Composition Structure Properties...
Transcript of Composition Structure Properties...
![Page 1: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/1.jpg)
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
![Page 2: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/2.jpg)
StructureKeytoProper-es:Carbon
Graphite Diamond
Graphene
• Hard• Expensive• Thermalconduc&vity
• So>• Inexpensive• Electricalconduc&vity
• Exuberance• Nature,Sciencepapers
![Page 3: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/3.jpg)
CanwepredictCrystalStructure?
In 1988 Maddox (Nature) described the inability to predict crystal structure as “scandalous” – Where are we now ?
![Page 4: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/4.jpg)
Structureismul--valuedfunc-onofcomposi-on
Composition Structure
Structure
Structure
Structure
Structure
Ground State
Metastable
Metastable
Metastable
Metastable
Howmuchofknowncompoundsareactuallymetastable?
![Page 5: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/5.jpg)
• Mathematical Simulated annealing Genetic algorithms …
• Guess (the grab bag)
• Machine learning
StructurePredic-onasanOp-miza-onProblem
Energy Model E({R})
Search Strategy
DFT
![Page 6: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/6.jpg)
Thesearchproblem
Mathematical: difficult to prove optimality
If I can only see local curvature, how do I know I am in global minimum ?
![Page 7: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/7.jpg)
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
![Page 8: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/8.jpg)
Theapproach
Upp
erbou
nd
Lowerbou
nd
Anyconfigura&oniseffec&velyanupperbound.Butneedtopushthisaslowaspossibleefficiently
EXACTMINIMUM
WenxuanHuang
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
![Page 9: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/9.jpg)
Minimizingtheupperbound:Rela-ontoLogicProblems
Witha4x4x4unitcell(264configura&ons),onamodern4GHzprocessor–manydecades!
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
ClusterExpansion:
MAX-SAT:
“and” “or”“not”
Binaryoccupa&on->binarylogic
![Page 10: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/10.jpg)
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.”
![Page 11: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/11.jpg)
Theapproach
Upp
erbou
nd
Lowerbou
nd
Anyconfigura&oniseffec&velyanupperbound.Butneedtopushthisaslowaspossibleefficiently
EXACTMINIMUM
WenxuanHuang
Importanttheorem:finiteminimiza&onwithoutimposingperiodicityprovideslowerbound
W.Huangetal.,FindingtheGroundStateofaGeneralizedIsingModelbyConvexOp@[email protected],134424(2016)
![Page 12: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/12.jpg)
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
![Page 13: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/13.jpg)
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
![Page 14: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/14.jpg)
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)
![Page 15: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/15.jpg)
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
![Page 16: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/16.jpg)
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
![Page 17: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/17.jpg)
• Mathematical Simulated annealing Genetic algorithms …
• Guess (the grab bag)
• Machine learning
StructurePredic-onasanOp-miza-onProblem
Energy Model E({R})
Search Strategy
DFT
![Page 18: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/18.jpg)
Canwemachinelearnstructurepredic-on?
We have tens of thousands of crystal structures (ICSD, computation)
z
yx
![Page 19: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/19.jpg)
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).
![Page 20: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/20.jpg)
“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)
![Page 21: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/21.jpg)
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).
![Page 22: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/22.jpg)
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).
![Page 23: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/23.jpg)
Novel
compounds
Novel
compounds
Known
compounds
Discoveringnovelcompounds
![Page 24: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/24.jpg)
Li9V3(P2O7)3(PO4)2
A.Jainetal.,J.ElectrochemicalSociety,159(5),pp.A622-A633(2012).
Computer“invented”compound
Li9Fe3(P2O7)3(PO4)2
![Page 25: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/25.jpg)
ComputerDesignedLi9V3(P2O7)3(PO4)2performswell
![Page 26: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/26.jpg)
Achallengeforthenextdecade• Compounddesignmachineryisbecomingincreasingly
morepowerful
• ButhowIknowwhatcanbesynthesized?Domainoverwhichtoperformmaterialsdesignispoorlybounded
Composition Structure
Structure
Structure
Structure
Structure
Ground State
Metastable
Metastable
Metastable
Metastable
Variational principle
Synthesis prediction ?
Synthesis prediction ?
![Page 27: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/27.jpg)
Howmanyknownstructuresaremetastable?Isthereaguidingprincipleforwhatcrystallinesolidscanbesynthesized?
Ques-ons
![Page 28: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/28.jpg)
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
![Page 29: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/29.jpg)
Largedatasetsareavailabletotestenergyhypothesis
ICSD:OBSERVATIONS
“Observed”
compounds
THERMOCHEMICALDATA
TheMaterialsProject
Result:≈50%ofknowncrystallinecompoundsaremetastable
![Page 30: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/30.jpg)
BinaryOxides:DataProvenanceandVeracity
Dataset:SubsetofICSDofObserved,CrystallinePhases,whoseenergiesarewell-describedbyDFTManuallyinves@gateddataprovenanceinICSDBinaryOxides
≈10kJ≈2.4kcal≈10.5BTU
WenhaoSunetal,“Thethermodynamicscaleofcrystalineinorganicmetastability”ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
![Page 31: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/31.jpg)
Median=15meV/atom
90thpercen-le=67meV/atom(ExcludingSpuriousStructures)
Remarkablesimilarityacrosschemistries…exceptfornitrides
WenhaoSunetal,“Thethermodynamicscaleofcrystalineinorganicmetastability”ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
![Page 32: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/32.jpg)
“Forms”ofmetastability
αβ
Polymorphism Metastableagainst
phasesepara-on
![Page 33: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/33.jpg)
• Polymorphismhaslowerenergyscalethanphasesepara&onmetastability
• Asnumberofcomponentsincreases,energyscaleofpolymorphismdecreases
• Frac&onofpolymorphismdecreaseswithnumberofcomponents
polymorphismPhasesepara&on
Phasesepara&onmetastabilityiseasierthanpolymorphism
WenhaoSunetal.,ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
![Page 34: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/34.jpg)
Therearemanyunobserved,low-energystructuresinverywell-studiedsystems–whyaren’ttheyseen?
Is“low”energyasufficientcondi&onformetastability?
WenhaoSunetal.,ScienceAdvancesVol.2,no.11,e1600225DOI:10.1126/sciadv.1600225
![Page 35: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/35.jpg)
Howmanyknownstructuresaremetastable?Isthereaguidingprincipleforwhatcrystallinesolidscanbesynthesized?
Ques-ons
![Page 36: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/36.jpg)
“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
![Page 37: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/37.jpg)
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
![Page 38: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/38.jpg)
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
![Page 39: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/39.jpg)
FeS2PyriteandMarcasite:AqueousSurfaceEnergy
Calculatebothsurfaceenergiesofbothphaseswithvariousadsorbates(H,OH,H2O
D.Kitchaev,G.Ceder."Nat.Comm.7,13799(2016).doi:10.1038/ncomms13799
![Page 40: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/40.jpg)
FeS2PyriteandMarcasite:AqueousSurfaceEnergy
BothphasesstronglyadsorbOH-,butmarcasitefavorsH3O+morethanpyrite
Marcasitenuclea&onpreferredatlowpH
D.Kitchaev,G.Ceder."Nat.Comm.7,13799(2016).doi:10.1038/ncomms13799
Cri&calnucleussizecalculatedfromreportedsupersatura&onnecessary
![Page 41: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/41.jpg)
CaCO3:andoldproblem
Calcite:Equilibriumphase Aragonite:precipitatesinseawatercondi&ons(presenceofMg2+ions)
![Page 42: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/42.jpg)
Mg2+increasesthesurfaceenergyofcalcite
W.Sun,S.Jayaraman,W.Chen,K.Persson,G.Ceder,Nuclea@onofMetastableAragoniteCaCO3inSeawater,PNAS,112(11),3199-3204(2015)
![Page 43: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/43.jpg)
Twohighlydis&nctapproaches
Deduc-ve–TheoryDriven
10
15
20
25
30
35
40
45
{1100}
{1120}
{0001}
Data-centric:Canwelearnfromtheliterature?
Collabora&onwithElsaOliveh-MIT
![Page 44: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/44.jpg)
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
![Page 45: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/45.jpg)
SynthesisGenome:iden&fypaderns,connecttothermodynamicsandkine&cs
Frequencyhea&ngtemperatureasafunc&onofsynthesisapproach
Collabora&onwithElsaOliveh-MIT
SeePosterTC2.6.21byEdwardKimetal.Tonight!!
![Page 46: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/46.jpg)
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.
![Page 47: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/47.jpg)
MyThanks
![Page 48: Composition Structure Properties Applicationsceder.berkeley.edu/Presentations/Ceder_MRS_Materials_Theory_Award_2016.pdfProperties Applications . Structure Key to Proper-es: Carbon](https://reader030.fdocuments.us/reader030/viewer/2022041008/5eb0eb2652053b34eb720ed2/html5/thumbnails/48.jpg)
HowaccurateareDFTMethodsinStructurePredic-on?
The “Test”
Experimental structure is
mixed in with other possible
structures . Can DFT pick
out correct one ?
With High-Throughput Computing