X-doped Graphene Interaction with Anodic Material LIBs HAMID REZA JALILIAN

The structures of graphite carbonadoes and hexagonal boron nitride or h-BN, parent materials for carbonadoes and boron nitride nano-compounds are quite similar. The measured reversible Li+ capacities of X-G// (h-BN)// X-G (X=Be, B, N) in theanode materials are extremely improved compared to the graphite structures in the based anodes. In this study Boron nitride sheet has been localized inside twoX-graphene electrodes as an option to enhance electrochemical ratio.Additionally, we have found the structure of G-X/(h-BN)n/X-G can beforimproving the capacities and electrical transports in the C-BN sheets of LIBs. In addition, the BN sheet modified and designed of X-G/ (h-BN)/X-G structures provide a strategyto improvethe yields of BN-G-sheet of anodes. X-G/h-BN/X-G could also be assembled into free standing electrode of any binder (current collector), which will causes for increasing specific energies and densities for the batteries design. Keyword: Graphene, Doping, Anode lithium, Ion battery, LIBs.


INTRODUCTION
The carbona does such as graphite are layered materials composed of hexagonal lattices sheets; graphite 1,2 is including of carbon atoms at all direction in the lattice points, while the h-BN is consist of alternating atoms from boron and nitrogen respectively.The lattice constants for graphite and h-BN are 2.46 Å and 2.50 Å repectively 1,2 .In other side, layered BN is transparent and is an insulator 2,3 compare to graphite.The layers of h-BN are arranged as boron atoms in one layer which are located directly 2 on the top of nitrogen 2 atoms in a neighboring section and vice versa 3 .In graphite structures, stacking 3 is slightly different 2 whilehexagons are offset 2 and cannot lie on the top of each other so interlayer distances can be consider similar: 3.35 Å for graphite 1  Recently, the theoretical approaches have been presented the band structures 3 of alone layer of graphite and h-BN whilefor a layer of graphite which called graphene, 2 bands cross each other at the Fermi 3 energies.For this matter, graphene is a semimetal 4 .In contrast graphene, for a alayer of the h-BN, equivalent 4   In 1842, Balmain 5 sensitized-BN as reaction products via boric-oxide and potassium cyanide 5 through1 atmosphere pressure.Then, various methods have been reported through h-BN and r-BN which formed under ambient 5 pressure and c-BN has been synthesized from h-BN via high pressure and high temperatures.It is notable that w-BN is prepared from h-BN via high pressure at room temperature 6 .
The discovery of amazing reversible, lowvoltage 7 Li-intercalation carbonaceous 8 materials, Sony Company realized the commercialization 7 of xC6/Li 1-x CoO2 cells in 1991 7 .Lithium ion batteries (LIBs) are widely used in small gridstorage systems.
LIBs generally consist of positive and negative electrodes including a conducting electrolytewhere store electrical energy in the two electrodes 8 in the form of Li-intercalation 8 compounds.Electrodes, separator, and electrolyte are the main components of the LIB where the anode plays an essential role in the performance of these devices.
In the charging mechanism of the LIBs, Li + released from the negative electrode and move inside the electrolyte then inserted into the positive electrode.In the discharging mechanism,Li + are extracted 8 from the (+) electrode and move back to the (-) electrode.Although the electrolyte establishes high ionic conductivity 9 between two electrodes, the electrolytes 9 are not responsible 8,9 for the conduction of free-electrons .So the electrons complete the 1/2 reaction will move in the way of an extra 9 external wire.
Various experiments have accomplished for confirming the utilization of graphene in the forms of nano-sheets or nano-ribbons for enhancing lithium storage 9 capacities and for improving recharge performance [9][10][11] .Furthermore in this study, semi-empirical MM calculations have been donefor investigatingLi + storage between two graphene 11 sheets 12 , as well as a few heteroatomsubstituted 11 carbon materials 13 .
Dis-charging or charging of Li+ in carbonadoes iswell established and arrangedup to now [18][19][20][21] .It has also been exhibitedthe mechanism of the repulsive forces 13 in the mixed stages which can result in the pure stages during intercalation 19,23 .In this study, chargingand discharging of Li-ions has investigated in h-BN with the positive electrode reaction as:LiCoO2 Li1-x CoO2 + x Li+ +x and the negative electrode reaction as: x B 3 N 3 + x Li + +x LiB 3 N 3, while the whole reaction is:LiCoO2 +xB 3 N 3 Li 1-x CoO2+x LiB 3 N 3 .It has been suggested 22 that lithium atoms are stored 23 via two mechanisms: intercalation and alloying 24 .
The electrical conductivities for the Li+-Graphene increases 25 via increasing intercalation levels due to the donor 26 nature of electronsfor the lithium.This is in contrast of ionic conduction 26 in which diffusivity 27 decreases 26 due to the insertion of Li ions 27 .In the case of amorphous 26 carbon as thedisorder 28 increases electrical conductivity 28 significantly decreases 29 .Recently, Fisher group fabricated [29][30] a tube-in-tube structure with Li + intercalation capacities 2 times higher than that of the template-synthesized 30,40 Carbon-NTs, as the inner tubules provided more electrochemical 40,43 active sites for intercalation of Li ions 28,51 .
In summary, Graphene and h-BN compounds as one kind of classical materials 42 with a mature studied history will play asignificant role in the battery market of the near future,but how to combine hybrid materials together to obtainsafe, stable, and high-capacity electrodes has always beenthe radical problem that many researchers are trying tosolve.

Theoretical background
Diffusion properties 45,51 of Li ion cell deter mines some of the keys performance metrics of Li + ion batteries cells, consist fo the charges and discharges rate, practical capacities and cycling stabilities.The governing equation describing the diffusion process is known as Fick' slaw as: where "ji " is ionic flux, mol cm −2 s −1 , Di is diffusivity of solute (i =1, 2), cm2 s −1 and C_i is concentration of species i , (mol cm3).The proportionality [40][41][42][43][44][45][46][47][48][49][50] .factor D is the diffusivity or diffusion coefficient as (3) Li + ion cells consist of, all Keyes phenomena involves conducting charged particles as a primary cell from cathodes to anode or vice versa as a secondarycell from anode to cathodes.Typical commercially used lithium-ion battery consists of several interconnected electrochemical cells, where each cell is composed of a graphite anode (such as Meso-carbon microbeads), a cathode formed by lithium metal oxide (such as LiCoO2) and electrolyte (such as LiPF6 dissolved in ethylene carbonate/dimethyl carbonate mixture) embedded in a separator felt.

Anode materials
In the case of anode, Li metal is found to be the most electropositive (-3.04 V versus standard hydrogen electrode) with large reversible capacity (≈ 4000 A h kg-1).However, due to safety considerations (explosion hazards as a result of dendrite growth during cycling), metallic Li has been substituted by various carbonaceous materials.
During discharge, Li + ions are extracted from the layered graphite, they pass 55 through the electrolytes and intercalate among the LiCoO2 layers (Fig. 2.).

Density and energy of lithium in diffusion model
The electron densities has been defined as 52,54 .Where η i is occupational number of orbitals (i), ϕ are orbitals wave functions, χ is basis function and C is coefficient matrix, the element of i th row j th column 52 corresponds to the expansion coefficient of orbital j respect to basis function i. Atomic unit for electron density can be explicitly 54 written as e/Bohr 3 .Electron localization and chemical reactivityies 55 have been built by Bader 55 . (5)

Fig. 2 a typical commercial lithium-ion battery
The Hamiltonian kinetics energies densities K(r) The kinetic energies densities are not defined, since it has been expected value for kinetic energies operators has been recovered via integrating kinetic energies densities from an alternative definition.One of general used definition can be demonstrated as: "G(r)" is famous as K(r) and G(r)

Local Entropies
Local information entropiesare quantification of information, which was proposed by Shannonto decompose di-atomic and tri-atomic molecules into space by a minimized information entropy 52,57 .Parr has discussed the relationship between information entropies and atom partition as well as molecular 54 similarity 54 .Noorizadeh and Shakerzadeh suggested using information entropy to study aromaticity.probability function is s=−∫P (χ) InP(χ)dχ (19).If P(x) is replaced by then the integrand can be called LIE of electrons.S(r)=− in (20)Where, N is the total number of electrons in current system.
At each inter-tube configuration, a singlepoint calculation is carried out and the total energy is recorded.The resulting sliding-rotation energy surfaces are used to fix our model in better position. (Ε total Ε xLi +Ε h-BNsheets )}+Ε BSSE Where the ΔΕ s is the stability energy of system.The contour line map has drawn via Multiwfn software [52][53][54] .The graph sareex habited on interactive interfaces and the methods in this work has based on our previous work  .

RESULT AND DISCUSSION
We have listed the data of density, energy, electron localization function (ELF), localized orbital locator (LOL) and local entropy, gap energy, charge from ESP, electrostatic potential ,ionization energy,the charges of two doped graphene electrodes and the stability energy of X-G-(h-BN) -X-G and dielectric in 4 tables (tables1-6) and these data have plotted in 10 the (Figures.1-10)   We have calculated the gradient norm and the Laplacianof electron density via equals7 and 8 for the lithium diffused in the X-G/(h-BN)/X-G system respectively and the data are listed in table1.For calculation the electron spin density from the difference between alpha and beta density, we have Used p s (r)=p α (r)−pβ(r) then the spin polarization parameter function will be returned instead of spin density = .The absolute value of going from zero to unity corresponds to the local region going from un-polarized case to completely polarized case Table1.In this work it has been calculated the local Information entropies for each of Li atoms via eqs.19-20 and the integrating of those functions over whole spaces yield the information entropies.The data of local Information entropies are listed in Tables 1-5.
Weak interaction (equals 20 and 21) has significant influence on conformation of macromolecules, however reproduction of electron densities by ab initio and grids data calculation of reduced density gradient (RDG) for such huge systems are always too time-consuming.In this work it has been exhibited the complex of X-G/(h-BN)/X-G which demonstrate a high electrical conductivity and a good mechanical strength, excellentflexibility, great chemical stabilities and high specific surfaces area.Thoseare especially noticeable when the graphene are chemically converted via greater proportion of functional groups, proving that they are suited for using as the basecomposite < (8) (9)   positive definite kinetic energies densities.
are directly related by Laplacian of electron density. (11)

Electron localization function (ELF)
Becke and Edgecombe noted that spherically averaged likespin conditional pair probability has direct correlation with the Fermi hole and then suggested electron localization function (ELF) [53][54] .where and ( 14) system, sinece terms can be simplified as D(r) = (15) 16) Savin, has reinterpreted the ELF 52 in the view of kinetics energies [52][53][54][55][56][57][58] .(17) where (18)   for spin-polarized system and close-shell system are defined in the same way as in ELF 53 .during the charge or discharge phenomenon.Further, the excellent electrical properties of X-G/(h-BN)/X-Gcan enhance the conductivity of metal electrodematerial.Finally, the lithium storage capacity for mostmetal oxide composite materials with X-G/(h-BN)/X-Gcan be useful greatly.

CONCLUSION
The structure of G-X/(h-BN)n/X-G can be for improving the capacities and electrical transports in the C-BN sheets of LIBs.In addition, the BN sheet modified and designed of X-G/ (h-BN)/X-G structures provide a strategy to improve the yields of BN-G-sheet of anodes.X-G/h-BN/X-G could also be assembled into free standing electrode of any binder (current collector), which will causes for increasing specific energies and densities for the batteries design.
bands cannot cross each other and amount 4.5 eV band gap forms.Via an experiment, h-BN has been calculated to have a band gap around 5.8 eV 4 .Crystallographic of BN is classified into four polymorphic 3 forms: Hexagonal 4 BN (h-BN) (Fig 1(a); rhombohedral 3,4 BN (r--BN); cubic B-N (c--BN); and wurtzite 4 BN (w--BN).