram of overview of the main subject concerned.components A and B showing identity and

Among the different discontinuous reactions, dis-composition of phases emerging from alloy ofcontinuous precipitation (DP) leads to isothermalinitial composition x

0in course of different

decomposition of a0 into an (a+b ) aggregate involv-discontinuous reactions. Note that xe

and xav ing heterogeneous precipitation of b on the reactionrepresent equilibrium and metastable solvus,

front and concurrent migration of the latter (Fig. 3).1,2respectively, and L refers to liquid phase (seetext) Thus, DP is a subset of solid state precipitation

reactions distinguished by a migrating reaction front(RF) that provides a conduit for faster mass transport.The reaction products of DP are usually stackeddecomposition process, involving nucleation and

growth of a precipitate phase b provided the necessary edgewise in alternate and parallel sequence, andaligned normal to the reaction front ( like pearlite insolute redistribution is feasible under the given

thermodynamic and kinetic conditions. This decom- steel ). The product morphology is often lamellar,occasionally fibrous or rod-type, and very rarely,position or precipitation process accounts for a large

scale modification in the microstructure, composition, globular. In the literature, DP is also referred to ascellular, grain boundary, recrystallisation, and auto-and phase stability, and hence, a marked change in

material properties and performance. Attempts to catalytic reactions.2 Among the proposed termin-ology, DP seems most logical as the reaction iscorrelate the microstructural changes with material

properties have always been, though a formidable characterised by a discontinuous change in the orien-tation and solute content between a0 and a acrossone, a major task for materials scientists and engin-

eers. The present paper reviews the present status of the reaction front.1If the interfacial energy for the a/b interfaces is veryunderstanding of an important set of solid state

reactions that is known to significantly alter the high and/or substantial residual solute supersat-uration remains in a following DP at T1 , the primaryproperties of engineering metals/alloys and ceramics.

Figure 1 is a schematic binary phase diagram that products of DP may be replaced with a structurallyand morphologically similar, yet distinctly coarser,shows the sequence of possible phase changes in a

binary alloy a0 of initial composition x0 . It is evident two-phase aggregate in the course of continued iso-thermal aging at the same or a different temperaturethat homogenisation at the temperature T1 develops

a single-phase microstructure comprising only the a0 through another moving boundary reaction calleddiscontinuous coarsening (DC) (Fig. 4).3,4 Discon-grains. As the temperature is reduced to T2 , the solid

solubility of B in A decreases, and consequently, b tinuous coarsening following DP at the same tem-perature is distinguished from DC occurring at anucleates and grows in the microstructure either in

divorced isolation or in alternate sequences with the temperature other than that for DP by designatingthe former as DCI and the latter as DCII, respectively.solute depleted matrix phase a as a function of time

t. The concerned solute migration in this process may Discontinuous coarsening may also succeed anothermoving boundary reaction (say, eutectoid transform-take place either through the bulk or along a moving

boundary that provides a short circuit path of ation, or eutectic solidification) or even continuouslamellar transformation during extended isothermaldiffusion.

Figure 2 provides a broad classification of the treatment to develop a coarser distribution of theprimary products. Apart from coarsening the distri-heterogeneous solid state transformations and, in

particular, the moving boundary reactions. The bution, the solute content in the matrix following DCis more likely to attain the equilibrium compositionmoving boundary reactions retaining a single-phase

microstructure with no compositional adjustment than that reached immediately following the primaryreaction. At this juncture, it is worth mentioning thatbefore or after the change derive the necessary driving

force for the transformation from the stored strain among the three types of DP reaction quoted by

International Materials Reviews 2001 Vol. 46 No. 2

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Manna et al. Discontinuous reactions in solids 55

2 General classification of solid state heterogeneous phase transitions. Note that discontinuous reactionsare a subset of moving boundary reactions

4 Schematic illustration of discontinuous3 Schematic representation of discontinuouscoarsening replacing a fine primary productprecipitation occurring at grain boundary (GB)aggregate of discontinuous precipitation (DP)and growing behind a migrating reaction frontwith a coarser distribution of same phase(RF) advancing into a supersaturated a

0grain

mixture across part of original grain boundary(OGB). This coarsening may take place behind

Williams and Butler,2 only the type 1 (a0�a+b) and reaction front (RF) at same or anothertype 2 (a0+c∞�a+c) precisely conform to the defi- temperature than that for DPnition of DP and the remaining one essentially rep-resents a DP reaction preceded or accompanied bythe coherent continuous precipitation. In fact, type 2 increase on that in the reactant aggregate. On the

other hand, the type 3 reaction (a0+c�a+d) maycould be a DC reaction if the precipitate morphologyis lamellar and the statistical repeat distance of the arise only under a special condition where the system

concerned allows formation of a metastable coherentlatter in the product colony undergoes a significant


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6 Schematic diagram explaining alloying bydiffusion induced grain boundary migration(cross-sectional view). Note that compositionchange across reaction front (RF) between A5 Schematic diagram showing discontinuous(pure component) and alloyed zone of B (vapourdissolution at temperature T

3of a prior

phase) in A is discontinuous: OGB refers todiscontinuous precipitation colony (formed atoriginal grain boundary, v is reaction frontT

2) such that T

2<T

3<T

sv(see Fig. 1). Note that

velocitybroken lines within a~

grain represent solutesegregation or ‘ghost images’:5 OGB refers tooriginal grain boundary, RF to reaction front

precursor preceding the precipitation of the equi-librium phase. However, the type 3 reaction is notDC because the latter, by definition, does not enter-tain a change in the crystal structure between thereactant and product phases.

Following DP or DC, a reversal in the direction ofreaction front migration at a higher temperature (say,T3<Tsv , the concerned solvus temperature) may leadto the formation of a single-phase structure (usually

7 Schematic representation of diffusion inducedinhomogeneous) at the expense of the primaryrecrystallisation (cross-sectional view). Note/secondary two-phase products through a movingthat population of alloyed grains a formed byboundary reaction called discontinuous dissolutiondissolution of B atoms (vapour) in solid A and(DD) (Fig. 5).5,6 Thus, the direction of migration ofconcomitant recrystallisation decreases asthe reaction front in a discontinuous reaction, asdepth increases

dictated by the temperature, may determine the courseof the reaction as DP/DC vis-a-vis DD. Indeed, it hasbeen suggested that an increase in temperature maylead to reversal in the direction of the reaction frontmigration and replace DP with DD.5,6

Diffusion induced grain boundary migration(DIGM) allows formation of an alloyed or de-alloyedzone in an area swept by the migrating reaction frontin the presence of a markedly different chemicalpotential of the vapour/liquid phase surrounding thesolid specimen (Fig. 6).7,8 According to Balluffi andCahn,9 DIGM is a grain boundary form of Kirkendalleffect wherein the differences in the diffusion 8 Schematic illustration of liquid film migrationcoefficients of the diffusing species along the grain involving migration of Ni–W liquid film along

grain boundaries of W to form a W–Ni alloyedboundary may give rise to a self-sustaining climb andzone (top view). Note that presence of a liquidmotion of grain boundary steps. Diffusion inducedfilm along boundary is unique to liquid filmgrain boundary migration is also referred to as chemi-migration among all discontinuous reactionscally induced interface migration or chemically

induced grain boundary migration.8 However, theformer abbreviation is preferred simply because it is across the solid grains, and is called liquid film

migration8 (Fig. 8). Strictly speaking, the last threea scientifically correct, earlier coined, and more fre-quently used term in the literature. Diffusion induced reactions, namely DIGM, DIR, and liquid film

migration do not involve a two-phase aggregate asgrain boundary migration may be accompanied bydiffusion induced recrystallisation (DIR) in the adjac- do the remaining discontinuous reactions. Never-

theless, DIGM, DIR, and liquid film migration areent grains possibly when solute concentration exceedsa critical value under identical conditions (Fig. 7). boundary diffusion controlled moving boundary reac-

tions and satisfy the essential conditions of discontin-Similar alloying or de-alloying is feasible in the pres-ence of a liquid phase along the boundaries sweeping uous change in composition and/or orientation


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Table 1 (Continued)Table 1 Occurrence of discontinuous precipitation(DP), discontinuous coarsening (DC), DP DC DD DIGMdiscontinuous dissolution (DD), and System (Ref.) (Ref.) (Ref.) (Ref.)diffusion induced grain boundary

Fe–W 115 .. . . . . . . .migration (DIGM) in binary andFe–Zn 116, 117 117–119 117, 120 121, 122multicomponent systemsGe–(Cu) ... . . . . . . 123

DP DC DD DIGM Ge–(Sn) ... . . . . . . 123System (Ref.) (Ref.) (Ref.) (Ref.) Mg–Ag 124 .. . . . . . . .

Mg–Al 125–128 .. . . . . . . .Ag–Au .. . . . . . . . 12Ag–Cu 13–15 16 ... 17 Mo–Fe 129 .. . . . . . . .Ag–Cd .. . . . . . . . 18 Mo–Ni 130, 131 .. . . . . 130, 132,Ag–O .. . . . . . . . 19 133Ag–Pd .. . . . . . . . 17 Nb–Cr 134 .. . . . . . . .Ag–Zn .. . . . . . . . 20 Nb–N 135 .. . . . . . . .Al–Ag 21 22 ... . . . Nb–Zr 136, 137 .. . . . . . . .Al–Cu 23 ... . . . 24 Ni–Al 138 .. . . . . . . .Al–Ga .. . . . . . . . 25 Ni–Au 2, 139 .. . . . . . . .Al–Hf 26 ... . . . . . . Ni–B ... . . . . . . 140Al–Li 27 27 ... . . . Ni–Be 141 .. . . . . . . .Al–Mg 28, 29 ... . . . . . . Ni–C ... . . . . . . 142Al–Zn 30 31 32 33, 34 Ni–Cr 143, 144 .. . . . . . . .Al–Zr 35 ... . . . . . . Ni–Cu ... . . . . . . 145, 146Au–Ag .. . . . . . . . 36 Ni–In 147, 148 149 150 ...Au–Al .. . . . . . . . 37 Ni–Fe ... . . . . . . 151Au–Co 38 ... . . . . . . Ni–Mo 152 .. . . . . 153Au–Cr 39 39 ... . . . Ni–Nb 154 .. . . . . . . .Au–Cu .. . . . . . . . 40 Ni–Pd ... . . . . . . 155Au–Fe 41* 42 ... . . . Ni–Si 156 .. . . . . . . .Au–Ni 43 ... . . . 17 Ni–Sn 157 158 .. . 140Au–Pd .. . . . . . . . 17 Ni–Ti 159 .. . . . . . . .Au–Pt 44 ... . . . . . . Ni–Zn 160 160 .. . 161Au–Ti 45 ... . . . . . . Pb–Ca 162 163 .. . . . .Cd–Ag 46 ... . . . . . . Pb–Cd 164 165 .. . . . .

Pb–Mg 166 166 .. . . . .Co–Al 47 48 48 . ..Pb–Na 167 167 .. . . . .Co–Be 49 49 ... . . .Pb–Sb 168 .. . . . . . . .Co–Cu .. . . . . . . . 50Pb–Sn 169, 170 171 172 ...Co–Fe 51 ... . . . . . .Pb–Te 173 .. . . . . . . .Co–Ge 52 ... . . . . . .

Co–Mo 53 53 ... . . . Pd–Ag ... . . . . . . 174Co–Nb 54 ... . . . . . . Pd–Cu ... . . . . . . 175Co–Si .. . 54 ... . . . Pd–Mo ... . . . . . . 176Co–Ta 54, 55†, 56 ... . . . . . . Pt–Au 177 .. . . . . . . .Co–Ti 56, 57 ... . . . . . . Pt–Pd ... . . . . . . 17Co–V 58 ... . . . . . .

Sb–Bi 178, 179 .. . . . . 178Co–W 59 59 ... . . .Sb–Sn 179 .. . . . . 179Co–Zn 60 60 ... . . .Si–P ... . . . . . . 180Cr–Ti 61 ... . . . . . .Sn–Bi 181 .. . . . . . . .Cr–W 62 ... . . . . . .Sn–Cd 182 .. . . . . . . .Cu–Ag 63–65 66 64 67Sn–Pd 183 .. . . . . . . .Cu–Al 68 ... . . . 37Ta–Cr 184 .. . . . . . . .Cu–As .. . . . . . . . 69

Cu–Au .. . . . . . . . 70, 71 Ti–Ag 185 185 .. . . . .Ti–Al 186 187Cu–Be 72–74 75 76 . ..

Cu–Bi .. . . . . . . . 77 Ti–Co 188 .. . . . . . . .Ti–Cr 189 .. . . . . . . .Cu–Cd 78–80 81 5, 82 83

Cu–Co 84, 85 ... . . . . . . Ti–Cu 190 .. . . . . . . .Ti–Mo 189, 191 .. . . . . . . .Cu–Fe 86 ... . . . . . .

Cu–In 87–89 90 90, 91 83 Ti–W 191 .. . . . . . . .Cu–Mg 92 ... . . . . . . U–Mo 192 193 .. . . . .Cu–Mn .. . . . . . . . 17 U–Nb 194 .. . . . . . . .Cu–Ni .. . . . . . . . 93 W–Cr 195 195 .. . 196Cu–O .. . . . . . . . 19 W–Ni ... . . . . . . 197Cu–Sb 90, 94 94 95 83 W–Pd ... . . . . . . 198Cu–Sn 96 ... . . . 83

Zn–Ag 199 200 .. . . . .Cu–Ti 97, 98 ... . . . . . .Zn–Al 201 .. . . . . . . .Cu–Zn .. . . . . . . . 99–101Zn–Au 202 .. . . . . . . .

Fe–Au 102 ... . . . . . . Zn–Cd ... 165 .. . 77Fe–Be 103, 104 ... . . . . . . Zn–Cu 203 .. . . . . . . .Fe–Co .. . . . . . . . 105‡

Al–Ag–Cu 204 .. . . . . . . .Fe–H .. . . . . . . . 106§Al–Cr–Mg 205 .. . . . . . . .Fe–Mn 107 107 ... 108Al–Cu–Li 206 .. . . . . . . .Fe–Mo 109* . . . . . . . . .Al–Li–Cu 207 207 .. . . . .Fe–Ni 110 ... . . . 111Al–Li–Zr 208 .. . . . . . . .Fe–Sb 112 ... . . . . . .Al

2O

3–Cr

2O

3. . . 209 .. . 209Fe–Sn 112, 113 ... . . . . . .

Al2O

3–(Fe

2O

3) . . . . . . . . . 210Fe–Ti 114 ... . . . . . .


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Table 1 (Continued)Table 1 (Continued)

DP DC DD DIGM DP DC DD DIGMSystem (Ref.) (Ref.) (Ref.) (Ref.)System (Ref.) (Ref.) (Ref.) (Ref.)

Au–Cu–Ag 211 ... . . . . . . Ni–Cr–Co–Mo– 278 .. . . . . . . .Ti–FeAu–Ni–Fe 212 ... . . . . . .

Au–Pt–Fe 213 ... . . . . . . Ni–Cr–Co–Mo 279 .. . . . . . . .Ni–Cr–Co–Nb 154 .. . . . . . . .CaCO

3–(SrCO

3) . . . . . . . . . 214

Ni–Cr–Fe–Mo 280 .. . . . . . . .CdS–(ZnCl2) . . . . . . . . . 215

Ni–Cr–Nb 281 .. . . . . . . .Co–Cr–C 216 ... . . . . . . Ni–Cr–Ti 282 .. . . . . . . .Co–Cu–(Sn) .. . . . . . . . 50 Ni–Cr–W 283 .. . . . . . . .Co–Fe–Au 217 ... . . . . . . Ni–Cu–Au 2 .. . . . . . . .Co–Fe–Be 218 ... . . . . . . Ni–Mo–S 284 .. . . . . . . .Co–Fe–Ti 219 219 ... . . . Ni–Zn–Cd 285 .. . . . . . . .Co–Ni–Al 220 ... . . . . . . Ni–Pd–(Cu) ... . . . . . . 286Co–Ni–Mn 221 ... . . . . . . NiO–(O) ... . . . . . . 287Co–Ni–Ti 222 222 ... . . . NiO–CaO ... 288 .. . . . .Co–Ni–Ti–Al 223 ... . . . . . . NiO–CoO ... . . . . . . 229Co–Ni–Ti–Fe–Al 223 ... . . . . . . Ni

3Al–(Cu) ... . . . . . . 271

Co–Ti–Fe 224, 225 224, 225 ... . . . Inconel 903 ... . . . . . . 289Co–W–C 226 ... . . . . . . Inconel 718 ... . . . . . . 290Co–W–Fe 227 ... . . . . . .

Pb–Ca–Sn 291 .. . . . . . . .Co–W–Ti 228 ... . . . . . .Pb–Sn–Sr–Al 292 .. . . . . . . .CoO–(O) .. . . . . . . . 229Pb–La–zirconate ... . . . . . . 293

Cu–Al–Co 68 ... . . . . . . titanate (PbO)Cu–Al–Cr 68 ... . . . . . .

Pd–Ag–Cu 294 .. . . . . . . .Cu–Al–Fe 68 ... . . . . . .SiO

2–(H

2O) ... . . . . . . 295Cu–Al–Ni 230 ... . . . . . .

Cu–Be–Co 231, 232 ... . . . . . . SrTiO3– . . . . . . . . . 296

(BaCO3,CaO)Cu–Be–Ni 233 ... . . . . . .

Cu–Co–Ni 234 234 ... . . . SrTiO3–Nb

2O

3– . . . . . . . . . 297

(CaO,BaO)Cu–Cr–Cd 235 ... . . . . . .Cu–Cr–Ti 236 ... . . . . . . TaC(Mn,Fe,Co,Ni) .. . . . . . . . 298Cu–Mn–Ni 237 ... . . . . . . Ti–Al–Nb 299 .. . 299 ...Cu–Ni–Al 238 ... . . . . . . Ti–Al–Mn–Nb ... 300 .. . . . .Cu–Ni–Co 239 ... . . . . . . TiC–Fe–(Fe) .. . . . . . . . 301Cu–Ni–Fe 240 240 ... . . . TiN–Ni(TiC) ... . . . . . . 302Cu–Ni–Mn 241 ... . . . . . .

W–Ni–Fe ... . . . . . . 303Cu–Ni–Si–Fe 242 ... . . . . . .ZrO

2–(CaO,MgO) ... . . . . . . 304Cu–Ni–Sn 243 ... . . . . . .

ZrO2–(CeO

2) . . . . . . . . . 305Cu–Ni–Ti 244 ... . . . . . .

ZrO2–Y

2O

3. . . . . . . . . 306Cu–Pd–Ag 245 ... . . . . . .

ZrO2–Y

2O

3–(MgO) ... . . . . . . 307Cu–Sn–Mg 246 ... . . . . . .

ZrO2–Y

2O

3– . . . . . . . . . 308Cu–Ti–Al 247 ... . . . . . .

(MgO,Y2O

3)Cu–Zn–Ni 248 ... . . . . . .

Fe–Al–(Zn) .. . . . . . . . 249 * Refs. 41 and 109 are dislocation-aided DP.Fe–Cr–Co–Mo 250 ... . . . . . . † Ref. 55 is a diffusion controlled DP.Fe–Mo–Au 251 ... . . . . . . ‡ Ref. 105 is a discontinuous ordering reaction.Fe–Ni–Al 252 ... . . . . . . § Ref. 106 is a diffusion induced dislocation glide reaction.Fe–Ni–Al–Co 253 ... . . . . . .Fe–Ni–Co–Al–Cu 253 ... . . . . . .Fe–Ni–Be 254 ... . . . . . . between the reactant and product across the reactionFe–Ni–Mn 255 255 ... . . .

front and, hence, justify their inclusion in the categoryFe–Ni–Sn 256 ... . . . . . .of discontinuous reactions. However, surface corru-Fe–Ni–Ti 257 257 ... . . .

Fe–Sb–Ni 112 ... . . . . . . gation is essentially considered a special form of liquidFe–Si–C(H) .. . . . . . . . 258 film migration distinguished by a characteristicKBr–(KOH) .. . . . . . . . 259 morphology but no separate mechanism. Hence, sur-KCl–NaCl 260 ... . . . . . .

face corrugation is not treated as a separate discon-Mg–Al–Zn 261 ... . . . . . .

tinuous reaction. Similarly, discontinuous ordering,Mg–Al–Zn–Mn 262 ... . . . . . .though a moving boundary reaction, is probably notMg–Li–Ag 263 ... . . . . . .

MgO–V2O

5– . . . . . . . . . 264 accompanied by a discontinuous change in compos-

(NiO,CaO) ition across the reaction front, and therefore, is notMo–Ni–(Co,Sn) .. . . . . . . . 265 included in the present review. It may be mentionedMo–Ni–(Fe) .. . . . . . . . 266 that DIR, liquid film migration, surface corrugation,Mo–Ni–(W) .. . . . . . . . 267

and discontinuous ordering should all bear closeNb–Zr–N 268 ... . . . . . .

similarity in reaction mechanism with DIGM.Nb–Zr–Ti 269 ... . . . . . .Friesel et al.10 have earlier considered DP, DC,Ni–Al–(Cu) .. . . . . . . . 270

DD, and DIGM together as a common class of solidNi–Al–B(Cu,Zn) .. . . . . . . . 271Ni–Al–Mo 272 273 ... . . . state reactions. Recently, Manna11 has reviewed theNi–Al–Mo–W 274 274 ... . . . mechanism and kinetics of grain boundary migrationNi–Be–Fe–Al–Si 275 ... . . . . . .

in these discontinuous reactions. However, both theseNi–Cr–Al 276 ... . . . . . .reviews focused more on the dynamic properties ofNi–Cr–Co–Mo– 277 ... . . . . . .

Fe–W–B the interfaces than on the genesis and mechanism of


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the transformations concerned. Thus, it is important cation. However, Table 1 also includes an updatedlist of systems showing DIGM, DIR, or liquid filmto compare and contrast these discontinuous reac-

tions to develop a general theory on moving boundary migration.Discontinuous reactions are a special class ofreactions and identify their scopes of application. In

this regard, a complete documentation of the systems moving boundary reactions characterised by distinc-tive features of discontinuous changes in orientationknown to undergo various discontinuous reactions

deserves an utmost priority. and composition between the matrix phases acrossthe reaction front. The reactions are capable of intro-Table 1 provides a comprehensive list of binary

and multicomponent systems (metallic/non-metallic) ducing significant changes in the microstructure,composition, and properties. Table 1 provides anknown to undergo DP, DC, DD, or DIGM. For

convenience, the list is arranged alphabetically and exhaustive survey of nearly all the systems reportedto undergo discontinuous reactions. However, it issystemwise with the first component being the solvent

as far as possible. Because of the nearly identical interesting to note that no generalised principle forthe occurrence of a particular discontinuous reactionmechanism and morphology, the systems amenable

to DIGM, DIR, and liquid film migration are listed in a given system emerges. Thus, Table 1 should serveas a basic tool to investigate the following unresolvedtogether. Interstitial solid solutions (e.g. steel ) are

excluded here simply because the solute transport questions, namely, (a) what are the necessary andsufficient conditions for the occurrence of a givenmechanism in these systems is different to that in the

substitutional solid solutions undergoing moving discontinuous reaction, and (b) why at times does agiven system undergo only a particular discontinuousboundary reactions or discontinuous reactions.

A few citations in Table 1 deserve a special mention. reaction, and not all possible discontinuous reactions?For instance, DP in Al–Li27 is preceded by theformation of coherent matrix precipitates and sub- Discontinuous precipitation (DP)sequent conversion of the latter into a coarse lamellar

Discontinuous precipitation is a solid state decompos-aggregate.2 Similarly, the early stage of DP in Au–Feition reaction that converts supersaturated solid solu-is actually a process of heterogeneous precipitationtion a0 into a two phase a+b aggregate behind aon lattice dislocations punched out due to volumemigrating reaction front (Fig. 3)1,2misfit.41 However, a moving boundary process does

initiate at the later stage in this system that dissolves a0�a+b . . . . . . . . . . . . (1)earlier precipitates and leads to a typical DP. An

The earliest study on DP, though without detailedidentical dislocation aided reaction is observed inmicrostructural analysis, may be credited to AgeewFe–Mo where precipitation nucleates on dislocations,et al.13,14 Unlike any other solid state heterogeneousproduces new dislocations in the process, and growsprocess, the combination of precipitation and concur-by pipe or volume diffusion.109 From the classicalrent boundary migration in DP necessitates a ratherpoint of view, such dislocation-based reaction iscomplex reaction mechanism to follow. The processnot DP because neither a sharp and mobile reactionis essentially a boundary diffusion controlled one andfront is involved nor does the orientation changehas faster kinetics than its volume diffusion controlleddiscontinuously.counterpart of continuous mode of precipitation (CP).Usually, DP is considered a boundary diffusion

controlled precipitation process. However,Criteria for occurrence of DPKorchynsky and Fountain55 have carried out a

detailed kinetic analysis of lamellar precipitation in The earliest occurrence of DP was reported in 1930.13Since then, over 700 publications on DP have beenCo–Ta to conclude that it is a volume diffusion

controlled reaction. This perhaps, is the only notable reported in the literature. However, it is amazing thatthe precise conditions during which DP occurs or isexception to the established fact that discontinuous

reactions are boundary diffusion governed transform- preferred over CP have not yet been identified.Initially, a minimum of 1% precipitate–matrixations. Nevertheless, the references cited in Table 1

are carefully selected according to the criteria that misfit223 or 11% solute–solvent atomic size differ-ence309 was postulated as the prerequisite for DP.they are authenticated reports (through micrographs/

specific mention) published in more common, peer However, the occurrence of DP in Al–Li (Ref. 27),Ni–Al (Ref. 138), Ni–Ti (Ref. 159) (where the misfitreviewed, and international journals (preferably in

English), and provide an extensive coverage of several strain<1%), and also in Al–Ag (Ref. 21) and Cu–Co(Ref. 85) (where atomic mismatch <3%) proved thatimportant aspects of the reaction concerned. It may

be pointed out that the earlier reviews on DP1,2 were neither misfit nor atomic mismatch strain could bethe necessary criterion for the occurrence of DP.3published at least 15 years ago and did not consider

the multicomponent and non-metallic systems. Over Similarly, Meyrick310 proposed that a sufficiently highrate of the decrease in the grain boundary energythe years, several other discontinuous reactions have

been defined and studied with a keen scientific inter- with the increase in solute segregation in front of acircular segment of the grain boundary would initiateest. However, a suitable review on DC and DD has

not been reported in the literature in recent years. the boundary migration in search of fresh solute andsustain the growth of the precipitate colony. However,On the other hand, the recent review on DIGM, DIR,

and liquid film migration by Yoon8 is both objective the uncertainty about the correlation between thegrain boundary segregation and maximum solid solu-and extensive and, therefore, makes detailed dis-

cussion on these discontinuous reactions unnecessary, bility limit casts fundamental doubt about the validityof Meyrick’s model.185 Subsequently, it was arguedexcept when necessary for comparison and clarifi-


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that maximum solubility limit was not the idealcriterion for predicting DP, and atomic misfit couldstill be the best indicator for the occurrence of DP inthe Cu-based alloy.310 As already pointed out, theatomic mismatch rule fails to justify the occurrenceof DP in Cu-based alloys too.85

To arrive at a general criterion for the occurrenceof DP, an investigation should attempt to identify thenecessary and sufficient conditions for it in a givensystem and investigate if a mere fulfillment of suchconditions alone could ensure DP in another ran-domly selected system. This exercise should continueuntil a failure is encountered and its genesis is estab-lished. Furthermore, it may be worthwhile to exploreif an artificially initiated grain boundary migration inthe presence of solute supersaturation may induce 9 Optical micrograph showing extent of variationDP in a system under a condition otherwise not of colony width from different boundaries inconducive for the same. On the other hand, an same microstructure following discontinuous

precipitation in Cd–6 at.-%Ag alloy at 353 K afterattempt to suppress or eliminate DP in a system5 h (Ref. 46)otherwise known to undergo DP may provide a clue

to the necessary condition for DP. Thus, a systematiceffort is warranted in this direction with several binary sented similar results on the variation of w∞ due to

the influence of boundary structure and inclinationsystems to generalise the conditions for the occurrenceof DP instead of the present practice of separate angle in a naturally grown Ag–Cu tricrystal. It may

be pointed out that the variation in w∞ is also likelyinvestigtions on individual systems.due to the possible difference in the orientation of agiven DP colony with respect to the plane of obser-

Influence of boundary structure vation. In order to average out such variation, Luck316suggested that w∞ may be normalised to yield the trueDiscontinuous precipitation involves heterogeneous

precipitation on boundaries and concurrent migration colony width w as followsof the latter. Naturally, boundary structure/

w= (p/4)w: ∞ . . . . . . . . . . . . (2)characteristics should have a profound influence onthe reaction as a whole. Although the relationship where w: ∞ represents an average estimate of w∞ meas-

ured from at least 30–40 separate boundaries withbetween boundary structure, energy, mobility, anddiffusivity is complex, it is generally accepted that DP colonies.

The absence of DP on twin and other boundarieshigh angle incoherent boundaries are the most likelycandidates for DP reaction fronts.2,41 Recently, it has with a rational orientation relationship and low

energy habit plane is attributed to either abeen reported that only boundaries with a minimummisorientation of 22° are likely to initiate DP in a perfect/near-perfect coincidence relationship314 or

poor mobility (due to low step density) of the lowCr–Ni austenitic stainless steel.311 Here, it is moreappropriate to anticipate that high energy (rather angle boundary concerned.317 In this regard, a corre-

lation between the boundary structure and DP occur-than only high angle) boundaries are likely toinitiate DP. rence may prove difficult because DP is found to be

absent even on boundaries having greater than ±5°Earlier, it was suggested that grain boundary pre-cipitation might be controlled by the force balance at misorientation from the coincidence site lattice

relationship in Al–Li which is known to undergothe precipitate/matrix interface rather than by theorientation relationship across the grains, particularly DP.27 Furthermore, the occurrence of DP even from

these erstwhile neutral boundaries with an increaseif the precipitate possessed a low energy interfacewith the matrix.312 On the other hand, experiments in aging time indicates that structural dependence of

boundary mobility need not be the sole criterion ofhave revealed that heterogeneous boundary precipi-tation is markedly dependent on the inclination,313 initiation of DP from a given boundary. The occur-

rence of DP from as unlikely a boundary as theor misorientation,314 orientation relationship betweenthe grain boundary and precipitate habit planes, and coherent faces of a twin in the Cu–Mg system substan-

tiates this point (Fig. 10).318 Earlier, Shapiro et al.241the existence of steps and ledges.315 Furthermore, thedynamic properties of grain and interphase bound- reported similar observations of nucleation of DP

from twins in Cu–Ni–Mn. Thus, generalisation of thearies are strongly dependent on their structure and,may widely vary from one boundary to another in a role or influence of the boundary structure on the

nucleation and growth of DP is not an easy task.polycrystalline aggregate.10,11 Thus, it is no wonderthat a non-uniform growth of DP colonies from However, a rational approach in this direction should

either be investigations on DP occurrence with welldifferent boundaries in the same microstructure isfrequently observed in the experimental studies. characterised bicrystals (synthetic or natural ),64 or in

situ observation directly under the transmission elec-Figure 9 reveals that the DP colony width w∞ fromthe random boundaries could substantially vary (by tron microscope to record the sequence of boundary

migration and precipitate nucleation and growtha factor of 1·5–3) in the same microstructure due tothe reasons cited above. Earlier, Gust et al.15 pre- accompanying DP.30


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10 Initiation of discontinuous precipitation (DP) inCu–8 at.-%Mg alloy from coherent faces of atwin at 648 K after 25 h. Dark nodules areeutectic colonies which do not nucleate DPpossibly due to their unfavourable curvature318

(a)

(c)

(b)

12 Schematic illustration of a eutectoidtransformation in Cu–In (b�a+d) from an a

0/b

interphase boundary advancing into b (brokenlines indicate coherent/semicoherentsegments), b subsequent coarsening andspheroidisation of d-lamellae in eutectoidcolony, and c thickening and transformationof former b/a

0boundary into a d/a

0incoherent

interphase boundary now capable of initiatingdiscontinuous precipitation

in this case and allows transformation of the originalgrain boundary into a solute rich incoherentprecipitate/matrix interface through a volumediffusion aided segregation and coarsening mechan-

11 Initiation and growth of eutectoid (grain 1) and ism illustrated in Fig. 12. In this regard, it is furtherdiscontinuous precipitation (DP) (grain 2) shown that the reaction kinetics and boundary diffu-colonies from same boundary in Cu–12 at.-%In sivity associated with DP initiated independentlyalloy aged at 648 K for 4 h after from the grain (a0/a0 ) and phase (d/a0 ) boundarieshomogenisation at 973 K for 14 days and water

(in the same microstructure) have been precisely thequenching. Note that interface between thesame. Hamana and Boumerzoug90 have noticed simi-two colonies is unusually thick and lamellae inlar initiation of DP, from both grain as well aseutectoid colony are thicker than those ininterphase boundaries, in Cu–In and Cu–Sb.adjacent DP colony89

Initiation of DP has also been reported from the twinboundaries in Cu–Ni–Mn (Ref. 241) and Cu–Mg,318

Initiation sites for DP small angle martensite lath boundaries in Zr–Al(Ref. 319), free surfaces in Cu–Sb (Ref. 94), interfaceOwing to its inherent mobility and high diffusivity, a

high angle incoherent boundary is most likely to between the free surface and interior of a grain inZn–Cu (Ref. 203) and Zn–Ag (Ref. 200) crystal sur-support the process of heterogeneous precipitation

and concurrent boundary migration required for the faces with prior deformation in Ni–In, Ni–Sn(Ref. 320), and Cu–Ag (Ref. 321), and synthetic graininitiation of DP. In addition to grain boundaries,

Manna et al.89 have demonstrated that the boundaries in Cu–Ag (Ref. 321).In this connection, Manna et al.318 have made aprecipitate/matrix type (d/a0 ) phase boundaries may

also initiate DP in the Cu–In system. Figure 11 reveals systematic effort to outline a general criterion for theselection of initiation site for DP from various kindsa rare event of initiation and growth of two independ-

ent moving boundary reactions, namely, eutectoid of solid/solid natural and artificial interfaces. It ispredicted that matrix grain boundaries (both naturaltransformation (in grain 1) and DP (in grain 2) from

the same boundary. This is surprising because the and synthetic) are most suitable candidates for DPinitiation, though non-conventional sites likea0/a segment of the rear boundary of a eutectoid

transformation or DP is usually a low mobility coher- precipitate/matrix phase boundaries (Fig. 11) orcoherent faces of a twin (Fig. 10) may also initiateent or semicoherent interface unlikely to support a

successive moving boundary reaction event. It is DP under suitable conditions. Thus, it has beensuggested that the ability of the concerned interfacesuggested that eutectoid transformation precedes DP


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13 Absence of discontinuous precipitation froman In-rich intermetallic alloyed zone (AZ) onsurface of Cu–7·5 at.-%In single crystal. Notethat only Widmannstatten continuousprecipitation is visible after 100 h aging at 423 K

(a)

(b)

(d)

(c)

a formation of boundary allotriomorph; b puckering of boundarydue to tendency to reduce difference between c

1and c

2arising

due to a strict habit relationship; c formation of anotherto undergo thermally activated migration at the pre- allotriomorph on boundary; d continuation of previous events

leading to boundary motion and a DP colony growthcipitation temperature constitutes the most essential14 Schematic diagram illustrating eventscriterion for DP initiation from a given interface.317

associated with precipitation inducedIt may be pointed out that the prior history or actualboundary motion leading to initiation ofmicrostructure plays a decisive role in determiningdiscontinuous precipitation (DP) by puckerwhether even the most likely candidate may actuallymechanisms323

initiate DP or not. For instance, Manna et al.322 havedemonstrated that DP initiation may be completelysuppressed by suitable de-activation of a usual

might lead to the boundary deflection necessary toinitiation site in Cu–In. Figure 13 shows that DP is

minimise the interfacial energy and maintain the rigidtotally absent from the surfaces of a Cu–7·5 at.-%In

orientation relationship between the precipitate andsingle crystal at 423 K even after 100 h of aging.

matrix (Fig. 14a and b). Continuation of this eventInstead, the solute supersaturation is relieved only

over a straight or curved boundary segment couldby CP. Under similar condition of aging, about

activate the initial boundary motion (Fig. 14c and d).300–400 mm wide DP colonies are likely to grow from

Naturally, a rigid precipitate/matrix habit relation-a boundary capable of initiating DP.87 Here, the

ship is a primary requirement to initiate DP by thissuppression of DP has been attributed to the

mechanism. Furthermore, it is predicted that a lowde-activation of the DP nucleation site by forming a

energy straight boundary segment could result insynthetic In-rich intermetallic alloyed zone that poss-

growth in one grain only, while a curved configurationibly is not capable of undergoing the thermally acti-

of the boundary might lead to nucleation on bothvated migration and initiation of DP.321 This result

sides of the same boundary with subsequent growthis of particular significance as the suppression of DP

in both grains. Baumann et al.232 have proposed thatis necessary to obtain the peak mechanical properties

the aging temperature primarily decides whetherdue to coherency or precipitation strengthening in

growth in one or on both sides of the boundarymany superalloys and alloy steels. Thus, boundary

concerned would be favoured. Apart from Pb–Sn, theimmobilisation in these systems could allow more

pucker mechanism was reported to be operative inconvenient processing/heat treatment, exposure to

Al–Zr (Ref. 35), Cu–Be–Co (Ref. 232), etc. However,high temperature, and increased creep/fatigue life of

this model appears to demand too many rigid con-components.

ditions to be regarded as a universal theory for DPinitiation. Moreover, DP initiation in a Pb–5 wt-%Sn

Initiation mechanism alloy was reported by a mechanism other than thepucker mechanism.324 Thus, it appears that the preciseThe DP initiation involves long range, solute trans-

port assisted nucleation of boundary allotriomorphs mechanism for precipitation initiation may alsodepend on the alloy composition amongst variousor precipitates at the boundaries, and concurrent

ability of the boundaries to undergo migration. It is other external parameters.On the other hand, Fournelle and Clark325 sug-generally believed that a deviation from the local

thermodynamic equilibrium following initiation of gested that a thermally activated motion of the bound-ary (as in recrystallisation, grain growth, etc.) mightthe boundary motion may sustain the growth of

the precipitate colony until the entire a0 grain is provoke the formation of precipitate cells on themobile front (Fig. 15). In contrast to the puckerconsumed.2 In this regard, the ‘pucker’ mechanism

proposed by Tu and Turnbull323 envisages that mechanism,323 the initial boundary motion is autocat-alytic. In fact, the precipitation of boundary allotri-nucleation of allotriomorphs on static boundaries


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has suggested that initial displacements or boundarybowing between pinning precipitates on a grainboundary due to capillary forces in response to theavailable chemical driving force is a necessary precur-sor of DP. This initial displacement or bowing beforeDP, which is analogous to DIGM in single-phasesolids, may arise due to the solute flow to the bound-ary from the neighbourhood and consequent accumu-lation of elastic energy. This elastic energy build up,in the absence of precipitate traction, may destabilisethe planar geometry of the boundary and lead tosubstantial bowing between the growing precipitates.

Manna et al.89 have for the first time demonstratedthat interphase boundaries like grain boundariesare equally capable of initiating DP (Fig. 11). Inthis connection, it has been suggested that a struct-ural transformation (based on compositionalre-adjustment in the vicinity of the boundary) maybe necessary before the interphase boundary attains(a) (c)(b)the required incoherent character to initiate DP in

a initial thermally activated migration of boundary segment leading Cu–In (Fig. 12). However, the subsequent sequenceto solute sweeping and precipitation of boundary allotriomorphs

and mechanism of initiation of DP remain identicalb; b boundary bowing between pinning allotriomorphs and growthof precipitates; c advancement of boundaries leading to further in interphase boundaries to those in grain boundaries.growth of precipitates into a colony

15 Schematic diagram explaining course ofMorphology, mechanism, and direction ofprecipitation on migrating boundaries leadinggrowthto initiation of discontinuous precipitation by

conventional mechanism:325 OGB refers to In an ideal DP colony, the precipitate lamellae areoriginal grain boundary, RF refers to reaction equidistant, parallel to each other, and aligned normalfront to a planar reaction front advancing into the super-

saturated matrix. More frequently, however, a non-omorphs is a consequence of this short initial

planar reaction front and Gaussian scattering ofmigration. Once precipitated, the allotriomorphs tend

interlamellar spacing are observed in a real DPto pin the boundaries causing them to bulge or bow

colony.48 Furthermore, the advancing reaction frontforward. Subsequently, the boundaries are set free to

is seldom completely planar. In fact, the reactionmigrate further when the following condition is

front is usually curved so that the isothermal colonyfulfilled

growth may continue by maintaining the necessaryP |DGcDP |L /(cVm )>2 . . . . . . . . . (3) chemical potential gradient across the migrating

boundary.325 Similarly, the steady state interlamellarHere, DGcDP is the Gibbs chemical energy change per

spacing is normally determined by the minimum ormole, P the fraction of DGcDP released, Vm the molar

critical spacing that maximises the integral rate ofvolume, c the concerned interfacial energy per unit

Gibbs energy dissipation.328 In this regard, Doherty329area, and L the half of the statistical repeat distance

observes that the earlier theories on the determinationof the allotriomorphs. Thus, initial boundary deflec-

of the critical spacing based on either the principle oftion or bowing alone does not guarantee the growth

a maximum growth velocity330 or rate of entropyof a DP colony. However, the lack or absence of any

production331 fail to predict a realistic precipitaterigid precipitate–matrix orientation relationship (as

repeat distance in both DP and DC. The interlamellarin the pucker mechanism323 ) makes this model more

spacing seems more closely related to the supersat-universally applicable to all systems showing discon-

uration in a given discontinuous reaction than totinuous type of moving boundary reactions. Initiation

either of the criteria mentioned above. Generallyof DP in many binary systems seems to follow this

speaking, the reaction front velocity and interprecipi-model, e.g. in the Cu–In (Ref. 325), Al–Zn (Ref. 326),

tate distance remain invariant under steady statePb–Sn (Ref. 324), and Al–Li (Ref. 27) systems. It isimportant to understand that either boundary bowing

Table 2 Initiation of discontinuous precipitationbetween pinning allotriomorphs and/or subsequentby pucker323 and conventional325solute depletion in the wake of boundary bulging domechanisms

not necessarily guarantee DP initiation.327 Therefore,Pucker Conventionalthe ability of the boundary to initiate and sustainmechanism Ref. mechanisms Ref.non-conservative motion into a supersaturated matrixAg–Cu 15 Al–Li 27under thermal activation seems most crucial for DPAl–Li–Zr 208 Al–Zn 326to occur. Table 2 cites a few examples of the binaryAl–Zr 35 Cu–In 89, 90, 325

systems known to initiate DP by either of the two Au–Fe 41 Cu–Sb 94proposed mechanisms. Cu–Be–Co 232 Mg–Al 126

Fe–Zn 118, 119 Ni–Au 2, 139Heterogeneous precipitation of allotriomorphs onMg–Al 126 Ni–Cu–Au 2stationary boundaries at sufficiently large distances isPb–Sn 323, 324 Pb–Sn 324a fairly common event before DP. Recently, Purdy327


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17 Initiation and growth of DP on both sides of16 Concurrent occurrence of branching (X) and same curved boundary leading to formation of

renucleation (Y) near surface front (RF) of a typical double seam in Cu–12 at.-%In alloy atdiscontinuous precipitation (DP) colony in 573 K (<0·5T

m) after 4 h

Cd–6 at.-%Ag alloy to maintain constancy of lat 393 K after 5 h. Extensive Widmanstattentype of continuous precipitation (CP) is seen

This may give rise to the so-called single-seam morph-on both sides of DP colonyology.232 Alternatively, growth in opposite directionsof an initially straight or curved boundary may

growth conditions. The constancy of the repeat dis-develop a double-seam morphology.41 This event is

tance of the precipitate phase behind a curved reactionmore likely at T<0·5TS , when boundary mobility is

front within a DP colony is maintained either bymore structure sensitive and hence, restricted. As a

branching of the existing lamellae, or by repeatedconsequence, the occurrence of double seams

nucleation of the precipitate on the advancing reac-decreases as the temperature increases.337 In this

tion front or in its recess.2 The former mechanismregard, the nucleation mechanism should play an

has been widely observed in many systems, e.g. Al–Zrimportant role in determining the direction of growth

(Ref. 332), Cu–In (Ref. 325), Fe–Zn (Ref. 333), andof a DP colony. It has been proposed that a double

Al–Zn (Ref. 326).seam is a likely consequence of the pucker mechan-

Similarly, renucleation of new lamellae on theism323 of DP initiation, chiefly operative at lower

advancing reaction front has been reported in a fewtemperatures (T<0·5TS ), while single-seam morph-

systems like Fe–Zn (Ref. 333), Al–Zn (Ref. 326), andology is expected when thermally activated migration-

Cu–Ti (Ref. 334), where rigidity of the precipitateinduced DP nucleation predominates the process of

habit plane may pose a perceptible difficulty forDP initiation at a higher temperature (T>0·5TS ).337lamellae branching. This is in accordance with anAt the same time, it is pointed out that temperature

earlier theoretical prediction.335 Tu and Turnbull336dependence for the occurrence of double seam or

have reported the occurrence of renucleation in thesingle seam is more likely to be related to the con-

Pb–Sn system under different circumstances ofcerned solvus instead of solidus temperature.

up-quenching or down-quenching experiments,However, Fig. 17 evidences the formation of a double

which, however, could be attributed to a change inseam in Cu–In at T>0·5TS , which means the double-

the characteristic precipitate repeat distance at theseam morphology may also develop following

lower or higher temperature. It may appear thatnucleation by the conventional route325 through the

branching or renucleation is a typical system specific‘S mechanism’.2 Thus, local thermodynamics, includ-

characteristic. However, it is intriguing to note thating boundary structure and its dynamics, may actually

both branching and re-nucleation are operative in thedecide the course to follow for growth leading to, say,

Zn–Cu (Ref. 202), Al–Zn (Ref. 326), and Fe–Znsingle- or double-seam morphology.

(Ref. 333) systems. Figure 16 demonstrates that boththese mechanisms have contributed towards main-

Driving force for initiation and growthtaining a statistically constant interlamellar spacingin the Cd–Ag system.46 Thus, it is difficult to outline Shapiro and Kirkaldy88 have proposed that DP is a

boundary diffusion controlled monotectoid reaction.the essential criterion for the occurrence of either ofthese two mechanisms a priori. Perhaps the available The necessary chemical driving force DGcDP to initiate

DP is derived from a metastable miscibility gapdriving force as well as boundary structure vis-a-visorientation relationship of the precipitate with the concerned with the monotectoid reaction. On the

other hand, Sulonen79,80 has suggested that the elasticconcerned reaction front are primarily responsible indeciding which of the mechanisms are preferred under coherency stress (due to the difference in lattice para-

meter) in the solute-enriched matrix immediatelythe local thermodynamic condition.Isothermal growth of a DP colony may consume ahead of the migrating reaction front could provide

the necessary driving force for DP. It has beenthe matrix either on one or on both sides of the sameboundary. It is predicted that growth in one direction demonstrated that unidirectional stresses acting par-

allel or perpendicular to the boundary plane couldis likely to predominate in the temperature rangeT>0·5TS (TS is the absolute solidus temperature). predictably increase or decrease the concerned


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migration rate depending on the sign of the applied DGcDP for a binary system showing ideal solutionbehaviour may be typically expressed asstress and local elastic coherency strain in Cu–Cd.

Subsequently, Hillert338,339 has presented a quantitat-ive thermodynamic analysis to substantiate this DGcDP=−RT Cx0 ln

x0xav+ (1−x0 ) ln

1−x01−xavD‘coherency strain’ theory. Recently, Chung et al.340

(5)have quantitatively shown that coherency strain mayindeed account for the change in growth velocity as where R is the gas constant, and x0 and xav refer toa function of the applied stress. Since then, several the compositions of the a0 and a phases, respectivelyreports on liquid film migration have drawn analogy (see Fig. 1). When composition of a is given by xewith DP and claimed that coherency strain effects instead of xav, equation (5) provides an estimate ofprovide the necessary driving force for DP.8,130 While DGc,eDP. Similarly, DG

cmay be written as

liquid film migration and DIGM have similar reactionDGcDP=2cVm/l . . . . . . . . . . . (6)

mechanisms, an analogy between DP and liquid filmwhere l is the true interlamellar spacing.migration is questionable because the latter reaction

does not involve precipitation of a second phase.Highest temperature for occurrence of DPEarlier, Bohm309 proposed that a minimum of 11%As Gibbs chemical energy change constitutes a majoratomic size mismatch between the solute and solventcomponent of the overall driving force for DP, it isatoms was necessary to initiate DP in Cu-basedlogical to anticipate that driving force continues toalloys. Subsequently, it was reported that DP coulddecrease as the aging temperature increases until anoccur in Cu–Co (where atomic mismatch <3%).84,85upper limit below the concerned solvus temperatureFurthermore, a careful scrutiny of randomly chosenTsv . Manna and Pabi341 have defined this upperbinary systems known to undergo DP (Table 1) wouldbound of temperature for DP occurrence as thereveal no universal criterion based on atomic sizehighest temperature for DP TDP , and have proposeddifference which could predict the occurrence of DP.a method of determining the latter by a resistometric

In this regard, Williams and Butler2 have concludedanalysis (Fig. 18a). The data are useful to define the

that neither precipitate–matrix misfit strain normetastable solvus for DP (Fig. 18b). TDP may also be

solute–solvent atomic size difference could satisfac-estimated from the microstructural data by extra-

torily define a universal criterion for the occurrencepolating the plot of 1/l as a function of temperature

of DP. Furthermore, the magnitude of DGcDP in DPto 1/l=0 (Fig. 19): 1/l=0 signifies an infinite inter-

is possibly too large to ignore and sufficient to accountlamellar spacing or practical cessation of DP.

for the necessary driving force. In fact, Doherty329Accordingly, TDP has been experimentally determined

observes that, except in DIGM, the experimental by resistometric method in Pb–Sn (Ref. 341) andevidence in support of the validity of the coherency microstructural measurements in Cu–In (Ref. 87),strain model in similar moving boundary reactions Zn–Cu (Ref. 203), etc. It may be mentioned thatlike DC, DD, and eutectoid transformation are not Sulonen5 had earlier proposed that the tendency fortoo convincing. Thus, continued efforts are needed to DP and DC should be the same at a similar upperestablish if coherency strain alone could be a sufficient bound of temperature of DP or lower bound for DD.condition for the occurrence of DP. Subsequently, Tu6 has demonstrated that a temper-

At this juncture, it is important to realize that the ature hysteresis exists between the occurrence of DPoccurrence and propagation of DP refer to the two and DD, and Tcr ( lowest temperature of DD) is notindependent events of nucleation and growth of the equal to TDP , at least in Pb–Sn. Further discussionDP products. In this regard, the available driving on Tcr and TDP is included in the sectionforce is spent: (a) to initiate DP by heterogeneous ‘Discontinuous dissolution (DD)’ below.nucleation either on static323 or mobile325 boundaries,and (b) to sustain the steady state growth under Temperature dependence of reaction frontisothermal condition. The former DGI is difficult to migration velocityquantify though Williams and Butler2 have identified Like any other diffusion controlled nucleation andthe possible components that may influence the growth process, the RF velocity v in DP usuallyinitiation as follows records an ‘inverse-C’ variation with temperature. In

other words, v is lower either at higher or lowerDGI=DGp+DGGB+DGd+DG

e. . . . (4)

temperatures and is maximum vmax at an intermediatetemperature Tv(max) , e.g. in Cd–Ag (Ref. 46), Ni–Inwhere the subscripts p, GB, d, and e to the DG terms(Ref. 149), Zn–Cu (Ref. 203), etc. Gust et al.343 haverefer to the precipitation (related to puckering-like323predicted that Tv(max) is related to Tsv by the empiricalphenomenon), grain boundary (related to grain coars-relationship: Tv(max)= (0·89±0·04)Tsv . However, theening tendency), deformation (related to stored strainvmax may occur at a lower temperature than thatenergy), and strain (related to compositional changespredicted by Gust et al.343 if a strong concurrent orincurred) components of the DGI term. Here, all thepreceding CP significantly diminishes the availableDG terms refer to the Gibbs energy change per mole.chemical driving force for DP (e.g. in Zn–AlThe precise importance and contribution of a given(Ref. 201)).component depend on the actual alloy system and

available thermodynamic conditions. On the otherAnalytical models on isothermal growthhand, the driving force for the steady state growthkineticsfor DP DGDP comprises two major components,

namely, the Gibbs chemical DGcDP and interfacial Once the precipitates are nucleated and subsequentedgewise growth of the precipitates has been initiatedDGcDP energy changes per mole associated with DP.


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l, µ

m

1/l, µ

m_

1

1/l, µ

m_

1

(a)

(b)

T, K

19 a variation of l and 1/l as function of T todetermine T

DPin Pb–9·87 at.-%Sn alloy342 (note

that TDP<T

sv) and b similar variation of 1/l as

function of T for Cu–12·0 at.-%In alloy.89 Lines,1, 2, 3, and 4 are from Refs. 89, 89, 88, and 87,respectively

(a)

(b)

T, °C

Tin, at.-%

T, °

CD

Rf/R

0, %

18 a variation of fractional change in resistivityequilibrium composition of the a phase at T2, and xav(DR

f/R

0) as function of temperature T to

the metastable composition of a, such that xav>xedetermine TDP

values for three Pb–Sn alloysat a given T . The segregation factor s is the ratioand b equilibrium x

eand metastable x

avin

between the solute concentration in the grain bound-Pb–Sn. Note that xav

for discontinuousary to that in the bulk.344 Cahn328 argued thatprecipitation is determined by resistometric

technique (solid and open symbols are from diffusion mechanism could not be the sole rate con-Ref. 341 and Ref. 172, respectively) trolling criterion for a discontinuous reaction. In

addition to recognising the effect of boundary friction,along with a migrating reaction front, the DP kinetics he has postulated that v has to be proportional tofollow a steady state rate that depends on several the change in Gibbs energy. By several simplifications,thermodynamic and kinetic factors. Several theories the final expression for v may beon such growth kinetics have been proposed whichassume either volume or boundary diffusion as the v=C

sdDbl2

. . . . . . . . . . . . (8)rate controlling mechanism. In general, all the modelsattempt to predict the growth rate in terms of v as a

where C is the Cahn’s parameter expressed by follow-function of the driving force for growth DG, iso-

ing equationthermal temperature T , boundary width d, segre-gation factor344 s, and true interlamellar spacing l. x0−xav

x0−xe=

2

�Ctanh

�C

2. . . . . . . (9)The earliest model, proposed by Zener,330 has

considered DP as a volume diffusion controlled reac-It may be noted that equation (9) is the result oftion and drawn analogy with eutectoid reaction tointegration of the function describing the solute distri-assume that the Gibbs energy available should bebution across the a lamella. A subsequent analyticalspent entirely to create a/b interfaces within themodel by Aaronson and Liu346 has taken into accountprecipitate colony. Subsequently, Turnbull345 hasthe effect of boundary curvature on the solid solubilityassumed for the first time that the reaction rate is

governed by diffusion through the advancing bound- of the lamellae and presented a more rationalary having an average thickness d and formulated expression for growth velocity. Conversely, Shapiro

and Kirkaldy88 have noticed similarities in morph-ology and kinetics between eutectoid and discontin-v=

x0−xavx0

dDbl2

. . . . . . . . . . (7)uous reactions and proposed a model, assumingdiscontinuous reaction to be analogous to a meta-where x0 is the initial composition of a0 , xe the


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stable monotectoid reaction controlled by grainboundary diffusion. Subsequently, Petermann andHornbogen167 have extended the original theory ofrecrystallisation and arrived at the followingexpression for reaction rate in discontinuous reactions

v=−8DGDPRT

sdDbl2

. . . . . . . . . (10)

where DGDP (having a negative value) refers to thetotal Gibbs energy change per mole of the growthprocess including strain energy.

For the migration velocity of the austenite/pearliteinterface, Sundquist347 has derived an expression inwhich the interlamellar spacing does not explicitlyappear. This model has subsequently been modified

20 Effect of continuous precipitation (CP) onto recognise the effect of boundary shape and capil-discontinuous precipitation (DP) in Zn–1·8larity and to consider boundary diffusion as the mainat.-%Al alloy at 348 K after 100 h. Note that

rate controlling parameter, even though it leads to interlamellar spacing near reaction front (RF)incomplete depletion of the matrix supersaturation. is greater than that in interior of colony.Finally, Hillert338,339 has modified his earlier theory Extensive CP ahead of RF (not resolved here)in order to take the residual supersaturation in the may pose physical hindrance to RF migrationinterlamellar spaces into account. This model takes and/or decrease local chemical driving forcethe contribution of coherency strain into account to (see Ref. 349)estimate the overall driving force for DP.

Since the kinetic models proposed to date on thekinetic analysis largely depends on the availablegrowth kinetics of DP have been discussed in severalexperimental and analytical data, type of study, andreviews,1,2,10,11 a detailed account in this subject ispast experience.avoided here. Instead, a summary of the relevant

models is presented in Table 3 in terms of the appro-priate expressions for v. Finally, it may be mentioned Effect of concurrent events on growth ratethat the selection of the appropriate model for a given and morphology

As pointed out above, the driving force for DP is anextensive parameter related to several thermodynamic

Table 3 Analytical models proposed for steady and kinetic functions. Thus, external parameters cap-growth kinetics of discontinuous able of influencing the driving force (e.g. stress, strain,precipitation

alloying addition, etc.) may have significant effects onModel Expression for v Ref. the precipitate nucleation and morphology, and

growth kinetics of DP. These external influences mayZener 330v=

x0−x

ex

0

2Dl change the morphology and rate of the reaction, and

result into a fundamental modification of the reactionTurnbull 345v=

x0−x

avx

0

dDb

l2 mechanism.

Cahn 328 Effect of continuous precipitation (CP)v=C

sdDb

l2, If Gibbs chemical energy change constitutes the main

driving force for DP, then a prior or concurrent CPwhere

x0−x

avx

0−x

e

=2

�Ctanh

�C2

of metastable or equilibrium phases may account fora significant loss of the overall driving force for DP.

Aaronson 346 This loss could be as high as 98% in the case of priorv=4(x

b−x

e)

xb−x

0

sdDb

l2=4

sdDb

l2and LiuCP in the Al–Ag system.21 This loss in chemical

for xb&x

eand x

b&x

0 driving force may significantly alter the reactionShapiro and 88 course. For instance, concurrent CP is reported toKirkaldy* v=48

sDb

l3

Vm

(k−1)q(0·5−p)2

, reduce the reaction front migration rate on theZn-rich side of the Zn–Al system to such an extentthat l in the latter stage of DP increases significantlywhere k=−

lDGcDP

2cVm over that in the early stage of the same transform-

Petermann and 167 ation.349 Figure 20 illustrates the effect of CP on lv=−8DGc

DPRT

sdDb

l2Hornbogenduring prolonged isothermal aging at a given T in a

Sundquist† v=4CKSsdD

bcos h 347 Zn–1·8 at.-%Al alloy. Furthermore, DP may cease to

Sundquist v#(DT )3 exp(−Qb/RT ) 348 occur well below the theoretically predicted maximum

Hillert‡ 338, 339 temperature for DP occurrence (TDP)349 due to thev=12l(x

av−x

a/b)

la(x

0−x

av)

sdDb

l2 loss of chemical driving force in Zn–Al (Ref. 349).Reduction in driving force for DP has also been

* p and q are thermodynamic functions defined in Ref. 88.reported in the Al-rich Al–Zn alloys due to prior

† KS

a constant; h angle between the growth direction and the normal tometastable R-phase or Guinier–Preston (GP) zonethe reaction front.347

‡ xa/b

solute content at the a/b interface; la

width of the a lamellae. formation,350,351 and in Co–Ti–Fe due to a prior


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spinodal decomposition.224,225 Similar results havebeen reported for Cu–Mg (Ref. 92), austeniteFe–Mn–V–C (Ref. 352), Cu–Sn (Ref. 353), andZn–Ag (Ref. 354). In general, it is concluded thatconcurrent CP may adversely affect the DP kineticseither by reducing the chemical driving force and/orby offering physical obstruction to the advancingreaction front.349 In this regard, a high-resolutionmicrostructural study may reveal the true mechanismof the effect of CP on the kinetics of concomitant DP.

Effect of plastic strainFrom the microstructural point of view, plasticdeformation introduces dislocations and hence strainin the matrix. It is known that prior plastic deforma-tion may either enhance or diminish the DP growth

21 Initiation and growth of discontinuouskinetics, depending on whether the stored strainprecipitation (DP) colony with its reaction frontenergy supplements the driving force for DP or(RF) moving away from hardness indentationpromotes CP over DP, respectively.2 For instance,(HI) with 10 kg load on strain-free externalprior deformation is reported to enhance the DP surface of Cu–7·7 at.-%Ag single crystal. Note

kinetics in Cu–In (Ref. 325), Ni–based superalloys that DP is absent all along surface except(Ref. 355), Pb–Na (Ref. 356), and Nb–Zr–Ti around indentation mark(Ref. 269). On the other hand, entirely the oppositeeffect has been observed in Cu–Be (Ref. 357),Cu–Ni–Mn (Ref. 241), and Al–Li (Ref. 2). A high Effect of externally applied stressmatrix dislocation density as a consequence of prior Sulonen79,80 has proposed that the driving force forstraining may enhance CP and thereby reduce the reaction front migration during DP arises from thedriving force for DP. In other words, such dislocations coherency stress in the matrix due to the change inmay facilitate heterogeneous nucleation of the matrix composition across the reaction front. Accordingly, itprecipitates, e.g. in Al–Li (Ref. 2) and Cu–Be has been demonstrated that an applied tensile stress(Ref. 357). Duly et al.358 have reported that prior has a profound influence on the DP growth rate instrain inhibits DP in Mg–Al due to the interaction Cu–Cd. The growth rate decreases for DP coloniesbetween a twin and the reaction front and enhances initiating from boundaries with a normal parallel tonucleation of the matrix precipitates on dislocations. the applied stress. The reverse trend is observed inPawlowski359 has attempted quantification of the DP colonies initiating from boundaries with a normaleffect of prior strain on DP growth kinetics and perpendicular to the direction of the applied stress.proposed that the mode of deformation is critical to In addition to the above observation, it has beendetermine whether DP kinetics are enhanced or proposed that the change in the DP kinetics is relateddecreased. It is suggested that the heterogeneity in to the relative size of the solute with respect to thatthe deformation band decreases the rate while more of the solvent atoms. Hillert338,339 has provided ahomogeneous deformation results in an enhancement. quantitative treatment of Sulonen’s observationsIt may be pointed out that the above mentioned based on the elastic interaction between the misfiteffects are related only to bulk deformation. stress field around the solute atoms ahead of the

On the other hand, localised deformation may reaction front and applied tensile stress. Chungconfine the plastic strain within a small volume and et al.340 have proposed a quantitative analysis of theaffect the DP kinetics heterogeneously. In this connec- effect of external stress on the velocity of the reactiontion, Manna and Pabi321 have demonstrated that front aligned parallel and normal to the axis oflocalised deformation has more pronounced influence applied stress in DP. It appears that the effects ofon nucleation events than on growth kinetics. For external stress strongly substantiate Sulonen’s theoryinstance, it has been shown that prior localised strain on the role of coherency strain on DP initiation.by hardness indentation or scratching on the external On the other hand, Dryden and Purdy361 havesurface of an otherwise strain-free single crystal or proposed a model on the effect of external stress onpolycrystal may initiate DP from the deformed/ DP kinetics based on the inelastic interaction betweenplastic zone in Cu–Ag (Refs. 318, 321, 360), and the applied stress and misfit strain of the transformedNi–Sn and Ni–In (Ref. 320). Figure 21 shows the regions. Guo et al.362 have studied the effect of theinitiation and growth of a DP colony only around applied stress on the morphology of DP in Cu–Cd.the indentation mark on the strain-free surface of a It has been reported that a spiked morphologyCu–Ag single crystal. Thus, it is concluded that local- develops for applied stresses above a critical level andised strain is capable of inducing recrystallisation at the average distance of the spikes is inversely relatedthe precipitation temperature and, thereby, generating to such applied stress. This morphological instabilitysuitable initiation sites for DP. Subsequently, Manna is attributed to the mechanical forces associated withand Pabi360 have demonstrated that localised the interaction between the transformation strain anddeformation, unlike bulk deformation, has no percep- applied stress, and opposed by the surface tensiontible effect on the overall growth kinetics except in forces. The overall effect has been viewed as a trans-

formation-assisted viscoelastic deformation. In orderoffering initiation sites for DP.


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to gain a better insight into the influence of external Discontinuous coarsening (DC)stress on DP, it may be worthwhile subjecting a single

Discontinuous coarsening is a moving boundary re-crystal plate to a three-point bending test at the aging

action that converts a finer distribution of thetemperature, and investigating the effect of tensile and

two-phase lamellar products of a primary reactioncompressive components on the DP morphology and

like DP,31,66,81,117,149,257,396 eutectoid transform-kinetics in the opposite faces of the same specimen.

ation,4,397–399 or eutectic solidification165 into acoarser distribution of the same (in terms of crystalEffect of ternary alloying additionstructure) aggregate (Fig. 4). In addition to the metal-Except for selected cases, DP is usually consideredlic alloys, DC is known to occur in an oxide soliddeleterious to the material properties of a largesolution too.209 Symbolically, the reaction may benumber of commercial alloys.2 In the past, severalexpressed asattempts have been made to suppress or eliminate

DP by suitable addition of an alloying element. (a+b)fine� (a+b)coarse . . . . . . . . (11)Ternary additions may interfere with the nucleation

Williams and Butler2 have earlier defined this movingevents by changing the precipitate characteristicsboundary reaction as the type 2 DP which necessitatesand/or modifying the boundary structure and energy.no change in crystal structure, but involves onlySimilarly, the growth kinetics may be affected bycompositional adjustment and redistribution of thesolute segregation along the reaction front or a/bsame aggregate by a separate nucleation and growthinterfaces. Among the theories proposed on the effect

of ternary additions, it is suggested that the specificvolume change,363 precipitate–matrix mismatch,364 Table 4 Effects of alloying additions onatomic size difference,365 deactivation of boundary discontinuous precipitation (DP)migration,317 valence electron difference,366 solute

System Addition(s) Effect Ref.drag effect,367 and vacancy–solute interaction368 couldAg–Cu Ga Rate increases 365account for the observed change in DP kinetics.

In, Tl, Pb Rate decreases 365Williams and Butler2 have reviewed the studies con-Al–Ag Ga Rate increases 22

cerning these proposed theories in detail. Table 4 Al–Li Mg Reaction suppressed 369provides an updated list of investigations concerning Cu Reaction suppressed 370

Cu Reaction suppressed except 207,the effect of ternary addition on DP kinetics. Recently,within a narrow range of Li and 370Manna and Pabi170 have carried out a systematicCu additionstudy to determine the origin of the effect of ternary

Al–Zn Sn Rate decreases 371additions on DP. Figure 22 shows that the DP kin- Cu, Mg Extent of DP reduces, Mg more 372etics have been reduced by over 50% due to the trace effective

Mg Extent of DP reduces 373additions of Cd (0·16 at.-%) and Sb (0·26 at.-%) to aSn, Mg Rate decreases 374Pb–9·87 at.-%Sn alloy. It has been found that neither

Co–Ti La, Nb No effect 57atomic size difference effect nor change in the valence Fe Rate increases 57electron/atom ratio could satisfactorily explain this Co–Fe–Be Nb, Ta, Ti DP nearly suppressed 218

Co–Mo–C C Rate decreases 375drastic reduction in the DP kinetics due to the traceCo–Mo–W W Rate decreases 376addition of Sb and Cd in Pb–Sn. It has been arguedCu–Ag Ni CP promoted 377that only the solute drag effect367 exerted by the CdCu–Be Al Rate increases 378

and Sb atoms on the advancing reaction front may Co Rate decreases 379account for the significant reduction in the kinetics In Reaction suppressed 380

Zr Rate decreases 378and an early termination of DP.170 Recently, it hasCu–Be–Sn Fe, Co, Ni, Cr, Ti DP retarded 381been reported that the occurrence of DP in Al–Li–Cu

Cd, Mn, Zn No effect 381strongly depends on the actual solute content and, Cu–In Al, As, Au, Ge, Pd, Morphology same, incubation 382hence, on the segregation behaviour of the concerned Pt, Sb, Si, Sn, Zn increased, reaction rate changed

Cu–Ni–Be Al Rate decreases 383solute.394 Therefore, it appears that more informationCu–Ti Al DP suppressed at high solute 384on the segregation behaviour of the ternary elements

contentis necessary to formulate a general theory on theB Rate increases 385

effect of ternary additions on the DP kinetics. Cr Rate decreases 385Zr Reaction suppressed 385Sn, Fe Rate decreases 385Zr, Be Rate decreases 386SummaryMg No effect 386

A comprehensive overview of DP suggests that good Fe–Cr–Ni Nb, Zr Reaction suppressed 387Fe–10Ni Al, Be Marked increase 388progress has been made in the past decades concern-

Nb, Ti, Mo Marked decrease 388ing initiation and growth mechanisms, initiation sites,Fe–32Ni Nb, Zr, Ti, Be Marked decrease 389

growth morphology and kinetics, and effect of exter- Fe–Ni–Cr Al Reaction suppressed 390nal factors like stress, strain, ternary addition, etc. Fe–Sb Ni Rate increases 112

Fe–Zn Mn Rate decreases 391Apart from the inability to develop a unique theoryGe, Sn Rate decreases 391on the occurrence of DP, most of the characteristicP Rate decreases 391features of DP in systems known to undergo this

Ni–Be Cr, Mo, W DP suppressed 218reaction have been studied thoroughly. However, Ni–Sn Al, Ga, In Rate decreases 392further investigations are necessary to probe the true Au, Cu, Ge, Zn Rate increases 392

Pb–Na Ag Rate decreases 393driving force of DP, particularly in the light of thePb–Sn Cd, Sb Rate decreases and DP ceases 170recent theoretical analysis by Cahn et al.395


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tation in a DC colony is usually different to that inthe primary aggregate. DC differs from continuousmodes of coarsening like Ostwald ripening in threemajor aspects: the mode of solute transport, absenceof coarsening of an individual phase, and prerequisiteof having a migrating reaction front, typical of amoving boundary reaction. Although DC may possessa faster reaction rate than that of a volume diffusioncontrolled coarsening reaction, the reaction kineticsof DC, in general, are several orders of magnitudeslower than that of the preceding primary reaction(say, DP).

Driving force for DCIt has initially been proposed that the origin of DCis entirely interfacial in nature.329 Kaya and Smith165have suggested that a difference in the interlamellarspacing and/or orientation between the adjacent col-onies may initiate DC in eutectoid transformationand eutectic solidification products. Earlier,Livingston and Cahn4 have attributed the initiationof boundary migration in DC to the difference in theinterlamellar spacing, tendency for faceting, andstored strain energy. Subsequently, Frebel andDuddek398,399 have mentioned, though without ver-ifying it experimentally, that a chemical driving forcemay be necessary to consider if the composition in

DR

t/R0, %

YM

(a)

(b)

t, min

the lamellar products deviates from the concerned22 Variation of fractional change in resistivityequilibrium values. Fournelle257 was the firstDR

t/R

0with time t for binary Pb–Sn and

researcher to demonstrate that the residual soluteternary Pb–Sn–Cd and Pb–Sn–Sb alloys atsupersaturation following DP amounts to a majora 308 K and b 323 K.170 Note that ternary

additions of Sb (0·26 at.-%) and Cd (0·16 at.-%) component of the driving force for DC in Fe–Ni–Ti.to binary Pb–9·87 at.-%Sn alloy have resulted Theoretically, the DC product may be a combinationin over 50% reduction in volume fraction of two solid solutions, or a solid solution and antransformed Y

Mby discontinuous precipitation intermetallic phase with a solubility range or a stoi-

(DP); solid symbols represent YM

data obtained chiometric compound. If the matrix phase is a solidfrom separate microstructural analysis of DPsolution or an intermediate phase, the average soluteat 308 K at selected values of tcontent in the matrix is unlikely to reach the equi-librium solvus value immediately following DP.328Furthermore, the boundary migration rate during DCprocess. As implied by the very name, the reduction

in interfacial energy is the principal driving force for in Al–Zn is reported to increase with an increase inthe solute content.400 Thus, the driving force for DCDC.329 The degree of coarsening is related to the

normalised repeat distance and not to the actual size following DP is likely to consist of a chemical com-ponent. In this regard, Manna et al.200,354 have dem-of the precipitate phase in a DC colony. In addition

to having a migrating reaction front, this is where onstrated that a measurable amount of solutesupersaturation does indeed remain in the matrixDC distinguishes itself from volume diffusion con-

trolled continuous coarsening of fine precipitates. phase following DP in the Zn–4 at.-%Ag alloy whichsupplements the overall driving force for DC duringSince the earliest study on DC of the lamellar prod-

ucts of eutectoid transformation in Cu–Be in 1950 by continued isothermal aging either at the same (DCI)or another (DCII) temperature.Fillnow and Mack,397 DC has been reported in the

lamellar products of eutectoid transformation, eutec- Earlier, Funkenbusch274 has similarly shown thatthe boundary diffusivity calculated from the DCtic solidification, and DP in over 30 binary and

multicomponent systems (Table 1). kinetics, assuming reduction in surface area being theonly driving force, is significantly higher than thatFigure 4 illustrates DC schematically. Like DP,

here too the transformation occurs behind a migrating reported for static boundaries. This difference, how-ever, could not be attributed to a possible enhance-reaction front that provides a short-circuit path for

diffusion. True to its name, the changes in the compos- ment in the migration rate due to higher jumpfrequency. On the other hand, a suitable correctionition and orientation between the matrix phases

across the reaction front are abrupt/discontinuous. It in computing the driving force by including thechemical component (due to residual supersaturation)may be mentioned that the reaction products of DC

are usually lamellar, maintaining a parallel and alter- does yield the appropriate measure of boundarydiffusivity. The thermodynamic principle for estimat-nate sequence unlike the isolated or divorced precipi-

tates distributed heterogeneously in the matrix in ing this chemical component of the driving force forDC has been illustrated by Fournelle,257 Gupta andcontinuous coarsening. However, the lamella orien-


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Nakkalil,149 and Manna et al.200,354 Experimentalevidence of the driving force for DC comprising bothinterfacial and chemical components has beenreported for Al–Zn (Refs. 3, 31, 400), Cu–Cd (Ref. 81),Ni–In (Ref. 149), and Ti–Al (Ref. 187). However,Gibbs interfacial energy change alone could alsoaccount for DC in Cu–Be (Ref. 401), Cu–In (Ref. 4),and Ni–Al–Mo (Ref. 274). In any case, the overalldriving force for DC may be calculated by a generalexpression comprising the relevant Gibbs energychange terms. The chemical and interfacial com-ponents here should represent the respective changesassociated only with the secondary reaction (i.e. DC).

In general, the overall Gibbs energy change DGDCper unit volume associated with a DC reaction may

23 Initiation and growth of DCI from interfacebe expressed asbetween two DP colonies in Zn–4 at.-%Ag alloy

DGDC=DGcDC+DGcDC+DGeDC . . . . . (12) at 433 K after 50 h.200 Note that precipitatelamellae in DCI and DP colonies are mostlywhere the superscripts c, c, and e to the DGDC termsparallel to each other: DC discontinuouson the right-hand side refer to the chemical, inter-coarsening; DP discontinuous precipitationfacial, and strain components of the Gibbs energy

changes per unit volume. DGeDC is usually very smalland hence ignored in DC. Originally, Livingston and

initiation sites for DP due to concomitant recrystallis-Cahn4 arrived at the following expression for DGDC ation of the deformed region at the isothermal temper-for steady state growth in DCature,318 see the section ‘Effect of plastic strain’ above.It may be pointed out that prior deformation may be

DGDC=DGcDC=−2cVm A 1lDP−

1

lDCB responsible for DP initiation but does not contributeto the driving force for the steady state growth inDP.360 Tsubakino et al.401 have similarly concluded=−

2cVmlDPA1− lDP

lDCB . . . . . . (13)

that prior plastic deformation does not influence theDC growth kinetics in Cu–Be. In this connection, it

where lDP and lDC refer to the interlamellar spacingis relevant to mention that experimental evidence in

in DP and DC reactions, respectively.support of coherency stress driven initiation or steady

As already pointed out, the residual solute supersat-state growth during DC has not been reported in the

uration in the matrix following DP may be substantialliterature. Since the role of solute supersaturation in

in many alloys. In that case, DGcDC may not be ignoredDC, if any, is not overwhelming (as that in say, DP

as done by Livingston and Cahn.4 Ju and Fournelle31or DIGM), it is logical to anticipate that coherency

have explained the thermodynamic basis for deducingstresses need not account for the boundary migration

DGcDC , and expressed DGDC asin DC. At least there is no such report to date

DGDC=DGcDC+DGcDC that even coherency stress may or may not affectDC.329 Thus, it is reasonable to conclude that theoverall driving force for DC is either interfacial or= (DGc,eDP−PDGc,eDP)+A2cVm

lDC−

2cVmlDPB (14)

chemical in origin, or derives from both of thesecontributions.where

Initiation sites and mechanismP=1−Axav−x0x0−xeB2 . . . . . . . . (14a)

Like DP, the process of DC involves heterogeneousnucleation on boundaries and subsequent/is the fraction of Gibbs chemical energy change for

DP in case of equilibrium (DGc,eDP) consumed in the concomitant migration of the latter. The boundaryconcerned is usually a high angle incoherent inter-DC reaction.344,402 It may be pointed out that equa-

tion (14) is valid when DP and DC are held at the phase boundary between two neighbouring DP,3,240,256eutectoid transformation,398,399 or eutectoid solidi-same temperature, i.e. DCI. If the temperature for

DC is different than that for DP, Manna et al.354 fication165 colonies. Figure 23 shows the initiation ofDC from the interface between two neighbouringhave demonstrated how equation (14) may be slightly

modified to obtain the true estimate of DGDC for DCII. DP colonies in Zn–4 at.-%Ag. As the reaction pro-gresses, the reaction front advances into the primaryInterestingly, Livingston and Cahn4 have demon-

strated that the stored strain energy due to prior colony to replace the fine lamellar products with acoarser one with identical morphology. The initiationdeformation is capable of initiating DC. A similar

phenomenon of DC of the coherent Ni3Al precipitates of DC does not necessitate that the primary reaction(i.e. DP or eutectoid transformation) should reach itsresulting from deformation induced boundary

migration or recrystallisation in Ni-based alloys indi- completion.90 Thus, DC may initiate from the reactionfront or original grain boundary of a primary colonycates that the stored strain energy of the dislocations

may suffice to initiate DC.329 However, this is ana- interfacing with an untransformed matrix undergoingDP.31,200 Figure 24 evidences the initiation of DClogous to the role of prior deformation in providing


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24 Initiation and growth of two DCI colonies fromsame initiation site, i.e. an original grainboundary (OGB) in Zn–4 at.-%Ag alloy at 433 Kafter 60 h.200 Note that original grain boundaryhas precipitate rich film on it and precipitatelamellae in DP and DCI colonies are alignednormal to each other in upper half ofmicrostructure: DC discontinuous coarsening;DP discontinuous precipitation

(a)

(c)

(b)

a interface between two DP colonies facing head on (i.e. a DPreaction front); b interface between two DP colonies havingcommon initiation site (i.e. an original grain boundary); c interfacebetween DP colony and free surface

25 Initiation of DCI from interface between DP 26 Schematic illustration of possible initiationcolony and free surface in Zn–4 at.-%Ag alloy sites for DCI or DCII: DC discontinuousat 423 K after 45 h (Ref. 200): DC discontinuous coarsening; DP discontinuous precipitationcoarsening; DP discontinuous precipitation

from a prior a0/a0 grain boundary during isothermal solidification. It may be mentioned that DC is mostlikely to initiate from an interface between two neigh-aging at 433 K for 60 h. Earlier, Gupta and

Parthiban118,119 have identified that the original grain bouring DP (Fig. 23 or 26a) or eutectoid transform-ation (Fig. 27) or eutectic solidification colonies.boundary or reaction front interfacing with a DP

colony or an a0 grain are the most probable initiation Unlike DP, DC possibly does not require hetero-geneous nucleation of the precipitate either as asites for DC in Fe–Zn. It is interesting to note that

DC may also initiate within a DP colony at the precursor of boundary deflection or a concomitantevent to boundary migration. In fact, extensive evi-interface between the primary colony and external

surface (Fig. 25). Similar evidence has been reported dence exists to indicate that some of the favourablyoriented precipitate lamellae/rods in the primarypreviously for the initiation of DP from prior

deformed external surfaces.150,319 colony actually continue to grow into the secondarycolony (Figs. 27 and 28).3,4,31,165,257 Obviously, theseIt is believed that plastic strain on the surface may

generate boundaries capable of thermally activated interconnected precipitate lamellae/rods are spacedwidely apart and are not the neighbouring ones inmigration and initiate DP. Identical effects have

also been reported for initiation of DC in eutectoid the primary colony. It is plausible that the soluteatoms from the lamellae/rods ahead of the DC reac-transformation from prior strained external surfaces

in Co–Si (Ref. 4) and Ti–Al–Mn–Nb (Ref. 300). tion front undergo short circuit diffusion along thereaction front and join the nearest lamellae/rod acrossFigure 26 schematically summarises the possible

initiation sites for DC from DP or a similar primary the interface, growing from the other primary colony.However, Fig. 29 evidences a rare event of formationcolony formed by eutectoid transformation or eutectic


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29 Initiation and growth of DCII colony from a27 Initiation of DC from interface between twoprecipitate phase enveloped original graineutectoid colonies in directionally grownboundary interfacing between two former DPCu–20·15 at.-%In alloy at 723 K after 186 h.398,399colonies in Zn–4 at.-%Ag alloy at 433 K afterNote that some of lamellae in eutectoid colony40 h following DP at 393 K for 60 h. Note thatcontinue to grow in DC colony with coarseranother DCII colony is about to initiate in DPrepeat distance: DC discontinuous coarseningcolony on right: DC discontinuous coarsening;DP discontinuous precipitation

28 b-lamellae growing from primary (DP) colonyinto secondary (DCI) reaction product

30 Initiation and growth of two DCII colonies fromaggregate in Zn–4 at.-%Ag alloy at 393 K afterprecipitate phase enveloped original grain200 h: DC discontinuous coarsening; DPboundary (OGB) interfacing between twodiscontinuous precipitationformer DP colonies in Zn–4 at.-%Ag alloy at453 K after 20 h following DP at 393 K for60 h: DC discontinuous coarsening; DPof boundary precipitates at the initial stage of DCdiscontinuous precipitationfrom an original grain boundary between two DP

colonies (cf. Fig. 26b) grown in opposite directions ina Zn–4 at.-%Ag alloy.403 Here the former original or growth of an advancing reaction front, pivoted at

a common point, into the origin of its counterpart.grain boundary is unusually thick with a precipitatefilm on it. Perhaps, the interface concerned might Experimental evidence supporting the above mechan-

ism has been reported in DC from DP in Al–Znhave undergone a transformation to develop a precipi-tate-rich film through the mechanism described in (Refs. 31, 326) and Fe–Zn (Ref. 117).

On the other hand, Shong and Kim104 have attri-Fig. 12 to be able to initiate DC. In this case, partition-ing of the excess solute in the matrix by volume buted the boundary displacement caused by the edge-

wise growth of the secondary lamellae to the origindiffusion near the interface at which DC initiationoccurs may assume significance, especially if the of boundary migration and growth of the DC colony

in Ti–Al. Recently, Denquin and Naka405 have notedinterface concerned develops a greater than usualwidth of a random boundary (Fig. 30).89 that DC in Ti–Al may initiate along with the primary

reaction on serrated boundaries. Here, it is felt thatSubsequently, these precipitates may grow in theusual fashion of DC at the expense of the finer DC is favoured over continuous coarsening as the

interfaces of the primary products are too stable andproducts in the primary colony ahead of the reac-tion front. the latter contains substantial residual solute super-

saturation. Interestingly, the secondary productsFournelle257 has proposed that DC may initiate viatwo possible mechanisms involving either an exten- maintain an identical crystallographic orientation

relationship to that between the primary reactionsion of the S-mechanism of growth of the DP colonies,


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products, though the reaction front in the secondarycolony is more corrugated. Earlier, Williams andEdington27 have suggested that the localised differ-ences in the coarsening rates of the spherical particlessituated on either side of a planar boundary maycorrugate the concerned boundary and initiate itsmigration for DC at the expense of smaller coherentmatrix precipitates in Al–Li.

Unlike the distinct stage of nucleation precedingthe steady state growth in DP, DC does not seem toneed a separate nucleation event. In fact, a systematicsurvey of the kinetic data on DC colony growthreported in the literature (e.g. Ref. 48) have indicatedthat initiation of DC requires no or practically negli-gible incubation time. Possibly, initiation of DC isdevoid of a perceptible nucleation barrier and is 31 Spheroidised morphology of precipitate phase

in DCII colonies across an original grainrelated only to the availability of a suitable initiationboundary (OGB) in Zn–4 at.-%Ag alloy formedsite capable of thermally activated migration.at 453 K after 20 h following DP at 393 KHowever, more definitive investigations into the initialfor 60 h: DC discontinuous coarsening; DPstage of DC are warranted to arrive at a definitivediscontinuous precipitationconclusion.

Interlamellar spacing (or coarsening ratio) is theMorphology, orientation relationship, and most authentic morphological evidence of DC. Basedmechanism of growth on the lamellar spacing and reaction front velocity of

the corresponding colonies, a second DC reaction (orThe DC products possess, with practically no excep-tertiary discontinuous reaction) has been identifiedtion, lamellar morphology in metallic systems with ain Ni–Sn (Ref. 158), Al–Zn (Ref. 400), and Ni–Instatistically constant repeat distance, characteristic of(Ref. 149). This second DC (or tertiary) reaction maythe isothermal transformation temperature, primaryconsume both DP (primary) and first DC (or second-product distribution, and alloy composition.ary) reaction products and replace with a relativelyHowever, particulate morphology of DC productscoarser (2–3 times) distribution of the identical phaseshas been reported in a ceramic system undergoingbehind a reaction front migrating into the primary/DC during partial reduction of Al2O3–Cr2O3 solidsecondary colonies at an order of magnitude or lowersolution.209 Although not a necessity, the a-phase invelocity. It is claimed that reduction in interfaciala DC colony may retain the same crystallographicarea provides the driving force for the tertiary reactionorientation relationship with b as that between theas practically no residual supersaturation is expectedsame in the DP colony.75,405to remain in the matrix following the secondary (i.e.In general, the DC products are more widely spacedDC) reaction.149 Although theoretically plausible, itthan the corresponding primary products, the ratioremains to be verified whether such tertiary reactionsof coarsening varying widely from relatively low (say,are indeed a separate discontinuous reaction or essen-2 in Cu–In (Ref. 402) and Al–Zn (Ref. 3)) to unusuallytially a sluggish secondary reaction (i.e. DC) pro-large (say, 1000 in Ti–Al–Mn–Nb (Ref. 300)) values.gressing with relatively slower kinetics (due to a lowerHowever, both morphology and interlamellar spacingmobility of the reaction front concerned for structuralmay show considerable variation in the microstructurereasons) and manifesting an upper bound of theif continuous coarsening of the lamellar structureGaussian distribution of interlamellar spacing (due toassumes a significant proportion at the transformationorientation effect with respect to the plane of obser-temperature. In an extreme situation, considerablevation). The latter doubt arises principally becausecontinuous coarsening may render a DC colony com-the tertiary reaction appears to be always concomi-pletely spherodised with practically no resemblancetant with the secondary (even primary) reaction.to a lamellar aggregate (Fig. 31). However, a mixtureHowever, more experimental evidence may be necess-of regular (or parallel ) and degenerate types of second-ary to establish whether tertiary reaction is unique toary reaction product403 is more often encountereda chosen few systems or may be a universally occur-than a completely spherodised aggregate as in Fig. 31.ring discontinuous reaction following DC if con-Therefore, it is of utmost importance that the inter-tinuous coarsening does not seriously impede itslamellar spacing in a DC colony is determined eitherscope.at the early stage of the reaction or from a region in

the microstructure that consists of reasonableOrientation relationship between primaryarea/width of undistorted and parallel lamellar prod-and secondary productsucts. Furthermore, normalisation of the apparent

lamellar spacing due to a Gaussian distribution of Livingston and Cahn4 have proposed that the direc-this quantity47 possibly arising out of the difference tion of growth of a DC colony is strongly related toin orientation of the colony growth with respect to the orientation relationship between the secondarythe plane of observation316 is desirable for a faithful and primary products. It is predicted that the grain

boundary generally migrates into that primary colonyrepresentation of DC growth kinetics.


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whose constituents are aligned normal to the bound- Models of DC growth kineticsary. In order to maintain this orientation relationship, The discussion in the initial part of this section hasthe reaction front becomes more convoluted giving already identified that the driving force for DC mayrise to a complex shape of the DC colony, and have an interfacial and chemical component, respect-thereby, increasing the total reaction front area (how- ively. The earliest models on the growth kineticsever, the total interfacial area of the colony decreases proposed by Livingston and Cahn4 assume that thedue to DC). Furthermore, it has been observed that driving force for the secondary reaction is derivedthe extent of growth is minimal in the segment where entirely from the reduction in Gibbs interfacial energythe secondary products are nearly parallel to the DGcDC involved. This driving force may be convertedprimary lamellae. Such a situation arises between the into a boundary concentration gradient through thesegments of reaction fronts migrating in opposite Gibbs–Thompson effect at the tip of the DC lamellae.directions during DC. Consequently, Fournelle257 has The solution of the steady state diffusion equationnoticed the existence of a stationary point on the for this boundary concentration gradient results inreaction front that pivots (about a common point) the following equation for the growth velocity vDCthe reaction front migration into opposite directions.Kaya and Smith165 have proposed that the difference vDC=

8xb

xb−xe

sdDbcVmf 2af 2bl2DClDPRT A1− lDP

lDCBin the orientation between the primary and secondary

products is necessary to set the intervening boundary . . . . . . . . (15)in motion for DC as the force for boundary migration

where xbis the equilibrium composition of the b phaseincreases as a function of the concerned angle of

(cf. Fig. 1), and fa

and fb

are the fractions of the amisorientation.and b phases, respectively. As predicted by Cahn,328Discontinuous coarsening products are almostthe composition of the matrix following DP seldomalways lamellar in morphology.257 However, thereaches the equilibrium solvus value. As a result, atendency for spherodisation alters the lamellarconsiderable amount of solute supersaturation maymorphology at higher temperatures. Frebel andremain in the DP colony that may supplement theDuddek398,399 have identified two types of growthoverall driving force for DC.200,354 Accordingly, themorphology in aligned Cu–In eutectoid products, thePetermann–Hornbogen theory on DP167 may betype I having a perpendicular alignment and type IIextended to DC as followshaving parallel orientation of DC lamellae with

respect to the reaction front. Growth of type II isalso reported in DC in Pb–Cd and Zn–Cd lamellar vDC=−8

DGDCRT

sdDbl2DC

. . . . . . . . (16)eutectics.165 Usually, the interlamellar spacing in thesecondary colony is lower in type I than that in Here DGDC (which has a negative value) may betype II growth. During isothermal growth, a consider- estimated using equation (14). It may be pointed outable amount of bending of the lamellae may be that equation (16) assumes a nearly identicalnecessary to maintain this parallel or perpendicular expression to that of equation (15) if DGDC (or equa-configuration and characteristic interlamellar spacing. tion (14)) is substituted in equation (16) under theFurthermore, the growth direction seems to be a special condition that P=1 in equation (14), i.e.strong function of the angle of misorientation between no solute supersaturation remains in the a lamellaethe primary and secondary lamellae, so much so that following DP.DC is unlikely between the adjacent primary cellshaving parallel lamellae.

In general, the above mentioned influence of orien- Summarytation relationship between the reaction products in Discontinuous coarsening is an identical movingthe adjacent primary colonies may be vital in the boundary reaction to DP, except that no crystalcases of eutectoid transformation4,398,399 and eutectic structure change is involved here between the reactantsolidification165 where residual solute supersaturation and product phases. The reaction kinetics are slowerin the primary products may be negligible. In the and the products are characterised by a coarserevent of a strong influence of DGcDC on DC succeeding distribution in this secondary change than that in theDP, say in Zn–Ag (Refs. 200, 354), maintenance of primary transformation. The product morphology isthe rigidity of orientation relationship between pri- usually lamellar. The coarsening ratio, which maymary and secondary reaction products does not seem vary by orders of magnitude, is a function of the alloytenable. For instance, Figs. 23 and 24 clearly violate composition, precise driving force, temperature, andthe stipulated condition of Livingston and Cahn4 that energetics of the primary products. Not all the systemsthe grain whose lamellae lie nearly parallel to the known to undergo DP are prone to coarsening by ainitial boundary (i.e. the DC reaction front) is more DC mechanism. However, it may be noted that DClikely to grow during DC.329 Possibly, the rigidity of may not succeed DP at the same temperature, butmaintaining a predicted growth direction is more may actually occur at a temperature other than thatdifficult to adhere to among the random boundaries for DP (e.g. in Ti–Al (Ref. 187)). It is now establishedin an initially polycrystalline aggregate than among that both Gibbs interfacial and chemical energythe special boundaries in a directionally grown crystal. changes may account for DC. In addition, severalIn this regard, it may be pointed out that lDC is also initiation sites and mechanisms for DC have beendependent on the solute supersaturation remaining identified. However, the true genesis of its occurrence,

as that for DP, still eludes a universal theory.in a following DP.406


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Initiation site and mechanismDiscontinuous dissolution (DD)Discontinuous dissolution may initiate from the reac-As illustrated in Fig. 5, dissolution of a two-phasetion front of a former DP or DC colony interfacinglamellar or particulate aggregate (say, at T3 in Fig. 1)with the supersaturated matrix,150,407 an originalformed by a prior DP, DC, eutectoid transformation,grain boundary (i.e. the former initiation site of theor eutectic solidification (say, at T2 in Fig. 1) behindprimary or secondary precipitation colony),78,150,407a receding boundary consuming the primary or sec-or an interface between two DP/DC colonies.150ondary precipitation products in a binary system isHowever, initiation of DD is never confined to onlycalled cellular dissolution or DD5,6one of these probable boundaries. For instance,Stiltz409 has observed that DD in Cu–Ag may initiatea+b�a

~. . . . . . . . . . . . (17)

simultaneously from the front (i.e. DP reaction front)Similar to its precipitation (i.e. DP) or coarsening and rear (initiation site of DP) ends of the same(i.e. DC) counterpart, DD is also characterised by a primary colony. Russew and Gust78 have concludeddiscontinuous change in composition and orient- that original grain boundaries are the most likelyation across the migrating reaction front that acts sites for initiation of DD in Cu–Cd. On the otheras a short circuit path of solute transport. Conse- hand, Chuang et al.150 have observed that the reactionquently, the reaction kinetics of DD are faster than front of the DP colony interfacing with a supersatu-those of volume diffusion controlled continuous rated or untransformed matrix grain is the mostdissolution.117,120 probable nucleation site for DD in Ni–In at the initial

stage, though other possible sites prove equally activeafter a short incubation time.

Occurrence of DD In contrast to DP or DC, it is proposed that DDThe earliest investigation on DD was reported by involves no distinct nucleation event as the requiredSulonen in Cu–Cd (Ref. 5). Subsequently, DD has non-conservative motion of the reaction front maybeen reported in several binary systems, e.g. Al–Zn originate by the process of precipitate dissolution(Refs. 32, 407), Cu–In (Refs. 90, 408), and Pb–Sn itself at the concerned boundary.5,172 This hypothesis(Refs. 6, 172). Table 1 enlists nine boundary and a is substantiated by the fact that an extrapolation oflone ternary system (Ti–Al–Nb (Ref. 299)) reported the available DD growth kinetic data on isothermalto undergo DD in metallic alloys. The strikingly low DD seam width as a function of time (e.g. for Cu–Cdnumber of systems known to undergo DD in compari- (Ref. 5) and Al–Zn (Ref. 410)) to the onset ofson with the large number of systems showing DP or the process usually yields zero intercept on theDC appears to suggest that, either adequate system- abscissa (i.e. time axis). However, Pawlowski andatic studies to explore the occurrence of DD in these Truszkowski411 have suggested that a series of parallelsystems have not been conducted, or the occurrence microcells formed on the receding reaction front mayof DD may indeed necessitate, despite the apparent join by lateral extension and connect with similarsimplicity in the reaction mechanism, a more stringent nuclei of the neighbouring colony across the reactionset of conditions to be complied with than those front to develop a broad band of solute supersaturatedsufficient for the occurrence of DP and DC. region to initiate DD. It is further proposed that DDFurthermore, continuous dissolution at a temperature is the preferred mode of dissolution for wider inter-higher than the concerned Tsv is always preferred. lamellar spacing in the primary (i.e. DP) colony,Generally speaking, DD is the more likely mode of lower temperature of dissolution, and smaller degreedissolution if the dissolution temperature is below the of prior deformation. In fact, the initial stage followsconcerned Tsv and Db is orders of magnitude greater a different rate equation than that for the later stagethan volume diffusivity D at this temperature. of the process.However, a mere fulfillment of these essential con- If initiation of DD is characterised by a precursorditions does not guarantee the occurrence of DD in event as this,411 a finite extent of time may be necess-a given system. ary to initiate the steady state DD process.

Moreover, the difference between D and Db at a Accordingly, Pawlowski and Zieba407 have indeedtemperature where DD occurs is not as large as that observed that a definite incubation time is necessarywhere DP or DC may take place. Just as in the case to initiate DD in Al–Zn. It has been suggested thatof DP and DC, it is not yet possible to predict a such an incubation is concerned with the nucleationpriori precisely why DD occurs in a given alloy and mechanism and thermodynamic metastability of thedoes not in others. It is even more intriguing that two-phase colony (i.e. DP/DC) being dissolved. ThisDD does not occur even in systems known to undergo incubation time is possibly temperature dependent.DP (say, Al–Mg (Ref. 28) or Cu–Co (Ref. 84)), both For instance, the kinetic data of DD in Cu–CdDP and DC (say, Pb–Mg (Ref. 166)), or even, DP, reported by Nakkalil and Gupta82 show that aDC, and DIGM (say, Ni–Zn (Refs. 160, 161) or W–Cr measurable incubation time is recorded to initiate(Refs. 195, 196)). On the other hand, a careful scrutiny DD only below 800 K. Since DD is essentially aof Table 1 reveals that the occurrence of DD in a heterogeneous diffusion controlled transformation, itgiven system does ensure that both DP and DC, or is plausible that, no matter how short, a finite timeat least DP, but not necessarily DIGM, occur in the should elapse before the steady state reaction may setsame system. Perhaps a general theory on the occur- in. However, this period being usually too short ( lessrence of DD may emerge with continued scientific than a minute), the experimental data concerned mustattention to the genesis and mechanism of DD in be very carefully recorded before drawing a firm

conclusion on the nucleation mechanism.several other binary and multicomponent systems.


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As already mentioned, Pawlowski et al.407,411 havenoticed that DD in Al–Zn initiates by the formationof a series of microcells (~130 nm width) at the triplephase junctions of a, b, and a0 (or a

~) along the

reaction front which subsequently coalesce to form aregion of solute-enriched solid solution (a

~). The a

~grains are usually inhomogeneous and contain a largedislocation density. Subsequently, Pawlowski andTruszkowski412 have identified several types of DDprocesses classified on the basis of the microstructureof the primary colony (precipitate morphology andinterlamellar spacing), concerned thermodynamicproperties (composition and specific boundaryenergy), and reaction temperature. Despite a pain-staking effort by the present authors, however, several

32 Ghost images (GI) formed during DD inof the proposed reaction types seem circumstantialFe–13·5 at.-%Zn alloy at 886 K after 28 minand warrant further experimental verification to befollowing DP at 723 K for 44 h. Beach marks areaccepted as a general basis of classification.due to solute segregation along intermediateposition of reaction front (RF) migrating in‘stop and go’ fashion:117 DD discontinuousSteady state growth mechanismdissolution; DP discontinuous precipitation

It has been suggested that steady state growthdepends on the microstructure/thermodynamic prop-erties of the precipitate (DP/DC) colony being dis-solved and the thermal condition of the DD process.32The driving force is primarily chemical in nature. Ithas been suggested that a macroscopic boundarycurvature term should be applied while calculatingthe driving force for DD. However, the mechanismof transformation remains primarily a boundarydiffusion controlled process. Zieba and Pawlowski32have found out that the apparent diffusion rateaccompanying DD could be two orders of magnitudehigher than the reported boundary diffusivity valuefor the concerned temperature. But this difference isattributed to the influence of volume diffusion in thevicinity of the reaction front which affects the pre-exponential factor more than to the activation energyof diffusion. On the other hand, the reaction frontmigration rate may vary by two orders of magnitudeduring DD.150 At higher temperatures, the dissolutionmay primarily be due to volume diffusion whichmight reduce the reaction front migration rate, oreven, suppress DD altogether.413

Usually, a~

is inhomogeneous and possesses a largedislocation density. In the event of excess solute beingpresent, the latter may prefer to segregate along thedislocations and produce differential contrast in theDD regions. Figure 32 reveals the traces of formerpositions of the receding reaction front during DD,seen as the ‘ghost images’ in an Fe–Zn alloy.117 It hasbeen suggested that such compositional inhomogen-eity is related to an intermittent ‘stop-and-go’ motionof the reaction front during DD. In fact, the spacings

a showing dislocations aligned both parallel and perpendicular tobetween these contour lines parallel to the reactionDP lamellae (or DD reaction front); b pronounced residual solute

front are the likely distances of stepwise migration of supersaturation segregated along primary b-lamellae regionsthe reaction front during a ‘go’ period. This obser- 33 Discontinuous dissolution (DD) invation is analogous to similar experimental evidence Al–21·55 at.-%Zn alloy at 603 K after 1 s

following discontinuous precipitation (DP) atobtained from in situ studies of DP in Al–Zn448 K for 540 s (Ref. 407)(Ref. 414). In general, the product phase in DD is an

inhomogeneous solid solution with residual/excesssolute network resembling the predissolution distri- subjected to DD at 603 K for 1 s. The close resem-

blance of the solute segregation in the DD regionbution of the precipitate phase.150 Figure 33 showsthe presence of dislocations and residual solute net- with the lamellar distribution in the DP colony being

dissolved strongly suggests that compositional homo-work behind the DD reaction front in an Al–Zn alloy


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geneity may only be achieved gradually by volumediffusion in the course of time. In this regard, Tu andTurnbull172 have earlier reported that DD yields ahigher than equilibrium solute content in the productphase (a

~) in Pb–Sn. Hackney and Biancaniello415

have attributed the presence of compositionalinhomogeneity in the microstructure following DDto a thermodynamic hysteresis. Indeed, Zieba andMorgiel416 have found that the solute content in thematrix behind the reaction front following DD couldbe twice as high as the initial (equilibrium) compos-ition of the alloy. Subsequently, Zieba and Gust417,418determined the solute concentration profiles leftbehind the receding reaction front in anAl–22 at.-%Zn alloy using analytical electron micros-copy. The experimentally determined profileresembled the classical U shape predicted by thediffusion models172,419 and computer simulation.420Despite the compositional inhomogeneity anticipated,Solorzano and Gust91 have noted a remarkable grainrefinement in Cu–In following DD, possibly due tothe formation of recrystallised boundaries from thesemicoherent interfaces left behind the prior DP pro-cess. Thus, DD following DP may be a mechanismof strengthening the alloys by grain refinementthrough a carefully designed thermal cycle.

Earlier, Sulonen5 has suggested that the tendency

T, K

v, 10_10 nm s_1

for DP and DD is equal at a critical temperature Tcr 34 Hysteresis of reaction front velocity v as(<Tsv ). Subsequently, Tu6 has identified a temperature function of temperature T showing T

cr(where

regime with an upper (=Tcr) and lower (=TDP v=0) in discontinuous dissolution (DD) and(Ref. 341)) bound within which the reaction front T

DP(where v=0 or l=2)341 in discontinuous

remains motionless (Fig. 34). Tcr is usually lower than precipitation (DP) in Pb–5·5 at.-%Sn alloy (afterthe corresponding Tsv , e.g. in Fe–Zn (by 34 K).120 Ref. 172)Similar temperature hysteresis between Tcr and TDPduring which the reaction front remains motionless

the steady state growth allows the determination of(i.e. v=0) has also been reported in Al–Zn (Ref. 410)the boundary diffusion triple product (sdDb ) usingand Cu–In (Ref. 408). Considering this temperatureexperimentally determined parameters of v (of DD)range in which the boundary remains motionless, itand c (of the DP colony being consumed) throughhas been suggested that the upper limit of c may besay, the Petermann–Hornbogen model (as modifiedcalculated from the DD kinetics as DD involvesby Gupta408)dissolution of an (a+b) aggregate of known and

statistically constant repeat distance with no incu-bation time or requirement of renucleation/branching sdDb=−

RT

8DGDDl2v . . . . . . . . (19)

during the steady state growth.172 Thus

where DGDD is the effective chemical driving force forDD (having a negative value). A more appropriatec<−0·5

lRTcrVmCx0 ln

xa~x0+ (1−x0 ) ln

1−xa~1−x0D estimate is possible by replacing the 8 with C

. . . . . . . . (18) (obtained from Cahn’s theory328 ) in the denominatorof the right-hand side of equation (19). C is obtainedwhere x

a~

corresponds to the metastable compositionas followsof a

~at T3 (Fig. 1). This equation could be a

convenient tool for determining c provided Tcr is2�C tanh �C/2=

xav−xa~xav−xe

at T∏Tsvaccurately determinable.

. . . . . . . (20a)Kinetics of DD

orMost of the kinetic studies on DD appear to beunanimous that the steady state growth kinetics of

2�C tanh �C/2=xav−x

a~xav−x0

at T>TsvDD are governed by diffusion along the migratingboundary.5,32,117,407,408 However, volume diffusion

. . . . . . . (20b)may significantly influence the dissolution process atelevated temperatures (above or close to Tsv ).421 DGDD is difficult to estimate directly from an analytical

expression. Utilising the fact that DGDD=DGDP at TcrRecently, it has been proposed that volume diffusionclose to the reaction front of the DD reaction plays (as v=0), Gupta408 has calculated DGDD indirectly

by determining the boundary mobility from thean important role in initiating DD even at lowertemperatures.407 In any case, the kinetic analysis of corresponding DP data. In the absence of a suitable


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ness of kinetic analysis of DD to unveil several aspectsof the kinetics and mechanism of grain boundarydiffusion and its related phase transitions.

SummaryDiscontinuous dissolution is a relatively less exten-sively studied phenomenon among the discontinuousreactions. The reaction may be useful in grain refine-ment91 and may enable repeated use of orientedbicrystals. Despite a number of studies on the reactionmechanisms, several aspects about its nucleation,driving force, and growth kinetics remain unresolved.Furthermore, the precise nature of boundarymigration, continuous or jerky, needs to be investi-gated in greater detail, preferably in situ. Perhaps thescope of commercial exploitation of DD may befeasible only with such a deeper understanding of thisreaction.

Diffusion induced grain boundarymigration (DIGM)Migration of grain boundaries caused by diffusion ofsolute atoms along the boundary from an externalsource or into a similar sink under a certain thermalactivation and chemical potential gradient between

Log

(sd

Db, m

3s_

1)

104/T, K_1

T, K

35 Arrhenius plot of grain boundary chemical the external source/sink and parent matrix was orig-diffusivity triple product sdD

bas function of inally termed DIGM,7 or more recently as chemically

reciprocal of temperature T determined for induced interface migration or chemically inducedFe–Zn system under different conditions of DP, grain boundary migration8 (Fig. 6). The externalDC, DD, and DIGM. Plots are compared with source/sink is normally a gaseous medium, but mightthe relevant data for stationary and migrating

instead be a liquid or solid phase. Solute transportboundaries. For details, see Ref. 344into or away from the matrix in the wake of boundary(p. 348): DC discontinuous coarsening; DDmigration leads to either solute enrichment (alloying)discontinuous dissolution; DIGM diffusionor depletion (de-alloying) in the area/volume sweptinduced grain boundary migration; DPby the boundary. The process deserves scientific atten-discontinuous precipitationtion not merely for academic interest (as a specialclass of moving boundary reaction), but as a potential

analytical model, the above approximation seemsmethod of heterogeneous compositional modulation

logical. However, Chuang et al.422 have subsequentlyon surfaces and selected areas of a solid with a

demonstrated the analytical technique of determiningfaster kinetics.

DGDD using the relevant experimental and thermo-Boundary migration due to or during solute

dynamic data.diffusion along the boundaries was first reported in

Figure 35 shows the Arrhenius plot of sdDb 1938 in the case of Cu bicrystals exposed to Znobtained from the kinetic analysis of DD in a

vapour by Rhines and Montgomery.423 However,Zn–13·5 at.-%Zn alloy using equation (19).422 For a

systematic DIGM studies were not conducted untilsuitable comparison, the relevant data obtained by

1972, for example, by den Broeder196 in a W–Crkinetic analysis of DP and DC in the same alloy

diffusion couple, and by Hillert and Purdy122 inusing the Petermann and Hornbogen model167 (equa-

polycrystalline Fe exposed to Zn vapour (from Fe–Zntion (10)), DIGM in Fe(Zn), and tracer diffusion of

turnings). Subsequently, Yoon and Huppman197 firstFe and Zn in polycrystalline a-Fe have also been

identified the occurrence of a DIGM-like phenom-included. The kinetic analysis yields an activation

enon in liquid phase sintering of W–Ni. King7 hasenergy value of 188 kJ mol−1 for DP and DC. The

reviewed the process and provided a list of about 30shaded region indicates the uncertainty in the sdDb binary and ternary systems showing DIGM. For thevalues obtained from the kinetic analysis of DC due

most recent update on the subject and a comprehen-to uncertainty in the comparison of the a lamellae. It

sive list of systems known to undergo DIGM, theis evident that the sdDb data obtained from the kinetic

reader may refer to the more recent and extensiveanalysis of DD are about an order of magnitude

review by Yoon.8lower than those obtained by similar analysis of DPand DC. This difference may arise due to the over

Occurrence and characteristicsestimation of DGDD. Finally, the discontinuities acrossthe Curie temperatures in DC of Fe–Zn or tracer Diffusion induced grain boundary migration may

occur in polycrystalline metals,33,121 intermetallicdiffusion of Fe or Zn in a-Fe may be attributed tothe corresponding change in v across such critical phases and compounds,298,301 and oxide296,307/non-

oxide215,259 compounds in the course of various typestemperatures. Thus, Fig. 35 demonstrates the useful-


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36 Alloying due to diffusion induced grainboundary migration (DIGM) in Cu/Ni/Cupolycrystalline diffusion couples at 1023 K for6 h on section 5 mm below surface.424 Note thatDIGM is absent on twins and is present butnon-uniform along high angle boundaries

of phase transition and material processing likedoping, evaporation, oxidation, precipitation, andincipient fusion or welding. Table 1 lists about 100binary and multicomponent systems known to showDIGM under specific conditions. Diffusion induced

37 Diffusion induced grain boundary migration ofgrain boundary migration is a thermally activated symmetric S19a {133} tilt boundary of pure Cuphenomenon, involving solid, liquid, or gaseous revealing pronounced tendency of faceting onphases in the temperature range where Db&D.71 either side of boundary at 693 K after 14 h.100Obviously, this transformation qualifies itself into the Note that sharp corners round off and step-category of discontinuous reactions because the com- like marks indicating intermediate boundary

positions disappear as depth z below surfaceposition profile across the migrating reaction front isincreasesdiscontinuous or changes abruptly.11

Figure 36 reveals typical evidence of DIGM of Cuin polycrystalline Ni at 1023 K after 6 h.424 It is

(S is the reciprocal of coincident site density along aapparent that DIGM is more probable in a high

special boundary) boundaries show a unique facetedangle random boundary than along a coherent or

morphology of growth which is a function of depthsemicoherent interface like a twin boundary.

and solute concentration (Fig. 37). Here, the degreeFurthermore, the extent of boundary migration or

of faceting depends on time and depth (and hence,DIGM seam width is non-uniform. Hence, DIGM

solute content). As a result, the sharp apex of theappears to be a structure sensitive property of the

isosceles triangles along the faceted boundary tendsconcerned interface.

to round off as the depth increases and consequentlythe solute concentration decreases. Furthermore,

Orientation dependence boundary migration occurs on both sides of theinitially symmetric boundary with parallel ‘ghost lines’Chen and King101 have systematically studied the

effect of angle of misorientation of symmetric tilt indicating intermediate positions of the boundaryduring migration. These ghost lines may arise due toboundaries on DIGM in Cu exposed to Zn vapour.

It is reported that boundary migration rate, solute solute segregation along dislocations punched outduring a stop-and-go motion of the boundary. Similarpenetration depth, and concentration are strongly

dependent on the misorientation angle and inclination jerky motion of the boundary during DIGM has beennoted earlier in S5(001) tilt boundaries.101of the boundary plane with respect to the diffusion

direction. Furthermore, it appears that DIGM occurs In addition to morphology, both boundarymigration rate (Fig. 38a) and diffusivity (Fig. 38b)due to climb of boundary dislocations aided by

generation of vacancy population due to unbalanced appear to be strong functions of the boundary typeand misorientation angle. The above evidence seemsfluxes of solute and solvent atoms along the boundary.

Subsequently, Schmelzle et al.100 have presented an to strongly indicate that neither Gibbs chemicalenergy change nor coherency strain alone may be theextensive investigation on the influence of misorien-

tation on the morphology, mechanism, and kinetics principal driving force for DIGM. In this regard,however, Yoon8 points out that faceting of the bound-of DIGM with several Cu bicrystals having

011�{011} symmetric and asymmetric tilt boundary depends on its velocity, and also perhaps, itsinherent mobility and structure. Hence, orientationaries with 10–172° angle of misorientation. All bound-

aries except low angle (<15°) and coherent twins dependence of DIGM may not actually disapprovethe coherency strain theory.migrate either on both or only on one side, depending

on whether the concerned boundary is symmetric or Figure 38a reveals that the reaction front migrationvelocity is anisotropic and strongly dependent on theasymmetric, respectively. The symmetric S19a{133}


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boundary and is not a simple function of the boundarymobility.100

Figure 38b records the variation of sdDb as a func-tion of misorientation angle. Like the variation invelocity with misorientation angle (Fig. 38a), diffusiv-ity too shows anisotropic variation with such angleand orientation of the boundary plane to the tilt axisat 693 K. The variation in Fig. 38b is in good agree-ment with the relevant data from static boundaries.Thus, migrating boundaries seem to possess identicaldynamic properties and diffusivity to those in staticboundaries. Here again, diffusivity along boundaryplanes parallel to the tilt axis is larger than that fordiffusivity along boundary planes normal to the tiltaxis. Thus, both dynamic properties and mass trans-port rates along boundaries are extremely structuresensitive characteristics.

Driving forceHillert and Purdy122 argued that the change in thechemical potential in the matrix (i.e. Gibbs energy ofmixing, DGcDIGM) concomitant with addition (alloying)or removal (de-alloying) of solute atoms may accountfor DIGM. Cahn et al.395 have proposed that thedifference in the diffusion rates between the soluteand solvent atoms along the random boundaries maygive rise to generation of vacancy sources or sinks(analogous to the Kirkendall effect in the matrix) andinitiate migration of grain boundaries in the directionnormal to the boundary plane by synchronous climbof dislocation ledges. Generation of compressivestresses or porosity in the matrix following alloyingor de-alloying, and reduction in the kinetics of DIGMdue to the restraints on contraction or expansionnormal to the grain boundary plane provide experi-

v, 1

0_2

m s

_1

sdD

b, 1

0_22

m3

s_1

h, deg

(a)

(b)

mental evidence that a net amount of solute is either38 Kinetics of diffusion induced grain boundaryadded or removed by DIGM.10 If the Gibbs energymigration in Cu bicrystals exposed to Znof mixing constitutes the overall driving force ofvapour in terms of a variation of boundary

velocity v, and b grain boundary chemical DIGM (i.e. v=MDGcDIGM , where M is the boundarydiffusion triple product sdD

b, as function of mobility and DGcDIGM has a negative value), the corres-

boundary misorientation angle h for diffusion ponding estimated value of M is orders of magnitudeparallel (d) and perpendicular ()) to �011� tilt smaller than the experimentally determined rates inaxis of symmetric grain boundaries (GBs) with Fe–Zn.122specific S values (see Ref. 100)

Doherty329 argues that the true driving force forDIGM arises due to elastic coherency stresses acrossthe boundary generated by a change in the lattice

misorientation angle, temperature, and inclination of parameter of the matrix following alloying orthe boundary plane (parallel or perpendicular) with de-alloying. Hence, the mobility should be calculatedrespect to the tilt axis. Velocity increases with an using the elastic strain energy instead of DGcDIGM ,increase in temperature for identical boundaries. which yields a value of M close to that obtainedSimilarly, the boundaries with the same misorien- experimentally. In this regard, it has been suggestedtation angle migrate faster if the concerned plane and that an initial diffusion of the solute atoms down thediffusion direction are parallel to the tilt axis at the stationary boundaries both enriches the grains withsame temperature. The low angle symmetric tilt solute atoms across the boundary up to a distanceboundaries (10° and 171·9°) do not record noticeable of �Dt, where t is the time, and builds up elasticmigration at 693 K, which is attributed to the sym- strain until plastic deformation sets in and relaxationmetry of the boundaries and corresponding low step occurs on one side by annihilation of edge dislo-density for dislocation climb to be operative.100,101 It cations. This creates an elastic strain energy gradientis felt that low angle boundaries may migrate if they across the boundary and causes the latter to migrate.are asymmetric. In addition to low angle grain bound- However, it is not clear as to how substantial volumearies, coherent twin boundaries also do not record diffusion (overtaking boundary diffusion) does occursignificant migration due to low diffusivity through ahead of the boundary when D%Db , and more so,them. Thus, it is concluded that boundary migration why should strain be selectively relieved (for identical

measures of �Dt) preferably on one side of therate is closely related to the diffusional flux along the


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boundary leaving the other side unaffected. Purdy327has pointed out that volume diffusion penetration(D/v) in DIGM could be of the same order as atomicdistance in Fe–Zn (Ref. 122) to as high as micrometresin Al–Zn (Ref. 17). In the event of a large D/v,DGcDIGM may be substantially reduced. Thus, bothelastic strain and chemical forces could play animportant role in DIGM.327

According to Sutton and Balluffi,425 the drivingforce for DIGM may arise due to one or a combi-nation of the following reasons: (a) dislocation climband Kirkendall effect, (b) coherency strain in thematrix, (c) solute segregation and related structuraltransformation, (d) diffusional vacancy flux, and(e) chemical gradient energy. Coherency strain theoryis reasonably successful in accounting for DIGM inseveral cases, particularly in Mo–Ni–(Co–Sn).265However, the occurrence of DIGM in Al–Cu (Ref. 24)and Au–Ag (Ref. 36), where coherency strain is inad-equate, casts fundamental doubt about the universalapplicability of this theory. Recently, Cahn et al.395have presented a comprehensive treatment on ident-ifying the driving force of DIGM. While rejecting thechemical gradient energy theory outright, it is sug-gested that a complex interaction function comprisingboth the composition and orientation dependentenergy terms may account for DIGM.

Diffusion induced recrystallisation (DIR)Diffusion induced recrystallisation refers to thenucleation and growth of new grains from the surfaceexposed to a solute source or sink. The new grainsusually have a higher solute content than that in thealloyed zone created by DIGM.8 Chongmo andHillert20 have first reported the occurrence of DIR inpolycrystalline Cu subjected to DIGM in Zn vapour.Subsequently, den Broeder99 has noted the occurrenceof DIR during de-alloying of brass above 673 K. Thesolute content is maximum at the surface anddecreases with the square root of annealing time.Diffusion induced recrystallisation has been observedin TiC(Cr3C2 ) type of carbide mixtures too.426Figure 39 shows a typical microstructure of DIR inCu(Zn). It is evident that the surface grains growlargest during DIGM or DIR as they receive thesolute supply for a longer period of time. Surfacecorrugation and ghost lines in Fig. 39a suggest thatthe DIR grains have formed during DIGM. Since Cualloyed with Zn, but not pure copper, may showtwins, the large density of twins, for example inFig. 39b, substantiates that alloying may be a precur-

a z=0 mm; b 5 mm; c 11 mm; d 14 mmsor of DIR.39 Formation of new grains by diffusion inducedFollowing DIR, the new grains seem to attain a

recrystallisation at different levels of depth zsolute content closer to the equilibrium composition.8on {011} surfaces of �011� tilt boundary CuHowever, the discontinuous change in compositionbicrystals exposed to Zn vapour at 693 K foracross the reaction front, characteristic of a discontin-300 h (Ref. 427)

uous reaction, is a typical feature of DIR. In mostcases, DIR accompanies DIGM at higher temper-atures and high accumulation of solute atoms in the that polygonisation of dislocation substructure and

subgrains in the diffusion zone may account formatrix. Yoon8 considers that the genesis of DIR, likethat of DIGM, lies in coherency strain. Apparently, nucleation of new grains by a process actually similar

to recrystallisation of cold worked structure.429 Thethe new grains may nucleate due to large compos-itional changes, as suggested by Mittemeijer and dislocations are created by differential diffusion rates

of solute and solvent atoms along the boundaryBeers.428 On the other hand, it has been suggested


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(Kirkendall effect) or due to lattice parameter change state reaction front migration velocity v and inter-lamellar spacing l in the cases of DP and DC needduring solute diffusion. Thus, both the Kirkendall

effect and coherency strain may be responsible for to be carefully determined by suitable experimentaltechniques over a given temperature range. Secondly,DIR.an accurate estimation of the driving force for thereaction is analytically obtained using appropriateSummarymodels.

Despite being the latest addition among the discontin-Figure 40 shows the Arrhenius plot of the respective

uous reactions, DIGM has received a tremendoussets of sdDb data determined by kinetic analysis of

amount of scientific attention, more due to its simi-isothermal DP kinetics in some Cu–In alloys in

larity to various moving boundary reactions and itsthe range 550–900 K using the analytical models

relation to both boundary migration and diffusionof Turnbull,345 Cahn,328 and Petermann and

than because of its scope of practical application.Hornbogen.167 It is interesting to note that the sdDbMainly from the contributions related to understand-data in Fig. 40 are comparable to the same for grain

ing liquid film migration and mechanistic similarityboundary radiotracer diffusion of In in Cu (Ref. 344).

between this reaction and DIGM, it is now widelySubsequent analysis has revealed that the activation

believed that coherency strain is a major driving forceenergy values calculated from the experimental data

for DIGM.8 However, more rigorous studies arelie in close proximity to that for grain boundary

advocated with well characterised bicrystals to corre-chemical diffusion of In in Cu–In, and are significantly

late dynamic properties and mass transport mechan-lower than that for volume diffusion of In in Cu–In.

ism of grain boundaries with boundary structure andFigure 41 presents the results of a similar exercise

orientation. Finally, it remains to be seen whetherof determination of sdDb as a function of the recipro-

interphase boundaries do manifest similar dynamiccal of temperature from the kinetic analysis of DC in

properties to those of grain boundaries, particularlythe Ni–7·5 at.-%In alloy. It is evident that the sdDbwith regards to DIGM.data obtained from the kinetic analysis of DC are inclose agreement with those obtained from the tracer

Determination of Arrhenius parameters by impurity diffusion and self-diffusion data of Ni.344kinetic analysis For further details see Ref. 344. Similar application of

this kinetic analysis has yielded sdDb data in Cu–AgIn general, the discontinuous reactions are known(Ref. 64), Cd–Ag (Ref. 46), Zn–Ag (Ref. 354), andto be boundary diffusion controlled transforma-Zn–Cu (Ref. 203).tions. Therefore, the steady state kinetic analysis of a

Finally, note that generation of these diffusivitygiven discontinuous reaction enables an indirect butdata has been very useful in the studies on DP andeffective and convenient method of determining theDC. Similar analysis on new systems known to underboundary chemical diffusivity as a function of temper-go DP or DC is, therefore, always warranted.ature by suitable application of the relevant growth

kinetic models.10,11 This approach has extensivelybeen utilised to determine the Arrhenius parameters Grain boundary migration inof boundary chemical diffusion in systems which discontinuous reactionsundergo DP or DC. Similar efforts have also been

Grain boundaries are higher energy regions (com-successful in kinetic analysis of DD and DIGM.pared with the grain body) in a polycrystalline aggre-Table 5 summarises about 30 binary systems in whichgate which may migrate under conducive conditionsArrhenius parameters of grain boundary diffusionby transfer of atoms or groups of atoms from onehave been determined by suitable kinetic analysis ofgrain to another by one or a combination of thethe discontinuous reaction concerned. This methodpossible mechanisms.425 Grain boundary migrationassumes a greater significance in view of the fact thatmay be accomplished by a conservative or non-boundary diffusivity is an extremely important funda-conservative motion under a suitable driving force,mental parameter useful in all diffusion controlledtemperature, and net boundary curvature in a giventransformations and material processing operationsdirection. The migration is said to be conservativeinvolving solid state phase transitions. Usually,when no net diffusional flux of a given species isboundary diffusivity is determined through radio-added or removed from the boundary. Conversely,tracer diffusion studies (with radio isotopes) or sec-the migration is called non-conservative if such aondary ion mass spectrometry (with stable isotopes).diffusional flux exists leading to a perceptible compos-In comparison, the kinetic analysis of a given discon-itional adjustment in the neighbouring grain followingtinuous reaction is a much simpler technique thatboundary motion. All discontinuous reactions arerequires a minimum of equipment.associated with non-conservative migration of grainThe temperature dependence of grain boundaryor interphase boundaries. In either case, grain bound-chemical diffusivity is generally expressed through anary migration is related to a large scale rearrangementArrhenius relationship as followsof atoms (or phase transformation) that may signifi-

sdDb= (sdDb )0 exp(−Qb/RT ) . . . . . (21)cantly alter the properties of solids, e.g. strength,ductility, conductivity, etc.where (sdDb )0 is the pre-exponential factor and Qb is

the activation energy. Determination of sdDb through Both conservative and non-conservative motion ofgrain boundaries are usually considered uniform andkinetic analysis of a discontinuous reaction is based

on two major types of data that are needed for the continuous. For instance, the reaction front isassumed to migrate at a constant velocity under acalculations. Firstly, the kinetic data on the steady


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Log

(sd

Db, m

3s_

1)

104/T, K_1

T, K

Log

(sd

Db, m

3s_

1)

104/T, K_1

T, K

40 Arrhenius plot of grain boundary chemical 41 Arrhenius plot of grain boundary chemicaldiffusion triple product sdD

bfor migrating diffusion triple product sdD

bfor migrating (M)

(M) boundaries determined from kinetic boundaries determined from kinetic analysisanalysis of discontinuous precipitation in of discontinuous coarsening (DC) inCu–4·6 at.-%In alloy using different kinetic Ni–7·5 at.-%In alloy.344 For comparison,models. Data for tracer diffusion (Cu/In*) relevant data from tracer diffusion (Ni/In*) andthrough stationary (S) boundary and self- self-diffusion (Ni/Ni*) of Ni through static (S)diffusion (Cu/Cu*) of Cu are included for boundaries have been includedcomparison. For details see Ref. 344, p. 329

Table 5 Selected binary systems in which sdDb

values have been calculated through kinetic analysis ofdiscontinuous reactions

System Composition, at.-% Reaction* Model† T, K Ref.

Ag–Cu Ag–6·2Cu DP PH 460–610 15Al–Ag Al–17·8Ag (wt-%) DP T, C 538–598 21Al–Zn Al–39·3,59·3Zn DC (PH)

m323–523 400

Au–Co Au–6,10,15,20Co DP AL, C, T, Z 500–900 38Au–Fe Au–30,40,50,60Fe DP, DC T, AL, PH, C 519–943 42Au–Ni Au–30,41·6,55Ni DP T, C, AL, PH, SK, S 723–923 43Cd–Ag Cd–6Ag DP T, AL, PH 353–523 46Co–Mo Co–6,8,10Mo DP T, AL, PH, S 823–1095 53Co–Zn Co–18·8,26·9Zn DP T, C, AL, S 673–923 60Cu–Ag Cu–3·8Ag DP, DD H, PH, T 555–893 64Cu–Cd Cu–2·7Cd DP, DD C, AL, TT, T 573–726 78Cu–In Cu–12In DP PH 573–683 89Cu–Mg Cu–2,2·6,3·2Mg DP T 573–873 92Cu–Sb Cu–4,4·5,5Sb DP T, C, PH, AL, SK, S 503–603 94Cu–Zn Cu(Zn) DIGM C‡ 623–773 100Fe–Zn Fe–13·5Zn DP, DC, DD PH 600–1050 107Mg–Al Mg–9Al DP C, H, S 336–583 128Ni–Cr Ni–42,45,48Cr DP T, AL, PH, S 823–1200 143Ni–In Ni–8In DP, DC C, H, T, PH 710–1025 149Ni–Mo Ni–17·5Mo DP T, AL, C, PH, S 823–1123 152Ni–Sn Ni–8·5Sn DP, DC PH, T, C, (PH)

m815–995 158

Pb–Cd Pb–17·4Cd (wt-%) DC LC, (PH)m

353–489 165Pb–Sn Pb–9·87Sn DP PH 258–333 341Ta–Cr Ta–15Cr DP Z, T, AL 1473–1693 184W–Cr W–20,30,40,50,60,70Cr DP C, PH, AL, S, T 1100–1493 195Zn–Ag Zn–4Ag DP, DC PH, (PH)

m, LC 353–513 354

Zn–Al Zn–1·8,2·0Al DP PH 248–358 201Zn–Cu Zn–2·5Cu DP PH, T, AL 383–583 203

* DC discontinuous coarsening; DD discontinuous dissolution; DIGM diffusion induced grain boundary migration; DP discontinuous precipitation.† AL Aaronson and Liu;346 C Cahn;328 H Hillert;338 LC Livingston and Cahn;4 PH Petermann and Hornbogen;167 (PH)

mPH modified by Fournelle et al.;3,31

S Sunquist;347,348 SK Shapiro and Kirkaldy;88 T Turnbull.345

‡ Schmelzle et al.100


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‘stop’ and ‘go’ during DP in an Al–15 at.-%Zn alloy(Fig. 42). The concept of jerky motion of boundariesduring DP has also been utilised for interpretingexperimental results in Al–22 at.-%Zn (Ref. 430),Mg–Al (Ref. 431), and Co–Al (Ref. 406). Con-ventionally, v is determined from the experimentaldata of w as a function of t as v= (dw/dt)T .11 Thus,such experimentally estimated v represents a timeaveraged value of both the instantaneous displace-ments rates (vmax ) as well as intervening stationaryperiods. Kaur et al.344 have pointed out v and vmaxmay differ by 1–3 orders of magnitude and result ina significant underestimation of sdDb obtained bykinetic analysis on the basis of Cahn’s model328because the latter requires the use of vmax (and not v)for estimating sdDb . In this connection, Mannaet al.430 have demonstrated that application of vmaxinstead of v is more appropriate for predictingthe metastable solute distribution profile in thematrix following DP. Subsequently, Zieba andGust417,418,432,433 have presented the localised reac-tion concepts of DP and DD, in which the sdDbvalues are determined for individual colonies throughsolute concentration profile measurements and aspecial method of determination of the growth velo-city.406,433 Such analyses have significantly removedthe divergence between tracer diffusion kinetic dataand the diffusivity determined from the kinetic analy-sis of discontinuous reactions using Cahn’s model.328

On the other hand, the Petermann and Hornbogen

Dis

tan

ce, µ

m

t, smodel167 on DP assumes a time averaged rate of

42 Variation of reaction front migrating distance atomic jumps across the boundary during DP. Thus,as function of time t during isothermal growth use of v instead of vmax may still yield a more realisticof discontinuous precipitation (DP) colony in (and close to the radiotracer diffusion data) estimateAl–15 at.-%Zn alloy at 433 K (hot stage in situ

of sdDb than that obtained directly by applying v inmeasurements).414 Note that boundarythe Cahn model.328 In this regard, it is proposed thatmigrates in ‘stop and go’ fashionthe more appropriate form of Petermann andHornbogen model may be expressed as344

steady state growth condition with a statisticallyconstant repeat distance between the precipitates sdDb=−

RT

CDG

xb−x0

xb−xav

l2v . . . . . . (22)behind the reaction front in DP and DC. Recently,Abdou et al.414 have reported that the reaction front where C is the Cahn’s parameter given by

equation (20).migrates in an alternate sequence of discrete steps of

Table 6 Possible beneficial and deleterious effects and applications of discontinuous reactions

DR* Beneficial Deleterious

DP Grain refinement436 Hardness decrease138

Strengthening317 Loss of coherency strengthening in Cu alloys231

Hardening437 Decrease in ductility438

Development of in situ lamellar composites89 Adverse effect on superconductivity439

Investigating dynamic properties of grain/interphase boundaries341 Deterioration of corrosion resistance280

Determination of metastable solvus for precipitation Edge cracking (hot tear)440

Determination of grain boundary chemical diffusivity by kinetic Increase in creep cavitation279

analysis (Table 5) Destruction of single phase microstructureDC Determination of grain boundary chemical diffusivity by kinetic Deterioration of mechanical properties

analysis (Table 5) Destruction of unidirectionally grown oriented in situlamellar composites165

DD Dissolution of precipitates at lower temperatures (below TSV

) Microstructural degradation (dissolution) of lamellarFaster kinetics than continuous dissolution below T

SVstructures at relatively lower temperatures (<T

SV)

Salvation of oriented bicrystals used for DP or DIGM (recycling) Compositional inhomogeneity in the dissolved matrix117

Determination of upper bound of interfacial energy from kineticanalysis172

DIGM Surface or localised alloying without melting Evaporation loss of high vapour pressure solutes from aPreparation of reactive and high melting temperature alloys solid alloy at elevated temperatures (de-alloying)Sintering of powder products by liquid film migration Structural dependence of boundary migration100

Application as a model moving boundary reaction to study thestructural dependence of dynamic properties and diffusivity ofgrain/phase boundaries100,101


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Grain boundary migration in discrete steps of stop- cations of discontinuous reactions, some of which areestablished facts and the rest are predictions stilland-go has earlier been reported in interdiffusion of

Cu–Ni (Ref. 428) and DIGM in Au–Cu (Ref. 40). The awaiting verification. Thus, continued efforts are war-ranted to find solutions to the existing problems andfrequently observed ghost images (e.g. Fig. 32) in DD,

besides indicating compositional inhomogeneity, may explore the possibility of useful applications of discon-tinuous reactions. In addition, as discontinuous reac-arise due to a similar jerky motion of the reaction

front. The presence of such ghost images in the tions are model moving boundary reactions, furtherdetailed studies with random boundaries as well asalloyed zone in DIGM in Cu(Zn) (Fig. 37) similarly

may suggest that step-like intermittent migration of characterised bicrystals are required to elucidate thehitherto unresolved theoretical and practical prob-the grain boundary may be a customary feature of

both non-conservative as well as conservative motion lems. However, studies on discontinuous reactionsare needed not necessarily for immediate technologi-of grain boundaries during a given phase transform-

ation rather than an accidental observation. This cal applications but, from an academic point of view,because of the striking similarity of discontinuoushypothesis is further substantiated by earlier experi-

mental evidence of a similar stop-and-go motion of reactions to the general class of moving boundarysolid state reactions.the grain boundary during recrystallisation of cold

worked Cu quoted by Friesel et al.10 In this regard,it would be worth investigating whether this intermit-

Acknowledgementstent or jerky motion of the boundaries is actuallyrelated to a series of discontinuous migration steps Partial financial support to one of the authors (IM)of the individual ledges or defects in the boundary. by the Department of Science and Technology,Perhaps, more experimental evidence (particularly in Government of India, and Deutscher Akademischersitu studies, e.g. Ref. 434) is needed to establish the Austauschdienst, Germany Collaborative Researchtrue nature of the dynamic properties of grain Project Fund and University of Stuttgart, and encour-boundaries. agement from the Indian Institute of Technology,

Recently, Rabkin et al.435 have pointed out another Kharagpur during the preparation of the review aresource of discrepancy that may contribute towards gratefully acknowledged. The authors are gratefulthe occasional orders of magnitude difference between to Profs. R. A. Fournelle, G. Gottstein, L. S.tracer diffusion data and diffusivities calculated from Svindlermann, E. Rabkin, P. Zieba, and Drs A. Das,the kinetic analysis of DP using Cahn’s model.328 It J. Dutta Majumdar, and J. Jha for useful technicalhas been argued that pronounced solute drag may discussions during the preparation of the review.drastically reduce the dynamic segregation factor sdynfor migrating boundaries with strong segregationtendencies. sdyn is a strong function of grain boundary Referencesvelocity, energy of segregation, and bulk diffusion

1. . : in ‘Phase transformations’, Vol. 1, II/27–II/68; 1979,coefficient. The small magnitude of the ratio between

London, The Institution of Metallurgists.sdyn and s at sufficiently high grain boundary velocity 2. . . and . . : Int. Met. Rev., 1981, 26,

153–183.and/or intermediate temperatures may account for3. . and . . : Mater. Sci. Eng. A, 1988,the above mentioned difference in sdDb and sdyndDb 102, 271–279.data obtained from the kinetic analysis of DP using4. . . and . . : Acta Metall., 1974, 22,

Cahn’s model and that determined by radiotracer 495–503.measurements. 5. . . : Acta Metall., 1960, 8, 669–676.

6. . . : Metall. T rans., 1972, 3, 2769–2776.7. . . : Int. Mater. Rev., 1987, 32, 173–189.8. . . : Int. Mater. Rev., 1995, 40, 149–179.Concluding remarks9. . . and . . : Acta Metall., 1981, 29, 493–500.

Discontinuous reactions can cause major changes in 10. . , . , and . : C. Phys., 1990, 51,C1, 381–390.the microstructure and properties of solid alloys.

11. . : Interface Sci., 1998, 6, 113–131.Among the different discontinuous reactions, DP and12. . . , . . , and . : Appl. Phys. L ett.,DC are usually deleterious to the mechanical, physi-

1976, 29, 772–774.cal, and chemical properties of a large number of 13. . and . : Z. Phys., 1930, 66, 293–303.alloys of commercial interest. For instance, the 14. . , . , and . : Z. Phys., 1930, 66,

350–376.Nimonic superalloys are known to lose their high15. . , . , and . : Z. Metallkd., 1977, 68,temperature strength if DP replaces the metastable

619–623; 1978, 69, 75–80, 445–449.coherent precipitates with coarser equilibrium prod-

16. . . . and . . : J. Inst. Met., 1947,ucts. On the other hand, the scope of a dramatic 73, 625–639.

17. . and . . : Scr. Metall., 1987, 21, 361–364.grain refinement or in situ development of aligned18. . . : Scr. Metall., 1989, 23, 1295–1300.lamellar composites are projected as the possible19. . . , . , . , and . .beneficial effects of DP. Similarly, DD may be useful

: Scr. Metall., 1983, 17, 1231–1235.in salvation of oriented bicrystals, and DIGM may 20. . and . : Acta Metall., 1982, 30, 1133–1145.be exploited for low temperature sintering and 21. . . and . . : Acta Metall., 1968, 16,

845–855.alloying of metal powders, controlled doping of elec-22. . and . : Mater. Sci. Eng., 1972, 10, 211–222.tronic materials, inter diffusion studies with thin films,23. . . . : J. Inst. Met., 1946, 72, 243–263; 1947,

and in situ alloying of polycrystalline aggregate under73, 681–691.

controlled atmosphere. Table 6 lists a number of 24. . and . . : Acta Metall. Mater., 1991, 39,2835–2845.notable beneficial and deleterious effects and appli-


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25. . . , . . , . . , and . . 69. . . , . . , . . , and . .: Metallography, 1983, 16, 349–360.: Phys. Met. (USSR), 1991, 11, 1039–1043.

26. . : J. Mater. Sci., 1975, 10, 2075–2081. 70. . . , . . , and . . : Scr. Metall., 1979,13, 503–509.27. . . and . . : Acta Metall., 1976,

24, 323–332. 71. . . and . . : Acta Metall., 1982, 30, 861–870.72. . and . : Z. Metallkd., 1975, 66, 525–533.28. . . . and . . : J. Inst. Met., 1951,

79, 19–34. 73. . and . : Acta Metall., 1976, 24, 639–650.74. . , . , and . : T rans. Jpn Inst.29. . , . , . , and . :

Philos. Mag., 1993, 67, 1143–1151. Met., 1981, 22, 153–162.75. . , . , and . : J. Mater. Sci.30. . . , . , and . . : Acta Metall.,

1973, 21, 517–524. L ett., 1982, 1, 306–307.76. . , . , and . : J. Jpn Inst. Met., 1989,31. . . and . . : Acta Metall., 1985, 33, 71–81.

32. . and . : Mater. Sci. Eng. A, 1994, 187, 53, 873–879.77. . . : Scr. Metall. Mater., 1995, 33, 901–905.57–63.

33. . and . : J. Mater. Sci., 1994, 29, 6231–6240. 78. . and . : Z. Metallkd., 1979, 70, 522–577.79. . . : Acta Metall., 1964, 12, 749–753.34. . and . . : Metall. T rans. A, 1989, 20,

1593–1600. 80. . . : Acta Polytech. Scand., 1964, 28, 3–20.81. . . : Z. Metallkd., 1986, 77, 472–477.35. . and . : Acta Metall., 1977, 25, 1039–1046.

36. . . , . . , . , and . . 82. . and . . : Acta Metall., 1989, 37, 1903–1911.83. . , . , and . . : Scr. Metall., 1983,: Scr. Metall., 1984, 18, 1005–1010.

37. . . . den , . , . . , and . . 17, 1435–1440.84. . and . : J. Mater. Sci., 1970, 5, 89–95.: Acta Metall., 1983, 31, 285–291.

38. . , . -, and . : J. L ess- 85. . and . . : Acta Metall., 1981, 29, 53–64.86. . , . , and . : T rans. Jpn Inst. Met., 1973,Common Met., 1981, 79, 11–26.

39. . -: PhD thesis, University of Stuttgart, 14, 82–88.87. . and . : Mater. Sci. Eng., 1975, 17, 41–50;Germany, 1980.

40. . . . : Acta Metall., 1985, 33, 579–586. 1974, 16, 239–249.88. . . and . . : Acta Metall., 1968, 16,41. . and . : Z. Metallkd., 1979, 70, 230–240.

42. . and . : Arch. Eisenhuttenwes., 1974, 45, 1239–1252, 579–585.89. . , . . , and . : Acta Metall. Mater., 1991,483–490.

43. . , . , and . -: Z. Metallkd., 1976, 39, 1489–1496.90. . and . : Z. Metallkd., 1994, 85,67, 110–117.

44. . . , . , and . . : Acta Metall., 479–486.91. . . and . : Mater. Sci. Forum, 1992,1957, 5, 310–321.

45. . : Unpublished work, Universty of Stuttgart, Germany. 94–96, 659–664.92. . and . : J. Mater. Sci., 1984, 19,46. . , . . , . . , and . : Acta Mater.,

1996, 44, 4587–4595. 3013–3020.93. . . . den and . : Scr. Metall., 1983,47. . , . , and . : Z. Metallkd., 1977, 68,

117–120. 17, 399–404.94. . and . : Metall. T rans. A, 1975, 6A, 1237–1244.48. . , . -, . , and . : Proc. 3rd

Conf. on ‘Applied mechanical engineering: Section 4: Materials 95. . , . , . . , and . : in ‘Solid–solid phase transformations’, (ed. H. I. Aaronson et al.),and materials processing (MP)’, 1–10; 1988, Cairo, Egypt,

Military Technical College. 933–937; 1982, Warrandale, PA, The Metallurgical Societyof AIME.49. . and . : J. Appl. Phys., 1970, 9, 161–173.

50. . . and . . : Acta Metall. Mater., 1994, 42, 96. . : Metallography, 1984, 17, 371–384.97. . : Metall. T rans. A, 1977, 8A, 751–761.913–919.

51. . : Unpublished result. 98. . . , . . , and . : Metall. T rans., 1972,3, 667–674.52. . . : Diploma thesis, University of Stuttgart,

Germany, 1974. 99. . . . den : T hin Solid Films, 1985, 124, 135–148.100. . , . , . , . , and . .53. . , . , and . . : Mater. Sci. Eng., 1975,

21, 131–138. : Acta Metall. Mater., 1992, 40, 997–1007.101. . . and . . : Acta Metall. Mater., 1988, 36,54. . . and . . : Fiz. Met. Metalloved.,

1970, 30, 595–601. 2827–2839.102. . : Acta Metall., 1962, 10, 525–533.55. . and . . : T rans. AIME, 1959, 215,

1033–1043. 103. . . and . . : T rans. AIME, 1966, 236,1551–1557.56. . . , . . , . . , and . .

: in ‘Precipitation from solid solution’, 449–494; 104. . , . . , and . : Acta Metall., 1974,22, 201–217.1959, Cleveland, OH, American Society of Metals.

57. . , . , and . : in ‘Solid–solid phase 105. . . : Scr. Metall., 1984, 18, 1409–1411.106. . . . , . . , and . . : Scr. Metall., 1986,transformations’, (ed. H. I. Aaronson et al.), 975–979; 1982,

Warrendale, PA, The Metallurgical Society of AIME. 20, 371–376.107. . and . : Arch. Eisenhuttenwes., 1972, 43,58. . and . : Z. Metallkd., 1955, 46, 195–197.

59. . , . , and . . : Acta Mater., 1997, 45, 721–726.108. . : Met. Mater. (Czech.), 1989, 27, 83–89.2093–2099.

60. . , . , and . : Z. Metallkd., 1976, 109. . : T rans. AIME, 1963, 227, 1411–1418.110. . and . : Arch. Eisenhuttenwes., 1972, 43,67, 57–61.

61. . . , . . , and . . : Proc. 2nd 657–663.111. . . , . . , and . . : Mater. Charact.,Federal Conf. ‘Crystal chemistry of intermetallic phases’,

80–84; 1974, Lvov, University Press of Lvov (in Russian). 1993, 30, 89–96.112. . , . , and . . c, r: Met.62. . . . den : Acta Metall., 1972, 20, 319–332.

63. . : Z. Metallkd., 1967, 58, 456–461. Sci., 1976, 10, 249–252.113. . and . : Metall. T rans., 1973, 4, 243–249.64. . , . , . , . , and . : Acta

Metall., 1986, 34, 1671–1680. 114. . : Unpublished result.115. . . : J. Appl. Phys., 1941, 12, 817–822.65. . and . : Acta Metall., 1981, 29, 1825–1830.

66. . , . , and . zur : Metall, 116. . and . : Acta Metall., 1972, 20, 1259–1268.117. . . , . . , . , and . :1968, 22, 405–411.

67. . , . , and . : Acta Metall. Mater., 1993, 41, Z. Metallkd., 1989, 80, 318–326.118. . . and . . : Metallography, 1988, 21,1293–1300.

68. . . : J. Inst. Met., 1953–54, 82, 117–128. 11–32.


Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd


119. . . and . . : Z. Metallkd., 1985, 76, 164. . and . : J. Jpn Inst. Met., 1973, 37,505–511. 571–578.

120. . and . . : Z. Metallkd., 1989, 80, 37–47. 165. . and . . : Acta Metall., 1989, 37, 1657–1666,121. and . : Acta Metall., 29, 1949–1960. 1667–1676.122. . and . . : Acta Metall., 1978, 26, 333–340. 166. . , . , and . : Bull. Himeji Inst.123. . . . and . . : in ‘Thin films and T echnol., 1992, 45, 86–96.

interfaces II’, (ed. J. E. E. Baglin), 305–310; 1984, Amsterdam, 167. . and . : Z. Metallkd., 1968, 59,Elsevier Science. 814–822.

124. . : J. Jpn Inst. Met., 1958, 22, 613–616. 168. . and . : Metall, 1967, 21,125. . . : Acta Metall., 1968, 16, 141–152. 811–821.126. . , . . , and . : Acta Metall. Mater., 169. . and . . : Acta Metall., 1955, 3, 43–54.

1995, 43, 101–106. 170. . and . . : Phys. Status Solidi (a), 1991,127. . , . , and . : Acta Metall. Mater., 123, 393–398.

1992, 40, 2289–2300. 171. . and . : Scr. Metall., 1975, 9, 1317–1320.128. . . and . . : Proc. R. Soc. (L ondon), 172. . . and . : Metall. T rans., 1971, 2, 2509–2515.

1977, A358, 335–350. 173. . c and . . : Metallurgia, 1950, 41,129. . , . , and . . : Z. 135–143, 219–222.

Metallkd., 1968, 59, 188–193. 174. . . : J. Appl. Phys., 1977, 48, 3400–3404.130. . . , . . , and . . : Acta Metall., 1987, 35, 175. . , . . , and . . : Mater. L ett., 1983,

2145–2150. 2, 155–159.131. . . and . . : Acta Metall. Mater., 1990, 38, 176. . . , . . , . . , and . .

1525–1534. : Scr. Metall. Mater., 1990, 24, 2407–2412.132. . . and . . : Acta Metall., 1985, 33, 1911–1917. 177. . : Z. Metallkd., 1965, 56, 216–221.133. . . and . . : Acta Metall. Mater., 1992, 40, 178. e. . : Phys. Met. Metallogr. (USSR), 1975,

107–111. 39, 815–820.134. . . and . . : J. L ess-Common Met., 1964, 179. e. . : Russ. Metall. (USSR), 1973, 6, 67–70.

6, 333–344. 180. . . , . . , and . . : Appl. Phys. L ett., 1986,135. . , . , and . : T rans. AIME, 1967, 49, 1381–1383.

239, 1625–1630. 181. . . and . . : T rans. AIME, 1942, 147, 300–309.136. . . and . . : T rans. AIME, 1966, 236, 182. . . and . . : in ‘Cellular precipitation in

430–435. supersaturated solid solutions’, 1–224: 1976, Kiev, Nauk137. . . . : J. L ess-Common Met., 1969, 17, 167–180. Dumka (in Russian).138. . . : T rans. AIME, 1959, 215, 1026–1032. 183. . and . : Ann. Rep. Sogoshikenjo, 1963,139. . . and . . : Proc. ‘Microscopie electronique 21, 26.

a haute tension’, 337–340; 1975, Fourth International 184. . , . , and . : Z. Metallkd., 1980, 71, 21–26.Conference, Toulouse. 185. . . , . . , . . , and . .

140. . . : ‘Diffusion and structure of metals’, 79–87; : Scr. Metall., 1979, 13, 407–412.1985, Washington, DC, National Bureau of Standards. 186. . . , . . , and . : T rans. AIME, 1952,

141. . . and . . : J. Mater. Sci., 1978, 13, 194, 609–614.1700–1708. 187. . . and . . : Acta Metall. Mater., 1993,

142. . . and . . : Scr. Metall., 1983,41, 387–398.

17, 943–946.188. . : PhD thesis, University of Stuttgart, Germany,

143. . , . -, and . : Mater. Sci. Eng., 1979,1976.

39, 15–25.189. . , . . . , and . : J. Mater.

144. . : Metall. T rans., 1970, 1, 1623–1627.Sci., 1978, 13, 1401–1410.

145. . . , . , and . : Acta Metall. Mater., 1995,190. . . , . , and . . : T rans.

43, 3113–3124.AIME, 1965, 233, 944–949.

146. . , . . , and . . : Acta Metall., 1989, 37,191. . . and . . : Metall. T rans., 1970, 1,

3367–3378.2648–2650.

147. . , . , and . : Z. Metallkd., 1978,192. . -, . , and . : J. Nucl.

69, 104–107.Mater., 1970, 36, 315–321.

148. . and . : Z. Metallkd., 1980, 71, 617–620.193. . . : J. Nucl. Mater., 1962, 7, 72–84.149. . . and . : Acta Metall. Mater., 1990, 38,194. . : J. Nucl. Mater., 1972, 44, 207–214.1871–1882.195. . , . , and . : J. L ess-Common Met., 1980,150. . . , . . , . , and . :

69, 331–353.T rans. Jpn Inst. Met., 1986, 27, 609–616.196. . . . den : Acta Metall., 1972, 20, 319–332.151. . . and . . : Metall. T rans. A,197. . . and . . : Acta Metall., 1979, 27,1983, 14A, 2560–2563.

973–977.152. . , . -, and . : Z. Metallkd., 1979,198. . . , . . , and . : J. Appl. Phys.,70, 241–246.

1970, 50, 6316–6320.153. . . : Mater. Sci. Eng. A, 1991, 138, 133–145.199. . , . . , and . . : Scr. Metall. Mater., 1993,154. . . , . , and . : Mem. Etud. Sci.

29, 817–822.Rev. Metall., 1975, 72, 159–170.200. . , . . , and . . : J. Mater. Sci., 1999,155. . . and . . : J. Vac. Sci. T echnol., 1969,

34, 773–781.6, 641–644.201. . , . , and . : Scr. Metall. Mater., 1990,156. . . and . : Z. Metallkd., 1966,

24, 1635–1640.57, 28–33.202. . : Unpublished work, University of Stuggart, Germany.157. . , . , and . : Z. Metallkd., 1974,203. . , . . , and . . : J. Mater. Sci., 1995, 30,65, 469–476.

1449–1454.158. . . : Acta Metall., 1987, 35, 747–757.204. . and . : Metall, 1969, 23, 210–216.159. . . and . . : T rans. AIME, 1960, 218,205. . : J. Inst. Met., 1953–54, 82, 463–464.507–515.206. . . and . . : J. Inst. Met., 1955–56,160. . : Diploma thesis, University of Stuttgart, Germany,

84, 423–428.1975.207. . and . : Scr. Metall. Mater., 1993,161. . . , . , . , and . :

29, 889–893.J. Phys. (France), 1988, 49, C5, 593–598.208. . . , . , and . . : Acta Metall.162. . , . , and . : Z. Metallkd., 1990,

Mater., 1994, 42, 419–433.81, 490–495.209. . . , . . , . . , . . ,163. . , . , and . : Z. Metallkd.,

1975, 66, 111–118. and . . : Mater. Sci. Eng. A, 1995, 195, 89–100.


Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd


210. . . and . . . : Acta Metall. Mater., 1990, 38, 258. . , . . , and . : Scr. Metall., 1986, 20,1423–1426.1307–1312.

259. . : ScD thesis, Massachusetts Institute of Technology,211. . . and . . : J. Dent. Res., 1977,Boston, MA, 1976.56, 335–345.

260. . . and . : Z. Metallkd., 1952, 43,212. . and . : Z. Metallkd., 1961, 52, 383–391.227–236.213. . . , . . , and . . ’: J. Biomed.

261. . . and . : Metall. T rans., 1974, 5,Mater. Res., 1973, 7, 471–480.949–951.214. . . and . : Acta Metall., 1987, 35, 2049–2062.

262. . . and . . : Acta Metall., 1974, 22,215. . . : MSc thesis, Korea Advanced Institute of Science557–562.and Technology, Seoul, Korea, 1990.

263. . . and . . : J. Inst. Met., 1959–60, 88,216. . , . . , and . . . : in Proc.209–216.‘Electron microscopy and structure of materials’, 639–646;

264. . . , . . , . . , and . .1972, Berkeley, University of California Press.: in ‘Ceramic microstructures ’86: Role of interfaces’, (ed.217. . . and . : Metall. T rans., 1970, 1, 2157–2161.J. Pask and A. G. Evans), 541–548; 1987, New York,218. .-. and . : Z. Metallkd., 1972, 63, 740–744.Plenum Press.219. . . and . . : Acta Metall., 1978, 26, 413–427.

265. . . , . . , and . . : Acta Metall., 1987,220. . and . : Z. Metallkd., 1966, 57, 130–135.35, 57–60.221. . and . : Z. Metallkd., 1954, 45, 639–642.

266. . . and . . : Acta Metall., 1986, 34, 2039–2044.222. . . , . . , . . , . .267. . . , . , and . . : Acta Metall., 1988,, and . . : Fiz. Met. Metalloved., 1971,

36, 695–699.32, 58–64.268. . . , . , and . : T rans. AIME,223. . . and . . , r: T rans. AIME, 1959,

1967, 239, 1625–1630.215, 967–976.269. . and . : J. Jpn Inst. Met., 1970, 34, 369–374.224. . , . , and . : J. Mater. Sci., 1980,270. . . : Scr. Metall. Mater., 1994, 30, 769–774.15, 2010–2016.271. . . , . , and . . : Scr. Metall. Mater.,225. . , . , and . : Z. Metallkd., 1981,

1992, 27, 1235–1239.72, 469–475.272. . . , . . , . . , and . . :226. . and . : J. Inst. Met., 1969, 97, 281–288.

Metall. T rans. A, 1983, 14A, 1561–1571.227. . and . : Metall, 1936, 15, 559–568.273. . . , . . , . c, and228. . . , . . , and . . : Fiz. Met.

. : Metall. T rans. A, 1985, 16A, 11–16.Metalloved., 1972, 34, 1213–1218.274. . . : Metall. T rans. A, 1983, 14A, 1283–1292.229. . . and . . : Scr. Metall., 1984,275. . . : Microstruct. Sci., 1977, 5, 5235–5244.18, 811–812.276. . . and . . : in Proc. 31st Annual Meeting of230. . . , u. . , and a. . : in Proc.

The Electron Microscopy Society of America, 144–146; 1973,‘European regional conference on electron microscopy’,Baton Rouge, LA, Claitors.145–146; 1964, Prague, Academy of Sciences.

277. . . : J. Mater. Sci., 1992, 27, 6481–6489.231. . and . . : J. Mater. Sci., 1974, 9,278. . . , r and . . : T rans. ASM, 1957,409–414.

49, 883–904.232. . . , . , and . . : Acta Metall.,279. . . : Scr. Metall., 1976, 10, 711–715.1981, 29, 1343–1355.280. . . : Corrosion, 1968, 24, 180–188.

233. . . : Acta Metall., 1961, 9, 216–224.281. . . , . . , and . . : Met.

234. . . and . . : T rans. AIME, 1948, 2444,Sci. Heat T reat. (Russia), 1975, 3, 8–13.

101–120.282. . . , . . , and . . : Sov.

235. . : Z. Metallkd., 1971, 62, 441–444.Phys. J., 1969, 12, 615–618.

236. . : J. Jpn Inst. Met., 1959, 23, 477–481.283. . , . , . , . , and . :

237. . and . . : Z. Metallkd., 1954, 45, 342–349.in ‘High temperature alloys: theory and design’, (ed. J. O.

238. . and . : T rans. Jpn Inst. Met., 1979, 20, 1–10.Stiegler), 359–379; 1984, Oak Ridge, TN, Oak Ridge

239. . and . . : Metall. T rans. A, 1985, 16,Laboratory.

1751–1757.284. . . , . . , and . . :

240. . and . : Acta Metall., 1975, 23, 1163–1171.J. Electrochem. Soc., 1976, 123, 1758–1760.

241. . , . . , and . : Metall. T rans., 1974,285. . , . , and . : Z. Metallkd., 1956,

5, 2457–2469. 47, 165–171.242. . . , . , and . : Z. Metallkd., 1966, 286. . . , . , . . , . , and . :

57, 521–528. Z. Metallkd., 1992, 83, 633–637.243. . . , . , and . . : Acta Metall., 287. . . and . . : Acta Metall., 1984,

1974, 22, 601–609. 32, 29–33.244. . and . : Acta Metall., 1973, 21, 1503–1514. 288. . . and . . : in ‘Solid–solid phase transform-245. . . , . . , and . . : Fiz. ation’, (ed. H. I. Aaronson et al.), 963–967; 1982, Warrendale,

Met. Metalloved., 1975, 39, 1275–1283. PA, The Metallurgical Society of AIME.246. . , . , and . : Z. Metallkd., 289. . , . . , and . . : Scr.

1976, 67, 467–472. Metall. Mater., 1992, 26, 1599–1604.247. . . , . . , . . , and . . 290. . and . . : Metall. T rans. A,

: Fiz. Met. Metalloved., 1969, 27, 127–134. 1993, 24A, 2773–2785.248. . and . : J. Mater. Sci., 1974, 9, 1775–1780. 291. . and . : Z. Metallkd., 1978, 69, 43–49.249. . . , . . , . . , . . 292. . . : Mater. Sci. Eng. A, 1984, 63, 111–119.

, and . : Scr. Metall. Mater., 1992, 26, 293. . . , . . , . . , and . . : Am. Ceram.901–906. Soc. Bull., 1986, 65, 1390–1392.

250. . . and . . . : J. Iron Steel Inst., 1972, 294. . . : J. Mater. Sci., 1978, 13, 2339–2346.210, 691–697. 295. . . , . . , . . , and . . :

251. . : Phys. Status Solidi (a), 1974, 26, K5–K9. J. Geophys. Res., 1986, 91, 12723–12741.252. . and . . : Z. Metallkd., 1977, 68, 712–718. 296. . . , . . , and . . . : Ceram. Int., 1990,253. . : T rans. ASM, 1951, 43, 70–104. 16, 151–155.254. . . and . : Acta Metall., 1971, 19, 1133–1141. 297. . . , . . . , . . , and . . : Ceram.255. . , . , and . : J. Jpn Inst. Met., 1991, T rans., 1994, 41, 35–51.

55, 353–359. 298. . and . : in ‘The electron microprobe’, (ed.256. . . , . , and . . : Acta Metall., 1975, 23, T. D. McKinly), 642–652; 1966, New York, Wiley.

1313–1320. 299. . . and . . : in ‘High-temperature ordered257. . . : Acta Metall., 1979, 27, 1135–1145, intermetallic alloys IV’, (ed. L. A. Johnson et al.), 449–454;

1991, Pittsburgh, PA, Materials Research Society.1147–1155.


Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd


300. . . : Acta Metall. Mater., 1994, 42, 2775–2781. 344. . , . , and . : in ‘Fundamentals of grainand interface boundary diffusion’, 3rd edn, 303–375; 1995,301. . . , . . , . . , . . , and . . :

J. Am. Ceram. Soc., 1990, 73, 1979–1982. Chichester, Wiley.345. . : Acta Metall., 1955, 3, 55–63.302. . . and . . : J. Am. Ceram. Soc., 1991, 74,

1397–1400. 346. . . and . . : Scr. Metall., 1968, 2, 1–7.347. . . : Metall. T rans., 1973, 4, 1919–1934.303. . . , . . , and . . : Acta Metall., 1985, 33,

1907–1910. 348. . . : Acta Metall., 1968, 16, 1413–1427.349. . : Z. Metallkd., 1991, 32, 96–98.304. . . and . . : J. Am. Ceram. Soc., 1985,

68, 197–202. 350. . . , . , and . . :J. Mater. Sci., 1974, 9, 240–244.305. . . : J. Am. Ceram. Soc., 1991, 74, 387–394.

306. . , . . , and . . : J. Am. Ceram. 351. . , . , . : Arch. Metall., 1986,31, 287–304.Soc., 1986, 69, 243–248.

307. . . , . . , and . . : J. Am. Ceram. Soc., 352. . . , . . , and . . : Scr. Metall.,1980, 14, 539–543.1992, 75, 2659–2664.

308. . . , . . , and . . : Acta Metall. Mater., 353. . : Metallography, 1984, 17, 371–382.354. . , . . , and . . : J. Mater. Sci., 1996, 31,1991, 39, 1275–1279.

309. . : Z. Metallkd., 1961, 52, 564–571. 2401–2407.355. . . and . . : T rans. AIME, 1968, 242,310. . : Scr. Metall., 1976, 10, 649–643; 1979, 13, 413–416.

311. . , . . , and . . : in ‘Solid–solid 1563–1568.356. . : Z. Metallkd., 1971, 62, 324–325.phase transformations’, (ed. W. C. Johnson et al.), 521–526;

1994, Warrendale, PA, The Minerals, Metals and Materials 357. . and . : Acta Metall., 1976, 24, 639–650.358. . , . , and . : Scr. Metall. Mater., 1993,Society.

312. . . : Scr. Metall., 1973, 7, 1043–1046. 29, 1593–1596.359. . : Scr. Metall., 1979, 13, 785–790, 791–794.313. . : Acta Metall., 1968, 16, 563–577.

314. . . . and . . : Acta Metall., 1969, 17, 360. . and . . : J. Mater. Sci. L ett., 1994, 13, 62–64.361. . . and . . : Acta Metall., 1990, 38,1379–1393.

315. . . and . . : Acta Metall., 1976, 24, 343–352. 1255–1262.362. . , . . , and . . : Acta Metall. Mater.,316. . : Z. Metallkd., 1975, 66, 488–491.

317. . : Metall. T rans., 1972, 3, 2717–2727. 1993, 41, 1183–1188.363. . and . : Z. Metallkd., 1965, 56, 421–437.318. . , . . , and . : J. Mater. Sci., 1991, 26,

4888–4892. 364. . . and . . : T rans. AIME, 1959, 215,967–976.319. . and . : Metallography, 1978, 11,

481–485. 365. . and . : Z. Metallkd., 1968, 59, 777–781.366. . and . : Arch. Eisenhuttenwes., 1973, 44,320. . . , . . , . , and . : Scr.

Metall., 1986, 20, 25–28. 395–401.367. . and . : Acta Metall., 1957, 5, 628–637.321. . and . . : J. Mater. Sci. L ett., 1990, 9, 1226–1228.

322. . , . , . , and . : Phys. Status 368. . . : Acta Metall., 1956, 4, 421–432.369. . . and . : J. Inst. Met., 1973, 101, 111–115.Solidi (a), 1990, 119, K19–K23.

323. . . and . : Acta Metall., 1967, 15, 369–376; 370. . and . . : Met. Sci. J., 1972, 6, 167–174.371. . . and . . : Metall. T rans., 1972, 3,1317–1323.

324. . . and . . : Phys. Met. Metallogr. 1521–1528.372. . . , . . , . , and . :(USSR), 1981, 52, 998–1004.

325. . . and . . : Metall. T rans, 1972, 3, J. Mater. Sci., 1990, 25, 391–398.373. . , . , . , . , and2757–2767.

326. . , . , and . . : . : Arch. Metall., 1987, 32, 421–426 (cited afterRef. 372).Acta Metall., 1982, 30, 1147–1156.

327. . . : in ‘Materials science and technology – a compre- 374. . . , . . , and . . : Scr. Metall.,1974, 8, 493–496.hensive treatment’, Vol. 5, ‘Phase transformations in mater-

ials’, (ed. R. W. Cahn et al.), 308–338; 1991, Weinheim, VCH. 375. . and . : Z. Metallkd., 1997, 88, 37–41.376. . and . : Z. Metallkd., 1995, 86, 256–259.328. . . : Acta Metall., 1959, 7, 18–28.

329. . . : in ‘Physical metallurgy’, 4th edn, (ed. R. W. 377. . and . : Metall, 1934, 13, 317–320.378. . . and . . : in Proc. 37th AnnualCahn and P. Haasen), 1451–1468; 1996, Amsterdam,

Elsevier Science. Meeting of The Electron Microscopy Society of America, 646;1979, Baton Rouge, LA, Claitors.330. . : T rans. AIME, 1946, 167, 550–595.

331. . . and . . : Metall. T rans., 1972, 3, 379. . . : J. Appl. Phys., 1949, 20, 666–668.380. . and . : J. Jpn Inst. Met., 1964,2777–2796.

332. . . , . . , and . . : Met. Sci., 1979, 28, 513–521.381. . and . : J. Jpn Inst. Met., 1971, 35, 261–268.13, 20–24.

333. . and . : J. Mater. Sci., 1971, 6, 208–212. 382. . and . : Mater. Sci. Eng., 1975, 19, 217–229.383. . , . , and . : J. Jpn Inst. Met., 1980,334. . . , . . , and . : in ‘Phase transformations’,

Vol. 2, II/22–II/24; 1979, London, The Institution of 44, 170–174.384. . . and . : Mater. Sci. Eng., 1976,Metallurgists.

335. . : in ‘The mechanism of phase transformations in 24, 143–152.385. . : J. Jpn Inst. Met., 1965, 29, 454–459, 460–466.crystalline solids’, 231–247; 1969, London, The Institute of

Metals. 386. . , . , and . : J. Jpn Inst. Met., 1976, 40,1105–1110.336. . . and . : Acta Metall., 1969, 17, 1263–1279.

337. . , . . , and . : in ‘Decomposition of 387. . and . : J. Jpn Inst. Met., 1976, 41, 791–795.388. . and . : J. Jpn Inst. Met., 1975, 39, 817–825.alloys: the early stages’, (ed. P. Haasen et al.), 208–213; 1984,

Oxford, Pergamon Press. 389. . and . : J. Jpn Inst. Met., 1976, 40, 419–425.390. . . : in ‘The mechanism of phase transformations in338. . : Metall. T rans., 1972, 3, 2729–2741.

339. . : Acta Metall., 1982, 30, 1689–1696. crystalline solids’, 16–21; 1969, London, The Insitute ofMetals.340. . . , . . , and . . : Acta Metall. Mater.,

1992, 40, 2177–2184. 391. . and . : Arch. Eisenhuttenwes., 1973, 44,395–401.341. . and . . : J. Mater. Sci. L ett., 1990, 9, 854–856.

342. . , . . , . , and . . : Z. Metallkd., 1995, 392. . , . , and . : Z. Metallkd., 1974,65, 727–630.86, 401–404.

343. . , . . , and . : in ‘Decomposition of 393. . and . : Z. Metallkd., 1969, 60, 475–481.394. . and . : Scr. Metall., 1993, 29,alloys: the early stages’, (ed. P. Haasen et al.), 208–213; 1984,

Oxford, Pergamon Press. 889–893.


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395. . . , . , and . : Acta Mater., 1997, 45, 420. . , . , and . : Z. Metallkd., 1997, 88,425–428.4397–4413.

421. . . : Acta Metall., 1969, 17, 407–418.396. . and . : Arch. Metall., 1991, 36, 25–64.422. . . , . , . , and . . :397. . . and . . : T rans. AIME, 1950, 188,

Mater. Sci. Eng. A, 1989, 112, 175–183.1229–1236.423. . . and . . : Nature, 1938, 141, 413.398. . and . : Mater. Sci. Eng., 1978, 32, 17–25.424. . . and . : Scr. Metall. Mater., 1994, 30, 509–514.399. . and . : Z. Metallkd., 1977, 68, 772–778.425. . . and . . : in ‘Interfaces in crystalline400. . . , . , and . . : Acta Metall.,

solids’, 514–521; 1995, Oxford, Clarendon Press.1988, 36, 1511–1520.426. . . , . . , . . , and . . : Acta Mater.,401. . , . , and . : J. Mater. Sci.,

1996, 44, 1793–1799.1991, 26, 2851–2856.427. . , . , . , . , and . .402. . . : Acta Metall., 1986, 34, 1279–1287.

: Scr. Metall. Mater., 1992, 26, 895–900.403. . . : PhD thesis, Indian Institute of Technology,428. . . and . . : T hin Solid Films, 1980,Kharagpur, 1997.

65, 125–135.404. . . and .-. : Scr. Metall., 1989, 23, 257–261.429. . . and . . : Acta Metall., 1958, 6, 428–438.405. . and . : Acta Mater., 1996, 44, 353–365.430. . , . , and . . : Z. Metallkd., 1994,406. . : Acta Mater., 1998, 46, 369–377.

85, 50–51.407. . and . : Mater. Sci. Eng. A, 1989, 108, 9–17.431. . , . . , and . : Acta Metall. Mater.,

408. . . : Mater. Sci. Eng. A, 1986, 83, 255–267.1994, 42, 3843–3854, 3855–3863.

409. . : PhD thesis, University of Stuttgart, Germany, 1981.432. . and . : Mater. Sci. Forum, 1999, 294–296,

410. . and . . : Acta Metall., 1987, 35, 2157–2165.145–148.

411. . and . : Acta Metall., 1982, 433. . and . : Acta Mater., 1999, 47, 2641–2650.30, 37–50. 434. . : Proc. 9th Int. Conf. on ‘Electron microscopy of

412. . and . : Acta Metall. Mater., solids’, (ed. A. Czyrska-Filemonowicz et al.), 545–548; 1996,1990, 38, 135–141. Cracow-Zakopane, Poland, Fotobit.

413. . and . : Z. Metallkd., 1990, 81, 278–281. 435. . , . , and . : Scr. Mater., 1997, 37,414. . , . , . , . , and . : 119–124.

Scr. Mater., 1996, 34, 1431–1436. 436. . . : Mater. Sci. Eng., 1975, 21, 211–220.415. . . and . . : Scr. Metall., 1987, 437. . and . : Acta Metall. Mater., 1990, 38,

21, 371–376. 2283–2286.416. . and . : Scr. Metall. Mater., 1994, 30, 438. . . and . : T rans. AIME, 1969, 245,

1177–1181. 1821–1824.417. . and . : Scr. Mater., 1998, 39, 13–20. 439. . : Philos. Mag., 1973, 28, 867–890.418. . and . : Interface Sci., 1998, 6, 307–315. 440. . . , . . , and . . : Metall. T rans.,

1973, 4, 827–834.419. . and . : Scr. Metall., 1986, 20, 1653–1656.


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