predicting new materials and their properties with ... · s. botti // predicting new perovskites //...

Predicting new materials and theirproperties with supercomputers

The example of perovskites

Silvana Botti

Friedrich-Schiller Universität JenaGermany

OSI, Dublin 29.6.2017

New perovskites for photovoltaics

1 Our toolsTheory, algorithms, codes and databases

2 Exploring the periodic tableHigh-throughput calculationsMore accurate characterizationImprove efficiency with machine learning

S. Botti // Predicting new perovskites // Uni Jena

How many materials do we know?

Ü Molecules: 112 million (CAS)Ü Inorganic crystals: 181 000 (ICSD)

but...

Ü Remove duplicatesÜ Remove alloysÜ Remove incomplete structures (e.g., missing hydrogens)

Materials Project Database: 50 000 structures!


Exploring the periodic table

The number of combinations of elements is enormous!


Searching for perovskites

Perovskites are some of the most interesting materials knownÜ Magnetism, ferroelectricity, piezoelectricity, photovoltaics,

thermoelectricity, superconductivity.Ü Composition ABX3 where X is O, S, Se, Te, F, Br, Cl, or I.Ü In most of the cases, perovskites crystallize in a deformed

version of the ideal cubic structure, with unit cells with10–40 atoms.

Can we find more perovskites?


Which tools do we need?

1. Reliable equations from quantum mechanics2. Efficient algorithms and codes3. Fast computers and databases


How to determine the stability of a compound?

The distance to the convex hull Ehull is a measure of stability

Energies are calculated with DFT (VASP) and structures arepredicted with the minima hopping method

S. Körbel, M.A.L. Marques, S. Botti, J. Chem. Mater. C 4, 3157 (2016)


Finding new structures

For a given composition, we are interested in finding the globalminimum of the ground-state Born-Oppenheimer surface.Other low-lying minima are also interesting as they may bestabilized by temperature, pressure, doping, etc.

...but the number of local minima increasesexponentially with the number of atoms inthe unit cell.

Ü Solution: Global Structural Predictionmethods (genetic algorithms, randomsearch, minima hopping method, etc.)

Ü Density functional theory to determineenergy and forces (VASP)


Minima Hopping Method

S. Goedecker, J. Chem. Phys. 120, 9911 (2004)M. Amsler and S. Goedecker, J. Chem. Phys. 133, 224104 (2010)


Materials Project database

The MP gathers already ≈ 1000 ABX3 structures

Ü We use the structures of the MP databaseÜ Our new structures are sent to the MP database

materialsproject.org


materialsproject.org

The quest for new materials

1 Our toolsTheory, algorithms, codes anddatabases

2 Exploring the periodic tableHigh-throughput calculationsMore accurate characterizationImprove efficiency with machinelearning


Nitride perovskites

Ü Composition ABX3 where X is O, S, Se, Te, F, Br, Cl, or I.

What about perovskites with X=N?


Stability map for ABN3

CsRb KNa LiBa SrCa YLa

ScZr HfTi TaNb VCr

MoW ReTc OsRu

IrRh PtPd

AuAg CuNi CoFe MnMg ZnCd HgBe AlGa InTl

PbSn GeSi

BC NP

AsSb BiTe

SeS OI BrCl FH

Cs

Rb

K

Na

Li

Ba

SrC

a

YLa

Sc

Zr

Hf

Ti

TaN

b

VC

r Mo

W

R

eTc

Os

Ru

Ir

Rh

Pt

Pd

AuAg

Cu

Ni

Co

Fe

M

nM

g

Zn

Cd

Hg

Be

AlG

a

InTl

Pb

Sn

G

eSi

B

C

NP

AsSb

Bi

Te

SeS

O

I Br

Cl

FH

A (1

a)

B (1b)

ABN3

-50

0

50

100

150

200

250

300

350

400

R. Sarmiento-Pérez, T.F.T. Cerqueira, S. Körbel, S. Botti, M.A.L. Marques, Chem.Mater. 27, 5957 (2015)


Nitride cubic perovskites

1

H

3

Li

11

Na

19

K

37

Rb

55

Cs

4

Be

12

Mg

20

Ca

38

Sr

56

Ba

21

Sc

39

Y

57

La

22

Ti

40

Zr

72

Hf

23

V

41

Nb

73

Ta

24

Cr

42

Mo

74

W

25

Mn

43

Tc

75

Re

26

Fe

44

Ru

76

Os

27

Co

45

Rh

77

Ir

28

Ni

46

Pd

78

Pt

29

Cu

47

Ag

79

Au

30

Zn

48

Cd

80

Hg

31

Ga

13

Al

5

B

49

In

81

Tl

6

C

14

Si

32

Ge

50

Sn

82

Pb

7

N

15

P

33

As

51

Sb

83

Bi

8

O

16

S

34

Se

52

Te

84

Po

9

F

17

Cl

35

Br

53

I

85

At

10

Ne

2

He

18

Ar

36

Kr

54

Xe

86

Rn

LaXN3400 eV

1

2

3

4

5

6

1 IA

2 IIA

3 IIIB 4 IVB 5 VB 6 VIB 7 VIIB 8 VIIIB 9 VIIIB 10 VIIIB 11 IB 12 IIB

13 IIIA 14 IVA 15 VA 16 VIA 17 VIIA

18 VIIIA

Ü 3906 cubic perovskites testedÜ Structural prediction for 23 compositionsÜ 21 stable ABN3 phases (3 perovskites)

Sarmiento-Pérez et al. Chem. Mater. 27, 5957 (2015)Körbel, Marques, Botti, J. Chem. Mater. C 4, 3157 (2016)


ABN3 structures

(a) spg 221 (b) spg 62 (c) spg 161

(d) spg 15 (d) spg 14 (e) spg 12

Sarmiento-Pérez et al. Chem. Mater. 27, 5957 (2015)Körbel, Marques, Botti, J. Chem. Mater. C 4, 3157 (2016)


High-throughput screening of ABX3 perovskites0

24

68

10

12

CsO

F3

RbInCl 3

CsSnI 3

LaW

N3

RbSnBr 3

CsSnBr 3

RbGeI

3

BaHfS

3

CsG

eI3

CsSnCl 3

RbSnCl 3

RbGeB

r 3KCuF3

RbCuF3

SrT

cO3

TlCuF3

CsG

eBr 3

BaSnO

3

KGeC

l 3TlSnCl 3

CsP

bBr 3

RbGeC

l 3TlFeF

3

RbHgF3

CsH

gF3

InSnCl 3

CsG

eCl 3

CsP

bCl 3

InGeC

l 3CsC

dCl 3

RbCdCl 3

PbTiO

3

KTaO

3

SrT

iO3

KNbO

3

RbMnCl 3

BaTiO

3

RbVF3

InMnF3

TlH

gF3

RbIO

3

TlM

nF3

KMnF3

CsSnF3

NaTaO

3

AgMgF3

TlN

iF3

TlIO

3

RbMnF3

PbHfO

3

PbZrO

3

CsM

nF3

BaZrO

3

CsP

bF3

RbPbF3

LaAlO

3

CsC

aI 3

BaHfO

3

RbNiF

3

CsSrB

r 3KNiF

3

RbCdF3

TlM

gF3

CsC

dF3

TlZnF3

RbMgCl 3

TlCdF3

RbCaBr 3

KMgCl 3

KZnF3

CsC

aBr 3

RbZnF3

CsSrC

l 3RbCaCl 3

CsC

aCl 3

CsSrF

3

KCaF3

RbCaF3

KMgF3

RbMgF3

CsC

aF3

Eg(eV)

01020304050607080

CsP

bF3

RbPbF3

KNbO

3

TlCdF3

NaTaO

3

BaTiO

3

InMnF3

TlIO

3

PbTiO

3

TlH

gF3

LaW

N3

|P|(µC/cm

2)

HSE directHSE indirect

LDA

S. Körbel, M.A.L. Marques, S. Botti, J. Chem. Mater. C 4, 3157 (2016)


Theoretical spectroscopy


2 Exploring the periodic tableHigh-throughput calculationsMore accurate characterizationImprove efficiency with machinelearning


The quest for new materials


2 Exploring the periodic tableHigh-throughput calculationsMore accurate characterizationImprove efficiency with machine learning


Machine learning

Given a set of N training features of the form {(xi, yi)}, wherey = Ehull, the learning algorithm seeks the function y(xi) thatbest fits the data.

Ü Create a large database of DFTcalculations (250 000 perovskites)

Ü Probe a training set for structure withmachine learning: ridge regression,random forests, extremely randomizedtrees (including adaptive boosting), andneural networks.

Ü Predict new data, validate the model, andspeed up calculations

Predicting the thermodynamic stability of solids combining density functional theoryand machine learning, Schmidt et al., Chem. Mat. 29 5090 (2017).


Benchmark dataset

DFT calculations of 250 000 cubic perovskites

Reliability:Ü 59% of experimental

compounds < 0Ü 76% < 25 meV/atomÜ 85% < 50 meV/atomÜ 95% < 150 meV/atom

Why?Ü It is possible to stabilize compounds above hullÜ Errors in databases (A↔ B)Ü ABX3 compounds that are not perovskites


Feature importance

The minimum MAE (120 meV/atom) is obtained using 11features per atom:

Ü atomic numberÜ Pauling electronegativityÜ most common oxidation stateÜ average ionic radiusÜ number of valence electronsÜ period in the periodic table

Ü group in the periodic tableÜ ionization energyÜ polarizabilityÜ number of s+ p valence

electronsÜ number of d or f valence

electrons.

The location of the elements in the periodic table is alreadysufficient to predict the distance to the convex hull with a MAEonly 20 meV/atom higher than the best MAE!


Energy distance to the convex hull

MAE (meV/atom) Machine learning model298.9± 0.3 Ridge regression155.5± 4.8 Neural network140.0± 0.6 Random forests126.6± 1.0 AdaBoost/Random forests123.1± 0.8 Extremely randomized trees121.3± 0.8 AdaBoost/Extremely randomized trees


Dependence on the size of the training set

50

100

150

200

250

300

0 10000 20000 30000 40000 50000

MAE

(eV/

atom

)

size of training set

errorpower

Ü Doubling the size of the training set only decreases theerror by 20%


Dependence of the MAE on the chemistry

1 H(145)

3 Li(126)

11Na(122)

19 K(117)

37Rb(121)

55Cs(149)

4 Be(137)

12Mg(122)

20Ca(106)

38Sr(106)

56Ba(112)

21Sc(111)

39 Y(113)

57La(130)

22Ti(105)

40Zr(105)

72Hf(116)

23 V(118)

41Nb(110)

73Ta(124)

24Cr(160)

42Mo(114)

74W(129)

25Mn(175)

43Tc(116)

75Re(125)

26Fe(127)

44Ru(109)

76Os(122)

27Co(103)

45Rh(109)

77 Ir(121)

28Ni(105)

46Pd(112)

78Pt(113)

29Cu(101)

47Ag(104)

79Au(114)

30Zn(110)

48Cd(109)

80Hg(108)

31Ga(106)

13Al(119)

5 B(149)

49 In(104)

81Tl(105)

6 C(163)

14Si(115)

32Ge(97)

50Sn(110)

82Pb(103)

7 N(184)

15 P(117)

33As(99)

51Sb(98)

83Bi(105)

8 O(196)

16 S(131)

34Se(110)

52Te(109)

84Po

9 F(194)

17Cl(139)

35Br(136)

53 I(129)

85At

10Ne

2 He

18Ar36Kr54Xe86Rn

MAE90 110 130 150 170 meV/atom

1

2

3

4

5

6

IA

IIA

IIIB IVB VB VIB VIIB VIIIB VIIIB VIIIB IB IIB

IIIA IVA VA VIA VIIA

VIIIA

Larger errors: first row anomaly, magnetic systems, problemwith pseudopotentials


Strategy: accelerate calculations!

1. DFT calculation of 20 000 cubic perovskites withrandom compositions;

2. train the learning machine (extremely random trees);3. predict the distance to the hull of the remaining≈230 000 possible compounds without performing onthem explicit DFT calculations;

4. remove all systems that lie higher than a certain cutoffenergy form the hull. For example, putting the cutoff at700 meV/atom allows us to recover 99.4% of allsystems that are stable within DFT;

5. calculate using DFT these compounds. In ourexample, this amounts to an extra 41 000 DFTcalculations, leading to a total saving of computationtime of 73%.


Conclusions and perspectives

Ü The dream to create new materials in silico is getting real

Ü Need for: accurate theories, efficient algorithms andcodes, materials databases, supercomputers

Ü New developments: from perfect crystals to real materials

Ü Which properties?Many possible application fields are open!New materials for photovoltaics is a great challenge!


Thank you to my coworkers!

Valerio ArmuzzaPedro BorlidoWenwen CuiSabine KörbelSun LinChristoph OtzenClaudia RödlJingming ShiIvan GuilhonTiago CerqueiraRafael SarmientoUniversity of Jena

[email protected]://www.ico.uni-jena.de/

Miguel MarquesJonathan SchmidtUniversity of Halle

Stefan GoedeckerUniversity of BaselMax AmslerNorthwestern UniversityFernando NogueiraUniversity of CoimbraLiming ChenEcole Centrale Lyon


http://www.ico.uni-jena.de/

Our toolsTheory, algorithms, codes and databases

Exploring the periodic tableHigh-throughput calculationsMore accurate characterizationImprove efficiency with machine learning

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