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10.4.3 Grain Boundary Diffusion of Oxygen in the

YBa

7x

Superconductor

As mentioned in Sec. 10.3, oxygen (

O) diffusion in YBCO lattice

is much faster than cation diffusion due to a preponderance of vacan-

cies in the basal plane; hence only vacancy migration energy is

required. Hence enhanced grain boundary diffusion of oxygen is gen-

erally not expected. However, enhanced grain boundary diffusion of

oxygen in polycrystalline YBCO by 3 to 4 orders of magnitude has

been reported.

[50–52]

Extensive SIMS studies of oxygen diffusion and

surface exchange kinetics in single-crystal and polycrystalline

YBa

7x

superconductor have been carried out by Claus et al.,

[52]

who also discuss the results of earlier investigations.

[50–51]

Figure 10.17

shows the results of their grain boundary diffusion of oxygen in poly-

crystalline YBa

7–x

and compares them with those in its lattice.

For easy comparison, d  1 nm has been taken out from the measured

combined grain boundary diffusion parameters, sdD

, obtained by

Claus et al. The oxygen diffusion data in the lattice and the grain

boundaries are listed in Tables 10.2 and 10.3, respectively.

Enhancement of grain boundary diffusion of oxygen is clearly seen in

Fig. 10.17, accompanied by larger values of sdD

and Q

of 4  10

12

and 135 kJ/mol, respectively. Figure 10.16 compares grain boundary

diffusion of

O by Claus et al.

[52]

with the

110

Ag tracer in YBCO and

PNN-PT-PZ perovskites. Oxygen grain boundary diffusion data in the

YBCO show a similar trend, implying a segregation effect similar to

that discussed for Ag cation grain boundary diffusion in YBCO and

PNN-PT-PZ. Larger values of sdD

and Q

for

O diffusion may be

attributed to s W1 and its accompanying temperature dependence,

respectively. However, unlike Ag, oxygen is not an extrinsic impurity.

It is indeed an integral part of the superconducting YBCO. Thus a

combined pre-exponential factor sdD

of the order of 10

15

/s and

 100 kJ/mol would have been expected. The oxygen segregation

effect may actually stem from its interaction with the likely presence

of second-phase domains and amorphous material at the grain bound-

aries, as proposed by Sabras et al.

[50, 51]

The presence of second-phase

particles of BaCO

, CuO, and carbides has been confirmed by AES and

SIMS studies by Claus et al.

[52]

The YBCO is known to be prone to

uptake of CO

and moisture during its exposure to the ambient and in

the handling process, which could account for its presence in the grain

boundaries. In any event, faster-than-lattice grain boundary diffusion

of oxygen in polycrystalline YBCO has been observed.

522 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

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DIFFUSION IN SOME PEROVSKITES, GUPTA 523

Figure 10.17 Comparison of

O diffusion in the YBa

7x

lattice and grain

boundaries. For an adequate comparison, d  1 nm is removed from the meas-

ured combined coefficients sdD

shown in Fig. 10.16. References are shown in the

brackets.

Ch_10.qxd 11/12/04 4:32 PM Page 523

10.5 Summary

Alarge body of data now exists in the literature on diffusion of cations

and anions in a variety of high-temperature superconducting cuprates and

some perovskites, which are reviewed and critically discussed in this

chapter. Diffusion data are available on the YBa

7x

superconductor

of the constituent cations, Cu, Ba, and Y, and also of the impurity Ni, Co,

Ag, and Zn cations. Self-diffusion of Cu takes place largely on the Cu

sites through thermal vacancies with an activation energy of 255 kJ/mol.

Self-diffusion of Ba and Yatoms also takes place on their respective sites

and is characterized by much larger activation energies, in the 900 to

1000 kJ/mol range, because they are deeply embedded in the lattice. The

large values of activation energies for Ba and Y reflect the difficulty of the

diffusion process due to long atomic-jump distances and the lack of

vacancies in which jumps can occur. The Ni, Co, Ag, and Zn impurity

cations have diffusion parameters similar to the Cu self-diffusion in

YBa

7x

because they all replace Cu. Some effect of ion charge is

seen in the case of heterovalent cations. Extensive diffusion data on the

anion species (O) also exist in about a dozen high-temperature supercon-

ducting cuprates, which are compiled and compared. The oxygen diffu-

sion data show scatter of many orders of magnitudes. This is attributed to

several factors, notably, the deviation from stoichiometry and the atomic

arrangements in the various Cu-O planes, which differ from material to

material. These factors, in fact, determine the upper and lower limits of

the diffusion data. Acomparison is also made between the diffusion kinet-

ics of the cation and anion species. Asemi-empirical relationship between

cation and anion diffusion processes is shown to hold through the activa-

tion energy and entropy of motion for vacancies responsible for diffusion

of the various species. Effects of diffusion and reaction between the

YBa

7x

films and the substrates are discussed. Finally, grain bound-

ary diffusion of several cations and the oxygen anion is briefly reviewed.

Acknowledgments

The author is indebted to Drs. S. J. Rothman and J. L. Routbort for

fruitful discussions and exchange of views on the subject matter discussed

in this chapter over a period of a decade. They have pioneered much of

the data and the concepts discussed, and permission to use them here is

gratefully acknowledged. Much of the material presented in this chapter

is reproduced from an earlier article by the author published in Metals,

Materials and Processes,11:233–246 (1999), with permission of Meshap

Science Publishers, Mumbai, India.

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DIFFUSION IN SOME PEROVSKITES, GUPTA 525

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Index

density–of–state effect 321

diffusion:

activation volume 17, 47, 79, 94

alloys 149

amorphous metallic alloys 60–63

anisotropy in grain boundary 44

atomistic simulation 113

bulk metallic glasses 63

coefficients in metals (Table1.1) 13

computer modeling 113

correlation factor (f) 11–12, 14–17

enthalpy 69

epitaxial thin films 37

free energy 69

frequency 97

Gaussian solution 4, 34, 498, 503

grain boundary 21–26, 145, 155

impurity 14, 87

Instantaneous source condition 4

interdiffusion coefficient 6–8

interstitials 9,47

isotope effect (DE) 18–20

kinetic factors (DK) 19

linear chemical 20

mass dependence 19

mechanism 8, 44, 145,155,157

modulated thin films 26

nonlinear chemical 23–25

polycrystalline bulk 32–34

polycrystalline thin films 37

pressure dependence 17

single crystals 8

thick–layer Geometry 5

under chemical gradient 6

diffusion barriers:

alloying of Cu 249, 269

APDB 235–239, 241–245, 271

borides 243, 260

carbides 243, 260

controlled microstructure 248

characteristics 240

electric field 259

free energy 258

heat of formation 258

high melting 242–243

ILD 240, 262, 275

impurity segregation 249–250

in Al technology 242, 248–250, 260, 272

in Cu technology 240, 248, 262

interdiffusion 246–247

accelerated dynamics: 162, 164–165

Arrhenius dependence:

lattice diffusion 12

grain boundary diffusion 32

solute segregation 52

atomic vibrations:

collective mechanisms 138, 140

entropy of 132

free energy of 122

frequency 123

harmonic approximation 122–125

local harmonic approximation

124–125,127

quasiharmonic approximation 128

back stress 386

Boltzmann–Matano Analysis 6

Borisov’s conjecture 48

bulk Properties 71

bulk modulus 87

compressibility 95

vacancy formation energy 70–73

melting point 70–71

volume thermal expansion coefficient

94–96

cap layer 379

chemical interactions 252, 330, 335–336,

353

condensation coefficient 6

cohesive energy 71,88

Coble creep 379

constrained diffusional creep 394

cracking of films 399

creep 379, 393–396

critical nucleus 330, 352

critical shear stress 383

damascence process:

single 461

dual 435, 462

Debye temperature 87

decagonal quasicrystals 57–60, 68

delamination of films 399

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530 INDEX

low-k 275

multilayer barriers 242, 261–262

nitrides 243, 260

phase diagram 250, 256

SAM 270

solid solubility 250–252

temperature effect 259

thin–film reactions 255

zero–Flux planes 272

dislocation in thin films:

core spreading 391–392

interfacial 383

parallel glide 396

pileup 381

thermally activated glide 385

channeling/theading 382

elastic anisotropy in films 367–368

elastic constants 82

elastic strain energy 54

electric field 243, 253, 265–266, 270

electromigration in copper films:

activation energy 425, 426

alloying effect 428

ambient effect 427

atomic flux 417

backflow 418

bamboo grain structure 412, 422,460

blocking boundaries 419 470

bulk diffusion 405

current density dependence 453

diffusion barriers 406

dual-damascene 474

drift velocity 414–415, 417

effective charge 415, 417, 426

effective diffusivity 416

electron wind 415

failure physics 406

fast diffusion paths 406 422

grain boundary diffusion 405, 415–416

grain thinning 459

interface diffusion 405, 474

Joule heating 453, 458

life time scaling rules 461

life time statistical distribution 433,

440–450

linewidth dependence 456

log-normal life time 411, 433

metal liner 405

microstructure 411, 412, 422, 460

multiple log-normal 419, 422, 454, 456, 463

reservoir effect 406

short line length 468

stress gradient 418

surface diffusion 423

test structure 409

texture 411

void growth 419, 422, 454, 463

electron microscopy 49, 332, 352, 404,

416, 486

electron–to–atom ratio 91

embedded–atom method 114

embedded–cluster method 125–126, 152

embedded–defect method 115

enthalpy of formation 279

entropy of mixing effects 306

fatigue 399

Fermi energy 91

Fick’s first law 2

Fick's second law 3,339, 347–348

Fick’s law, difficulties 286

first–principles calculations 118

film passivation 379

film/substrate interface 382–383

fluoropolymers 349, 353

Frenkel defect 12

germanides:

Co 320

Ti 316

grain boundary:

diffusion 21–26, 28,

energy 49–50,

Grüneisen relation 99–103

Harrison's kinetic regime 28–29

hyperdynamics 162–163

high temperature super conductors:

anion (o) diffusion 503

anion-grain boundary diffusion 516

anion- grain boundary segregation

516–517

Ba self-diffusion 494

cation/anion diffusion comparison 507

Cu self-diffusion 492

film/substrate interaction 487

grain boundary diffusion-anion 505

grain boundary diffusion-cation 509–515

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INDEX 531

grain boundary doping 509–510

grain boundary segregation 514

impurity cation diffusion 497

impurity cation diffusion-charge effect 501

lattice structure 595

Ni diffusion in single crystals 501

Oxygen diffusion parameters 505

Y self-diffusion 492

icosahedral solids 57–60

immobilization 328–329, 341, 345,

347–351, 353

ions 241, 336–337, 351–352, 507–508

interconnection integration 407

intermetallic compounds:

Al-Co 285

NiAl:

diffusion mechanism 182–184, 210,

213

grain boundary diffusion 229

interdiffusion 210

self-diffusion 205

solute diffusion 212

state of defects 180

Al:

diffusion mechanism 184,

189–193,195

grain boundary diffusion 225

interdiffusion 193–195

self-diffusion 189

solute diffusion 195

TiAl:

diffusion mechanism 187–188

grain boundary diffusion 229

interdiffusion 203–204

self-diffusion 199

solute diffusion 204–205

Fe-Al:

diffusion mechanism 216–218

grain boundary diffusion 232

interdiffusion 219

self-diffusion 213–218

solute diffusion 212

state of defects 180

melting :

entropy of fusion 75

latent heat 71–73

melting point 75

metallic glasses 60–63

micro–tensile testing 380

minimum energy path 139

modified embedded atom method 118

molecular dynamics: 153

accelerated dynamics 162

hyperdynamics 162

parallel replica dynamics 163

temperature–accelerated dynamics 164

Monte Carlo method: 143

kinetic 143

on–the–fly 150–151

Monte Carlo simulations 113–114, 118,

143, 150–151, 190,

Nernst–Einstein equation 75, 285, 415

polymer-metal nucleation 336

nudged elastic band method 141

ordered Cu

Au rule 47, 294, 301

parallel glide 389–391

passivation 379, 404, 412

phase growth:

amorphous phases 315

Au-Cu 309

Co-Au 297

Cu6Sn5 300

first phase formed 294

formation energies 297, 301

grain boundary diffusion in 293, 307

impurity effect 307

lattice diffusion in 293

linear-parabolic kinetics 290

metastable phases Ni-Al 304

metastable phases NiSi 309

nucleation controlled NiSi2 301

nucleation controlled TiSi2 315

parabolic 285

reaction constants 292–293

sequential 292, 301

single 284

two 287

photoelectron spectroscopy 337, 342

piezoelectric ceramics:

cation-ion diffusion 502

grain boundary diffusion 509

grain boundary segregation 41, 52, 54, 514

point defects: 9–12,47

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