# Diffusion mechanism and electrochemical investigation of 1T phase Al-
MoS2@rGO nano-composite as a high-performance anode for sodium-ion batteries

Manish Kr. Singh  These authors contributed equally to this work Department of
Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016,
India  Jayashree Pati  These authors contributed equally to this work
Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New
Delhi-110016, India  Deepak Seth  Renewable Energy and Chemicals Group,
Department of Chemical Engineering, Indian Institute of Technology Delhi, Hauz
Khas, New Delhi-110016, India  Jagdees Prasad  Department of Physics, Indian
Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India  Manish
Agarwal  Computer Service Center, Indian Institute of Technology Delhi, Hauz
Khas, New Delhi- 110016 India  M. Ali Haider  Renewable Energy and Chemicals
Group, Department of Chemical Engineering, Indian Institute of Technology
Delhi, Hauz Khas, New Delhi-110016, India  Jeng-Kuei Chang  Department of
Materials Science and Engineering, National Yang Ming Chiao Tung University,
Hsinchu 30010 Taiwan Rajendra S. Dhaka<EMAIL_ADDRESS>Department
of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016,
India

###### Abstract

We report the electrochemical investigation of 5% Al doped MoS2@rGO composite
as a high-performance anode for sodium (Na)-ion batteries. The x-ray
diffraction (XRD), Raman spectroscopy and high-resolution transmission
electron microscopy characterizations reveal that the Al doping increase the
interlayer spacing of (002) plane of MoS2 nanosheets and form a stable 1T
phase. The galvanostatic charge-discharge measurements show the specific
capacity stable around 450, 400, 350, 300 and 200 mAhg-1 at current densities
of 0.05, 0.1, 0.3, 0.5 and 1 Ag-1, respectively. Also, we observe the capacity
retentions of 86% and 66% at 0.1 and 0.3 Ag-1, respectively, over 200 cycles
with a consistent Coulombic efficiency of nearly 100%. The cyclic voltammetry,
galvanostatic intermittent titration technique, and electrochemical impedance
spectroscopy are used to find the kinetic behavior and the obtained value of
diffusion coefficient falls in the range of 10–10 to 10–12 cm2s–1.
Intriguingly, the in-situ EIS also explains the electrochemical kinetics of
the electrode at different charge-discharge states with the variation of
charge transfer resistance. Moreover, the post cycling investigation using ex-
situ XRD and photoemission spectroscopy indicate the coexistence of 1T/2H
phase and field-emission scanning electron microscopy confirm the stable
morphology after 500 cycles. Also, the Na-ion transport properties are
calculated for 1T Al–MoS2@rGO interface and Al–MoS2–MoS2 interlayer host
structure by theoretical calculations using density functional theory.
Key words: sodium-ion batteries; anode materials; Al–MoS2@rGO; electrochemical
performance.

##  I  Introduction

The gradual depletion of fossil fuels and emission of greenhouse gases due to
their combustion, pave the way toward renewable energy resources like solar
and wind [1, 2, 3]. However, the conversion of energy through these resources
depend on several environmental factors and not ample to meet the energy
demands when required. Therefore, the present research is geared towards
energy storage and conversion devices for the restoration of renewable energy.
As we know, the lithium-ion batteries (LIBs) are one of the most efficient
technology among various energy storage devices on the subject of energy
density and power density [4, 5, 6]. The LIBs are virtually the heart of all
portable devices such as laptops, mobiles, as well as the electric vehicles
[7, 8, 9, 10]. However, due to the increasing demand with time, and the uneven
geographical and limited distribution of lithium across the world, the LIBs
are becoming more expansive and not affordable for common society [11, 12]. In
this context, sodium being widely and evenly distributed throughout as well as
its similar electrochemistry make the sodium-ion batteries (SIBs) potential
candidates for cost-effective and complementing the LIBs [13, 14]. However, it
is not that easy as there are great challenges, mainly coming from the larger
size of sodium (1.02 Å), which need to be resolved in order to design
efficient electrode materials with appealing characteristics for energy
storage applications [15, 16, 17, 18]. Among the bottlenecks, searching the
anode materials with high capacity, better rate capability, and excellent
cycle life are major challenges, because graphite cannot be used due to its
reactivity/thermodynamic unstability with sodium [20, 19].

At present, the SIB anode materials based on alloying and conversion are
widely used because of their high theoretical capacity [21, 22]. On the other
hand, the insertion based materials provide excellent cycle life, but with a
low specific capacity in SIBs [23]. The sodium-ion uptake is limited for
insertion based compounds due to their rigid frameworks [24]. However, the
metals and metalloids based materials have the ability of multiple sodium-ion
uptakes per single atom resulting in capacities ranging from 300 to 2000
mAhg-1 with operational voltages below 1 V vs Na/Na+ as anode in SIBs. Mostly,
group-15 (pnictogen), group-16 (chalcogen), and transition metals are used for
the production of alloying and conversion based complexes [14]. Among these,
the transition metal dichalcogenides (TMDs) and particularly sulfides are of
much importance because of their low cost, high capacity, and environment
friendly nature. Furthermore, the low activation energy between transition
metal and sulfur in TMDs facilitates the Na-ion migration during charging-
discharging, while its high theoretical capacity offers high energy density
for SIBs [25]. Particularly, the molybdenum disulfide (MoS2) with a two-
dimensional open framework has attracted considerable attention among TMDs due
to its structural flexibility and high theoretical capacity as an anode
material for both LIBs and SIBs [26] as well as Zn-ion batteries [27, 28]. The
MoS2 is found in three phases namely 1T, 2H, and 3R where the 1T phase shows
metallic nature with better ion and electron transport as compared to 3R and
2H phases because of two reasons [29, 30, 31, 32, 33, 34, 35, 36]: (i) it has
a distorted octahedral coordination structure which results in high electronic
conductivity as compared to 2H and 3R phases, (ii) another advantage is its
high hydrophilic nature which enables affinity of electrolytes [37, 38]. In
addition to these factors, its revealing electrochemical active sites and
large interlayer spacing (0.93 nm) with wide and fast ion-diffusion channels
make the 1T phase more suitable for Na+ ion storage [33].

In this line, one of the most effective ways to enhance the electrochemical
activity of MoS2 as an anode in SIBs, is to fabricate nano-composite of MoS2
particles through different synthesis routes to minimize the diffusion length
of Na-ion during sodiation/de-sodiation [39, 40]. Chen et al. developed a
scalable chemical vapor deposition method to prepare MoS2 deposited
electrospun carbon nanofiber hybrid to enhance the ionic conductivity, that
provides large contact area for electrolyte and prevent the MoS2 nanosheets
agglomeration. This anode material exhibited a reversible capacity of 198
mAhg-1 after 500 cycles at a current density of 1 Ag-1 [41]. In order to study
the effect of conductive carbon matrices, Sahu et al. synthesized modified 3-D
framework of MoS2@rGO hybrid through hydrothermal route, which was observed to
deliver high discharge capacities of 588 mAhg-1 and 501 mAhg-1 at current
densities of 100 and 500 mAg-1 with capacity retention of 98% and 92.3% after
80 and 250 cycles, respectively [42]. Here, the rGO nano-sheets act as
backbone to hold the MoS2 nano-plates during cracking of the material owing to
its high surface area and mechanical strength [42]. Also, one way to enhance
the electronic conductivity and to adhere the volume expansion, is to modify
MoS2 with different conductive carbon matrices like rGO, CNT, carbon-doped
with nitrogen and sulfur, etc. Additionally, the hetero-atom doping is also
another efficient approach for improved structural stability and boosting
volume expansion in MoS2 [36, 43, 44]. Li et al. proposed the improved cycling
stability of Co-doped 1T MoS2 than the pristine MoS2, where the introduction
of Co mitigates the volume expansion up to 52% during cycling [34].
Interestingly, a moderate Sn-doped 1T–2H MoS2 anode was reported by Zeng et
al., which provides a significant rate capability of 167 mAhg-1 at a current
rate of 15 Ag-1 with cycling retention of 320 mAhg-1 after 500 cycles at 1
Ag-1 [45]. Moreover, using first-principles calculations the sodium-ion
intercalation and diffusion mechanism are reported in different phases of
MoS2/graphene layer [46].

Here, we have synthesized MoS2, MoS2@rGO, CNT-MoS2@rGO, and 5% Al doped
MoS2@rGO composites by a simple hydrothermal method. We found that the doping
of Al ions enhance the interlayer spacing of (002) crystal plane of pure
MoS2@rGO nano-sheets and stabilize in a stable 1T phase, as confirmed by x-ray
diffraction (XRD), Raman spectroscopy and transmission electron microscopy
(TEM) measurements. Interestingly, we observe significant enhancement in the
electrochemical performance of Al doped MoS2@rGO, which exhibits the discharge
specific capacity of around 400 mAhg-1 at a current density of 100 mAg-1,
which found to be highly stable for more than 200 cycles even at faster
charge-discharge rates with about 100% Coulombic efficiency. The diffusive
behavior in the electrode material is also investigated through detailed
analysis of CV, EIS, and GITT data, and the diffusion coefficient was found to
be in the range of 10–10 to 10–12 cm2s–1. The post-cycling analysis performed
after 500 cycles at a current density of 500 mAg-1 through room temperature
XRD and FE-SEM measurements confirm the structural evolution and morphological
stability of the anode material. The photoemission results indicate the 1T
phase of pristine sample and coexistence of 1T/2H hetero-structure phase for
the cycled anode material. We have also employed density functional theory to
understand the Na-ion migration in the inter-layered structures of 1T phase
Al–MoS2@rGO.

##  II  Methods

2.1.1 Synthesis of graphite oxide (GO): The GO nano-sheets were synthesized by
chemical oxidation of bulk graphite powder using a slightly modified Stauden-
maier process [47]. In this typical procedure, 180 ml of concentrated H2SO4
was gradually combined with 90 ml of HNO3 in a 500 ml beaker while stirring
with an ice bath. We added 10 gms of graphite powder slowly into the prepared
solution with continuous stirring for 30 minutes. Then, 110 gms of KClO3 was
added for an extended time of 2–2.5 hrs. The ice bath was withdrawn, and the
solution was left to stir at ambient temperature for the next 5 days. The
obtained GO solution was first washed 7-8 times with DI water and then with
10% solution of hydrochloric acid to remove (SO4)2- ions and other impurities.
The resulting material was centrifuged 6-7 times in purified DI water. The
obtained GO powder was finally vacuum dried overnight at 80°C.

2.1.2 Synthesis of MoS2, MoS2@rGO, CNT-MoS2@rGO: The pure MoS2, composite of
MoS2@rGO and CNT-MoS2@rGO were prepared by a simple one step hydrothermal
method. For the preparation of pure MoS2 nano-sheets, 30 mmol of thiourea
[(NH2)2CS] and 1 mmol of ammonium molybdate tetrahydrate [(NH4)6Mo7O24·4H2O]
were homogeneously dispersed for 1 hr under the constant magnetic stirring in
40 ml of DI water. The obtained black colored homogeneous solution was
transferred into a 100 mL Teflon-lined stainless steel autoclave and heated at
a constant temperature of 220°C for 24 hrs. It was followed by cooling the
system to room temperature naturally so that the obtained black powder can be
washed with absolute ethanol and DI water several times. Then, the obtained
precipitate was dried in a vacuum oven at 65°C for 12 hrs and the resultant
powder of MoS2 was obtained. For the synthesis of MoS2@rGO and CNT-MoS2@rGO
composites, we use 140 mg of GO powder and 100 mg of CNT, which were dispersed
homogeneously in 40 ml of DI water with the help of sonication for 1.5 hrs.
After that, all the other steps were similar to the formation of pure MoS2.

2.1.3 Synthesis of Al-doped MoS2@rGO: The Al–MoS2@rGO nano-hybrids were
synthesized using a facile hydrothermal method. First we mix 140 mg (3.5
mg/mL) of GO powder and 12.70 mg of AlCl3.6H2O in 40 mL DI water under steady
ultra-sonication for 2 hrs at room temperature to make a homogenous suspended
solution. After that, 30 mmol (NH2)2CS and 1 mmol (NH4)6Mo7O24·4H2O were
slowly added to the above formed suspension along with constant stirring for 1
hr. A homogenous dark black solution was obtained, which then placed into a
Teflon-lined stainless-steel autoclave (100 mL). A box furnace was used to
heat the autoclave at 220°C for 24 hrs, and then cooled to room temperature
when the reaction time was completed. To remove the residual ions, the
obtained black precipitate was centrifuged at 3000 rpm for at least 4-5 times
using DI water and absolute ethanol. Finally, a black powder of Al–MoS2@rGO
was obtained by drying the washed product in a vacuum oven at 65°C for 12 hrs.

2.2 Structural and physical characterizations: To investigate the
crystallographic structure of the active material, we perform the x-ray
diffraction (XRD) measurements (Panalytical Xpert 3) with CuK$\alpha$
radiation (1.5406Å) in 2$\theta$ range of 5$\degree$ to 80$\degree$. We use
high-resolution transmission electron microscopy (HR-TEM) with a Tecnai G2-20
system, and field emission scanning electron microscope (FE-SEM) and energy
dispersive x-ray (EDX) using the Quanta 200 FEG system to study the
morphology, structure, elemental composition, and the distribution of elements
across the sample. The Raman spectra were recorded with 532 nm wavelength
laser using a Renishaw inVia confocal microscope having 2400 lines/mm grating
and 10mW power on the sample. The x-ray photoelectron spectroscopy (XPS) with
Al Kα source (1486.6 eV), from Thermo Fisher Scientific, was used to
investigate the core-level binding energy (BE) of different elements present
in the sample before and after cycling.

2.3 Coin-cell fabrication: The uniform slurry was prepared by taking
5%Al–MoS2@rGO as an active material, CNT as conductive carbon, and
polyvinylchloride (PVDF) binder in N-methylpyrrolidone (NMP) solvent in a
weight ratio of 8:1:1. The slurry was then coated on a copper foil using a
doctor blade method with active material mass loading about 1 mg cm-2 followed
by vacuum drying at 120°C overnight to evaporate the excess solvent and
moisture. The electrodes were cut and dried in vacuum before inserting them
into the glove box (UniLab Pro SP from MBraun). The CR2032 coin cells were
fabricated in Ar filled glove box under a controlled level of O2 and H2O (less
than 0.1 ppm). The Na foil was used as the counter and reference electrode.The
electrolyte used was 1 M NaPF6 in a mixture of ethylene carbonate (EC) and
diethyl carbonate (DEC) 1:1 (vol %) with 5 wt % fluoroethylene carbonate (FEC)
.

2.4 Electrochemical measurements: The galvanostatic charge-discharge (GCD)
profiles were obtained by using a Neware battery analyzer BTS400 in voltage
window 0.005–2.5 V (vs Na+/Na) at different current densities. The cyclic
voltammetry (CV) was conducted at different scan rates using a Biologic VMP-3
model in the same voltage range as in GCD measurements. The electrochemical
impedance spectroscopy (EIS) measurements were performed using a Biologic
VMP-3 model in the frequency range of 10 mHz to 100 kHz, and the ac voltage
amplitude was set to 10 mV at the open circuit voltage (OCV) state of the
cells.

2.5 Theoretical calculations:

A model MoS2@rGO interface is constructed with a monolayer of MoS2 in a
supercell size of 5$\times$4$\times$1 and 20 formula units, which are stacked
with a 5$\times$5$\times$1 supercell of rGO layer. On geometry optimization of
the structure, a sodium atom was introduced at one of the stable sites.
Similarly, 5% Al doped MoS2–MoS2 interlayer structure is constructed. The
transport of sodium-ion in these host materials interlayer is simulated using
plane wave basis set code of DFT as implemented in vienna ab initio simulation
package (VASP-6.2) [48]. A plane wave cut-off energy of 500 eV is considered
for the basis set expansion. The electron–ion core interactions are described
by gradient-corrected projector augmented wave (PAW) [49] pseudo potential
using Perdew-Burke-Ernzeerhof (PBE) exchange-correlation functional [50], to
solve the Kohn-Sham equations, which estimate the ground state energy of the
structures. A 2$\times$2$\times$2 gamma-centred k-point mesh is used for
Brillouin zone integration. The convergence criteria for energy and force are
kept at 10-6eV and 0.05 eV/Å, respectively, for structural optimization using
the conjugate gradient algorithm. To determine the minimum energy path (MEP)
for sodium-ion migration and calculation of energy barriers, the Cl-NEB
(climbing image nudge elastic band) method is implemented [51, 52]. The
optimized structure of Na-Al-MoS2 @rGO is taken as the initial state (IS) and
corresponding structure after sodium-ion migration to the next available site
is taken as the final state (FS) respectively, for transition state (TS)
calculations. We use eight linearly interpolated images along the MEP between
IS and FS. The convergence criteria considered for TS calculations are 10-5 eV
and 0.05 eV/Å for energy and forces respectively. The activation energy (Eact)
for sodium-ion migration is calculated as the difference in energy of the TS
and IS.

##  III  Results and discussion

3.1 Structural/morphological characterization:

Figure 1: (a) The XRD patterns and (b) the Raman spectra of MoS2, MoS2@rGO,
CNT-MoS2@rGO and Al–MoS2@rGO measured at room temperature. The HR-TEM images
of MoS2@rGO (c, d), CNT-MoS2@rGO (e, f), and Al-MoS2@rGO (g, h) with the
respective SAED patterns and the magnified views in the insets of (d, f, h).
The FE-SEM images in (i, j), and the EDX mapping of Al, Mo and S in (k-n) for
the Al-MoS2@rGO composite.

First the crystal structure of as prepared MoS2, MoS2@rGO, CNT-MoS2@rGO, and
Al–MoS2@rGO composites is investigated using the XRD measurements at room
temperature. The diffraction patterns of MoS2 MoS2@rGO and CNT-MoS2@rGO are
appeared to be very similar to each other having four major peaks located at
about 2$\theta$= 14.14°, 33.30°, 39.34°, and 59.06°, which are indexed to the
lattice planes (002), (100), (103), and (110) of the crystalline 2H phase of
MoS2, respectively [Fig. 1(a)]. The peak corresponding to (002) with an
interlayer spacing of about 6.3 Å signifies the crystalline multilayers of
pure MoS2 with hexagonal phase and the peak (100) depicts the stacking of Mo–S
edges in vertical planes as well as the number of S active ions in the edge,
as shown in Fig. 1(a). More importantly, the Al–MoS2@rGO composite exhibits a
new second order diffraction peak (004) located at about 2$\theta$ = 17.06°
and the (002) peaks shifted to lower 2$\theta$ = 9.1° value where the
calculated $d$ spacing found to be 5.2 and 9.3 Å, respectively. This confirms
the transformation from 2H phase to 1T phase with Al doping in MoS2@rGO
composite. This new phase has an increased interlayer spacing upon the
intercalation of Al and NH3/NH4+ ions released as by-products of thiourea used
as a reductant in the hydrothermal reaction [53, 54, 55]. Notably, the
negatively charged surface of GO inhibits the approaching process of MoO42-
precursors, which prevents the nucleation of MoS2 with proper spacing between
interlayers [42]. However, in the present case of Al doped MoS2@rGO, the
modification through Al3+ dopant increases the electrostatic interaction
between MoO42- and negatively charged GO surfaces. This phenomenon accelerates
the MoS2 nucleation and provides large space for NH4+ ions occupation at the
proper sites, which increases the interlayer distance along (002) direction
[56]. For example, the presence of NH4+ ions between the layers is evident
from the increment in the interlayer distance by about $\Delta$d=3 Å, which is
comparable to the size of NH4+ ions (3.75 Å) [56]. Additionally, no peaks
corresponding to any impurity were detected, which further indicating the
phase purity of the composites. We successfully prepared 1T phase by doping 5%
Al in MoS2@rGO composite having $d=$ 9.3 Å, which is considered to be a
potential anode for sodium-ion batteries [57, 58]. The Raman measurement are
performed to further explore the structure of all these samples, as shown in
Fig. 1(b). The spectra of MoS2, MoS2@rGO, and CNT-MoS2@rGO display intense E2g
and A1g peaks at about 380 and 405 cm-1, respectively, corresponding to in-
plane and out of plane vibration of S–Mo–S and peak at around 455 cm-1 is
correspond to longitudinal acoustic phonon mode [59]. In case of the
Al–MoS2@rGO, the E2g, A1g and peak corresponds to longitudinal acoustic phonon
mode are obtained at around 377, 403 and 453.5 cm-1, respectively.
Interestingly, the specific phonon modes J1 (147.8 cm-1), J2 (237 cm-1) and J3
(335.7 cm-1) of Al–MoS2@rGO corresponds to the formation of superlattice
structure and symolized as the characteristic peaks of metallic 1T phase.
Further, the broadening and weak intensity ratio of A1g to E2g modes also
suggest for the 1T phase due to the intercalated cations as well as that the
Mo is coordinated octahedrally in 1T phase [60]. The XRD and Raman studies
demonstrate that the Al doping drives the stabilization of 1T phase in
MoS2@rGO composite. Also, the defects due to disorder graphitic structures are
determined for these composites taking the intensity ratio of D and G bands
observed in the Raman spectra, as shown in Fig. 1 of [61].

Figure 2: The electrochemical measurements of Al–MoS2@rGO electrode: (a) the
cyclic voltammetry curves at a scan rate of 0.05 mVs-1 for first 3 cycles in a
voltage window of 0.005–2.5 V, (b) the GCD profiles at 50 mAg-1 for the first
10 cycles, (c) the rate capability test with the Coulombic efficiency, and (d)
the second cycle GCD profiles at each current densitiy.

Figs. 1(c-j) show the high-resolution TEM and FE-SEM images to analyze the
microscopic structure and the morphology of all the samples, MoS2@rGO, CNT-
MoS2@rGO, and Al–MoS2@rGO, respectively. In Fig. 1(c), the flowery
architecture is clearly visible due to the 3-D interconnected MoS2@rGO nano-
sheets, whereas the CNT wrapped MoS2 flakes are shown in the Fig. 1(e). These
nano architectures flower like morphology show porous structures, where rGO
nano-sheets are intercalated into MoS2 forming nano petals. The flexible and
porous rGO nano-sheets increase the electronic conductivity and active surface
area of the MoS2 composites due to the 3-D interconnected paths. The HR-TEM
images in Figs. 1(d, f, h) display some ripples in the nano-sheets with few
folded edges of MoS2, which can be seen as the dark contrast objects well
dispersed over a grey background of rGO nano-sheets. The curled edges also
reveal the lattice fringes having an inter-planar spacing of 6.3 Å, 6.3 Å and
9.5 Å corresponding to (002) crystal planes of the 2H phase of MoS2@rGO and
CNT-MoS2@rGO, and 1T phase of Al–MoS2@rGO, respectively, which are found to be
consistent with the XRD patterns. The SAED patterns in the insets of Figs.
1(d, f, h) display hazy and broad diffraction rings. The porous nano
architectures flowery like structure of Al–MoS2@rGO composite with its
relatively large interlayer distance provides a significant charge-storage
capacity by facilitating a large number of Na-ion intercalation and also
enhances the stability owing to the higher mechanical strength of rGO nano-
sheets [62]. The FE-SEM images in Figs. 1(i, j) are also conforming the flower
like morphology of Al–MoS2@rGO composite. In Figs. 1(k-n), the elemental
mapping images of Al–MoS2@rGO confirm the uniform distribution of Al, Mo and S
elements. The thermogravimetric analysis (TGA) confirms around 7wt% of the rGO
content in the sample, as shown in Fig. 2 of [61].

3.2 Cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD)
investigation:

In order to demonstrate the redox mechanism during sodium ion intercalation in
1T Al–MoS2@rGO host electrode, the CV measurement are performed at a scan rate
of 0.05 mVs-1 in the voltage window of 0.005–2.5 V. Fig. 2(a) displays first
few cycles of CV profile, which depicts three reduction (cathodic)
peaks/shoulders at 1.1, 0.66 and 0.005 V and three corresponding oxidation
(anodic) peaks at 1, 1.8 and 2.2 V. The first cathodic peak at 1.1 V involves
the formation of NaxMoS2 due to the Na-ion insertion into the MoS2 host
structure as well as the SEI formation [43, 63], whereas the peak at 0.66 V is
assigned to the conversion of Nax MoS2 resulting disintegration of MoS2 into
Mo particles embedding in Na2S matrix [64], see for example below equations:

$\mathrm{MoS}_{2}+x\mathrm{Na}^{+}+x\mathrm{e}^{-}\rightarrow\mathrm{Na}_{x}\mathrm{MoS}_{2}$
(1)
$\mathrm{Na}_{x}\mathrm{MoS}_{2}+(4-x)\mathrm{Na}^{+}+(4-x)\mathrm{e}^{-}\rightarrow
2\mathrm{Na}_{2}\mathrm{S}+\mathrm{Mo}$ (2)

Additionally, the third sharp cathodic peak at 0.005 V indicates the
intercalation of Na-ion between Na2S and Mo interface [35]. The oxidation peak
at 1.8 V is attributed to the reverse reaction of metallic Mo nano-grains and
Na2S as described below [42]:

$\mathrm{Mo}+2\mathrm{Na}_{2}\mathrm{S}\rightarrow
4\mathrm{Na}^{+}+\mathrm{MoS}_{2}+4\mathrm{e}^{-}$ (3)

whereas, a small anodic peak at 2.2 V represents the oxidation of Na2S to S or
polysulfide [65]. The subsequent CV curves of 1T Al–MoS2@rGO anode are almost
overlapped after the 1st cycle, implying a reversible sodiation/desodiation
process and electrochemical stability.

Figure 3: The GCD curves of Al–MoS2@rGO electrodes for selected cycles at a
current density of (a) 100 mAg-1, (b) 300 mAg-1, and (c) 500 mAg-1. (d) The
specific capacity during long cycling up to 200 cycles at different current
densities.

Fig. 2(b) shows the galvanostatic charge-discharge (GCD) curves in the voltage
window of 0.005–2.5 V for first 10 cycles at current density of 50 mAg-1. The
GCD curves show sloping features in the initial cycle and gradually
inconspicuous plateaus are observed in the subsequent cycles during sodiation
process. Notably, three plateaus are clearly visible in the initial sodiation
process, which are consistent with the CV scans, where the first plateau
located around 1.1 V denotes the insertion of Na-ions into the interlayers of
MoS2 (as discussed in equation 1), whereas the second plateau originates at
0.6 V corresponds to the conversion reaction involving the formation of
metallic Mo and Na2S matrix, and the third plateau at 0.4-0.005 V represents
the intercalation of Na-ion into the interface of Mo and Na2S, as marked in
Fig. 2(b). On the other hand, the sloping region at 1.9 V is clearly visible
in case of charge, representing the reversible oxidation of Mo to MoS2. We
find a significant enhancement in the electrochemical performance of
Al–MoS2@rGO composite due to its stable metallic 1T phase with a larger
interlayer spacing. The first discharge specific capacity is found to be 703
mAhg-1 at the current density of 50 mAg-1, which is higher than the
theoretical specific capacity of MoS2 (670 mAhg-1, this theoretical capacity
is evaluated on the basis of conversion reaction between one MoS2 molecule and
four sodium ions). The stable specific capacity retention of about 400 mAhg-1
was observed at 50 mAg-1 in the following cycles. The additional capacity
obtained in the first discharge cycle may be attributed to the formation of
SEI layer at the electrode-electrolyte interface, which is caused by
electrolyte reduction and also exposure to vacancy defects of rGO [66].

The remarkable rate performance of 1T Al–MoS2@rGO anode is presented in Figs.
2(c, d). Here, we observe high rate capability at different current densities
of 50, 100, 300, 500, 800 and 1000 mAg-1, approaching 446 mAhg-1 at 50 mAg-1
to a specific capacity of 169 mAhg-1 at 1000 mAg-1 and the corresponding GCD
profiles are shown in Fig. 2(d) for the second cycle at each current density.
The electrodes display 91% and 95% specific capacity retention as the current
density returns to 50 and 100 mAg-1 indicating high stability of the formed
SEI layer in FEC added electrolyte [35]. In order to elucidate the long
stability of the cell performance, Figs. 3(a, b, c) display the GCD profiles
for every 50th cycle at current densities of 100, 300 and 500 mAg-1,
respectively. The GCD curves in Fig. 3(c) are measured on the same cell after
5 cycles at 50 mAg-1 (shown in Fig. 3(a) of [61]). Moreover, the long cycling
performance of Al–MoS2@rGO anode is shown in Figs. 3(d) at different current
density over 200 cycles. The composite as an anode shows capacity retention of
86%, 66%, 58%, and 45% at the current densities of 100, 300, 500, and 1000
mAg-1 with almost 100% Coulombic efficiency, showing better stability at
slower current rates. The Al doping in MoS2@rGO lowers the activation barrier
of Na-ion for ease insertion/extraction into the host-structure by increasing
the interlayer distance, which improves the specific capacity and stability.
However, the slow capacity fading during the long cycling process, as shown in
Fig. 3 of [61], may involve some polarization effect, surface stability as
well as the transition-metal cation (Mo) dissolution leading the formation of
a thick SEI layer [67]. Here, the particle size, surface engineering by
decorating conducting materials as well as morphology control may help to
further improve the cyclic stability [68].

3.3 Analysis of cyclic voltammetry data:

Figure 4: (a) The cyclic voltammetry curves of Al–MoS2@rGO at different scan
rates ranging from 0.08 to 0.7 mVs-1 in a potential window of 0.005–2.5 V, (b)
the linear fit between peak current ip and square root of scan rate, and (c)
the linear fit between log(ip) and log($\nu$) for different scan rates, (d)
the linear fit between ip/$\nu$1/2 and $\nu$1/2 for different scan rates, (e)
the shaded area showing capacitive contribution at a scan rate of 0.2 mVs-1,
and (f) the capacitive and diffusive contributions for the total current
extracted at various scan rates.

Further, to explore the sodium-ion storage mechanism in Al–MoS2@rGO anode, the
kinetic behavior of the ions is studied by detailed CV measurements performed
at various scan rates ranging from 0.08 to 0.7 mVs-1 in a voltage window of
0.005–2.5 V, as presented in Fig. 4(a). The diffusion coefficient is
calculated using Randles-Sevcik equation as given below [69]:

$i_{p}=\left(2.69\times
10^{5}\right)AD^{\frac{1}{2}}Cn^{\frac{3}{2}}\nu^{\frac{1}{2}}$ (4)

where, $i_{p}$ is the peak current (mA), $A$ is the active surface area of the
electrode (cm2), $D$ is the diffusion coefficient (cm2s-1), C is the sodium
ion concentration in the bulk (mol cm-3), $n$ is the electron transferred in
the redox reaction and $\nu$ is the scan rate (mVs-1). In order to calculate
the value of $D$, we fit the oxidation/reduction peak current versus square
root of $\nu$ with linear behavior, as shown in Fig. 4(b) and the slope is
extracted. The $D$ values were found to be 1.60$\times$10-10 and
0.91$\times$10-10 cm2s-1 correspond to the anodic and cathodic peaks,
respectively. In the anodic case, the relatively fast Na-ion kinetics is due
to the disappearance of non-conductive Na2S [39, 65], which is also consistent
with the gradual decreasing trend of resistance in the EIS spectra during the
charging from 0.005 to 2.5 V [as shown later in Figs. 5(b, d)].

Figure 5: The gavanostatic charge-discharge profile of the (a) first cycle and
(c) second cycle with seven different points marked where the EIS measurements
are carried out. The in-situ Nyquist plot during the (b) first cycle and (d)
second cycle at different critical voltages ranging from OCV to fully
sodiated/discharged state (0.005 V), and then fully desodiated/charged state
(2.5 V), (e) the fitted Nyquist plots, with the corresponding equivalent
circuit, measured in fully discharged states after 1st, 5th, 10th, 20th and
50th cycles of GCD at 500 mAg-1, (f) the plot of the real part of impedance
versus the inverse square root of angular frequency in Warburg region at
different cycles obtained from data in (e).

Moreover, the current response of the electrode at different potentials can be
attributed to the surface-controlled and diffusion-controlled currents. The
net current obeys the following relation [70]:

$i=a\nu^{b}$ (5)

where $i$ is the net current in mA, $\nu$ (mVs-1) is the scan rate and $a$ and
$b$ are adjustable parameters. Here, we can identify different charge storage
mechanisms by the value of $b$, which normally varies between 0.5 to 1; for
example, $b=$ 0.5 represents a diffusion-controlled mechanism and $b=$ 1
represents a surface capacitive current. It is important to note that the
value of $b$ can be obtained by the slope of liner fitting of log(peak current
ip) versus log($\nu$), as shown in Fig. 4(c). The obtained values of $b$ for
anodic peaks (A) and cathodic peaks (C) are 0.98 and 0.82, respectively,
suggesting the pseudo-capacitive behavior of the Al–MoS2@rGO electrode, which
shows a faradic like charge storage mechanism with capacitor like
electrochemical response. This type of behavior is basically observed in nano-
structured MoS2, which enable the system to achieve high energy and power
densities [71]. Moreover, based on the previously reported analysis by Dunn
and his co-workers, the current response during voltage sweep can be written
as the sum of both capacitive and diffusive current, as given below [26, 72,
73]:

$i=k_{1}\nu+k_{2}\nu^{1/2}$ (6)

After rearranging the above equation, we can write as:

$i/\nu^{1/2}=k_{1}\nu^{1/2}+k_{2}$ (7)

where, k1 and k2 are the adjustable parameters and k1$\nu$ and k2$\nu^{1/2}$
show the contribution from capacitive and diffusive currents, respectively. To
calculate the value of k1 and k2, we perform the linear fit to the peak
current $i_{p}/\nu^{1/2}$ versus $\nu^{1/2}$ plot, as shown in Fig. 4(d). The
slope and intercept of the line give the values of k1 and k2, respectively.
The obtained values of k1 for anodic/cathodic peaks are found to be 0.90/0.51,
respectively. Using the values of k1 and k2, the calculated capacitive and
diffusive contributions are found to be 50% each, as plotted for the scan rate
of 0.2 mVs-1 in Fig. 4(e). The variation in the diffusive and capacitive
contributions (in percentage scale) for different scan rates is shown in Fig.
4(f), where 0.7 mVs-1 attributes lowest diffusion controlled current. The
increasing trend of capacitive contribution indicates that at higher scan
rates most of the charge is being stored by the surface redox reaction.

3.4 Electrochemical impedance spectroscopy:

Figure 6: The GITT measurements of Al–MoS2@rGO electrodes at a current density
of 500 mAg-1 in a voltage window of 0.005–2.5 V (a) during 4th cycle, and (b)
500th cycle, (c) a schematic labeling of different parameters of a single
titration curve before, during and after application of a current pulse for 5
min. The logarithimic diffusion-coefficient profile as a function of cell
voltage during charge–discharge for 4th cycle in (c), and for 500th cycle in
(d).

To reveal the electrochemical reaction kinetics of the 1T phase Al–MoS2@rGO
composite, the EIS measurements are performed at room temperature in the
frequency range of 100 kHz to 10 mHz at seven different states during the
first sodiation/de-sodiation cycle, as marked across the potential vs time
curve in Fig. 5(a). The corresponding Nyquist plot at OCV in Fig. 5(b)
consists of a compressed semicircle in the high and middle range of frequency
regions, which are attributed to the charge transfer resistance (Rct) and RSEI
at the electrode-electrolyte interface and the straight line in the low-
frequency region is related with the diffusion of sodium-ion in the bulk
region of electrode material. During the first discharge from 1.1 V to 0.005 V
(as shown in Fig. 5(b)), nearly two semicircles are evolved in the high and
mid frequency range, depicting the SEI formation and the intercalation of
sodium-ion in the MoS2 host matrix. Also, the non-conductive Na2S matrix due
to the constant volume change of the active material occurring during
discharging of the cell. The formation of nano-clusters like NaxMoS2 gradually
decreases the charge transfer resistance during de-sodiation. However, in the
case of charging, the semi-circle in the intermediate frequency range
disappears and a single semi-circle formed in the entire frequency region,
elucidating the dominance of charge transfer resistance over the SEI impedance
[74]. The subsequent decrement in the diameter of the semicircle, when
charging from 0.5 V to 2.5 V, shows the dissolution of the thick SEI layer.
Note that the first cycle is also complicated having some irreversible nature
possibly due to SEI formation and electrolyte reduction, which is also
reflected in Fig. 5(b) where the Rct found to decrease with discharge/charge
voltages. Therefore, to understand the reaction mechanism in more stable
state, we present the similar data on a fresh cell for the 2nd cycle in Figs.
5(c, d), which clearly show the increasing/decreasing trend in the Rct values
during discharge/charge process confirming the reversible mechanism from
second cycle.

Furthermore, the EIS measurements are performed to study the variation in Rct
values and diffusion coefficient after several cycles where the Nyquist plots
are shown in Fig. 5(e). The value of the physical components corresponding to
different regions can be calculated by fitting the equivalent circuit model
[43], as shown in the inset of Fig. 5(e) at different cycles. Here, the high
value of Rct in 1st cycle as compared to the 5th cycle is a bit unusual and
not consistent with the observed specific discharge capacity during the
initial cycles, as shown in Fig. 3(a) of [61]. This could be due to several
reasons like complex reaction at electrode/electrolyte interface; however, a
similar observation in refs. [75, 76] is said to be the activation process
during initial cycle(s). After the 5th cycle, the subsequent increase in the
Rct value determines the in-filtration of sodium-ion and the formation of high
activation barrier to hinder the sodium-ion kinetics. This phenomenon proves
that the surface stability of MoS2 decreases during cycling, which is
consistent with the long cycling measurement of MoS2, as shown in Fig. 3(d).
The diffusion coefficient of sodium-ion in the bulk of Al–MoS2@rGO electrode
can be calculated by the following equations [77]:

$D_{\mathrm{Na}^{+}}=R^{2}T^{2}/2n^{4}F^{4}\sigma_{\mathrm{w}}^{2}A^{2}C^{2}$
(8a) $Z^{\prime}=R_{s}+R_{ct}+\sigma\omega^{-0.5}$ (8b)

where $R$, $T$, $n$, $F$, $\sigma_{w}$, $A$, and $C$, are the universal gas
constant (8.314 J mol–1 $K^{-1}$), temperature, the number of electrons
exchanged in the reaction, the Faraday’s constant (96485 C mol-1), the Warburg
coefficient ($\ohm-s^{-1/2}$), the surface area of the electrode (1.13 cm2)
and the Na-ion concentration in the electrode material (mol-cm-3),
respectively. The Warburg coefficient $\sigma_{w}$ is related to the real part
of impedance (Z′) by equation 8, where Rs is the solution resistance. In order
to calculate the $D_{\mathrm{Na}^{+}}$, the real part of impedance is plotted
as a function of the inverse square root of angular frequency $\omega^{-1/2}$
in the Warburg region at different cycles and fitted linearly as shown in Fig.
5(f). The values of the apparent sodium diffusion coefficient are found to be
in the range from 0.18$\times$10-11 to 1.84$\times$10-11 cm2s-1.

3.5 Galvanostatic intermittent titration technique (GITT) investigation:

The chronopotentiometry based GITT measurements were performed on the
electrode to demonstrate the structural evolutions and the origin of the
electrochemical kinetics during the Na-ion insertion/extraction process. Figs.
6(a, b) elucidate the overall potential response profiles as a function of
time at 4th cycle and 500th cycle, respectively, and are consistent with the
galvanostatic charge-discharge curves. The GITT measurements were carried out
by first charging the cells with a current density of 500 mAg-1 to maximum
cut-off voltage for a short duration of 5 min, which was followed by a
relaxation period of 30 min to reach a steady-state value (Es), then the same
condition was repeated to discharge the cells up to the minimum voltage. To
calculate the diffusion coefficient under thermodynamic equilibrium
conditions, the Fick’s second law of diffusion is simplified by using the
following equation with some assumptions [78].

$\displaystyle D_{Na^{+}}=\frac{4}{\pi\tau}\left[\frac{mV_{\rm
M}}{MA}\right]^{2}\left[\frac{\Delta E_{s}}{\tau(\Delta
E_{t}/d\sqrt{\tau})}\right]^{2}$ (9)

where, $\tau$=L2/D${}_{Na^{+}}$, L is the diffusion length of sodium ion
(thickness of the electrode), VM (cm${}^{3}mol^{-1}$) is the molar volume of
Al–MoS2@rGO composite, which is deduced using the equation “NA*V${}_{unit}/Z$”
(here NA is the Avogadro’s number, Vunit is the volume of a unit cell and $Z$
is the number of unit cells). The m(gm) and M(gm mol-1) are the mass and
molecular weight of Al doped MoS2, respectively, $A$ is the active surface
area between the electrode and electrolyte, $\Delta$Es and $\Delta$Et are the
changes in steady-state voltage after the OCV stand of 30 min, and the
transient change in voltage due to the current pulse after excluding the IR
drop, respectively, as depicted in Fig. 6(c). Here, the molar volume is
assumed to be constant with the variation of the state of charge (SOC) for
diffusion coefficient calculation. The insets of Figs. 6(a, b) shows a linear
relationship between the variation of cell voltage and the square root of time
($\tau$1/2), which is used as a fact to simplify the equation 9, and that can
be written as below:

$\displaystyle
D_{Na^{+}}=\frac{4}{\pi\tau}\left[\frac{m_{B}V_{M}}{M_{B}A}\right]^{2}\left[\frac{\Delta
E_{s}}{\Delta E_{t}}\right]^{2};\tau=L^{2}/D_{Na^{+}}$ (10)

The Na-ion diffusion coefficient profiles as a function of cell voltage during
charge and discharge processes for 4th and 500th cycles are shown in Figs.
6(d, e), respectively. In the case of discharge process, the diffusion
coefficient of Na+ gradually decreases, showing a gradual increment of over-
potential during insertion of sodium ions into Al–MoS2@rGO host. However, the
charging process shows a stable profile, elucidating lower potential barriers
for sodium-ions. The diffusion coefficient profile for 500th cycle, as
demonstrated in Fig. 6(e) represents slightly slow diffusion of Na-ions in the
host structure, i.e., diffusion coefficient is somewhat lower than the 4th
cycle. These results are consistent with the long cycling data in Fig. 3,
where there is a gradual degradation in capacity after 200 cycles. The minimum
in the profile depicts the phase transition points, leading to strong
interactions between sodium-ion and the host matrix.

3.6 Post cycling XRD and FESEM:

The post-cycling tests are carried out to investigate the effect of cycling on
the structure and morphology of the extracted active material. We have
dismantled the cell after 500 cycles at a current density of 500 mAg-1 and
washed the electrode with DEC to retrieve the active material.

Figure 7: (a) The XRD pattern and (b) the corresponding FE-SEM image of
extracted active material from the cell after 500 cycles at a current density
of 500 mAg-1.

Fig. 7(a) depicts the XRD pattern, which shows the peaks located at 14° and
33.3° that are attributes to the (002) and (100) planes, indicating the
crystalline nature of the MoS2 after cycling. The (220) peak at 39 ∘ (JCPDS
No.03-0933) reflects the existence of Na2S due to the incomplete reaction
after cycling [39] and some peaks at around 43° and 51° are observed from the
Cu-foil [35]. The shifting of (002) peak towards higher 2$\theta$ suggests for
a structural transformation of some percentage of 1T phase to 2H phase in the
active material, which can be the primary cause of capacity fading after long
cycling. The corresponding FE-SEM image is shown in Fig. 7(b) where the
morphology of the active material indicates no cracking and discontinuity in
the structure, which attributes to the corresponding capacity retention of the
composite at 500 mAg-1 after long cycling.

3.7 X-ray photoemission spectroscopy study:

Figure 8: The Mo 3$d$, S 2$p$ and C 1$s$ core-level XPS spectra of Al–MoS2@rGO
pristine sample (a–c) as well as powder extracted from electrode after long
cycling (d–f), respectively.

We use x-ray photoelectron spectroscopy (XPS) to investigate the electronic
structure of Al–MoS2@rGO pristine sample as well as after long cycling. In
Fig. 8(a), the Mo 3$d$ core-level of pristine sample consists of two spin-
orbit coupled peaks 3$d$5/2 and 3$d$3/2 at the binding energies around 228.8
eV and 231.8 eV, respectively, which are consistent and confirm the presence
of Mo in 4+ oxidation state [33, 77, 79]. The de-convoluted peaks that
detected around 232.1 eV and 235 eV could be related to MoO3 or MoO42-, which
are found during the decomposition of Mo precursor (NH4)6Mo7O24·4H2O in the
hydrothermal synthesis [80]. Also, we can clearly observe S 2$s$ core-level at
binding energy (BE) of 225.8 eV, which originate from the sulfide species
[81]. In case of the S 2$p$ spectrum of pristine sample, as shown in Fig.
8(b), there are two intense peaks at BEs around 161.4 and 162.4 eV denoting
the S 2$p_{3/2}$ and S 2$p_{1/2}$ doublet, respectively, of the S2- oxidation
state. The peak located at 168.5 eV can be assigned to the sulfate groups
[82]. The C 1$s$ core-level of pristine sample is displayed in Fig. 8(c) where
the most intense peak at 284.6 eV indicates the C-C boning, and the peaks
located at 286 eV and 288.7 eV can be ascribed to the oxygenated functional
groups C-O and C=O, respectively, which show the intercalative mixing of rGO
and MoS2 [80].

More importantly, we perform the XPS measurements (ex-situ) of anode powder
that was extracted from the electrode after long cycling, which reveal the
presence of both 1T and 2H phases of MoS2 due to the transition reaction
mechanism in 1T–MoS2 after long cycling. Note that the Mo 3$d$ orbitals of
trigonal prismatically co-ordinated 2H–MoS$2$ splits in to three degenerate
energy levels forming (i) $d_{z^{2}}$, (ii) $d_{xy}$ \+ $d_{x^{2}-y^{2}}$ and
(iii) $d_{yz}$ \+ $d_{xz}$ due to crystal field splitting and there is a
finite energy gap of $\mathtt{\sim}$1 eV between the first two orbital sets.
Moreover, the two Mo $d$ electrons fill the lower $d_{z^{2}}$ orbital,
indicating the semi-conducting behavior of 2H–MoS2. However, in case of
1T–MoS2, there are two degenerate energy levels namely, (i) $d_{xy}$ \+
$d_{yz}$ \+ $d_{xz}$ and $d_{z^{2}}$ \+ $d_{x^{2}-y^{2}}$ due to the
octahedral co-ordination and having two un-paired electrons in the lower (dxy
\+ dyz \+ dxz) orbitals make the 1T–MoS2 metallic [83, 84]. The more
conductive nature of 1T–MoS2 helps to enhance the electro-chemical kinetics
due to fast electron transfer process as compared to the 2H–MoS2. The
intercalation of sodium-ions during cycling form the stable 2H phase and
metastable 1T phase due to the charge transfer from alkali metal atoms to the
MoS2 nano-sheets. Fig. 8(d) depicts the Mo 3$d$ spectrum of cycled material,
where the co-existence of both 1T (octahedral) and 2H (trigonal) phases in the
nano-sheets forming a 2D in-plane 1T/2H hetero-structure is clearly visible.
The evolution of a peak at 227.8 eV gives a clear evidence of the presence of
Mo 3$d_{5/2}$, which is formed during the conversion reaction of NaxMoS2 [85].
According to the composition, the cycled material consists of Na2MoO4, 1T–MoS2
and 2H–MoS2. Moreover, the Mo6+ always exist in both pristine and cycled
material indicating the formation of MoO42- where the Na2MoO4 acts as a
protective sheath and provides stability during long cycling [85]. Further,
the S 2$p$ core-level of cycled anode material is shown in Fig. 8(e), which
indicates the evolution of a pair of new peaks (at 162.2 eV and 163.2 eV for
the doublet 2$p_{3/2}$ and S 2$p_{1/2}$, respectively). These components are
consistent with the presence of 2H phase after long cycling and observed a
shift of 0.8 eV towards higher BE as compared to the peaks of 1T–MoS2 (at
161.4 and 162.4 eV) phase [86]. Moreover, the Al 2$p$ core-level of cycled
material is found to be at 74.5 eV BE, see Fig. 4 of [61], which indicates the
bonding between Al and S in the anode material. Fig. 8(f) shows the C 1$s$
core-level spectrum of the cycled anode material where there is no shift in
the peak positions as compared to the pristine material, indicating no change
in oxidation state and stable nature of rGO. The evolution of mixed 1T/2H
phase after long cycling affects the electrochemical performance owing to the
formation of less conductive 2H–MoS2 phase [87], which is compatible with the
long cycling results in Fig. 3.

3.8 Theoretical results and discussion:

Figure 9: (a) The top view of sodium atom (blue) at 2H site in the host Al
(purple) doped 1T–MoS2@rGO structure where grey hexagonal block shows the
coordination of sodium with MoS2 having Mo (cyan), S (yellow), C (black), O
(red) and H (white). (b) The front view of optimized structure of sodium-ion
intercalation in layered 1T phase of Al–MoS2@rGO interface, where the sodium-
ion activation barrier is visible. (c) The sodium-ion migration (blue-white-
red) pathways in 1T Al–MoS2@rGO interlayer and the activation barrier of
sodium-ion along the migration path.

Finally, using density functional theory (DFT) we investigate the Na-ion
migration in 1T phase of Al–MoS2@rGO interface and Al–MoS2–MoS2 interlayer
host structures. We consider a monolayer MoS2 supercell by cleaving a layer
from the primitive unit cell of MoS2. The unit cell of 1T-MoS2 has one formula
unit with hexa-coordinate geometry corresponding to the
$\mathrm{P}\overline{3}\mathrm{~{}m}1$ space group [88]. Here the boing of Al
and S is considered based on the XPS measurements, which are consistent with
the observation in ref. [89] that the Al bonded with S atoms when doped in
MoS2. Also, the DFT calculations have further confirmed a greater stability of
Al doping at the Mo site, which is bonded with the S atoms [90, 91], as shown
in Fig. 9(a). The rGO is modelled in a supercell with approximately similar
lattice parameters to that of MoS2 supercell. The optimised structures are
considered for the formation of layered 1T-MoS2 at rGO layer with the initial
interspace distance (distance between a carbon atom of rGO and its nearest S
atom of MoS2 layer) of 3.5 Å. Here, the layering of Al–MoS2 bulk and rGO is
formed as an extended layer, one above the other with slight difference in the
lattice parameters of individual structures but, the binding energy of this
system is comparable with that of MoS2/graphene interface, after the geometry
optimisation of the structure [46]. This initial interspace distance is used
for the optimization of 1T–MoS2@rGO as the stable configuration, which is
similar to the one obtained in MoS2/graphene structure [92]. In order to
introduce the sodium-atom in the structure, four different sites are available
as explored by Massaro and co-workers on sodium-ion intercalation in the host
MoS2/graphene interface, which were explained as hollow-edge, hollow-hollow,
top-edge and top-hollow where the sodium could be introduced between
MoS2-graphene layer. Interestingly, the calculated sodium-ion intercalation
energy ($\Delta$$E$int) is to be the same and all these sites are considered
stable sites for sodium atoms [46]. In the present work, the sodium-ion is
introduced on structural optimization of Al–MoS2/rGO composite at the hollow-
hollow site, which comprised of one of the four sites mentioned above, see
Fig. 9(a). The intercalation energy of sodium-ion at these sites is calculated
by using the equation [$\Delta$$E$int = $E$Na@site – $E$site – $E$Na]. The
sodium sites have intercalation energy of -87.61 kJ/mol (= –0.908 eV), which
is comparable to that of MoS2/graphene and considered a stable site for sodium
atom in the host Al-MoS2@rGO structure. The optimized structure of 1T
Al–MoS2@rGO interface is shown in Fig. 9(b).

Moreover, the sodium-ion migration is performed along the $x-$axis for
migration distances corresponding to 0–2 Å and 2–4 Å where the reference is
considered as the initial ($x=$ 0) position of sodium-ions at the hollow-
hollow site, as represented in Fig. 9(a). An estimate for sodium-ion
diffusivity is obtained using an Arrhenius type fit [93]
$\mathrm{D}_{\mathrm{Na^{+}}}=\mathrm{D}_{0}\exp\left(-E_{act}/k_{B}T\right)$,
where D0 = $a^{2}$$v$, $a=$ sodium-ion migration length, $v=$ phonon frequency
($\sim$1013 Hz) [52], Eact = activation energy, kB is the Boltzmann constant
and $T$ is the temperature. At 300 K (kBT = 0.0265 eV), the activation
energies of sodium-ion are calculated as $\sim$57.9 kJ/mol and $\sim$40.3
kJ/mol in 1T Al–MoS2@rGO interface for $a=$ 0–2 Å and $a=$ 2–4 Å,
respectively. For the comparison, we have shown the activation energy values
of un-doped 1T phase of MoS2/rGO composite, which are found to be $\sim$68.3
kJ/mol and $\sim$50.2 kJ/mol for $a=$ 0–2 Å and $a=$ 2–4 Å, respectively. This
suggests that the Al doped 1T phase have lower energy barrier as compared to
the un-doped system. From the calculated activation energies using DFT, the
corresponding diffusion coefficient of sodium-ions (D${}_{Na^{+}}$) are
estimated as $\sim$10-13 and $\sim$10-10 cm2/s, respectively, which are
comparable with the experimental values and indicate the faster diffusion of
sodium-ion in the doped system. Note that the DFT simulations suggest that the
sodium-ion activation energies vary from $\sim$40.3 kJ/mol to $\sim$57.9
kJ/mol with respect to the sodium-ion migration in 1T phase Al–MoS2@rGO
interface system and corresponding fits for D${}_{Na^{+}}$ may vary from
$\sim$10-10 cm2/s to $\sim$10-13 cm2/s. For the second model, the 1T phase
Al–MoS2–MoS2 interlayer, a similar procedure is followed to study the sodium-
ion migration. The interlayer distance (between two Mo atoms along $c-$axis)
of 9.3 Å is considered for DFT calculations, similar to the distances
indicated in the experiment. The activation energies for sodium-ion migration
are estimated as $\sim$49.8 kJ/mol to $\sim$59.6 kJ/mol, respectively for the
aforementioned initial migration distances, i.e., from $a=$ 0–2 Å to $a=$ 2–4
Å. Fig. 9(c) shows the pathways of sodium-ion along the $x-$direction in the
structure. The corresponding D${}_{Na^{+}}$ values are estimated in the range
of $\sim$10-11–10-13 cm2/s, which suggests that sodium-ion transport is
enhanced when moving from bulk to 2D layered structure [94].

##  IV  Conclusion

The 1T phase of 5% Al doped MoS2@rGO was synthesized successfully through the
hydrothermal route, which resulted in the larger interlayer distance of around
0.93 nm and the morphological studies confer the 3-D nano-flower-like
architecture of the composite. This composite material as an anode for SIBs
has displayed the first discharge specific capacity of about 764 mAhg-1 with a
reversible capacity retention of 383 mAhg-1 over 10 cycles at a current
density of 50 mAg-1. We observed capacity retention of 86%, 68%, 58%, and 45%
at current densities of 100, 300, 500, and 1000 mAg-1 respectively, when the
composite electrode was cycled over 200 cycles for stability test. The CV,
EIS, and GITT analyses are performed to explore the sodium ion storage and
diffusion mechanism in the composite host material. The calculated diffusion
coefficient was found to be in the range of 10–10–10–12 cm2s–1 depending on
the respective parameter of the experiment. The enhanced electrochemical
performance of 1T phase Al–MoS2@rGO composite is attributed to the
collaborative effect of enlarged interlayer distance and larger electronic
conductivity, which facilitate the storage of sodium ions and electron
transportation. These results further motivate to explore 1T phase of 2D
layered material as anode for sodium-ion batteries. The ex-situ XPS study
confirm the presence of both 1T and 2H phases in the anode material, which
reflects the small capacity fading after long cycling. The sodium-ion
activation energies for migration in the layered 1T phase Al–MoS2@rGO
interface and Al–MoS2–MoS2 interlayer host structure are estimated using DFT.

##  V  Acknowledgments

This work and setting-up the research facilities for sodium-ion battery
project at IIT Delhi are financially supported from DST through “DST–IIT Delhi
Energy Storage Platform on Batteries” (project no. DST/TMD/MECSP/2K17/07) and
from SERB-DST through core research grant (file no.: CRG/2020/003436). Manish,
Jayashree and Jagdees thank MHRD, UGC, and DST (DST/TMD/MECSP/2K17/07),
respectively for the fellowship. RSD and JKC thank IIT Delhi (IRD no.
MI02186G) and NCTU, Taiwan, for the financial support through M-FIRP project.
We thank IIT Delhi for providing research facilities for sample
characterization (XRD and Raman scattering at the physics department, and FE-
SEM and HR-TEM at CRF). The authors would like to acknowledge high performance
computing (HPC) facility for all the computational work at IIT Delhi.

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