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Evgeny Blokhin
Chelyabinsk SUSU’2013 summer workshop
Max‐Planck Institute for Solid State Research
Stuttgart, Germany
Theory and practice of ab initiomaterials modeling
Part I
Who am i?
M.Sc. in Saint‐Petersburg, SPSU
PhD in Stuttgart,
MPI‐FKF
My scientific interests
• Defective d‐metal oxides
• Phonons and vibration thermodynamics
• Cheminformatics and database‐driven modeling
• Automation in computational materials science
Outlook
1. Introduction to d‐metal oxides and their applicationsSolid oxide fuel cellsLi‐ion batteries
2. Theory stack of nano‐scale modelingOverview of ab initio methodsNano‐scale crystalline structure
3. Scientific problemsFormation of defectsVibrational thermodynamics from ab initioProcesses in ultrathin films
Technological application
d‐metal oxides
Storage devices (flash memory)
Solid oxide fuel cells
Electrochemical sensors
PhotovoltaicsBatteries
High capacity devices
Solid oxide fuel cells
Anode Cathode
½ O2+2e+VO→ O2H2+2O → 4e+2H2O
Solid oxide fuel cells
Cathode AnodeElectrolyte
1. La1‐xSrxMnO3
2. La(Sr,Co,Fe,Ga)O3
3. other perovskite‐based systems
1. Al2O3 ceramics
2. BeO
3. MgO
1. ZrO2 + Y2O3 (YSZ)
2. ZrO2 + Sc2O3 (ScSZ)
3. CeO2 + Gd (GDC)
Solid oxide fuel cells
Li‐ion batteries
AnodeCathode
e−
e−
charge
discharge
LiCoO2↔
Li1‐nCoO2 + nLi+ + ne−
nLi+ + ne− + C ↔
LinC
Li‐ion batteries
Cathode Anode
1. LiMn2O4 (spinel)
2. LiCo(or Ni, Mn)O2
3. LiFePO4 (olivine)
1. LiSn, LiSi
2. Si, C nanowires/ nanotubes
3. Lithium / titanium oxides
Electrolyte
1. Li2NH
2. Organic polymers
3. Carbonates
Li‐ion batteries
Surface (2D)
PerfectmaterialsBu
lk (3
D)
Defectivematerials
A
OB
Nano‐scale research areas
Basis sets
Gaussian‐type orbitals Plane waves
But the same computational task:
1) Calculate matrix elements of H over the basis set2) Solve variational problem iteratively
χk(r) = exp(ikr)χς, n, l, m(r, θ, µ) = nY(θ,µ)r2n‐2‐lexp(−ς r2)
Aim: localized e‐densities Aim: delocalized & slowly varied e‐densities
( )14
hyb GGA HF GGAxc xc x xE E E E= + −
Zoo of DFT functionals
Semiconductors
Band gap problem:
1) underestimation by fictitious KS eigenvalues of unoccupied states
2) overestimation due to orbital relaxation and electron correlation
ABO3 perovskites
Goldschmidt tolerance factor for ABO3: 0.71 < (rA+rO)/√2(rB+rO) < 1.02
Wyckoff positions: sets of inequivalent points for a space group, for which site symmetry groups are conjugate subgroups
Real atoms occupation: not to mix with space groups (space
subdivision)!
Space groups: symmetry group of configuration in space
(crystallographic or Fedorov groups)
Na (4a) 0.0 0.0 0.0
Cl (4b) 0.5 0.5 0.5
Ca (4a) 0.0 0.0 0.0
F (8c) 0.25 0.25 0.25
Space group is the same, Wyckoff positions are different!
NaCl CaF2
1. 0‐, 1‐, 2‐, 3‐periodic objects consistently, full symmetry account
2. Hartree‐Fock, DFT and hybrid Hamiltonians
3. Gaussian‐type basis sets (+ pseudopotentials)
4. Vibrational, electronic, magnetic, dielectric and elastic properties
5. Full parallelization (+ massive parallel version)
My PhD thesis
• Vibrational thermodynamics from ab initio
• Modeling of perfect bulk SrTiO3
• Iron impurities and oxygen vacancies in bulk SrTiO3
• Perfect and defective surfaces of SrTiO3
Ab initiomodeling scheme
Hamiltonian:
Basis sets:
Pseudopotentials:
Phonon calculations:
Implemented in:
hybrid HF‐DFT PBE0 [1]
LCAO Gaussians, taken from [2], [3]
small‐core [2](developed in Stuttgart University by Prof. Stoll)
Direct frozen‐phonon method(harmonic approximation)
CRYSTAL09 [3]
[1] J. Perdew et al., J.Chem.Phys. 22, 105 (1996)[2] H. Stoll, University of Stuttgart, http://www.theochem.uni‐stuttgart.de/pseudopotentials[3] R. Dovesi et al., University of Turin, http://www.crystal.unito.it
T, K37 1050
“Tetragonal FE” Tetragonal AFD Cubic
R4+Гt1u Sr
OTi
Soft‐mode driven phase transitionsin perfect SrTiO3
Phonon contributionto thermodynamic properties
Calculated Helmholtz free energyCalculated heat capacity
max2
2
0
3 csc ( )2 2v B
B B
C nk h g dk T k T
ω ω ω ω ω⎛ ⎞ ⎛ ⎞
= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
∫ħ ħ max
0
ln 3 ln 2sinh ( )2B B
B
F k T Z nk T g dk T
ω ω ω ω⎧ ⎫
= − = ⎨ ⎬⎩ ⎭
∫ħ
V
FE F TT∂⎛ ⎞= − ⎜ ⎟∂⎝ ⎠ V
FST∂⎛ ⎞= −⎜ ⎟∂⎝ ⎠ 0G E E TS pV= + − +
Expt.: I. Hatta, Y. Shiroishi, K. A. Mueller, and W. Berlinger, PRB 16, 1138 (1977)
and further:
Iron impurity in SrTiO3: Jahn‐Teller effect
Fe
Oax
Oax
Opl
OplOpl
Opl
E. Blokhin, E. A. Kotomin, and J. Maier, J.Phys.:Cond.Matt. 24, 104024 (2012)
* M.Vracar, A.Kuzmin, R.Merkle, J.Purans, E.Kotomin, J.Maier, O.Mathon, PRB 76, 174107 (2007)** E.Blokhin, E.Kotomin, J.Maier, J.Phys.Cond.Matt. 24, 104024 (2012)
* **
Sr(FexTi1−x)O3 phonon properties
Oxygen vacancy in SrTiO3: Jahn‐Teller effect
R. Evarestov, E. Blokhin, D. Gryaznov, E. Kotomin, R.Merkle, J. Maier, Phys. Rev. B 85, 174303 (2012)D. Gryaznov, E. Blokhin, A. Sorokin, E. A. Kotomin, R. A. Evarestov, A. Bussmann‐Holder and J. Maier,
J. Phys.Chem.C 117, 13776 (2013)
Formation energy of VO in bulk SrTiO3
212
OV OpF tot tot totE E E E∆ = − +
( )2
0 01( ) ( ) ( ) ( ) ( )2
O O O O
O
V V V V p p p pF tot vib vib tot vib vibG T E E T TS T pV E E T TS T pV Tµ⎡ ⎤ ⎡ ⎤∆ = + − + − + − + +⎣ ⎦⎣ ⎦
( )2
0 01 ( )2
O
O
V pF tot totG T E E Tµ∆ = − +“without phonons”:
“with phonons”:
at 0°K:
Expt.: R. Moos and K. H. Haerdtl, J.Am.Cer.Soc. 80, 2549 (1997)Modeling: R. Evarestov, E. Blokhin, D. Gryaznov, E. Kotomin, R.Merkle, J. Maier, PRB 85, 174303 (2012)
Fe : VO complexes in SrTiO3
FeO
Ti
VO
Model 1Fe3+−VO−Fe3+
Model 2Fe3+−O−Fe3+−VO
Model 3Fe3+−O−Fe3+−O−Ti−VO
XANES modeling
E. Blokhin, E. Kotomin, A. Kuzmin, J. Purans, R. Evarestov, J. Maier, APL 102, 112913 (2013)
{
Interatomic distances, Å
1.972.009.503. Fe3+−O−Fe3+−O−Ti−VO
1.971.96
2.001.95
9.352. Fe3+−O−Fe3+−VO
1.961.959.131. Fe3+−VO−Fe3+
EXAFS expt.Fe – O
averaged
ab initioFe – O
averaged
Complexformationenergy,Eform, eV
Model of complex
Expt.: C.Lenser, A.Kalinko, A.Kuzmin, D.Berzins, J.Purans et. al., PCCP 13, 20779 (2011)Modeling: E. Blokhin, E. Kotomin, A. Kuzmin, J. Purans, R. Evarestov, J. Maier, APL 102, 112913 (2013)
Soft‐mode driven phase transitionsin perfect SrTiO3 surface
z
Γ
Γ
M
3‐dimensional Brillouin zone
2‐dimensional Brillouin zone
548517B1g
447439B1g460, 447454Eg
394421Eg
175180Eg235, 229157B2g
162155Eg
147153A1g
129129A1g143, 144142Eg
4848Eg48, 5285A1g
37133iEg15, 4017Eg
Expt.TheoryIrrepExpt.TheoryIrrep
Surface AFD STOBulk AFD STO
Soft‐mode driven phase transitionsin perfect SrTiO3 surface
* E.Kotomin, V.Alexandrov, D.Gryaznov, R.Evarestov, J.Maier, PCCP, 13, 923 (2011)
Formation energy of VO in the SrO‐terminatedSrTiO3 ultrathin films
at 0°K at finite temperatures
212
OV OpF tot tot totE E E E∆ = − +
( )2
0 01( ) ( ) ( ) ( ) ( )2
O O O O
O
V V V V p p p pF tot vib vib tot vib vibG T E E T TS T pV E E T TS T pV Tµ⎡ ⎤ ⎡ ⎤∆ = + − + − + − + +⎣ ⎦⎣ ⎦
( )2
0 01 ( )2
O
O
V pF tot totG T E E Tµ∆ = − +“without phonons”:
“with phonons”:
at 0°K:
Summary
1. The known structural, electronic and phonon properties of perovskites can be excellently represented by our modeling scheme
2. The Fe4+ and VO defects in SrTiO3 induce Jahn‐Teller‐type structural distortions and new local IR and Raman phonons
3. The recent IR, Raman, XANES and EXAFS experiments on defective perovskites can be interpreted
4. Experimental estimate of the formation energy of VO in SrTiO3 is confirmed, its phonon component is quite minor (~5% at 1000°K)
5. Preliminary: in SrTiO3 surfaces the VO formation energy is very similar to bulk 3D case, as well as its phonon component (~1% at 1000°K)