obliczenia kwantowe a magazynowanie energii · •hydrogen storage & calculations •solid...
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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!