Obliczenia kwantowe a magazynowanie energii

Zbigniew Łodziana NZ31

Nothing about quantum computing!

Outline

• Problem of energy storage • Problem of quantum mechanics calculations • Hydrogen storage & calculations • Solid state electrolytes & calculations • Conclusions

Problem of energy storage

Solar energy

Planetary movement

fossil mineral

fossil biogenic

Heat, Wind Waves Precipitation Streams

Uranium Thorium

Geothermal heat

Tide

Gravitation

Nuclear fission

Nuclear fusion

Biomass biogenic

Photosynthesis

Energy fluxes

Coal, Crude oil Natural gas

Earth crust

The Future: Energy Fluxes

1

10

100

1000

10000

100000

0,001 0,01 0,1 1 10 100

En

erg

y d

ensi

ty [k

Wh

/m3]

Energy density [kWh/kg]

Pb-acid battery

Li-ion battery

mag. coil

EDLC

comp. air

hot water

biomass

coal

oil

fusion

fission

hydrogen storage

capacitor

hydro- power

hydrogen

natural gas

flywheel

NH3

GRAVITATION

ELECTROSTATIC

NUCLEAR

CHEMICAL

ELECTROCHEMICAL INERTIA

A. Züttel et al., Phil. Trans. R. Soc. A 2010 368, 3329

hydrides

Energy storage

Problem of quantum mechanics calculations

Development of computational methods

Density Functional Theory Start from N electron wave function:

)....,( 21 NrrrΨ

Hohenberg-Kohn lemmas: ground state energy is determined uniquely by electron density

)(rn

Kohn-Sham principle: electron density of H-K equivalent to density of N one electron orbitals

∑∫=

−−

==−ΨN

ii

SKKH

iNN rrnrrrrrdrrddrN1

222121 |)(|)()()....,(.... ψδ

)()....()( 21 Nrrr ΨΨΨ

⇓

⇓

The Method Reproducibility in density functional theory calculations of solids

Kurt Lejaeghere,1* Gustav Bihlmayer,2 Torbjörn Björkman,3,4 Peter Blaha,5 Stefan Blügel,2 Volker Blum,6 Damien Caliste,7,8 Ivano E. Castelli,9 Stewart J. Clark,10 Andrea Dal Corso,11 Stefano de Gironcoli,11 Thierry Deutsch,7,8 John Kay Dewhurst,12 Igor Di Marco,13 Claudia Draxl,14,15 Marcin Dułak,16 Olle Eriksson,13 José A. Flores-Livas,12 Kevin F. Garrity,17 Luigi Genovese,7,8 Paolo Giannozzi,18 Matteo Giantomassi,19 Stefan Goedecker,20 Xavier Gonze,19 Oscar Grånäs,13,21 E. K. U. Gross,12 Andris Gulans,14,15 François Gygi,22 D. R. Hamann,23,24 Phil J. Hasnip,25 N. A. W. Holzwarth,26 Diana Ius¸an,13 Dominik B. Jochym,27 François Jollet,28 Daniel Jones,29 Georg Kresse,30 Klaus Koepernik,31,32 Emine Küçükbenli,9,11 Yaroslav O. Kvashnin,13 Inka L. M. Locht,13,33 Sven Lubeck,14 Martijn Marsman,30 Nicola Marzari,9 Ulrike Nitzsche,31 Lars Nordström,13 Taisuke Ozaki,34 Lorenzo Paulatto,35 Chris J. Pickard,36 Ward Poelmans,1,37 Matt I. J. Probert,25 Keith Refson,38,39 Manuel Richter,31,32 Gian-Marco Rignanese,19 Santanu Saha,20 Matthias Scheffler,15,40 Martin Schlipf,22 Karlheinz Schwarz,5 Sangeeta Sharma,12 Francesca Tavazza,17 Patrik Thunström,41 Alexandre Tkatchenko,15,42 Marc Torrent,28 David Vanderbilt,23 Michiel J. van Setten,19 Veronique Van Speybroeck,1 John M. Wills,43 Jonathan R. Yates,29 Guo-Xu Zhang,44 Stefaan Cottenier1,45*

Science, 25 MARCH 2016 • VOL 351 ISSUE 6280

~1% Δ~0.4%

The Method

Hydrogen storage & calculations

Ref: A. Züttel, “Materials for hydrogen storage”, materialstoday, Septemper (2003), pp. 18-27

Hcov H±

H2

Hydrogen Density

lightweight

com

pact

Stability of metal borohydrides Empirical relation between Pauling electronegativity and enthalpy of formation

Y. Nakamori et al., Phys. Rev. B 74, 045126 (2006) L. H. Rude et al., Phys. Status Solidi A 208, 1754 (2011)

Mixed cation borohydrides

Ionic potential is a good descriptor of the stability unfortunately of limited usability – cannot be known a priori it has to be calculated for each compound

Phys. Rev. B 90, 054114 (2014) & submitted

Ionic potential: Effective charge (calculated)

Ionic radius (known, in principle) Φ =

𝑄𝑟

1.0 1.5 2.0 2.5 3.0

100

200

300

400

500

T deco

mpo

sitio

n (°C)

φ 0.5

ScAl

RbAl KAl

CsAlNaAl

LiAl

Be

KMn

ZrY

NaSc

KScLiPr-Cl

Mg

NaY-Cl

Sm

CaLi

LiK

Na

K

Mixed cations: Al(BH4)3 + Li(Na,K,Rb,Cs)(BH4)

Li[Al(BH4)4] Na[Al(BH4)4] NH4[Al(BH4)4]

submitted

Rb[Al(BH4)4] Cs[Al(BH4)4]

High pressure phases Mn(BH4)2

0 2 4 6 8 10 12 14 1660

65

70

75

80

85

90

95

100

105

110

115

second phase transition

I41acd

Fddd

P3112: V0 = 114.4(10) Å3, B = 13(2) GPa P42nm: V0 = 93.44(18) Å3, B = 33.8(10) GPa B' = 5.8

P3112

coexist oncompression

Volu

me

of th

e M

n(BH

4) 2 uni

t, Å3

Pressure, GPa

deviation from EOS

EOS can not be reliably determinedfirst phase transition

The structure of the high pressure phases was determined by combination of non-local energy minimization, normal mode analysis, ground state optimization; experimental data were refined in theoretically determined symmetries.

Chem. Mater., 28, 274 (2016)

Basic research

Borohydrides as hydrogen storage media

M(BH4)n

M n/12B12H12

n/2B2H6

(2n-n/12)H2

(2n-n/2)H2

M nB 2nH2

M

T Li(BH4) Na(BH4) K(BH4)

Mg(BH4)2 Ca(BH4)2

Zn(BH4)2 Al(BH4)3

Li diffusion in LiBH4

Adv. Energy Mater. 2011, 2, 1–12 Phys. Rev. 81 144108 (2010) PCCP, 12, 5061 (2010); JACS, 131, 16389 2009

LiI ~ 7.5*10-7 Scm-1 (370K) LiID2O ~ 1.1*10-3 Scm-1 (370K)

F.W. Poulsen, Sol. St. Ion. 2, 53, 1981

Superionic conductor Na2B12H12 Sodium superionic conduction in Na2B12H12

L. He, H.i-W. Li, et al, Chem. Mater. 2015, 27, 5483−5486

Phase transitions: P21n Pm-3n Im-3m Sodium conductivity is of the order 0.1 S/cm 4% volume contraction at the phase transition 530 K 1% volume expansion at the phase transition 545 K B12H12

2- – 1011 jumps/s at 530K Na+ - 108 jumps/s at 530K Activation barrier for B12H12 reorientation 25 kJ/mol

529K 545K

T. J. Udovic, et al, Chem. Commun., 2014, 50, 3750

Solid state electrolytes & calculations

Ionic conductors

0 1 2 3 4 51E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10250K

Na2SO4

Li2SO4

330K500K

log(

σ) (S

/cm

)

1000/T (1/K)

AgI H2SO

4

Na β-Al2O3

CaF2

β-PbF2

NaCl

1000K

When a piece of that substance, which had been fused and cooled, was introduced into the circuit of a voltaic battery, it stopped the current. Being heated, it acquired conducting powers before it was visibly red hot in daylight. . ..’

Michael Faraday on PbF2

Ionic conductors – solid state • Ag+ Ion Conductors

– AgI & RbAg4I5 • Na+ Ion Conductors

– Sodium β-Alumina (i.e. NaAl11O17, Na2Al16O25) – NASICON (Na3Zr2PSi2O12)

• Li+ Ion Conductors – LiCoO2, LiNiO2 – LiMnO2

• O2- Ion Conductors – Cubic stabilized ZrO2 (YxZr1-xO2-x/2, CaxZr1-xO2-x) – δ-Bi2O3

– Defect Perovskites (Ba2In2O5, La1-xCaxMnO3-y, …) • F- Ion Conductors

– PbF2 & AF2 (A = Ba, Sr, Ca)

Mg2+ Ion Conductors ?? Ca2+ Ion Conductors ?? Al3+ Ion Conductors ??

Sodium β-Alumina

New Li solid state conductor

A lithium superionic conductor Nature Materials, 10, 682 (2011)

Li10GeP2S12

Solid electrolytes

Tang et al., Energy Environ. Sci., 2015 8 3637

Complex hydrides based solid conductors

Solid vs. liquid electrolyte Liquid electrolyte: High conductivity Compatibility with many electrode materials Thermal stability Safety issues (flammable) Cycle life (dendrite formation) Solid electrolyte: Thermal stability Higher energy densities No leakage Low conductivity Compatibility issue

LiCoO2 LiMn2O4 LiNiMnCoO2 LiFePO4 LiNiCoAlO2

Graphite Li4Ti5O12

Problems with Li batteries

Tesla car Boeing 787 Dreamliner

Replacement of liquid electrolyte with a solid state one practically solves safety problems

What is ionic conductor?

Sulphur Oxygen

+

Li10GeP2S12 Li10SnP2S12 Li3.45Si0.45P0.55S4 Li10Ge0.95Si0.05P2S12 Li3.25Ge0.25P0.75S4 Li3.4Si0.4P0.6S4 Li2SnS3 Li2S–Al2S3–GeS–P2S5 (Al:Ge = 30 : 70) Li3PS4 Li7P2S8I Li0.34La0.51TiO2.94 (La0.63Li0.1)(Mg1/2W1/2)O3 Li3OCl Li3O(Br0.5Cl0.5) Li7La3Zr2O12 (bulk)

10-3

– 1

0-5 S

/cm

10

-2 –

10-4

S/c

m

Diffusion

Vacancy mechanism Interstitial mechanism

σ = n Ze μ

𝒓(𝒕)2 = � 𝒓𝒊 𝑡 − 𝒓𝒊(0) 2 lim𝑡→∞

𝒓(𝒕)2/𝑡 = 2𝑑𝑑

σ = A exp(-Ea/RT)exp(-ΔHS/2kT)

Fick’s laws: 𝐽 = −𝑑𝛻𝛻 𝜕𝛻𝜕𝑡

= 𝑑∆𝛻

𝑃(𝑁𝑡 = 𝑘) =𝜆𝑡 𝑘

𝑘!exp (−𝜆𝑡) Poisson process: 𝑃(𝑡,𝑑𝑡) = 𝜆𝑑𝑡

𝑑 = 𝜇𝑘𝑘/𝑍𝑍

Rules for ion diffusion

Nature Materials, 14, 1026, 2015

Structure for x=3: many vacant sites Li diffusion via vacancy hopping

For x<3, LiNH2 vacancies are created, structure becomes more open

Li1+x(BH4)(NH2)x 1LiBH4 : 3LiNH2

Ion Conduction Mechanism

Li+ diffusion path and energy barriers for stoichiometric composition (x=3) 1.) the excitation of Li+ (red balls) into a neighbouring vacant site (event 1) 2.) Li+ migration along the vacancy channel (events 2 and 3 ).

Potential energy for a migrating [Li]+, calculated by DFT

1 2 3

x=3

Li1+x(BH4)(NH2)x

Low temperature Medium temperature High temperature

1Å 1Å 1Å

Li migration in Li-BH4-NH2

Deatils – no diffusion Deatils – diffusion

1Å

Li migration in Li-BH4-NH2

Li1+x(BH4)(NH2)x

The transition is accompanied by a thermal event and an decrease in the linewidth of 7Li as well as in 1H in static NMR spectroscopy Note the linear dependence of the conductivity and the entropy change with concentration

New class of superionic conductors

Na2B12H12

fcc bcc hcp

T>0K

Na2B12H12

fcc bcc hcp

Na mean square displacement

0 4 8 12 16 200

200

400

600

800

1000

msq

(Å2 )

time (ps)

bcc fcc hcp

T – T rule does not hold for B12H12 High conductivity is expected in hexagonal phase – if it would exist

It does – requires modification of the anion, synthesized in Geneva

~6Dt

Summary

• Computational methods might be useful in designing new materials with tailored properties

• They can provide simple guidelines • Borohydrides, at present seem to be useless for hydrogen storage –

smart catalyst is required • First sulphur and oxygen free superionic conductor was designed with

strong aid of quantum calculations • New dodecaborane based systems with high Na conductivity are made

with guide of calculations

Research supported by a grant from Switzerland through the Swiss Contribution to the enlarged European Union

Acknowledgements: Piotr Błoński IFJ-PAN Arndt Remhof, Yigang Yan, Corsin Battaglia, EMPA, Switzerland Petra de Jongh, Utreht University, The Netherlands Yaroslav Filinchuk UCL, Belgium Pascal Schouwink, Radovan Cerny, University of Geneva, Switzerland Torben Jensen, Aarhus University, Denmark Gert Ceder, MIT & U. Berkeley, USA

Thank you for your kind attention!