composition structure properties...
TRANSCRIPT
Abini&omaterialsscience
AxByOz
Composition
H = ∇i2
i=1
Ne
∑ + Vnuclear (ri )i=1
Ne
∑ +12
1rj − rij≠i
Ne
∑i
Ne
∑
Alltheseelementstogetherformacompletedesignsuite
Structure
A"B$plane$
Properties Applications
StructureKeytoProper-es:Carbon
Graphite Diamond
Graphene
• Hard• Expensive• Thermalconduc&vity
• So>• Inexpensive• Electricalconduc&vity
• Exuberance• Nature,Sciencepapers
CanwepredictCrystalStructure?
In 1988 Maddox (Nature) described the inability to predict crystal structure as “scandalous” – Where are we now ?
Structureismul--valuedfunc-onofcomposi-on
Composition Structure
Structure
Structure
Structure
Structure
Ground State
Metastable
Metastable
Metastable
Metastable
Howmuchofknowncompoundsareactuallymetastable?
• Mathematical Simulated annealing Genetic algorithms …
• Guess (the grab bag)
• Machine learning
StructurePredic-onasanOp-miza-onProblem
Energy Model E({R})
Search Strategy
DFT
Thesearchproblem
Mathematical: difficult to prove optimality
If I can only see local curvature, how do I know I am in global minimum ?
Exactgroundstatesolu-onsoflaBcemodels
H σ{ }( ) = V0 +V1 σ i + 12
i∑ Vi, jσ i
i, j∑ σ j + 1
6Vi, j,kσ i
i, j,k∑ σ jσ k ...
Problemofdistribu&ngitemsonpre-definedsetofsites
Surfaceadsorp&on AlloyOrdering VacancyOrdering
DFT
CoarseGraining
Theapproach
Upp
erbou
nd
Lowerbou
nd
Anyconfigura&oniseffec&velyanupperbound.Butneedtopushthisaslowaspossibleefficiently
EXACTMINIMUM
WenxuanHuang
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
Minimizingtheupperbound:Rela-ontoLogicProblems
Witha4x4x4unitcell(264configura&ons),onamodern4GHzprocessor–manydecades!
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
ClusterExpansion:
MAX-SAT:
“and” “or”“not”
Binaryoccupa&on->binarylogic
The“Logic”Olympics
MAX-SATsolversac&velydeveloped:– Annualcompe&&onstodesignMAX-SAT
solvers– Stateoftheart–solvethe4x4x4casein
seconds
hdp://vsl2014.at/olympics/
“TheaimoftheFLoCOlympicGames2014istostartatradi@oninthespiritoftheancientOlympicGames,aPanhellenicsportfes@valheldeveryfouryearsinthesanctuaryofOlympiainGreece,this@meinthescien@ficcommunityofcomputa@onallogic.”
Theapproach
Upp
erbou
nd
Lowerbou
nd
Anyconfigura&oniseffec&velyanupperbound.Butneedtopushthisaslowaspossibleefficiently
EXACTMINIMUM
WenxuanHuang
Importanttheorem:finiteminimiza&onwithoutimposingperiodicityprovideslowerbound
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
Lowerboundisgivenbysmallclusterop&miza&on
H σ{ }( ) = Ji, jσ ii, j∑ σ j
J Absolutelowestpossibleenergy
Emin=–J
1DChain
TriangularlaBce
?σ iσ j min
= −1/ 3 Emin=–1/3J
Minimizingtheenergyofafiniteblockofspinsisalwaysalowerboundtotheenergy
λ-shi>ing
J0s0
J1s0s1
J0s1
J1s0s1
0.5J0s1
J1s0s1
0.5J0s0
Allofthesetransforma&onleavetheenergyoftheinfinitelahceunchanged
H ≥mins0 ,s1
J0s1 + J1s0s1( ) H ≥ mins0 ,s1,s2
0.5J0s0 + 0.5J0s1 + J1s0s1( )
H ≥ mins0 ,s1,s2
λ J0s0 + (1− λ)J0s1 + J1s0s1( )
H ≥mins0 , s1
J0s0 + J1s0s1( )
Lineartransforma&onsofHamiltonianthatleaveinfinitelahceenergyunchanged,butchangefiniteclusterop&miza&onenergy
Lowerboundcalcula&onisamax-minproblem
• Eλ,sislinearwithrespecttoλ
maxλ
mins∈{0,1}B
Eλ ,s
Eλ ,s = J0 λ1s0 + λ2s1 + 1− λ1 − λ2( ) s2( ) + J1 λ3s0s1 + 1− λ3( ) s1s2( ) + J2s0s2( )
λ
Eλ,s_1=(001)
Eλ,s_1=(100)Eλ,s_1=(110)
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
Example:LixTi(1-x)O2
15
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull1
DFTon600Structures
Exp.structureknown,butnotaddedtoinputset
Exp.Compound,butstructureunknown
H σ{ }( ) = V0 +V1 σ i + 12
i∑ Vi, jσ i
i, j∑ σ j + 1
6Vi, j,kσ i
i, j,k∑ σ jσ k ...
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull1
Hull2
Groundstatepredic&on
TiO Li2TiO3
16
Threeitera&onsleadstocorrectstructureatLi2TiO3aswellasseveralnovelstructures
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull1
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull1
Hull2
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull2
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull2
Hull3
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull3
Fo
rmati
on
en
erg
y (
eV
/f.u
.)
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
x in LixTi(1-x)O 0 0.1 0.2 0.3 0.4 0.5 0.6
Hull3
Hull4
• Mathematical Simulated annealing Genetic algorithms …
• Guess (the grab bag)
• Machine learning
StructurePredic-onasanOp-miza-onProblem
Energy Model E({R})
Search Strategy
DFT
Canwemachinelearnstructurepredic-on?
We have tens of thousands of crystal structures (ICSD, computation)
z
yx
MachineLearningThroughBayesianInference
P(X=x1,x2,…,xn)
A
B C
?
??
Canknowledgeofsomecrystalstructuresina
systemteachmethestructuresatother
composi-ons?P(A|B)
Predic&on=P(X |knowninforma&on)
“learning”P(X)islearningwhichcrystalstructuresexisttogetherinchemicalsystems
DATA
ICSD
≈100,000
crystal
structure
assignments
Fischer, C., Tibetts, K., Morgan, D. & G, C. Predicting Crystal Structure by merging data mining with Quantum Mechanics. Nature Materials, 5, 641(2006).
“Learned”crystalstructurepredic-onisremarkablyeffec-ve
1580ternaryoxidesystems
90% probability to get correct structure by investigating 17 - 18 structures
Probabilitythatcorrectgroundstateisamongthesugges-ons
Over300newcompoundspredicted
Hau0er,G.,Fischer,C.,Jain,A.,Mueller,T.,Ceder,G.ChemistryofMaterials(2010)
LearningSimilarityBetweenIonsfromData
Whatisthesimilarityoftwoionswithrespecttostructureforma&on?
A2B3O6 A2C3O6
DATABASE:ICSD
Subs&tu&on
Canweextractthesubs@tu@onrules? CdMn2O4ZnMn2O4MgMn2O4
Allthesamestructure
G.Hau&er,etal,InorganicChemistry,50(2),656-663(2011).
L.Yang,S.Dacek,G.Ceder,PhysicalReviewB,90(5),054102(2014).
Lanthanides
Transi&onmetals
Ba2+,Ca2+,Sr2+havehighsubs&tu&onalprobability
Oxidesonly
G.Hau&er,etal,InorganicChemistry,50(2),656-663(2011).L.Yang,S.Dacek,G.Ceder,PhysicalReviewB,90(5),054102(2014).
Novel
compounds
Novel
compounds
Known
compounds
Discoveringnovelcompounds
Li9V3(P2O7)3(PO4)2
A.Jainetal.,J.ElectrochemicalSociety,159(5),pp.A622-A633(2012).
Computer“invented”compound
Li9Fe3(P2O7)3(PO4)2
ComputerDesignedLi9V3(P2O7)3(PO4)2performswell
Achallengeforthenextdecade• Compounddesignmachineryisbecomingincreasingly
morepowerful
• ButhowIknowwhatcanbesynthesized?Domainoverwhichtoperformmaterialsdesignispoorlybounded
Composition Structure
Structure
Structure
Structure
Structure
Ground State
Metastable
Metastable
Metastable
Metastable
Variational principle
Synthesis prediction ?
Synthesis prediction ?
Howmanyknownstructuresaremetastable?Isthereaguidingprincipleforwhatcrystallinesolidscanbesynthesized?
Ques-ons
IsEnergyaGuidingPrinciple?
Frequencyhea&ngtemperatureasafunc&onofsynthesisapproach
A2B AB AB2A B
β2
Form
a-onenergy
α1
γ1
α3
α2
γ2
β1
β3
Thermodynamicgroundstates
Metastablephases.WhatisE-scale?Whichonescanbemade?
ConvexHull
WenhaoSun
WenhaoSunetal,“Thethermodynamicscaleofcrystalineinorganicmetastability”ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
Largedatasetsareavailabletotestenergyhypothesis
ICSD:OBSERVATIONS
“Observed”
compounds
THERMOCHEMICALDATA
TheMaterialsProject
Result:≈50%ofknowncrystallinecompoundsaremetastable
BinaryOxides:DataProvenanceandVeracity
Dataset:SubsetofICSDofObserved,CrystallinePhases,whoseenergiesarewell-describedbyDFTManuallyinves@gateddataprovenanceinICSDBinaryOxides
≈10kJ≈2.4kcal≈10.5BTU
WenhaoSunetal,“Thethermodynamicscaleofcrystalineinorganicmetastability”ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
Median=15meV/atom
90thpercen-le=67meV/atom(ExcludingSpuriousStructures)
Remarkablesimilarityacrosschemistries…exceptfornitrides
WenhaoSunetal,“Thethermodynamicscaleofcrystalineinorganicmetastability”ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
“Forms”ofmetastability
αβ
Polymorphism Metastableagainst
phasesepara-on
• Polymorphismhaslowerenergyscalethanphasesepara&onmetastability
• Asnumberofcomponentsincreases,energyscaleofpolymorphismdecreases
• Frac&onofpolymorphismdecreaseswithnumberofcomponents
polymorphismPhasesepara&on
Phasesepara&onmetastabilityiseasierthanpolymorphism
WenhaoSunetal.,ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
Therearemanyunobserved,low-energystructuresinverywell-studiedsystems–whyaren’ttheyseen?
Is“low”energyasufficientcondi&onformetastability?
WenhaoSunetal.,ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
Howmanyknownstructuresaremetastable?Isthereaguidingprincipleforwhatcrystallinesolidscanbesynthesized?
Ques-ons
“Remnantmetastability,”AGuidingPrinciple?
• High temperature stable phases can be “quenched”
• High pressure phases can be retained at normal pressure
Can we extend the idea that metastable phases are made under thermodynamic conditions where they were stable and retained in conditions where the are metastable ?
• Composition ?
• Size ?
• Stress ?
d G X YΔ = Δ
Surfaceareaasahandletoformmetastablephases
A. Navrotsky, Geochem. Trans. 4(6), 34-37 (2003).
TiO2:anataseversusru&le
β
α
Moststablephasebuthighnuclea@onbarrier
(Desired)
metastablephasebutlownuclea@onbarrier
Size dependent phase stability will be important in nucleation
Surfaceenergy
Adsorp-on
Charge
FeS2PyriteandMarcasite
• Phases:
– Pyrite(Pa3)isgroundstate,Marcasite(Pmnn)ispolymorph
• Synthesis:
– Marcasiteformshydrothermallyinacid(pH<4)
– Pyriteformsinneutralandalkalinesolu&ons(pH>6)
• Adsorp-oncharacteris-cs:
– Pyritehasisoelectricpoint(IEP)atpH~1.4
– MarcasitehasIEPsomewherearoundpH<3
Pyrite
MarcasiteSSI2ProgramledbyDMorganUW-NSFD.Kitchaev,G.Ceder."Evalua&ngstructureselec&oninthehydrothermalgrowthofFeS2pyriteandmarcasite."[email protected],13799(2016).doi:10.1038/ncomms13799
DaniilKitchaev
FeS2PyriteandMarcasite:AqueousSurfaceEnergy
Calculatebothsurfaceenergiesofbothphaseswithvariousadsorbates(H,OH,H2O
D.Kitchaev,G.Ceder."Nat.Comm.7,13799(2016).doi:10.1038/ncomms13799
FeS2PyriteandMarcasite:AqueousSurfaceEnergy
BothphasesstronglyadsorbOH-,butmarcasitefavorsH3O+morethanpyrite
Marcasitenuclea&onpreferredatlowpH
D.Kitchaev,G.Ceder."Nat.Comm.7,13799(2016).doi:10.1038/ncomms13799
Cri&calnucleussizecalculatedfromreportedsupersatura&onnecessary
CaCO3:andoldproblem
Calcite:Equilibriumphase Aragonite:precipitatesinseawatercondi&ons(presenceofMg2+ions)
Mg2+increasesthesurfaceenergyofcalcite
W.Sun,S.Jayaraman,W.Chen,K.Persson,G.Ceder,Nuclea@onofMetastableAragoniteCaCO3inSeawater,PNAS,112(11),3199-3204(2015)
Twohighlydis&nctapproaches
Deduc-ve–TheoryDriven
10
15
20
25
30
35
40
45
{1100}
{1120}
{0001}
Data-centric:Canwelearnfromtheliterature?
Collabora&onwithElsaOliveh-MIT
Machine-readSynthesisRecipesfromPublica&ons
NaNi1/3Co1/3Fe1/3O2wassynthesizedbysolid-statereac&on.ExcessamountsofNa2O,NiO,Co3O4andFe2O3weremixedandballmilled
for4hat500rpmrate,andtheresul&ngmaterialwascollectedintheglovebox.About0.5gofpowderwasfiredat800°CunderO2for14hbeforeitwasquenchedtoroom
temperatureandmovedtoagloveboxfilledwithargon.
Parsesynthesissec&onsthroughmachinelearningandrule-based
methods
Generatecodified,computeinterpretabledatabaseof
recipesRecipe
database
AllknowncompoundsthathavebeenexperimentallysynthesizedLivingdatabase
Route1Step1 Step2 Stepn
Condi&ons Condi&ons Condi&ons
Route2Step1 Step2 Stepn
Condi&ons Condi&ons Condi&ons
RoutenStep1 Step2 Stepn
Condi&ons Condi&ons Condi&ons
Collabora&onwithElsaOliveh-MIT
SynthesisGenome:iden&fypaderns,connecttothermodynamicsandkine&cs
Frequencyhea&ngtemperatureasafunc&onofsynthesisapproach
Collabora&onwithElsaOliveh-MIT
SeePosterTC2.6.21byEdwardKimetal.Tonight!!
Summary
• Thereissignificantprogressinthepredic&onofstructure.Exactsolu&onsforlahcemodelgroundstates.
• Machinelearningmethods+high-throughputcompu&ngmay“smart–brute–force”thisproblem
• Sta&s&callearningmethodsarehighlysuccessfulinlearningtopredictcrystalstructures
Groundstatestructure
Metastablepolymorphs/Synthesis• Energyscaletendstobe<100meV/atomformostcrystallineinorganic
solids
• “Remnantmetastability”->Lookforbroadcondi&onswherethemetastablepolymorphisstable:size,chemistry,etc.
MyThanks
HowaccurateareDFTMethodsinStructurePredic-on?
The “Test”
Experimental structure is
mixed in with other possible
structures . Can DFT pick
out correct one ?
With High-Throughput Computing