Hillert M. Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis
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Index 505
Le Chatelier 124
Le Chatelier modification 124
Le Chatelier principle 124
Legendre transformation 25
LE-partitionless transformation 307, 309
lever rule 70, 369
LFM 365
Lifshitz 326
limit of stability 116, 118
line of coexistence 160, 170
liquid film migration 365
liquid metal, model of 423
liquidus 194
Liu 366
local equilibrium 60, 144, 309
local equilibrium, deviation from 302, 306
localized spin 429
logarithmic phase diagram 153
long- and short-range order 486
long-range order 479, 483
loss of work 17, 57
M
2
C 278
M
6
C 278
magnetic disorder 32, 429, 431
magnetic domain 429
magnetic enthalpy 430
magnetic entropy 431
magnetic moment 429, 431
magnetic order 493
martensitic transformation 310
Masing 194
mass action, law of 482
massive transformation 310
matrix 281, 295
matrix, notation 301
Maxwell relation 43, 116, 123, 198, 444
Maxwell’s construction 401
mechanical energy 11
mechanical mixture 441
mechanical work 6
melting, congruent 244
metastable 110
metatectic 262
microcanonical ensemble 50
microscopic fluctuations 82
microscopic reversibility 82
microstructurally gradual 259, 261
microstructurally sharp 259
microstructure 259
migrating interface 306
migration mechanism of boundaries 378
migration, induced by diffusion 365
minimum entropy production 385
miscibility gap 330, 333, 335, 338, 342,
445
miscibility gap, coherent 371
mixed character of variable 76
mixed phase diagram 205
mixing quantity 443
mixture, mechanical 441
mixture, random 434
mixture, restricted random 436
Mn–O–S 210
Mn–O–S, potential diagram 210
mobile component 291, 294
mobility of grain boundary 378
mobility of interface 146
mobility, individual 380
model, mathematical 400
model, physical 400
modelling 400
molar content 47
molar diagram 185
molar diagram, topology of 194
molar enthalpy 7
molar entropy 15
molar Gibbs energy 47
molar Gibbs energy diagram 72, 126
molar phase diagram 185
molar phase diagram, complete 195
molar phase diagram, topology of 188
molar quantity 47
molar quantity of mixing 443
molar variable 189
mole fraction 47
molecular reactions 58
molten salt model 487
Mo–N, diagram 192
monatomic gas 412
monolayer 61
monotectic 262
monovariant, see univariant
Morral 203
MPL boundary rule 221
MPL rule 194
Muggianu 458
multicomponent solution 456
multinary system 166
Murnaghan’s equation 409
mutual diffusion coefficient 383
NaCl in CaCl
2
473, 474
Na–K–Cl–Br, composition space for 297
natural variable 6, 21, 30
natural zero point 27, 404
nearest neighbour 476
Nernst’s heat theorem 27
Neumann–Kopp rule 406
neutral combination 473
neutral line 473, 474
next-nearest neighbour 466
506 Index
Ni–O–Be 276
non-configurational 420, 421, 432
non-equilibrium 3
non-equilibrium state 3
non-hydrostatic stress 6
non-random solution 479
non-spherical interface 350
non-stoichiometric 282
notation 63
for derivative of G
m
119
for determinant 178
for matrix 301
for partial quantity 63
for univariant equilibrium 205
Nowotny 203
nucleation 351
nucleation of pore 422
nucleus, critical 357
number-fixed frame 101, 380
off-diagonal 121
Onsager 82, 95, 104
Onsager’s extremum principle 386, 396, 398
Onsager’s reciprocal relation 383
opalescence 483
open system 2, 7
order parameter, generalized 339
order, variable 469
order–disorder transformation, magnetic 434
order–disorder transition 324, 471
ordering, in interstitial solution 490
oscillator 425
Ostwald ripening 61, 351
overall composition 438
overlapping 185, 213
overlapping gradual transformation 257
overlapping phase fields 304
overlapping sharp transformations 257
pair energy 477
pair of conjugate variables 21, 28
pair-wise interaction 456
Palatnik 194
Pan 61
paraequilibrium 311
parallel tangent construction 357, 367
paramagnetic 430
partial chemical equilibrium 311
partial derivative 63
partial derivative, notation for 37
partial equilibrium 302
partial excess Gibbs energy 446
partial ideal entropy 442
partial molar Gibbs energy 126
partial molar volume 71, 101
partial pressure 415
partial quantities, relations of 65
partial quantity 63
partial quantity of mixing 443
partial volume, role for inclusion 356
partition coefficient 233
partition function 50, 420
partitional transition 325
partitioning of alloy element 320
partitionless phase transformation 375
partitionless reaction 374
partitionless transformation 144, 302, 308
partitionless transition 325
Pb–Sn, phase diagram 200, 224
Pb–Sn, solid solution 141
pearlite 275, 283, 287, 317, 319
pearlite, formation of 291
Pelton 455
peritectic 262
peritectoid transformation 262
perpetuum mobile 13
phase 76
phase assemblage 285
phase boundaries, direction of 233, 234
phase boundary 193
allotropic 235
direction of 240
retrograde 248
slope of 249
vertical 248
phase diagram 2
phase diagram, dimensionality of 209
phase diagram, true 224
phase equilibrium, at interface 346
phase equilibrium, coherent 371
phase field 163
phase field rule 169, 208, 220
phase field rule, at fixed composition 279
phase field, dimensionality of 164, 208
phase transformation in alloys 261
phase transformation
adiabatic 303
allotropic 236
character of 257
class I, II, III 264, 283
phases with variable order 469
phenomenological coefficient 100, 379, 386
phenomenological equation 81, 102, 104
physical model 408, 410, 411
pile-up 145
Planck constant 377, 417, 425
point of reference 27
positive definite 82
potential 3, 21, 47
potential difference 253
potential phase diagram 155, 162
potential phase diagram, complete 168
Index 507
potential phase diagram, section of 168
potential, dependent 189
power series 407
precipitation, coherent 366
precipitation, discontinuous 364
precipitation, proeutectoid 268, 319
pressure dependence 408
pressure difference 251, 346
pressure difference, effect on composition 357
pressure extremum 181
pressure gradient 100
pressure, negative 164
pressure, power series of 407
pressure-induced diffusion 388
Prigogine 84, 385
Prigogine’s extremum principle 386
principle of detailed balance 377
principle of minimum entropy production
385
probability 27
process, independent 102
process, spontaneous 108
processes, conjugate 86
processes, set of 85, 102
product 282
proeutectoid 268, 319
projected diagram 212
projected phase diagram 205
projected surface 215
projection 217
property diagram 2, 4, 157
pseudo-binary 461
pure compound 151
quadratic formalism 455
quantum mechanics 425
quasi-adiabatic transformation 305
quasi-binary 297, 461
quasi-binary phase 464
quasi-binary side 466
quasi-chemical approach 477, 490
quasi-chemical method 482
quasi-chemical model for interstitials 491
quasi-diffusionless transformation 309
quasi-paraequilibrium 314, 315
quasi-ternary 297, 461
quaternary 167, 211
quinary 167
R coefficient 85, 105
radioactive isotope 382
random mixture 434
Raoult’s law 129, 446, 448
rate of entropy production 81, 91, 105
reactant 282
reaction coefficient 92, 280, 281, 283, 285
reaction coefficient, at fixed chemical potential
294
reaction diagram 270
reaction formula 92
reaction path 57, 160
reaction rate, absolute 377
reaction, extent of 93
reaction, heterogeneous 303
reaction, homogeneous 303
reaction, independent 92
reactions, competing 258
real gas 412
real solution 448
reciprocal reaction 95
reciprocal relation 82, 84, 97
reciprocal relation, in diffusion 383
reciprocal solution phase 464
reciprocal system 298
reconstructive transition 325
Redlich 445
Redlich–Kister polynomial 445
reference for element 404
reference state 128, 402
refrigerator 12
regular solution 445, 477
regular solution parameter 484
relative amounts 67
relative composition 266
relaxation of surface layer 344
renormalization group 483
restricted random mixture 436
retrograde phase boundary 248
reversible 10
reversible change 22
reversible conditions 20, 442
reversible process 15
reversible reaction 36
Richard’s rule 247, 423
ripening 61
saturation magnetization 429
Scheil 270
Scheil reaction diagram 270
scheme
content 53
energy 28
entropy 28, 53
volume 53
Schreinemakers 197
Schreinemakers’ projection 205, 212, 231, 266
Schreinemakers’ rule 197, 250
second law 6, 13, 15, 81, 104
second-order transition 322, 327, 471
section of potential phase diagram 168
sectioned molar diagram 201
sectioned molar diagram, topology of 201
508 Index
segregation to grain boundary 372
segregation to interface 371
segregation to surface 361
SER, stable element reference 404
set
of components 92
of conjugate pairs 52, 224
of processes 85
of stability conditions 114, 116
sharp transformation 255, 262, 280
sharp transformation, classification of 262
sharp transformation, driving force of 287
shear stress 6
short-range order 479, 482, 488
short-range order, magnetic 434
Si
3
N
4
475
Sialon 475
side system 465
simulation 400
simultaneous processes 81
singular curve 226, 268
singular equilibrium 226, 229, 231, 296
singular point 226
singular, doubly 229, 230, 268
Si–O–N, phase diagram 175
site fraction 76, 460
six-phase equilibrium 218
size of system 69, 189
slightly imperfect gas 413
solidification of droplet 304
solidification, quasi-adiabatic
solidus 194
solubility product 152
solute drag 372
solute drag in grain growth 372
solute traping 392
solution phase 406, 434
solution phase with sublattices 460
solution
ideal 127, 442
ideal substitutional 442
interstitial 439, 462
interstitial and substitutional 468
real 448
regular 445
subregular 445
solvus 194
species 76, 472
specific quantity 48
specific surface energy 344
spherical particle, stability of 350
spike
composition 317
enthalpy 306
of composition 374
temperature 306
spin, localized 429
spinel 250
spinodal 331
decomposition 89, 335, 352
calculation of 446
coherent 371
conditional 339
spinode 331
spontaneous process 15, 19, 108
stability 108
stability condition 111, 113
stability condition, molar variable in 189
stability condition, set of 114
stability function 119
stability limit 330
stability limit for solid/liquid 486
stability of spherical particle 350
stability, limit of 116, 326
stable element reference 404
stable equilibrium 108
standard Gibbs energy of formation 129
state diagram 2, 155
state equation 33
state function, characteristic 401
state functions 1
state of equilibrium 1
state variables 1
stationary flow 384
statistical thermodynamics 27, 420
steady-state 145, 307
Stefan constant 417
stereographic pair 205
stoichiometric coefficient 92
stoichiometric compound 77, 132
stoichiometric constraint 77, 297, 464
stoichiometric phase 439, 464
stoichiometric vacancy 437
stoichiometry, deviation from 439
sublattice 76, 460
subregular solution 445
substitutional 101
substitutional diffusion 101, 379
substitutional solution 435
subsystem 23
surface energy 344
surface energy, effect on composition 359
surface energy, specific 344
surface free energy 344
surface Gibbs energy 344
surface layer, coherent 344, 364
surface of reference 464
surface segregation 361
surface stress 344, 353, 354, 359
surface tension 345
surroundings 1
Svoboda 396
Index 509
swallowtail 224
syntectic 262
system 1
system, discontinuous 95
tangent construction, parallel 357
tangent plane 72, 149
tangent, common 357, 367
tangent, parallel 367
temperature extremum 181
temperature spike 306
temperature, power series of 407
terminal solution 152
ternary phase diagram 233, 234
ternary system 72, 149, 173
ternary system, diffusion in 382
thermal activation 377
thermal energy 11
thermal equation of state 33
thermal equilibrium 10
thermal expansivity 39
thermal potential 13
thermal vacancy 422
thermal vibrations 419, 425
thermochemistry 1
thermodynamic factor for diffusion 382
thermodynamic force 80, 91, 96, 99,
102
thermodynamics 1
thermophysical properties 1
third law 27
tie-line 71
tie-line rule 71
tie-triangle 185
Ti–O–Cl, phase diagram 174
Ti–O–Cl, potential diagram 173
topological disorder 423, 486
topology 162, 212, 217
topology of molar diagram 194
topology of molar phase diagram 188
topology of sectioned molar diagram
201
tracer diffusion 382
transferred material, composition of 390
transformation of set of processes 83
transformation
allotropic 137
azeotropic 257
congruent 244
diffusionless 309
eutectic 262
eutectoid 262
four-phase 264
gradual 255, 272, 285
in steel 315
LE-partitionless 307, 309
martensitic 310
massive 310
overlapping gradual 257
overlapping sharp 257
partitionless 308
peritectoid 262
quasi-diffusionless 309
sharp 255, 262
true diffusionless 309
transient 306
transient stage of growth 316
transition line 339, 484
transition of second order 471
transition point 324, 326
transition temperature 341
transition
diffusional 325
diffusionless 325
displacive 324
first-order 322
order–disorder 324
partitional 325
partitionless 325
reconstructive 325
second-order 322, 323
transport of enthalpy 96
transport of heat 95
transport process 90, 384
transportation process 96
trapping of solute atoms 392
tri-critical point 339, 495
triple point 163, 185
true diffusionless transformation 309
true phase diagram 224
Truesdell 82
truncated power series 408
two-phase equilibrium 135, 138, 139
two-phase field, coherent 369
two-sublattice model 487
unary system 158
uncompensated heat 17
undercooled melt 424
univariant equilibrium 179
univariant equilibrium, notation for
205
unstable equilibrium 17, 108, 470
up-hill diffusion 335
vacancies in diffusion 378
vacancy 17, 101, 420
chemical potential of 78, 462
driving force of disappearance
423
mechanism of diffusion 379, 380
stoichiometric 437
510 Index
Va n der Waals 414
vapour pressure 353, 359
variable, change of 45
variables for composition 67
variance 156
variation analysis 385
velocity, extremely high 306
vertical phase boundary 248
vibration frequency 403
virial coefficient 413
viscous state 486
volume change, local 388
volume scheme 53
volume-fixed frame 101
Vo n Alkemade 296
Vo n Alkemade’s rule 181, 230
Wagner 250
Wagner integration 452
Wagner’s dilute solution model 454
wavelength 335
W–C, phase diagram 170
W–C, potential diagram 170
Williams point 369
work 5
w¨ustite 248, 253
zero point 6
zero point energy 427
zero point, natural 404
zero-dimensional phase field 164
zero-phase-fraction 222
zero-phase-fraction line 203