First-principles investigations of solid solution strengthening in Al alloys

318 Pages·2012·3.98 MB·English

First-principles investigations of solid solution
strengthening in Al alloys
VonderFakultätfürGeoressourcenundMaterialtechnik
derRheinisch-WestfälischenTechnischenHochschuleAachen
zurErlangungdesakademischenGradeseines
DoktorsderIngenieurwissenschaften
genehmigteDissertation
vorgelegtvonM.Sc.
DuanchengMa
ausLiaoning/China
Berichter: ProfessorDr.-Ing. DierkRaabe
Univ.-Prof. Dr. rer. nat. Dr. h.c. GünterGottstein
TagdermündlichenPrüfung: 16. Dezmber2011
DieseDissertationisaufdenInternetseitenderHochschulbiliothekonlineverfügbar

WICHTIG: D 82 überprüfen !!!
Berichte aus der Materialwissenschaft
Duancheng Ma
First-principles investigations of
solid solution strengthening in Al alloys
Shaker Verlag
Aachen 2012
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche
Nationalbibliografie; detailed bibliographic data are available in the Internet at
http://dnb.d-nb.de.
Zugl.: D 82 (Diss. RWTH Aachen University, 2011)
Copyright Shaker Verlag 2012
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior permission
of the publishers.
Printed in Germany.
ISBN 978-3-8440-0892-0
ISSN 1618-5722
Shaker Verlag GmbH • P.O. BOX 101818 • D-52018 Aachen
Phone: [phone] • Telefax: 0049/2407/9596-9
Internet: www.shaker.de • e-mail: [email protected]
Acknowledgments
The completion of this dissertation would not be not possible without any of the following in-
dividuals:
Foremost, I would like to express my sincere gratitude to Prof. Dierk Raabe for his continu-
oussupport,guidanceandencouragementforthiswork,alsoforhisvisionaryperspectivesand
immenseknowledge.
MyappreciationistoDr. MartinFriák,Prof. JörgNeugebauerandDr. JohannvonPezold
fortheirinsightfulcommentsandsuggestions.
I also would like to thank the other colleagues who ever participated the discussion during the
inter-department meetings: Dr. Tilmann Hickel, Dr. Blazej Grabowski, Dr. Philip Eisen-
lohr,Dr. StefanieSandlöbes,Dr. FranzRoters,Dr. WilliamCounts,Dr. LiveriosLymper-
akis,andDr. MiraTodorova.
My appreciation is also to Dr. Alexey Dick for doing a excellent job as a queuing system ad-
mistrator,andourbrilliantadministrators,AchimKuhlandBertholdBeckschäferforhelping
mewithvarioussoftwareandhardwareinstallations. IwouldliketothankDr. AlexanderAuer
for his mini lecture given in our institute which enlightened me of the basics of first-principles
calculations. My gratitude is also to our librarians, Christa Regner and Petra Siegmund, for
doingtheirjobsinafastandreliablefashion.
Lastbutnotleast,Iwouldliketoappreciatetheothercurrentorformercolleagues,andvisiting
scientistswithwhomIhadfruitfulscientificdiscussionsinvariousareas(inalphabeticalorder):
Currentcolleagues:
Ugur Aydin, Kemal Davut, Martin Diehl, Nahid-Nora Elhami, Pavlína Elstnerová, Dr.
Helge Fabritius, Albert Glensk, Dr. Ivan Gutierrez, Dr. Masood Hafez Haghighat, Nima
Hamidi Sibani, Dr. Clara Herrera Pulgarin, Tom Jäpel, Dr. Anahita Khorashadizadeh,
Helene Knoll, Christoph Kords, Dr. Aleksander Kostka, Dr. Yujiao Li, Bing Liu, Dr.
Tao Liu, Julio Millán, Dr. Roman Nazarov, Dr. Dirk Ponge, Konda Gokuldoss Pradeep,
Farangis Ram, David Steinmetz, Dr. Cem Tasan, Natalie Tillack, Dr. Alexander Udyan-
sky, Ute Witt, Xia Wu, Lei Yuan, Dr. Stefan Zaefferer, Dr. Claudio Zambaldi, and Dr.
LifangZhu.
Formercolleagues:
Dr. Alankar Alankar, Dr. Keerthika Balasundaram, Dr. Marion Calcagnotto, Prof. Yan-
ping Cao, Dr. Eralp Demir, Dr. Olga Dmitrieva, Luc Hantcherli, Dong He, Olga Kim, Dr.
Timm Krüger, Prof. Satoru Kobayashi, Prof. Hongyang Li, Dr. Patricia Romano, Beni-
dikt Sander, Igor Schestakow, Dr. Denny Dharmawan Tjahjanto, Florian Weber, Prof.
GuilinWu,andDr. NadarZaafarani.
Othervisitingscientists:
Prof. Craig Hartley (US Air Force Research Lab), Dr. Ricardo Lebensohn (Los Alamos
National Lab), Dr. Anxin Ma (Interdisciplinary Centre for Advanced Materials Simulation
(ICAMS)),Prof. HelenaVanSwygenhoven(PaulScherrerInstitute),Prof. SvetoslavNikolov
(Institute of Mechanics, Bulgarian Academy of Sciences), Dr. Fathollah Varnik (ICAMS),
Prof. VaclavVitek(UniversityofPennsylvania),andDr. XiaohuiZeng(ICAMS).,
4
Contents
Contents i
I Introduction, Motivation, and Fundamentals 1
1 Introduction 3
1.1 Bridgingquantummechanicsandmaterialsscienceandengineering . . . . . . 4
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Outlinesofeachchapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Fundamentalsofsolidsolutionstrengthening 9
2.1 Experimentalobservationofsolidsolutionstrengthening . . . . . . . . . . . . 10
2.1.1 fccsolidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 bccsolidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 hcpsolidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Theoreticalmodelsofsolidsolutionstrengthening . . . . . . . . . . . . . . . . 14
2.2.1 Elasticeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Chemicaleffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Electrostaticeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Shortrangeordering(SRO) . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Statisticaltreatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Difficultiesinexperimentsandalternatives . . . . . . . . . . . . . . . . . . . . 20
2.5 Electroniccorrelationsofthesolidsolutionstrengthening . . . . . . . . . . . . 20
CONTENTS
3 Theoreticalmethodsusedinthisthesis 21
3.1 DensityFunctionalTheory(DFT) . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 GeneralformulationofDFT . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Exchange-correlationfunctional . . . . . . . . . . . . . . . . . . . . . 25
3.1.3 AccuracyandefficiencyinDFTcalculations . . . . . . . . . . . . . . 27
3.1.3.1 Cut-offenergy . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.3.2 k-pointsampling . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.3.3 Fermisurfacesmearing . . . . . . . . . . . . . . . . . . . . 28
3.1.3.4 Pseudopotential . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 EquationofStates(EOS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 MurnaghanEOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Birch-MurnaghanEOS . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2.1 2nd orderBirch-MurnaghanEOS . . . . . . . . . . . . . . . 33
3.2.2.2 3rd orderBirch-MurnaghanEOS . . . . . . . . . . . . . . . 34
3.3 Energy-strainrelationofanelasticbody . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Generalformulationofenergy-strainrelationofanelasticbodyincubic
symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Tetragonalandtrigonalshear(C −C andC ) . . . . . . . . . . . . 37
11 12 44
3.4 Homogenizationmethodofelasticconstants . . . . . . . . . . . . . . . . . . . 39
3.5 AtomicvolumedeterminedbyBaderAnalysis . . . . . . . . . . . . . . . . . . 41
3.6 Ashby’smaterialspropertyanddesignchart . . . . . . . . . . . . . . . . . . . 42
II Results and Discussion 47
4 EquationofstatesofstudiedAlbinarysolidsolutions 49
4.1 Equationofstatesofselectedelementsinpurebulkphases . . . . . . . . . . . 50
4.2 Latticeparameters(a )andbulkmoduli(B )ofstudiedAlbinarysolidsolutions 52
0 0
4.2.1 a and B calculatedbyDFT . . . . . . . . . . . . . . . . . . . . . . . 52
0 0
4.2.2 Comparisonofa and B byDFTandexperiments . . . . . . . . . . . 54
0 0
ii
CONTENTS
4.2.3 ComparisonofDFTwithVegard’slaw . . . . . . . . . . . . . . . . . 57
4.3 EnthalpiesofstudiedAlbinarysolidsolutions . . . . . . . . . . . . . . . . . . 58
4.3.1 Denotationofenthalpies . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.2 EnthalpyofmixingofstudiedAlbinarysolidsolutions . . . . . . . . . 59
4.3.2.1 Enthalpy of mixing per atom, ∆H of studied Al binary
mix
solidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.2.2 Enthalpy of mixing per solute, ∆H (persolute) of studied
mix
Albinarysolidsolutions . . . . . . . . . . . . . . . . . . . . 60
4.3.3 SolubilityenthalpyofstudiedAlbinarysolidsolutions . . . . . . . . . 63
4.3.3.1 StudiedAlbinaryintermetalliccompounds . . . . . . . . . . 63
4.3.3.2 Solubilityenthalpyperatom,∆H ofstudiedAlbinarysolid
sol
solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.3.3 Solubilityenthalpypersolute,∆H (persolute)ofstudiedAl
sol
binarysolidsolutions . . . . . . . . . . . . . . . . . . . . . 65
5 ElasticpropertiesofstudiedAlbinarysolidsolutions 67
5.1 Elasticconstantsofselectedpureelementsinfccstructure . . . . . . . . . . . 68
5.2 ElasticconstantsofstudiedAlbinarysolidsolutions . . . . . . . . . . . . . . 69
5.2.1 C −C andC ofAl-CaandAl-Srsolidsolutions . . . . . . . . . . 69
11 12 44
5.2.2 C −C andC ofAl-IrandAl-Cusolidsolutions . . . . . . . . . . 72
11 12 44
5.2.3 C −C andC ofAl-MgandAl-Lisolidsolutions . . . . . . . . . . 75
11 12 44
5.2.4 C −C andC ofAl-Znsolidsolutions . . . . . . . . . . . . . . . . 78
11 12 44
5.3 Discussiononsupercellsizedependence . . . . . . . . . . . . . . . . . . . . . 80
5.4 HomogenizedelasticmoduliofstudiedAlbinarysolidsolutions . . . . . . . . 82
5.4.1 HomogenizedelasticmoduliofAl-CaandAl-Srsolidsolutions . . . . 82
5.4.2 HomogenizedelasticmoduliofAl-IrandAl-Cusolidsolutions . . . . 85
5.4.3 HomogenizedelasticmoduliofAl-MgandAl-Lisolidsolutions . . . . 88
5.4.4 HomogenizedelasticmoduliofAl-Znsolidsolutions . . . . . . . . . . 91
iii
CONTENTS
6 StrengtheningparametersofstudiedAlsolidsolutions 93
6.1 Validationofcalculatedstrengtheningparameters . . . . . . . . . . . . . . . . 94
6.1.1 Modelparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.1.2 Strengtheningparameters . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2 Limitationsandapplicabilitiesofmodulusandvolumemismatchparameters . . 97
6.2.1 Modulusmismatchmodelparameter . . . . . . . . . . . . . . . . . . . 97
6.2.2 Volumemismatchmodelparameter . . . . . . . . . . . . . . . . . . . 98
6.3 Chemicaltrendofsolidsolutionstrengtheningonperiodictable . . . . . . . . 102
6.3.1 ChemicaltrendofsolidsolutionstrengtheninginAlbinarysystems . . 102
6.3.2 Chemicaltrendofsolidsolutionstrengtheninginpreviousstudies . . . 112
6.3.2.1 Mgbasedbinarysystems . . . . . . . . . . . . . . . . . . . 112
6.3.2.2 Nibasedbinarysystems . . . . . . . . . . . . . . . . . . . . 115
6.3.3 Discussionofthechemicaltrend . . . . . . . . . . . . . . . . . . . . . 118
6.4 Correlationbetweensolubilityandstrengtheningparameter . . . . . . . . . . . 122
7 PerturbationcausedbysoluteatomsinstudiedAlbinarysolidsolutions 129
7.1 Purposeofthischapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2 Atomic volume and charge transfer of solute atoms in studied Al binary solid
solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.3 AverageelectrondensityofeachAlatominstudiedAlbinarysolidsolutions . 134
7.3.1 Separatingelasticandchemicaleffect . . . . . . . . . . . . . . . . . . 134
7.3.2 Average electron density of each Al atom in relaxed supercells (elastic
effectandchemicaleffect) . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3.2.1 Average electron density of each Al atoms in Al-Ca, Al-Sr
andAl-Mgsolidsolutions . . . . . . . . . . . . . . . . . . . 136
7.3.2.2 AverageelectrondensityofeachAlatominAl-IrandAl-Cu
solidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.3.2.3 AverageelectrondensityofeachAlatominAl-LiandAl-Zn
solidsolutions . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.3.3 AverageelectrondensitiesofeachAlatomduetoeitherchemicaleffect
orelasticeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4 Correlationbetweenperturbationandsolidsolutionstrengthening . . . . . . . 150
7.5 Correlationbetweenperturabtionandsupercellsizedependence . . . . . . . . 152
iv