First principles calculations as a tool for understanding...

First principles calculations as a tool for understanding redox reaction mechanisms of electrode materials

for Na batteries

M. E. Arroyo y de Dompablo

MALTA-Consolider TEAMDepartamento de Química Inorgánica I Universidad Complutense de Madrid

Vitoria-Gasteiz, October 2013

Understand and Predict properties of materials

Density Functional Theory (DFT)

Basic Laws of Quantum mechanics

Structure and Composition

Density Functional TheoryLocal Density approximation (LDA)

Generalized Gradient Approximation (GGA)DFT+U Hubbard correction term (DFT+U)

)(rixcV

Total Energy, Crystal and Electronic Structures

''

)'()( drrr

rrV MF ∫ −=

ρ

∑ ∑−

+∑ ∑−

+∑∑−

−∇∑ −+∇∑ −=≠≠==

e en nnn N

i

N

j j

N

I

N

J IJ

JINe

i

N

I Ii

II

N

iI

iNe

i e rire

RReZZ

RreZ

mmH

1

2

1

222

1

2

1 21

21

2

2

2

2 hh

Power

CyclabilityLife‐Tim

e

Voltage

Capacity (mA /g and mA/l)Energy

Electronic Mobility

Ionic Mobility

Structural Stability

Safety and

en

vironm

ent

Thermal Stability

Toxicity

Materials´ Abundance

Rate

Capa

bility

Cost ($/kWh)Processability

Y.S. Meng and M.E. Arroyo-de Dompablo, Energy and Environmental Science 2010Y.S. Meng and M.E. Arroyo-de Dompablo, Accounts of Chem. Research 2012

Battery performance Intrinsic properties of electrode materials

DFT

DFT: FULL CONTROL OF STRUCTURE

AT ATOMIC LEVEL

UNDERSTANDING Na INTERCALATION

IN ELETRODE MATERIALS

• Na and Li insertion in layered‐A2Ti3O7 (A = Na, Li)• Discussion of Na vs Lithium intercalation voltages

Outline

Methodology• VASP package• DFT, DFT+ U (Generalized Gradient Approximation, GGA, GGA+U)• PAW pseudopotentials (PBE)• Conjugate gradient algorithm for ionic relaxation (EDIFFG = 10-4 eV)

Total Energy

Na insertion in Na2Ti3O7

Chiba et al 2008

Li insertion at 1.6 V

Questions1) Why is the voltage so “low” for the Na-titanate?. 2) What is the structure of Na4Ti3O7?

Na insertion at 0.3 V

Palacín et al 2011

G. Rousse, M. E. Arroyo y de Dompablo, P. Senguttuvan,A. Ponrouch, J.M. Tarascon and M .R. Palacín, Chem. Mat. submitted

Na2Ti3O2 + 2A →A2Na4MO2

3-4 eV 10-5 eV 10-3 eV, RT

Er = - [Etotal (A2Ti3O7) + 2Etotal (A)] + Etotal (A4Ti3O7)

M. K. Aydinol, A.F. Kohan, G. Ceder, K. Cho and J. Joannopoulos, PRB 1997

Li2Ti3O2 + 2A →A2Li2MO2

NaC.N. = 7,8

LiC.N. = 4

To calculate the voltage we need a model for the intercalated structure

Calculated Average Insertion Voltage

.Na4Ti3O7 structure : occupation models in Na2Ti3O7

12

12

12

12

124

6

3

6

45

4

6

3

6

45

4

11 possibilitiesNa1 Na2 Na3 Na5Na1 Na2 Na4Na1 Na2 Na3 Na6Na1 Na2 Na5 Na6Na1 Na3 Na4Na1 Na3 Na5 Na6Na2 Na3 Na4Na2 Na3 Na5 Na6Na3 Na4 Na5Na3 Na4 Na6Na4 Na5 Na6

Na in the starting materialNa1 2e 0.66098 0.25 0.58441Na2 2e 0.49173 0.25 0.14880

Energy of Na4Ti3O7 models and average intercalation voltage

•Large energy variation among the Na‐occupancy models: wide range of average intercalation voltages

• All models yield negative voltages: intercalated structures are not stable enough.

1235

1236

1256

2356

1356 124

134

234

345

346

456 --

0

1

2

3

Cal

cula

ted

tota

l ene

rgy

diffe

renc

e (e

V / f

.u.)

A4Ti3O7 (A = Li, Na) model

1235

1236

1256

2356

1356 124

134

234

345

346

456 --

-2.5

-2.0

-1.5

-1.0

-0.5

Cal

cula

ted

aver

age

volta

ge (V

)


VNa =( [2 Etotal (Na) + Etotal (Na2Ti3O7)] - Etotal (Na4Ti3O7))/2

Na2Ti3O7 + 2Na Na4Ti3O7

Exp. 0.3 V

124−1st optimization 1236 −1st optimization

Structural relaxation withoutsymmetry constraints

fully optimizedNa4Ti3O7

d (Na-Na) = 2.05 AC.N. = 4,5Voltage: -0.8 V

d (Na-Na) = 2.98 AC.N. = 6Voltage: 0.37 V

d (Na-Na) = 2.11 AC.N. = 4,5Voltage= -1 V

Structural optimization of 1236 and 124 models

G. Rousse, M. E. Arroyo y de Dompablo, P. Senguttuvan,A. Ponrouch, J.M. Tarascon and M .R. Palacín, Chem. Mat. submitted

rVINa+= 1.02 Å

dNa-Na = 1.724 AC.N. = 7,8,4V = 303.84 Å3

dNa-Na = 2.085 AC.N. = 7,4V = 354.72 Å3

dNa-Na = 2.114 AC.N. = 4,5V = 359.63 Å3

dNa-Na = 2.994 AC.N. = 4,5,6V= 344.25 Å3

dNa-Na = 3.020 AC.N. = 5,6V= 336.23 Å3

dNa-Na = 2.986 AC.N. = 6V= 321.95 Å3

-1.3 V -1.0 V

0.28 V0.30 V0.37 V

10 15 20 25 30 35 40 45

Inte

nsity

(arb

. uni

ts)

2θ (°) [λCu]

(100) (101)(110)

(111)(‐302)

(104)(020)

(003)(013)

Confrontation with experiments

322.27(306.94(22))

90, 97.87, 90(90, 97.32(2), 90)

9.8029.664(5)

4.442(4.381(2))

7.472(7.309(3))

Na4Ti3O7

303.84(291.05(1))

90, 101.7, 90(90, 101.597,90)

9.280(9.1265(3))

3.867(3.8012(1))

8.646(8.5642(8))

Host-Na2Ti3O7

V (Å3)α, β, γ (º)c (Å)b (Å)a (Å)Compound

Calculated Voltage : 0.37 VExperimental Voltage: 0.3 V

Calculated lattice parameters and cell volume differ in less than 5% with experimental values


Na4Ti3O7 In situ XRD, laboratory Bruker D8, CuKαhomemade Swagelok type cellusing Be window C/25

Optimized Structure of Na4Ti3O7

The a lattice parameter contractsExperimentally: 15 %Computational: 13 %

Cell Volume ExpansionExperimental: 6 %Computational: 5.4 %


rVINa+= 1.02 ÅTi4+ reduction

Li4Ti3O7 models yield too low voltages; the intercalated models are not stable enough. Further structural optimization of 1236 and 124 models results in a rock‐salt structure

1235

1236

1256

2356

1356 124

134

234

345

346

456 --

-1.0

-0.5

0.0

0.5

Cal

cula

ted

aver

age

volta

ge (V

)


1235

1236

1256

2356

1356 124

134

234

345

346

456

0

1

2

3

C

alcu

late

d to

tal e

nerg

y di

ffere

nce

(eV

/ f.u

.)


Li Na

Energy of Li4Ti3O7 models and average intercalation voltage

Exp. 1.6 V

Li2Ti3O7 + 2Li Li4Ti3O7

Intercalated Li4Ti3O7 and Na4Ti3O7 are isostructural

10 15 20 25 30 35 40 45

Inte

nsity

(arb

. uni

ts)

2θ (°) [λCu]

(100)

(101)(110)

(211)(‐113)

(‐302)

(104)(020)

a lattice parameter contractsExperimentally: 10 %Computational: 11 %

c lattice parameter contractsExperimentally: 0.7 %Computational: 0.4 %

Li2Ti3O7 + 2Li Li4Ti3O7

The more polarizingLi ions cause a

cell volume contraction

Confrontation with experiments (in situ XRD)

Cell Volume ContractionExperimental: 2.9 %Computational: 2.6 %

Li insertion at 1.6 Vin Li2Ti3O7

Questions1) Why is the voltage so “low” for the Na-titanate?. 2) What is the structure of Na4Ti3O7? Rock salt type structure

Na insertion at 0.3 Vin Na2Ti3O7

1

1.5

2

2.5

0 0.4 0.8 1.2 1.6 2 2.4

Pot

entia

l Vs.

Li+ /L

i0 (V)

No of exchanged electrons/mol of Li

2Ti

3O

7

b)

0

0.5

1

1.5

2

2.5

0 1 2 3 4

Pot

entia

l Vs.

Na+ /N

a0 (V)

No of electrons exchanged/mol of Na

2Ti

3O

7

a)

A insertion in Na2Ti3O7 and Li2Ti3O7 (A = Li, Na)


Li2Ti3O7 + 2 Li Li4Ti3O7 (1.6V)

Li2Ti3O7 + 2Na Na2Li2Ti3O7

Na2Ti3O7 + 2 Li Li2Na2Ti3O7

Na2Ti3O7 + 2Na Na4Ti3O7 (0.3V)VLi-VNa ??

1

1.5

2

2.5

0 0.4 0.8 1.2 1.6 2 2.4

Pot

entia

l Vs.

Li+ /L

i0 (V)


2Ti

3O

7

b)

0

0.5

1

1.5

2

2.5

0 1 2 3 4Pot

entia

l Vs.

Na+ /N

a0 (V)


2Ti

3O

7

a)

0

0.5

1

1.5

2

2.5

0 1 2 3 4P

oten

tial V

s. N

a+ /Na0 (V

)No of electrons exchanged/

mol of Na2Ti

3O

7

a)

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5

Pot

entia

l Vs.

Li+ /L

i0 (V)

No of exchanged electrons/mol of Na

2Ti

3O

7

c)

For a givenframework

• VLi > VNa

¿Cuantification?

70% NTO, LTO+ 20-30 % SP carbon 1 M LiPF6 in EC:DMC 1 M NaClO4 in PCSwagelok C/25


0.700.78

--

2.161.832.1

1.461.05

--

GGA+U; U = 5 eVGGA

Experimental

Ramsdellite –Ti2O4// ATi2O4

0.530.63

--

0.900.73

--

0.370.100.3

GGA+U; U = 3 eVGGA

Experimental

Layered Na2Ti3O7

0.690.75

--

1.461.341.6

0.770.59---

GGA+U; U= 3 eVGGA

Experimental

Layered Li2Ti3O7

VLi-VNa, Voltage

difference (V)

Li (V)Na (V)MethodHost compound//Inserted

Compound

Li2Ti3O7 + 2 Li Li4Ti3O7 (1.6V)

Li2Ti3O7 + 2Na Na2Li2Ti3O7

Na2Ti3O7 + 2 Li Li2Na2Ti3O7

Na2Ti3O7 + 2Na Na4Ti3O7 (0.3V)VLi-VNa ??

VLi‐VNa in various titanium oxides is of the order of 0.7 V

DOES IT MAKE SENSE??

DOShost

OC

V

VLi

LiA

OC

V

Na

VNa

DOSIntercalated

VLi-VNa

G. Compton et al., Chem. Phys. Lett.2010

Intercalation voltages of Li vs Na

0.3 V ?

E (V): M + aq —> M +(aq) + e-

Li Na K Rb Cs+3.05 +2.71 +2.93 +2.99 +2.99

Conclusions

Acknowdlegments

Ministerio de Ciencia e Innovación for grants MAT2011-24757, MAT 2011-22753 and CSD2007-00045.

•DFT calculations have allowed to determine a structural model for A4Ti3O7(A=Li, Na) which has been successfully confronted to the available experimental data

•Factors that account for Li vs. Na insertion voltage has been rationalized : Na2Ti3O7 displays a rather high specific capacity at a low potential as a result of the flexibility of a layered host to accommodate high amounts of the large Na ion.

•Lithium and sodium are similar but not alike, and presuming analogies in their intercalation chemistry may not be straightforward: new avenues are open for the exploration of novel Na electrode materials which are not necessarily those having the best performance in Li‐ion batteries.

First principles calculations as a tool for understanding...

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