Zero strain insertion, high cycling stability, and a stable charge/discharge plateau are promising properties rendering Lithium Titanium Oxide (LTO) a possible candidate for an anode material in solid state Li ion batteries. However, the use of pristine LTO in batteries is rather limited due to its electronically insulating nature. In contrast, reduced LTO shows an electronic conductivity several orders of magnitude higher. Studying bulk reduced LTO, we could show recently that the formation of polaronic states can play a major role in explaining this improved conductivity. In this work, we extend our study toward the lithium-terminated LTO (111) surface. We investigate the formation of polarons by applying Hubbard-corrected density functional theory. Analyzing their relative stabilities reveals that positions with Li ions close by have the highest stability among the different localization patterns.

1.
M.
Armand
and
J.-M.
Tarascon
, “
Building better batteries
,”
Nature
451
,
652 EP
(
2008
).
2.
A. S.
Aricò
,
P.
Bruce
,
B.
Scrosati
,
J.-M.
Tarascon
, and
W.
van Schalkwijk
, “
Nanostructured materials for advanced energy conversion and storage devices
,”
Nat. Mater.
4
,
366
377
(
2005
).
3.
B.
Zhao
,
R.
Ran
,
M.
Liu
, and
Z.
Shao
, “
A comprehensive review of Li4Ti5O12-based electrodes for lithium-ion batteries: The latest advancements and future perspectives
,”
Mater. Sci. Eng., R
98
,
1
71
(
2015
).
4.
T.
Yuan
,
X.
Yu
,
R.
Cai
,
Y.
Zhou
, and
Z.
Shao
, “
Synthesis of pristine and carbon-coated Li4Ti5O12 and their low-temperature electrochemical performance
,”
J. Power Sources
195
,
4997
5004
(
2010
).
5.
B.
Yan
,
M.
Li
,
X.
Li
,
Z.
Bai
,
J.
Yang
,
D.
Xiong
, and
D.
Li
, “
Novel understanding of carbothermal reduction enhancing electronic and ionic conductivity of Li4Ti5O12 anode
,”
J. Mater. Chem. A
3
,
11773
11781
(
2015
).
6.
J.
Wolfenstine
and
J. L.
Allen
, “
Electrical conductivity and charge compensation in ta doped Li4Ti5O12
,”
J. Power Sources
180
,
582
585
(
2008
).
7.
C. H.
Chen
,
J. T.
Vaughey
,
A. N.
Jansen
,
D. W.
Dees
,
A. J.
Kahaian
,
T.
Goacher
, and
M. M.
Thackeray
, “
Studies of mg-substituted Li4-xMgxTi5O12 spinel electrodes (0 ≤ x ≤ 1) for lithium batteries
,”
J. Electrochem. Soc.
148
,
A102
(
2001
).
8.
J.
Qiu
,
C.
Lai
,
E.
Gray
,
S.
Li
,
S.
Qiu
,
E.
Strounina
,
C.
Sun
,
H.
Zhao
, and
S.
Zhang
, “
Blue hydrogenated lithium titanate as a high-rate anode material for lithium-ion batteries
,”
J. Mater. Chem. A
2
,
6353
6358
(
2014
).
9.
D.
Young
,
A.
Ransil
,
R.
Amin
,
Z.
Li
, and
Y.-M.
Chiang
, “
Electronic conductivity in the Li4/3Ti5/3O4–Li7/3Ti5/3O4 system and variation with state-of-charge as a Li battery anode
,”
Adv. Energy Mater.
3
,
1125
1129
(
2013
).
10.
J.
Wolfenstine
,
U.
Lee
, and
J. L.
Allen
, “
Electrical conductivity and rate-capability of Li4Ti5O12 as a function of heat-treatment atmosphere
,”
J. Power Sources
154
,
287
289
(
2006
).
11.
K.
Liang
,
H.
He
,
Y.
Ren
,
J.
Luan
,
H.
Wang
,
Y.
Ren
, and
X.
Huang
, “
Ti3+ self-doped Li4Ti5O12 with rich oxygen vacancies for advanced lithium-ion batteries
,”
Ionics
26
,
1739
1747
(
2020
).
12.
R. N.
Nasara
,
P.-C.
Tsai
, and
S.-K.
Lin
, “
One-step synthesis of highly oxygen-deficient lithium titanate oxide with conformal amorphous carbon coating as anode material for lithium ion batteries
,”
Adv. Mater. Interfaces
4
,
1700329
(
2017
).
13.
H.
Kaftelen
,
M.
Tuncer
,
S.
Tu
,
S.
Repp
,
H.
Göçmez
,
R.
Thomann
,
S.
Weber
, and
E.
Erdem
, “
Mn-substituted spinel Li4Ti5O12 materials studied by multifrequency EPR spectroscopy
,”
J. Mater. Chem. A
1
,
9973
9982
(
2013
).
14.
P.
Jakes
,
J.
Granwehr
,
H.
Kungl
, and
R.-A.
Eichel
, “
Mixed ionic-electronic conducting Li4Ti5O12 as anode material for lithium ion batteries with enhanced rate capability - impact of oxygen non-stoichiometry and aliovalent Mg2+-doping studied by electron paramagnetic resonance
,”
Z. Phys. Chem.
229
,
1439
1450
(
2015
).
15.
P.-c.
Tsai
,
R. N.
Nasara
,
Y.-c.
Shen
,
C.-c.
Liang
,
Y.-w.
Chang
,
W.-D.
Hsu
,
N. T.
Thuy Tran
, and
S.-k.
Lin
, “
Ab initio phase stability and electronic conductivity of the doped-Li4Ti5O12 anode for Li-ion batteries
,”
Acta Mater.
175
,
196
205
(
2019
).
16.
A. J.
Cohen
,
P.
Mori-Sánchez
, and
W.
Yang
, “
Insights into current limitations of density functional theory
,”
Science
321
,
792
794
(
2008
).
17.
P.
Mori-Sánchez
,
A. J.
Cohen
, and
W.
Yang
, “
Many-electron self-interaction error in approximate density functionals
,”
J. Chem. Phys.
125
,
201102
(
2006
).
18.
M.
Kick
,
C.
Grosu
,
M.
Schuderer
,
C.
Scheurer
, and
H.
Oberhofer
, “
Mobile small polarons qualitatively explain conductivity in lithium titanium oxide battery electrodes
,”
J. Phys. Chem. Lett.
11
,
2535
2540
(
2020
).
19.
V. I.
Anisimov
,
J.
Zaanen
, and
O. K.
Andersen
, “
Band theory and Mott insulators: Hubbard U instead of Stoner I
,”
Phys. Rev. B
44
,
943
954
(
1991
).
20.
M.
Kick
,
K.
Reuter
, and
H.
Oberhofer
, “
Intricacies of DFT+U, not only in a numeric atom centered orbital framework
,”
J. Chem. Theory Comput.
15
,
1705
1718
(
2019
).
21.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
, “
Ab initio molecular simulations with numeric atom-centered orbitals
,”
Comput. Phys. Commun.
180
,
2175
2196
(
2009
).
22.
J.
Hubbard
, “
Electron correlations in narrow energy bands
,”
Proc. R. Soc. London, Ser. A
276
,
238
257
(
1963
).
23.
S. L.
Dudarev
,
G. A.
Botton
,
S. Y.
Savrasov
,
C. J.
Humphreys
, and
A. P.
Sutton
, “
Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
,”
Phys. Rev. B
57
,
1505
1509
(
1998
).
24.
A. I.
Liechtenstein
,
V. I.
Anisimov
, and
J.
Zaanen
, “
Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators
,”
Phys. Rev. B
52
,
R5467
R5470
(
1995
).
25.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
26.
M. T.
Czyżyk
and
G. A.
Sawatzky
, “
Local-density functional and on-site correlations: The electronic structure of La2 CuO4 and LaCuO3
,”
Phys. Rev. B
49
,
14211
14228
(
1994
).
27.
B.
Himmetoglu
,
A.
Floris
,
S.
de Gironcoli
, and
M.
Cococcioni
, “
Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
,”
Int. J. Quantum Chem.
114
,
14
49
(
2014
).
28.
J. E.
Moussa
,
P. A.
Schultz
, and
J. R.
Chelikowsky
, “
Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space
,”
J. Chem. Phys.
136
,
204117
(
2012
).
29.
O.
Lamiel-Garcia
,
K. C.
Ko
,
J. Y.
Lee
,
S. T.
Bromley
, and
F.
Illas
, “
When anatase nanoparticles become bulklike: Properties of realistic Tio2 nanoparticles in the 1–6 nm size range from all electron relativistic density functional theory based calculations
,”
J. Chem. Theory Comput.
13
,
1785
1793
(
2017
).
30.
K. J.
Hameeuw
,
G.
Cantele
,
D.
Ninno
,
F.
Trani
, and
G.
Iadonisi
, “
The rutile TiO2 (110) surface: Obtaining converged structural properties from first-principles calculations
,”
J. Chem. Phys.
124
,
024708
(
2006
).
31.
Z.
Liang
,
M.
Kim
,
T.
Li
,
R.
Rai
,
A.
Asthagiri
, and
J. F.
Weaver
, “
Adsorption and oxidation of ethylene on the stoichiometric and O-rich RuO2(110) surfaces
,”
J. Phys. Chem. C
121
,
20375
20386
(
2017
).
32.
R.
Martin
,
M.
Kim
,
C. J.
Lee
,
M. S.
Shariff
,
F.
Feng
,
R. J.
Meyer
,
A.
Asthagiri
, and
J. F.
Weaver
, “
Molecular chemisorption of N2 on IrO2(110)
,”
J. Chem. Phys.
152
,
074712
(
2020
).
33.
N. A.
Deskins
,
R.
Rousseau
, and
M.
Dupuis
, “
Distribution of Ti3+ surface sites in reduced TiO2
,”
J. Phys. Chem. C
115
,
7562
7572
(
2011
).
34.
T.
Shibuya
,
K.
Yasuoka
,
S.
Mirbt
, and
B.
Sanyal
, “
A systematic study of polarons due to oxygen vacancy formation at the rutile TiO2(110) surface by GGA+U and HSE06 methods
,”
J. Phys.: Condens. Matter
24
,
435504
(
2012
).
35.
B.
Dorado
,
B.
Amadon
,
M.
Freyss
, and
M.
Bertolus
, “
DFT + U
,”
Phys. Rev. B
79
,
235125
(
2009
).
36.
J. P.
Allen
and
G. W.
Watson
, “
Occupation matrix control of d- and f-electron localisations using DFT+U
,”
Phys. Chem. Chem. Phys.
16
,
21016
21031
(
2014
).
37.
Q.
Wu
and
T.
Van Voorhis
, “
Direct optimization method to study constrained systems within density-functional theory
,”
Phys. Rev. A
72
,
024502
(
2005
).
38.
B. J.
Morgan
,
J.
Carrasco
, and
G.
Teobaldi
, “
Variation in surface energy and reduction drive of a metal oxide lithium-ion anode with stoichiometry: A DFT study of lithium titanate spinel surfaces
,”
J. Mater. Chem. A
4
,
17180
17192
(
2016
).
39.
P.
Hohenberg
and
W.
Kohn
, “
Inhomogeneous electron gas
,”
Phys. Rev.
136
,
B864
B871
(
1964
).
40.
F.
Wu
and
Y.
Ping
, “
Combining Landau–Zener theory and kinetic Monte Carlo sampling for small polaron mobility of doped BiVO4 from first-principles
,”
J. Mater. Chem. A
6
,
20025
20036
(
2018
).
41.
Z.
Wang
,
C.
Brock
,
A.
Matt
, and
K. H.
Bevan
, “
Implications of the DFT + U method on polaron properties in energy materials
,”
Phys. Rev. B
96
,
125150
(
2017
).
42.
J. R.
De Lile
,
S. G.
Kang
,
Y.-A.
Son
, and
S. G.
Lee
, “
Investigating polaron formation in anatase and brookite TiO2 by density functional theory with hybrid-functional and DFT+U methods
,”
ACS Omega
4
,
8056
8064
(
2019
).
43.
M.
Setvin
,
X.
Hao
,
B.
Daniel
,
J.
Pavelec
,
Z.
Novotny
,
G. S.
Parkinson
,
M.
Schmid
,
G.
Kresse
,
C.
Franchini
, and
U.
Diebold
, “
Charge trapping at the step edges of TiO2 anatase (101)
,”
Angew. Chem., Int. Ed.
53
,
4714
4716
(
2014
).
44.
N. A.
Deskins
,
R.
Rousseau
, and
M.
Dupuis
, “
Localized electronic states from surface hydroxyls and polarons in TiO2(110)
,”
J. Phys. Chem. C
113
,
14583
14586
(
2009
).
45.
H.
Jiang
,
R. I.
Gomez-Abal
,
P.
Rinke
, and
M.
Scheffler
, “
First-principles modeling of localized d states with the GW@LDA + U approach
,”
Phys. Rev. B
82
,
045108
(
2010
).
46.
O.
Bengone
,
M.
Alouani
,
P.
Blöchl
, and
J.
Hugel
, “
Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of nio
,”
Phys. Rev. B
62
,
16392
16401
(
2000
).
47.
S.
Chrétien
and
H.
Metiu
, “
Electronic structure of partially reduced rutile TiO2(110) surface: Where are the unpaired electrons located?
,”
J. Phys. Chem. C
115
,
4696
4705
(
2011
).
48.
M.
Reticcioli
,
M.
Setvin
,
M.
Schmid
,
U.
Diebold
, and
C.
Franchini
, “
Formation and dynamics of small polarons on the rutile TiO2(110) surface
,”
Phys. Rev. B
98
,
045306
(
2018
).
49.
T.
Shibuya
,
K.
Yasuoka
,
S.
Mirbt
, and
B.
Sanyal
, “
Bipolaron formation induced by oxygen vacancy at rutile TiO2(110) surfaces
,”
J. Phys. Chem. C
118
,
9429
9435
(
2014
).
50.
N.
Bondarenko
,
O.
Eriksson
, and
N. V.
Skorodumova
, “
Polaron mobility in oxygen-deficient and lithium-doped tungsten trioxide
,”
Phys. Rev. B
92
,
165119
(
2015
).
51.
B.
Ziebarth
,
M.
Klinsmann
,
T.
Eckl
, and
C.
Elsässer
, “
Lithium diffusion in the spinel phase Li4Ti5O12 and in the rocksalt phase Li7Ti5O12 of lithium titanate from first principles
,”
Phys. Rev. B
89
,
174301
(
2014
).
52.
Z.
Su
,
J.
Liu
,
M.
Li
,
Y.
Zhu
,
S.
Qian
,
M.
Weng
,
J.
Zheng
,
Y.
Zhong
,
F.
Pan
, and
S.
Zhang
, “
Defect engineering in titanium-based oxides for electrochemical energy storage devices
,”
Electrochem. Energy Rev.
3
,
286
343
(
2020
).

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