Dissertation for the degree of Doctor of Philosophy
First-Principles Design and Investigation of a
Two-Dimensional Anode and a Ni-Rich Layered
Oxide Cathode Materials for Alkali Metal-Ion
Battery
Arindam Sannyal
Department of Nano Fusion Technology
The Graduate School
Pusan National University
February 2022
First-Principles Design and Investigation of a Two-Dimensional Anode and a
Ni-Rich Layered Oxide Cathode Materials for Alkali Metal-Ion Battery
Arindam Sannyal
Feb. 2022
First-Principles Design and Investigation of a
Two-Dimensional Anode and a Ni-Rich Layered
Oxide Cathode Materials for Alkali Metal-Ion
Battery
A Dissertation submitted to the graduate school of
Pusan National University in partial fulfillment of
the requirements for the degree of Doctor of
Philosophy in Nano Fusion Technology
under the direction of Joonkyung Jang
The dissertation for the degree of Doctor of Philosophy
by Arindam Sannyal
has been approved by the committee members.
December 09, 2021
Chair
Sungu Hwang
Member
Myung Won Lee
Member
Minjoon Park
Member
Dong Hwa Seo
Member
Joonkyung Jang
Contents
List of Figures ....................................................................................................................... v
List of Tables........................................................................................................................ ix
Abstract ................................................................................................................................. 1
CHAPTER 1.......................................................................................................................... 3
Introduction ........................................................................................................................... 3
1.1 Energy Storage System ................................................................................................ 3
1.2 Fundamentals of Lithium Ion Battery ......................................................................... 6
1.3 Electrode Materials of LIBs ........................................................................................ 8
1.3.1 Anode Materials .................................................................................................... 8
1.3.1.1 Two-Dimensional Materials as Anode........................................................ 13
1.3.2 Cathode Materials ............................................................................................... 18
1.3.2.1 Layered Oxide Cathodes ............................................................................. 21
1.3.2.2 Evaluation of the NCM Cathodes ............................................................... 23
1.3.2.3 LiNixCoyMn1−x−yO2 (NCM) Cathodes ......................................................... 26
1.3.2.4 Doping in NCM Cathodes ........................................................................... 31
1.4 Challenges in LIBs .................................................................................................... 32
1.5 Alternatives to LIBs .................................................................................................. 35
1.5.1 Sodium Ion Battery ............................................................................................. 35
1.5.2 Potassium Ion Battery ......................................................................................... 36
1.6 Outlines of the Dissertation ....................................................................................... 36
CHAPTER 2........................................................................................................................ 37
Theoretical Methods............................................................................................................ 37
2.1 Quantum Mechanics .................................................................................................. 37
i
2.1.1 Born-Oppenheimer Approximation .................................................................... 38
2.1.2 Hartree-Fock Method .......................................................................................... 39
2.2 Density Functional Theory ........................................................................................ 40
2.2.1 Hohenberg-Kohn Theorems ................................................................................ 40
2.2.2 Kohn-Sham Approach ......................................................................................... 41
2.2.3 Exchange-Correlation Functional ....................................................................... 42
2.2.3.1 Local Density Approximation ..................................................................... 43
2.2.3.2 Generalized-Gradient Approximation ......................................................... 44
2.2.3.3 Corrections of Exchange-Correlation Functional ....................................... 46
2.2.3.4 Dispersion Corrections ................................................................................ 47
2.3 Treating Solids........................................................................................................... 47
2.3.1 Bravais Lattice .................................................................................................... 47
2.3.2 Boundary Conditions .......................................................................................... 48
2.3.3 Bloch’s Theorem ................................................................................................. 48
2.4 Computational Approximations ................................................................................ 49
2.4.1 k-Points Sampling ............................................................................................... 49
2.4.2 Plane Waves ........................................................................................................ 49
2.4.3 Pseudopotential Approximation .......................................................................... 50
2.5 Calculation of Properties ........................................................................................... 52
2.5.1 Ewald Summation ............................................................................................... 52
2.5.2 Nudged Elastic Band Method ............................................................................. 53
2.5.3 Crystal Orbital Hamiltonian Population .............................................................. 54
CHAPTER 3........................................................................................................................ 55
First-Principles Study on the Two-Dimensional Siligene as an Anode Material for Alkali
Metal Ion Batteries .......................................................................................................... 55
Abstract............................................................................................................................ 55
3.1 Introduction ............................................................................................................... 56
ii
3.2 Simulation Methods................................................................................................... 57
3.3 Results and Discussion .............................................................................................. 58
3.3.1 Structural Properties ............................................................................................ 58
3.3.2 Adsorption of Li/Na/K Atoms ............................................................................ 60
3.3.3 Diffusion of Li/Na/K Atoms ............................................................................... 70
3.3.4 Voltage Profile and Specific Capacity ................................................................ 72
3.4 Conclusion ................................................................................................................. 80
CHAPTER 4........................................................................................................................ 81
First-Principles Study on Stabilizing the Ni-Rich LiNi0.89Co0.055Mn0.055O2 Cathode
Material by Doping with Zirconium or Molybdenum ..................................................... 81
Abstract............................................................................................................................ 81
4.1 Introduction ............................................................................................................... 82
4.2 Simulation Methods................................................................................................... 83
4.3 Results and Discussion .............................................................................................. 84
4.3.1 Structural Properties ............................................................................................ 84
4.3.2 Electronic Structure and Electrochemical Redox Behavior ................................ 91
4.3.3 Electrochemical Stability and Average Intercalation Voltage .......................... 104
4.3.4 Stabilization of the NCM-89 Material by Zr or Mo Doping ............................. 110
4.3.5 Li-Ion Diffusion ................................................................................................ 116
4.3.6 Phase Transition from the Layered to Spinel Structure .................................... 120
4.4 Conclusion ............................................................................................................... 122
CHAPTER 5...................................................................................................................... 123
Summary........................................................................................................................ 123
References ......................................................................................................................... 125
iii
요약 ................................................................................................................................... 150
Acknowledgment .............................................................................................................. 152
iv
List of Figures
CHAPTER 1
Figure 1.1: Comparison of the different battery technologies with respect to their
volumetric and gravimetric energy density. (From J. M. Tarascon et al., Nature, 2001, 414,
359-367) ................................................................................................................................ 5
Figure 1.2: Illustration of a standard LIB with LiCoO2 as cathode and graphite as an anode.
(From M. M. Thackeray et al., Energy Environ. Sci., 2012, 5, 7854-7863) ......................... 7
Figure 1.3: Crystal structure of graphite (a), silicon (b), and rutile and anatase TiO2 (c).
(From M. Inaba, Encyclopedia of Electrochemical Power Sources, Elsevier: Amsterdam,
2009, 198-208) .................................................................................................................... 10
Figure 1.4: Top and side view of 2D graphene (a), silicene (b), phosphorene (c), borophene
(d), TiO2 (e), MoS2 (f), Ti3C2 (g), and h-BN (f). (From L. Shi et al. J. Mater. Chem. A, 2017,
5, 3735–3758) ..................................................................................................................... 14
Figure 1.5: Crystal structures of (a) the layered (LiCoO2), (b) the spinel (LiMn2O4), and (c)
the olivine (LiFePO4) materials. (From N. Nitta et al., Mater. Today, 2014, 18, 252-264) 19
Figure 1.6: The crystal structures of different phases of Li xTMO2. Green and blue octahedra
represent the Li sites and the MO6 units, respectively. (From M. D. Radin et al., Adv. Energy
Mater., 2017, 7, 1602888) ................................................................................................... 22
Figure 1.7: The compositional phase diagram of layered LiNi xCoyMn1-x-yO2. (From A.
Chakraborty et al. Chem. Mater., 2020, 32, 915−952) ....................................................... 30
Figure 1.8: Abundance of different elements in the Earth’s crust. (From R. S. Carmichael
et al., Practical Handbook of Physical Properties of Rocks and Minerals; CRC Press: Boca
Raton, FL, 1989) ................................................................................................................. 34
CHAPTER 2
Figure 2.1: Illustration of a standard DFT calculation. (From J. G. Lee, Computational
Materials Science: an Introduction, CRC Press: Boca Raton, FL, 2017, 2 nd edition) ........ 45
Figure 2.2: Schematic of pseudo- electron (dashed lines) and all electron (solid lines)
potentials and their wave functions. rc is the cutoff radius. (From Payne et al., Rev. Mod.
Phys., 1992, 64, 1045-1097) ............................................................................................... 51
v
CHAPTER 3
Figure 3.1: Optimized structure of the 2D SiGe, (a) top and (b) side views. The circle
represents the unit cell and the H, T Ge, TSi, and B labels denote the possible binding sites.
(c) The phonon dispersion spectra of the SiGe sheet. ......................................................... 59
Figure 3.2: Structure of the 2D SiGe with alkali metal atom initially positioned at site B (a).
With optimization, the metal atoms diffuse from site B to T Si (b)...................................... 61
Figure 3.3: The charge density differences between the SiGe sheet and adsorbed (a) Li, (b)
Na, and (c) K atom plotted with isosurface value of 0.001‫׀‬e‫ ׀‬bohr-3. The cyan and yellow
colors, respectively, characterize electron depletion and accumulation. ............................ 63
Figure 3.4: Band structures of the (a) pristine monolayer of SiGe, (b) Li 0.11SiGe, (c)
Na0.11SiGe, and (d) K0.11SiGe. ............................................................................................ 65
Figure 3.5: Total and PDOSs of the (a) pristine SiGe, (b) Li0.11SiGe, (c) Na0.11SiGe, and (d)
K0.11SiGe. ............................................................................................................................ 66
Figure 3.6: Charge distribution and total density of states for Li 1.0SiGe (a), Na2.0SiGe, and
K2.0SiGe demonstrating their metallic characters. .............................................................. 68
Figure 3.7: (a) The charge density differences of the fully lithiated 2D SiGe before (left)
and after (right) the relaxation of the Si and Ge atoms. (b) PDOS of Li 2.0SiGe, demonstrating
the band gap broadening. .................................................................................................... 69
Figure 3.8: (a) Diffusion pathways of the metal atoms on the 2D SiGe. Minimum energy
profiles of the migrating alkali metal atoms in Path-2 (b) and Path-3 (c)........................... 71
Figure 3.9: Primary (left) and optimized (right) structures of the 2D SiGe (3 × 3) adsorbed
with 36 Li atoms. Li atoms in different adsorption layers of the SiGe sheet are shown in
different colors. ................................................................................................................... 73
Figure 3.10: Optimized geometries of the 2D SiGe adsorbed with the maximum capabilities
of 18 Li (a), 36 Na (b), and 18 K (c) atoms (3 × 3 supercell). Na atoms in the different layers
are shown in different colors. .............................................................................................. 74
Figure 3.11: Electron localization function plots in the (110) cross-sections for the (a) Na
and (c) K multilayers on both sides of the sheet of SiGe. The related PDOSs of the sheet of
SiGe adsorbed with Na (b) and K (d).................................................................................. 76
Figure 3.12: (a) Convex hulls of the formation energies at different metal concentrations
and (b) the corresponding voltage profiles (vs M/M+) of LixSiGe, NaxSiGe, and KxSiGe. 79
vi
CHAPTER 4
Figure 4.1: Relaxed structure of the NCM-89 material, LiNi0.89Co0.055Mn0.055O2, (a) side
view and (b) top view. In this and all the subsequent figures, we utilize the identical color
outline for Li, Ni, Co, Mn, and O ions. ............................................................................... 85
Figure 4.2: The c lattice constant of (a) the undoped (Li xNi0.89Co0.055Mn0.055O2), (b) the Zrdoped
(LixNi0.862Co0.055Mn0.055Zr0.028O2)
and
(c)
the
Mo-doped
(LixNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 cathodes at different levels of delithiation. (d)
The volumes of the undoped and doped NCM-89 cathodes at different levels of delithiation,
computed by employing the PBE+D3 approach. ................................................................ 90
Figure 4.3: The total DOSs of the undoped (a), the Zr-doped (c), and the Mo-doped (e)
NCM-89 cathodes. The PDOSs are also plotted for the undoped (b), the Zr-doped (d), and
the Mo-doped (f) NCM-89 cathodes. .................................................................................. 93
Figure 4.4: Radial distribution functions of the TM-O pairs, 𝑔𝑟𝑠, in the undoped
(LiNi0.89Co0.055Mn0.055O2), Zr-doped (LiNi0.862Co0.055Mn0.055Zr0.028O2), and Mo-doped
(LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 materials computed by employing the PBE
approach. ............................................................................................................................. 97
Figure 4.5: Oxidation states of transition metals in the pristine (Li xNi0.89Co0.055Mn0.055O2)
(a),
Zr-doped
(LixNi0.862Co0.055Mn0.055Zr0.028O2)
(b),
and
Mn-doped
(LixNi0.862Co0.055Mn0.055Mo0.028O2) (c) NCM-89 cathodes at different levels of delithiation.
............................................................................................................................................. 99
Figure 4.6: Projected density of states of the undoped NCM-89 material,
LixNi0.89Co0.055Mn0.055O2, calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x = 0.33,
(e) x = 0.16, and (f) x = 0.0 by using the PBE method. .................................................... 100
Figure 4.7: Projected density of states of the Zr-doped NCM-89 material,
LixNi0.862Co0.055Mn0.055Zr0.028O2, calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x
= 0.33, (e) x = 0.16, and (f) x = 0.0 by using the PBE method. ........................................ 102
Figure 4.8: Projected density of states of the Mo-doped NCM-89 material,
LixNi0.862Co0.055Mn0.055Mo0.028O2, calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x
= 0.33, (e) x = 0.16, and (f) x = 0.0 by using the PBE functional..................................... 103
Figure 4.9: Convex hull of formation energies of the undoped, Zr-doped, and Mo-doped
NCM-89 cathodes at different levels of delithiation. The PBE method was employed in the
computation. ...................................................................................................................... 105
Figure 4.10: Voltage profiles of the pristine and doped NCM-89 cathodes at different levels
of delithiation. ................................................................................................................... 108
vii
Figure 4.11: Average values of ICOHP for various (a) TM-O and (b) TM-TM bonds in the
pristine, Zr-doped, and Mo-doped NCM-89 cathodes. ..................................................... 111
Figure 4.12: Oxygen binding energies (a) and average charges (Bader) on the oxygen atoms
(b) computed for the pristine and doped NCM-89 cathodes at different levels of delithiation.
........................................................................................................................................... 115
Figure 4.13: Pathways and energy profiles of Li+ diffusing in the current NCM-89 cathodes.
We have shown results along the ODH (a and b) and TSH (c and d) routes of the Li +
migration adjacent a dopant position of the doped NCM-89 cathode, beside the results for
the pristine material. The local minimum along the TSH route resembles to the NEB image
at the intermediate tetrahedral site. The doping position and diffusing Li + are sketched as
cyan and yellow spheres, respectively. ............................................................................. 117
Figure 4.14: Pathways and minimum energy profiles of Li+ migrating along the ODH (a
and b) and TSH (c and d) routes in the vicinity of adjacent Ni ion of the doping site in the
undoped and doped NCM-89 cathodes. Sketched as cyan and yellow spheres are the doping
position and diffusing Li+, respectively. ........................................................................... 119
Figure 4.15: Representations for two routes of a TM ion migrating from a TM layer to a Li
layer (a). Positions F and E resemble to the octahedral face and edge shared by the adjacent
octahedra, respectively. The first route of Ni2+ diffusing from a TM layer to a Li layer (b)
and the corresponding minimum energy profile (c) for the pristine NCM-89 cathode. The
second route (d) and minimum energy profile (e) of a diffusing Ni 2+ in the doped NCM-89
cathodes. Displayed in (d) is the route sketched for the Zr-doped NCM-89. ................... 121
viii
List of Tables
CHAPTER 1
Table 1.1: Comparison of different anode materials in terms of their specific capacity,
volume expansion, and potential. (From J. W. Zhang, J. Power Sources, 2011, 196, 13-24)
............................................................................................................................................. 12
Table 1.2: Electrochemical properties of the different classes of cathode materials for LIBs.
(From M. Yoshio et al., Lithium-ion Batteries: Science and Technologies, Springer: New
York, 2009) ......................................................................................................................... 20
CHAPTER 3
Table 3.1: Adsorption energies (Eadss) of the metal atoms at different adsorption sites of the
2D SiGe. The charge transfers from metals to 2D SiGe (∆ρs) are also listed at H sites
evaluated by the Bader charge. ........................................................................................... 62
CHAPTER 4
Table 4.1: The lattice parameters a and c (Å) of the undoped (LixNi0.89Co0.055Mn0.055O2),
Zr-doped
(LixNi0.862Co0.055Mn0.055Zr0.028O2),
and
Mo-doped
(LixNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 materials. Results are listed for different
lithiation levels, xs by using four different theoretical methods. ........................................ 87
Table 4.2: Magnetic moments and oxidation states of the 36 transition metal (TM) ions in
the undoped (LiNi0.89Co0.055Mn0.055O2), Zr-doped (LiNi0.862Co0.055Mn0.055Zr0.028O2), and
Mo-doped (LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 materials. ..................................... 94
Table 4.3: Average voltage of the pristine (LiNi0.89Co0.055Mn0.055O2), Zr-doped
(LiNi0.862Co0.055Mn0.055Zr0.028O2), and Mo-doped (LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM89 materials. ...................................................................................................................... 109
Table 4.4: The charges (Bader) on oxygen atoms and oxygen binding energies in the fully
lithiated states computed by employing the PBE approach. The charge on oxygen was
averaged around the dopant octahedra. ............................................................................. 113
ix
First-Principles Design and Investigation of a Two-Dimensional Anode and a NiRich Layered Oxide Cathode Materials for Alkali Metal-Ion Battery
Arindam Sannyal
Department of Nano Fusion Technology
The Graduate School
Pusan National University
Abstract
Lithium-ion batteries (LIBs) have attracted tremendous interest due to their excellent performances in an
energy storage system (ESS) and electric vehicles (EVs). The high cost and low abundance of lithium
resources, however, make it critical to develop other battery systems, especially sodium- and potassiumion batteries (NIBs and KIBs). Optimizing electrode materials of high energy density and ionic conductivity
is a key challenge for developing next-generation batteries. The purpose of this dissertation is to develop
electrode materials with high energy density by using the density functional theory calculations for
applications in LIBs, NIBs, or KIBs. Compared to the conventional graphite anode, silicon (Si) and
germanium (Ge) based anode materials have very high energy density. However, the commercialization of
these materials is hindered by the extreme expansion of volume during the insertion-deinsertion process of
metal ions. Recently, two-dimensional materials of high surface areas have attained intense consideration
as potential anode materials for next-generation batteries. Two-dimensional Si, Ge, or Sn can deliver higher
specific capacities than the graphite anode for LIBs and NIBs. The integration of Ge into Si can further
improve the diffusivity of lithium diffusivity and electronic conductivity of Si. We evaluate the applicability
of a SiGe sheet as an anode for the LIBs, NIBs, or KIBs. Our first-principle calculations show that the SiGe
sheet possesses low average open-circuit voltages, high diffusivity of metal ions, and provides high
theoretical capacities for LIBs, NIBs, or KIBs. The structure and chemical composition of the cathode
materials largely control the performance and cost of the current LIB technology. A Ni-rich cathode
material, LiNixCoyMn1−x−yO2 (NCM), with a Ni content of 80% can provide a high energy density of 400
1
W-h kg-1, however, it endures a poor thermal stability and rapid decay in capacity. Cationic doping is
proposed to greatly enhance the structural stability and cycling performance of a Ni-rich NCM. We
investigate the role of zirconium (+4) or molybdenum (+6) doping in stabilizing a Ni-rich,
LiNi0.89Co0.055Mn0.055O2 (NCM-89), cathode material. Our study reveals that the Zr4+ or Mo6+ doping can
inhibit a layered-to-spinel phase transition and decrease the evolution of oxygen gas in NCM-89, resulting
in improved structural stability. We consider these studies will direct the rational design and development
of electrode materials with high energy density for next-generation batteries.
2
CHAPTER 1
Introduction
1.1 Energy Storage System
Fossil fuels including petroleum, coal, and gas are the largest source of energy to date and will
continue to dominate the energy market for the next two decades.1 However, the resources
associated with fossil fuels are limited and will be expended in the next 50-70 years.2 Furthermore,
the use of fossil fuels leads to several adverse effects on the environment such as global warming
and air pollution from sulfide and nitride gases. Currently, transportation uses most of the fossil
fuels and largely contributes to the emission of greenhouse gas. Therefore, it is highly demanding
to advance alternative and renewable energy resources for the future. Nuclear energy is one of the
prospective alternative sources of energy, however, involves a high threat of radiation and high
cost for operation.3 Therefore, immense efforts have been carried out to develop a clean and
renewable energy resource, such as solar, wind, and hydro energies.4-6 However, all of these
renewable sources have several technical and environmental aspects to concern. For example,
hydro energy tremendously affects the ecosystem of rivers and oceans, leading to the annihilation
of several living beings. Solar and wind energy can produce a high amount of electricity but largely
depend on the location and time of the operation. Moreover, these energies are only limited to
apply directly in the grid systems.7 Therefore, an efficient energy storage system is required to
produce and accumulate high energy for future use. Besides, the use of petroleum in the
transportation sector needs to be reduced by developing electric vehicles (EVs).
Lithium-ion battery (LIB) technology has grown as the foremost technology for the storage of
energy in portable electronic devices as well as for EVs and grids. LIBs have outperformed the
preceding lead-acid, nickel-cadmium, or nickel-metal hydride batteries by their high energy
density and steady electrochemical performance. 8 Although, LIBs have been successfully
integrated into the EVs, however, the extensive usage of EVs is hampered by the high cost and
low ranges of driving. The driving range can be increased either by enhancing the size or energy
3
density of the battery pack. With the increasing battery size, the cost and weight of the EVs also
increase, lowering the driving range. Therefore, it is viable to preferentially enhance the energy
density of the LIB with improved safety and low cost.
4
Figure 1.1: Comparison of the different battery technologies with respect to their volumetric and
gravimetric energy density. (From J. M. Tarascon et al., Nature, 2001, 414, 359-367)
5
1.2 Fundamentals of Lithium Ion Battery
Initially, molten sulfur and Li, respectively, were considered as cathode and anode materials for
LIB, which were later replaced by metal sulfide and Li metal alloys, respectively. In 1991, Sony
commercialized the LIB by introducing the intercalation chemistry of LiCoO 2 as cathode and
graphite as anode, which is still generally used in several fields of LIBs.9 Figure 1.1 represents the
major components of a standard LIB and its operating mechanism. A standard LIB has four major
components, namely, a cathode, an anode, an electrolyte, and a separator. In addition to these,
copper and aluminum foils, respectively, are also used as current collectors for anode and cathode.
In LIBs, Li transition metal (TM) oxides and phosphates are commonly used as cathode material,
whereas, graphite or other carbon-based materials are used as anode material.10-11 The two
electrodes are immersed in an electrolyte containing a Li salt dissolved in a mixture of carbonatebased solvent. A membrane of polymer is used in between the electrodes as a separator which
allows the Li-ion to pass through but blocks the electron transfer. During the charging of LIBs, the
Li-ions are pulled out from the cathode materials in conjunction with the electrochemical oxidation
of the transition metal ions due to the applied potential on the two electrodes. The extracted Li+s
then travel through the electrolyte and then insert into the anode material. In the meantime, the
electrons move from cathode side to the anode side through the external circuit. In this charging
process, the electrical energy is transformed to the chemical energy. During the discharging of
LIBs, the Li+s and electrons are brought back to the cathode side, where electricity is produced
from the chemical energy, providing power to the devices. The electrochemical reactions in a LIB
having LiCoO2 as cathode and graphite as an anode are as follows:
Li1-xCoO2 + xLi+ + xe- ↔ LiCoO2
at Cathode
LiC6 ↔ xLi+ + Li1-xC6 + xe-
at Anode
C6 + LiCoO2 ↔ LixC6 + Li1-xCoO2 Overall reaction
6
Figure 1.2: Illustration of a standard LIB with LiCoO2 as cathode and graphite as an anode. (From
M. M. Thackeray et al., Energy Environ. Sci., 2012, 5, 7854-7863)
7
Although, electrolyte and separator are of great importance for LIBs, however, the cost and
weight of a LIB pack mostly govern by the active materials of the electrodes. An enhanced specific
capacity can raise the energy density of a battery pack and thereby the size of the battery can be
reduced. In order to extend the EVs to a wide community, the LIB must meet several criteria such
as have an energy density of 500 Wh L-1, which can be cycled at least 1000 times for 15 years. 12
The standard LIB consisting of graphite as anode and Li transition metal (TM) oxide as a cathode
cannot fulfill such benchmarks. Therefore, the development of new electrode materials and redox
chemistry is essential to enhance the energy density and cycle life for the commercialization of
next-generation batteries into EVs and beyond. In the next section, we will discuss the
development of different anode and cathode materials over the years.
1.3 Electrode Materials of LIBs
1.3.1 Anode Materials
Before the commercialization of the graphite anode, Li metal was the first studied anode
material for LIBs because of its extremely high specific capacity of 3860 mAh g -1 and lowest
electrode potential of -3.05 V vs. standard hydrogen electrode (SHE).13 However, Li metal is yet
to be commercialized because pure Li metal anode has a serious threat of forming Li dendrite.
Since, unlike other anodes, Li metal is host-less, thereby, the incoming Li-ions from the cathode
deposits on the Li metal surface. The inhomogeneous deposition of the Li-ions on Li metal can
lead to the uncontrolled growth of Li to a spike or dendritic shape. The Li dendrite can penetrate
through the separator to the cathode and initiate a short circuit and consequently a thermal runway.
Besides, the electrolyte can decompose electrochemically and forms a solid electrolyte interphase
(SEI) on the Li metal surface, resulting in low Coulombic efficiency. In recent years, immense
efforts have grown to mitigate the formation of Li dendrite. Yi Cui et al. introduced a thin film of
carbon nanostructure in between the electrolyte and the Li metal and showed that the formation of
uncontrolled Li dendrite, as well as the unstable SEI, can be alleviated.14 Another study showed
that the formation of dendrite can be prevented by incorporating the Li metal in a porous network
of graphene.15 By using the Brownian dynamic motion study, Kisang et al. proposed that a thin
8
SEI layer slowed down the formation of Li dendrite and thus leads to a mossy shape, whereas a
thick SEI layer stimulate a dendritic growth of the Li metal. 16
The Li metal anode was substituted by the carbonaceous materials due to the safety issues
associated with the Li metal. At first, coke and microstructure of carbon were considered as anodes,
however, rapidly replaced by the graphite anode because of its high abundance, low cost, and
higher theoretical capacity of 372 mAh g-1.17 Moreover, graphite has a low electrode potential of
0.05 V vs. Li/Li+, which benefits to obtain a high energy density of the LIB. During charging and
discharging, the Li-ions can intercalate/deintercalate in the interstitial sites of the graphite layers,
without disrupting the lattice structure significantly. Different kinds of carbon nanostructures have
been studied such as carbon nanotube (CNT), carbon nanowire (CNW), and carbon nanofiber
(CNF) for enhanced specific capacity, especially electrospun CNF has a high specific capacity of
450 mAh g-1.18 However, the practical capacity of these carbonaceous materials are still far from
the required value to apply in the LIBs for EVs.19 A sheet of graphite i.e., graphene itself was
considered as an anode material for LIBs because graphene can hold Li-ions on both sides together
with the edges and thereby have a higher specific capacity of 500 mAh g-1.20 However, graphene
anode has poor capacity retention because of the formation of a SEI and cost of electrolyte.
Due to the insufficient specific capacity of the carbon-based anode materials, it is crucial to find
new anode materials with a higher specific capacity, low cost, enhanced safety, and longer
cyclability. Materials that can form an alloy with the Li-ions are of great interest, especially
elements of Group IV of the periodic table such as silicon (Si), germanium (Ge), and tin (Sn). 18
The theoretical capacity of Si, Ge, and Sn, respectively, are 4200, 1625, and 994 mAhg -1, much
higher than the carbon-based anodes.21-22 However, with the insertion of Li-ions, these materials
experience huge volume expansion (~300%), resulting in severe mechanical stress and grinding
of the active particles, which leads to the rapid fading of capacity. 21-22 Besides, the alloy particles
can aggregate themselves and irreversibly trap some Li-ions, resulting in poor rate capability.23
9
Figure 1.3: Crystal structure of graphite (a), silicon (b), and rutile and anatase TiO 2 (c). (From M.
Inaba, Encyclopedia of Electrochemical Power Sources, Elsevier: Amsterdam, 2009, 198-208)
10
In addition to the Li, carbon-based, and alloy type materials, other materials were also studied
for LIBs such as intercalation and conversion anodes. Similar to the graphite anode, the Li-ions
can intercalate and deintercalate in the intercalation anodes without changing the host structure
significantly. Two familiar intercalation type anodes are the anatase and rutile phase of TiO 2, and
Li4Ti5O12.24 However, these materials have a high intercalation potential of ~1.5 V vs. Li/Li+, thus
can be applied in the application of high power. Conversion anodes are usually the metal oxides
such as SnO2, CuO, Co3O4, and Fe2O3, which go through conversion reaction to form pure metals
and Li2O with the insertion of Li.25-26
11
Table 1.1: Comparison of different anode materials in terms of their specific capacity, volume
expansion, and potential. (From J. W. Zhang, J. Power Sources, 2011, 196, 13-24)
Material
Theoretical capacity
Average voltage vs.
Volume expansion
(mAh g-1)
Li/Li+ (V)
(%)
Li metal
3862
0
100
Graphite
372
0.05
12
Li4Ti5O12
175
1.6
1
Si
4200
0.4
420
Ge
1625
0.5
370
Sn
994
0.6
260
12
1.3.1.1 Two-Dimensional Materials as Anode
The established anode materials such as carbonaceous and intercalation materials are limited by
low specific capacity, whereas the Li metal and alloy type materials have poor capacity retention
and severe safety issues. Two-dimensional (2D) materials have a high surface area and thus can
provide a higher specific capacity than their corresponding three-dimensional counterparts. The
2D materials can be either synthesized by the chemical vapor deposition method or exfoliated from
the bulk materials by liquid or mechanical exfoliation.27 Stimulated from graphene, in recent years,
2D materials have fascinated great attention for their potential application as anode materials for
LIBs. A 2D material can be either used as an active anode material itself for LIBs or to form a
composite with other anode materials. In the following section, we will discuss several 2D
materials that have been reported for LIBs.
1.3.1.1.1 Graphene
The graphite anode for LIBs is limited by its low specific capacity and poor rate capability. 28
On the other hand, graphene can accumulate Li-ions on its both side, rendering higher theoretical
capacity for LIBs than the graphite.29 However, the graphene has very weak binding energy for
Li-ions which can lead to the clustering of the Li-ions.27 This problem can be solved by either
introducing vacancies or B-/N-dopant into the graphene structure.27 Zhou et al. showed that Bdoped graphene has a higher binding affinity of Li than pristine graphene. 30 By experiments,
Reddy et al. compared the reversible capacities of the pristine and N-doped graphene and showed
that the specific capacity of the N-doped graphene can be doubled than the pristine graphene. 31
It has been reported that the graphene layers with parallel orientation to the diffusion of Li-ions
have higher electrochemical performances compared to the perpendicularly oriented graphene
layer.32 Li et al. revealed that nanosheets of graphene with having more defects and less number
of the layer have superior performances for LIBs.33 Shu et al. synthesized porous graphene which
can deliver a high capacity of 400 mAh g-1 at the current density of 2000 mA g-1.34 Cohn et al.
synthesized a hybrid foam of graphene-CNT nanostructure and attained a very high capacity of
2640 mAh g-1 at 186 mA g-1.35
13
Figure 1.4: Top and side view of 2D graphene (a), silicene (b), phosphorene (c), borophene (d),
TiO2 (e), MoS2 (f), Ti3C2 (g), and h-BN (f). (From L. Shi et al. J. Mater. Chem. A, 2017, 5, 3735–
3758)
14
1.3.1.1.2 Analogs of Graphene
Black phosphorus has a similar structure of graphite where Li-ion can intercalate into the layers
of phosphorene, however, forms alloys at high concentration of li-ions, leading to a significant
volume expansion.36 Experimentally, Xu et al. proposed that a few layers of phosphorene can
mitigate the problem of structural deterioration. 37 Consequently, researchers investigated the
possibility of a single layer of phosphorene in order to use as an anode material for LIBs. DFT
studies showed that a monolayer of phosphorene has a specific capacity of 432 mAh g-1.
Anisotropic diffusion has been observed for the migration of Li-ions on the phosphorene layer
with a low diffusion barrier of 0.08 eV across the zigzag direction, whereas the diffusion barrier
across the armchair direction was found to be 0.68 eV. 27 Furthermore, the adsorption of Li-ions
can enhance the electrical conductivity of phosphorene. Zhang et al. revealed that the occurrence
of point defects in the phosphorene structure increases the diffusion barrier of Li-ion, suggesting
to prevent the defects during the synthesis process.38
2D structure of other Group-IV elements such Si, Ge, and Sn have been investigated for their
promising applications for LIBs. Unlike, graphene and phosphorene, the 2D monolayer of Si
(silicene), Ge (germanene), and Sn (stanene) cannot be exfoliated as a single layer rather
synthesized on metal substrates such as Ag (111) or Au (111) by the CVD method. 27 Recent studies
showed that graphene and MgX2 (X = Cl, Br, or I) can also be used as promising substrates for
synthesizing silicene and germanene and reported to enhance the stability and electronic
conductivity as well as the storage performance of Li-ions.39 Computational studies reported that
the theoretical capacities of the silicene, germanene, and stanene, respectively, are 954, 369, and
226 mAh g-1.27 A single layer of boron, namely borophene is another analog of graphene which
has a high theoretical capacity of 1860 mAh g -1 and very low diffusion barrier of 0.0026 eV for
LIB.27
15
1.3.1.1.3 2D Transition Metal Oxides
Layered transition metal oxides (TMOs) have superior thermal stability and high specific
capacity. TiO2-B is the most widely studied TMO anode for LIBs due to its highest capacity among
all polymorphs of TiO2.40 Theoretical studies reported that the TiO2-B can accommodate a
maximum amount of Li with a Li-Ti ratio of 1.25 without disrupting the structure significantly. 41
Dylla et al. showed that the 3D and 2D structures of TiO2-B can provide the same specific capacity
at 1.0 V vs. Li/Li+, however, the lithiation processes are essentially different. 42 Procházka et al.
synthesized a thin porous film TiO2-B which has capacity retention of 80% even after 800 cycles. 43
Beuvier et al. showed that nanoribbons of TiO2-B have a specific capacity of 200 and 100 mAh g, respectively, at 0.3 and 15C.44 Liu et al. synthesized nanosheets of TiO2–B with a thickness of
1
5–10 nm which can provide a high reversible capacity of 216 mA h g-1 at 10C has been achieved.45
Other TMOs have been also investigated to be used as an anode for LIBs. Ni et al. showed that a
composite material of MoO2 in a carbon matrix can provide a high reversible capacity of 1051
mAh g-1 at 0.5 A g-1 current density.46 Nanosheets of Nb2O5 has also been studied for LIBs,
however, shows a low specific capacity of 184 mAh g-1 at a voltage range of 1.0-2.5 V.47
1.3.1.1.4 2D Transition Metal Dichalcogenides
In recent years, 2D transition metal dichalcogenides (TMDs) have been extensively investigated
due to their diverse electrochemical properties for LIBs. The 2D TMDs can be used as anode for
LIBs in their pristine forms as well as heterostructure and composite materials. 27 2D MoS2 is one
of the most studied TMDs for LIBs because of its semi-metallic nature. By using the DFT
calculations, Li et al. reported that compared to the bulk MoS 2 a 2D sheet of MoS2 has a lower
diffusion barrier for the migration of Li-ions.48 Theoretical study also showed that the 2D structure
of MoS2 experiences severe structural deterioration with lithiation which can be suppressed by
incorporating the MoS2 into graphene layers.49 Later, by experiments, Liu et al. showed that a
composite of MoS2/graphene can deliver a high reversible capacity of 1351 mAh g-1 at the current
density of 100 mA g-1.50 Xiao et al. synthesized a composite of MoS2/polyethylene oxide for
16
stabilizing the 2D structure of the MoS2 and the composite is found to deliver a very high capacity
of 1000 mAh g-1.51
Other 2D TMDs have been also reported as anodes for LIBs by using experiments and
theoretical studies. A composite material of SnS2/graphene can provide a high specific capacity of
1005 mAh g-1.27 Bhandavat et al. successfully synthesized the 2D WS2, however, the reversible
capacity of 118 mAh g-1 was found to be lower than the 2D MoS2 and SnS2.52 By using the DFT
calculations, Jing et al. reported that a sheet of VS2 has a high theoretical capacity of 466 mAh g1
and low diffusion barrier of 0.25 eV for the migration of Li-ions.53 Wang et al. investigated
several heterostructures of 2D TMDs (MX2, where M = Mo, W; X = S, Se) and revealed that a
heterostructure of MoS2/WS2 has the optimum performance in terms of ionic mobility and
electronic conductivity.54
1.3.1.1.5 2D Transition Metal Carbides
2D transition metal carbides, commonly known as MXenes can be exfoliated from the bulk
structures. The MXenes have been investigated as promising anode materials for LIBs due to their
metallic or semi-metallic nature. The physiochemical properties of the MXenes can be changed
significantly by introducing different functional groups for example –O, -OH, or –F. By using DFT
calculations, Tang et al. showed that the pristine Ti 3C2 has a higher specific capacity of 320 mAh
g-1 and a lower energy barrier of 0.07 eV for Li-ion migration than the Ti3C2 terminated by the –
OH or –F groups.55 Later, Sun et al. synthesized a 2D Ti 3C2 and showed that the 2D Ti3C2 can
provide an initial capacity of 123.6 mAh g-1 at 1C with low Coulombic efficiency of 47%.56 Naguib
et al. showed that 2D V2C and Nb2C have much higher capacity (260 and 170 mAh g-1) than the
Ti3C2 at 1C.57 DFT studies reported that the pristine 2D V2C and Nb2C have high theoretical
capacities of 940 and 542 mAh g-1, respectively, and low migration barrier of Li-ions, however, OH or –F terminated V2C and Nb2C have lower capacities and higher migration barrier.27 Halim
et al. synthesized a functionalized 2D Mo2C and then fabricated it with CNT to form a
functionalized composite of Mo2C/CNT. The synthesized composite material can provide
reversible capacities of 250 and 76 mAh g-1 at a high C rate of 20 and 131C, respectively.58 Sun
17
et al. proposed that –O functionalized Ta2C, Cr2C, or V2C may undergo reversible phase transition
during the charging and discharging process and thereby have potential application in LIBs. 59
Over the few years, new 2D materials are emerging for their potential applications as anode
material for LIBs as well as next-generation batteries. A possible new material is SiGe which has
been reported to be promising in the applications of electronic and optoelectronic devices. 60 The
possibility of this material in LIBs is still unknown. In this dissertation, we have investigated the
scope of the 2D SiGe sheet to be used as a prospective anode material.
1.3.2 Cathode Materials
The energy density of a LIB can be enhanced either by increasing the voltage or the specific
capacity of the electrode materials. The current electrolytes are electrochemically unstable at high
operating voltages, rendering that the energy density can only be enhanced by increasing the
specific capacity of the electrode materials.61 Compared to the anode materials, the cathode
materials have a lower capacity in accumulating the Li +s, thus govern the overall energy density
of the battery pack.62 Based on the crystallographic structure and the corresponding dimension for
the diffusion of Li+, the cathode materials can be classified into three types: the layered materials
e.g., LiCoO2, the spinel materials e.g., LiMn2O4, and the olivine materials e.g., LiFePO4.63 Figure
1.5 illustrates the crystal structure of these materials. The layered oxide materials are generally
used for applications where high energy is required due to their higher specific capacity than the
spinel and olivine materials, whereas, the spinel and olivine materials are applied to systems
involving high power due to their safety and low cost. 63 Among these materials, the layered oxide
materials are the most engaging ones for application in EVs due to their high specific capacity.
18
Figure 1.5: Crystal structures of (a) the layered (LiCoO2), (b) the spinel (LiMn2O4), and (c) the
olivine (LiFePO4) materials. (From N. Nitta et al., Mater. Today, 2014, 18, 252-264)
19
Table 1.2: Electrochemical properties of the different classes of cathode materials for LIBs. (From
M. Yoshio et al., Lithium-ion Batteries: Science and Technologies, Springer: New York, 2009)
Material
Structure
Average voltage
Theoretical
vs. Li/Li+ (V)
capacity (mAh g-1)
Safety
Cost
LiCoO2
Layered
3.9
280
Fair
High
LiMn2O4
Spinel
4.1
150
Good
Low
LiFePO4
Olivine
3.45
170
Good
Low
20
1.3.2.1 Layered Oxide Cathodes
The layered lithium transition metal (TM) oxides with a common formula of LiTMO 2 (TM=Co,
Ni, or Mn) have a rock salt type structure where the oxygen anions remain in the close pack order.
Figure 1.6 represents different phases of the LixTMO2, where the oxygen layers are denoted by the
characters: A, B, and C showing the repeating layers of the oxygen. The metal ions are regularly
oriented at the interstitial sites of the crystal structure. The TMO 2 slabs are formed by sharing
edges of the MO6 octahedron and the Li+s can occupy either the prismatic (P), octahedral (O), or
tetrahedral (T) sites in between the layers of TMO 2.64 The number of the TMO2 layers in a unit
cell is denoted by a number following the interstitial sites (P, O, or T). The TMO2 layer can be
stacked in five sequences: O1, O2, O3, P2, and P3, which can be classified into two groups:
O1/O3/P3 and O2/P2. Within the same group, the TMO2 layers can easily transform from one
structure to another by gliding, whereas, the transformation of the structures from one group to
another is associated with the breaking of the TM-O bonds and thus requires more energy than the
gliding. Thereby, during the battery cycling, the cathode materials usually transform within the
same group.65
The O3 structure consists of three layers of TMO2 with an ‘AB CA BC’ stacking, whereas, in
the O1 structure a single layer of TMO2 is repeated with an ‘ABAB’ stacking in the unit cell. 66
The H1-3 structures are the hybrid of the O1 and O3 structures in an alternating fashion, typically
observed in the partially delithiated states. The metastable P2 and O2 structures are also
synthesizable for LiTMO2. At elevated temperatures, an O3 structure can transform to an
irreversible spinel or rock salt structure. The transformation of the O3 structures to the spinel
structures is associated with the migration of the TM-ions from the TM layer to the Li-layer. In
the fully delithiated state, the TMO2 layer can transform to the rock salt (TMO) structure with the
release of oxygen. However, the layered oxides usually undergo a reversible phase transition at
room temperature due to the diffusion limits of the TM-ions.67
21
Figure 1.6: The crystal structures of different phases of Li xTMO2. Green and blue octahedra
represent the Li sites and the MO6 units, respectively. (From M. D. Radin et al., Adv. Energy
Mater., 2017, 7, 1602888)
22
The early studied layered oxide materials such as LiCoO2, LiNiO2, or LiMnO2 suffer from poor
capacity retention and safety issues because these materials suffer from phase transition and
structural deterioration with deintercalation of Li +s.68 Extensive research has been carried out over
the last two decades to develop a new class of mixed TM oxides with the general formula of
LiNixCoyMn1-x-yO2 (NCM).69-72 NCM material with Ni content 80% (LiNi0.8Co0.1Mn0.1O2) can
supply an energy density of 400 W-h kg−1.73 Therefore, a Ni-rich NCM material with Ni content
of >80% is widely being studied for the application in EVs, however, showed irreversible phase
transition and structural instability with Li deintercalation. Therefore, it is essential to understand
the associated phase transition and structural stability of these materials with Li deintercalation.
1.3.2.2 Evaluation of the NCM Cathodes
In order to improve the electrochemical performance of a Ni-rich NCM material with Ni content
~90%, it is essential to understand the electrochemical behavior of the end members of this class
as well as the commercialized NCM materials e.g., NCM-333, NCM-424, NCM-523, NCM-622,
or NCM-811.
1.3.2.2.1 LixCoO2 Cathode
LiCoO2 is the first commercialized layered oxide cathode material for LIB with intercalation
chemistry. LiCoO2 has an O3 structure which is often characterized as the H1 phase due to the
presence of hexagonal unit cells of LiCoO 2.74 LiCoO2 can provide a specific capacity of 270 mAh
g-1 with an average potential of 4.0 V vs. Li/Li+, however, its practical capacity is limited to 140
mAh g-1.75 This is because LiCoO2 shows a large change in volume and have an irreversible phase
transition in highly delithaited states.76 Ménétrier et al. showed that the a and c lattice parameters
of LiCoO2 decreases and increases respectively in the deintercalation range of 1.0 ≥ x ≥ 0.70 by
experiments. They proposed that the decrease in a is because of the oxidation of the Co-ions,
whereas the increase in c is due to the reduction of the interlayer cohesive force.77 Laubach et al.
reported that the c lattice parameter increases in the deintercalation range of 1.0 ≥ x ≥ 0.50 and
then steadily decreases with further delithiation.78 By using DFT, Koyama et al. reported a steady
decrease and increase in the a and c lattice parameters, respectively, in the deintercalation range
23
of 1.0 ≥ x ≥ 0.33, however, the a and c lattice parameters, respectively, increases and decreases at
0.33 > x.79
Reimers et al. revealed that at delithiation level of x = 0.50, the LiCoO2 undergo a phase
transition from the hexagonal to the monoclinic (H → M), which again experience another phase
transition from O3 → O1 at x → 0.80 From the DFT study, Van der Ven et al. showed that the
CoO2 structure prefers the be in the O1 phase instead of the O3 phase. In contrast to Reimers’s
finding, they proposed a phase transition of H1-3 rather than the H → M phase transformation.81
1.3.2.2.2 LixNiO2 Cathode
Ni is cheaper than the Co and thereby, the LiNiO2 has low production cost than the LiCoO2.
The LiNiO2 have the same crystal structure as that of the LiCoO2 and can provide a similar specific
capacity of 275 mAh g-1 with an average potential of 3.8 V vs. Li/Li+ to the LiCoO2.82 However,
the Ni-ions in the LiNiO2 can have oxidation states of 2+ and 3+ due to the presence of nonstoichiometric Li1-xNi1+xO2 phases. The Ni2+-ions prefer to migrate to the Li + sites due to their
similar ionic radius and thus reduces the specific capacity. 67 The LiNiO2 provide a much higher
practical capacity of 200 mAh g-1 at 4.15 V vs. Li/Li+ than the LiCoO2.83 This can be ascribed from
the fact that the redox reaction in LiNiO 2 involves the eg orbitals of Ni-ions instead of the t2g
orbitals as LiCoO2.67 Therefore, the LiNiO2 is expected to be a promising cathode for LIBs. The
surface particles of LiNiO2 tend to react with the electrolyte, rendering a critical safety problem,
which can be suppressed by replacing Ni with Mn. 84 The LiNiO2 also experiences large volume
changes with delithiation, rendering poor capacity retention.85 This problem can be overcome by
doping with Co or Al.67
Cho et al. revealed that the a lattice parameter of LiNiO2 steadily decreases in the deintercalation
range of 1.0 ≥ x ≥ 0.20, whereas the c lattice parameter primarily increases in the deintercalation
range of 1.0 ≥ x ≥ 0.50 and the decreases in the range of 0.50 ≥ x ≥ 0.20.86 They also observed that
the LiNiO2 endure a number phase transition from H1 → M → H3 → H3 (O1) with the cycle of
delithiation and lithiation. By using the DFT calculations, Koyama et al. also reported that the a
24
lattice parameter gradually decreases in the deintercalation range of 1.0 ≥ x ≥ 0.0, while the c lattice
parameter first increases in the deintercalation range of 1.0 ≥ x ≥ 0.33 and then decreases in the
range of 0.33 ≥ x ≥ 0.0.79 The LiNiO2 have a larger reduction in the c lattice parameter than the
LiCoO2. Radin et al. studied the phase transition and Jahn-Teller (J-T) effect in LiNiO2 by using
the DFT method and proposed that the long-range distortion of the LiNiO2 is governed by the J-T
active Ni-ions.87
1.3.2.2.3 LixMnO2 Cathode
Due to the high abundance of Mn in the earth’s crust, the LiMnO2 is cheaper than the LiNiO2
and also less toxic than the LiCoO2 or LiNiO2.88 Both the monoclinic and orthorhombic LiMnO 2
were considered as cathodes for LIBs.89 The monoclinic LiMnO2 (m-LiMnO2) structure has a
lower theoretical capacity than the orthorhombic LiMnO2 (o-LiMnO2) due to the presence of spinel
and orthorhombic phases.90 Although, o-LiMnO2 can provide a high specific capacity of 285 mAh
g-1 with an average potential of 3.3 V vs. Li/Li+, however, shows poor capacity retention due to
the layered to spinel phase transition, accompanying by the migration of the Mn-ions from the TM
layer to the Li layer.90 Hwang et al. showed the J-T distortion of the Mn-ions by experiments.89 By
using the DFT calculations, Koyama et al. revealed that the a lattice parameter of the m-LiMnO2
decreases in the deintercalation range of 1.0 ≥ x ≥ 0.0, whereas the c lattice parameter decreases in
the deintercalation range of 1.0 ≥ x ≥ 0.67 and then increases in the range of 0.67 ≥ x ≥ 0.33, which
again decreases at x < 0.33.79 The LiCoO2 or LiNiO2 has higher contraction in the c lattice
parameter than the m-LiMnO2.
On the other hand, for o-LiMnO2, Chakraborty et al. revealed that the a lattice parameter steadily
increases in the deintercalation range of 1.0 ≥ x ≥ 0.0, whereas the c lattice parameter primarily
increases in the deintercalation range of 1.0 ≥ x ≥ 0.5 and then decreases monotonically at x <
0.5.91 The LiMnO2 has a smaller change in volume than the LiNiO2. Although, LiMnO2 can lower
the cost significantly, however, cannot be used for real application of the LIBs, because Mn 3+-ions
react with the electrolyte, providing poor cyclability.92 This drawback can be improved by
25
substituting the Mn-ions with the Co or Ni in order to change the oxidation states of Mn-ions from
3+ to 4+.67, 93
1.3.2.3 LiNixCoyMn1−x−yO2 (NCM) Cathodes
In order to obtain the beneficial electrochemical performances of the LiCoO 2, LiNiO2, and
LiMnO2, the NCM materials of mixed transition metals (Co, Ni, and Mn) have been developed.
The electrochemical performances such as rate capability, capacity retention, and structural
stability of the NCM materials can be enhanced by optimizing the Ni, Co, and Mn composition.
In particular, Ni-rich NCM provides high discharge capacity; Co-rich NCM shows excellent rate
capability; while Mn-rich NCM offers superior thermal stability and lifetime. 70,
94-95
In the
following section we will discuss the phase stability and electrochemical properties of different
NCM materials.
1.3.2.3.1 LiNi0.3Co0.3Mn0.3O2 Cathode
The first member of the NCM family, LiNi0.3Co0.3Mn0.3O2 (NCM-333) was first introduced by
Ohzuku et al., providing a reversible capacity of 160 mAh g-1 at 4.3 V vs. Li/Li+.96 In NCM-333,
the Ni, Co, and Mn, respectively, have formal oxidation states of 2+, 3+, and 4+.97 The Ni2+/Ni3+
redox couple mainly governs the electrochemical reaction of the NCM-333 with insignificant
contribution from the Co3+/Co4+ redox couple. Besides, the Mn4+-ions remain electrochemically
inactive, while the oxygen ions oxidize at a high voltage of 4.5 V, leading to the release of
oxygen.97
Choi et al. displayed that the a lattice parameter of the NCM-333 decreases in the deintercalation
range of 1.0 ≥ x ≥ 0.3, whereas, the c lattice parameter increases in the range of 1.0 ≥ x ≥ 0.5 and
then decreases in the range of 0.5 ≥ x ≥ 0.0.98 Koerver et al. reported that the LiCoO 2 has a larger
change in volume than the NCM-333 at x ≈ 0.50, however, the volume of NCM-333 further
reduced with the delithiation level, leading to the cracking. 99 The reduction in the a lattice
parameter can be ascribed from the fact that with delithiation the TM oxidizes to smaller radii. On
the other hand, the enhancement of the c lattice parameter is due to the enhanced electrostatic
26
repulsion between the oxygen ions, while at highly delithiated states the c lattice parameter
decreases due to the oxidation of the oxygen ions along with the TM-ions.81 Experiments showed
that the NCM-333 can retain its initial O3 structure up to the delithiation level of x = 0.75 without
any release of oxygen. However, more delithiation will cause a phase transition from O3 → O1.98
Therefore, it was suggested to operate the NCM-333 material within the cut-off voltage of 4.3-4.4
V. The capacity provided by the NCM-333 is still inadequate to be implemented in EVs application,
thereby, requires to increase the capacity by increasing the Ni content in the NCM material.
1.3.2.3.2 LiNi0.4Co0.2Mn0.4O2 Cathode
In order to decrease the cost of production of the NCM materials, researchers have lowered the
Co content to 0.33 ≤ y ≤ 0.5 in the LiNixCoyMn1−x−yO2 and found that the LiNi0.4Co0.2Mn0.4O2
(NCM-424) has the best electrochemical performances within the above-mentioned range of Co.100
The NCM-424 provides higher discharge capacity (180 mAh g-1) than the NCM-333, where the
TM-ions have random orientation in the TM layer.101 Ngala et al. synthesized the NCM-424 at an
optimum temperature of 800-900°C and observed that the Ni- and Mn-ions mainly have 2+ and
4+ oxidation states, respectively.100 In NCM-424, the electrochemical redox reaction is governed
by the Ni- and Co-ions, and Mn-ions are electrochemically inactive because of their oxidation
states of 4+.97
1.3.2.3.3 LiNi0.5Co0.2Mn0.3O2 Cathode
The specific capacity of the NCM materials can be further increased by increasing the Ni content
in the LiNixCoyMn1−x−yO2, for example, the LiNi0.5Co0.2Mn0.3O2 (NCM-523). NCM materials
containing a Ni content of ≥50%, are usually called Ni-rich NCM cathodes.102 Since, the number
of Ni- and Mn-ions are different in the NCM-523 and beyond, therefore, in order to keep the charge
neutrality of the whole structure, some Ni2+-ions oxidize to Ni3+-ions.103 Having the high specific
capacity (175 mAh g-1) and superior rate capability, the NCM-523 is the most widely studied
material among the Ni-rich NCM materials.104 The surface particles of the NCM-523 showed a
phase transition from the layered to spinel or rock salt structure at a high voltage of 4.8 V, however,
27
no phase transition to O1 was observed because of the enhanced mixing between the Li- and Niions.105 Shu et al. investigated the evolution of different phases of the NCM-523 for two different
cut-off voltages (4.3 and 4.9 V) and observed that an H3 phase evolves at 4.7 V, reducing the
structural stability and poor capacity retention.102
1.3.2.3.4 LiNi0.6Co0.2Mn0.2O2 and LiNi0.8Co0.1Mn0.1O2 Cathodes
In principle, the specific capacity will be increased more by increasing the Ni content of
LiNixCoyMn1−x−yO2 to x = 0.6 – 0.8 for instance, LiNi0.6Co0.2Mn0.2O2 (NCM-622) and
LiNi0.8Co0.1Mn0.1O2 (NCM-811), however, show inferior thermal stability than the prior NCM
members.106 Among the Ni-rich NCM materials, the NCM-622 has the highest tap density with a
primary specific capacity of 172 mAh g-1 at 4.3 V. The NCM-622 can retain 94% of its initial
capacity even after 100 cycles.107
The NCM-811 can provide a high specific capacity of ~200 mAh g-1 at 4.5 V, however, suffers
from serious structural deterioration and large capacity fading due to the formation of a
microcrack.108 Noh et al. showed that the NCM-811 has larger changes in the lattice parameters
than the NCM-333.70 By using the DFT calculations, Min et al. displayed that the a lattice
parameter of the NCM-811 steadily decreases in the deintercalation range of 1.0 ≥ x ≥ 0.2 and then
slightly increases in the range of 0.2 ≥ x ≥ 0.0, whereas the c lattice parameter steadily increases
in the range of 1.0 ≥ x ≥ 0.25 and then decreases at 0.25 > x.109 By using the crystal orbital Hamilton
populations (COHP) analysis, Dixit et al. investigated the structural changes of the NCM materials
with different Ni content and showed that the degree of covalency between the TM-O bonds
increases with oxidation states of Ni-ions.110 Noh et al. showed that similar to the LiNiO2, the
NCM-811 experiences several phase transitions from H1 → M → H2 → H3.70 Yang et al. revealed
that the critical phase transition from H2 → H3 takes place at 4.2 V, which can be suppressed by
introducing a little amount of Li2MnO3.111 Kondrakov et al. showed that with delithiation in NCM811, the oxygen ions undergo oxidation, leading to the shrinkage of the O-Li-O layers.112
28
Therefore, the initial capacity of the NCM materials increases with the increasing amount of Ni,
however, the capacity retention drastically decreases also. This is because the Ni-rich NCM
materials experience the irreversible phase transition at high operating voltage. Several approaches
have been proposed such as the concentration gradient method, surface coating, and lattice doping
to improve the phase stability of these materials. Among them, lattice doping is considered to be
the most prominent to improve the structural stability of the Ni-rich NCM materials.
29
Figure 1.7: The compositional phase diagram of layered LiNi xCoyMn1-x-yO2. (From A.
Chakraborty et al. Chem. Mater., 2020, 32, 915−952)
30
1.3.2.4 Doping in NCM Cathodes
A low amount of cationic doping can effectively improve the structural stability and
electrochemical performances of an NCM material. Several dopants for example Mo, Zr, W, Al,
and Te have been suggested for the NCM materials. 113-117 Liu et al. have investigated the
performance of the Al, Cr, or Mg dopants in NCM-111 and showed that the Cr-doped NCM-111
had superior cyclability than the other materials. They suggested that the larger particle size of the
Cr-doped NCM-111 imposed better structural stability than the undoped, Mg-, or Al-doped NCM111.118 Wang et al. revealed that the lattice parameters and the volume of NCM-111 increased with
the increasing doping concentration of Mo.119 They showed that the doping with Mo can enhance
the stability of the NCM-111 by reducing the gliding of the O-TM-O layer and Mo can participate
in the electrochemical redox reaction during delithiation, delivering higher discharge capacity.
Furthermore, they also proposed that the capacity retention can be improved by optimum doping
of Mo.
Breuer et al. reported that doping NCM-523 with 1 mol % of Mo6+ can effectively improve its
structural and surface properties.113 They showed that the Mo-doped NCM-523 has higher specific
capacities and lower capacity fading. For the first time, they proposed that the Mo-ions inclined to
the surface and thus reduces the reactivity between the electrolyte and the surface particles of the
NCM-523. By using the DFT study, they revealed that the Mo-doping preferably occurred at Ni
sites and increases the number of Ni 2+ ions and decreases the number of Ni3+ ions in order to
compensate the extra charge originating from the Mo 6+, enhancing the discharge capacity.
Schipper et al. have investigated the effect of Zr-doping in NCM-622 material by using
experiments and DFT calculations.114 They found that the Zr-doping increased the lattice
parameters of the NCM-622 material, however, can maintain the cationic ordering after cycling.
They showed that after subsequent cycling, the Zr-doped NCM-622 was comparatively more
stable than the undoped one. By using the DFT calculations, they proposed a mechanism to surpass
the layered spinel phase transition by inhibiting the migration of Ni-ions from the TM layer to the
Li layer.
31
Susai et al. have also used experiments and theory to explore the effect of 1-3 mol % of Modoping on the electronic structures and electrochemical properties of NCM-811.120 They observed
that the lattice parameters of the NCM-811 increased with the doping concentration of Mo. Their
DFT calculations suggested that the Mo-doping preferably occurred at the Ni sites. From the
calculation of the magnetic moment, they showed that Ni-ions in the NCM-811 were in three
different oxidation states and the number of the Ni-ions with different oxidation sate also changes
with the different concentrations of Mo in NCM811. The number of Ni2+s was higher in the Modoped NCM-811 than the undoped one, providing a higher discharge capacity. An NCM material
with a Ni content of ~90% is highly desirable for application in EVs and ESS. Since Zr and Mo
are the most widely studied dopant for NCM materials, therefore, in this dissertation, we have
investigated the effect of Zr- or Mo-doping in order to stabilize a Ni-rich NCM cathode having a
Ni content of 89%.
1.4 Challenges in LIBs
Even though LIB has been successfully applied in EVs and ESS, the current LIB technology
confronts severe challenges in terms of production cost, energy density, and safety. Although, the
Li is broadly distributed in the crust of Earth, however, it is not considered an abundant element.
The relative abundance of Li to the total crust is about 20 ppm. Furthermore, the resources of Li
are mostly allocated in South America, therefore, the production cost of LIBs is largely governed
by the importation of Li. The cost of Li2CO3 from which different cathode materials of LIBs are
produced was sharply rose over the last few years.121 Currently, the LIBs can be designed in three
types, namely: the cylindrical cell, the prismatic cell, and the pouch cell. Among these, the
cylindrical cell is the best choice in terms of electrochemical performance and cost, whereas, the
pouch cell has outstanding safety features and can be designed in various shapes, which makes it
tolerable to explosion in extreme operating conditions. However, the production cost associated
with the pouch cell is much higher than those of the cylindrical and prismatic cells. Moreover, in
LIB, aluminum (Al) cannot be used as a current collector at the anode side because Li forms an
alloy with Al at low voltages and thereby only used at the cathode side of high voltages (3-5 V).
Therefore, comparatively expensive copper (Cu) which is stable at lower voltages (<3 V), is used
32
as a current collector at the anode side in LIBs.122
The capacity of the LIBs can be enhanced up to 5-8% each year by developing the electrode
materials. For instance, the Ni-rich NCM cathodes and Si-based anodes are considered to be the
potential electrode materials for the next-generation LIBs.21, 123 However, it requires more effort
to improve the structural stability of the electrode materials for enhanced cycle life and higher cutoff voltage. The safety of using the LIB is one of the critical issues for its application in EVs as
well as in portable electronic devices. The accidents involved with the Tesla EVs, Boeing 787
Dreamliner, and Samsung Note 7 imposed new concerns in designing the battery packs of LIBs.
Considering, the above facts, it is crucial to develop alternative battery technology to replace the
current LIB to store energy in the future.
33
Figure 1.8: Abundance of different elements in the Earth’s crust. (From R. S. Carmichael et al.,
Practical Handbook of Physical Properties of Rocks and Minerals; CRC Press: Boca Raton, FL,
1989)
34
1.5 Alternatives to LIBs
As shown in Figure 1.8, the relative abundances of sodium (Na) and potassium (K) are much
higher than that of lithium. Moreover, being in the same group of the periodic table, Na and K
show similar chemical properties as Li. In so doing, Sodium-ion batteries (SIBs) and potassiumion batteries (KIBs) have attracted tremendous interest over the last decade because of the high
availability of the Na and K resources, and their similar intercalation chemistries to LIB. The NIB
or KIB has an important advantage from a materials point of view is that both Na or K does not
form an alloy with Al at low voltage and thereby do not require the expensive Cu as the current
collector.
1.5.1 Sodium Ion Battery
Before the development of LIBs, the SIBs were also first studied in the 1980s but did not
commercialize because of the rapid growth of LIB technologies. 124 However, in recent years the
NIBs are being commercialized such as the ZEBRA battery which can be operated at a higher
temperature.125 The key components in NIBs as well as the working mechanism are essentially
similar to the LIBs except for the ion carrier. The critical differences between Na and Li are that
Na-ion is comparatively larger (1.02 Å ) and heavier (23 g mol -1) than the Li-ion (0.76 Å ; 6.9 g
mol-1), which will affect the electrochemical performances of NIB. 126 The electrode potential of
Na (-2.71 V vs. SHE) is also higher than that of the Li (-3.02 V vs. SHE), thereby will have a lower
energy density. However, the mass contribution of the Na or Li to the overall weight of the
electrode materials is very small and thus the energy density is expected to be mainly governed by
the host structures of NIBs or LIBs.121 Thereby, it is quite important to understand the insertion
and de-insertion process of Na in the host structures. The development of cathode materials for
NIBs is much more successful than compared to the anode materials due to the unavailability of
an anode material with promising performances for NIBs. For instance, the commercially available
graphite anode of LIB can be used as anode material for NIB because of the larger ionic radius of
Na.127 Si-based materials also cannot be considered for NIBs due to difficulty in insertion of Na. 128
Also, Na metal itself cannot be used as anode material because of the formation of a unsteady
35
passivation layer and the hazardous nature of Na. Therefore, it is quite demanding to develop anode
materials with high specific capacity and superior structural stability for NIBs.
1.5.2 Potassium Ion Battery
Compared to the Li and Na, K-ion is larger in size (1.38 Å ) and heavier in weight (39.10 g mol 1
). However, considering the mass contribution of K to the total mass of the electrode materials,
the energy density should not be reduced significantly for KIBs than the NIBs.129 The K-ion is a
weaker Lewis acid than the Li or Na and thereby forms a smaller number of solvated ions.
Therefore, the transport number and the conductivity of the solvated K-ions are much higher than
those of the Li- or Na-ions. With the use of suitable electrode materials, this similar diffusion
kinetics of K-ions can be achieved at the interface between electrode and electrolyte of KIBs as
well.130 KIBs have another advantage over NIBs is that the graphite anode can provide a discharge
capacity of ~279 mAh g-1 with a voltage of ~0.2 V (vs. K/K+).130 The voltage for KIBs is much
higher than that of the NIBs (0.05 V vs. Na/Na+), indicating that the chances of K-plating at
graphite is less than the Na-plating at graphite. Since K is extremely flammable and thus requires
much more caution. Although, KIBs showed comparable performances to the LIBs or NIBs,
however, require to develop promising anode materials for the application in next-generation
battery technology. In this dissertation, we have explored the possibility of a sheet of SiGe for the
application in NIBs and KIBs as well as in LIBs.
1.6 Outlines of the Dissertation
The focus of this dissertation is to computationally design and investigate electrode materials in
order to enhance their energy density and structural stability. The remaining chapters of this
dissertation are organized as follows; Chapter 2 described the theoretical methods. Chapter 3
presents the investigation of two-dimensional anode material for LIBs, NIBs, or KIBs. Chapter 4
reveals the effect of doping for stabilizing a Ni-rich cathode material for LIB. Chapter 5 provides
the summary of this dissertation.
36
CHAPTER 2
Theoretical Methods
2.1 Quantum Mechanics
The electronic properties of a system can be calculated by solving the time-independent
Schrödinger equation given by
̂ 𝜓(𝑟, 𝜎; 𝑅) = 𝐸𝜓(𝑟, 𝜎; 𝑅),
𝐻
(2.1)
where, r and σ are the spatial and spin coordinates of electrons, while R is the spatial coordinates
̂ is the Hamiltonian operator acting on the wave function 𝜓(𝑟, 𝜎; 𝑅) and E is the
of nucleus. 𝐻
eigenvalue which signifies the total energy of a material. The Hamiltonian of a system consisting
of n and M number of electrons and nucleus, respectively, can be expressed as follows
𝑍𝐼 𝑍𝐽
𝑍𝐼
1
𝑛
𝑛
𝑛
2
𝑀
𝑀
𝑀
̂ = − 1 ∑𝑛𝑖=1 ∇2𝑖 − 1 ∑𝑀
𝐻
𝐼=1 ∇𝐼 − ∑𝑖=1 ∑𝐼=1 |𝑟 −𝑅 | + ∑𝑖=1 ∑𝑗>𝑖 |𝑟 −𝑟 | + ∑𝐼=1 ∑𝐽>𝐼 |𝑅 −𝑅 | ,
2
2𝑚
𝑁
𝑖
𝐼
𝑖
𝑗
𝐼
𝐽
(2.2)
where, i or j represents the electrons, whereas, I or J is for the nucleus. N, mN, and Z, respectively,
are the number of interacting particles, the mass, and the atomic number of the nucleus. The
Hamiltonian can be simplified as
̂ = 𝑇̂𝑒 + 𝑇̂𝑁 + 𝑉̂𝑒𝑁 + 𝑉̂𝑒𝑒 + 𝑉̂𝑁𝑁 ,
𝐻
(2.3)
where, 𝑇̂𝑒 and 𝑇̂𝑁 are the kinetic energies of electrons and nucleus, respectively, while 𝑉̂𝑒𝑁 , 𝑉̂𝑒𝑒 ,
and 𝑉̂𝑁𝑁 are the potential energies arising from the nucleus-electron, electron-electron, and
nucleus-nucleus interactions, respectively. Solving the Schrödinger equation exactly for a manybody system is impracticable, thereby, requires several approximations of theory in order to get
the eigenvalues and eigenstates of the Hamiltonians.
37
2.1.1 Born-Oppenheimer Approximation
Since the mass of the nucleus is much higher than that of the electrons, therefore, the electrons
can react immediately to the movement of the nucleus. The locations of the nucleus, thereby, can
be considered to be frozen and become just only parameters for electrons. This decoupling nature
of electronic and nuclear dynamics is known as the Born-Oppenheimer approximation.131
According to this approximation, the kinetic energy term (𝑇̂𝑁 ) of nucleus becomes zero and the
nucleus-nucleus potential energy term (𝑉̂𝑁𝑁 ) can be considered to be constant. Furthermore, as the
electrons encounter an external potential from the nucleus, thereby, the nucleus-electron potential
energy term (𝑉̂𝑒𝑁 ) can be renamed as 𝑉̂𝑒𝑥𝑡 . Now the Hamiltonian of the electronic part can be
expressed as
̂≡𝐻
̂𝑒 = 𝑇̂𝑒 + 𝑉̂𝑒𝑥𝑡 + 𝑉̂𝑒𝑒 ,
𝐻
(2.4)
The total energy of a system then can be written in terms of the electronic energy and the nucleusnucleus repulsion energy as follows
𝑍𝑍
𝐼 𝐽
𝑀
𝐸 ≡ 𝐸𝑡𝑜𝑡 = 𝐸𝑒 + ∑𝑀
𝐼=1 ∑𝐽>𝐼 |𝑅 −𝑅 |,
𝐼
𝐽
(2.5)
The Born-Oppenheimer approximation can reduce the computation time significantly, however,
calculating the potential energy of the electron-electron interactions (𝑉̂𝑒𝑒 ) is still quite challenging.
This potential energy consists of two parts itself: one is the exchange energy between two electrons
of the same spin arising from the Pauli’s exclusion principle and the other one is the Coulomb
correlation energy of electrons with a different spin. In order to describe these electron-electron
interactions, two different approximations have been proposed. One is the Hartree-Fock (HF)
method, where the eigenvalue is calculated from the wave function of the system. Another one is
the density functional theory (DFT) method, where the charge density is the variable to calculate
the total energy of a system.
38
2.1.2 Hartree-Fock Method
Hartree first proposed a simple idea of the product of wave functions to solve the Schrödinger
equation.132 In this method, electrons can feel an average field of electrostatic potential, called
Hartree potential (𝑉̂𝐻 ). The wave function can be written as a product of single electron orbitals
(𝜑𝑖 (𝑥 )).
𝜓𝑒 (𝑥 ) ≡ 𝜓𝐻𝑃 (𝑥1 , 𝑥2 , … . . , 𝑥𝑛 ) = 𝜑1 (𝑥1 )𝜑2(𝑥2 ) … . . 𝜑𝑛 (𝑥𝑛 ),
(2.6)
The Hartree method fails to illustrate the antisymmetric characteristic of the wave functions,
considering the fact that the Pauli exclusion principle should be obeyed by the electrons. The wave
function, thereby, should change when the electrons interchange their locations in the same orbital.
Fock introduced a Slater determinant in order to meet this criterion.133-134
𝜑1 (𝑥1 )
1 𝜑1 (𝑥2 )
|
𝜓𝑒 (𝑥 ) ≡ 𝜓𝐻𝐹 (𝑥1 , 𝑥2 , … . . , 𝑥𝑛 ) =
√𝑛!
⋮
𝜑1(𝑥𝑛 )
𝜑2 (𝑥1 ) …
𝜑𝑛 (𝑥1 )
𝜑2 (𝑥2 ) …
𝜑𝑛 (𝑥2 )
|,
⋮
⋱
⋮
𝜑2 (𝑥𝑛 )
𝜑𝑛 (𝑥𝑛 )
(2.7)
The wave function of a system having two electrons can be simplified as
𝜓𝐻𝐹 (𝑥1 , 𝑥2 ) =
1
√2!
[𝜑1 (𝑥1 )𝜑2 (𝑥2 ) − 𝜑2 (𝑥1 )𝜑1(𝑥2 )] = −𝜓𝐻𝐹 (𝑥1 , 𝑥2 ),
(2.8)
The lowest total energy can be calculated by considering the variational principle where the
expectation value of a trial wave function 𝜓𝑡𝑟𝑖𝑎𝑙 should be equal or larger than the ground-state
energy (E0).
∗
̂ 𝜓𝑡𝑟𝑖𝑎𝑙 𝑑𝑥 ≥ 𝐸0 ,
𝐻
∫ 𝜓𝑡𝑟𝑖𝑎𝑙
(2.9)
Now, the electronic energy of the HF wave function can be expressed as follows
1
𝑍
1
𝐼
𝑛
𝑛
𝐸𝐻𝐹 ≡ ∑𝑛𝑖=1 ∫ 𝜓𝑖∗ (𝑥 ) [− 2 ∇2𝑖 − ∑𝑀
𝐼=1 |𝑟 −𝑅 |] 𝜑𝑖 (𝑥 )𝑑𝑥 + 2 ∑𝑖=1 ∑𝑗=1(𝐽𝑖𝑗 − 𝐾𝑖𝑗 ),
𝑖
𝐼
39
(2.10)
where, 𝐽𝑖𝑗 is the Coulomb repulsion energy between an electron and the average electrostatic field,
while 𝐾𝑖𝑗 is the exchange energy that can switch the positions. Consequently, the n-electrons
Schrödinger equation can be simplified to n single-electron orbitals with the HF equation.
Although, the Schrödinger equation can be simplified by the HF method, however, the total energy
of a system is greatly overestimated because the HF method does not include the exchangecorrelation arising from the interactions between the electrons. Therefore, an alternative method is
required to compute the electronic properties of a system.
2.2 Density Functional Theory
The density functional theory (DFT) was first proposed by Hohenberg and Kohn, and then
further developed by Kohn and Sham.135-136 In this dissertation we used the DFT to calculate the
chemical and physical properties of the materials.
2.2.1 Hohenberg-Kohn Theorems
Hohenberg and Kohn proposed that the external potential (𝑉̂𝑒𝑥𝑡 ) arising from the nucleuselectron interaction can be calculated from the electron density of a system. 135 This is known as
the Hohenberg-Kohn (HK) theorems. The electronic contribution to the total energy can be
expressed as follows
𝐸𝑒 [𝜌(𝑟)] = 𝑇𝑒 [𝜌(𝑟)] + ∫ 𝑣𝑒𝑥𝑡 (𝑟)𝜌(𝑟)𝑑𝑟 + 𝑉𝑒𝑒 [𝜌(𝑟)],
(2.11)
The kinetic energy of electrons (𝑇𝑒 [𝜌]) and the electron-electron potential energy (𝑉𝑒𝑒 [𝜌]) can be
stated as HK functional. Thus we have,
𝐸𝑒 [𝜌(𝑟)] = 𝐸𝐻𝐾 [𝜌(𝑟)] = 𝐹𝐻𝐾 [𝜌(𝑟)] + ∫ 𝑣𝑒𝑥𝑡 (𝑟)𝜌(𝑟)𝑑𝑟 + 𝑉𝑒𝑒 [𝜌(𝑟)],
(2.12)
The mathematical form of 𝐹𝐻𝐾 [𝜌] will be equal for all systems due to its universal performance.
The electron-electron potential energy (𝑉𝑒𝑒 [𝜌]) can be expressed as follows
𝑉𝑒𝑒 [𝜌(𝑟)] = 𝑉𝐻 [𝜌(𝑟)] + 𝑉𝑛𝑐𝑙 [𝜌(𝑟)],
40
(2.13)
where, 𝑉𝐻 [𝜌(𝑟)] and 𝑉𝑛𝑐𝑙 [𝜌(𝑟)] , respectively, are the classical and non-classical Coulomb
repulsion energies consisting of the exchange-correlation (XC) energy. According to the HK
theorems, the 𝐸𝐻𝐾 [𝜌] functional can reach the minimum value if and only if the electron density
becomes the true ground-state density. Now, the total energy can be expressed in terms of the trial
electron density (ρtrial)
𝐸𝐻𝐾 [𝜌𝑡𝑟𝑖𝑎𝑙 (𝑟)] ≥ 𝐸𝐻𝐾 [𝜌0 (𝑟)] = 𝐸0 ,
(2.14)
Thus, the ground-state properties of a system can be calculated by determining an electron density
that lowers the total energy. The total energy, however, cannot be accurately calculated because
the exact expression of the 𝐹𝐻𝐾 [𝜌] is still undefined in the HK theorems. Kohn and Sham proposed
a realistic method to estimate the universal performance of the 𝐹𝐻𝐾 [𝜌].
2.2.2 Kohn-Sham Approach
Kohn and Sham developed a fabricated non-interacting system to determine the 𝐹𝐻𝐾 [𝜌].136 The
kinetic energy of an electron can be divided into two parts in the Kohn-Sham (KS) approach.
𝑇𝑒 [𝜌(𝑟)] = 𝑇𝑒,𝑠 [𝜌(𝑟)] + 𝑇𝑒,𝑟 [𝜌(𝑟)],
1
𝑇𝑒,𝑠 [𝜌(𝑟)] = − 2 ∑𝑛𝑖=1⟨𝜑𝑖 (𝑟)|∇2 |𝜑𝑖 (𝑟)⟩,
(2.15)
(2.16)
where, 𝜑𝑖 (𝑟) and 𝑇𝑒,𝑠 [𝜌], respectively, are the wave functions and kinetic energies of the noninteracting electrons, while the 𝑇𝑒,𝑟 [𝜌] is the residue of the kinetic energy that is neglected in the
fictional non-interacting electrons. Now, the exchange-correlation (XC) energy can be obtained
by combining the 𝑇𝑒,𝑟 [𝜌] with the non-classical Coulomb interaction 𝑉𝑛𝑐𝑙 [𝜌].
𝐸𝑋𝐶 [𝜌(𝑟)] = 𝑇𝑒,𝑟 [𝜌(𝑟)] + 𝑉𝑛𝑐𝑙 [𝜌(𝑟)],
(2.17)
Thereby, the 𝐹𝐻𝐾 [𝜌] can be expressed as
𝐹𝐻𝐾 [𝜌(𝑟)] = 𝑇𝑒,𝑠 [𝜌(𝑟)] + 𝑉𝐻 [𝜌(𝑟)] + 𝐸𝑋𝐶 [𝜌(𝑟)],
41
(2.18)
The total energy can be written to KS equations which is the determining equation of the KS
orbitals.
𝐸𝑒 [𝜌(𝑟)] ≡ 𝐸𝐾𝑆 [𝜌(𝑟)] = 𝑇𝑒,𝑠 [𝜌(𝑟)] + 𝑉𝑒𝑥𝑡 [𝜌(𝑟)] + 𝑉𝐻 [𝜌(𝑟)] + 𝐸𝑋𝐶 [𝜌(𝑟)],
(2.19)
The effective KS potential can be now expressed in terms of the exchange-correlation potential.
𝜌(𝑟𝑗 )
𝐾𝑆 ( )
𝑉𝑒𝑓𝑓
𝑟 = 𝑉𝑒𝑥𝑡 (𝑟) + ∫ |𝑟 −𝑟 | 𝑑𝑟𝑗 + 𝑉𝑋𝐶 (𝑟),
𝑖
𝑉𝑋𝐶 (𝑟) =
𝑗
𝛿𝐸𝑋𝐶 [𝜌(𝑟)]
𝛿𝜌(𝑟)
,
(2.20)
(2.21)
The KS orbitals 𝜑𝑖 (𝑟) now can be written as
1
𝐾𝑆 ( )]
[− ∇2 + 𝑉𝑒𝑓𝑓
𝑟 𝜑𝑖 (𝑟) = 𝜖𝑖𝐾𝑆 𝜑𝑖 (𝑟),
2
(2.22)
where, 𝜖𝑖𝐾𝑆 is the energy of the KS orbital. The electron density can be formed from the KS orbitals
as follows
𝑁
𝑂𝐶𝐶
|𝜑𝑖 (𝑟)|2 ,
𝜌(𝑟) = ∑𝑖=1
(2.23)
𝐾𝑆 ( )
In order to solve the KS equation, the 𝑉𝑒𝑓𝑓
𝑟 is first calculated from an initial guess of electron
density 𝜌(𝑟). Then from equation 2.22, we can have the 𝜑𝑖 (𝑟) and new 𝜖𝑖𝐾𝑆 . The new 𝜑𝑖 (𝑟) is
then used to get new 𝜌(𝑟) from equation 2.23. These self-consistent steps are repeated until 𝜌(𝑟)
met the desired value. The unknown 𝐸𝑋𝐶 [𝜌(𝑟)] term is further approximated by developing
various exchange-correlation functional.
2.2.3 Exchange-Correlation Functional
Though the exchange-correlation (XC) functional has little contribution to the total energy of
the system, however, cannot be ignored in DFT calculations. Perdew et al.137 proposed several
approximations of the XC functional which can be expressed as follows
42
𝐸𝑋𝐶 [𝜌] = ∫ 𝜌(𝑟)𝜀𝑋𝐶 [𝜌, ∇𝜌, 𝜏]𝑑𝑟,
(2.24)
where, ρ(r), ∇𝜌(r), and 𝜏(r), respectively, are the electron density, the gradient of electron density,
and the density of kinetic energy.
2.2.3.1 Local Density Approximation
In local density approximation (LDA), the varying electron densities of a system are assumed
to be a collection of many pieces having uniform electron densities of different values. The electron
density is constant in such a single piece. The total energy contribution of XC functional within
the LDA is the summation of the energies of the corresponding local pieces, which can be
expressed as
𝐿𝐷𝐴 [ ]
𝐿𝐷𝐴 [ ]
𝐸𝑋𝐶
𝜌 = ∫ 𝜌(𝑟)𝜀𝑋𝐶
𝜌 𝑑𝑟,
(2.25)
𝐿𝐷𝐴 [ ]
𝜀𝑋𝐶
𝜌 = 𝜀𝑋𝐿𝐷𝐴 [𝜌] + 𝜀𝐶𝐿𝐷𝐴[𝜌],
(2.26)
𝐿𝐷𝐴 [ ]
𝐿𝐷𝐴 [ ]
where, 𝜀𝑋𝐶
𝜌 is the exchange-correlation energy per electron. 𝜀𝑋𝐿𝐷𝐴 [𝜌] and 𝜀𝑋𝐶
𝜌 are the
energy contribution from the exchange and correlation terms, respectively. The accurate exchange
energy can be calculated by the HF method, however, requires much computational time.
Therefore, the exchange energy is calculated by considering the homogeneous electron gas model.
⁄
3 3 1 3
𝜀𝑋𝐿𝐷𝐴[𝜌] = − ( )
4 𝜋
𝜌 (𝑟 )1⁄ 3 ,
(2.27)
The correlation energy can be estimated by using a quantum Monte Carlo simulation for a
homogeneous electron gas of different electron densities. Several analytic forms such as the
Perdew-Zunger (PZ),138 the Vosko-Wilk-Nusair (VWN),139
and the Perdew-Wang (PW)140
correlation functional were proposed in order to estimate the correlation energy. The LDA works
very accurately where the electron density changes very slowly, for example in simple metals or
materials involving covalent bonds. However, LDA fails to accurately predict the lattice parameter,
cohesive energy, and bulk modulus of solids. Moreover, the LDA has limitations in describing the
strongly correlated and weekly bonded systems.
43
2.2.3.2 Generalized-Gradient Approximation
In order to accurately describe a system of inhomogeneous electron density, the gradient of
electron density is considered in generalized-gradient approximation (GGA)137,
141
for the
approximation of the XC functional.
𝐺𝐺𝐴 [ ]
𝐺𝐺𝐴 [ ( )
𝐸𝑋𝐶
𝜌 = ∫ 𝜌(𝑟)𝜀𝑋𝐶
𝜌 𝑟 , ∇𝜌(𝑟)] 𝑑𝑟,
(2.28)
𝐸𝑋𝐺𝐺𝐴 [𝜌] = ∫ 𝜌(𝑟)𝜀𝑋𝑢𝑛𝑖𝑓 [𝜌]𝐹𝑋 (𝑠) 𝑑𝑟,
(2.29)
The exchange term is
|∇𝜌|
𝑠 = 2(3𝜋2𝜌)1/3 𝜌,
(2.30)
The exchange energy per electron in GGA is the same as the LDA method. FX(s) is an
enhancement factor for the exchange energy used to improve the drawback of the LDA method.
Different exchange functional can be obtained in GGA by changing the FX(s), for example, the
Perdew, Burke, and Ernzerhof’s (PBE)142 can be expressed as follows
𝐹𝑋 (𝑠) = 1 + 𝑘 −
𝑘
𝜇𝑠2
𝑘
1+
, 𝑘 ≈ 0.804, 𝜇 ≈ 0.2195,
(2.31)
The correlation energy of the GGA method can be obtained in terms of analytic forms, such as the
Perdew, Burke, and Ernzerhof’s (PBE)142 and the Perdew and Wang’s 1991 (PW91)143 correlation
functional.
𝐸𝐶𝐺𝐺𝐴 [𝜌(𝑟)] = ∫ 𝜌(𝑟){𝜀𝐶𝑢𝑛𝑖𝑓 [𝜌(𝑟)] + 𝐻 [𝜌(𝑟)], 𝜔} 𝑑𝑟,
(2.32)
The PBE functional is the most widely used exchange-correlation functional which can be further
improved by using the revPBE and RPBE functional.144 However, it is not possible to calculate all
the properties of a material with the same accuracy by a single functional. We used the GGA-PBE
functional to describe the exchange-correlation energy.
44
Figure 2.1: Illustration of a standard DFT calculation. (From J. G. Lee, Computational Materials
Science: an Introduction, CRC Press: Boca Raton, FL, 2017, 2nd edition)
45
2.2.3.3 Corrections of Exchange-Correlation Functional
In the LDA and GGA functionals, electrons encounter an average repulsive force because of the
mean-field approximation. Thereby, the DFT calculations based on LDA or GGA functional
provide inadequate estimations of EXC[ρ] in a strongly correlated system where electrons are more
localized such as transition metals with d or f electrons.145 Hubbard proposed a method to
overcome this problem by introducing a Hamiltonian operator consisting of a kinetic energy
operator, an on-site Coulomb potential, and a chemical potential (μ).146-147
†
†
̂𝐻𝑢𝑏 = −𝑡 ∑⟨𝑖,𝑗⟩,𝜎(𝑐̂𝑖,𝜎
𝐻
𝑐̂𝑗.𝜎 + 𝑐̂𝑗,𝜎
𝑐̂𝑖,𝜎 ) + 𝑈 ∑𝑁
̂𝑖↑ 𝑛̂𝑖↓ − 𝜇 ∑𝑖,𝜎 𝑛̂𝑖,𝜎 ,
𝑖=1 𝑛
(2.33)
where, t, N, and U, respectively, are the hopping integral, the number of electrons, and the strength
of correlation i.e. Hubbard U value. μ and σ denote the chemical potential and spin of an electron,
†
respectively. The first term 𝑐̂𝑖,𝜎
𝑐̂𝑗.𝜎 defines the creation of an electron at site i and its extinction at
site j, whereas, the second term switches the positions. The Coulomb repulsive force between the
electrons is defined by the doubly filled electrons located at the same site. 𝑛̂𝑖↑ and 𝑛̂𝑖↓ , respectively,
are the number of electrons with spin up or down at site i. The final term on the Hubbard
Hamiltonian governs the filling of electrons in the orbitals indicating the changes in energy with
the change of electron density in a system (μ = δE/δρ). Accordingly, the XC energy term of
equation 2.33 can be written in terms of the Hubbard U as follows
𝐿𝐷𝐴+𝑈 [
𝐿𝐷𝐴 [ ]
𝐿𝐷𝐴 ( )
𝐸𝑋𝐶
𝜌, 𝑛̂] = 𝐸𝑋𝐶
𝜌 + 𝐸𝐻𝑢𝑏 (𝑛̂) − 𝐸𝑑𝑐
𝑛̂ ,
(2.34)
The last energy term of equation 2.34 is to avoid the error of double counting of the correlation
energy which was partly considered in the LDA energy. The Hubbard U correction can be used in
DFT calculations by considering two different schemes. Liechtenstein et al. separately considered
the correlation (U) and exchange (J) parameters, whereas, Dudarev et al. developed an effective
U parameter (Ueff = U - J) for equation 2.34.148-149 We used the effective U parameter for the PBE
functional.
46
2.2.3.4 Dispersion Corrections
The long-range van der Waals (vdW) force extensively governs the electronic characteristics of
materials.150 The vdW interaction force originated from the instant dipole moment caused by the
charge distribution of the constituent elements in the material. The LDA or GGA based DFT
methods can not solely describe the vdW force especially for the layered materials. Several
methods have been suggested to taken into account such weak interaction into DFT. Grimme et al.
included the vdW interaction into the DFT method by adding an empirical potential, namely
dispersion-corrected DFT (DFT-D).151 They also developed the approach to DFT-D2 and DFTD3.152-153 The dispersion-corrected total energy of a system can be calculated as follows
𝐸𝑡𝑜𝑡 ≡ 𝐸𝐷𝐹𝑇+𝐷 = 𝐸𝐷𝐹𝑇 + 𝐸𝐷𝑖𝑠𝑝 ,
𝐸𝐷𝑖𝑠𝑝 = − ∑𝑀
𝐽>𝐼 ∑𝑛 𝑆𝑛
𝐶𝑛,𝐼𝐽
𝑛
𝑅𝐼𝐽
𝑓𝑛,𝑑𝑎𝑚𝑝 (𝑅𝐼𝐽 ),
(2.35)
(2.36)
where I and J are the interacting atoms and sn is a scaling factor with n (6,8,10….) as the order of
dispersion contributions, and fn, damp is a damping function of order n at the interatomic distance of
RIJ to remove the double-counting error of DFT method at short-ranges.150
2.3 Treating Solids
The DFT method has limitations in solving the KS equations for a crystal structure with a large
number of electrons and atoms. Periodic boundary conditions (PBC) and Bloch theorem are
applied in order to overcome such limitations of modeling and investigating the crystalline
structure on an atomic and electronic scale.
2.3.1 Bravais Lattice
A periodic system can be modeled by choosing a unit cell of possible smallest size that can
represent the system repeatedly. The crystal can be mapped into the original unit cell by operating
a translational vector (R) in the real space
𝑅 = 𝑢𝑎1 + 𝑣𝑎2 + 𝑤𝑎3 ,
47
(2.37)
where, u, v, and w are integers, whereas a1, a2, and a3 are lattice parameters in the unit cell. The
modeled lattice is called the Bravais lattice, while the unit cell is called the Wigner-Seitz cell. A
Fourier transformation is used to transfer the Baravais lattice from real space to the reciprocal
space or k-space to elucidate the electronic structure of a material. In the reciprocal space, vectors
(G) are expressed as a linear combination of the primitive vectors (b1, b2, and b3) as follows
𝑮 = ℎ𝑏1 + 𝑘𝑏2 + 𝑙𝑏3 ,
(2.38)
where, h, k, and l are the Miller indices of the crystal. The primitive unit cell in k-space is called
the Brillouin zone (BZ), which characterizes the Wigner-Seitz cell of the reciprocal lattice.
2.3.2 Boundary Conditions
In principle, a system of infinite periodicity can be designed by considering a unit cell and then
applying a boundary condition. The electronic properties of a crystal can be stimulated by
calculating the wave functions within the given boundary condition as
𝜑(𝒓) = 𝜑(𝒓 + 𝑹),
(2.39)
2.3.3 Bloch’s Theorem
The calculations of electronic structures in the DFT method can be simplified by using the Bloch
theorem. According to Bloch’s theorem, the wave function can be expressed as a product of a
plane wave and periodic function (un,k(r))
𝜑𝑛,𝑘 (𝑟) = 𝑢𝑛,𝑘 (𝑟)𝑒 𝑖𝑘.𝑟 ,
(2.40)
where n is the band index indicating the KS orbitals of a crystal. k is the wave vector in the BZ.
The periodic function now can be expressed by a linear combination of plane-wave basis sets in
the reciprocal space as follows
𝑁
𝑢𝑛,𝑘 (𝑟) = ∑𝐺 𝑐𝑒𝑙𝑙 𝑐𝑛,𝐺 𝑒 𝑖𝐺.𝑟 ,
48
(2.41)
where Ncell, G, and cn, G, respectively, are the number of atoms in the unit cell, the lattice vectors
in reciprocal space1, and the coefficients of plane waves.
2.4 Computational Approximations
Several approximations have been developed in order to ease the calculation of wave functions
and enhance the simulation speed with considerable accuracy. In the following section, we will
discuss these approaches based on the Vienna Ab initio Simulation package (VASP) code as we
used this code for all the DFT calculations.154-155
2.4.1 k-Points Sampling
The total energy and electron density of material are calculated by integrating the wave functions
across the BZ in the k-space.
𝑁
2
1
𝑜𝑐𝑐
𝜌(𝑟) = ∑𝑛=1
𝛺
𝐵𝑍
∫𝑘∈𝛺𝐵𝑍|𝜑𝑛,𝑘 (𝑟)| 𝑑𝑘,
(2.42)
where n, ΩBZ, and 𝜑𝑛,𝑘 (𝑟), respectively, are the bands of the KS orbitals, the volume of the BZ,
and the KS orbitals. Due to the computational difficulty in integrating across a continuous space
of k-point, numerical integration was introduced as follows
𝑁
2
𝑁
𝑘𝑝𝑡
𝑜𝑐𝑐
∑𝑘∈𝐵𝑍
𝜌(𝑟) = ∑𝑛=1
𝜔𝑘 |𝜑𝑛,𝑘 (𝑟)| ,
(2.43)
where, Nocc, Nkpt, and 𝜔𝑘 respectively, are the number of occupied orbitals, the number of k-points,
and the weighting factor. Among several methods, the Gamma centered and the Monkhorst-Pack
(MP) grids are the most popular methods. Furthermore, the number of k-points can be reduced by
considering the symmetry of the lattice structure.
2.4.2 Plane Waves
It is computationally very demanding to consider a large number of plane waves to completely
describe the wave function. Therefore, only those plane waves are considered which have kinetic
energy less than a specific cutoff value (Ecut).
49
1
2
= |𝑘 + 𝐺 |2 ≤ 𝐸𝑐𝑢𝑡 ,
(2.44)
However, the wave functions have strong oscillatory behavior near the nucleus, thereby, have
difficulties in computing the electronic structure. This problem can be solved by using the
pseudopotential approach.
2.4.3 Pseudopotential Approximation
The core electrons have stronger ionic potential than the valence electrons because of the strong
interaction between the core electrons and the nucleus, thereby, requires more grid points for
integrating the BZ and thus more computation time. Since the electronic properties of a material
are mostly governed by the valence electrons, hence, an effective potential called pseudopotential
is used to avoid the strong oscillation of the wave functions in the core region.
In 1994, Blöchl proposed the projector augmented-wave (PAW) method to describe the wave
functions of all electron (AE) by mapping the pseudo wave functions. 156 The PAW method
transforms the wave functions of AE into the computationally less demanding pseudo wave
functions. Therefore, a fewer number of grid points or fewer plane-wave basis sets are required to
calculate the electronic properties of a material. All the DFT computations of this dissertation were
performed by using the PAW method as implemented in the VASP code.
50
Figure 2.2: Schematic of pseudo- electron (dashed lines) and all electron (solid lines) potentials
and their wave functions. rc is the cutoff radius. (From Payne et al., Rev. Mod. Phys., 1992, 64,
1045-1097)
51
2.5 Calculation of Properties
2.5.1 Ewald Summation
The Ewald summation technique is widely used to find different arrangements of metal ion
vacancies and the substitution of atoms in a crystal structure by computing the electrostatic
interactions. We used the Pymatgen program to generate all the possible configurations of metal
ion vacancies and compute their electrostatic energies. The electrostatic (Coulomb) energy of a
crystal can be calculated as
𝑞𝑖 𝑞𝑗
1
𝑁
𝐸𝐶𝑜𝑢𝑙 = 2 ∑†𝑅∈𝑍 3 ∑𝑁
𝑖=1 ∑𝑗=1 |𝑟
𝑖𝑗 +𝑅|
,
(2.45)
where qi and qj are the atomic charges of ith and jth atoms. rij, R, and N, respectively, are the
interatomic distances, the translational vectors, and the number of particles. The error of doublecounting is canceled out by factor 1/2. However, the electrostatic energy calculated from equation
2.45 varies with the degree of the summation and hence, converges very slowly. Electrostatic
energy calculated from the Ewald summation method can converge rapidly by considering the
charge neutrality of the system.
𝐸𝐶𝑜𝑢𝑙 ≡ 𝐸𝐸𝑤𝑎𝑙𝑑 = 𝐸𝑅 + 𝐸𝐺 − 𝐸𝑠𝑒𝑙𝑓 ,
1
𝑁
𝐸𝑅 = 2 ∑†𝑅 ∑𝑁
𝑖=1 ∑𝑗=1 𝑞𝑖 𝑞𝑗
1
4𝜋
𝑒𝑟𝑓𝑐(𝛼|𝑟𝑖𝑗 +𝑅|
𝐺2
|𝑟𝑖𝑗 +𝑅|
(2.46)
,
𝑁
𝐸𝐺 = 2𝛺 ∑𝐺≠0 𝐺 2 exp (− 4𝛼2 ) ∑𝑁
𝑖=1 ∑𝑗=1 𝑞𝑖 𝑞𝑗 𝑒𝑥𝑝(−𝑖𝐺 ∙ 𝑟𝑖𝑗 ),
𝐸𝑠𝑒𝑙𝑓 =
𝛼
√𝜋
2
∑𝑁
𝑖=1 𝑞𝑖 ,
(2.47)
(2.48)
(2.49)
where, ER, EG, and Eself, respectively, are the energy in real space, the energy in reciprocal space,
and the self-interaction term. α, Ω, and erfc(z), respectively, are the Ewald constant, volume of the
system, and error function.
52
2.5.2 Nudged Elastic Band Method
The nudged elastic band (NEB) method is used for calculating the minimum energy path (MEP)
of a reaction by optimizing a given number of intermediate structures across the reaction
coordinates. An elastic band having N+1 number of structures can be represented by [R0, R1, R2,
….., RN], with R0 and RN regarded as the initial and final structure, respectively. Each intermediate
structure then optimizes to the possible lowest energy by conserving an identical spacing to the
neighboring structures. In order to do the controlled optimization, a spring force is used across the
elastic band and the component of the spring force is projected out perpendicular to the band. In
the NEB method, the spring force acts along the local tangent, whereas, the true force acts
perpendicular to the local tangent.157-158
𝐹𝑖 = 𝐹𝑖𝑠 │║ − ∇𝐸(𝑅𝑖 )│┴ ,
∇𝐸 (𝑅𝑖 )│┴ = ∇𝐸 (𝑅𝑖 ) − ∇𝐸 (𝑅𝑖 ) ∙ 𝜏̂𝑖 ,
𝐹𝑖𝑠 │║ = 𝑘(│𝑅𝑖+1 − 𝑅𝑖 │ − │𝑅𝑖 − 𝑅𝑖−1 │)𝜏̂,𝑖
(2.50)
(2.51)
(2.52)
where E, 𝜏̂,
𝑖 and k, respectively, are the energy of a system, the normalized local tangent at the
image i, and the spring constant. Predictably, none of the intermediate structure places at or even
near the saddle point and thereby requires interpolation of energy of the saddle point.
The climbing image NEB (CI-NEB) method has a little reformation to the NEB method in
which the intermediate structure with the highest energy is pushed to the saddle point.158-159 The
spring force does not act on this structure, instead, the true force at this structure is inverted along
the tangent. Thus, the structure attempts to maximize the energy along with the band, and minimize
in all other directions. The force on this structure is given by
𝐹𝑖𝑚𝑎𝑥 = −∇𝐸(𝑅𝑖𝑚𝑎𝑥 ) + 2∇𝐸(𝑅𝑖𝑚𝑎𝑥 )│║ ,
53
(2.53)
After the optimization, this structure will be exactly at the saddle point. This additional feature
does not require any additional significant computational effort. We used the CI-NEB for
calculating the diffusion barriers of the metals ions.
2.5.3 Crystal Orbital Hamiltonian Population
The First-principles calculation is usually conveyed in reciprocal space, causing a critical
problem in evaluating the chemical insight. In 1993, the crystal orbital Hamilton population
(COHP) was introduced in order to overcome this difficulty in DFT calculations. 160-161 In COHP
analysis, the energy of band-structure (Eband) is partitioned into the contributions of orbital-pair. It
can also be referred to as the bond weighted density of states (DOS) between two neighboring
atoms.
𝜀
𝐸𝑏𝑎𝑛𝑑 ≡ ∫ 𝐹 𝑑𝜀 ∑𝑗 𝑓𝑗 𝜀𝑗 𝛿(𝜀𝑗 − 𝜀),
(2.54)
∑𝑗 𝑓𝑗 𝜀𝑗 𝛿(𝜀𝑗 − 𝜀) = ∑𝑅 𝐿 ∑𝑅′ 𝐿′ 𝐻𝑅𝐿,𝑅′ 𝐿′ 𝑁𝑅𝐿,𝑅′ 𝐿′ (𝜀),
(2.55)
where, j, R, and L, respectively, are the band index, atomic sites, and angular momentum quantum
number. 𝜀 and fj are the eigenvalue and occupations number, respectively. Since the interaction of
two neighboring orbitals can be estimated by their Hamiltonian matrix, thereby, an energy integral
of COHP reveals the contribution of the particular bond to the band structure energy or chemically,
the bond strength. We used the LOBSTER code to study the bond strength of transition metaloxygen bonds.
54
CHAPTER 3
First-Principles Study on the Two-Dimensional Siligene as an Anode Material for Alkali
Metal Ion Batteries
Comput. Mater. Sci. 2019, 165, 121-128
Abstract
Anode materials with superior ionic conductivity and improved energy density are key
parameters in developing high performance next-generation batteries. Accordingly, twodimensional materials and their potential usages in energy storage systems have appealed to great
interest. From the First-principle study, we propose that the monolayer of SiGe can be a
prospective anode for Li-, Na-, or K-ion batteries (LIBs, NIBs, or KIBs). The energy of formation
and phonon distribution exhibit the thermodynamic and dynamic stability of a monolayer of SiGe.
The monolayer of SiGe delivers low diffusion barriers of 0.14 - 0.36 eV for the Li/Na/K atoms,
indicating a high rate of charging and discharging. The pristine monolayer of SiGe holds a Dirac
cone-shaped band distribution with a small band gap of 12 meV at the ‘K’ point. The noteworthy
charge relocation from the metal atoms to the SiGe sheet changes this semiconducting nature to
the metallic state. We found that the full lithiation of SiGe regenerates the band gap (0.97 eV) due
to the charge transfer from the SiGe sheet to the Li atoms, whereas Na and K do not show this
behavior. The high specific capacities and steady voltage profile offer the suitability of the
monolayer of SiGe as a future anode material.
55
3.1 Introduction
Given the high scarcity and high price of lithium, it is extremely preferred to design an alternate
secondary battery.162-163 In this regard, NIBs, and KIBs are being widely investigated due to their
higher resources and comparable chemistries of battery. 124, 130, 164 Developing anode materials of
improved electrochemical properties is quite challenging in enhancing the energy density of a nextgeneration battery.125, 165 To date, the established graphite anode for LIB is inapplicable to NIBs
and KIBs due to the sluggish insertion of Na or K into graphite giving a low rate of charging and
discharging.166-167 Silicon (Si) and germanium (Ge) based anode materials appear as promising
candidates for LIBs because of their high specific capacities 168-169 and low intercalation
potentials.170-171 However, the bulk structure of Si or Ge could not be commercialized yet due to
the extreme volume expansion during the insertion-deinsertion of Li, Na, or K, which leads to poor
cyclability and safety problems.171 Novel properties can be attained by merging the properties of
two components close in the periodic table, such as Si and Ge. 172-174 Owing to the high electrical
conductance and high diffusion rate of Li in Ge, alloying Ge with Si is considered to enhance the
electronic conductivity and diffusion rate of Li in Si. 170, 175-176 Moreover, when the Li inserts into
one component in a Si-Ge alloy material, the other can reduce the volume change as a buffer. 17
Experiments showed that having high capacity retention, the porous nanoparticles of SiGe alloy
can be used as a potential anode material for LIBs.170, 176-178
Recently, two-dimensional (2D) materials, having elevated surface areas, are being studied for
the application as anode materials, involving phosphorus (P), 179-180 boron (B),181-182 Si,183-184
Ge,185-186, and tin (Sn)-based anodes.187-188 Prior computations showed that the 2D Si (silicene)
does not undergo any permanent structural transformation during the insertion of lithium. 189 The
DFT study demonstrated that 2D Si or Ge (germanene) can provide a high theoretical capacity for
LIBs or NIBs.190-191 However, the 2D Si and Ge are volatile in ambient environments, causing
them inapplicable in the real battery system.192-193 Given the widespread interest in 2D layered
materials, a configuration of SiGe namely siligene, alike graphene, was lately explored by means
of DFT study and realized to be dynamically more steady compared to the 2D Ge. 60, 194 The bent
structure of the 2D SiGe has similar band dispersion as graphene. Considerably, the Si and Ge
56
atoms in the SiGe sheet have distinct tendencies of hydrogenation, which are crucial in tuning the
electronic structures of the 2D SiGe for application in nanoscale electronic devices.60
Currently, the applicability of the 2D SiGe as a potential anode material is unexplored. Herein,
by using the DFT simulation, we assessed the applicability of the 2D SiGe as anode materials for
LIBs, NIBs, and KIBs. Our calculations showed that the sheet of SiGe sheet was
thermodynamically stable. The sheet of SiGe possessed low migration barriers ranging from 0.14
to 0.35 eV and average open-circuit voltages (OCV) ranging from 1.08 to 1.38 V. Furthermore,
the 2D SiGe provided high theoretical capacities of 532 mAh g-1 for Li and K, and 1064 mAh g-1
for Na, much superior to other reported 2D materials. We also unraveled the physical
understandings for the adsorption natures of Na and K atoms on the 2D SiGe. For the first time,
we proposed that the 2D SiGe was a potential anode material giving rise to improved battery
performance.
3.2 Simulation Methods
We completed all the DFT computations by employing the Vienna ab initio simulation package
(VASP).154-155 We employed the PAW pseudopotentials to characterize the core electrons.156 We
employed the GGA including the PBE functional.142 We used plane-wave cutoff energy of 520 eV.
We incorporated the dispersion corrections by using the Grimme DFT+D2 method.152 We built a
4 × 4 slab of SiGe sheet, repeated in X- and Y- directions in order to evaluate the adsorption and
migration of metal ions. We introduced a vacuum space of 20 Å in the Z-direction in order to
eradicate the fabricated interactions among the SiGe sheet and the corresponding periodic images.
We used a 3 × 3 sheet of SiGe to calculate the theoretical capacities and voltage profiles. The
geometries were relaxed until the maximum force was < 0.01 eV Å-1.
We used the Phonopy code to inspect the dynamic strength of the 2D SiGe by computing the
phonon distribution spectra.195 We used k-point meshes of 3 × 3 × 1 and 3 × 3 × 2 of MonkhorstPack196, respectively, to sample the Brillouin zone of the 2D and bulk SiGe. We considered 9 × 9
× 1 k-point mesh for studying the band structures and density of states (DOSs). We calculated the
Bader charges197-199 to ascertain the degree of charge transfer between 2D SiGe and alkali metals.
57
The CI-NEB technique with the usual PBE method was used to compute the migration barriers of
metal atoms.158-159
3.3 Results and Discussion
3.3.1 Structural Properties
The calculated a and c lattice parameters of the bulk SiGe were 3.88 Å and 6.40 Å , whereas, the
2D SiGe had a lattice constant of a = 3.91 Å . This agrees with the prior theoretical reports based
on the DFT-LDA and DFT-GGA (PW91) functionals.60, 194 As shown in Figures 3.1a and 3.1b,
the 2D SiGe has a hexagonal buckled geometry wherein the Ge and Si atoms are interchangeably
positioned in two sublattices. The 2D SiGe had a buckling amplitude (Δ) of 0.58 Å , less than that
of the bulk SiGe (0.81 Å ). In the 2D SiGe, the bond length of Si and Ge was 2.34 Å , which was
longer than the bond length of Si-Si of 2.28 Å in silicence and smaller than the bond length of GeGe of 2.40 Å in germanene.60 The buckling amplitude and lattice parameter of the sheet of SiGe
(Δ = 0.58 Å and a = 3.91 Å ) lied between the related values of silicene (Δ = 0.42 Å and a = 3.86
Å ) and germanene (Δ= 0.67 Å and a=4.03 Å ).60, 194
We estimated the thermodynamic strength of the 2D SiGe by computing the energy of formation,
𝐸𝑓 , defined as
𝐸𝑓 = 𝐸SiGe − 𝐸Si − 𝐸Ge ,
where 𝐸SiGe was the energy of the sheet of SiGe and 𝐸Si and EGe , respectively, were the energies
of Si and Ge atoms in bulk. The 𝐸𝑓 was calculated to be −1.51 eV per unit cell, validating the
thermal solidity of the sheet of SiGe. We did not consider the effect of entropy which is
insignificant at room temperature. We studied the dynamic strength of the 2D SiGe by computing
the phonon dispersion spectra based on the DFPT.200 The phonon spectra did not show any
negative frequency (Figure 3.1c), demonstrating the dynamic solidity of the 2D SiGe.
58
Figure 3.1: Optimized structure of the 2D SiGe, (a) top and (b) side views. The circle represents
the unit cell and the H, TGe, TSi, and B labels denote the possible binding sites. (c) The phonon
dispersion spectra of the SiGe sheet.
59
3.3.2 Adsorption of Li/Na/K Atoms
An undesirable metal cluster formation will be avoided if alkali metal atoms strongly adsorb on
an anode material.201 Thereby, we investigated the interactions of the alkali metal atoms with the
sheet of SiGe. We first evaluated the best favorable adsorption sites of metal atoms on the SiGe
sheet. As shown in Figure 3.1a, we found four adsorption sites: on top of the hexagonal ring (H
site), on top of the Si atom (TSi site), on top of the Ge atom (TGe site), and top of the center of the
Si-Ge bond (B site). The adsorption energy of metal M, 𝐸𝑎𝑑𝑠 , was calculated as
𝐸𝑎𝑑𝑠 = (𝐸MSiGe − 𝐸SiGe − 𝑁 × 𝐸M )/𝑁,
where 𝐸SiGe and 𝐸MSiGe were the energies of the pristine sheet of SiGe and of the sheet of SiGe
bound with N number of metal atoms, respectively, and 𝐸M was the energy of a metal atom
(Li/Na/K) in bulk. The more negative is 𝐸𝑎𝑑𝑠 , the robust is the binding. As shown in Figure 3.2,
during adsorption, the metal atoms move from the B site to the nearby TSi site, revealing that metal
atoms cannot be bound at the B site. Table 3.1 lists 𝐸𝑎𝑑𝑠 s for numerous binding sites. The binding
of metal atoms at the H site was the strongest due to its highest number of coordination.185, 202 The
calculated 𝐸𝑎𝑑𝑠 s at H site were -0.85, -0.84, and -1.24 eV, respectively, for Li, Na, and K atoms.
The nature of the binding of metal atoms to the 2D SiGe was investigated by determining the
differences in charge density, ∆𝜌, as
∆𝜌 = 𝜌MSiGe − 𝜌SiGe − 𝜌M ,
where 𝜌SiGe , 𝜌MSiGe, and 𝜌M , respectively, were the charge densities of the pristine and metaladsorbed sheets of SiGe, and an isolated alkali metal atom. Figure 3.3 illustrates ∆𝜌s for the
adsorption of Li, Na, or K atoms at the H site, signifying a considerable charge transfer from alkali
metal atoms to SiGe. The studies of Bader charges gave charge transfers of 0.87e, 0.85e, or 0.94e,
respectively, from Li, Na, or K metal atoms to 2D SiGe. The alkali metals, therefore, were
essentially chemically bound on the SiGe sheet and were in cationic states. The degree of charge
transfers from metal to SiGe (Na<Li<K) indicates that the adsorption of K was strongest among
the metal atoms considered.
60
Figure 3.2: Structure of the 2D SiGe with alkali metal atom initially positioned at site B (a). With
optimization, the metal atoms diffuse from site B to TSi (b).
61
Table 3.1: Adsorption energies (Eadss) of the metal atoms at different adsorption sites of the 2D
SiGe. The charge transfers from metals to 2D SiGe (∆ρs) are also listed at H sites evaluated by the
Bader charge.
Metal
Li
Na
K
Adsorption energy (eV)
H
TSi
TGe
-0.85
-0.84
-1.24
-0.55
-0.65
-1.12
-0.25
-0.40
-0.91
62
∆𝝆𝑯 (І𝒆І)
0.87
0.85
0.94
Figure 3.3: The charge density differences between the SiGe sheet and adsorbed (a) Li, (b) Na,
and (c) K atom plotted with isosurface value of 0.001‫׀‬e‫ ׀‬bohr-3. The cyan and yellow colors,
respectively, characterize electron depletion and accumulation.
63
An anode must have high electronic conductivity favoring the rapid electrochemical reactions
during the charging and discharging steps. Therefore, we studied band structure and electronic
density of states (DOSs) of the pristine and metal-adsorbed 2D SiGe. As shown in Figure 3.4a, the
pristine sheet of SiGe had a band dispersion of Dirac cone-shape at the point ‘K’. The calculated
band gap was 12 meV. Other Dirac-fermion materials for instances graphene,203-204 silicence,205206
, and germanene.206-207 also have analogous Dirac-cones at point K. The partial density of states
(PDOSs) shown in Figure 3.5, illustrate that the DOS near the Fermi level was uniformly promoted
by the Ge and Si atoms, specifying that the observed Dirac cone was a combination of Ge and Si
states.194 The significant charge transfer from the metals to the 2D SiGe essentially lifted the Fermi
level in the conduction band. Thereby, the binding of a single alkali metal atom improved the
electronic conductivity of 2D SiGe (Figure 3.5).
64
Figure 3.4: Band structures of the (a) pristine monolayer of SiGe, (b) Li0.11SiGe, (c) Na0.11SiGe,
and (d) K0.11SiGe.
65
Figure 3.5: Total and PDOSs of the (a) pristine SiGe, (b) Li 0.11SiGe, (c) Na0.11SiGe, and (d)
K0.11SiGe.
66
We explored the electronic responses of the 2D SiGe by raising the loading of metal atoms. At
a low concentration of Li, electron transfer took place from the Li atoms to the 2D SiGe, governing
the metallic nature of Li1.0SiGe (Figure 3.6a). However, in the fully lithiated Li2.0SiGe, electron
transfer took place from the 2D SiGe to the Li layer (Figure 3.7a). Adsorption of a Li layer on 2D
SiGe can be comprehended in two steps. Firstly, electrons shifted from the Li atoms into the
valence band of 2D SiGe. The 2D SiGe then optimizes the bonds between Si and Ge and mitigates
the strain inside the rings of SiGe. Consequently, electron transfer took place from the 2D SiGe to
the Li atoms, widening the band gap from 0.012 eV to 0.98 eV. This in turn should hinder the
practical application of 2D SiGe in Li-ion batteries. Previous computational studies reported that
the inferior electronic conductivities of phosphorene208 and SnS2209 can be improved by using
sheets of graphene. Presumably, the present poor electrical conductivity of the 2D SiGe with Liloading can be improved by using a SiGe-graphene heterostructure. As shown in Figures 3.6b and
3.6c, the band gaps vanished for the fully sodiated and potassiated 2D SiGe, indicating the metallic
nature of these structures.
67
Figure 3.6: Charge distribution and total density of states for Li1.0SiGe (a), Na2.0SiGe, and
K2.0SiGe demonstrating their metallic characters.
68
Figure 3.7: (a) The charge density differences of the fully lithiated 2D SiGe before (left) and after
(right) the relaxation of the Si and Ge atoms. (b) PDOS of Li2.0SiGe, demonstrating the band gap
broadening.
69
3.3.3 Diffusion of Li/Na/K Atoms
The alkali metal ions should be very movable on the SiGe. We explored the migrations of Li,
Na, and K ions between the adjacent centers of the hexagonal ring (site H) of the SiGe. Different
migration routes of the metal ions were studied for three distinct pathways (Figure 3.8a): one
straight across the Si-Ge bond (Path-1), another above the Si (Path-2), and another above the Ge
(Path-3). During optimization, the metal ions differed from Path-1, instead followed Path-2. This
is because, throughout the surface loading procedure, metal ions migrated from the bridging site
to the above of the Si, as attained in the adsorption procedure (Figure 3.2). Metal ions, thereby,
obeyed the zigzag routes (Path-2 and Path-3).
Figures 3.8b and 3.8c, respectively, show the energy profiles of the metal ions along Path-2 and
Path-3. Along Path-2, the metal ions had two diffusion barriers with equal heights and a metastable
phase (TSi). The calculated migration barriers of the diffused Li-, Na-, or K-ions, respectively,
were 0.35, 0.21, or 0.14 eV. Alternatively, the diffusion barriers in Path-3 were 0.60, 0.43, or 0.34
eV, respectively, for Li-, Na-, or K-ions, which were higher than the calculated ones in Path-2.
Along Path-3, the migration of Li involved two diffusion barriers, whereas the migrations of Na
and K ions had no metastable phase, probably due to the greater ionic radii of Na or K. The
diffusion constant 𝐷 can be estimated by employing the Arrhenius equation, 179, 210
𝐷 ≈ 𝑒𝑥𝑝 (−
𝐸𝑎
𝑘𝐵 𝑇
),
where 𝐸𝑎 was the activation energy and 𝑘𝐵 was the Boltzmann constant. At room temperature, Li-,
Na-, or K-ions in Path-2, respectively, diffuse 1.69 × 104, 5.25 × 103, or 2.41 × 103 times quicker
than in Path-3. The calculated migration barrier was reduced with the increased atomic number of
the metal ions in both pathways. This arose from the fact that Na and K ions with bigger ionic radii
were located at longer distances than the Li ion from the 2D SiGe and thereby faced less attractive
forces from the surface of SiGe. The current diffusion barriers of migration are much inferior to
those found for Si2BN,183 MoN2,211 Si,212 and TiO2-based polymorphs213-214 but are similar to other
anode materials such as TiS3,215 hexagonal boron phosphide,181 TiC3,216 and popgraphene.217
70
Figure 3.8: (a) Diffusion pathways of the metal atoms on the 2D SiGe. Minimum energy profiles
of the migrating alkali metal atoms in Path-2 (b) and Path-3 (c).
71
3.3.4 Voltage Profile and Specific Capacity
The loading behavior of the 2D SiGe was calculated by investigating the concentrationdependent loading performance of the alkali metal atoms. We loaded both sides of the sheet of
SiGe with layers of metal atoms. The average adsorption energy of the metal atom in 𝑛th layer
𝐸𝑎𝑣𝑒 was calculated by
𝐸𝑎𝑣𝑒 =
𝐸(M18𝑛 SiGe) − 𝐸(M18(𝑛−1) SiGe) − 18𝐸𝑀
18
,
where 𝐸 (M18𝑛 SiGe) and 𝐸(M18(𝑛−1)SiGe), respectively, were the energies of the sheets of
SiGe loaded with 𝑛 and 𝑛– 1 of layers of the metal atoms. The 𝐸𝑀 was the energy of a metal
atom in bulk. 𝐸𝑎𝑣𝑒 designates whether the metal atoms in the nth layer rather adsorbs on the sheet
of SiGe (𝐸𝑎𝑣𝑒 < 0) or forms clusters (𝐸𝑎𝑣𝑒 >0).166, 218-219 The metal atoms were placed on the H
site for the first layer of adsorption. The metal atoms in the next layer were placed on TSi sites and
then TGe sites. The calculated 𝐸𝑎𝑣𝑒 in first layer of Li was −0.91 eV. However, the loading of the
Li second layer leads to an irreversible distortion of the sheet of SiGe (Figure 3.9). Thereby, the
2D SiGe can hold only one Li layer. For the Na adsorption, the 𝐸𝑎𝑣𝑒 s of the first, second, or third
layers, respectively, were -0.85, -0.039, or 0.06 eV, signifying the formation of Na metal cluster
in the third layer. The 𝐸𝑎𝑣𝑒 for the second layer of Na atoms is moderately weak, however, yet
similar or more robust than observed for Na on Ca2N (-0.003 eV),220 MoN2 (-0.02 eV),211 and GeS
(-0.02 eV).185 The 𝐸𝑎𝑣𝑒 s of K first or second layers, respectively, were -0.77 or 0.0075 eV,
signifying that the K atoms will form cluster in second layer. Figure 3.10 shows the maximum
layer by layer adsorption patterns for Li, Na, and K atoms.
72
Figure 3.9: Primary (left) and optimized (right) structures of the 2D SiGe (3 × 3) adsorbed with
36 Li atoms. Li atoms in different adsorption layers of the SiGe sheet are shown in different colors.
73
Figure 3.10: Optimized geometries of the 2D SiGe adsorbed with the maximum capabilities of 18
Li (a), 36 Na (b), and 18 K (c) atoms (3 × 3 supercell). Na atoms in the different layers are shown
in different colors.
74
To elucidate the origin of the multilayer Na and K adsorption performances, we assessed the
electron localization functions (ELFs) along the (110) planes of the sheet of SiGe loaded with
three and two layers of Na and K, respectively (Figure 3.11). The ELF plot for Na’s third layer
shows a noteworthy concentration of electrons that existed in the Na atoms, demonstrating robust
binding between them. As shown in Figure 3.11b, the PDOS of Na first layer had minor
involvement near the Fermi level, signifying very weak repulsive interactions between Na atoms
and the 2D SiGe. However, the Na atoms in the second or third layers essentially participated in
the PDOS at the Fermi level. The resulting strong repulsive interaction between Na atoms and the
2D SiGe reduced the bonding strengths of Na in the corresponding second or third layers. Likewise,
the K second layer is inclined to develop K-metal clusters. In the case of the second layer of K,
the electrons are further localized in between the K-atoms. In the PDOS of KxSiGe (Figure 3.11d),
there were small contributions from the first layer of K atoms near the Fermi level, leading to a
repulsive interaction between K atoms and the 2D SiGe. This repulsive force reduced the bonding
strength of the K first layer than the Li or Na atoms in their corresponding first layer. Besides, the
Na or K atoms in their outmost layer were extremely far from the sheet of SiGe (7.35 and 6.46 Å
in distances, respectively) to be adsorbed to SiGe.
75
Figure 3.11: Electron localization function plots in the (110) cross-sections for the (a) Na and (c)
K multilayers on both sides of the sheet of SiGe. The related PDOSs of the sheet of SiGe adsorbed
with Na (b) and K (d).
76
The electrochemical potential is fundamentally one of the critical properties of an anode material
because it governs the energy density of anode material. We evaluated the potential and specific
capacity for the given half-cell (vs. M/M+) electrochemical reaction:
SiGe + 𝑥 M + + 𝑥 𝑒 − ↔ M𝑥 SiGe
We investigated the relative stabilities of the intermediate phases (𝑀𝑥 𝑆𝑖𝐺𝑒) with respect to two
end configurations: the pristine sheet of SiGe and the 2D SiGe adsorbed with the maximum loading
of Li-, Na-, and K-ions (Li2SiGe, Na4SiGe, or K2SiGe, respectively). We determined the voltage
profile by calculating a convex hull of formation energy. We generated various configurations with
distinct symmetry at different concentrations of the metal atoms by the Pymatgen package.221 The
formation energy 𝛥𝐸𝑓𝑜𝑟𝑚 was calculated as183
𝛥𝐸𝑓𝑜𝑟𝑚 = 𝐸M𝑥 SiGe − [
𝑥𝐸M𝑦 SiGe +(𝑦−𝑥)𝐸SiGe
𝑦
],
where 𝑦 and 𝑥, respectively, were the maximum and intermediate concentrations of metal atoms.
𝐸SiGe , 𝐸M𝑦 SiGe, and 𝐸M𝑥 SiGe, respectively, were the energies of the pristine sheet of SiGe, and a
sheet of SiGe loaded with y and x metal atoms. Figure 3.12a displays relative formation energy
where the intermediate states were lying. The stable phases of M𝑥 SiGe had 𝑥s of 0.00, 0.33, 1.00,
and 2.00 for Li. On the contrary, 𝑥 values for Na were 0.00, 0.33, 2.00, and 4.00 and for K 0.00,
0.33, 0.66, 1.00, 1.33, and 2.00. These structures were then employed to calculate the anode
potential 𝑉222-223 given as
𝑉= −
𝐸(M𝑥2 SiGe)− 𝐸(M𝑥1 SiGe)− (𝑥2 −𝑥1 )𝐸𝑏𝑢𝑙𝑘
(𝑥2 −𝑥1)𝑒
,
where 𝐸(M𝑥2 SiGe) and 𝐸(M𝑥1 SiGe), respectively, were the energies of the 2D SiGe loaded with
𝑥2 and 𝑥1 atoms and 𝐸𝑀𝑏𝑢𝑙𝑘 was the energy of a metal atom in bulk. To calculate the voltage, the
Gibbs free energy G ( = 𝛥𝐸 + 𝑃𝛥𝑉 − 𝑇𝛥𝑆 ) should be included, but the volume (𝑃𝛥𝑉 ≈
10−5 𝑒𝑉) and entropic contributions (𝑇𝛥𝑆 ≈ 25 𝑚𝑒𝑉) are insignificant at room temperature.222
The calculated potentials of Li xSiGe were 0.92 – 1.38 V and the average OCV was 1.15 V. The
77
NaxSiGe or KxSiGe had potentials in the range of 0.49 – 1.34 V (OCV, 0.91V) or 0.47 – 1.08 V
(OCV, 0.78 V). The computed voltages fall in the range of common anodes such as graphite (0.10
V)224 and TiO2 (1.50 V).225
The 2D SiGe had a maximum of 2 Li, 4 Na, or 2 K atoms (Figure 3.12) with the stoichiometries
of Li2SiGe, Na4SiGe, and K2SiGe, respectively. The specific capacity 𝐶 was calculated by
𝐶=
𝑥𝑚𝑎𝑥 𝐹
𝑀𝑊𝑆𝑖𝐺𝑒
,
where 𝑥𝑚𝑎𝑥 was the maximum concentration of alkali metal ions in 𝑀𝑥 𝑆𝑖𝐺𝑒, 𝐹 was the Faraday
constant, and 𝑀𝑊𝑆𝑖𝐺𝑒 was the molar weight of SiGe. The calculated specific capacities for Li-,
Na-, and K-ions, respectively, were 532.13, 1064.247, and 532.13 mAh g-1. These specific
capacities for LIBs, NIBs, and KIBs were considerably higher than other 2D anodes, for example
MXenes (Li<450, Na<350, and K<150 mAh g-1),226 group-IV monochalcogenides (Li<450,
Na<710, and K<530 mAh g-1),186 MoN2 (Li=432, Na=864, and K=432 mAh g-1),211 Ti3C2 (Li=448,
Na=352, and 192 mAh g-1),227 ScO2 (Li/Na/K=348 mAh g-1),228 TiS3 (Li/N =282 mAh g-1),215 and
VS2 (Li=466 and Na=233 mAh g-1).53,
229
From the calculated average OCVs and specific
capacities, we estimated the energy densities of the SiGe anode by considering the LiCoO2,
NaCoO2, and K0.6CoO2, respectively, as the reference cathodes for LIBs, NIBs, and KIBs. The
relative potentials of LiCoO2 (vs. Li/Li+), NaCoO2 (vs. Na/Na+), and K0.6CoO2 (vs. K/K+) were
considered to be 3.9, 3.0, and 2.70 V, respectively. 230-232 Consequently, the relative potentials of
the 2D SiGe were 2.75 V (vs. LiCoO2), 2.09 V (vs. NaCoO2), and 1.92 V (vs. K0.6CoO2). The
calculated energy densities of the SiGe anode for LIBs, NIBs, and KIBs, respectively, were 1463,
2223, and 1021 Wh Kg-1.
78
Figure 3.12: (a) Convex hulls of the formation energies at different metal concentrations and (b)
the corresponding voltage profiles (vs M/M+) of LixSiGe, NaxSiGe, and KxSiGe.
79
3.4 Conclusion
We thoroughly investigated the structural and electrochemical performances of the 2D SiGe for
the application in LIBs, NIBs, or KIBs by employing the DFT calculations. The 2D SiGe was
thermodynamically stable. The alkali metal atoms are preferably adsorbed on the center of the
hexagonal ring of SiGe lacking the growth of the metal cluster. The strong adsorption of the alkali
metal atoms signifies a rapid charge-discharge rate of the present 2D SiGe. The adsorption of the
alkali metals improved the electronic conductivity of the 2D SiGe. The band gap of the fully
lithiated sheet of SiGe regenerated due to the rearrangement of the charge distribution, but with
full sodiation and potassiation, the 2D SiGe showed metallic behavior. The diffusion of the metal
atoms followed the zigzag pathways with low migration barriers. With the prominent storage
performance, the proposed 2D SiGe showed promising properties for application in alkali metalion batteries.
80
CHAPTER 4
First-Principles Study on Stabilizing the Ni-Rich LiNi0.89Co0.055Mn0.055O2 Cathode Material
by Doping with Zirconium or Molybdenum
J. Phys. Chem. C 2021, 125 (50), 27543-27555
Abstract
The Ni-rich layered oxides have shown promising performances as potential cathode materials
in lithium-ion batteries (LIBs). The layered cathode materials with a Ni content of over 80% have
limited applications due to their poor cycling performance. Lattice doping can enhance the
structural stability and electrochemical performance of Ni-rich cathode materials. In this work, we
perform first-principles calculations to study the effect of zirconium (+4) and molybdenum (+6)
doping on LiNi0.89Co0.055Mn0.055O2 (NCM-89). The extensive studies of the projected density of
states and magnetic structure show that the high-valence cation doping increases Ni 2+ content in
the NCM-89. Our atomistic studies suggest that the current doping confines the transition metal
layer by strong Zr−O and Mo-O bonds. The doping also restrains the layered to spinel phase
transition by hindering the Ni2+ migration and thus alleviating the evolution of oxygen gas.
81
4.1 Introduction
Lithium-ion battery (LIB) functions excellently in the field of energy storage, power grid, or
electric vehicle. Therefore, there are continuous needs for a unique LIB having superior energy
density, prolonged cycle life, and inferior cost. Among several components, the cathode material
fundamentally regulates the operation and expense of a LIB.110, 233-234 A layered oxide of transition
metal (TM), (LiNiO2, LiCoO2, and LiMnO2) supplies a capacity (~280 mAh g-1) greater than the
olivine (~170 mAh g-1) or spinel (~150 mAh g-1) materials.88, 235-236 In the past years, broad
attempts have been presented to advance a mixed-TM oxide having the common formula of
LiNixCoyMn1−x−yO2 (NCM).69-72,
113, 237-239
The rate proficiency, capacity maintenance, and
structural steadiness of such an NCM cathode can be regulated by changing the concentration of
Ni, Co, or Mn. For instance, a Ni-rich NCM offers a great specific capacity; a Co-rich NCM
surpasses in the rate proficiency; a Mn-rich NCM is finer in its thermal solidity and cycle life.70,
94-95
Regrettably, an NCM cathode having a Ni composition of 80% (LiNi0.8Co0.1Mn0.1O2) supplies
a specific capacity of 210 mAh g-1 merely.115 A NCM cathode with a Ni composition of ~90% is
consequently warmly anticipated for an improved specific capacity. Still, the feasibility of such a
Ni-rich NCM cathode is obstructed by its inferior thermal solidity, insufficient rate proficiency,
and fast deterioration in capacity. LiNi0.89Co0.055Mn0.055O2 (NCM-89) can give a high early specific
capacity of 226 mAh g-1 although endures from inferior capacity preservation (54%).240 A NCM
cathode weakens through the relief of oxygen because of an enhanced composition of Ni from 40%
to 80%.106,
110
This release of molecular oxygen, in turn, results from the permanent phase
̅ 𝑚) material to a spinel (𝐹𝑑3
̅ 𝑚) material and finally to a rock-salt
transition from a layered (𝑅3
̅ 𝑚) material.234, 241 The mixing of Li+-Ni2+ is generally accountable for the phase transition
(𝐹𝑚3
and the consequential structural volatility in electrochemical cycling.117, 242 Also, the Ni2+s at the
Li positions obstruct the migration routes of Li.235
Currently, it endures a challenge to advance a steady Ni-rich NCM cathode having an energy
density appropriate for an electric vehicle. Different tactics have been recommended to enhance
82
the structural steadiness and cycling behavior of a Ni-rich NCM: such as, a concentration gradient
technique,243-244 protecting surface with a fine coating of oxide or fluoride,245-248 and lattice doping
with cation or anion.73, 249-251 A full-concentration gradient process to acquire a Ni-rich NCM
cathode is problematic due to the interdiffusion of the TM ions throughout the lithiation
procedure.233 A surface covering slightly enriches the firmness of the bulk structure.252 Instead,
lattice doping can uplift the structural solidity of the bulk structure by restraining the diffusion of
cations.114 A cationic doping can hold the TM-O structure firmly by toughening the dopant-oxygen
bond. Different dopants, involving Al3+, Cr3+, Ti4+, Zr4+, Te6+, W6+, and Mo6+, have been evaluated
to boost the steadiness of Ni-rich cathodes.113-117, 249, 253
Especially, Zr4+ or Mo6+ dopant has
demonstrated to advance the cycleability of an NCM cathode by preserving the primary hexagonal
arrangement throughout the charge-discharge course.113-114, 120, 235, 254 Moreover, the Zr4+ doping
enlarges the spacing of the Li+ layers in the NCM cathodes, accelerating the migration of Li+ during
the electrochemical cycles.235, 255 The Mo-doped LiNi0.8Co0.1Mn0.1O2 (NCM-811) stems a steady
interface between the cathode and electrolyte and affords a higher cycleability compared to the
undoped materials.120
Currently, the consequences of doping on the steadiness of an NCM cathode of Ni content ~90%
have not been investigated. In this study, we report the density-functional-theory (DFT) study on
the low-level Zr4+ or Mo6+ doping (2.80%) of the NCM-89 cathode material. We unveiled how
doping affects the electronic structure, strength, and electrochemical activities of the NCM-89
cathode. We relatively investigated the chemical bondings, binding energies of oxygen, and
diffusions of Li+ and Ni2+ for the undoped and doped NCM-89 cathodes. We showed that the
current doping restrained the layered-to-spinel phase transition and thus suppressed the evolution
of gaseous oxygen, increasing the structural steadiness of the NCM-89 cathode.
4.2 Simulation Methods
We finished the DFT computations by employing the Vienna ab initio simulation package
(VASP).154-155 We employed the projector augmented wave (PAW) pseudopotentials to
characterize the core electrons.156 The GGA with the PBE method was used to explain the
83
exchange-correlation term.142 We used the plane-wave cutoff energy of 520 eV. We utilized the
on-site Coulomb interaction (U) potential plus GGA (GGA+U) to count the intense correlations
of electrons in the confined d orbitals in the TM ions. The values of U for Mo, Mn, Co, and Ni
were chosen to be 5.0, 5.1, 5.0, and 5.96, respectively.120 We incorporated the dispersion
corrections by employing the DFT+D3 approach.153 We modelled 4 × 3 supercells of thirty six
̅ 𝑚 space group and the structures were relaxed till the highest force was <
formula units of the 𝑅3
0.01 eV Å-1. We applied a gamma-centered 2 × 3 × 1 mesh to model the Brillouin zone.
We examined the chemical bonding strength by inspecting the crystal orbital Hamilton
populations (COHPs) executed in the LOBSTER code.160-161, 256 We analyzed the average charges
on oxygen atoms by the Bader analysis to comprehend the effect of dopant on the binding energies
of oxygen.197-199 We utilized the climbing-image-nudged-elastic-band (CI-NEB) technique with
the usual PBE method to compute the diffusion barriers of Li and Ni ions.158-159 In the GGA+U
computation, the migration of Li+ complements the jumping of an electron of the TM ion near the
migrating Li+.257 Therefore, we prevented this integration of the migrations of Li+ and electron by
dismissing the on-site Coulomb interaction in the CI-NEB computations.
4.3 Results and Discussion
4.3.1 Structural Properties
In the completely lithiated NCM cathode, TM ions hold an ordering of (√3 × √3) R30°, not a
linear or random ordering.62, 110, 114, 258-259 We screened various configurations of the √3-ordering
and selected the structure with the lowest energy for further computation. In the relaxed structure
of the undoped NCM-89 cathode, TM, Li, and O ions filled 3b (0, 0, 0.5), 3a (0, 0, 0), and 6c (0,
0, 0.24) Wyckoff positions, respectively (Figure 4.1).260-262 The lattice constants of the undoped
NCM-89 cathode, computed by employing the PBE approach, were a = 2.872 Å and c = 14.201
Å, in accord with the experimental lattice constants (a = 2.875 Å and c = 14.206 Å).240
84
Figure 4.1: Relaxed structure of the NCM-89 material, LiNi0.89Co0.055Mn0.055O2, (a) side view and
(b) top view. In this and all the subsequent figures, we utilize the identical color outline for Li, Ni,
Co, Mn, and O ions.
85
We revealed the favorable site for doping by computing the dopant formation energies of Zr or
Mo at three distinct cation positions (Ni, Co, and Mn) of the NCM-89 cathode.
The formation energy of the Zr-doped NCM-89 cathode, 𝐹𝐸Zr, was computed as
𝐹𝐸Zr = [𝐸 (Zr@NCM89) + 𝐸(LiMO2 )] − [𝐸 (NCM89) + 𝐸(Li) + 𝐸 (ZrO2 )],
where 𝐸(Zr@NCM89) and 𝐸 (NCM89) were the energies of the Zr-doped and undoped cathodes,
respectively. 𝐸(LiMO2 ) was the energy of per formula unit of the bulk LiNiO2, LiCoO2, or
LiMnO2, with given doping site (Ni, Co, or Mn). 𝐸(ZrO2 ) and 𝐸 (Li) were the energies of the bulk
monoclinic ZrO2 and a single Li atom in the bulk Li metal, respectively. Also, the formation energy
of the Mo-doped NCM-89 cathode (𝐹𝐸Mo) was computed by
𝐹𝐸Mo = [𝐸 (Mo@NCM89) + 𝐸 (M) + 2𝐸 (Li) + 2𝐸 (O2 )] − [𝐸 (NCM89) + 𝐸 (Li2 MoO4 )],
where 𝐸(Mo@NCM89) was the energy of the Mo-doped NCM-89 cathode and 𝐸 (M) the energy
of a single TM atom (Ni, Co, or Mn) in the corresponding bulk. 𝐸 (O2 ) was the energy of molecular
oxygen and 𝐸 (Li2 MoO4 ) the energy of Li2MoO4. By exploring all the TM positions for the Zr or
Mo doping, we obtained 𝐹𝐸Zrs at the Ni, Co, and Mn sites, respectively, were -1.69, -1.37, and 1.07 eV. Likewise, the 𝐹𝐸Mos at the Ni, Co, and Mn sites , respectively, were -4.19, -3.25, and 1.31 eV. Thus, both the Zr and Mo doping suitably happened at the Ni sites. This accorded with
the findings of the prior experiments.113-114, 120, 254
In the completely lithiated state, the current Zr or Mo doping enlarged the lattice constants, a
and c, of the NCM-89 cathode (Table 4.1). This might be realized by stating that the excessive
charge of dopant had to be balanced by raising the amount of Ni2+ (69 pm) which has a larger ionic
radius than the other TM ions (Ni3+: 56 pm, Ni4+: 48 pm, Co3+: 54 pm, and Mn4+: 53 pm).114, 120,
263
The Zr-doped NCM-89 cathode had a and c lattices higher than those of the Mo-doped cathode
since Zr4+ (72 pm) was bigger in radius than Mo6+ (59 pm).263 During delithiation, the c and a
lattices altered prominently and marginally, respectively (Table 4.1). The previous experiments
showed that the c lattice of an NCM cathode primarily enlarged with delithiation (up to x > 0.4)
and then reduced at a high level of delithiation (x < 0.4).239, 264
86
Table 4.1: The lattice parameters a and c (Å) of the undoped (LixNi0.89Co0.055Mn0.055O2), Zr-doped
(LixNi0.862Co0.055Mn0.055Zr0.028O2), and Mo-doped (LixNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89
materials. Results are listed for different lithiation levels, xs by using four different theoretical
methods.
LixNi0.89Co0.055Mn0.055O2:
PBE
PBE+D3
PBE+U
PBE+U+D3
a
c
a
c
a
c
a
c
x = 1.00
2.87
14.20
2.87
14.18
2.83
14.31
2.85
14.16
x = 0.83
2.86
14.30
2.86
14.25
2.82
14.42
2.84
14.23
x = 0.66
2.84
14.51
2.85
14.40
2.80
14.58
2.83
14.36
x = 0.50
2.82
14.75
2.84
14.51
2.79
14.82
2.81
14.49
x = 0.33
2.81
14.93
2.82
14.46
2.77
15.06
2.80
14.50
x = 0.16
2.79
14.96
2.80
14.06
2.76
15.12
2.78
14.09
x = 0.00
2.78
14.79
2.79
13.39
2.75
14.91
2.76
13.42
LixNi0.862Co0.055Mn0.055Zr0.028O2:
PBE
PBE+D3
PBE+U
PBE+U+D3
a
c
a
c
a
c
a
c
x = 1.00
2.89
14.27
2.89
14.24
2.86
14.37
2.87
14.22
x = 0.83
2.87
14.35
2.88
14.29
2.84
14.45
2.86
14.26
x = 0.66
2.85
14.55
2.87
14.41
2.82
14.63
2.84
14.40
x = 0.50
2.84
14.72
2.85
14.45
2.81
14.85
2.83
14.49
x = 0.33
2.82
14.96
2.83
14.38
2.80
15.10
2.81
14.46
x = 0.16
2.81
14.71
2.82
14.06
2.78
15.02
2.79
14.30
x = 0.00
2.79
14.63
2.81
13.32
2.77
14.93
2.78
13.43
87
LixNi0.862Co0.055Mn0.055Mo0.028O2:
PBE
PBE+D3
PBE+U
PBE+U+D3
a
c
a
c
a
c
a
c
x = 1.00
2.88
14.24
2.88
14.21
2.85
14.34
2.86
14.18
x = 0.83
2.86
14.34
2.87
14.29
2.84
14.42
2.85
14.24
x = 0.66
2.85
14.55
2.86
14.41
2.83
14.60
2.84
14.35
x = 0.50
2.83
14.80
2.85
14.50
2.81
14.82
2.83
14.49
x = 0.33
2.82
15.11
2.84
14.46
2.80
15.05
2.82
14.47
x = 0.16
2.81
15.06
2.82
14.13
2.79
15.00
2.80
14.19
x = 0.00
2.80
15.00
2.81
13.36
2.78
14.94
2.77
13.47
88
As displayed in Figure 4.2, the c lattice as of the dispersion corrected method (DFT-D3)
primarily enlarged with varying the portion of Li, x, from 1.0 to 0.5 and then steeply reduced by
decreasing x under 0.33. The steep shrinkage of the c lattice was because of the van der Waals
force acting among the layers of TM at a low content of Li, x < 0.33. The PBE and PBE+U methods,
deprived of the dispersion corrections in them, overrated the c lattice at a low level of lithiation
(Figures 4.2 a-c).62, 265 Conversely, the volume of NCM-89 cathode shrank with delithiation,
regardless of the occurrence of dopant (Figure 4.2d). The volumes of the NCM-89 cathodes
reduced because with delithiation, the Ni2+ (69 pm in radius) and Ni3+ (56 pm in radius) were
oxidized to Ni4+ (48 pm in radius). The pristine cathode was constantly smaller in volume than the
Mo-doped cathode which sequentially was smaller than the Zr-doped cathode (Figure 4.2d).
Generally, the volume change due to doping was very trivial (1.82 % max) to distort the NCM-89
cathode.
89
Figure 4.2: The c lattice constant of (a) the undoped (LixNi0.89Co0.055Mn0.055O2), (b) the Zr-doped
(LixNi0.862Co0.055Mn0.055Zr0.028O2) and (c) the Mo-doped (LixNi0.862Co0.055Mn0.055Mo0.028O2) NCM89 cathodes at different levels of delithiation. (d) The volumes of the undoped and doped NCM89 cathodes at different levels of delithiation, computed by employing the PBE+D3 approach.
90
4.3.2 Electronic Structure and Electrochemical Redox Behavior
We inspected the effect of Zr or Mo doping on the electronic property of the NCM-89 cathode
by investigating the density of states (DOS). In the total DOS (TDOS) computed by employing the
PBE approach, the Ni 3d-states predominated near the Fermi level (Figures 4.3a, 4.3c, and 4.3e),
implying that the redox activity primarily comprised the Ni ions. The partial DOS (PDOS) clarifies
that the Ni ions had three oxidation states (Ni2+, Ni3+, and Ni4+) in the undoped and doped cathodes
(Figure 3). The PDOS, jointly with the magnetic moments (Table 4.2), presents that Ni2+, Ni3+,
and Ni4+ had electronic configurations, t2g6 (|↑↓|↑↓|↑↓|) eg2 (|↑|↑|), t2g6 (|↑↓|↑↓|↑↓|) eg1 (|↑||), and t2g6
(|↑↓|↑↓|↑↓|) eg0 (|||), respectively. Besides, the undoped NCM-89 cathode had 6 Ni2+s (16.67%), 22
Ni3+s (61.11%), and 4 Ni4+s (11.11%). It was testified that in the NCM-622 and NCM-811
cathodes, the Ni3+s (38.33% and 53.33%, respectively) had a population than that of Ni 2+s (21.67%
and 18.33%, respectively) or Ni4+s (8.33%).110, 114, 120 In the current analysis, amplifying the
composition of Ni exceeding 80% increased the compositions of Ni3+ and Ni4+ but lessened the
content of Ni2+s. The Co and Mn ions were in the formal oxidation states of 3+ and 4+, respectively,
having the electronic configurations of t2g6 (|↑↓|↑↓|↑↓|) eg0 (|||) and t2g3 (|↑|↑|↑|) eg0 (|||). The valence
band maximum (VBM) involved the eg states of Ni2+ and Ni3+, while the conduction band minimum
(CBM) was constructed by the eg states of Ni3+ and Ni4+. The magnetic moments, beside the
unfilled d-orbitals (in the conduction bands) of Zr and Mo in PDOS, exhibited that the oxidation
states of Zr and Mo were 4+ and 6+, respectively.
As shown in Figures 4.3b, 4.3d, and 4.3f, the Zr- or Mo-doping enlarged the involvement of the
eg states of Ni2+ near the Fermi level however reduced the involvement of the eg states of Ni3+. The
completely lithiated Zr-doped cathode had 7 Ni2+ (19.44%), 20 Ni3+ (55.55%), and 4 Ni4+ (11.11%)
ions; the Mo-doped NCM-89 cathode consists of 8 Ni2+ (22.22%), 18 Ni3+ (50.00%), and 5 Ni4+
(13.88%) ions. Therefore, Ni2+s and Ni3+s enhanced and reduced in number with doping,
respectively, so that the extra charges of Zr4+ or Mo6+ can be compensated. Besides, the Mo doping
additionally enhanced the amount of Ni4+s. Also, Susai et al. showed that minor doping of Mo
(1.66%) in the NCM-811 material increased the contents of Ni 2+ (from 27.1% to 29.8%) and Ni4+
ions (from 10.4% to 10.6%).120 Noticeably, the current Mo-doping results more Ni2+s than the Zr-
91
doping due to the higher charge of Mo6+. The magnetic moments (Table 4.2) and PDOS (Figures
4.3e and 4.3f) signified that the oxidation states of Co and Mn stayed unaffected after the Zr- or
Mo- doping.
92
Figure 4.3: The total DOSs of the undoped (a), the Zr-doped (c), and the Mo-doped (e) NCM-89
cathodes. The PDOSs are also plotted for the undoped (b), the Zr-doped (d), and the Mo-doped
(f) NCM-89 cathodes.
93
Table 4.2: Magnetic moments and oxidation states of the 36 transition metal (TM) ions in the
undoped (LiNi0.89Co0.055Mn0.055O2), Zr-doped (LiNi0.862Co0.055Mn0.055Zr0.028O2), and Mo-doped
(LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 materials.
LiNi0.89Co0.055Mn0.055O2
LiNi0.862Co0.055Mn0.055Zr0.028O2
LiNi0.862Co0.055Mn0.055Mo0.028O2
Oxidation
state
Ni3+
Magnetic
moment (μB)
0.790
Oxidation
state
Ni3+
Magnetic moment
(μB)
0.774
Oxidation
state
Ni3+
Magnetic
moment (μB)
0.783
Ni2+
1.498
Ni2+
1.479
Ni2+
1.462
Ni2+
1.484
Ni2+
1.471
Ni2+
1.465
Ni3+
0.735
Ni3+
0.727
Ni4+
0.087
Ni3+
0.799
Ni3+
0.711
Ni3+
0.711
Ni3+
0.763
Ni3+
0.758
Ni3+
0.752
Ni3+
0.792
Ni3+
0.788
Ni3+
0.794
Ni4+
0.076
Ni4+
0.088
Ni4+
0.090
Ni3+
0.752
Ni3+
0.720
Ni2+
1.426
Ni3+
0.719
Ni3+
0.722
Ni3+
0.722
Ni3+
0.728
Ni3+
0.788
Ni3+
0.776
Ni3+
0.722
Ni3+
0.754
Ni3+
0.769
Ni3+
0.739
Ni3+
0.733
Ni3+
0.742
Ni3+
0.729
Ni2+
1.423
Ni2+
1.409
Ni3+
0.701
Ni3+
0.778
Ni3+
0.789
Ni3+
0.721
Ni3+
-0.719
Ni3+
-0.714
Ni3+
0.758
Ni3+
-0.799
Ni3+
-0.720
Ni3+
-0.746
Ni3+
-0.744
Ni3+
-0.739
Ni4+
0.021
Ni4+
0.087
Ni4+
0.061
Ni3+
0.705
Ni3+
-0.711
Ni3+
-0.716
Ni2+
-1.453
Ni2+
-1.464
Ni2+
-1.484
Ni3+
-0.721
Ni3+
-0.710
Ni3+
-0.708
94
Ni3+
0.784
Ni3+
0.768
Ni3+
0.781
Ni4+
0.059
Ni4+
0.053
Ni4+
0.049
Ni3+
-0.766
Ni3+
-0.767
Ni3+
-0.745
Ni2+
-1.452
Ni2+
-1.463
Ni2+
-1.469
Ni3+
0.754
Ni3+
0.721
Ni3+
0.796
Ni3+
0.700
Ni2+
-1.493
Ni2+
-1.494
Ni2+
-1.497
Ni2+
-1.458
Ni2+
-1.452
Ni2+
-1.421
Ni4+
0.022
Ni4+
0.034
Ni4+
0.159
Ni3+
0.730
Ni3+
0.740
Ni3+
0.723
Co3+
0.043
Co3+
-0.012
Co3+
-0.061
Co3+
-0.163
Co3+
-0.160
Co3+
-0.165
Mn4+
2.653
Mn4+
2.652
Mn4+
2.651
Mn4+
2.650
Mn4+
2.651
Mn4+
2.653
Zr4+
0.002
Mo6+
-0.038
95
This was also demonstrated from the calculation of radial distribution function of the TM-O
pair, 𝑔TM−O(𝑟), in the completely lithiated cathode (Figure 4.4): the Ni-O bonds imparted two
peaks in 𝑔Ni−O(𝑟) positioned at 1.93 and 2.05 Å. The existence of two peaks in 𝑔Ni−O(𝑟) and one
peak at 1.93 Å proved the Jahn-Teller distortion of Ni3+. The Zr or Mo doping reduced the
involvement of the Ni-O peak at 1.93 Å and increased the contribution of the peak at 2.05 Å. This
implied the Zr- or Mo- doping decreased the Jahn-Teller active Ni3+ ions and thus boosted the
structural solidity of the NCM-89 cathode.
96
Figure 4.4: Radial distribution functions of the TM-O pairs, 𝑔(𝑟)𝑠, in the undoped
(LiNi0.89Co0.055Mn0.055O2),
Zr-doped
(LiNi0.862Co0.055Mn0.055Zr0.028O2),
and
Mo-doped
(LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89 materials computed by employing the PBE approach.
97
Exhibited in Figure 4.5 are the oxidation states of the TM ions in the NCM-89 cathodes
(anticipated from the values of magnetic moments). With decreasing the content of Li in the
pristine cathode x from 1 to 0.83, the quantity of Ni3+s stayed the equal (=22) but 3 Ni2+s were
oxidized to Ni3+s, and 3 Ni3+s to Ni4+s (Figure 4.5a). The PDOS of the pristine NCM-89 at x =
0.83 also verified the existence of Ni2+s, Ni3+s, and Ni4+s (Figure 4.6a). Similarly, the Ni2+/Ni3+
and Ni3+/Ni4+ redox pairs were likewise realized for 0.83 ≥ x ≥ 0.67. For 0.67 ≥ x ≥ 0.16, the eg
state of Ni3+ moved to and even traversed the Fermi level (Figures 4.6b-e), suggesting the existence
of Ni3+/Ni4+ redox pair. With delithiation, Ni3+ and Ni4+ ions steadily decreased from 22 to 4 and
increased from 10 to 28 in number, respectively (Figure 4.5a). This signifies that the Ni3+/Ni4+
redox pair dominated the electrochemical process in the range, 0.67 ≥ x ≥ 0.16. In the completely
delithiated state (x = 0), all the Ni3+s were oxidized to Ni4+s. Besides, 2 Co3+s were also oxidized
to Co4+s (Figure 4.5a). The PDOS of Co4+ demonstrated an exchange splitting (Figure 4.6f) caused
by the singly filled t2g orbital of Co4+ by the electronic configuration of t2g5 (|↑↓|↑↓|↑|) eg0 (|||).
Similarly, Dixit et al. showed a Co3+/Co4+ redox pair at x = 0 in the NCM-523 cathode.62 The
oxidation states of Mn ions endured unaffected from 4+ during the deintercalation activity.
98
Figure 4.5: Oxidation states of transition metals in the pristine (LixNi0.89Co0.055Mn0.055O2) (a), Zrdoped (LixNi0.862Co0.055Mn0.055Zr0.028O2) (b), and Mn-doped (LixNi0.862Co0.055Mn0.055Mo0.028O2) (c)
NCM-89 cathodes at different levels of delithiation.
99
Figure 4.6: Projected density of states of the undoped NCM-89 material, LixNi0.89Co0.055Mn0.055O2,
calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x = 0.33, (e) x = 0.16, and (f) x = 0.0 by
using the PBE method.
100
Through removing Li from the completely lithiated Zr-doped cathode (x=1), 4 Ni2+s were
oxidized to Ni3+s, and 2 Ni3+s were oxidized to Ni4+s at x = 0.83 (Figure 4.5b). At x = 0.83, the
VBM comprised the eg states of Ni2+ and Ni3+, while the CBM included the eg states of Ni3+ and
Ni4+, implying the existence of Ni2+/Ni3+ and Ni3+/Ni4+ redox pairs (Figure 4.7a). The continual
lessening of Ni2+ (from 3 to 0 in number) and Ni3+ (from 22 to 16 in number) during delithiation
in the range, 0.83 ≥ x ≥ 0.50, implied that the redox pairs of Ni2+/Ni3+ and Ni3+/Ni4+ were involved
(Figure 4.5b). We noted that, different from the undoped NCM-89 cathode, 1 Ni ion stayed in the
2+ oxidation state at x = 0.67. The Ni3+/Ni4+ redox pair regulated the deintercalation in the range,
0.50 ≥ x ≥ 0.16. The Zr-doped NCM-89 cathode obeyed the same Ni3+/Ni4+ and Co3+/Co4+ redox
activity at a high delithiation level, 0.16 ≥ x ≥ 0.0. In the Mo-doped cathode, the noteworthy
increase (from 18 to 22 in number) in Ni3+ and decrease (from 8 to 0 in number) in Ni2+ suggested
that Ni2+/Ni3+ redox pair was mostly involved in the range, 1.0 ≥ x ≥ 0.67 (Figures 4.5c and 4.8).
As in the pristine NCM-89 cathode, the Mo-doped cathode comprised the Ni3+/Ni4+ redox pair in
the range, 0.67 ≥ x ≥ 0.16 (Figures S4c-e). At x = 0, all the TMs conquered the 4+ oxidation state
(Figure 4.8f).
101
Figure
4.7:
Projected
density
of
states
of
the
Zr-doped
NCM-89
material,
LixNi0.862Co0.055Mn0.055Zr0.028O2, calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x = 0.33,
(e) x = 0.16, and (f) x = 0.0 by using the PBE method.
102
Figure
4.8:
Projected
density
of
states
of
the
Mo-doped
NCM-89
material,
LixNi0.862Co0.055Mn0.055Mo0.028O2, calculated at (a) x = 0.83, (b) x = 0.67, (c) x = 0.50, (d) x = 0.33,
(e) x = 0.16, and (f) x = 0.0 by using the PBE functional.
103
4.3.3 Electrochemical Stability and Average Intercalation Voltage
We evaluated the steadiness of a partly delithiated state by computing the energy of formation,
𝐸𝑓 , expressed as
𝐸𝑓 = 𝐸 (Li𝑥 MO2 ) − 𝑥𝐸(LiMO2 ) − (1 − 𝑥 )𝐸 (MO2 ),
where 𝐸(Li𝑥 MO2 ), 𝐸 (LiMO2 ), and 𝐸(MO2 ) the energies of the partly and completely lithiated,
and the completely delithiated states, respectively. E(Li𝑥 MO2 ) was computed, for a certain x, by
obtaining the structure with the smallest energy for different vacancy arrangements of Li+. The
𝐸𝑓 s of the pristine, Zr- or Mo-doped cathodes are presented in Figure 4.9. A negative 𝐸𝑓 implies a
solid solution nature of a partly delithiated state.266 The 𝐸𝑓 s of the Zr- or Mo- doped cathodes were
somewhat more negative than that of the undoped NCM-89 cathode, meaning that the current Zr
or Mo doping steadied the partly delithiated states.
104
Figure 4.9: Convex hull of formation energies of the undoped, Zr-doped, and Mo-doped NCM89 cathodes at different levels of delithiation. The PBE method was employed in the computation.
105
The intercalation of Li in the NCM was analyzed by taking into account the following reaction
Li𝑥 NCM + 𝑑𝑥Li ⇌ Li𝑥+𝑑𝑥 NCM,
where 𝑑𝑥 was the amount of Li ions inserted. The intercalation voltage 𝑉 was computed by
𝑉=−
𝐸 (Li𝑥+𝑑𝑥 NCM) − 𝐸(Li𝑥 NCM) − 𝑑𝑥 ∙ 𝐸 (Li)
,
𝑑𝑥 ∙ 𝑒
where 𝐸(Li𝑥+𝑑𝑥 NCM) and 𝐸 (Li𝑥 NCM) were the energies (per formula unit) of the lithiated and
delithiated phases, respectively, of the NCM cathode. 𝐸(Li) was the energy of a single Li atom in
the bulk Li metal, and 𝑒 was the electronic charge. Since the PBE method commonly underrated
the average voltage with 1 V,113 a shifting was commonly employed in the DFT computation of
cathodes.267-268 We, thus, shifted the voltages with 0.9 and 0.6 V for the PBE and dispersion
corrected (PBE+D3) methods, respectively.62 The average voltage of the pristine NCM-89 cathode
from the PBE and PBE+D3 (4.04 and 4.08 V) methods matched fairly with the experimental
voltage (~4.0 V).240 The average voltages computed from the PBE+U and PBE+U+D3 approaches
were smaller and larger, respectively, than those from the PBE and PBE+D3 approaches. The
PBE+U and PBE+U+D3 approaches somewhat inadequately anticipated the voltage profiles since
the electron correlation in TM alters with delithiation and thus needed various U values.62 The
voltage profiles of the undoped and doped NCM-89 cathodes (Figure 4.10) exhibit that the
deintercalation potential gradually increased by elevating the delithiation level. The undoped
NCM-89 cathode had five phases in the range of 3.65 to 4.55 V (by PBE approach). The quantity
of phases in the voltage profile stayed unaffected by doping, implying that the doped NCM-89
cathodes provided stable currents comparable to those in the pristine NCM-89 cathode. At x=1,
the undoped and doped NCM-89 cathodes had analogous initial voltages, while, at x=0, the Zrand Mo-doped cathodes had greater (4.60 V) and lesser (4.48 V) voltages, respectively, than that
of the undoped NCM-89 cathode (4.55 V). The computed voltages were in the adjusted voltage
range (3.5-4.8 V) for the cathodes of LIBs.251, 269 Irrespective of the method utilized, the average
voltages (Table 4.3) followed the order: the Zr-doped cathode> the undoped cathode > the Modoped cathode, in good accord with the earlier experimental reports on the Ni-rich NCM
cathodes.114, 120 The variances among the average voltages of the undoped and Mo-doped cathodes
106
were fewer than 0.05 V, designating that the current Mo-doping would not considerably decrease
the energy density of the NCM-89 cathode.
107
Figure 4.10: Voltage profiles of the pristine and doped NCM-89 cathodes at different levels of
delithiation.
108
Table
4.3:
Average
voltage
of
the
pristine
(LiNi0.89Co0.055Mn0.055O2),
Zr-doped
(LiNi0.862Co0.055Mn0.055Zr0.028O2), and Mo-doped (LiNi0.862Co0.055Mn0.055Mo0.028O2) NCM-89
materials.
Method
LiNi0.89Co0.055Mn0.055O2
LiNi0.862Co0.055Mn0.05
LiNi0.862Co0.055Mn0.055Mo0
5Zr0.028O2
.028O2
PBE
4.04
4.06
4.02
PBE+D3
4.08
4.10
4.05
PBE+U
3.90
3.95
3.88
PBE+U+D3
4.15
4.19
4.13
109
4.3.4 Stabilization of the NCM-89 Material by Zr or Mo Doping
The solidity of a cathode is regulated via the chemical bonding among the component
elements.110 Therefore, we inspected the bond stability of TM-O and TM-TM bonds through
integrating the COHP till the Fermi level. Figure 4.11 displayed the integrated COHPs (ICOHPs)
of numerous TM-O and TM-TM bonds. Irrespective of the occurrence of a dopant, the ICOHP
values of Ni-O bonds reduced by progressing from Ni2+-O to Ni4+-O bond, specifying the
covalency of the Ni-O bonds enhanced with the oxidation states of Ni. The ICOHP values of the
Ni3+-O and Co3+-O bonds in the pristine cathode were more negative than in the doped cathodes
(Figure 4.11a), signifying the current doping lessened the degree of covalency of the TM-O bonds.
An elevated degree of covalency results in the delocalization of electrons within the TM-O bonds.
During the delithiation activity in the NCM cathodes, the electrons involved in the TM-O bonds
participate in electrochemical oxidation, deteriorating the TM-O bonds.110 This implies that an
elevated degree of covalency in the TM-O bond leads to more oxygen release.110, 270-271 The
decreased covalency of the Ni3+-O and Co3+-O bonds in the current doped cathodes are likely to
minimize the release of oxygen and enhance the stability of the lattice structure during the
delithiation process.
The negative ICOHPs of the Zr-O and Mo-O bonds implied the robust Zr-O and Mo-O bonds
stemming from the considerable overlaps between Zr/Mo(d) and O(p) orbitals (Figure 4.11a). A
robust Zr-O or Mo-O bond sequentially should alleviate the current doped cathode by avoiding the
oxygen release. As displayed in Figure 4.11b, the current doping toughened the TM-TM bonds,
notably those comprising Ni ions. The stability of the Co-Co, Co-Mn, or Mn-Mn bonds barely
altered with doping, as the oxidation states of Co or Mn did not alter with the current Zr- or Modoping. Among the TM-TM bonds, the Ni-Mn and Mn-Mn bonds were the toughest and softest,
respectively.
110
Figure 4.11: Average values of ICOHP for various (a) TM-O and (b) TM-TM bonds in the pristine,
Zr-doped, and Mo-doped NCM-89 cathodes.
111
The firmness of a TM-O bond was evaluated by computing the molecular oxygen binding
energy, ∆𝐸Obind
, defined as
2
∆𝐸O𝑏𝑖𝑛𝑑
= 𝐸(NCM89O2 −vacant ) + 𝐸 (O2 ) − 𝐸(NCM89perfect),
2
where 𝐸(NCM89O2 −vacant ) was the energy of the NCM-89 cathode having two adjacent oxygen
vacancies, 𝐸 (O2 ) the energy of a molecule of oxygen, and 𝐸(NCM89perfect ) the energy of the
NCM-89 cathode deprived of any vacancy of oxygen. We considered the over-binding energy
error for O2 molecules at 0 K, proposed by Ceder et al. and added a correction of -1.36 eV (per O2
molecule) to the electronic energy.272 Dixit et al. stated that the oxygen release from an NCM
cathode was accelerated by enhancing the composition of Ni from 40% to 80%.110 In the
completely lithiated state, the Zr- or Mo-doped NCM-89 cathode had oxygen binding energies
greater than that of the undoped cathode (Table 4.4). Apparently, Zr or Mo efficiently shifted extra
charges to oxygen ions than Ni did in the pristine cathode (Table 4.4). The preceding DFT studies
also exhibited that Nb, Zr, or Al in an NCM material contributes additional charges to the oxygen
ions than the Ni. 266, 269
112
Table 4.4: The charges (Bader) on oxygen atoms and oxygen binding energies in the fully lithiated
states computed by employing the PBE approach. The charge on oxygen was averaged around the
dopant octahedra.
NCM-89 Material
Average charge on oxygen (e)
-1.16
Charge on
dopant (e)
1.36 (Ni)
Oxygen binding energy
(eV)
3.39
Pristine
Zr-doped
-1.27
2.45 (Zr)
5.41
Mo-doped
-1.22
2.57 (Mo)
5.17
113
With the intention of studying the progress of oxygen release, we inspected the oxygen binding
energy and charges on oxygen (Bader) with delithiation (as displayed in Figure 4.12). Irrespective
of the occurrence of a dopant, the oxygen binding energy reduced with the level of delithiation in
the NCM-89 cathode (Figure 4.12a). Likewise, the charges on the oxygen ions reduced in
magnitude with the level of delithiation in the undoped and doped NCM-89 cathodes. This drift is
coherent with the reduction in the oxygen binding energy with the level of delithiation displayed
in Figure 4.12a since a decreased amount of oxygen charge should contribute lesser oxygen
binding energy. This indicates that the evolution of oxygen gas in the NCM-89 cathodes turn out
to be favorable at the high delithiation level. The previous experiments exhibited that the relief of
gaseous oxygen occurs at ~4.7 V and ~4.3 V (vs. Li/Li+) for NCM-622 and NCM-811 cathodes,
respectively.273-274 Regardless of the delithiation level, the Zr- and Mo-doped NCM-89 cathodes
had oxygen binding energies greater than that of the pristine NCM-89 cathode, directing that the
current low Zr- or Mo-doping should decrease the evolution of oxygen gas from the NCM-89
cathode.
114
Figure 4.12: Oxygen binding energies (a) and average charges (Bader) on the oxygen atoms (b)
computed for the pristine and doped NCM-89 cathodes at different levels of delithiation.
115
4.3.5 Li-Ion Diffusion
A cathode material with a high-power density demands for fast migration of Li+ in it. Such a
migration depends on various points, comprising the host structure, the level of lithiation, the
special and electrostatic interactions with adjacent ions, and the amount of vacancies of Li.275 The
migration of Li+ in a layered oxide pursues two distinct routes subject to the configuration of the
vacancies of Li+s.276 In presence of a single vacancy of Li adjacent the doping position, the
migration pursued a route stated to as the oxygen-dumbbell hop (ODH) where the Li+ diffused
from one octahedral site (Oh) to another (Figure 4.13a) through an oxygen-dumbbell. The diffusion
barriers of the migration of Li+ in this route for the pristine, Zr-doped, Mo-doped NCM-89
cathodes were 0.52, 0.73, and 0.74 eV, respectively (Figure 4.13b). The enhanced diffusion barrier
of migration by the doping could be attributed to the fact that Li+ more intensely resists Zr4+ or
Mo6+ of the doped cathode than Ni3+ of the pristine cathode.
With a di-vacancy of Li+s, the migration pursued the tetrahedral site hop (TSH) route where Li+
diffused via a tetrahedral position (Figure 4.13c). Similar to the ODH route, the migration barrier
of Li+ of the pristine NCM-89 cathode (0.14 eV) was inferior than those of the Zr-doped (0.23 eV)
and Mo-doped (0.24 eV) cathodes (Figure 4.13d). Likewise, Dixit et al. stated an Al-doped NCM523 cathode had a migration barrier greater than the pristine cathode.266 The diffusion barrier of
migration along the TSH route was inferior than the related barrier along the ODH route. This can
be clarified as follows. Along the ODH route, a diffusing Li+ act together with the adjacent TM
ion, adjacent Li+, and oxygen ions. In contrast, the diffusing Li+ along the TSH route did not
interact with the adjacent Li+ because of an extra Li+ vacancy.
116
Figure 4.13: Pathways and energy profiles of Li+ diffusing in the current NCM-89 cathodes. We
have shown results along the ODH (a and b) and TSH (c and d) routes of the Li+ migration adjacent
a dopant position of the doped NCM-89 cathode, beside the results for the pristine material. The
local minimum along the TSH route resembles to the NEB image at the intermediate tetrahedral
site. The doping position and diffusing Li+ are sketched as cyan and yellow spheres, respectively.
117
Additionally, we computed the diffusion barriers of Li+ migration near the adjacent Ni ion of
the doping position (Figures 4.14 a and c). Along the ODH (TSH) route, the migration barriers of
Li+ in the pristine, Zr-doped, and Mo-doped cathodes were 0.59 (0.20), 0.46 (0.11), and 0.54 (0.12)
eV, respectively (Figures 4.14 b and d). In these occasions, the migration barriers of Li+ in the Zrand Mo-doped NCM-89 cathodes were inferior than those of the pristine cathode: from the
calculation of magnetic moments, we noted that the current doping altered the oxidation state of
the adjacent Ni ion of the dopant position from Ni3+ to Ni2+, to balance the additional charge of
Zr4+ or Mo6+. The reduced migration barrier of Li+ of the Zr- or Mo-doped cathode occurred from
the decreased repulsive force between Li+ and Ni2+ related to the repulsion between Li+ and Ni3+
in the pristine cathode. Thus, the overall migration rate of Li+ in the doped NCM-89 cathode might
be similar to that of the undoped NCM-89 cathode.
118
Figure 4.14: Pathways and minimum energy profiles of Li+ migrating along the ODH (a and b)
and TSH (c and d) routes in the vicinity of adjacent Ni ion of the doping site in the undoped and
doped NCM-89 cathodes. Sketched as cyan and yellow spheres are the doping position and
diffusing Li+, respectively.
119
4.3.6 Phase Transition from the Layered to Spinel Structure
The layered arrangements of the current NCM-89 cathodes will experience phase transitions
when the TM ions diffuse to the Li layer.277 As illustrated in Figure 4.15a, the TM ion can diffuse
from the layer of TM to the layer of Li across two routes.278 In the shortest route, the TM ion
diffuses from the Oh position of the TM layer to the Oh position of the Li layer across the edge (E)
shared by the adjacent octahedral (Oh→E→Oh). Along the longer pathway, the TM ion diffuses
across an intermediary tetrahedral position (Td) through the faces (F) shared with the adjacent
octahedral (Oh→Td→Oh). In the preceding reports, the layered-to-spinel phase transition of a Nirich NCM cathode was described to be principally propelled by the migration of Ni2+.106, 279
Schipper et al., by investigating the Ni 2+ migration in LiNi0.6Co0.2Mn0.2O2,114 showed that the
migration barrier of Ni2+ decreases from ~1.2 to 0.23 eV with increasing the Li vacancy (divacancy and tri-vacancy) near the migrating Ni2+. We calculated the migration barrier of Ni2+ with
two vacancies of Li close to the migrating Ni2+ and one vacancy of Li at the final diffusion position,
to comprehend the consequences of doping on the diffusion behavior of Ni2+. Figures 4.15b and
4.15d, respectively, show the migration paths of Ni 2+ from one Oh position of the layer of TM to
the Oh position of the layer of Li for the pristine and doped materials. In the pristine cathode, the
migration of Ni2+ followed the Oh→Td→Oh route with a diffusion barrier of 0.93 eV (Figure 4.15c).
But, the backward diffusion barrier from the final Oh position of the layer of Li to the intermediate
Td position was so low as 0.039 eV. So, the diffued Ni2+ might jump back to the neighboring Td
position of the layer of Li, easing the occupation of Ni2+ at the Td position (Figure 4.15c).
Conversely, Zr4+ or Mo6+ in the doped cathode disrupted the intermediate Td positions by the strong
electrostatic repulsions. Hence, the migration routes of Ni2+ in the doped NCM-89 cathodes did
not comprise such Td positions. As an alternative, they obeyed the Oh→E→Oh route containing an
energetically uncomplimentary oxygen dumbbell position. The robust Pauli repulsion from the
electron clouds of oxygen stemmed in a high diffusion barrier of Ni2+ in the doped NCM-89
cathodes. The diffusion barriers of Ni2+ in the Zr- and Mo-doped NCM-89 cathodes, respectively,
were 1.48 and 1.88 eV (Figure 4.15e). Our calculation indicates that the current Zr- or Mo-doping
can avoid the layered-to-spinel structural modification by delaying the diffusion of Ni2+.
120
Figure 4.15: Representations for two routes of a TM ion migrating from a TM layer to a Li layer
(a). Positions F and E resemble to the octahedral face and edge shared by the adjacent octahedra,
respectively. The first route of Ni2+ diffusing from a TM layer to a Li layer (b) and the
corresponding minimum energy profile (c) for the pristine NCM-89 cathode. The second route (d)
and minimum energy profile (e) of a diffusing Ni2+ in the doped NCM-89 cathodes. Displayed in
(d) is the route sketched for the Zr-doped NCM-89.
121
4.4 Conclusion
A Ni-rich NCM cathode delivers an elevated discharge capacity however endures from little
capacity retention because of its structural weakening. Earlier, a surface coating of metal oxide or
doping with cation of high-valency was revealed to increase the structural strength of a Ni-rich
cathode. In this study, we investigated how Zr4+ or Mo6+ doping influences the structural strength
and electrochemical performance of NCM-89 (LiNi0.89Co0.055Mn0.055O2) cathode. The Ni ions,
jointly with Co ions at the highly delithiated state, regulated the electrochemical activity of the
NCM-89 cathodes. The current Zr- or Mo-doping enhanced the strength of the NCM-89 cathode
by the robust Zr-O or Mo-O bonds and by decreasing the Jahn–Teller active Ni3+s, thus inhibiting
the release of the oxygen gas. The current Zr- or Mo- doping enlarged the diffusion barriers of Li+
close to the dopant position, but, reduced the diffusion barriers of Li+ remote to the dopant position,
signifying the migration rates of Li+ in undoped and doped NCM-89 cathodes could be similar.
Furthermore, the Zr or Mo- doping inhibited the phase transition of the NCM-89 material from a
layered structure to a spinel structure by decreasing the migration of Ni2+. The current study
presents a major understanding of the rational strategy of superior Ni-rich cathodes.
122
CHAPTER 5
Summary
The dissertation contains the computational design and investigation of electrode materials
having high energy density for applications in LIBs, NIBs, or KIBs. Chapter 1 provides the
introduction of the secondary battery. It describes the electrochemical properties of different
electrode materials and different approaches to enhance the energy density of the alkali metal ion
battery.
Chapter 2 focuses on the theoretical details of density functional theory (DFT) and
computational details.
Chapter 3 describes the possibility of using a two-dimensional (2D) material as a prospective
anode material for an alkali metal ion battery. The standard graphite anode of LIB can not be used
in NIB or KIB due to the sluggish kinetics of Na or K ion. Having high storage capacities, 2D Si
and Ge are recently being studied as potential anode materials. Alloying Ge with Si can further
improve the electrical conductivity and diffusion rate of alkali metal ions in Si. This chapter
proposes that a sheet of SiGe has promising electrochemical properties for the application in LIBs,
NIBs, or KIBs. The DFT calculations show that the SiGe sheet was thermodynamically stable. The
considered alkali metals ions have low diffusion barriers and average open-circuit voltages
(OCVs). From the calculated OCVs and high specific capacities, the energy densities of the SiGe
sheet were estimated. The physical insights of multilayer adsorption behavior were also
investigated.
In chapter 4, the effect of zirconium (Zr4+) or molybdenum (Mo6+) doping on the
electrochemical performance and structural stability of a Ni-rich, LiNi0.89Co0.055Mn0.055O2 (NCM89) material, was investigated by using the DFT calculations. A Ni-rich NCM material undergoes
an irreversible phase transition leading to the release of oxygen gas with delithiation. This chapter
shows that the present doping restrains the phase transition by mitigating the Li+-Ni2+ mixing. The
123
strong Zr-O or Mo-O bonds inhibit the release of molecular oxygen from the lattice structure of
NCM-89 material. The migration of Li-ions elucidated the comparable diffusion rates of Li + in
undoped and doped NCM-89 materials.
124
References
(1)
Administration, U. S. E. I., International Energy Outlook 2017. Available online at
https://www.eia.gov/outlooks/ieo/pdf/0484(2017).pdf 2017.
(2)
S. Shafiee, E. T., When will Fossil Fuel Reserves be Diminished? Energy Policy 2009, 37,
181-189.
(3)
J. B. Goodenough, K. S. P., The Li-ion Rechargeable Battery: A Perspective. J. Am. Chem.
Soc. 2013, 135, 1167-1176.
(4)
S. Liu, Z. R. T., Y. Sun, J. C. Colmenares, Y. J. Xu, One-Dimension-Based Spatially
Ordered Architectures for Solar Energy Conversion. Chem. Soc. Rev. 2015, 44, 5053-5075.
(5)
S. Rehman, L. M. A.-H., Md. M. Alam,, Pumped Hydro Energy Storage System: A
Technological Review. Renew. Sust. Energy Rev. 2015, 44, 586-598.
(6)
Tomabechi, K., Energy Resources in the Future. Energies 2010, 3, 686-695.
(7)
Tomabechi, K., Greenband. Available online at http://www.greenbang.com/peak-water-
worries-energy-experts_22514.html 2013.
(8)
V. Etacheri, R. M., R. Elazari,G. Salitra, D. Aurbach, Challenges in the Development of
Advanced Li-ion Batteries: A Review. Energy Environ. Sci. 2011, 4, 3243-3262.
(9)
Ozawa, K., Lithium-Ion Rrechargeable Batteries with LiCoO2 and Carbon Electrodes: The
LiCoO2/C System. Solid State Ion. 1994, 69, 212-221.
(10)
M. M. Thackeray, W. I. F. D., P. G. Bruce, J. B. Goodenough, Lithium Insertion into
Manganese Spinels. Mater. Res. Bull. 1983, 18, 461-472.
(11)
A. K. Padhi, K. S. N., J. B. Goodenough, Phospho-Olivines as Positive-Electrode Materials
for Rechargeable Lithium Batteries. J. Electrochem. Soc. 1997, 144, 1188-1194.
(12)
U.S. Advanced Battery Consortium LLC, EV Battery Goals. Available online at
http://www.uscar.org/guest/article_view.php?articles_id=85.
(13)
Whittingham, M. S., Electrical Energy Storage and Intercalation Chemistry. Science 1976,
192, 1126-1127.
(14)
G. Zheng, S. W. L., Z. Liang, H. W. Lee, K. Yan, H. Yao, H. Wang, W. Li, S.Chu, Y. Cui,
Interconnected Hollow Carbon Nanospheres for Stable Lithium Metal Anodes. Nat. Nanotechnol.
125
2014, 9, 618-623.
(15)
R. Mukherjee, A. V. T., D. Datta, E. Singh, J. Li, O. Eksik, V. B. Shenoy, N. Koratkar,
Defect-Induced Plating of Lithium Metal within Porous Graphene Networks. Nat. Commun. 2014,
5, 3710.
(16)
B. Kisang, J. K. S., J. Jang, Role of a Solid-Electrolyte Interphase in the Dendritic
Electrodeposition of Lithium: A Brownian Dynamics Simulation Study. J. Phys. Chem. C 2020,
124, 9134-9141.
(17)
Zhang, W. J., A Review of the Electrochemical Performance of Alloy Anodes for Lithium-
Ion Batteries. J. Power Sources 2011, 196, 13-24.
(18)
L. Ji, Z. L., M. Alcoutlabi, X. Zhang, Recent Developments in Nanostructured Anode
Materials for Rechargeable Lithium-Ion Batteries. Energy Environ. Sci 2011, 4, 2682-2689.
(19)
F. Zheng, Y. Y., Q. Chen, High Lithium Anodic Performance of Highly Nitrogen-Doped
Porous Carbon Prepared from a Metal-Organic Framework. Nat. Commun. 2014, 5, 5261.
(20)
P. Guo, H. S., X. Chen, Electrochemical Performance of Graphene Nanosheets as Anode
Material for Lithium-Ion Batteries. Electrochem. Commun. 2009, 11, 1320-1324.
(21)
H. Wu, Y. C., Designing Nanostructured Si Anodes for High Energy Lithium Ion Batteries.
Nano Today 2012, 7, 414-429.
(22)
L. Zhang, R. R., H. Guo, X. Hu, S. Dou, H. Liu, A Green and Facile Way to Prepare
Granadilla-Like Silicon-Based Anode Materials for Li-Ion Batteries. Adv. Funct. Mater. 2016, 26,
440-446.
(23)
Q. Wang, H. L., L. Chen, X. Huang, Novel Spherical Microporous Carbon as Anode
Material for Li-Ion Batteries. Solid State Ion. 2002, 152-153, 43-50.
(24)
H. Ren, R. Y., J. Wang, Q. Jin, M. Yang, D. Mao, D. Kisailus, H. Zhao, D. Wang,
Multishelled TiO2 Hollow Microspheres as Anodes with Superior Reversible Capacity for Lithium
Ion Batteries. Nano Lett. 2014, 14, 6679-6684.
(25)
N. Zhang, X. H., Y. Liu, X. Hu, Q. Zhao, J. Chen, 3D Porous γ-Fe2O3@C Nanocomposite
as High-Performance Anode Material of Na-Ion Batteries. Adv. Energy Mater. 2015, 5, 1401123.
(26)
D. Wang, Y. Y., H. He, J. Wang, W. Zhou, H. D. Abruña, Template-Free Synthesis of
Hollow-Structured Co3O4 Nanoparticles as High-Performance Anodes for Lithium-Ion Batteries.
126
ACS Nano 2015, 9, 1775-1781.
(27)
L. Shi, T. Z., Recent Advances in Inorganic 2D Materials and Their Applications in
Lithium and Sodium Batteries. J. Mater. Chem. A 2017, 5, 3735-3758.
(28)
V. Chabot, D. H., A. Yu, X. Xiao, Z. Chen, J. Zhang, A Review of Graphene and Graphene
Oxide Sponge: Material Synthesis and applications to Energy and the Environment. Energy
Environ. Sci. 2014, 7, 1564-1596.
(29)
Liu, J., Charging Graphene for Energy. Nat. Nanotechnol. 2014, 9, 139-741.
(30)
L. Zhou, Z. H., B. Gao, T. Frauenheim, Doped Graphenes as Anodes with Large Capacity
for Lithium-Ion Batteries. J. Mater. Chem. A 2016, 4, 13407-13413.
(31)
A. L. M. Reddy, A. S., S. R. Gowda, H. Gullapalli, M. Dubey, P. M. Ajayan, Synthesis of
Nitrogen-Doped Graphene Films For Lithium Battery Application. ACS Nano 2010, 4, 6337-6342.
(32)
A. Mukhopadhyay, F. G., A. Tokranov, X. Xiao, R. H. Hurt, B. W. Sheldon, Engineering
of Graphene Layer Orientation to Attain High Rate Capability and Anisotropic Properties in LiIon Battery Electrodes. Adv. Funct. Mater. 2013, 23, 2397-2404.
(33)
X. Li, Y. H., J. Liu, A. Lushington, R. Li, X. Sun, Structurally Tailored Graphene
Nanosheets as Lithium Ion Battery Anodes: an Insight to Yield Exceptionally High Lithium
Storage Performance. Nanoscale 2013, 5, 12607-12615.
(34)
K. Shu, C. W., M. Wang, C. Zhao, G. G. Wallace, Graphene Cryogel Papers with Enhanced
Mechanical Strength for High Performance Lithium Battery Anodes. J. Mater. Chem. A 2014, 2,
1325-1331.
(35)
A. P. Cohn, L. O., R. Carter, S. Chatterjee, A. S. Westover, K. Share, C. L. Pint, Assessing
the Improved Performance of Freestanding, Flexible Graphene and Carbon Nanotube Hybrid
Foams for Lithium Ion Battery Anodes. Nanosclae 2014, 6, 4669-4675.
(36)
W. Xia, Q. Z., F. Xu, H. Ma, J. Chen, K. Qasim, B. Ge, C. Zhu, L. Sun, Visualizing the
Electrochemical Lithiation/Delithiation Behaviors of Black Phosphorus by In Situ Transmission
Electron Microscopy. J. Phys. Chem. C 2016, 120, 5861-5868.
(37)
F. Xu, B. G., J. Chen, A. Nathan, L. L. Xin, H. Ma, H. Min, C. Zhu, W. Xia, Z. Li, S. Li,
Scalable
Shear-Exfoliation
of
High-Quality
Phosphorene
Nanoflakes
Electrochemical Cycleability in Nano Batteries. 2D Mater. 2016, 2016, 025005.
127
with
Reliable
(38)
R. Zhang, X. W., J. Yang, Blockage of Ultrafast and Directional Diffusion of Li Atoms on
Phosphorene with Intrinsic Defects. Nanoscale 2016, 8, 4001-4006.
(39)
J. Zhu, A. C., U. Schwingenschlögl, Silicene/Germanene on MgX 2 (X = Cl, Br, and I) for
Li-Ion Battery Applications. Nanoscale 2016, 8, 7272-7277.
(40)
A. G. Dylla, G. H., K. J. Stevenson, Lithium Insertion in Nanostructured TiO 2 (B)
Architectures. Acc. Chem. Res. 2013, 46, 1104-1112.
(41)
C. Arrouvel, S. C. P., M. S. Islam, Lithium Insertion and Transport in the TiO 2−B Anode
Material: A Computational Study. Chem. Mater. 2009, 21, 4778-4783.
(42)
A. G. Dylla, P. X., G. Henkelman, K. J. Stevenson, Morphological Dependence of Lithium
Insertion in Nanocrystalline TiO2 (B) Nanoparticles and Nanosheets. J. Phys. Chem. Lett. 2012, 2,
2015-2019.
(43)
J. Procházka, L. K., M. Zukalová, O. Frank, M. Kalbáč, A. Zukal, M. Klementová, D.
Carbone, M. Graetzel, Novel Synthesis of the TiO2 (B) Multilayer Templated Films. Chem. Mater.
2009, 21, 1457-1464.
(44)
T. Beuvier, M. R.-P., M. Mancini-Le Granvalet, T. Brousse, O. Crosnier, L. Brohan, TiO2
(B) Nanoribbons as Negative Electrode Material for Lithium Ion Batteries with High Rate
Performance. Inorg. Chem. 2010, 49, 8457-8464.
(45)
S. Liu, H. J., L. Han, J. Wang, P. Gao, D. Xu, J. Yang, S. Che, Nanosheet-Constructed
Porous TiO2–B for Advanced Lithium Ion Batteries. Adv. Mater. 2012, 24, 3201-3204.
(46)
J. Ni, Y. Z., L. Li, L. Mai, Ultrathin MoO2 Nanosheets for Superior Lithium Storage. Nano
Energy 2015, 11, 129-135.
(47)
M. Liu, C. Y., Y. Zhang, Fabrication of Nb2O5 Nanosheets for High-rate Lithium Ion
Storage Applications. Sci. Rep. 2015, 5, 8326.
(48)
Y. Li, D. W., Z. Zhou, C. R. Cabrera, Z. Chen, Enhanced Li Adsorption and Diffusion on
MoS2 Zigzag Nanoribbons by Edge Effects: A Computational Study. J. Phys. Chem. Lett. 2012,
3, 2221-2227.
(49)
H. Shu, F. L., C. Hu, P. Liang, D. Cao, X. Chen, The Capacity Fading Mechanism and
Improvement of Cycling Stability in MoS2-Based Anode Materials for Lithium-Ion Batteries.
Nanoscale 2016, 8, 2918-2926.
128
(50)
Y. C. Liu, Y. P. Z., L. F. Jiao, J. Chen, A Graphene-Like MoS2/Graphene Nanocomposite
as a High Performance Anode for Lithium Ion Batteries. J. Mater. Chem. A 2014, 2, 13109-13115.
(51)
J. Xiao, D. C., L. Cosimbescu, P. Koech, J. Liu, J. P. Lemmon, Exfoliated MoS2
Nanocomposite as an Anode Material for Lithium Ion Batteries. Chem. Mater. 2010, 22, 45224524.
(52)
R. Bhandavat, L. D., G. Singh, Synthesis of Surface-Functionalized WS2 Nanosheets and
Performance as Li-Ion Battery Anodes. J. Phys. Chem. Lett. 2012, 3, 4779-4788.
(53)
Y. Jing , Z. Z., C. R. Cabrera, Z. Chen, Metallic VS2 Monolayer: A Promising 2D Anode
Material for Lithium Ion Batteries. J. Phys. Chem. C 2013, 117, 25409-25413.
(54)
D. Wang, L. M. L., S. J. Zhao, Z. Y. Hu, H. Liu, Potential Application of Metal
Dichalcogenides Double-Layered Heterostructures as Anode Materials for Li-Ion Batteries. J.
Phys. Chem. C 2016, 120, 4779-4788.
(55)
Q. Tang, Z. Z., P. Shen, Are MXenes Promising Anode Materials for Li Ion Batteries?
Computational Studies on Electronic Properties and Li Storage Capability of Ti 3C2 and Ti3C2X2
(X = F, OH) Monolayer. J. Am. Chem. Soc. 2012, 134, 16909-16916.
(56)
D. Sun, M. W., Z. Li, G. Fan, L. Z. Fan, A. Zhou, Two-Dimensional Ti3C2 as Anode
Material for Li-Ion Batteries. Electrochem. Commun. 2014, 47, 80-83.
(57)
M. Naguib, J. H., J. Lu, K. M. Cook, L. Hultman, Y. Gogotsi, M. W. Barsoum, New Two-
Dimensional Niobium and Vanadium Carbides as Promising Materials for Li-Ion Batteries. J. Am.
Chem. Soc. 2013, 135, 15966-15969.
(58)
J. Halim, S. K., M. R. Lukatskaya, M. Naguib, M. Q. Zhao, E. J. Moon, J. Pitock, J. Nanda,
S. J. May, Y. Gogotsi, M. W. Barsoum, Synthesis and Characterization of 2D Molybdenum
Carbide (MXene). Adv. Funct. Mater. 2016, 26, 3118-3127.
(59)
D. Sun, Q. H., J. Chen, X. Zhang, L. Wang, Q. Wu, A. Zhou, Structural Transformation of
MXene (V2C, Cr2C, and Ta2C) with O Groups during Lithiation: A First-Principles Investigation.
ACS Appl. Mater. Interfaces 2016, 8, 74-81.
(60)
H. Zhou, M. Z., X. Zhang, W. Dong, X. Wang, H. Bu, A. Wang, First-Principles Prediction
of a New Dirac-Fermion Material: Silicon Germanide Monolayer. J. Phys.: Condens. Matter 2013,
25, 395501.
129
(61)
B. L. Ellis, K. T. L., L. F. Nazar, Positive Electrode Materials for Li-Ion and Li-Batteries.
Chem. Mater. 2010, 22, 691-714.
(62)
M. Dixit, M. K., O. S. Lavi, B. Markovsky, D. Aurbach, D. T. Major, Thermodynamic and
Kinetic Studies of LiNi0.5Co0.2Mn0.3O2 as a Positive Electrode Material for Li-Ion Batteries using
First Principles. Phys. Chem. Chem. Phys. 2016, 18, 6799-6812.
(63)
C. M. Julien, A. M., K. Zaghib, H. Groult, Comparative Issues of Cathode Materials for
Li-Ion Batteries. Inorganics 2014, 2, 132-154.
(64)
C. Delmas, C. F., P. Hagenmuller, Structural Classification and Properties of the Layered
Oxides. Physica B+ C 1980, 99, 81-85.
(65)
C. Delmas, J. J. B., P. Hagenmuller P, A New Variety of LiCoO2 with an Unusual Oxygen
Packing Obtained by Exchange Reaction. Mater. Res. Bull. 1982, 17, 117-123.
(66)
H. B. Yahia, M. S., H. Kobayashi, Phase Transition Mechanisms in Li xCoO2 (0.25≤ x≤
1) Based on Group‐Subgroup Transformations. Chem. Mater. 2013, 25, 3687-3701.
(67)
M. D. Radin, S. H., M. Sina, C. Fang, H. Liu, J. Vinckeviciute, M. Zhang, M. S.
Whittingham, Y. S. Meng, A. Van der Ven, Narrowing the Gap between Theoretical and Practical
Capacities in Li-Ion Layered Oxide Cathode Materials. Adv. Energy Mater. 2017, 7, 1602888.
(68)
C. Daniel, D. M., J. Li, D. L. Wood, Cathode Materials Review. AIP Conf. Proc. 2014,
1597, 26-43.
(69)
L. Ma, M. N., J. Xia, J.R. Dahn, A Systematic Study on the Reactivity of Different Grades
of Charged Li[NixMnyCoz]O2 with Electrolyte at Elevated Temperatures using Accelerating Rate
Calorimetry. J. Power Sources 2016, 327, 145-150.
(70)
H. J. Noh, S. Y., C. S. Yoon, Y. K. Sun, Comparison of the Structural and Electrochemical
Properties of Layered Li[Ni xCoyMnz]O2 (x = 1/3, 0.5, 0.6, 0.7, 0.8 and 0.85) Cathode Material for
Lithium-Ion Batteries. J. Power Sources 2013, 233, 121-130.
(71)
A. Chakraborty, S. K., S. Kumar, B. Markovsky, D. Aurbach, M. Dixit, D. T. Major,
Layered Cathode Materials for Lithium-Ion Batteries: Review of Computational Studies on
LiNi1−x−yCoxMnyO2 and LiNi1−x−yCoxAlyO2. Chem. Mater. 2020, 32, 915-952.
(72)
A. Chakraborty, S. K., M. Dixit, D. T. Major, Review of Computational Studies of NCM
130
Cathode Materials for Li-ion Batteries. Isr. J. Chem. 2020, 60, 1-14.
(73)
C. Li, W. H. K., H. Xie, Y. Jiang, Z. Zhao, C. Zhu, Y. Xia, J. Zhang, K. Xu, D. Mu, F. Wu,
Inducing Favorable Cation Antisite by Doping Halogen in Ni-Rich Layered Cathode with
Ultrahigh Stability. Adv. Sci. 2019 6, 1801406.
(74)
K. Märker, P. J. R., C. Xu, K. J. Griffith, C. P. Grey, Evolution of Structure and Lithium
Dynamics in LiNi0.8Mn0.1Co0.1O2 (NMC811) Cathodes During Electrochemical Cycling. Chem.
Mater. 2019, 31, 2545-2554.
(75)
S. T. Myung, F. M., K. J. Park, C. S. Yoon, P. Lamp, S. J. Kim, Y. K. Sun, Nickel-Rich
Layered Cathode Materials for Automotive Lithium-Ion Batteries: Achievements and Perspectives.
ACS Energy Lett. 2017, 2, 196-223.
(76)
M. Yoshio, H. N., A Review of Positive Electrode Materials for Lithium-Ion Batteries.
Springer: New York 2009, 9-48.
(77)
M. Ménétrier, I. S., S. Levasseur, C. Delmas, The Insulator-Metal Transition upon Lithium
Deintercalation from LiCoO2: Electronic Properties and 7Li NMR Study. J. Mater. Chem. 1999, 9,
1135-1140.
(78)
S. Laubach, S. L., P. C. Schmidt, D. Ensling, S. Schmid, W. Jaegermann, A. Thißen, K.
Nikolowski, H. Ehrenberg, Changes in the Crystal and Electronic Structure of LiCoO 2 and LiNiO2
upon Li Intercalation and De-intercalation. Phys. Chem. Chem. Phys. 2009, 11, 3278-3289.
(79)
Y. Koyama, N. Y., I. Tanaka, H. Adachi, T. Ohzuku, Solid-State Chemistry and
Electrochemistry of LiCo1/3Ni1/3Mn1/3O2 for Advanced Lithium-Ion Batteries I. First-Principles
Calculation on the Crystal and Electronic Structures. J. Electrochem. Soc. 2004, 151, A1545A1551.
(80)
J. N. Reimers, J. R. D., Electrochemical and In Situ X-Ray Diffraction Studies of Lithium
Intercalation in Li xCoO2. J. Electrochem. Soc. 1992, 139, 2091-2097.
(81)
A. Van der Ven, M. K. A., G. Ceder, G. Kresse, J. Hafner, First-Principles Investigation of
Phase Stability in LiCoO2. Phys. Rev. B 1998, 58, 2975-2987.
(82)
H. Arai, S. O., Y. Sakurai, J. Yamaki, Reversibility of LiNiO 2 Cathode. Solid State Ion.
1997, 95, 275-282.
(83)
Y. Koyama, Y. M., I. Tanaka, H. Adachi, T. Ohzuku, Systematic Research on Insertion
131
Materials Based on Superlattice Models in a Phase Triangle of LiCoO2-LiNiO2-LiMnO2. I. FirstPrinciples Calculation on Electronic and Crystal Structures, Phase Stability and New
LiNi1/2Mn1/2O2 Material. J. Electrochem. Soc. 2004, 151, A1499.
(84)
N. Nitta, F. W., J. T. Lee, G. Yushin, Li-Ion Battery Materials: Present and Future. Mater.
Today 2015, 18, 252-264.
(85)
W. Liu, P. O., X. Liu, M. J. Lee, W. Cho, S. Chae, Y. Kim, J. Cho, Nickel-Rich Layered
Lithium Transition-Metal Oxide for High-Energy Lithium-Ion Batteries. Angew. Chem. Int. Ed.
2015, 54, 4440-4457.
(86)
J. Cho, T. J. K., Y. J. Kim, B. Park, High-Performance ZrO2-Coated LiNiO2 Cathode
Material. Electrochem. Solid-State Lett. 2001, 4, A159.
(87)
M. D. Radin, A. V. d. V., Simulating Charge, Spin, and Orbital Ordering: Application to
Jahn–Teller Distortions in Layered Transition-Metal Oxides. Chem. Mater. 2018, 30, 607-618.
(88)
P. He, H. Y., D. Li, H. Zhou, Layered Lithium Transition Metal Oxide Cathodes Towards
High Energy Lithium-Ion Batteries. J. Mater. Chem. 2012, 22, 3680-3695.
(89)
S. J. Hwang, H. S. P., J. H. Choy, G. Campet, Evolution of Local Structure around
Manganese in Layered LiMnO2 upon Chemical and Electrochemical Delithiation/Relithiation.
Chem. Mater. 2002, 12, 1818-1826.
(90)
Y. S. Horn, S. A. H., A. R. Armstrong, P. G. Bruce, R. Gitzendanner, C. S. Johnson, M.
M. Thackeray, Structural Characterization of Layered LiMnO 2 Electrodes by Electron Diffraction
and Lattice Imaging. J. Electrochem. Soc. 1999, 146, 2404-2412.
(91)
A. Chakraborty, M. D., D. Aurbach, D. T. Major, Predicting Accurate Cathode Properties
of Layered Oxide Materials using the SCAN meta-GGA Density Functional. npj Comput. Mater.
2018, 4, 60.
(92)
W. Choi, A. M., Comparison of Metal Ion Dissolutions from Lithium Ion Battery Cathodes.
J. Electrochem. Soc. 2006, 153, A1760.
(93)
A. R. Armstrong, R. G., A. D. Robertson, P. G. Bruce, The Intercalation Compound
Li(Mn0.9Co0.1)O2 as a Positive Electrode for Rechargeable Lithium Batteries. Chem. Commun.
1998, 1833-1834.
(94)
H. Sun, K. Z., Electronic Structure and Comparative Properties of LiNi xMnyCozO2 Cathode
132
Materials. J. Phys. Chem. C 2017, 121, 6002-6010.
(95)
M. H. Kim, H. S. S., D. Shin, Y. K. Sun, Synthesis and Electrochemical Properties of
Li[Ni0.8Co0.1Mn0.1]O2 and Li[Ni0.8Co0.2]O2 via Co-Precipitation. J. Power Sources 2006, 159,
1328-1333.
(96)
T. Ohzuku, Y. M., Layered Lithium Insertion Material of LiCo1/3Ni1/3Mn1/3O2 for Lithium-
Ion Batteries. Chem. Lett. 2001, 30, 642-643.
(97)
B. J. Hwang, Y. W. T., D. Carlier, G. Ceder, A Combined Computational/Experimental
Study on LiNi1/3Co1/3Mn1/3O2. Chem. Mater. 2003, 15, 3676-3682.
(98)
J. Choi, A. M., Role of Chemical and Structural Stabilities on the Electrochemical
Properties of Layered LiNi1/3Mn1/3Co1/3O2 Cathodes. J. Electrochem. Soc. 2005, 152, A1714.
(99)
R. Koerver, W. Z., L. de Biasi, S. Schweidler, A. O. Kondrakov, S. Kolling, T. Brezesinski,
P. Hartmann, W. G. Zeier, J. Janek, Chemo-Mechanical Expansion of Lithium Electrode Materials
- on the Route to Mechanically Optimized All-Solid-State Batteries. Energy Environ. Sci. 2018,
11, 2142-2158.
(100) J. K. Ngala, N. A. C., M. Ma, M. Mamak, P. Y. Zavalij, M. S. Whittingham, The Synthesis,
Characterization, and Electrochemical Behavior of the Layered LiNi 0.4Mn0.4Co0.2O2 Compound.
J. Mater. Chem. 2004, 14, 214-220.
(101) M. Ma, N. A. C., B. H. Toby, P. Y. Zavalij, M. S. Whittingham, Structural and
Electrochemical Behavior of LiMn0.4Ni0.4Co0.2O2. J. Power Sources 2007, 165, 517-534.
(102) J. Shu, R. M., L. Shao, M. Shui, K. Wu, M. Lao, D. Wang, N. Long, Y. Ren, In-Situ X-ray
Diffraction Study on the Structural Evolutions of LiNi 0.5Co0.3Mn0.2O2 in Different Working
Potential Windows. J. Power Sources 2014, 245, 7-18.
(103) D. Li, Y. S., M. Kageyama, K. Kobayakawa, Y. Sato, Structure, Morphology and
Electrochemical Properties of LiNi0.5Mn0.5-xCoxO2 Prepared by Solid State Reaction. J. Power
Sources 2005, 148, 85-89.
(104) S. Yang, X. W., X. Yang, Y. Bai, Z. Liu, H. Shu, Q. Wei, Determination of the Chemical
Diffusion Coefficient of Lithium Ions in Spherical Li[Ni0.5Mn0.3Co0.2]O2. Electrochim. Acta 2012,
66, 88-93.
(105) S. K. Jung, H. G., J. Hong, K. Y. Park, D. H. Seo, H. Kim, J. Hyun, W. Yang, K. Kang,
133
Understanding the Degradation Mechanisms of LiNi 0.5Co0.2Mn0.3O2 Cathode Material in Lithium
Ion Batteries. Adv. Energy Mater. 2014, 4, 1300787.
(106) S. M. Bak, E. H., Y. Zhou, X. Yu, S. D. Senanayake, S. J. Cho, K. B. Kim, K. Y. Chung,
X. Q. Yang, K. W. Nam, Structural Changes and Thermal Stability of Charged LiNi xMnyCozO2
Cathode Materials Studied by Combined In Situ Time-Resolved XRD and Mass Spectroscopy.
ACS Appl. Mater. Interfaces 2014, 6, 22594−22601.
(107) L. Liang, K. D., W. Lu, Z. Peng, Y. Cao, G. Hu, Synthesis and Characterization of LiNi 0.
6CoxMn0. 4-xO2
(x= 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3) with High-Electrochemical Performance for
Lithium-Ion Batteries. Electrochim. Acta 2014, 146, 207-217.
(108) J. H. Kim, K. J. P., S. J. Kim, C. S. Yoon, Y. K. Sun, A Method of Increasing the Energy
Density of Layered Ni-rich Li[Ni1-2xCoxMnx]O2 Cathodes (x = 0.05, 0.1, 0.2). J. Mater. Chem. A
2019, 7, 2694-2701.
(109) K. Min, K. K., C. Jung, S. W. Seo, Y. Y. Song, H. S. Lee, J. Shin, E. Cho, A Comparative
Study of Structural Changes in Lithium Nickel Cobalt Manganese Oxide as a Function of Ni
Content During Delithiation Process. J. Power Sources 2016, 315, 111-119.
(110) M. Dixit, B. M., F. Schipper, D. Aurbach, D. T. Major, Origin of Structural Degradation
During Cycling and Low Thermal Stability of Ni-Rich Layered Transition Metal-Based Electrode
Materials. J. Phys. Chem. C 2017, 121, 22628−22636.
(111) J. Yang, Y. X., Suppressing the Phase Transition of the Layered Ni-Rich Oxide Cathode
During High-Voltage Cycling by Introducing Low Content Li2MnO3. ACS Appl. Mater. Interfaces
2016, 8, 1297-1308.
(112) A. O. Kondrakov, H. G., K. Galdina, L. de Biasi, V. Meded, E. O. Filatova, G. Schumacher,
W. Wenzel, P. Hartmann, T. Brezesinski, J. Janek, Charge-Transfer-Induced Lattice Collapse in
Ni-Rich NCM Cathode Materials During Delithiation. J. Phys. Chem. C 2017, 121, 24381-24388.
(113) O. Breuer, A. C., J. Liu, T. Kravchuk, L. Burstein, J. Grinblat, Y. Kauffman, A. Gladkih,
P. Nayak, M. Tsubery, A. I. Frenkel, M. Talianker, D. T. Major, B. Markovsky, D. Aurbach,
Understanding the Role of Minor Molybdenum Doping in LiNi 0.5Co0.2Mn0.3O2 Electrodes: from
Structural and Surface Analyses and Theoretical Modeling to Practical Electrochemical Cells. ACS
Appl. Mater. Interfaces 2018, 10, 29608−29621.
134
(114) F. Schipper, M. D., D. Kovacheva, M. Talianker, O. Haik, J Grinblat, E. M. Erickson, C.
Ghanty, D. T. Major, B. Markovsky, D. Aurbach, Stabilizing Nickel-Rich Layered Cathode
Materials by a High-Charge Cation Doping Strategy: Zirconium-Doped LiNi0.6Co0.2Mn0.2O2. J.
Mater. Chem. A 2016, 4, 16073–16084.
(115) G. T. Park, H. H. R., N. Y. Park, C. S. Yoon, Y. K. Sun, Tungsten Doping for Stabilization
of Li[Ni0.90Co0.05Mn0.05]O2 Cathode for Li-Ion Battery at High Voltage. J. Power Sources 2019,
442, 227242.
(116) Aurbach, D., Studies of Aluminum-Doped LiNi0.5Co0.2Mn0.3O2: Electrochemical Behavior,
Aging, Structural Transformations, and Thermal Characteristics. J. Electrochem. Society, 2015,
162, A1014-A1027.
(117) Y. Huang, X. L., R. Yu, S. Cao, Y. Pei, Z. Luo, Q. Zhao, B. Chang, Y. Wang, X. Wang,
Tellurium Surface Doping to Enhance the Structural Stability and Electrochemical Performance
of Layered Ni-Rich Cathodes. ACS Appl. Mater. Interfaces 2019, 11, 40022-40033.
(118) L. Liu, K. S., N. Zhang, T. Yang, Improvement of High-voltage Cycling Behavior of
Li(Ni1/3Co1/3Mn1/3)O2 Cathodes by Mg, Cr, and Al Substitution. J. Solid State Electrochem. 2009,
13, 1381-1386.
(119) L. Q. Wang, L. F. J., H. T. Yuan, J. Guo, M. Zhao, H. X. Li, Y. M. Wang, Synthesis and
Electrochemical Properties of Mo-doped Li[Ni1/3Mn1/3Co1/3]O2 Cathode Materials for Li-Ion
Battery. J. Power Sources 2006, 162, 1367-1372.
(120) F. A. Susai, D. K., A. Chakraborty, T. Kravchuk, R. Ravikumar, M. Talianker, J. Grinblat,
L. Burstein, Y. Kauffmann, D. T. Major, B. Markovsky, D. Aurbach, Improving Performance of
LiNi0.8Co0.1Mn0.1O2 Cathode Materials for Lithium-Ion Batteries by Doping with MolybdenumIons: Theoretical and Experimental Studies. ACS Appl. Energy Mater 2019, 2, 4521−4534.
(121) M. D. Slater, D. K., E. Lee, C. S. Johnson, Sodium-Ion Batteries. Adv. Funct. Mater. 2013,
23, 947-958.
(122) S. T. Myung, Y. H., Y. K. Sun, Electrochemical Behavior and Passivation of Current
Collectors in Lithium-Ion Batteries. J. Mater. Chem. 2011, 21, 9891-9911.
(123) M. M. Thackeray, C. W., E. D. Isaacs, Electrical Energy Storage for TransportationApproaching the Limits of, and Going Beyond, Lithium-Ion Batteries. Energy Environ. Sci. 2012,
135
5, 7854-7863.
(124) J. Y. Hwang, S. T. M., Y. K. Sun, Sodium-Ion Batteries: Present and Future. Chem. Soc.
Rev. 2017, 46, 3529-3614.
(125) J. C. Pramudita, D. S., D. Goonetilleke, N. Sharma, An Initial Review of the Status of
Electrode Materials for Potassium-Ion Batteries. Adv. Energy Mater. 2017, 7, 1602911.
(126) P. Adelhelm, P. H., C. L. Bender, M. Busche, C. Eufinger, J. Janek, From Lithium to
Sodium: Cell Chemistry of Room Temperature Sodium-Air and Sodium-Sulfur Batteries. J.
Nanotechnol. 2015, 6, 1016–1055.
(127) M. M. Doeff, Y. P. M., S. J. Visco, L. C. Dejonghe, Electrochemical Insertion of Sodium
into Carbon. J. Electrochem. Soc. 1993, 140, L169-L170.
(128) V. L. Chevrier, G. C., Challenges for Na-Ion Negative Electrodes. J. Electrochem. Soc.
2011, 158, A1011-A1014.
(129) A. Eftekhari, Z. J., X. Ji, Potassium Secondary Batteries. ACS Appl. Mater. Interfaces 2017,
9, 4404−4419.
(130) X. Wu, D. P. L., X. Ji, Emerging Non-Aqueous Potassium-Ion Batteries: Challenges and
Opportunities. Chem. Mater. 2017, 29, 5031-5042.
(131) M. Born, R. O., Zur Quantentheorie der Molekeln. Ann. d. Phys. 1927, 389, 457-484.
(132) Hartree, D. R., The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part
I. Theory and Methods. Math. Proc. Cambridge Philos. 1928, 24, 89-110.
(133) Fock,
V.
V.,
Näherungsmethode
zur
Lösung
des
Quantenmechanischen
Mehrkörperproblems. Z. Phys. 1930, 61, 126-148.
(134) Slater, J. C., The Theory of Complex Spectra. Phys. Rev. 1929, 34, 1293-1322.
(135) P. Hohenberg, W. K., Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864-B871.
(136) W. Kohn, L. J. S., Self-Consistent Equations Including Exchange and Correlation Effects.
Phys. Rev. 1965, 140, A1133-A1138.
(137) J. P. Perdew, K. S., Jacob's Ladder of Density Functional Approximations for the
Exchange-Correlation Energy. AIP Conf. Proc. 2001, 577, 1-20.
(138) J. P. Perdew, A. Z., Self-Interaction Correction to Density-Functional Approximations for
Many-Electron Systems. Phys. Rev. B 1981, 23, 5048-5079.
136
(139) S. H. Vosko, L. W., M. Nusair, Accurate Spin-Dependent Electron Liquid Correlation
Energies for Local Spin Density Calculations: A Critical Analysis. Can. J. Phys. 1980, 58, 12001211.
(140) J. P. Perdew, Y. W., Accurate and Simple Analytic Representation of the Electrongas
Correlation Energy. Phys. Rev. B 1992, 45, 13244-13249.
(141) J. P. Perdew, W. Y., Accurate and Simple Density Functional for the Electronic Exchange
Energy: Generalized Gradient Approximation. Phys. Rev. B 1986, 33, 8800-8802.
(142) J.P. Perdew, K. B., M. Ernzerhof, Generalized Gradient Approximation Made Simple.
Phys. Rev. Lett. 1996, 77, 3865–3868.
(143) Perdew, J. P., Unified Theory of Exchange and Correlation Beyond the Local Density
Approximation. In Ziesche, P. & Eschrig, H. (eds.) Electronic Structure of Solids '91 1991, 17,
11-20.
(144) B. Hammer, L. B. H., J. K. Nørskov, Improved Adsorption Energetics within Density
Functional Theory using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B 1999, 59,
7413-7421.
(145) B. Himmetoglu, A. F., S. de Gironcoli, M. Cococcioni, Hubbard-Corrected DFT Energy
Functionals: The LDA+U Description of Correlated Systems. Int. J. Quantum Chem. 2014, 114,
14-49.
(146) J. Hubbard, B. H. F., Electron Correlations in Narrow Energy Bands. Proc. Math. Phys.
Eng. Sci. 1963, 276, 238-257.
(147) Hubbard, J., Electron Correlations in Narrow Energy Bands. II. Proc. Math. Phys. Eng. Sci.
1964, 277, 237-259.
(148) A. I. Liechtenstein, V. I. A., J. Zaanen, Density-Functional Theory and Strong Interactions:
Orbital Ordering in Mott-Hubbard Insulators. Phys. Rev. B 1995, 52, R5467-R5470.
(149) S. L. Dudarev, G. A. B., S. Y. Savrasov, C. J. Humphreys, A. P. Sutton, Electron-EnergyLoss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B 1998,
57, 1505-1509.
(150) J. Tao, J. P. P., A. Ruzsinszky, Accurate van der Waals Coefficients from Density
Functional Theory. PNAS 2012, 109, 18-21.
137
(151) Grimme, S., Density Functional Theory with London Dispersion Corrections. Wiley
Interdiscip. Rev. Comput. Mol. Sci. 2011, 1, 211-228.
(152) Grimme, S., Semiempirical GGA-Type Density Functional Constructed with a LongRange Dispersion Correction. J Comput. Chem. 2006, 27, 1787-1799.
(153) S. Grimme, J. A., S. Ehrlich, H. Krieg, A Consistent and Accurate ab initio Parametrization
of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys.
2010, 132, 154104.
(154) G. Kresse, J. F., Efficient Iterative Schemes for ab initio Total-Energy Calculations using
a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11186.
(155) G. Kresse, D. J., From Ultrasoft Pseudopotentials to the Projector Augmented-Wave
Method. Phys. Rev. B 1999, 59, 1758-1775.
(156) Blöchl, P. E., Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979.
(157) H. Jónsson, G. M., K. W. Jacobsen, Nudged Elastic Band Method for Finding Minimum
Energy Paths of Transitions. Classical and Quantum Dynamics in Condensed Phase Simulations
1998, World Scientific, 385.
(158) G. Henkelman, H. J., Improved Tangent Estimate in the Nudged Elastic Band Method for
Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978–9985.
(159) G. Henkelman, B. P. U., H. Jónsson, A Climbing Image Nudged Elastic Band Method for
Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901–9904.
(160) R. Dronskowski, P. E. B., Crystal orbital Hamilton populations (COHP): Energy-Resolved
Visualization of Chemical Bonding in Solids Based on Density-Functional Calculations. J. Phys.
Chem. 1993, 97, 8617−8624.
(161) V. L. Deringer, A. L. T. e., R. Dronskowski, Crystal Orbital Hamilton Population (COHP)
Analysis as Projected from Plane-Wave Basis Sets. J. Phys. Chem. A 2011, 115, 5461−5466.
(162) Tarascon, J. M., Is Lithium the New Gold? Nat. Chem. 2010, 2, 510.
(163) Tahil, W., The Trouble with Lithium. Meridian International Research 2007.
(164) P. K. Nayak, L. Y., W. Brehm, P. Adelhelm, From Lithium-Ion to Sodium-Ion Batteries:
Advantages, Challenges, and Surprises. Angew. Chem. Int. Ed. 2018, 57, 102-120.
(165) N. Yabuuchi, K. K., M. Dahbi, S. Komaba, Research Development on Sodium-Ion
138
Batteries. Chem. Rev. 2014, 114, 11636-11682.
(166) P. Bhauriyal, A. M., B. Pathak, Graphene-like Carbon−Nitride Monolayer: A Potential
Anode Material for Na- and K‑Ion Batteries. J. Phys. Chem. C 2018, 122, 2481-2489.
(167) S. Komaba, T. H., M. Dahbi, K. Kubota, Potassium Intercalation into Graphite to Realize
High-Voltage/High-Power Potassium-Ion Batteries and Potassium-Ion Capacitors. Electrochem.
Commun. 2015, 60, 172-175.
(168) C. K. Chan, H. P., G. Liu, K. McIlwrath, X. F. Zhang, R. A. Huggins, Y. Cui, HighPerformance Lithium Battery Anodes using Silicon Nanowires. Nat. Nanotechnol. 2008, 3, 31-35.
(169) M. H. Park, K. K., J. Kim, J. Cho, Flexible Dimensional Control of High-Capacity Li-IonBattery Anodes: From 0D Hollow to 3D Porous Germanium Nanoparticle Assemblies. Adv. Mater.
2010, 22.
(170) Y. Yang, S. L., X. Bian, J. Feng, Y. An, C. Yuan, Morphology- and Porosity-Tunable
Synthesis of 3D Nanoporous SiGe Alloy as a High-Performance Lithium-Ion Battery Anode. ACS
Nano 2018, 12, 2900-2908.
(171) W. Li, X. S., Y. Yu, Si-, Ge-, Sn-Based Anode Materials for Lithium-Ion Batteries: From
Structure Design to Electrochemical Performance. Small Methods 2017, 1, 1600037.
(172) M. Amato, M. P., S. Ossicini, SiGe Nanowires: Structural Stability, Quantum Confinement,
and Electronic Properties. Phys. Rev. B 2009, 80, 235333.
(173) S. Ciraci, I. P. B., Strained Si/Ge Superlattices: Structural Stability, Growth, and Electronic
Properties. Phys. Rev. B 1988, 38, 1835-1848.
(174) G. Katsaros, P. S., M. Stoffel, F. Fournel, M.Mongillo, V. Bouchiat, F. Lefloch, A. Rastelli,
O. G. Schmidt, S. De Franceschi, Hybrid Superconductor–Semiconductor Devices Made from
Self-Assembled SiGe Nanocrystals on Silicon. Nat. Nanotechnol. 2010, 5, 458-464.
(175) J. Wang, N. D., H. Zhang, J. Yu, D. Yang, Cu–Ge Core–Shell Nanowire Arrays as ThreeDimensional Electrodes for High-Rate Capability Lithium-Ion Batteries. J. Mater. Chem. 2012,
22, 1511-1515.
(176) J. Wang, N. D., Z. Song, H. Wu, H. Zhang, D. Yang, Synthesis of SiGe-Based ThreeDimensional Nanoporous Electrodes for High Performance Lithium-Ion Batteries. J. Power
Sources 2013, 229, 185-189.
139
(177) Y. Zhang, N. D., C. Xiao, S. Wu, Y. Chen, Y. Lin, J. Jiang, Y. He, D. Yang, Simple
Synthesis of SiGe@C Porous Microparticles as High-Rate Anode Materials for Lithium-Ion
Batteries. RSC Adv. 2017, 7, 33837-33842.
(178) J. Yu, N. D., J. Wang, H. Zhang, D. Yang, SiGe Porous Nanorod Arrays as HighPerformance Anode Materials for Lithium-Ion Batteries. J. Alloys Compd. 2013, 577, 564-568.
(179) W. Li, Y. Y., G. Zhang, Y. W. Zhang, Ultrafast and Directional Diffusion of Lithium in
Phosphorene for High-Performance Lithium-Ion Battery. Nano Lett. 2015, 15, 1691-1697.
(180) V. V. Kulish, O. I. M., C. Persson, P. Wu, Phosphorene as an Anode Material for Na-Ion
Batteries: A First-Principles Study. Phys. Chem. Chem. Phys. 2015, 17, 13921-13928.
(181) H. R. Jiang, W. S., M. Liu, L. Wei, M. C. Wu, T. S. Zhao, Boron Phosphide Monolayer as
a Potential Anode Material for Alkali Metal-Based Batteries. J. Mater. Chem. A 2017, 5, 672-679.
(182) Rao, D.; Zhang, L.; Meng, Z.; Zhang, X.; Wang, Y.; Qiao, G.; Shen, X.; Xia, H.; Liu, J.;
Lu, R., Ultrahigh energy storage and ultrafast ion diffusion in borophene-based anodes for
rechargeable metalion batteries. J. Mater. Chem. A 2017, 5, 2328-2338.
(183) V. Shukla, R. B. A., N. K. Jena, R. Ahuja, The Curious Case of Two Dimensional Si2BN:
A High-Capacity Battery Anode Material. Nano Energy 2017, 41, 251-260.
(184) H. Wang, M. W., X. Lei, Z. Tian, B. Xu, K. Huang, C. Ouyang, Siligraphene as a Promising
Anode Material for Lithium-Ion Batteries Predicted from First-Principles Calculations. Nano
Energy 2018, 49, 67-76.
(185) F. Li, Y. Q., M. Zhao, Germanium Sulfide Nanosheet: A Universal Anode Material for
Alkali Metal Ion Batteries. J. Mater. Chem. A 2016, 4, 8905-8912.
(186) A. Sannyal, Z. Z., X. Gao, J. Jang, Two-Dimensional Sheet of Germanium Selenide as an
Anode Material for Sodium and Potassium Ion Batteries: First-Principles Simulation Study.
Comput. Mater. Sci. 2018, 154, 204-211.
(187) A. Huang, X. S., S. Dong, Tin Monooxide Monolayer as Promising Anode Materials for
Recharge Ion Batteries. Int. J. Electrochem. Sci. 2017, 12, 10534-10541.
(188) C. S. Liu, X. L. Y., J. Liu, X. J. Ye, Theoretical Prediction of Two-Dimensional SnP3 as a
Promising Anode Material for Na-Ion Batteries. ACS Appl. Energy Mater. 2018, 1, 3850-3859.
(189) G. A. Tritsaris, E. K., S. Meng, E. Wang, Adsorption and Diffusion of Lithium on Layered
140
Silicon for Li-Ion Storage. Nano Lett. 2013, 13, 2258-2263.
(190) B. Mortazavi, A. D., G. Cuniberti, T. Rabczuk, Application of Silicene, Germanene, and
Stanene for Na or Li Ion Storage: A Theoretical Investigation. Electrochim. Acta 2016, 213, 865870.
(191) J. Zhu, U. S., Silicene for Na-Ion Battery Applications. 2D Mater. 2016, 3, 035012.
(192) G. Liu, X. L. L., M. S. Wu, B. Xu, C. Y. Ouyang, Comparison of the Stability of FreeStanding Silicene and Hydrogenated Silicene in Oxygen: A First Principles Investigation. J. Phys.:
Condens. Matter 2014, 26, 355007.
(193) G. Liu, S. B. L., B. Xu, C. Y. Ouyang, H. Y. Song, First-Principles Study of the Stability
of Free-Standing Germanene in Oxygen Atmosphere. J. Appl. Phys. 2015, 118, 124303.
(194) P. Jamdagni, A. K., A. Thakur, R. Pandey, P. K. Ahluwalia, Stability and Electronic
Properties of SiGe-Based 2D Layered Structures. Mater. Res. Express 2015, 2, 016301.
(195) A. Togo, I. T., First Principles Phonon Calculations in Materials Science. Scr. Mater. 2015,
108, 1-5.
(196) H. J. Monkhorst, J. D. P., Special Points for Brillonin-Zone Integrations*. Phys. Rev. B
1976, 13, 5188-5192.
(197) W. Tang, E. S., G. Henkelman, A Grid-Based Bader Analysis Algorithm Without Lattice
Bias. J. Phys.: Condens. Matter 2009, 21, 084204.
(198) E. Sanville, S. D. K., R. Smith, G. Henkelman, Improved Grid-Based Algorithm for Bader
Charge Allocation. J. Comput. Chem. 2006, 28, 899-908.
(199) G. Henkelman, A. A., H. Jonsson, A Fast and Robust Algorithm for Bader Decomposition
of Charge Density. Comput. Mater. Sci. 2006, 36, 354-360.
(200) X. Gonze, C. L., Dynamical Matrices, Born Effective Charges, Dielectric Permittivity
Tensors, and Interatomic Force Constants from Density-Functional Perturbation Theory. Phys.
Rev. B 1997, 55, 10355-10368.
(201) S. Karmakar, C. C., A. Datta, Two-Dimensional Group IV Monochalcogenides: Anode
Materials for Li-Ion Batteries. J. Phys. Chem. C 2016, 120, 14522-14530.
(202) H. Sahin, F. M. P., Adsorption of Alkali, Alkaline-Earth, and 3d Transition Metal Atoms
on Silicene. Phys. Rev. B 2013, 87, 085423.
141
(203) K. S. Novoselov, A. K. G., S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S.
V. Dubonos, A. A. Firsov, Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nat.
Lett. 2005, 438, 197-200.
(204) J. C. Garcia, D. B. d. L., L. V. C. Assali, J. F. Justo, Group IV Graphene- and GraphaneLike Nanosheets. J. Phys. Chem. C 2011, 115, 13242-13246.
(205) N. D. Drummond, V. Z., V. I. Falko, Electrically Tunable Band Gap in Silicene. Phys. Rev.
B 2012, 85, 075423.
(206) Z. Ni, Q. L., K. Tang, J. Zheng, J. Zhou, R. Qin, Z. Gao, D. Yu, J. Lu, Tunable Bandgap
in Silicene and Germanene. Nano Lett. 2012, 12, 113-118.
(207) Cahangirov, S.; Topsakal, M.; Aktu¨rk, E.; ahin, H. S.; Ciraci, S., Two- and OneDimensional Honeycomb Structures of Silicon and Germanium. PHYSICAL REVIEW LETTERS
2009, 102, 236804.
(208) G. C. Guo, D. W., X. L. Wei, Q. Zhang, H. Liu, W. M. Lau, L. M. Liu, First-Principles
Study of Phosphorene and Graphene Heterostructure as Anode Materials for Rechargeable Li
Batteries. J. Phys. Chem. Lett. 2015, 6, 5002-5008.
(209) A. Samad M. N. A. Alam, Y. H. S., First Principles Study of a SnS 2/Graphene
Heterostructure: A Promising Anode Material for Rechargeable Na Ion Batteries. J. Mater. Chem.
A 2016, 4, 14316-14323.
(210) A. Urban, D. H. S., G. Ceder, Computational Understanding of Li-Ion Batteries. npj
Comput. Mater. 2016, 2, 16002.
(211) X. Zhang, Z. Y., S. S. Wang, S. Guan, H. Y. Yang, Y. Yao, S. A. Yang, Theoretical
Prediction of MoN2 Monolayer as a High Capacity Electrode Material for Metal Ion Batteries. J.
Mater. Chem. A 2016, 4, 15224-15231.
(212) W. Wan, Q. Z., Y. Cui, E. Wang, First Principles Study of Lithium Insertion in Bulk Silicon.
J. Phys.: Condens. Matter 2010, 22, 415501.
(213) M. V. Koudriachova, N. M. H., S. W. de Leeuw, Effect of Diffusion on Lithium
Intercalation in Titanium Dioxide. Phys. Rev. Lett. 2001, 86, 1275-1278.
(214) M. Wagemaker, R. v. d. K., A. P. M. Kentgens, A. A. van Well, F. M. Mulder, Two Phase
Morphology Limits Lithium Diffusion in TiO2 (Anatase): A 7 Li MAS NMR Study. J. Am. Chem.
142
Soc. 2001, 123, 11454-11461.
(215) J. Wu, D. W., H. Liu, W. M. Lau, L. M. Liu, An ab initio Study of TiS3: A Promising
Electrode Material for Rechargeable Li and Na Ion Batteries. RSC Adv. 2015, 5, 21455-21463.
(216) T. Yu, Z. Z., L. Liu, S. Zhang, H. Xu, G. Yang, TiC3 Monolayer with High Specific
Capacity for Sodium-Ion Batteries. J. Am. Chem. Soc. 2018, 140, 5962-5968.
(217) S. Wang, B. Y., H. Chen, E. Ruckenstein, Popgraphene: a New 2D Planar Carbon Allotrope
Composed of 5–8–5 Carbon Rings for High Performance Lithium-Ion Battery Anodes from
Bottom-Up Programming. J. Mater. Chem. A 2018, 6, 6815-6821.
(218) M. Liu, A. K., Y. Liu, B. I. Yakobson, First-Principles Studies of Li Nucleation on
Graphene. J. Phys. Chem. Lett. 2014, 5, 1225-1229.
(219) A. M. G. Tapia, A. H. R., V. Barone, Lithium Adsorption on Graphene: From Isolated
Adatoms to Metallic Sheets. J. Chem. Theory Comput. 2012, 8, 1064-1071.
(220) J. Hu, B. X., S. A. Yang, S. Guan, C. Ouyang, Y. Yao, 2D Electrides as Promising Anode
Materials for Na-Ion Batteries from First-Principles Study. ACS Appl. Mater. Interfaces 2015, 7,
24016-24022.
(221) S. P. Ong, W. D. R., A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier,
K. A. Persson, G. Ceder, Python Materials Genomics (Pymatgen): A Robust, Open-Source Python
Library for Materials Analysis. Comput. Mater. Sci. 2013, 68, 314-319.
(222) M. K. Aydinol, A. F. K., G. Ceder, K. Cho, J. Joannopoulos, Ab initio Study of Lithium
Intercalation in Metal Oxides and Metal Dichalcogenides. Phys. Rev. B 1997, 56, 1354-1365.
(223) X. Lv, W. W., Q. Sun, L. Yu, B. Huang, Y. Dai, Sc2C as a Promising Anode Material with
High Mobility and Capacity: A First-Principles Study. ChemPhysChem 2017, 18, 1627-1634.
(224) Dahn, J. R., Phase Diagram of Li xC6. Phys. Rev. B 1991, 44, 9170-9177.
(225) Z. Yang, D. C., S. Kerisit, K. M. Rosso, D. Wang, J. Zhang, G. Graff, J. Liu, Nanostructures
and Lithium Electrochemical Reactivity of Lithium Titanites and Titanium Oxides: A Review. J.
Power Sources 2009, 192, 588–598.
(226) Y. Xie, Y. D. A., M. Naguib, Y. Gogotsi, M. W. Barsoum, H. L. Zhuang, P. R. C. Kent,
Prediction and Characterization of MXene Nanosheet Anodes for Non-Lithium-Ion Batteries. ACS
Nano 2014, 8, 9606-9615.
143
(227) D. Er, J. L., M. Naguib, Y. Gogotsi, V. B. Shenoy, Ti 3C2 MXene as a High Capacity
Electrode Material for Metal (Li, Na, K, Ca) Ion Batteries. ACS Appl. Mater. Interfaces 2014, 6,
11173-11179.
(228) Z. Liu, H. D., S. Zhang, W. Hu, F. Gao, A First-Principles Investigation of the ScO2
Monolayer as the Cathode Material for Alkali Metal Ion Batteries. J. Mater. Chem. A 2018, 6,
3171-3180.
(229) D. B. Putungan, S. H. L., J. L. Kuo, Metallic VS2 Monolayer Polytypes as Potential
Sodium-Ion Battery Anode via ab Initio Random Structure Searching. ACS Appl. Mater. Interfaces
2016, 8, 18754-18762.
(230) C. Liu, Z. G. N., G. Cao, Understanding Electrochemical Potentials of Cathode Materials
in Rechargeable Batteries. Mater. Today 2016, 19, 109-123.
(231) Abraham, K. M., How Comparable are Sodium-Ion Batteries to Lithium-Ion Counterparts?
ACS Energy Lett. 2020, 5, 3544-3547.
(232) H. Kim, J. C. K., S. H. Bo, T. Shi, D. H. Kwon, G. Ceder, K‐Ion Batteries Based on a P2‐
Type K0.6CoO2 Cathode. Adv. Energy Mater. 2017, 7, 1700098.
(233) K. J. Park, H. G. J., L. Y. Kuo, P. Kaghazchi, C. S. Yoon, Y. K. Sun, Improved Cycling
Stability of Li[Ni0.90Co0.05Mn0.05]O2 Through Microstructure Modification by Boron Doping for
Li-Ion Batteries. Adv. Energy Mater. 2018, 8, 1801202.
(234) L. Liang, W. Z., F. Zhao, D. K. Denis, F. Zaman, L. Hou, C. Yuan, Surface/Interface
Structure Degradation of Ni-Rich Layered Oxide Cathodes toward Lithium-Ion Batteries:
Fundamental Mechanisms and Remedying Strategies. Adv. Mater. Interfaces 2020, 7, 1901749.
(235) J. Choi, S. Y. L., S. Yoon, K. H. Kim, M. Kim, S. H. Hong, The Role of Zr Doping in
Stabilizing Li[Ni0.6Co0.2Mn0.2]O2 as a Cathode Material for Lithium-Ion Batteries. ChemSusChem.
2019, 12, 2439-2446.
(236) L. Wang, J. L., X. He, W. Pu, C. Wan, C. Jiang, Recent Advances in Layered
LiNixCoyMn1−x−yO2 Cathode Materials for Lithium Ion Batteries. J. Solid State Electrochem. 2009,
13, 1157-1164.
(237) K. J. Park, J. Y. H., H. H. Ryu, F. Maglia, S. J. Kim, P. Lamp, C. S. Yoon, Y. K. Sun,
Degradation Mechanism of Ni-Enriched NCA Cathode for Lithium Batteries: Are Microcracks
144
Really Critical? ACS Energy Lett. 2019, 4, 1394-1400.
(238) W. Liu, G. H., K. Du, Z. Peng, Y. Cao, Enhanced Storage Property of LiNi0.8Co0.15Al0.05O2
Coated with LiCoO2. J. Power Sources 2013, 230, 201-206.
(239) J. H. Kim, H. H. R., S. J. Kim, C. S. Yoon, Y. K. Sun, Degradation Mechanism of Highly
Ni-Rich Li[NixCoyMn1-x-y]O2 Cathodes with x > 0.9. ACS Appl. Mater. Interfaces 2019, 11,
30936−30942.
(240) W. Li, S. L., A. Manthiram, High-Nickel NMA: A Cobalt-Free Alternative to NMC and
NCA Cathodes for Lithium-Ion Batteries. Adv. Mater. 2020, 32, 202002718.
(241) B. Chu, S. L., L. You, D.a Liu, T. Huang, Y. Li, A. Yu, Enhancing the Cycling Stability of
Ni-Rich LiNi0.6Co0.2Mn0.2O2 Cathode at a High Cutoff Voltage with Ta Doping. ACS Sustainable
Chem. Eng. 2020, 8, 3082-3090.
(242) S. Hwang, S. M. K., S. M. Bak, B. W. Cho, K. Y. Chung, J. Y. Lee, W. Chang, E. A. Stach,
Investigating Local Degradation and Thermal Stability of Charged Nickel-Based Cathode
Materials through Real-Time Electron Microscopy. ACS Appl. Mater. Interfaces 2014, 6, 1514015147.
(243) J. L. Shi, R. Q., X. D. Zhang, P. F. Wang, W. G. Fu, Y. X. Yin, J. Xu, L. J. Wan, Y. G.
Guo, High-Thermal- and Air-Stability Cathode Material with Concentration-Gradient Buffer for
Li-Ion Batteries. ACS Appl. Mater. Interfaces 2017, 9, 42829-42835.
(244) Y. K. Sun, D. H. K., C. S. Yoon, S. T. Myung, J. Prakash, K. Amine, A Novel Cathode
Material with a Concentration- Gradient for High-Energy and Safe Lithium-Ion Batteries. Adv.
Funct. Mater 2010, 20, 485-491.
(245) Y. K. Sun, K. J. H., J. Prakash, K. Amine, Electrochemical Performance of Nano-sized
ZnO-Coated LiNi0.5Mn1.5O4 Spinel as 5 V Materials at Elevated Temperatures. Electrochem.
Commun. 2002, 4, 344-348.
(246) S. T. Myung, K. I., S. Komaba, Y. K. Sun, H. Yashiro, N. Kumagai, Role of Alumina
Coating on Li-Ni-Co-Mn-O Particles as Positive Electrode Material for Lithium-Ion Batteries.
Chem. Mater. 2005, 17, 3695-3704.
(247) S. K. Hu, G. H. C., M. Y. Cheng, B. J. Hwang, R. Santhanam, Cycle Life Improvement of
ZrO2-Coated Spherical LiNi1/3Co1/3Mn1/3O2 Cathode Material for Lithium Ion Batteries. J. Power
145
Sources 2009, 188, 564-569.
(248) S. U. Woo, C. S. Y., K. Amine, I. Belharouak, Y. K. Sun, Significant Improvement of
Electrochemical Performance of AlF3-Coated Li[Ni0.8Co0.1Mn0.1]O2 Cathode Materials. J.
Electrochem. Soc. 2007, 154, A1005-A1009.
(249) Fergus, J. W., Recent Developments in Cathode Materials for Lithium Ion Batteries. J.
Power Sources 2010, 195, 939-954.
(250) C. Liang, F. K., R. C. Longo, C. Zhang, Y. Nie, Y. Zheng, K. Cho, Site-Dependent
Multicomponent Doping Strategy for Ni-Rich LiNi1-2yCoyMnyO2 (y = 1/12) Cathode Materials for
Li-Ion Batteries. J. Mater. Chem. A 2017, 5, 25303-25313.
(251) F. Kong, C. L., R. C. Longo, D.-H. Yeon, Y. Zheng, J.-H. Park, S.-G. Doo, K. Cho,
Conflicting Roles of Anion Doping on the Electrochemical Performance of Li-Ion Battery Cathode
Materials. Chem. Mater. 2016, 28, 6942-6952.
(252) W. Zhao, L. Z., H. Jia, J. Zheng, D. Wang, J. Song, C. Hong, R. Liu, W. Xu, Y. Yang, J.
Xiao, C. Wang, J.-G. Zhang, Optimized Al Doping Improves Both Interphase Stability and Bulk
Structural Integrity of Ni-Rich NMC Cathode Materials. ACS Appl. Energy Mater. 2020, 3, 33693377.
(253) T. Weigel, F. S., E. M. Erickson, F. A. Susai, B. Markovsky, D. Aurbach, Structural and
Electrochemical Aspects of LiNi0.8Co0.1Mn0.1O2 Cathode Materials Doped by Various Cations.
ACS Energy Lett. 2019, 9, 508-516.
(254) F. Schipper, H. B., M. Dixit, E. M. Erickson, T. Weigel, M. Talianker, J. Grinblat, L.
Burstein, M. Schmidt, J. Lampert, C. Erk, B. Markovsky, D. T. Major, D. Aurbach, From Surface
ZrO2 Coating to Bulk Zr Doping by High Temperature Annealing of Nickel-Rich Lithiated Oxides
and Their Enhanced Electrochemical Performance in Lithium Ion Batteries. Adv. Energy Mater.
2018, 8, 1701682.
(255) S. Sivaprakash, S. B. M., Understanding the Role of Zr4+ Cation in Improving the
Cycleability of LiNi0.8Co0.15Zr0.05O2 Cathodes for Li Ion Rechargeable Batteries. J. Alloys Compd.
2009, 479, 561-568.
(256) S. Maintz, V. L. D., A. L. Tchougréeff, R. Dronskowski, Analytic Projection From PlaneWave and PAW Wavefunctions and Application to Chemical-Bonding Analysis in Solids. J.
146
Comput. Chem. 2013, 34, 2557−2567.
(257) S. P. Ong, V. L. C., G. Hautier, A. Jain, C. Moore, S. Kim, X. Ma, G. Ceder, Voltage,
Stability and Diffusion Barrier Differences between Sodium-Ion and Lithium-Ion Intercalation
Materials. Energy Environ. Sci. 2011, 4, 3680–3688.
(258) L. S. Cahill, S.-C. Y., A. Samoson, I. Heinmaa, L. F. Nazar, G. R. Goward, 6 Li NMR
Studies of Cation Disorder and Transition Metal Ordering in Li[Ni 1/3Mn1/3Co1/3]O2 using Ultrafast
Magic Angle Spinning. Chem. Mater. 2005, 17.
(259) E. Flores, P. N. k., U. Aschauer, E. J. Berg, Cation Ordering and Redox Chemistry of
Layered Ni-Rich LixNi1-2yCoyMnyO2: An Operando Raman Spectroscopy Study. Chem. Mater.
2020, 32.
(260) M. I. Aroyo, J. M. P.-M., C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov,
H. Wondratschek, Bilbao Crystallographic Server: I. Databases and Crystallographic Computing
Programs. Z. Kristallogr. − Cryst. Mater 2006, 221.
(261) E. Flores, P. N., E. J. Berg, In Situ and Operando Raman Spectroscopy of Layered
Transition Metal Oxides for Li-Ion Battery Cathodes. Front. Energy Res. 2018, 6, 1-16.
(262) E. Flores, N. V. t., P. Novák, U. Aschauer, E. J. Berg, Elucidation of Li xNi0.8Co0.15Al0.05O2
Redox Chemistry by Operando Raman Spectroscopy. Chem. Mater. 2018, 30, 4694−4703.
(263) Shannon, R. D., Revised Effective Ionic Radii and Systematic Studies of Interatomic
Distances in Halides and Chalcogenides. Acta Crystallogr. Sect. A 1976, 32, 751−767.
(264) U. H. Kim, L. Y. K., P. Kaghazchi, C. S. Yoon, Y. K. Sun, Quaternary Layered Ni-Rich
NCMA Cathode for Lithium-Ion Batteries. ACS Energy Lett. 2019, 4, 576−582.
(265) M. Aykol, S. K., C. Wolverton, van der Waals Interactions in Layered Lithium Cobalt
Oxides. J. Phys. Chem. C 2015, 119, 19053−19058.
(266) M. Dixit, B. M., D. Aurbach, D. T. Major, Unraveling the Effects of Al Doping on the
Electrochemical Properties of LiNi0.5Co0.2Mn0.3O2 using First Principles. J. Electrochem. Soc.
2017, 164, A6359-A6365.
(267) A. Van der Ven, G. C., Ordering in Li x(Ni0.5Mn0.5)O2 and its Relation to Charge Capacity
and Electrochemical Behavior in Rechargeable Lithium Batteries. Electrochem. Commun. 2004,
6, 1045–1050.
147
(268) H. Yu, Y. Q., M. Otani, D. Tang, S. Guo, Y. Zhu, H. Zhou, Study of the Lithium/Nickel
Ions Exchange in the Layered LiNi0.42Mn0.42Co0.16O2 Cathode Material for Lithium Ion Batteries:
Experimental and First-Principles Calculations. Energy Environ. Sci 2014, 7, 1068–1078.
(269) Y. H. Chen, J. Z., Y. Li, Y. F. Zhang, S. P. Huang, W. Lin, W. K. Chen, Effects of Doping
High-Valence Transition Metal (V, Nb and Zr) Ions on the Structure and Electrochemical
Performance of LIB Cathode Material LiNi0.8Co0.1Mn0.1O2. Phys. Chem. Chem. Phys. 2021, 23,
11528-11537.
(270) C. Liang, R. C. L., F. Kong, C. Zhang, Y. Nie, Y. Zheng, J. S. Kim, S. Jeon, S. Choi, K.
Cho, Obstacles Toward Unity Efficiency of LiNi 1-2xCoxMnxO2 (x = 0 ~ 1/3) (NCM) Cathode
Materials: Insights from ab initio Calculations. J. Power Sources 2017, 340, 217-228.
(271) H.
Maleki,
K.,
Sari,
X.
Li,
Controllable
Cathode–Electrolyte
Interface
of
Li[Ni0.8Co0.1Mn0.1]O2 for Lithium Ion Batteries: A Review. Adv. Energy Mater. 2019, 9, 1901597.
(272) L. Wang, T. M., G. Ceder, Oxidation Energies of Transition Metal Oxides within the
GGA+U Framework. Phys. Rev. B 2006, 73, 195107.
(273) R. Jung, M. M., F. Maglia, C. Stinner, H. A. Gasteiger, Oxygen Release and its Effect on
the Cycling Stability of LiNixMnyCozO2 (NMC) Cathode Materials for Li-Ion Batteries. J.
Electrochem. Soc. 2017, 164, A1361-A1377.
(274) J. Wandt, A. T. S. F., A. Ogrodnik, H. A. Gasteiger, Singlet Oxygen Evolution from
Layered Transition Metal Oxide Cathode Materials and its Implications for Lithium-Ion Batteries.
Mater. Today 2018, 21, 825-833.
(275) M. Dixit, H. E., R. Eitan, D. Aurbach, M. D. Levi, M. Kosa, D. T. Major, Classical and
Quantum Modeling of Li and Na Diffusion in FePO4. J. Phys. Chem. C 2015, 119, 15801–15809.
(276) A. Van der Ven, G. C., Lithium Diffusion in Layered Li xCoO2. Electrochem. Solid-State
Lett. 2000, 3, 301–304.
(277) J. Reed, G. C., A. Van Der Ven, Layered-to-Spinel Phase Transition in Li xMnO2.
Electrochem. Solid-State Lett. 2001, 4, A78-A81.
(278) J. Reed, G. C., Role of Electronic Structure in the Susceptibility of Metastable TransitionMetal Oxide Structures to Transformation. Chem. Rev. 2004, 104, 4513-4534.
(279) J. Bŕeger, Y. S. M., Y. Hinuma, S. Kumar, K. Kang, Y. Shao- Horn, G. Ceder, C. P. Grey,
148
Effect of High Voltage on the Structure and Electrochemistry of LiNi 0.5Mn0.5O2: A Joint
Experimental and Theoretical Study. Chem. Mater. 2006, 18, 4768-4781.
149
알칼리 금속 이온 배터리를 위한 2 차원 양극 및 니켈이 풍부한 층상
산화물 음극 재료의 제 1 원리 설계 및 조사
아리담 싼니얼
부산대학교 대학원 나노융합기술학과
요약
리튬 이온 배터리 (LIB)는 에너지 저장 시스템 (ESS) 및 전기 자동차 (EV)에서 뛰어난 성능으로
인해 큰 주목을 받고 있다. 그러나 높은 비용과 낮은 리튬 자원양으로 인하여 다른 배터리 시스템,
특히 나트륨 및 칼륨 이온 배터리 (NIB 및 KIB)를 개발하는 것이 중요하다. 높은 에너지 밀도와
이온전도성을 가지는 전극 소자를 최적화하는 것은 차세대 배터리 개발의 핵심 과제다. 이 논문의
목적은 밀도 범함수 이론 계산을 이용하여 LIB, NIB 또는 KIB 에 응용하기 위한 에너지 밀도가
높은 전극 재료를 개발하는 것이다. 기존의 흑연계 음극에 비해 실리콘 (Si), 게르마늄 (Ge)계
음극재는 에너지 밀도가 매우 높다. 그러나 이들 물질의 상용화는 금속 이온의 삽입-탈착
과정에서 과도한 부피 팽창으로 인해 걸림돌이 되고 있다. 최근에는 차세대 전지의 잠재적인
음극재로 고표면적의 2 차원 물질에 대한 관심이 높아지고 있다. 2 차원 Si, Ge 또는 Sn 은 LIB 및
NIB 용 흑연 양극보다 더 높은 비용량을 제공할 수 있다. Si 에 Ge 를 첨가하면 리튬의 확산도와
Si 의 전자 전도도를 더욱 향상시킬 수 있는 것을 확인했다. 이를 통해 LIB, NIB 또는 KIB 의 양극에
대해 SiGe 시트의 적용 가능성을 평가한다. 제 1 원리 계산을 통해 SiGe 시트는 평균 개방 회로
전압이 낮고 금속 이온의 확산성이 높으며 LIB, NIB 또는 KIB 에 대해 높은 이론적 용량을
150
제공한다는 것을 확인했다. 양극재의 구조와 화학적 조성은 현재 LIB 기술의 성능과 비용을 크게
좌우한다. Ni 함량이 80%인 Ni 이 풍부한 양극 재료인 LiNixCoyMn1−x−yO2 (NCM)는 400 W-h kg1
의 높은 에너지 밀도를 제공할 수 있지만 열 안정성이 낮고 용량이 급격히 감소하는 문제점이
있다. Ni 가 풍부한 NCM 의 구조적 안정성과 사이클링 성능을 크게 향상시키기 위한 양이온
도핑을 제안하였다. 본 연구에서는 Ni 가 풍부한 LiNi0.89Co0.055Mn0.055O2 (NCM-89) 음극 물질을
안정화하는데 있어 지르코늄 (+4) 또는 몰리브덴 (+6) 도핑의 역할을 조사하였다. 이 연구를 통해
Zr4+ 또는 Mo6+ 도핑이 층상-스피넬 상 전이를 억제하고 NCM-89 에서 산소 가스의 발생을
감소시켜 구조적 안정성을 향상시킬 수 있음을 확인했다. 우리는 이러한 연구가 차세대 배터리를
위한 고에너지 밀도 전극 재료의 합리적인 설계 및 개발을 이끌 것이라고 생각한다.
151
Acknowledgment
I would like to thank several people who helped me a lot in the past years. The experiences at
the Pusan National University are the most wonderful memories of my life. I greatly appreciate
the encouragement and help of my advisor, colleagues, family, and friends. The thesis contains
my major work for the doctoral study about the electrode materials of batteries. The works could
not be done without the passionate support of my advisor.
Firstly, I would like to sincerely and gratefully thank my thesis advisor, Prof. Joonkyung Jang
for his research instruction and inspiration. Prof. Joonkyung Jang devoted a lot to my research
work. I am very grateful for his precious reassurance and support that I can step into the battery
research and keep exploring the battery field by computational chemistry. I am greatly motivated
by his immense personality, which improves me to develop as an independent researcher. I value
his patience, kindness, and motivation to share his experience with me.
I appreciate several colleagues of Prof. Jang’s research group (MMCS), notably Dr. Ramesh
Kumar Chitumalla, Dr. Zhengqing Zhang, Dr. Srimai Chitumalla, Dr. Joyanta K. Saha, Dr. Bai
Liyi, Dr. Mengdi Zhao, Kisang Byun, Kiduk Kim, Seyong Choi, Jaeyoung Kim, and Bareera
Mehmood. They supported me a lot in my academic and personal affairs at Pusan National
University.
I would like to show gratitude to all the honorable members of my thesis evaluation committee
for their constructive discussions and important suggestions.
I acknowledge the funding of Brain Korea (BK 21+) provided by the Korea Research
Foundation.
Lastly, I am very grateful to my parents for their endless support over the past years. I am also
very thankful to my wife, for her support, inspiration, patience, and love.
Busan, Republic of Korea
February 2022
Arindam Sannyal
152