Computational Study of Chemical and Electrochemical Intercalation of

Subscriber access provided by - Access paid by the | UCSB Libraries

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Computational Study of Chemical and Electrochemical Intercalation of Li into Li TiO Spinel Structures 1+x

2

4

Shannon K. Stauffer, and Linas Vilciauskas J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00873 • Publication Date (Web): 13 Mar 2018 Downloaded from http://pubs.acs.org on March 14, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Computational Study of Chemical and Electrochemical Intercalation of Li into Li1+xTi2O4 Spinel Structures Shannon K. Stauer† and Linas Vil£iauskas∗ ‡ ,

†Center

for Physical Sciences and Technology, Sauletekio

al. 3, LT-10257 Vilnius, Lithuania

‡Institute

of Chemistry, Faculty of Chemistry and Geosciences, Vilnius University, Sauletekio

al. 3, LT-10257 Vilnius, Lithuania

E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Li1+x Ti2 O4 spinel structures are used as model systems to study the complex environment of electrode/electrolyte interfaces in lithium-ion batteries. Lithiation pathways and the potential dependence of delithiation on corresponding Li1+x Ti2 O4 surfaces were explored using the density functional theory. Low index surfaces are found to be highly reactive with Li forming a fully lithiated phase (Li2 Ti2 O4 ) before more Li can penetrate farther into the bulk. The calculated activation energies for the formation of Li2 Ti2 O4 at the surface are found to be much lower than for Li diusion through LiTi2 O4 , suggesting a two-phase lithiation process taking place during cycling. Additionally, the delithiation reaction mechanism in Li2 Ti2 O4 is studied by evaluating the free energies for Li+ transfer to an ethylene carbonate electrolyte by employing a Born-Haber thermodynamic cycle. The eects of an applied (external) potential are eectively incorporated into the thermodynamic cycle and provides means to calibrate the bias potential to the experimentally known scale. Finally, the eects of an applied electrode potential are studied on the Li2 Ti2 O4 delithiation energetic pathways in various environments emphasizing the dierent contributions to the charge transfer energetics in these electrode materials.

2


Page 2 of 46

Page 3 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Electronics technology has advanced rapidly over the past several decades. The digital processors doubled their performance nearly every two years keeping up with the prediction known as the Moore's Law. Unfortunately, electrical energy storage technologies have not seen comparable gains apart from a handful of breakthroughs, such as the discovery and commercialization of Li-ion batteries (LIB) which eventually spawned the mobile electronics revolution.

1

Improvements to the energy/power densities, charging rates, safety and cost of

rechargeable batteries are needed in order to keep up with the increasing power of portable electronics, development of hybrid and fully electric vehicles and implementation of stationary storage units in areas with intermittent solar and wind power sources. Li-ion batteries, in principle, have a potential to fulll most of these demands, however the future developments require a much better understanding of electrodes and electrolytes as well as their interactions which govern their performance. Presently, standard Li-ion batteries are comprised of transition metal oxide or phosphate cathodes, graphitic anodes and electrolytes, containing various Li salts dissolved in small molecule organic liquid mixtures. In certain situations, the electrolytes can react with electrode surfaces and the reaction products may form a stable layer known as solid electrolyte interphase (SEI).

2

On one hand, the SEI protects the electrode and electrolyte from further

reactions during the battery cycling, but on the other hand it often leads to capacity loss, kinetic limitations and subsequent safety concerns. The actual structure and properties of SEI are strongly dependent on the type of electrode/electrolyte interface and the stage/conditions of battery operation and are still under heavy debate among dierent research groups.

3

Electrolyte components start to react on/to the surface of graphite anodes at around

∼1.6

+ 0 V vs. Li /Li (s) and form SEI which eventually prevents the further decomposition

and exfoliation of graphite. A number of experimental studies show most of the SEI formation taking place during the rst charge-discharge cycle resulting in a stable layer which is electronically insulating but severely hindering Li-ion diusion.

3


211

However, it is not only


Page 4 of 46

the actual composition and structure of SEI which are not completely known, but there is also a very limited understanding of Li

+

interactions and behavior at LIB interfaces.

8,1218

Although the popularity of graphitic anodes made the SEI a standard feature of most current LIBs, there is an enormous interest in anode materials able to operate within the electrolyte stability window not only from an industrial but also from a fundamental point of view.

11

Such systems serve a special role for the understanding of LIB interfaces since the key

interfacial processes like Li

+

transfer and intercalation can be studied without considering

the much more complicated SEI contributions. In this study, we focus on the LiTi2 O4 spinel phase as a model system for modeling electrochemical processes related to Li-ion transfer and intercalation. There has been a signicant amount of research dedicated to the end members of the cubic spinel solid solution, Li1+x Ti2−x O4 where

0 ≤ x ≤ 1/3,

as anode materials. First of

+ 0 all, they operate at higher voltages (∼1.5 V vs. Li /Li (s)) resulting in higher electrolyte stability and signicantly less SEI formation.

Although for a long time, lithium titanate

spinels were deemed to be SEI-free, the presence of interfacial reactions in typical organic solvents is now unequivocally proven and is probably the leading cause for the cell gassing phenomena.

19

Nevertheless, it seems that the origins and mechanisms of these phenomena

are still quite controversial with some of the research showing the solvent decomposition mediated by traces of water or that it is the specic surface electronic structure or charge transfer between Ti

3+

/Ti

4+

which are responsible for the reactions.

1922

Furthermore, they are zero-strain materials, showing minimal volume (95%

even at high rates) and long battery lifetime.

23

The

end members, namely LiTi2 O4 and Li4 Ti5 O12 show only slightly dierent charge capacities 161 vs. 175 mAh g

−1 11 , respectively, making them compatible with current LIB cathodes

and suitable to be used as anodes for commercial 2-3 V batteries.

11,23

Nevertheless, these ma-

terials dier signicantly in terms of their electronic structure, with end members LiTi2 O4

4


Page 5 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and Li4 Ti5 O12 being respectively metallic and insulating.

Although, much more experi-

mental and theoretical work has been dedicated to the more stable and easily obtainable Li4 Ti5 O12 , in this study we focus on the LiTi2 O4 spinel phase, because the metallic nature of Li1+x Ti2 O4 allows us to eectively incorporate the electrode potential into our electronic structure calculations using some of the existing schemes.

2427

The electrode potential dierences (also called voltages) can be related to the free energy dierences between the products and reactants of an electrochemical redox reaction. In practice, the open-circuit voltage can be determined using only the internal energy dierence of bulk electrode systems, and this approximation has generally held when describing electrode properties where the

V dP

and

SdT

contributions to Gibbs free energies are orders

of magnitude lower than the potential energy dierence. hold anymore when the eects of become signicant.

SdT

28,29

This approximation does not

or the electrode/electrolyte interfacial contributions

26

Computational studies of interfaces are intrinsically more complex than those of bulk because, in additon to two phases, one must also consider their boundary.

The simplest

interface model is the one of a solid slab in vacuum. In the modeling of electrochemical systems, the complexity increases even further as one must consider electron and mass transfer, an externally applied eld and the induced eld at the interface of a solid and liquid which creates the electric double layer.

Several approximations have been developed over time

which allow for eective computational investigations of electrochemical interfaces including Li-ion battery electrode/electrolyte interfaces.

2427,30

To the best of our knowledge, there has not been any studies of lithiation and delithiation mechanisms on the Li1+x Ti2 O4 surfaces. In the rst part, we study the surface stability along the major symmetry planes and atomistic energetic details of lithiation in LiTi2 O4 . Therein we employ a slab-in-vacuum model and neglect the applied electrode potential or interfacial eects due to the presence of electrolyte. In the second part, we propose a simple and ecient method to calibrate a density functional theory model to a realistic electrode potential scale

5



for the delithation of Li2 Ti2 O4 . By combining several previous approaches,

Page 6 of 46

2427,30

we model

a virtual circuit of charge transfer from Li2 Ti2 O4 electrode to an ethylene carbonate (EC) electrolyte with the help of a thermodynamic cycle, which allows us to relate the simulations with the experimental onset potential of Li2 Ti2 O4 delithation. This gives us an eective scale to perform further computational studies under realistic electrochemical conditions. In the third part, we employ the newly calibrated computational electrode model together with the nudged elastic band (NEB) methodology to study the mechanism and associated energetics of lithium deintercalation as a function of electrode potential from the Li2 Ti2 O4 anode.

Methods All calculations were performed using the density functional theory (DFT) as implemented in the Vienna Ab-initio Simulation Package (VASP). projector augmented wave (PAW) method

35

3134

Core electrons were treated using the

and valence electron orbitals were expanded in a

plane-wave basis set with a plane-wave kinetic energy cuto of 400 eV. Electronic exchangecorrelation terms were calculated within the generalized gradient approximation using the Perdew-Burke-Enzerhof (PBE) functional.

36

All reported calculations were spin polarized.

Partial occupancies were treated by the Methfessel-Paxton method with 0.1 eV smearing at the Fermi-level.

k -point

scheme and the density of

meshes were automatically generated using the Monkhorst-Pack

k -points

was converged to less than 1 meV/atom.

All systems

were optimized to their ground-state geometry until the forces on each atom were less than 0.01 eV/Å. Slabs were constructed with 1x1x2 unit cells and cleaved along the high symmetry planes. Supercells included 14 Å of vacuum on top and the lower 4.0 Å of atoms frozen in bulk lattice positions, unless stated otherwise. The nudged elastic band method was used to nd Li-ion migration pathways and barrier energies.

37

For those instances when the transition

state was not converged after NEB, the dimer method was used to rene the transition state

6


Page 7 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energy.

38

In the delithiation study, Li2 Ti2 O4 slabs were constructed by cleaving the bulk along

2 (100) plane and taking 4x4 supercells with large surface area (274 Å ). In order to induce and vary excess charge on the metallic slabs, an appropriate number of extra Li and F atoms were xed to surface positions suciently far, at a distance of roughly half the box length, from any surface defects. The Li (F) adatoms give up an electron, resulting in Li

+

− (F ) on

the surfaces. To prevent any surface dipoles, adatoms are added 1 per side, resulting in an overall charge neutral system. A continuum solvation model as implemented in the VASPsol package

39

was employed

to account for implicit solvent eects when calculating the energetics of delithiation reaction pathways. The dielectric parameters consistent with ethylene carbonate (ε0

= 90

at 20

◦

C)

were used for setting up the model.

Results and Discussion When used as an intercalation electrode Li1+x Ti2 O4 can be cycled between and has been shown to be unstable when cycled below type structure with a cubic lattice and

F d¯3m

x . 0. 4042

0 ≤ x ≤ 1 (Eq. 1)

LiTi2 O4 adopts a spinel

space group. Our calculated lattice constants

for LiTi2 O4 (a=8.363 Å) and for Li2 Ti2 O4 (a=8.284 Å), are in good agreement with available experimental data: a=8.403 Å and a=8.376 Å, respectively.

40,43

Each unit cell is comprised of eight stoichiometric units, with Li occupying tetrahedral

8a,

Ti octahedral

16d

and O

32e

sites forming a cubic-close packed arrangement. The fully

lithiated Li2 Ti2 O4 phase is a stable rock-salt type structure where Li fully occupy octahedral

16c

sites whereas all tetrahedral

8a

sites are vacant:

[Li]8a [Ti2 ]16d [O4 ]32e + Li+ + e− ←−→ [Li2 ]16c [Ti2 ]16d [O4 ]32e

(1)

Earlier studies on Li intercalation into LiTi2 O4 have focused on local electronic and struc-

7



Page 8 of 46

tural distortions or diusion pathways of excess Li in the bulk.

44,45

During lithiation, Li atoms

are inserted into octahedral sites which results in a repulsive interaction with neighboring Li occupying tetrahedral sites.

44,45

For Li1+x Ti2 O4 in a

0 ≤ x ≤ 0.65

concentration range,

Li with one or more vacant octahedral neighbors will be located o-center in octahedral

16c

sites. This shortens Li[16c] -Li[16c] distances from 3.1 to 2.8 Å

forces on neighboring tetrahedral Li.

44

and reduces the repulsive

At the later stages of lithiation,

0.65 ≤ x ≤ 1,

TiO6

establish a more regular structure found in Li2 Ti2 O4 and octahedral Li tend to reside in the site centers.

The reverse stability of octahedral versus tetrahedral sites comes as a result

of small O-Ti-O angles opening to form regular O-Ti-O angles of 90 length increase to 2.1 Å

◦

as well as Li-O bond

in octahedral site and decrease to 1.8 Å in tetrahedral sites .

44

The formation energies of LiTi2 O4 , Li1.5 Ti2 O4 , and Li2 Ti2 O4 show that the thermodynamic LiTi2 O4 and Li2 Ti2 O4 ground-states will tend to phase-separate as reported in previous studies. method

47

46

Low energy congurations of Li1.5 Ti2 O4 are found using the basin-hopping

by swapping of interstitial Li and are 4.4 eV above formation energies of both end-

members, LiTi2 O4 and Li2 Ti2 O4 , showing that mixed-phase states are thermodynamically unstable. The DFT calculated equilibrium voltage (closely related to the experimental open-circuit voltage) between the LiTi2 O4 and Li2 Ti2 O4 phases using the PBE functional is 1.11 V per Li and the use of hybrid HSE06

28,48

functional brings it up to 1.27 V. These results are

reasonably close to the experimental nding of 1.34 V

41,43

and indicate that it is possible

to predict the experimental open-circuit voltage using an appropriate choice of exchangecorrelation functional with high accuracy. Furthermore, the less computationally intensive PBE functional is a reasonable choice for the following surface study since only the energy dierences and relative redox potentials will be of interest. Our calculations also conrm that the LiTi2 O4 and Li2 Ti2 O4 are metallic. As shown in Fig. 1, the bottom of the conduction band sits below the Fermi energy in these systems.

8


Page 9 of 46

LiTi2O4 Li2Ti2O4 Density of states N(E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-5

-4

-3

-2

-1 0 E-Ef (eV)

1

2

3

Figure 1: Total density of states for LiTi2 O4 (black) and Li2 Ti2 O4 (red). The Fermi level (Ef ) is marked by a vertical dotted line.

Surface study of Li1Ti2O4 In order to study the stability of each surface in vacuum, LiTi2 O4 is cleaved along its respective (100), (110), and (111) planes. For each surface study only stoichiometric multiples of the unit cell are used which implies that such slabs may have dierent terminating species. As seen in a previous study of analogous LiMn2 O4 spinel slab, the surface terminating species also play an important role in the system stability by forming dierent surface dipoles.

49,50

In the case of LiTi2 O4 (100) face, there are alternating planes of Li and Ti-O, so a resulting slab would have one polarized Li-terminated surface and one unpolarized Ti-O-terminated surface, possesing a net surface dipole. One way to minimize the resulting surface dipole is to have identical surface compositions.

49,50

Here, we place an equivalent number of surface

species, in this case Li atoms, on each side of the slab while still preserving the overall stoichiometry. In those cases where such scheme is used e.g. for LiTi2 O4 (100), we term them symmetrically terminated surfaces. The surface energy of each system is calculated using Eq. 2 and the results are reported in Table 1.

γ=

N Eslab − N Ebulk 2A

9


(2)


Page 10 of 46

Table 1: Comparison of Dierent LiTi2 O4 Surface Planes γ

2 (meV/Å )

facet

terminating species

(111)

Li

210.7

(111)

Ti-O

160.9

(110)

Li-Ti-O

115.4

(110)

Ti-O

99.1

(100)

Li

65.3

(100)

Ti-O

69.0

(100)

symmetric-Li

66.1

In all cases, surface energies are similar among like facets. Upon geometric relaxation, Literminated (111) and (110) slabs show little surface rearrangement and have higher surface energy than (100) slabs by 145 meV and 50 meV, respectively. In both, the Li-terminated and symmetrically terminated (100) surfaces, Li relax to surface-truncated octahedral positions. Fig. 2 shows the unrelaxed and relaxed symmetrically terminated (100) surfaces and highlights the distances which change signicantly during the relaxation. In the symmetrically terminated (100) surface, there is one Li on each surface which relaxes to an o-center, surface-truncated octahedral positions as shown in Fig. 2 (b).

The surface Li relaxes to-

wards the slab and towards a neighboring Li in the plane of the surface, shortening one Li-O distance (labeled 1) from 3.49 to 2.57 Å, two Li-O distances (labeled 2) from 3.50 to 2.63 Å and one Li-Li distance (labeled 3) from 3.62 to 2.62 Å. The low energy geometry of the Li-terminated (100) surface has both Li atoms relaxed to o-center, surface-truncated octahedral sites with similar geometry (Fig. 2 (b)). This shows that the surface structure of Li on the low energy facet of LiTi2 O4 is strongly dependent on the amount of Li present. We use the (100) symmetrically terminated slab as the starting and reference structure to investigate the energetics of lithium intercalation into LiTi2 O4 .

While there are many

ways to explore the energy landscape of a system, previous studies have reported the lowest energy congurations of local Li[8a]/[16c] arrangements and the energy barrier between them, so we start our search of stable surface congurations from those ndings.

44,45

Minimum

energy congurations for each additional Li were found from the possible Li crystallographic

10


Page 11 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b)

(a)

2

1

2 3 Figure 2: Top view of stable surface structures at symmetrically terminated (100) face of LiTi2 O4 . Surface Li atoms are highlighted with yellow crosses at (a) surface truncated tetrahedral site and (b) surface truncated octahedral site. Bond lengths that change signicantly are marked by green lines.

(1) and (2) Li-O bonds and (3) Li-Li bonds shorten when Li

moves from (a) to (b) site.

sites and the formation energy for each additional Li was calculated using Eq. 3.

The

relative surface redox potential is calculated using Eq. 4 and reported along with the resulting formation energies in Table 2. To get a sense of the relative stability and ease of lithiation for each Li added, we compare the surface redox potential to the average bulk voltage of 1.11 V. Congurations having surface redox potentials greater than the average bulk potential are stable and should occur spontaneously. Conversely, charge states with a lower than bulk redox potential will form weaker bonds and will not occur spontaneously.

Table 2: Formation Energies and Potentials for Li16+x Ti32 O64 Surface Lithiation x Li

Ef ormation (eV)

voltage (V)

1

-1.28

1.28

2

-1.14

0.99

3

-1.12

1.08

4

-1.06

0.90

5

-1.09

1.21

Ef ormation = V =

ELix (Li1 T i2 O4 )n − En(Li1 T i2 O4 ) − xELi x

(ELix (Li1 T i2 O4 )n − ELiy (Li1 T i2 O4 )n ) ELibcc − n|e| (x − y)|e|

(3)

(4)

In the charge state of Li16+1 Ti32 O64 , we nd the most stable conguration having a formation energy of -1.28 eV, above our reference potential of 1.11 V, indicating that {100}

11



surfaces are highly reactive towards Li. In the case of three surface Li in Li16+2 Ti32 O64 , for the rst time we see an energetic ground state where a subsurface Li is in an octahedrally coordinated site (Fig. 3). The barrier for a tetrahedrally coordinated subsurface Li to move to a neighboring octahedral position is determined using the NEB method and found to be

Computational Study of Chemical and Electrochemical Intercalation of

Recommend Documents