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@miza@onandMAX-SATPhys.Rev.B94,134424(2016)

Minimizingtheupperbound:Rela-ontoLogicProblems

Witha4x4x4unitcell(264configura&ons),onamodern4GHzprocessor–manydecades!

W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@miza@onandMAX-SATPhys.Rev.B94,134424(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@miza@onandMAX-SATPhys.Rev.B94,134424(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@miza@onandMAX-SATPhys.Rev.B94,134424(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."NatureCommunica@ons.7,13799(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