- The author investigated anode materials for lithium-ion batteries through density functional theory calculations. - They found that the hexagonal site is the most stable position for lithium ion adsorption on graphene and silicene. - Calculations showed that silicon's volume expansion increases significantly with higher lithium ion concentration, reaching up to 400%. - Creating a composite of silicon and tin reduced silicon's volume expansion, improving its potential as a lithium-ion battery anode material.

1. Abridgment of master’s thesis
I have completed my dual degree course (B.Tech – M.Tech) in the discipline of Nanoscience
and Nanotechnology at Centre for Converging Technologies, Jaipur, India. To accomplish
this degree I worked on a project entitled as “ab inito investigation of anode materials for Li-
ion battery”.
Exigency of battery:
Increasing global energy demand, the limited supply of fossil fuels and mandates to
minimize CO2 emissions has increased demand for alternative energy sources such as nuclear
energy, wind power, solar cells and tidal power. The trend to adopt clean and renewable
energy is increasing around the world and requires innovative research of the chemistry and
physics of materials. Batteries and supercapacitors are two kinds of typical electrochemical
energy storage devices which can be used as alternate energy source.
Li-ion battery:
1. Due to high cyclability its life time is long
2. Low self discharging
3. These batteries are less hazardous because of used electrode materials
Theoretical investigations:
 In the present work I have worked on a composite of silicon and tin (anode) to reduce
volume expansion of anode materials (silicon shows ~400% volume expansion).
 I have calculated volume expansion of silicon anode with increasing concentration of
Li ion in silicon
 Determination of most stable site for Li ion adsorption on graphene (2D layer of
carbon) and its specific capacity.
Computational details:
Present work is performed using first-principles calculations within the framework of Kohn-
Sham density functional theory (DFT) along with projected augmented wave (PAW) pseudo
-potentials. PBE is used as exchange correlation functional, as implemented in Vienna ab
initio simulation package (VASP). The relaxation process continues until forces are below
0.01 eV/Ă.
Adsorption site for Li ion on graphene:
Graphene: Graphene is a at monolayer of carbon atoms tightly packed into a two dimen-
sional (2D) honeycomb lattice. One of the most useful property of graphene is that it is a zero
overlap semimetal with very high electrical conductivity.
Stability of graphene: I considered a cluster (N= 2, 4, 8. 16) of carbon atom and calculated
total and binding energies of systems.

2. Total energy of clusters:
S.No No of carbon
atoms
Total energy(eV) Energy per
atom(eV)
1 2 -18.4714 -9.2357
2 4 -36.9034 -9.2258
3 8 -73.7588 -9.2281
4 16 -147.5290 -9.2205
Table1: Total energy of clusters
Binding energy of clusters:
S.No No of carbon
atoms
Binding
energy(eV)
Energy per
atom(eV)
1 2 0.0015 0.00075
2 4 0.1162 0.02905
3 8 0.2843 0.03553
4 16 0.6742 0.04213
Table2: Binding energy of clusters
From table1 it can be seen that total energy of systems (clusters) is decreasing with increasing number
of carbon atom which favours stability of system. From table2 it also can be seen that binding energy
of system is increasing with increasing number of carbon atoms.
Stable adsorption site for Li ion on graphene:
To determine stable adsorption site for Li ion on graphene sheet, some cases were taken under
consideration. Which are as follows:
Hexagonal: In this configuration Li atom was placed on top of hexagon of graphene
sheet.
Bond Center: In this Li atom was placed on bond of C-C atoms.
Top of Carbon: In this con_guration Li atom was placed on top of carbon atom.
Total energy of systems corresponding to different Li adsorption site (shown in figure):
S.No Adsorption site Total enery(eV)
1 Hexagonal -143.8282
2 Bond center -143.7121
3 Top of carbon atom -143.8084

3. Table3: Total energy of systems corresponding to different Li adsorption site
Li ion on hexagonal Li ion bond center Li ion top of carbon atom
Table3 shows that system has minimum energy when Li ion was placed on hexagonal site of
graphene sheet. Thus we can remark that hexagonal site is most favourable site for Li ion
adsorption. I also calculated the binding energy of systems.
 Similarly, I calculated the stable site for Li ion on silicene (2D layer for silicon) and found
that hexagonal site is most stable (energetically favourable ) site for Li ion.
Specific capacity of graphene based anode:
Specific capacity is the amount of charge that can be stored in a material per unit of volume.
Specific capacity = N * F / Atomic weight
N = No of Li ion transfer during reaction i.e. effective number
F = Faraday Constant
Specific capacity of graphene = 1 * 96485/6 * 12.01 C/mol * amu
= 1 * 96485 * 1000 / 6 * 12.01 * 3600 mAh/g
= 371.93 mAh/g
Volume expansion of silicon with increasing concentration of Li ion:
Recently graphite is material which is successfully used as anode material for lithium ion
battery because graphite has high theoretical specific capacity (372 mAh/g). But it could not
accomplish increasing demand of portable electronic device, thus over few decades engineers
are trying to replace graphite by some other material that helps to increase capacity of lith
-ium battery without any disaster. Silicon, a well known material that can be used as anode
for the next generation of Li ion batteries and has a high theoretical specific capacity (4200
mAh/g) because it adsorbs 4.4 Li per atom.
Single Li dopant in silicon:
Stable site for Li atom in silicon:

4. To find most stable site, Li atom was inserted at different site such as hexagonal (Hex),
tetrahedral (Td), Bond center and substitutional. Total and binding energy was calculated to
find most stable (energetically favourable) site in silicon.
Total energy for different nonequivalent sites:
S.No Position / sites Total energy (eV)
1 Tetrahedral -349.5716
2 Hexagonal -349.0041
3 Bond center -347.0801
4 Substitutional -341.8063
Table4: The total energies of single Li in silicon
Binding energy for different nonequivalent sites:
Binding energy is the energy required to separate a whole system into parts.
Mathematically, binding energy can be written as follows:
Eb = ESi + nELi - ELi-Si
S.No Position / sites Total energy (eV)
1 Tetrahedral 1.3947
2 Hexagonal 0.8360
3 Bond center -1.094
4 Substitutional -6.367
Table5: The binding energies of single Li in silicon
From above total and binding energies calculation we can say tetrahedral site (see figure
below) is most stable site for lithium ion adsorption in silicon.
Tetrahedral site for Li atom adsorption in silicon
As above mentioned tetrahedral site is most stable site for Li ion adsorption in silicon. Thus
tetrahedral site is being taken under consideration.
Different doping concentration of Li ions in silicon :
Two Li atoms were inserted into 64 silicon atoms which were located on the tetrahedral site.
Further I have changed the distance between these two lithium atoms and I calculated binding

5. energy. As distance increases between Li atoms, simultaneously repulsion force decreases
due this binding energy of system increases as mention in diagram below.
Binding energy of systems with increasing distance between Li atoms
Volume Expansion:
Silicon undergoes upto 400% volume expansion after full lithiation (Li4.4Si). This happens
due to weak Si-Si bond compared to C-C bond as well as it also depends on alloying mech
-anism. It has been known that the large volume change of Si during Li (de)insertion makes
stable cycling very difficult to achieve. A stress is generated within active material due to the
large volume expansion that leads to fracture and capacity fading
No. Of Li atoms Distance between Li
atoms (Angstrom )
%Volume
expansion
1 0 100.30
2 2 100.68
2 4 100.66
2 6 100.64
2 7 100.63
8 Nearest Td sites 103.22
Table6: Volume expansion of silicon with increasing concentration of Li atoms on
Td sites
Volume expansion increases as number of Li atoms increases in supercell. Above table
indicate that volume expansion increases as number of Li atoms increases in super -cell. This
can be overcome using Si and Sn composites.
Band structure of pure silicon and after lithiation (Li at Td site)
Pure silicon Silicon after lithiation (Li at Td site)

6. In above figure electronic band structure of pure silicon and Li atom on Td sites are shown.
From figure we can see that when Li is introduced, the shape of band structure does not
change but the Fermi level (fermi energy) is moved to the bottom of conduction band
Position/ site Fermi energy
Pure silicon 5.606
Tetrahedral 6.427
Table7: The Fermi energy of bulk silicon , Li atom on Td site and Li atom on Hex site
which indicates that the Li-doped Si material is approaching to metal.
Silicon-Tin Composites:
In this section a composites of Si and Sn is created to reduce volume expansion of silicon as
well as to over come growth of dendrites of Sn. I started with pure silicon (64 silicon atom in
super cell) and further all silicon atoms are replaced by tin atom one by one. In this process I
found a transition point of Si and Sn from Si35Sn29 to Si23Sn41.
Energy variation with increasing concentration of Sn
From above configurations Si64-xSnx three geometry are considered x = 13, 26, 51. In each
geometry a Li atom was placed on Td position and volume expansion was calculated.
Configuration No of Li atoms %Volume
expansion
Si51Sn13 1 100.43
Si48Sn26 1 99.56
Si13Sn51 1 99.34
Table8: Volume expansion of silicon with increasing concentration of Li atoms on Td sites
It can be compared from table (6) and (8) that volume expansion is reducing as Sn
concentration is increases in silicon system.
Conclusions:
 Hexagonal site is the most stable (energetically favourable) site for Li ion adsorption
on graphene and silicene

7.  Volume expansion (upto 400%) of silicon increases which was measured by varying
distance between Li ions in silicon.
 As concentration of Li ion increases in silicon, its Fermi level start moving towards
conduction band i.e. metallic characters increases.
 Volume expansion in silicon anode can be reduced by making composite of silicon
and tin.
Note: References of above work are properly cited in my thesis.