441 25.8 Products of solubility× effective diffusivity × correlation factor for Cu, Ag, and Au diffusion in Ge with various dislocation densities compared to the Ge tracer diffusivity accord
Trang 1632 List of Figures
25.6 Diffusion profiles of substitutional Zn (Zns) at 1021◦C for
various diffusion times according to Bracht et al [17] Top: Dislocation-free Si wafers; solid lines show calculated profiles
based on the kick-out model using one set of parameters C eq
s and C I eq D I Bottom: Highly dislocated Si; solid lines show
fitting with complementary error functions 438 25.7 Comparison of Cu penetration profiles in almost dislocation-free
Ge (1126 K, 900 s) and in a crystal with high dislocation density (1124 K, 780 s) according to [17] 441 25.8 Products of solubility× effective diffusivity × correlation factor
for Cu, Ag, and Au diffusion in Ge with various dislocation
densities compared to the Ge tracer diffusivity according to [17] 442 25.9 Penetration profile of60Co in Nb after 10.3 days of annealing
at 1422 K in double-logarithmic representation according to [34] 444 26.1 Ionic conductivity of halide crystals The corresponding
activation enthalpies are listed For comparison the conductivity
of the fast ion conductor RbAg4I5is also shown 450 26.2 Examples of point defects in ionic crystals: Schottky defects,
Frenkel defects, divalent cation impurity and cation vacancy,
complex of divalent cation and cation vacancy, vacancy pair 451 26.3 Schematic diagram of charge diffusivity, D σ, and tracer
diffusivities of anions and cations, D ∗
A and D ∗
C, in alkali halides
Parallel lines in the extrinsic region correspond to different
doping contents Ci 462 26.4 Conductivity of a NaCl single crystal doped with a site fraction
of 1.2 × 10 −5 Sr2+ ions according to Beni`ere et al.[22] 463 26.5 Self-diffusion of22Na and36Cl in intrinsic NaCl Also indicated
is the product of charge diffusion coefficient Dσ and correlation
factor fV = 0.781 From Laskar [15] 464
26.6 Diffusion of the homovalent impurities Cs, Rb F, I, and Br in NaCl according to [32–34] Self-diffusion of Na and Cl is also
indicated for comparison 466 26.7 Concentration dependence of the diffusion coefficient of divalent
cations, D2, relative to its saturation value, D2(sat), according
to [39] The curves refer to three values of the association
enthalpy, ∆G iV C , normalised with kBT 467
26.8 Left : migration of interstitial Ag+ions via the direct interstitial
and by the interstitialcy mechanism Right : pathways for
Ag+ movements by the colinear (double arrows) and the
non-colinear (solid arrows) interstitialcy mechanism 469
26.9 Tracer self-diffusion coefficients for the constituents of
AgCl [41] and AgBr [24, 42] Dσ was calculated from the ionic conductivity via the Nernst-Einstein relation [37] 470
Trang 2List of Figures 633 26.10 Schematic illustration of the effect of divalent cationic impurity doping on the temperature dependence of the conductivity of AgCl 471 26.11 Schematic illustration of the effect of divalent cationic impurity
doping on the isothermal conductivity of AgCl The dashed
lines represent the effect of anionic impurity doping 472
27.1 Electrical dc conductivity of several fast ion conductors Some ordinary solid electrolytes and concentrated H2SO4 are shown for comparison 476 27.2 Crystal structure of α-AgI Large circles: I − ions; filled small
circles: octahedral sites; filled squares: tetrahedral sites; filled triangles: trigonal sites Octahedral, tetrahedral, and trigonal
sites can be used by Ag+ions 478 27.3 Probabiliy distribution of Ag in α-AgI at 300 ◦C according to
Cava, Reidinger, and Wuensch[42] 478 27.4 Cation pathway in an fcc anion sublattice according to
Funke[19] Filled squares: tetrahedral sites; small filled circles:
octahedral sites 479 27.5 Fluorite structure (prototype CaF2): Filled circles represent
anions and open circles cations Diamonds represent sites for
anion interstitials 481 27.6 Perovskite structure 482 27.7 Sites for Na+ ions in the conduction plane of β-alumina.
m: mid-oxygen position, br: Beevers-Ross site, abr:
anti-Beevers-Ross site Open circles: O2− , grey circles: O2− spacer
ions 483 27.8 Conductivities of some single crystal β-aluminas according to
West[45] 484 27.9 Schematic illustration of ion solvation and migration in
amorphous polymer electrolytes according to [62] 487 27.10 Tracer diffusion coefficients of22Na and125I in an amorphous PEO–NaI polymer electrolyte compared to the charge
diffusivity, D σ, according to Stolwijk and Obeidi [62, 63]
The dashed line is shown for comparison: it represents the sum
D(22Na) + D(125I) 487 28.1 X-ray diffractogram of a crystal (left ) and of a glass (right ) 493
28.2 Volume (or enthalpy) versus temperature diagram of
a glass-forming liquid 495 28.3 Differential Scanning Calorimetry (DSC) thermogram of
a 0.2(0.8Na2O 0.2 Rb2O) 0.8B2O3 glass measured at a heating rate of 10 K/min from [9] The glassy and undercooled liquid
state are indicated The strong exothermic signal (near 650◦C)
corresponds to the crystallisation of the undercooled melt 496
Trang 3634 List of Figures
28.4 Schematic time-temperature-transformation diagram (TTT
diagram) for the crystallisation of an undercooled melt 497 29.1 Structure of an ordered binary crystalline solid (schematic) 503 29.2 Structure of a binary metallic glass (schematic) 504 29.3 Schematic illustration of structural relaxation in the V-T (or
H-T) diagram of a glass-forming material 507 29.4 Time-averaged diffusivities 59Fe in as-cast Fe40Ni40B20
as functions of the annealing time according to Horvath and Mehrer [23] 508 29.5 Instantaneous diffusivities D(t) of several conventional metallic
glasses as functions of annealing time according to Horvath
et al [24] 509 29.6 Arrhenius diagram of self- and impurity diffusion in relaxed
metal-metalloid and metal-metal-type conventional metallic
glasses according to Faupel et al [37] 510 29.7 Arrhenius diagram of tracer diffusion of Be, B, Fe, Co, Ni, Hf in the bulk metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5 (Vitreloy4) according to Faupel et al [37] 511 29.8 Arrhenius diagram of tracer diffusion of B and Fe in
Zr46.75Ti8.25Cu7.5Ni10Be27.5 (Vitreloy4) according to Faupel
et al [37] Open symbols: as-cast material from [31]; filled
symbols: pre-annealed material from [39] 512
29.9 Correlation between D0 and ∆H for amorphous and crystalline metals according to [37] Solid line: conventional metallic
glasses; dotted line: bulk metallic glasses; dashed line: crystalline
metals 513 29.10 Pressure dependence of Co diffusion in Co81Zr19 at 563 K
according to [37] The dashed line would corresponds to an
activation volume of one atomic volume 514 29.11 Isotope effect parameter as function of temperature for Co
diffusion in bulk metallic glasses according to [37]; data taken from Ehmler et al [46, 47] 515 29.12 Chain-like collective motion of atoms in a Co-Zr metallic glass according to molecular dynamics simulations by Teichler [55] 516 29.13 Tracer diffusion coefficients of P and Co in comparison with
viscosity diffusion coefficients of the alloy Pd43Cu27Ni10P20
according to Bartsch et al [58] 518 30.1 Viscosity of a soda-lime-silicate glass (standard glass I of
the Deutsche Glastechnische Gesellschaft, DGG) Particular
viscosity points are indicated 524 30.2 Schematic fragility diagram for various melts 526
Trang 4List of Figures 635 30.3 Diffusion penetration profiles of 22Na obtained by grinder
sectioning (left ) and of86Rb obtained by sputter sectioning
(right ) according to Imre et al [14] 527
30.4 Conductivity (real part) of a soda-lime silicate glass (standard
glass I of DGG) versus frequency for various temperatures
according to Tanguep-Nijokep and Mehrer [15] 528 30.5 Permeability of gases through vitreous SiO2 according to
Shelby[2] 530 30.6 Diffusion in vitreous silica and in quartz (for references see text) 531 30.7 Structure of a soda-lime silicate glass (schematic in two
dimensions) 533 30.8 Viscosity diffusion coefficient, Dη, tracer diffusivities, D ∗
N a,
D ∗
Ca , and charge diffusion coefficient Dσ, of soda-lime
silicate glass (standard glass I of DGG) according to
Tanguep-Nijokep and Mehrer[15] 533 30.9 Tracer diffusivities, D ∗
N a , D ∗
Ca, and charge diffusion coefficient,
D σ, of soda-lime silicate glass (standard glass II of DGG)
according to Tanguep-Nijokep and Mehrer [15] 534 30.10 Haven ratios of soda-lime silicate glasses according to
Tanguep-Nijokep and Mehrer[15] 536 30.11 Structure of sodium-rubidium borate glass (schematic in two
dimensions) 537 30.12 Glass-transition temperatures of alkali borate glasses according
to Berkemeier et al [28] 537 30.13 Arrhenius diagram of the dc conductivity (times temperature) for Y Na2O (1-Y)B2O3 glasses according to Berkemeier
et al.[28] 538 30.14 Electrical dc conductivity of Li, Na, K, and Rb borate glasses according to Berkemeier et al [28] 538
30.15 Charge diffusion coefficient Dσ of mixed 0.2 [X Na2O
(1-X)Rb2O] 0.8 B2O3 glasses according to Imre et al [29] 539 30.16 Composition dependence of the activation enthalpy for
conductivity diffusion of Fig 30.15 [29] 540 30.17 Composition dependence of22Na and86Rb diffusion in mixed 0.2[X Na2O(1-X)Rb2O]0.8 B2O3 glasses according to Imre
et al.[14] Na diffusion: full symbols; Rb diffusion: open
symbols 540
30.18 Composition dependence of the charge diffusion coefficient,
D σ, and of the mean tracer diffusion coefficient,
Na-Rb borate glasses 0.2[X Na2O (1-X)Rb2O]0.8 B2O3 541 31.1 Schematic illustration of high-diffusivity paths in a solid 547 31.2 Schematic illustration of the diffusion spectrum for metals in
a reduced temperature scale; Tmdenotes the melting temperature549
Trang 5636 List of Figures
32.1 Tilt boundary (left ) and twist boundary (right ) 555
32.2 Low-angle tilt boundary after Burgers [19] 556 32.3 Random high-angle grain boundary (schematic) 556 32.4 A coherent twin boundary (left ) Twin-boundary energy γ as
a function of the orientation φ of the grain-boundary plane
(right ) 557
32.5 A special large-angle boundary according to Gleiter [24] 558 32.6 A high-resolution transmission electron microscope image of
a (113)[113] symmetric tilt boundary in gold according to
Wolf and Merkle[25] 558 32.7 Fisher’s model of an isolated grain boundary D: lattice
diffusivity, Dgb: diffusivity in the grain boundary, δ:
grain-boundary width 559 32.8 Isoconcentration contours for various values of the Le Claire
parameter β 562
32.9 Concentration contours for constant source (left ) and
a thin-film source solutions (right ) for an arbitrary value of
β = 50 according to Suzuoka [30] 564
32.10 Illustration of the type A, B, and C diffusion regimes in
a polycrystal according to Harrisons classification [38] 569 32.11 Schematic illustration of a penetration profile in a bi-crystal for type B kinetics 572
32.12 Average thin-layer concentration at depth z of a diffuser
entering via a grain boundary versus the normalised penetration depth η = z/ √
Dt for β = 100 (∆ = 2 × 106and√
Dt = 10µm) according to Suzuoka [29] The concentrations are expressed
in units of M/(L √
π) in the case of an instantaneous source
and in units of c0
√ Dt/L for a constant source 573
32.13 Logarithm of the average thin layer concentration at depth z of the diffuser entering via a grain boundary versus z 6/5
(z = section depth, ∆ = 2 × 106 and√
Dt = 10µm) according
to Suzuoka [29] The concentrations are expressed in units of
M/(L √
π) for an instantaneous source and in units of c0 √
Dt/L
for a constant source 574 32.14 Type B kinetics penetration profiles of self-diffusion in Ag
polycrystals according to Sommer and Herzig [35] 575
32.15 Arrhenius diagram of the triple product sδD gb and of sD gb
from Te diffusion along grain boundaries in Ag according to
Herzig et al [48] Type B and C kinetics prevail above
600 K and below 500 K, respectively The range 500–600 K
corresponds to a transient regime 578
Trang 6List of Figures 637 32.16 Grain-boundary segregation factors for Te in Ag according
to Herzig et al [48] and Au in Ag according to Surholt
et al [49] determined from combined type B and type C
measurements 579 33.1 Smoluchowski model of a dislocation pipe 584 33.2 Dislocation diffusion: mean thin-layer concentrations of the
constant and instantaneous source solutions, Q I and Q II, for
α = 10 −2 and (∆− 1) = 105 according to Le Claire and
Rabinovitch[6] 588 33.3 Dislocation diffusion: constant source solution Q I (left )
and instantaneous source solution Q II (right ) versus η for
α = 10 −1 , 10 −2 , 10 −3 , αβ = 10 (full lines) and αβ = 102
(dashed lines) according to Le Claire and Rabinovitch [6] 588
33.4 Dislocation diffusion: The quantity A(α) is plotted as a function
of α for various values of αβ according to Le Claire and
Rabinovitch[6] 589 34.1 Schematic view of a nanocrystalline material 594 34.2 Schematic drawing of an ECAP device used for severe plastic deformation according to Valiev et al [18] 597 34.3 Tracer distribution in various kinetic regimes and subregimes
of diffusion in polycrystals according to Kaur, Mishin and
Gust[29] 601 34.4 Models representing grains (dark ) and boundaries in
a nanostructured material Left : parallel arrangements of grains and grain boundaries in the diffusion direction Middle: serial
of arrangement of grains and grain boundaries Right : grains
represented as cubes 604 34.5 Penetration profiles of59Fe diffusion in Fe-40 % Ni nanoalloys representing either type A or type B kinetics according to
Divinski et al.[50]: Fe diffusion plotted as function of y2
(left ) Fe diffusion plotted as function of y 6/5 (right ) 609
34.6 Penetration profiles of59Fe diffusion in Fe-40 % Ni nanoalloys
as function of y2 representing type C kinetics according to
Divinski et al.[51] Two types of grain boundaries contribute
to the diffusion profiles 610 34.7 Arrhenius diagram of Fe grain-boundary diffusion in Fe-40 %
Ni nanoalloys according to Divinski et al [51] Open
circles and solid line: D gb for agglomerate boundaries Filled
circles and solid line: D gb for intra-agglomerate boundaries
For comparison, grain-boundary diffusion in conventional
polycrystals is shown as dashed lines: Ni in Fe-Ni [53]; Fe in
γ-iron [54] 611
34.8 Conductivity of LiI:Al O composites according to Liang [61] 613
Trang 7638 List of Figures
34.9 Defect concentration profiles in nanostructures of ionic
materials with dimension d LD is the Debye screening length 614 34.10 Conductivity of nanocrystalline CaF2 (circles) and of
microcrystalline material (diamonds) according to Heitjans
and associates [66, 67] The solid has been calculated from the space charge layer model 615 34.11 Conductivity of CaF2-BaF2 layered heterostructures parallel
to the layers of thickness L according to Maier and
coworkers [69] 616 34.12 Oxygen diffusion in ZrO2 and YSZ n-ZrO2: nanocrystalline
zirconia (squares: bulk diffusion, diamonds: interface
diffusion); m-ZrO2: microcrystalline zirconia; YSZ: yttrium
stabilised zirconia (dashed-dotted lines) After Schaefer and
associates[70] 617
Trang 8activation energy 133
activation enthalpy 127, 128, 133, 143,
242, 246, 260, 263, 297, 299, 300,
310, 321, 328, 330, 332, 345, 395,
416, 418, 450, 459, 462, 510, 512,
525, 535, 540, 549, 550, 577
activation enthalpy of self-diffusion
132, 144
activation enthalpy of solute diffusion
132
activation parameters 128, 130, 133,
299, 300, 313, 321, 398
activation parameters and elastic
constants 146
model of Zener 146
activation volume 132, 135, 145, 298,
305, 332, 376, 401, 514
activation volume and melting point
145
activation volume of ionic crystals
140
activation volume of ionic conduction
133
activation volume of self-diffusion
135
activation volume of solute diffusion
139
effective activation volume 133
formation volume of a divacancy
136
formation volume of a monovacancy
136
formation volume of a self-interstitial
136
formation volume of Schottky pairs
140
migration volume 137
migration volume of the cation vacancy 140
AgCl and AgBr 469 alkali halide 458, 461, 467 anelastic relaxation 237, 456, 457 anelasticity 237, 239
anisotropic media 33 anisotropy ratio 308 Arrhenius diagram 127, 246, 287,
289, 301, 304, 317, 332, 333, 345, 374–376, 465, 471, 510–512, 536,
538, 578, 611 Arrhenius relation 127, 297, 316, 508 Arrhenius, Svante August 4 atomic jump process 55, 64 Debye frequency 64 saddle point 65 simulation of atomic jump processes 66
attempt frequency 65, 129, 132, 143,
152, 297, 302, 316, 396 Auger-electron spectroscopy (AES) 230
Auger electron 230 Auger emission 229 axial flow 32, 38 B2 intermetallics 346 antistructural-bridge (ASB) mecha-nism 350
B2 Fe-Al 353 B2 NiAl 351 B2 order 361 coupling between diffusivities 347 six-jump-cycle (6JC) mechanism 347
triple-defect mechanism 348 vacancy-pair mechanism 350
Trang 9640 Index
Bardeen, John 10, 62, 105, 386
Beke, Desz¨o 13
Bessel functions 51, 587
binary alloy 80
Lomer equation 82, 100
solute 81
solute-vacancy pair 81, 118
solvent 81
vacancies in concentrated alloys 82
vacancies in dilute alloys 81
binary intermetallics 341
B2 (or CsCl) structure 342
C11bstructure 343
D03 (or Fe3Si) structure 342
D019structure 343
L10 (or CuAu) structure 343
L12 (or Cu3Au) structure 343
Bokstein, Boris 13
Boltzmann transformation 162
Boltzmann-Matano method 163, 165,
229
Boltzmann-Matano equation 164
Matano plane 162, 164
borate glasses 537
Bracht, Hartmut 15
Brown, Robert 1, 5
Brownian motion 1, 55
cartesian coordinates 32
centrifugal forces 181
charge diffusion coefficient 185, 285,
287, 461, 463, 487, 533–535, 539,
541
chemical diffusion 161
chemical diffusion coefficient 162, 183,
212
chemical potential 161, 170, 180, 184,
194
thermodynamic activity 170
classical ion conductors 83
colinear and non-colinear jumps 468
collective correlation factor 201, 204
collective mechanism 97, 155, 159, 516
direct exchange 97
interstitialcy mechanism 98
non-defect mechanisms 98
ring mechanism 97
collective motion 580
configurational entropy 71
continuum theory of diffusion 27 correlation factor 62, 105, 106, 111,
112, 114, 132, 151, 158, 185, 195,
200, 308, 316, 329, 356, 397, 419,
428, 461, 465 activation enthalpy of the correlation factor 123
correlation factor for diamond lattice 121
correlation factor of self-diffusion 115
escape probability 119, 121, 122 geometric correlation factor 153 impurity form 123, 151
recursion formula 113 solute correlation factor 119, 123, 139
solute correlation factor bcc 120 vacancy trajectory 114
Cottrell atmospheres 181 crystallisation 496, 504, 506, 510, 523, 598
Cu3Au rule 365, 366 majority element 366 minority element 366 cylindrical coordinates 32 D03 inremetallics 367 D03 intermetallics 357
Cu3Sn 358 D03 Fe3Si 358 sublattice vacancy mechanism 358 Danielewski, Marek 13
Darken equations 170, 171, 188, 193,
203, 215 Darken-Dehlinger equations 171 Darken-Manning equations 172, 203,
215, 356 Manning factor 172 vacancy-wind factor 172, 173 Dayananda, Mysore 14
dc conductivity 285, 456, 476, 527,
538, 613, 615, 616 dielectric relaxation 457 differential dilatometry (DD) 74 diffusion and ionic conduction in oxide glasses 521
alkali borate glasses 535 annealing point 524
Trang 10Index 641 fragile melts 525
fragility diagram 525
fragility of melts 525
gas permeation 529
glass-forming oxides 522
glass-transition temperature 537
intermediate ions 522
mixed-alkali effect 538
network-former ions 522
network-modifier ions 522
non-bridging oxygen (NBO) 534
permeability 529
soda-lime silicate glass 532
softening point 524
strong melts 525
structure of network glasses 521
structure of soda-lime silicate glass
533
structure of sodium-rubidium borate
glass 537
viscosity 524
viscosity of glass-forming melts 523
vitreous silica and quartz 530
working point 524
working range 524
diffusion coefficient 28, 57, 59
diffusivity tensor 33
principal diffusion coefficients 33
principal diffusivities 33
diffusion couple 41, 214
diffusion entropy 129, 297, 300, 398
diffusion equation 30, 31, 37
diffusion in a plane sheet 47
desorption and absorption 49
eigenvalues 48
out-diffusion from a plane sheet 48
separation of variables 47
diffusion in a sphere 51
diffusion in metallic glasses 503
bulk amorphous steels 506
bulk metallic glasses 506
chain-like collective motion of atoms
516
conventional metallic glasses 505
correlation between D0 and ∆H
512
diffusion and viscosity 517
diffusivity enhancement 508
equilibrium melt 517 excess volume 506 families of metallic glasses 505 instantaneous diffusivity 508 isotope effect parameter for bulk metallic glasses 515
melt-spinning 505 mode-coupling theory 517 molecular-dynamics simulations 516
pressure dependence 513 quasi-vacancies 508 structural relaxation and diffusion 506
temperature dependence for bulk metallic glasses and their supercooled melt 510 temperature dependence for conventional metallic glasses 509
time-averaged diffusivity 507 Turnbull criterion 504 diffusion in nanocrystalline materials 593
agglomerate boundaries 608 characteristic length scales for diffusion 600
chemical and related synthesis methods 598
coarse-grained polycrystals 600 Debye screening length 614 devitrification of amorphous precursors 598
diffusion and ionic conduction in ZrO2 and related materials 615 diffusion in nanocrystalline metals 606
dispersed ionic cinductors (DIC) 613
effective diffusivity of solutes 605 effective self-diffusivity 604 fine-grained polycrystals 602 grain size and diffusion regimes 599 Hart equation 605
Hart-Mortlock equation 606 heavy plastic deformation (SPD methods) 596
high-energy milling 595