Hume-Rothery Rules for Structurally Complex Alloy Phases

358 Pages·2010·5.98 MB·English

by  Uichiro Mizutani

Hume-Rothery Rules for
Structurally Complex
Alloy Phases

Uichiro Mizutani
Nagoya Industrial Science Research Institute
Japan
Boca Raton London New York
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Table of Contents
Preface, xi
Chapter 1 ◾ I ntroduction 1
1.1 What Is the DefInItIon of the hume-RotheRy
Rules? 1
1.2 hIstoRIcal suRvey of chemIstRy anD
metalluRgy 6
1.3 hIstoRIcal suRvey of cRystallogRaphy 1 1
1.4 hIstoRIcal suRvey of physIcs 1 4
RefeRences 1 7
Chapter 2 ◾ c hemical Bonding and phase Diagrams in
alloy phase stability 21
2.1 cohesIve eneRgy of a solID 21
2.2 fRee eneRgy of foRmatIon anD enthalpy of
foRmatIon 2 6
2.3 KInetIc eneRgy of electRons anD the Role
of the pseuDogap 3 0
RefeRences 34
Chapter 3 ◾ e arly theories of alloy-phase stability 37
3.1 mott-Jones moDel foR alpha-, Beta-, anD
gamma-BRasses 3 7
3.2 the moDel of Jones (I) 3 8
3.3 the moDel of Jones (II) 4 4
RefeRences 46
v
vi   ◾   table of contents
Chapter 4 ◾ f irst-principles Band calculations using the
muffin-tin potential 49
4.1 fIRst-pRIncIples BanD calculatIons veRsus
the hume-RotheRy electRon concentRatIon
Rule 4 9
4.2 oRIgIn of the pseuDogap: oRBItal
hyBRIDIzatIons veRsus fsBz InteRactIons 5 0
4.3 What aRe fIRst-pRIncIples BanD
calculatIons? 5 5
4.4 all-electRon BanD calculatIons WIthIn the
muffIn-tIn appRoxImatIon 5 7
4.5 Wave functIons InsIDe anD outsIDe the mt
spheRe 6 1
4.6 oRthogonalIty conDItIon WIth coRe
electRon states 6 3
4.7 KKR-asa equatIon 6 5
4.8 lIneaRIzatIon methoD 7 0
4.9 lmto-asa methoD 7 4
4.10 extRactIon of spd-d oRBItal hyBRIDIzatIons
In the lmto-asa methoD 8 1
4.11 apW methoD 8 5
4.12 lapW methoD 8 8
RefeRences 95
Chapter 5 ◾ h ume-Rothery electron concentration Rule
concerning the α/β phase transformation in
cu-x (x = zn, ga, ge, etc.) alloy systems 9 7
5.1 staBle fcc-cu veRsus metastaBle Bcc-cu 9 7
5.2 fIRst-pRIncIples BanD calculatIons foR fcc-
anD Bcc-cu In lIteRatuRe 9 8
5.3 flapW electRonIc stRuctuRe calculatIons
foR fcc- anD Bcc-cu 9 9
5.4 total-eneRgy anD valence-BanD stRuctuRe
eneRgy 102
table of contents   ◾   vii
5.5 Dos foR fcc- anD Bcc-cu 106
5.6 RelatIve staBIlIty of the α- anD β-phases In
cu-x (x = zn, ga, ge, etc.) alloy systems 109
5.7 summaRy 117
RefeRences 119
Chapter 6 ◾ s tructure of structurally complex metallic
alloys 121
6.1 What aRe stRuctuRally complex alloys? 121
6.2 gamma-BRasses 125
6.3 1/1-1/1-1/1 appRoxImants 129
RefeRences 137
Chapter 7 ◾ s tabilization mechanism of gamma-Brasses
characterized by a fsBz-Induced pseudogap 139
7.1 staBIlIzatIon mechanIsm DRIven By a fsBz-
InDuceD pseuDogap 139
7.2 flapW BanD calculatIons foR cu zn anD
5 8
cu al gamma-BRasses 140
9 4
7.3 extRactIon of the fsBz InteRactIon at the
symmetRy poInts N of the BRIllouIn zone 143
7.4 the hume-RotheRy staBIlIzatIon mechanIsm
foR cu zn anD cu al gamma-BRasses 151
5 8 9 4
7.5 e/a DepenDent physIcal pRopeRtIes of noBle
metal alloys 156
7.6 cu-zn anD cu-cd gamma-BRasses In solID
solutIon Ranges 159
7.7 cu-al anD cu-ga gamma-BRasses In solID
solutIon Ranges 164
7.8 summaRy 170
RefeRences 171
viii   ◾   table of contents
Chapter 8 ◾ s tabilization mechanism of gamma-
Brasses characterized by Increasing orbital
hybridizations: Role of d-states-mediated-
fsBz Interactions 173
8.1 gamma-BRasses In gRoup (II) 173
8.2 tm-zn (tm = ni, pd, co, anD fe) gamma-BRasses 174
8.2.1 Construction of the Model Structure 174
8.2.2 Electronic Structure Calculations and Stabilization
Mechanism 175
8.2.2.1 Ni Zn and Pd Zn Gamma-Brasses 175
2 11 2 11
8.2.2.2 Co Zn and Fe Zn Gamma-Brasses 183
2 11 2 11
8.3 al v gamma-BRass 191
8 5
8.3.1 Construction of the Model Structure 191
8.3.2 Electronic Structure Calculations and Stabilization
Mechanism 192
8.4 ag-li gamma-BRass 199
8.4.1 Construction of the Model Structure 200
8.4.2 Electronic Structure Calculations 200
8.4.3 Stabilization Mechanism 203
8.5 ni-zn anD co-zn gamma-BRasses In solID
solutIon Ranges 210
8.6 summaRy 213
RefeRences 214
Chapter 9 ◾ s tabilization mechanism of 1/1-1/1-1/1
approximants 217
9.1 electRonIc stRuctuRe of 1/1-1/1-1/1
appRoxImants 217
9.2 al-mg-zn 1/1-1/1-1/1 appRoxImant 219
9.2.1 Construction of the Model Structure 219
9.2.2 Electronic Structure Calculations 221
9.2.3 Stabilization Mechanism 223
table of contents   ◾   ix
9.3 al-li-cu 1/1-1/1-1/1 appRoxImant 231
9.3.1 Construction of the Model Structure 231
9.3.2 Electronic Structure Calculations 232
9.3.3 Stabilization Mechanism 233
9.4 al-cu-tm-si (tm = fe oR Ru) 1/1-1/1-1/1
appRoxImants 236
9.4.1 Construction of the Model Structure 236
9.4.2 Electronic Structure Calculations and Stabilization
Mechanism 238
9.4.2.1 LMTO-ASA Band Calculations 238
9.4.2.2 FLAPW Band Calculations 241
9.5 al-Re-si 1/1-1/1-1/1 appRoxImant 244
9.5.1 Atomic Structure Free from Chemical Disorder 244
9.5.2 Electronic Structure Calculations 244
9.6 Role of vacancIes to maIntaIn a constant
e/uc In the 1/1-1/1-1/1 appRoxImants 245
9.7 summaRy 246
RefeRences 247
Chapter 10 ◾ t he Interplay and contrasts Involved in the
chemistry, physics, and crystal structures of
alloys and compounds 249
10.1 e/a oR VEC as an electRon concentRatIon
paRameteR 249
10.2 exIstIng pRoposals on e/a foR the
tRansItIon metal element 253
10.3 hume-RotheRy plot foR the B2-compounDs 255
10.4 (e/a) value foR the tRansItIon metal
tm
element In the peRIoDIc taBle 261
10.5 physIcs BehInD the matchIng conDItIon 262
10.6 unIveRsal test of the matchIng conDItIon 269
10.7 oRBItal hyBRIDIzatIons veRsus fsBz
InteRactIons 273