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First principle calculations on structural, electronic and transport properties of Li2TiS3 and Li3NbS4 positive electrode materials

First principle calculations on structural, electronic and transport properties of Li2TiS3 and... Mater Renew Sustain Energy (2016) 5:8 DOI 10.1007/s40243-016-0072-2 ORIGINAL PAPER First principle calculations on structural, electronic and transport properties of Li TiS and Li NbS positive electrode materials 2 3 3 4 1,3 2,3 • • Thiyagarajan Gnanapoongothai Balasubramaniam Rameshe 3 4 3 • • Kaliaperumal Shanmugapriya Ramaswamy Murugan Balan Palanivel Received: 3 September 2015 / Accepted: 25 March 2016 / Published online: 9 April 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract First principle calculations based on density of states clearly reveals that the extraction lithium from functional theory have been performed on lithium con- these electrode materials does not change their metallic taining transition metal sulfides Li TiS and Li NbS nature. The electronic conductivities of both lithiated and 2 3 3 4 which are recently identified as novel positive electrode delithiated phases have been calculated by employing materials for rechargeable Li batteries. The calculations BoltzTrap which can be interfaced with WIEN2K. The were performed to investigate the structural stability, topological distributions of electron charge density at var- electronic and transport properties of Li TiS and Li NbS ious critical points within the system were analyzed with 2 3 3 4 along with their corresponding delithiated phases LiTiS the use of CRITIC code which is based on Bader’s theory and Li NbS . In this study it has been observed that these of atoms in molecules (AIM). From the charge density 2 4 lithium containing sulfur materials maintain their face- calculations, it was observed that, there is strong ionic bond centered cubic structure upon extraction of Li . To cal- and weak covalent bond between atoms of the compounds culate the structural stability and volume change due to Li TiS and Li NbS . But the ionic bond nature was found 2 3 3 4 lithium extraction, the total energies of Li TiS ,Li NbS to decrease in the delithiated phases LiTiS and Li NbS . 2 3 3 4 3 2 4 and their corresponding delithiated phases LiTiS and The calculated values of electronic conductivities and Li NbS have been computed by applying full potential discharge voltages for both electrodes are found to be in 2 4 linearized augmented plane wave (FP-LAPW) method accordance with the recent experimental reports. implemented in WIEN2K. The equilibrium structural parameters for all the phases were determined by achieving Keywords Li battery  Positive electrodes  First total energy convergence. These electrode materials exhibit principle calculation  Discharge voltage  Electronic very small percentage of volume change with change in conductivity Li concentration which accounts for excellent structural stability. The computed band structure along high sym- metry lines in the Brillouin zone, total and partial density Introduction Li batteries are the most significant rechargeable power & Balan Palanivel sources which are being successful in powering bpvel@pec.edu portable consumer electronic devices. The extensive research on Li batteries over the last few decades have Department of Physics, Sri Manakula Vinayagar Engineering College, Puducherry 605 017, India tremendously increased the performance of Li battery, their safety, cost and environmental compatibility. In the Department of Physics, Rajiv Gandhi College of Engineering ? ? and Technology, Puducherry 607 402, India Li battery technology, the cell voltage, Li transportation rate and specific capacities are mainly determined by the Department of Physics, Pondicherry Engineering College, Puducherry 605 014, India positive electrode materials [1]. The practical reversible capacities of conventional pos- Department of Physics, Pondicherry University, Puducherry itive electrode materials with layered structure and olivine 605 014, India 123 8 Page 2 of 12 Mater Renew Sustain Energy (2016) 5:8 structure are usually limited by the intrinsic structural (DFT) with approximations such as local density approxi- instability at low lithium concentration [2]. Even though mation (LDA) and generalized gradient approximation the olivine LiMPO and spinel LiMn O were proposed as (GGA) have been extensively applied in the field of Li 4 2 4 the positive electrode materials with better cyclic perfor- batteries [26]. The aim of this work is to present a detailed mance and low cost, they have lower electronic conduc- theoretical description of electronic, structural and trans- tivity [3–15]. Li MnO [4], Li V O (x = 1, 2, 3) [16], port properties of positive electrode materials Li TiS , 2 3 x 2 5 2 3 Li FeS [17] and Li FeSiO [18] are reported to have high Li NbS and their delithiated phases. 2 2 2 4 3 4 -1 specific capacity ranging from 300 to 400 mA h g due to the transformation of more than one electron during charging and discharging. Also, Li S, Li Se and Li O Method of calculation 2 2 2 exhibit high capacities due to multi electron reaction [19– 21]. Therefore, it is clear that electrodes involved in multi In the present calculation, full potential linearized aug- electron reactions exhibit high specific capacity. mented plane wave (FP-LAPW) method within the gen- The research on sulfur containing positive electrodes has eralized gradient approximation (GGA) is used as been growing consistently in the last two decades. Among incorporated in WIEN2K code [29]. The principal moti- the high energy density storage systems, lithium sulfur vation of this computational method is to obtain detailed -1 batteries with energy density of 2600 W h kg holds the information about the structural and electronic properties potential to serve as next generation of high energy battery including discharge voltage and electronic conductivities [23]. The remarkable advantages of lithium sulfur batteries of the positive electrodes Li TiS ,Li NbS and also for 2 3 3 4 are that the sulfur is abundant in nature, non-toxic, low cost their corresponding delithiated phases LiTiS and Li 3 2- -1 and possess high theoretical capacity of 1673 mA h g . NbS .To perform these calculations, the exchange–corre- The limitations are that sulfur slowly dissolves in the lation potential according to the Perdew–Burke–Ernzerhof electrolyte and slow down the ion movement result into parameterization is used [30]. In this method, the space is poor cyclic performance and low electronic conductivity divided into an interstitial region and non-overlapping due to the insulator characteristic of elemental sulfur. To muffin-tin (MT) spheres centered at the atomic sites. In the overcome these limitations, appropriate transition metals interstitial region, the basis set consists of plane waves. are added to prevent sulfur from dissolving in the elec- Inside the MT spheres, the basis set is described by radial trolyte. Since Ti and Nb have very good mechanical solutions of the one particle Schro¨dinger equation (at fixed strength, light in weight, ductile, corrosion resistive, energy) and their energy derivatives multiplied by spheri- abundant in nature, nontoxic and low cost, they received cal harmonics. To determine the equilibrium volume (V ) considerable attention to prepare the suitable electrode and the structural parameters for all the compounds the material. Lithium containing transition metal sulfides total energies are computed. For these calculations, self- LiTiS ,Li TiS ,Li NbS have been reported experimen- consistency is obtained with the use of 5000 k points in the 2 2 3 3 4 tally and theoretically to have increased specific capacity entire Brillouin zone [28]. The electronic properties are and electronic conductivity [6, 22–28]. Among these calculated within GGA approximation. The variations in lithium metal sulfides, Li TiS and Li NbS have been electronic conductivity due to extraction of lithium are 2 3 3 4 experimentally reported that they exhibit high specific determined with the BoltzTrap code interfaced with capacity and very low volume expansion [25]. The unique WIEN2K [31]. advantage of these compounds is that the number of elec- trons in the valence state of transition metal will be increased due to multi electron reaction in charging and Results and discussions discharging which in turn increases the electronic con- ductivity of the positive electrode. Moreover, these com- Structural properties pounds are found to crystallize in rock salt structure with face-centered cubic array which provides three dimen- According to experimental investigations by Sakuda et al. sional interstitial spaces to accommodate large amount of on Li TiS and Li NbS , the compounds crystallize in face- 2 3 3 4 lithium as well as it contributes to the excellent centered cubic structure belongs to the space group and reversibility of the electrode compared to other structures they retain the same structure upon Li extraction process [22, 28]. Hence, Li TiS and Li NbS have gained more [22, 24]. To investigate the structural stability of these 2 3 3 4 attraction as potential materials for Li batteries with high electrodes and to determine the equilibrium volume for the energy and good electronic conductivity. host compounds and their corresponding delithiated pha- The computational methods by the application of first ses, a primitive unit cell is constructed. The self-consistent principle calculations based on density functional theory total energy calculations were performed by employing FP- 123 Mater Renew Sustain Energy (2016) 5:8 Page 3 of 12 8 Table 1 Calculated lattice parameters for the electrodes and their accommodate Li ions without lattice strain to the host delithiated phases material. Hence, these compounds exhibit excellent struc- ˚ tural stability which is a key factor in determining the Compound a (A) References volumetric and gravimetric capacity of the electrode Present calculation Experiment material. The crystal structures of the compounds Li TiS , 2 3 Li TiS 5.0568 5.06 [22] Li NbS and their respective delithiated phases LiTiS and 2 3 3 4 3 LiTiS 5.0390 5.06 [22] Li NbS are illustrated in Figs. 1 and 2. 3 2 4 Li NbS 5.1642 5.13 [22, 24] 3 4 Li NbS 5.1023 5.13 [22, 24] Electronic properties 2 4 The preliminary idea to investigate the electronic proper- LAPW method. The minimization of total energy of the ties of a potential electrode material is to determine its system was achieved by computing the total energy for metallic, semiconducting or insulating character. Informa- different unit cell volumes over a range ±15 % around tion about the energy gaps between valence and conduction experimental volume which is similar to our previous bands can be deduced from the calculated density of states. works [32–36]. The total energy calculations were con- To investigate the electronic properties of Li TiS Li NbS 2 3, 3 4 -5 verged within 10 Ry. The equilibrium volumes for all the and their corresponding delithiated phases, the band investigated compounds were obtained by fitting the total structure calculations were performed within GGA along energy as a function of volume to the Brich–Murnaghan’s with high symmetry directions of Brillouin zone. The equation of state [34]. The lattice parameters determined computed band structure of Li TiS , shown in Fig. 3a 2 3 from the equilibrium volume are in good agreement with exhibits its metallic nature. The bands crossing Fermi level the experimental reports and listed in Table 1. (E ) and the bands which are lying above E are primarily F F From the above calculations, a small percentage of originated from the valence electrons of Ti and S atoms. volume change was observed due to Li extraction. It has The band profile of delithiated LiTiS shown in Fig. 3b been noted that the cubic array of the host material pro- reveals that the extraction of lithium from Li TiS pushed 2 3 vides a three dimensional and isotropic interstitial space to the conduction band to higher energy and valence band to Fig. 1 Crystal structures of a Li TiS b LiTiS 2 3 3 Fig. 2 Crystal structures of a Li NbS b Li NbS 3 4 2 4 123 8 Page 4 of 12 Mater Renew Sustain Energy (2016) 5:8 Fig. 3 Electronic band structures of a Li TiS b LiTiS 2 3 3 c Li NbS and d Li NbS 3 4 2 4 lower energy with respect to E . This is because of the Li TiS and Li NbS with their respective delithiated F 2 3 3 4 removal of electrons from the host band structure due to the phases LiTiS and Li NbS concludes that extraction of 3 2 4 delithiation [37, 38]. The metallic nature of the host Li does not imply any transition in the metallic nature of compound is retained in its delithiated phase which con- the host compounds. firms that the bands crossing E are from valence electrons To perform a widespread study on electronic properties, of Ti. The metallic nature of Li NbS is revealed from the the partial and total DOS for all the investigated com- 3 4 calculated electronic band structure of the compound along pounds were computed and are illustrated in Figs. 4,5,6 the high symmetry directions of Brillouin zone which is and 7. The partial and total DOS for Li TiS presented in 2 3 presented in Fig. 3c. The valence electrons of transition Fig. 4a indicated that the maximum number of electronic metal atom Nb are the major contributors for the bands states obtained at E was primarily originated from the d crossing E and above Fermi level. However, from the orbital electrons of transition metal atom. However, there is sulfur atom, the p state electrons have coordinated with the significant contribution from the p orbital electrons of electrons of Nb. The electronic band structure in Fig. 3d chalcogenide atom. From the partial DOS of Li TiS pre- 2 3 indicates the metallic character of Li NbS . The compar- sented in Fig. 4a, it can be witnessed that the electronic 2 4 ison of electronic band structures of the host compounds states at -4 eV below E are purely contributed by the p 123 Mater Renew Sustain Energy (2016) 5:8 Page 5 of 12 8 Fig. 5 a Partial DOS of sulfur in Li TiS and b partial DOS of sulfur 2 3 in LiTiS Fig. 4 a Partial and total DOS of Li TiS and b partial and total DOS 2 3 of LiTiS orbit electrons from the three sulfur atoms. All the elec- tronic states lying above E are absolutely raised from d state electrons of three S and Ti atoms. The contribution of electronic states of sulfur above this energy range is dominant. The contribution of electronic states of transition metal atom at this energy range is negligible. The DOS distribution for the delithiated phase LiTiS is presented in Fig. 4b. In the partial and total DOS, the electronic states at E are completely due to the d state electrons of transition metal atom, and above E the electronic states are mainly originated due to the chalcogenide atom. Thus, it is clearly evident that the distribution of electronic states at E for the host compound is almost similar to its delithiated phase which implies that the transition metal atom is not affected by Li extraction. In the partial DOS of LiTiS given in Fig. 4b, the maximum number of electronic states at the energy -2.5 eV is increased compared to that of the host compound which might be due to the removal of electrons from host compound due to delithiation. From Fig. 5a, b it was observed that the electronic states at the energy 5 eV above E for both compounds Li TiS and LiTiS are F 2 3 3 Fig. 6 a Partial DOS of sulfur in Li NbS and b partial DOS of sulfur 3 4 attributed to the d state electrons of Ti and S atoms which in Li NbS 2 4 123 8 Page 6 of 12 Mater Renew Sustain Energy (2016) 5:8 observed that there is substantial decrease in the electronics states at conduction band of delithiated phase which may have influence in electronic conductivity. Bonding properties To have a clear perception about the nature of chemical bonding between atoms, the valence charge density dis- tribution for all the investigated compounds were calcu- lated and plotted in two dimensional grid as shown in Figs. 8 and 9. The valence charge density contour plot for Li TiS along (001) direction in Fig. 8a showing localized 2 3 charge distribution which is a sign of ionic bonding ? 4? 2- between electropositive Li ,Ti and electronegative S . It has also been identified that the isolines in charge density contour for the same compound Li TiS along (112) 2 3 direction in Fig. 8b reveal weak covalent bond between valence electrons of sulfur and titanium atoms. Therefore, the material is neither ionic nor covalent in nature as it exhibits the mixture of both. However, the charge density plots clearly reveal that the ionic bonding character dom- inates the covalent character in Li TiS . Since electrodes 2 3 acquire complete ionic character at high concentration of lithium, may undergo a brittle fracture which may in turn Fig. 7 a Partial and total DOS of Li NbS and b partial and total 3 4 decreases their life cycle[39]. This mixed bonding char- DOS of Li NbS 2 4 acter of the electrode materials is an advantage over the electrodes with complete ionic nature at high lithium is an evident for the covalent bonding nature of these concentration. The valence charge density for the delithi- atoms. ated phase LiTiS along (001) direction is shown as Figure 7a depicts the partial and total DOS for Li NbS . Fig. 8c. At this direction, the isolines of charge density are 3 4 The electronic states at E were raised from the d state not shared between Li, Ti and S atoms, which indicate electrons of transition metal atom and from p state elec- ionic bond between these atoms. In Fig. 8d, the electronic trons of chalcogenide atom. But the contribution of tran- charge density distribution of the same compound along sition metal atom is much dominant at this level. Maximum (112) direction illustrates there is a strong covalent bonding contribution of chalcogenide atom is at the energy range between the valence electrons of Ti and S. Therefore, -3to -4 eV. This can be identified from the partial DOS LiTiS show strong covalent nature and weak ionic nature of Li NbS shown as Fig. 7a. The peaks obtained in the due to extraction of Li . 3 4 DOS at energies above E were due to the d state electrons The valence charge distribution for Li NbS was com- F 3 4 from the four sulfur atoms. Also, it has been observed that, pletely dominated by ionic bond nature between Li, Nb and valence electrons of niobium were not having significant S atoms (Fig. 9a) calculated along (100) direction. How- importance at these energies. To identify the effect of Li ever, there is sharing of valence electrons between Nb and extraction from Li NbS in electronic structure, the partial S atoms which has been identified through the charge 3 4 and total DOS of Li NbS was calculated and illustrated as density plot along (112) direction as in Fig. 9b. Hence, 2 4 Fig. 7b. The electronic states at E for the delithiated phase Li NbS also exhibit mixed bonding character, whereas the 3 4 Li NbS in Fig. 7b was found to be identical with the states ionic bonding nature weakens the covalent character. To 2 4 of Li NbS at this level (Fig. 7a). This is quite normal investigate the impact of Li extraction in the nature of 3 4 since the role of transition metal atom was absolutely same chemical bonding, the charge density contour plot for the in both phases. The partial DOS pattern in Fig. 6a, b delithiated phase Li NbS was calculated. From Fig. 9c, it 2 4 clearly reveals that the electronic states below E were is observed that the isolines are not shared by Nb, S and Li purely originated from p state electrons of sulfur and above atoms. Therefore, the bonding along (100) direction is E they were due to d state electrons of the four sulfur completely ionic. The sharing of valence electrons between atoms. DOS observation infers that there is no significant Nb and S atoms along (112) direction in Fig. 9d infer that difference in electronic states below E , but it has been the delithiated phase shows partially covalent and partially 123 Mater Renew Sustain Energy (2016) 5:8 Page 7 of 12 8 Fig. 8 Valence charge density contour for a Li TiS along 2 3 (001) direction, b Li TiS along 2 3 (112) direction, c LiTiS along (001) direction and d LiTiS along (112) direction ionic bonding nature. From the electron charge density interaction corrections to obtain the ionic charge distribu- calculations, it is observed that the ionic bond character tion inside the atomic basins for the electrodes Li TiS and 2 3 dominates the covalent nature in the host compounds Li Li NbS as well as for their delithiated phases. The 2- 3 4 TiS and Li NbS , whereas covalent bonding nature topology of electron density (q) for all the compounds have 3 3 4 dominates the ionic nature in their corresponding delithi- been observed with the application of Bader’s theory based ated phases LiTiS and Li NbS . Hence, it is clearly evi- on atoms in molecules theory. For various self-interaction 3 2 4 dent that even though increase in Li concentration corrections, even though there is change in total energy of increases the ionic nature of the compound, there was not the compounds, there is a slight change in global minima of complete transfer of valence electrons between elec- total energy curve which corresponds to equilibrium vol- ? 4? 2- tropositive Li ,Ti and electronegative S . ume of the compounds. Table 2 illustrates the atomic charges within the atomic basins of Li, Ti, Nb and S Electron charge distribution obtained from GGA and LDA ? U (U = 3, 5 and 7 eV). From the Table 2, it has been noted that removal of Li Electron correlation effects are important for the electronic results in considerable change in the ionic charge distri- structure of transition metal compounds, thus we also tes- bution within the atomic basins of Ti, Nb and S, however, ted two LDA ? U corrections. The self-interaction cor- Li site has negligible change in charge distribution. This rected (SIC) LDA ? U is a method going beyond the LDA implies that extraction of Li has not much influence in the by special treatment of a chosen set of states, which in our total charge distribution of the compound. The charge case are the 3 d states of Ti and 4 d states of Nb. To find the distribution in the delithiated phases are balanced between imbalanced redox potential in the delithiated phases, we the transition metal atoms and sulfur atoms. In the have considered electron self-interaction (SIC) and delithiated phase LiTiS , the ionic charge of Ti increases employed LDA ? U method with three different self- by ?0.35 and the ionic charge of sulfur decreases by -0.45 123 8 Page 8 of 12 Mater Renew Sustain Energy (2016) 5:8 Fig. 9 Valence charge density contour for a Li NbS along 3 4 (100) direction, b Li NbS 3 4 along (112) direction, c Li NbS 2 4 along (100) direction and d Li NbS along (112) direction 2 4 Table 2 Atomic charges (e ) within the atomic basins of Li, Ti, Nb and S calculated according to Bader’s topological analysis Li TiS LiTiS Li NbS Li NbS 2 3 3 3 4 2 4 Li Ti S Li Ti S Li Nb S Li Nb S GGA 1.65 0.88 -2.53 0.83 1.21 -2.04 2.41 0.06 -2.47 1.65 0.48 -2.13 LDA ? U U = 3 eV 1.65 0.98 -2.63 0.85 1.33 -2.18 2.45 0.15 -2.60 1.66 0.59 -2.25 U = 5 eV 1.66 1.06 -2.72 0.85 1.38 -2.23 2.45 0.09 -2.54 1.66 0.62 -2.28 U = 7 eV 1.67 1.08 -2.75 0.85 1.43 -2.28 2.45 0.20 -2.65 1.66 0.65 -2.31 In delithiated phase Li NbS , the ionic charge of Nb associated atomic interaction line. Since the CP (3, -1) 2 4 increases by ?0.45 and the ionic charge of sulfur decreases indicated the saddle point of q linked to nucleus and pro- by -0.35. vides information about the bonding character of the atoms, Moreover, to have a complete analysis of the chemical it is known as bond CP. The calculated Hessian matrix of q bonding of the compounds, topological analysis is applied is diagonalized to yield a set of eigenvalues. The eigen- with CRITIC program. The electron density is character- values correspond to the three principal curvatures of q. ized by a well-defined set of critical points (CP). The The CP (3, -1) has one positive and two negative eigen- existence of a (3, -1) CP indicates that electron density is values. From these curvatures, the nature of chemical accumulated between the nuclei that are linked by the bonding can be known. Table 3 depicts the positions, 123 Mater Renew Sustain Energy (2016) 5:8 Page 9 of 12 8 Table 3 Position, curvatures, Laplacians and charge density at the (3, -1) critical points from GGA calculations -5 -5 -5 -3 2 -3 ˚ ˚ ˚ ˚ ˚ System xyz h (A ) h (A ) h (A ) r q (A ) q (A ) 1 2 3 Li TiS -0.3252 0.0000 0.0000 1.484 -0.237 -0.236 1.010 0.015 2 3 -0.2264 0.0000 -0.2261 -0.007 -0.174 0.423 0.241 0.087 LiTiS -0.2227 -0.2227 0.0000 0.414 -0.100 -0.111 0.202 0.058 -0.1705 0.0000 0.3002 0.446 -0.148 -0.099 0.198 0.082 Li NbS 0.0000 0.0000 -0.3374 -0.466 -0.468 2.453 1.517 0.145 3 4 -0.2124 -0.2725 0.0000 0.564 -0.023 -0.213 0.327 0.097 Li NbS 0.0000 0.0000 0.3379 -0.474 -0.477 2.542 1.592 0.146 2 4 -0.2423 0.0000 -0.2424 0.573 -0.217 -0.004 0.351 0.100 curvatures, Laplacian of q and magnitude of q at the bond found. The distribution of q obtained for the ring and cage CP (3, -1). The ratio of principal curvatures h /h together cps are identical for the electrodes Li TiS ,Li NbS with 1 2 2 3 3 4 with the Laplacian provides information for a classification their corresponding delithiated phases. Therefore, the core of chemical bonding. A small value h /h  1 is typical electrons are not affected by the extraction of Li from the 1 2 for closed shell interactions. While for covalent bond this electrodes. ratio increases with bond strength. The magnitude of q is positive and large for ionic bonding, and it is small or Transport properties negative for covalent bonding [40–44]. From Table 3 it has been noted that there are two different topological distri- The calculations for the transport properties such as bution of q, which indicates the electrode materials exhibit electronic conductivities are carried out using the Boltz- two different bonding characters. Positions associated with Trap code which is interfaced with WIEN2K. BoltzTrap -3 Laplacian B0.3 A and other positions associated with is a computational tool for evaluating the transport -3 Laplacian C1.5 A were attributed to strong and weak properties using the Boltzmann transport theory [45–49]. ionic bond, respectively. The analysis of distribution of q The band energies of the compounds Li TiS ,Li NbS 2 3 3 4 for the electrode materials and their corresponding and their respective delithiated phases LiTiS and Li 3 2- delithiated structures indicates very little change in the NbS are computed with self-consistent total energy cal- electron charge density which is clearly evident for the culation with the use of WIEN2K and given as input to structural stability of the compounds Li TiS and Li NbS BoltzTrap. The transport properties as a function of the 2 3 3 4 during delithiation process. carrier concentration are computed with the results of the The bonding CPs (3, 1) and (3, 3) are described in electronic band structure calculated above. The Fourier Table 4. The distribution of charge density obtained from expansion of band energies is carried out to determine the the CPs (3, 1) and (3, 3) occurs as consequences of par- gradient along the energy bands to obtain the group ticular geometrical arrangement of bond paths, and they velocities. The group velocities are calculated as deriva- define the remaining elements of molecular structure rings tives of the energies. The transport property happens to be and cages. (3, 1) CP is found at the interior of the ring. If extremely dependent on the chemical potential. However, the bond paths are arranged so as to enclose the interior of the chemical potential is related to the number of charge a molecule with the ring surfaces, then a (3, 3) cage CP is carriers. Table 4 Position, curvatures, Laplacian and charge density at critical points other than (3, -1) from GGA Calculations -5 -5 -5 -3 2 -3 ˚ ˚ ˚ ˚ CP System xy z h (A ) h (A ) h (A ) r q (A ) q (A ) 1 2 3 (3, 1) Li TiS -0.1820 -0.2743 -0.1820 0.170 0.069 -0.025 0.214 0.043 2 3 LiTiS -0.1605 -0.2857 -0.1524 0.149 -0.039 0.084 0.194 0.041 Li NbS -0.2428 -0.2376 0.0000 0.011 0.557 -0.217 0.351 0.097 3 4 Li NbS -0.1720 -0.3126 -0.1720 0.206 0.073 -0.033 0.247 0.425 2 4 (3, 3) Li TiS 0.0000 0.5000 0.0000 0.051 0.023 0.051 0.126 0.019 2 3 LiTiS 0.0000 0.5000 0.0000 0.508 0.027 0.050 0.128 0.020 Li NbS -0.2564 -0.2563 -0.2560 0.100 0.118 0.118 0.338 0.043 3 4 Li NbS -0.2425 -0.2659 -0.2425 0.146 0.102 0.052 0.301 0.043 2 4 123 8 Page 10 of 12 Mater Renew Sustain Energy (2016) 5:8 Table 5 Calculated electronic conductivity for the electrodes and ½E ðLi TiS Þ E ðLiTiS Þ E ðLiÞ total 2 3 total 3 total V ¼ ð3Þ their delithiated phases -1 Compound Electronic conductivity in S cm References ½E ðLi NbS Þ E ðLi NbS Þ E ðLiÞ total 3 4 total 2 4 total V ¼ Present calculation Experiment ð4Þ -6 -6 Li TiS 8.755 9 10 8 9 10 [22] 2 3 -6 LiTiS 7.949 9 10 – In both reactions (Eqs. 3 and 4), one electron transferred -3 -3 Li NbS 2.582 9 10 2 9 10 [22, 24] through outer circuit. Where, E refers to the total energy 3 4 total -3 Li NbS 1.831 9 10 – per formula unit. The calculated voltage for the Li 2 4 extraction process with Li TiS is 2.35 V, and with 2 3 Li NbS it is 2.27 V. Both values are found to agree well 3 4 with the experimental value of 2.2 V [22]. Electronic conductivity Volume change An accurate assessment of the electronic conductivity of electrodes is necessary for understanding and optimizing The extraction of Li from the positive electrodes Li TiS 2 3 the battery performance. Electronic conductivity of a pos- and Li NbS during charging of battery was not accom- 3 4 itive electrode material has significant effect on the per- ? panied by any structural change. But it has been observed formance of Li battery. The electronic conductivities for that there was a small change in volume of the electrodes the electrode materials and their corresponding delithiated due to delithiation. First principle calculation can predict phases were calculated at room temperature and are listed the volume change in the electrode material during Li in Table 5. The value of electronic conductivity found to insertion and extraction. The percentage of volume change have generous agreement with the recent experimental is computed by comparing the computed equilibrium vol- results available [22, 24]. umes of the two limiting structures of the electrode [10, 55]. The change in volume (Dv) for the positive electrodes Discharge voltage Li TiS and Li NbS upon the extraction of Li have been 2 3 3 4 calculated from Eq. (5), which is given by The cell voltage is linearly related to the chemical potential of lithium within the positive electrode material. The vðLi HostÞ vðLi HostÞ x1 x2 Dv ¼ ð5Þ average equilibrium voltage (V) is related to the difference vðLi HostÞ x2 in the Gibbs free energy (DG) between the delithiated The calculated volume change for Li TiS with its 2 3 phase at charged state and lithiated phase at discharged delithiated phase LiTiS was 1.05 %, and for Li NbS with 3 3 4 state. It has previously been reported that the average Li NbS was found to be 3.5 %. The low volume change is 2 4 potential for Li extraction from a material is given by the considered as an added advantage for the positive electrode following equations [7, 8] materials to ensure very good structural stability. DG V ¼ ð1Þ ðx2  x1ÞF Conclusions ½GðLi HostÞ GðLi HostÞðx2  x1ÞGðLiÞ x2 x1 V ¼ ðx2  x1ÞF In the present work, first principle calculations within GGA ð2Þ is carried out by employing WIEN2 K to investigate the structural parameters of the rock salt type ternary lithium where, G is the Gibbs free energy of the compound. F is the Faraday’s constant. The free energy change associated with metal sulfides Li TiS and Li NbS as positive electrodes 2 3 3 4 the transfer of one mole of lithium between the two for lithium battery. To acquire knowledge about the impact composition limits. The above Eq. (2) provides the average of lithium extraction in the electronic and bonding prop- of the equilibrium potential between the lithium erties of the host compounds, the electronic band structure, compositions x1 and x2. In DFT calculations, Free density of electronic states and valence charge distribution energies can be replaced by the ground state energies are calculated. With a view to have a better insight into the with very little error [50–54]. Therefore, the discharge transport properties due to the impact of Li extraction, the voltage can be determined by computing the total energies electronic conductivity has been calculated and found to of the compounds and their delithiated phases. For agree well with the experimental reports. Discharge voltage delithiation of Li TiS and Li NbS , the voltage is obtained from the total energy difference for the investi- 2 3 3 4 gated compounds were in significant agreement with the calculated from the equations given below. 123 Mater Renew Sustain Energy (2016) 5:8 Page 11 of 12 8 9. Lu, L.: Transition metal oxides, sulphite and sulphur composites available experimental data. Li extraction from the elec- of Lithium battery. PhD Thesis, University of Wollongong, trode upon charging does not show any structural change. December (2012) This structural similarity of the electrodes accounts for 10. Qi, Yue, Hector, Louis G., James, Christine, Kim, Kwang Jin: their high volumetric and gravimetric capacity. Moreover, Lithium concentration dependent elastic properties of battery electrode materials from first principles calculations. J. Elec- the lithium extraction process with these electrodes was trochem. 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First principle calculations on structural, electronic and transport properties of Li2TiS3 and Li3NbS4 positive electrode materials

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Material Science; Materials Science, general; Renewable and Green Energy; Renewable and Green Energy
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Mater Renew Sustain Energy (2016) 5:8 DOI 10.1007/s40243-016-0072-2 ORIGINAL PAPER First principle calculations on structural, electronic and transport properties of Li TiS and Li NbS positive electrode materials 2 3 3 4 1,3 2,3 • • Thiyagarajan Gnanapoongothai Balasubramaniam Rameshe 3 4 3 • • Kaliaperumal Shanmugapriya Ramaswamy Murugan Balan Palanivel Received: 3 September 2015 / Accepted: 25 March 2016 / Published online: 9 April 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract First principle calculations based on density of states clearly reveals that the extraction lithium from functional theory have been performed on lithium con- these electrode materials does not change their metallic taining transition metal sulfides Li TiS and Li NbS nature. The electronic conductivities of both lithiated and 2 3 3 4 which are recently identified as novel positive electrode delithiated phases have been calculated by employing materials for rechargeable Li batteries. The calculations BoltzTrap which can be interfaced with WIEN2K. The were performed to investigate the structural stability, topological distributions of electron charge density at var- electronic and transport properties of Li TiS and Li NbS ious critical points within the system were analyzed with 2 3 3 4 along with their corresponding delithiated phases LiTiS the use of CRITIC code which is based on Bader’s theory and Li NbS . In this study it has been observed that these of atoms in molecules (AIM). From the charge density 2 4 lithium containing sulfur materials maintain their face- calculations, it was observed that, there is strong ionic bond centered cubic structure upon extraction of Li . To cal- and weak covalent bond between atoms of the compounds culate the structural stability and volume change due to Li TiS and Li NbS . But the ionic bond nature was found 2 3 3 4 lithium extraction, the total energies of Li TiS ,Li NbS to decrease in the delithiated phases LiTiS and Li NbS . 2 3 3 4 3 2 4 and their corresponding delithiated phases LiTiS and The calculated values of electronic conductivities and Li NbS have been computed by applying full potential discharge voltages for both electrodes are found to be in 2 4 linearized augmented plane wave (FP-LAPW) method accordance with the recent experimental reports. implemented in WIEN2K. The equilibrium structural parameters for all the phases were determined by achieving Keywords Li battery  Positive electrodes  First total energy convergence. These electrode materials exhibit principle calculation  Discharge voltage  Electronic very small percentage of volume change with change in conductivity Li concentration which accounts for excellent structural stability. The computed band structure along high sym- metry lines in the Brillouin zone, total and partial density Introduction Li batteries are the most significant rechargeable power & Balan Palanivel sources which are being successful in powering bpvel@pec.edu portable consumer electronic devices. The extensive research on Li batteries over the last few decades have Department of Physics, Sri Manakula Vinayagar Engineering College, Puducherry 605 017, India tremendously increased the performance of Li battery, their safety, cost and environmental compatibility. In the Department of Physics, Rajiv Gandhi College of Engineering ? ? and Technology, Puducherry 607 402, India Li battery technology, the cell voltage, Li transportation rate and specific capacities are mainly determined by the Department of Physics, Pondicherry Engineering College, Puducherry 605 014, India positive electrode materials [1]. The practical reversible capacities of conventional pos- Department of Physics, Pondicherry University, Puducherry itive electrode materials with layered structure and olivine 605 014, India 123 8 Page 2 of 12 Mater Renew Sustain Energy (2016) 5:8 structure are usually limited by the intrinsic structural (DFT) with approximations such as local density approxi- instability at low lithium concentration [2]. Even though mation (LDA) and generalized gradient approximation the olivine LiMPO and spinel LiMn O were proposed as (GGA) have been extensively applied in the field of Li 4 2 4 the positive electrode materials with better cyclic perfor- batteries [26]. The aim of this work is to present a detailed mance and low cost, they have lower electronic conduc- theoretical description of electronic, structural and trans- tivity [3–15]. Li MnO [4], Li V O (x = 1, 2, 3) [16], port properties of positive electrode materials Li TiS , 2 3 x 2 5 2 3 Li FeS [17] and Li FeSiO [18] are reported to have high Li NbS and their delithiated phases. 2 2 2 4 3 4 -1 specific capacity ranging from 300 to 400 mA h g due to the transformation of more than one electron during charging and discharging. Also, Li S, Li Se and Li O Method of calculation 2 2 2 exhibit high capacities due to multi electron reaction [19– 21]. Therefore, it is clear that electrodes involved in multi In the present calculation, full potential linearized aug- electron reactions exhibit high specific capacity. mented plane wave (FP-LAPW) method within the gen- The research on sulfur containing positive electrodes has eralized gradient approximation (GGA) is used as been growing consistently in the last two decades. Among incorporated in WIEN2K code [29]. The principal moti- the high energy density storage systems, lithium sulfur vation of this computational method is to obtain detailed -1 batteries with energy density of 2600 W h kg holds the information about the structural and electronic properties potential to serve as next generation of high energy battery including discharge voltage and electronic conductivities [23]. The remarkable advantages of lithium sulfur batteries of the positive electrodes Li TiS ,Li NbS and also for 2 3 3 4 are that the sulfur is abundant in nature, non-toxic, low cost their corresponding delithiated phases LiTiS and Li 3 2- -1 and possess high theoretical capacity of 1673 mA h g . NbS .To perform these calculations, the exchange–corre- The limitations are that sulfur slowly dissolves in the lation potential according to the Perdew–Burke–Ernzerhof electrolyte and slow down the ion movement result into parameterization is used [30]. In this method, the space is poor cyclic performance and low electronic conductivity divided into an interstitial region and non-overlapping due to the insulator characteristic of elemental sulfur. To muffin-tin (MT) spheres centered at the atomic sites. In the overcome these limitations, appropriate transition metals interstitial region, the basis set consists of plane waves. are added to prevent sulfur from dissolving in the elec- Inside the MT spheres, the basis set is described by radial trolyte. Since Ti and Nb have very good mechanical solutions of the one particle Schro¨dinger equation (at fixed strength, light in weight, ductile, corrosion resistive, energy) and their energy derivatives multiplied by spheri- abundant in nature, nontoxic and low cost, they received cal harmonics. To determine the equilibrium volume (V ) considerable attention to prepare the suitable electrode and the structural parameters for all the compounds the material. Lithium containing transition metal sulfides total energies are computed. For these calculations, self- LiTiS ,Li TiS ,Li NbS have been reported experimen- consistency is obtained with the use of 5000 k points in the 2 2 3 3 4 tally and theoretically to have increased specific capacity entire Brillouin zone [28]. The electronic properties are and electronic conductivity [6, 22–28]. Among these calculated within GGA approximation. The variations in lithium metal sulfides, Li TiS and Li NbS have been electronic conductivity due to extraction of lithium are 2 3 3 4 experimentally reported that they exhibit high specific determined with the BoltzTrap code interfaced with capacity and very low volume expansion [25]. The unique WIEN2K [31]. advantage of these compounds is that the number of elec- trons in the valence state of transition metal will be increased due to multi electron reaction in charging and Results and discussions discharging which in turn increases the electronic con- ductivity of the positive electrode. Moreover, these com- Structural properties pounds are found to crystallize in rock salt structure with face-centered cubic array which provides three dimen- According to experimental investigations by Sakuda et al. sional interstitial spaces to accommodate large amount of on Li TiS and Li NbS , the compounds crystallize in face- 2 3 3 4 lithium as well as it contributes to the excellent centered cubic structure belongs to the space group and reversibility of the electrode compared to other structures they retain the same structure upon Li extraction process [22, 28]. Hence, Li TiS and Li NbS have gained more [22, 24]. To investigate the structural stability of these 2 3 3 4 attraction as potential materials for Li batteries with high electrodes and to determine the equilibrium volume for the energy and good electronic conductivity. host compounds and their corresponding delithiated pha- The computational methods by the application of first ses, a primitive unit cell is constructed. The self-consistent principle calculations based on density functional theory total energy calculations were performed by employing FP- 123 Mater Renew Sustain Energy (2016) 5:8 Page 3 of 12 8 Table 1 Calculated lattice parameters for the electrodes and their accommodate Li ions without lattice strain to the host delithiated phases material. Hence, these compounds exhibit excellent struc- ˚ tural stability which is a key factor in determining the Compound a (A) References volumetric and gravimetric capacity of the electrode Present calculation Experiment material. The crystal structures of the compounds Li TiS , 2 3 Li TiS 5.0568 5.06 [22] Li NbS and their respective delithiated phases LiTiS and 2 3 3 4 3 LiTiS 5.0390 5.06 [22] Li NbS are illustrated in Figs. 1 and 2. 3 2 4 Li NbS 5.1642 5.13 [22, 24] 3 4 Li NbS 5.1023 5.13 [22, 24] Electronic properties 2 4 The preliminary idea to investigate the electronic proper- LAPW method. The minimization of total energy of the ties of a potential electrode material is to determine its system was achieved by computing the total energy for metallic, semiconducting or insulating character. Informa- different unit cell volumes over a range ±15 % around tion about the energy gaps between valence and conduction experimental volume which is similar to our previous bands can be deduced from the calculated density of states. works [32–36]. The total energy calculations were con- To investigate the electronic properties of Li TiS Li NbS 2 3, 3 4 -5 verged within 10 Ry. The equilibrium volumes for all the and their corresponding delithiated phases, the band investigated compounds were obtained by fitting the total structure calculations were performed within GGA along energy as a function of volume to the Brich–Murnaghan’s with high symmetry directions of Brillouin zone. The equation of state [34]. The lattice parameters determined computed band structure of Li TiS , shown in Fig. 3a 2 3 from the equilibrium volume are in good agreement with exhibits its metallic nature. The bands crossing Fermi level the experimental reports and listed in Table 1. (E ) and the bands which are lying above E are primarily F F From the above calculations, a small percentage of originated from the valence electrons of Ti and S atoms. volume change was observed due to Li extraction. It has The band profile of delithiated LiTiS shown in Fig. 3b been noted that the cubic array of the host material pro- reveals that the extraction of lithium from Li TiS pushed 2 3 vides a three dimensional and isotropic interstitial space to the conduction band to higher energy and valence band to Fig. 1 Crystal structures of a Li TiS b LiTiS 2 3 3 Fig. 2 Crystal structures of a Li NbS b Li NbS 3 4 2 4 123 8 Page 4 of 12 Mater Renew Sustain Energy (2016) 5:8 Fig. 3 Electronic band structures of a Li TiS b LiTiS 2 3 3 c Li NbS and d Li NbS 3 4 2 4 lower energy with respect to E . This is because of the Li TiS and Li NbS with their respective delithiated F 2 3 3 4 removal of electrons from the host band structure due to the phases LiTiS and Li NbS concludes that extraction of 3 2 4 delithiation [37, 38]. The metallic nature of the host Li does not imply any transition in the metallic nature of compound is retained in its delithiated phase which con- the host compounds. firms that the bands crossing E are from valence electrons To perform a widespread study on electronic properties, of Ti. The metallic nature of Li NbS is revealed from the the partial and total DOS for all the investigated com- 3 4 calculated electronic band structure of the compound along pounds were computed and are illustrated in Figs. 4,5,6 the high symmetry directions of Brillouin zone which is and 7. The partial and total DOS for Li TiS presented in 2 3 presented in Fig. 3c. The valence electrons of transition Fig. 4a indicated that the maximum number of electronic metal atom Nb are the major contributors for the bands states obtained at E was primarily originated from the d crossing E and above Fermi level. However, from the orbital electrons of transition metal atom. However, there is sulfur atom, the p state electrons have coordinated with the significant contribution from the p orbital electrons of electrons of Nb. The electronic band structure in Fig. 3d chalcogenide atom. From the partial DOS of Li TiS pre- 2 3 indicates the metallic character of Li NbS . The compar- sented in Fig. 4a, it can be witnessed that the electronic 2 4 ison of electronic band structures of the host compounds states at -4 eV below E are purely contributed by the p 123 Mater Renew Sustain Energy (2016) 5:8 Page 5 of 12 8 Fig. 5 a Partial DOS of sulfur in Li TiS and b partial DOS of sulfur 2 3 in LiTiS Fig. 4 a Partial and total DOS of Li TiS and b partial and total DOS 2 3 of LiTiS orbit electrons from the three sulfur atoms. All the elec- tronic states lying above E are absolutely raised from d state electrons of three S and Ti atoms. The contribution of electronic states of sulfur above this energy range is dominant. The contribution of electronic states of transition metal atom at this energy range is negligible. The DOS distribution for the delithiated phase LiTiS is presented in Fig. 4b. In the partial and total DOS, the electronic states at E are completely due to the d state electrons of transition metal atom, and above E the electronic states are mainly originated due to the chalcogenide atom. Thus, it is clearly evident that the distribution of electronic states at E for the host compound is almost similar to its delithiated phase which implies that the transition metal atom is not affected by Li extraction. In the partial DOS of LiTiS given in Fig. 4b, the maximum number of electronic states at the energy -2.5 eV is increased compared to that of the host compound which might be due to the removal of electrons from host compound due to delithiation. From Fig. 5a, b it was observed that the electronic states at the energy 5 eV above E for both compounds Li TiS and LiTiS are F 2 3 3 Fig. 6 a Partial DOS of sulfur in Li NbS and b partial DOS of sulfur 3 4 attributed to the d state electrons of Ti and S atoms which in Li NbS 2 4 123 8 Page 6 of 12 Mater Renew Sustain Energy (2016) 5:8 observed that there is substantial decrease in the electronics states at conduction band of delithiated phase which may have influence in electronic conductivity. Bonding properties To have a clear perception about the nature of chemical bonding between atoms, the valence charge density dis- tribution for all the investigated compounds were calcu- lated and plotted in two dimensional grid as shown in Figs. 8 and 9. The valence charge density contour plot for Li TiS along (001) direction in Fig. 8a showing localized 2 3 charge distribution which is a sign of ionic bonding ? 4? 2- between electropositive Li ,Ti and electronegative S . It has also been identified that the isolines in charge density contour for the same compound Li TiS along (112) 2 3 direction in Fig. 8b reveal weak covalent bond between valence electrons of sulfur and titanium atoms. Therefore, the material is neither ionic nor covalent in nature as it exhibits the mixture of both. However, the charge density plots clearly reveal that the ionic bonding character dom- inates the covalent character in Li TiS . Since electrodes 2 3 acquire complete ionic character at high concentration of lithium, may undergo a brittle fracture which may in turn Fig. 7 a Partial and total DOS of Li NbS and b partial and total 3 4 decreases their life cycle[39]. This mixed bonding char- DOS of Li NbS 2 4 acter of the electrode materials is an advantage over the electrodes with complete ionic nature at high lithium is an evident for the covalent bonding nature of these concentration. The valence charge density for the delithi- atoms. ated phase LiTiS along (001) direction is shown as Figure 7a depicts the partial and total DOS for Li NbS . Fig. 8c. At this direction, the isolines of charge density are 3 4 The electronic states at E were raised from the d state not shared between Li, Ti and S atoms, which indicate electrons of transition metal atom and from p state elec- ionic bond between these atoms. In Fig. 8d, the electronic trons of chalcogenide atom. But the contribution of tran- charge density distribution of the same compound along sition metal atom is much dominant at this level. Maximum (112) direction illustrates there is a strong covalent bonding contribution of chalcogenide atom is at the energy range between the valence electrons of Ti and S. Therefore, -3to -4 eV. This can be identified from the partial DOS LiTiS show strong covalent nature and weak ionic nature of Li NbS shown as Fig. 7a. The peaks obtained in the due to extraction of Li . 3 4 DOS at energies above E were due to the d state electrons The valence charge distribution for Li NbS was com- F 3 4 from the four sulfur atoms. Also, it has been observed that, pletely dominated by ionic bond nature between Li, Nb and valence electrons of niobium were not having significant S atoms (Fig. 9a) calculated along (100) direction. How- importance at these energies. To identify the effect of Li ever, there is sharing of valence electrons between Nb and extraction from Li NbS in electronic structure, the partial S atoms which has been identified through the charge 3 4 and total DOS of Li NbS was calculated and illustrated as density plot along (112) direction as in Fig. 9b. Hence, 2 4 Fig. 7b. The electronic states at E for the delithiated phase Li NbS also exhibit mixed bonding character, whereas the 3 4 Li NbS in Fig. 7b was found to be identical with the states ionic bonding nature weakens the covalent character. To 2 4 of Li NbS at this level (Fig. 7a). This is quite normal investigate the impact of Li extraction in the nature of 3 4 since the role of transition metal atom was absolutely same chemical bonding, the charge density contour plot for the in both phases. The partial DOS pattern in Fig. 6a, b delithiated phase Li NbS was calculated. From Fig. 9c, it 2 4 clearly reveals that the electronic states below E were is observed that the isolines are not shared by Nb, S and Li purely originated from p state electrons of sulfur and above atoms. Therefore, the bonding along (100) direction is E they were due to d state electrons of the four sulfur completely ionic. The sharing of valence electrons between atoms. DOS observation infers that there is no significant Nb and S atoms along (112) direction in Fig. 9d infer that difference in electronic states below E , but it has been the delithiated phase shows partially covalent and partially 123 Mater Renew Sustain Energy (2016) 5:8 Page 7 of 12 8 Fig. 8 Valence charge density contour for a Li TiS along 2 3 (001) direction, b Li TiS along 2 3 (112) direction, c LiTiS along (001) direction and d LiTiS along (112) direction ionic bonding nature. From the electron charge density interaction corrections to obtain the ionic charge distribu- calculations, it is observed that the ionic bond character tion inside the atomic basins for the electrodes Li TiS and 2 3 dominates the covalent nature in the host compounds Li Li NbS as well as for their delithiated phases. The 2- 3 4 TiS and Li NbS , whereas covalent bonding nature topology of electron density (q) for all the compounds have 3 3 4 dominates the ionic nature in their corresponding delithi- been observed with the application of Bader’s theory based ated phases LiTiS and Li NbS . Hence, it is clearly evi- on atoms in molecules theory. For various self-interaction 3 2 4 dent that even though increase in Li concentration corrections, even though there is change in total energy of increases the ionic nature of the compound, there was not the compounds, there is a slight change in global minima of complete transfer of valence electrons between elec- total energy curve which corresponds to equilibrium vol- ? 4? 2- tropositive Li ,Ti and electronegative S . ume of the compounds. Table 2 illustrates the atomic charges within the atomic basins of Li, Ti, Nb and S Electron charge distribution obtained from GGA and LDA ? U (U = 3, 5 and 7 eV). From the Table 2, it has been noted that removal of Li Electron correlation effects are important for the electronic results in considerable change in the ionic charge distri- structure of transition metal compounds, thus we also tes- bution within the atomic basins of Ti, Nb and S, however, ted two LDA ? U corrections. The self-interaction cor- Li site has negligible change in charge distribution. This rected (SIC) LDA ? U is a method going beyond the LDA implies that extraction of Li has not much influence in the by special treatment of a chosen set of states, which in our total charge distribution of the compound. The charge case are the 3 d states of Ti and 4 d states of Nb. To find the distribution in the delithiated phases are balanced between imbalanced redox potential in the delithiated phases, we the transition metal atoms and sulfur atoms. In the have considered electron self-interaction (SIC) and delithiated phase LiTiS , the ionic charge of Ti increases employed LDA ? U method with three different self- by ?0.35 and the ionic charge of sulfur decreases by -0.45 123 8 Page 8 of 12 Mater Renew Sustain Energy (2016) 5:8 Fig. 9 Valence charge density contour for a Li NbS along 3 4 (100) direction, b Li NbS 3 4 along (112) direction, c Li NbS 2 4 along (100) direction and d Li NbS along (112) direction 2 4 Table 2 Atomic charges (e ) within the atomic basins of Li, Ti, Nb and S calculated according to Bader’s topological analysis Li TiS LiTiS Li NbS Li NbS 2 3 3 3 4 2 4 Li Ti S Li Ti S Li Nb S Li Nb S GGA 1.65 0.88 -2.53 0.83 1.21 -2.04 2.41 0.06 -2.47 1.65 0.48 -2.13 LDA ? U U = 3 eV 1.65 0.98 -2.63 0.85 1.33 -2.18 2.45 0.15 -2.60 1.66 0.59 -2.25 U = 5 eV 1.66 1.06 -2.72 0.85 1.38 -2.23 2.45 0.09 -2.54 1.66 0.62 -2.28 U = 7 eV 1.67 1.08 -2.75 0.85 1.43 -2.28 2.45 0.20 -2.65 1.66 0.65 -2.31 In delithiated phase Li NbS , the ionic charge of Nb associated atomic interaction line. Since the CP (3, -1) 2 4 increases by ?0.45 and the ionic charge of sulfur decreases indicated the saddle point of q linked to nucleus and pro- by -0.35. vides information about the bonding character of the atoms, Moreover, to have a complete analysis of the chemical it is known as bond CP. The calculated Hessian matrix of q bonding of the compounds, topological analysis is applied is diagonalized to yield a set of eigenvalues. The eigen- with CRITIC program. The electron density is character- values correspond to the three principal curvatures of q. ized by a well-defined set of critical points (CP). The The CP (3, -1) has one positive and two negative eigen- existence of a (3, -1) CP indicates that electron density is values. From these curvatures, the nature of chemical accumulated between the nuclei that are linked by the bonding can be known. Table 3 depicts the positions, 123 Mater Renew Sustain Energy (2016) 5:8 Page 9 of 12 8 Table 3 Position, curvatures, Laplacians and charge density at the (3, -1) critical points from GGA calculations -5 -5 -5 -3 2 -3 ˚ ˚ ˚ ˚ ˚ System xyz h (A ) h (A ) h (A ) r q (A ) q (A ) 1 2 3 Li TiS -0.3252 0.0000 0.0000 1.484 -0.237 -0.236 1.010 0.015 2 3 -0.2264 0.0000 -0.2261 -0.007 -0.174 0.423 0.241 0.087 LiTiS -0.2227 -0.2227 0.0000 0.414 -0.100 -0.111 0.202 0.058 -0.1705 0.0000 0.3002 0.446 -0.148 -0.099 0.198 0.082 Li NbS 0.0000 0.0000 -0.3374 -0.466 -0.468 2.453 1.517 0.145 3 4 -0.2124 -0.2725 0.0000 0.564 -0.023 -0.213 0.327 0.097 Li NbS 0.0000 0.0000 0.3379 -0.474 -0.477 2.542 1.592 0.146 2 4 -0.2423 0.0000 -0.2424 0.573 -0.217 -0.004 0.351 0.100 curvatures, Laplacian of q and magnitude of q at the bond found. The distribution of q obtained for the ring and cage CP (3, -1). The ratio of principal curvatures h /h together cps are identical for the electrodes Li TiS ,Li NbS with 1 2 2 3 3 4 with the Laplacian provides information for a classification their corresponding delithiated phases. Therefore, the core of chemical bonding. A small value h /h  1 is typical electrons are not affected by the extraction of Li from the 1 2 for closed shell interactions. While for covalent bond this electrodes. ratio increases with bond strength. The magnitude of q is positive and large for ionic bonding, and it is small or Transport properties negative for covalent bonding [40–44]. From Table 3 it has been noted that there are two different topological distri- The calculations for the transport properties such as bution of q, which indicates the electrode materials exhibit electronic conductivities are carried out using the Boltz- two different bonding characters. Positions associated with Trap code which is interfaced with WIEN2K. BoltzTrap -3 Laplacian B0.3 A and other positions associated with is a computational tool for evaluating the transport -3 Laplacian C1.5 A were attributed to strong and weak properties using the Boltzmann transport theory [45–49]. ionic bond, respectively. The analysis of distribution of q The band energies of the compounds Li TiS ,Li NbS 2 3 3 4 for the electrode materials and their corresponding and their respective delithiated phases LiTiS and Li 3 2- delithiated structures indicates very little change in the NbS are computed with self-consistent total energy cal- electron charge density which is clearly evident for the culation with the use of WIEN2K and given as input to structural stability of the compounds Li TiS and Li NbS BoltzTrap. The transport properties as a function of the 2 3 3 4 during delithiation process. carrier concentration are computed with the results of the The bonding CPs (3, 1) and (3, 3) are described in electronic band structure calculated above. The Fourier Table 4. The distribution of charge density obtained from expansion of band energies is carried out to determine the the CPs (3, 1) and (3, 3) occurs as consequences of par- gradient along the energy bands to obtain the group ticular geometrical arrangement of bond paths, and they velocities. The group velocities are calculated as deriva- define the remaining elements of molecular structure rings tives of the energies. The transport property happens to be and cages. (3, 1) CP is found at the interior of the ring. If extremely dependent on the chemical potential. However, the bond paths are arranged so as to enclose the interior of the chemical potential is related to the number of charge a molecule with the ring surfaces, then a (3, 3) cage CP is carriers. Table 4 Position, curvatures, Laplacian and charge density at critical points other than (3, -1) from GGA Calculations -5 -5 -5 -3 2 -3 ˚ ˚ ˚ ˚ CP System xy z h (A ) h (A ) h (A ) r q (A ) q (A ) 1 2 3 (3, 1) Li TiS -0.1820 -0.2743 -0.1820 0.170 0.069 -0.025 0.214 0.043 2 3 LiTiS -0.1605 -0.2857 -0.1524 0.149 -0.039 0.084 0.194 0.041 Li NbS -0.2428 -0.2376 0.0000 0.011 0.557 -0.217 0.351 0.097 3 4 Li NbS -0.1720 -0.3126 -0.1720 0.206 0.073 -0.033 0.247 0.425 2 4 (3, 3) Li TiS 0.0000 0.5000 0.0000 0.051 0.023 0.051 0.126 0.019 2 3 LiTiS 0.0000 0.5000 0.0000 0.508 0.027 0.050 0.128 0.020 Li NbS -0.2564 -0.2563 -0.2560 0.100 0.118 0.118 0.338 0.043 3 4 Li NbS -0.2425 -0.2659 -0.2425 0.146 0.102 0.052 0.301 0.043 2 4 123 8 Page 10 of 12 Mater Renew Sustain Energy (2016) 5:8 Table 5 Calculated electronic conductivity for the electrodes and ½E ðLi TiS Þ E ðLiTiS Þ E ðLiÞ total 2 3 total 3 total V ¼ ð3Þ their delithiated phases -1 Compound Electronic conductivity in S cm References ½E ðLi NbS Þ E ðLi NbS Þ E ðLiÞ total 3 4 total 2 4 total V ¼ Present calculation Experiment ð4Þ -6 -6 Li TiS 8.755 9 10 8 9 10 [22] 2 3 -6 LiTiS 7.949 9 10 – In both reactions (Eqs. 3 and 4), one electron transferred -3 -3 Li NbS 2.582 9 10 2 9 10 [22, 24] through outer circuit. Where, E refers to the total energy 3 4 total -3 Li NbS 1.831 9 10 – per formula unit. The calculated voltage for the Li 2 4 extraction process with Li TiS is 2.35 V, and with 2 3 Li NbS it is 2.27 V. Both values are found to agree well 3 4 with the experimental value of 2.2 V [22]. Electronic conductivity Volume change An accurate assessment of the electronic conductivity of electrodes is necessary for understanding and optimizing The extraction of Li from the positive electrodes Li TiS 2 3 the battery performance. Electronic conductivity of a pos- and Li NbS during charging of battery was not accom- 3 4 itive electrode material has significant effect on the per- ? panied by any structural change. But it has been observed formance of Li battery. The electronic conductivities for that there was a small change in volume of the electrodes the electrode materials and their corresponding delithiated due to delithiation. First principle calculation can predict phases were calculated at room temperature and are listed the volume change in the electrode material during Li in Table 5. The value of electronic conductivity found to insertion and extraction. The percentage of volume change have generous agreement with the recent experimental is computed by comparing the computed equilibrium vol- results available [22, 24]. umes of the two limiting structures of the electrode [10, 55]. The change in volume (Dv) for the positive electrodes Discharge voltage Li TiS and Li NbS upon the extraction of Li have been 2 3 3 4 calculated from Eq. (5), which is given by The cell voltage is linearly related to the chemical potential of lithium within the positive electrode material. The vðLi HostÞ vðLi HostÞ x1 x2 Dv ¼ ð5Þ average equilibrium voltage (V) is related to the difference vðLi HostÞ x2 in the Gibbs free energy (DG) between the delithiated The calculated volume change for Li TiS with its 2 3 phase at charged state and lithiated phase at discharged delithiated phase LiTiS was 1.05 %, and for Li NbS with 3 3 4 state. It has previously been reported that the average Li NbS was found to be 3.5 %. The low volume change is 2 4 potential for Li extraction from a material is given by the considered as an added advantage for the positive electrode following equations [7, 8] materials to ensure very good structural stability. DG V ¼ ð1Þ ðx2  x1ÞF Conclusions ½GðLi HostÞ GðLi HostÞðx2  x1ÞGðLiÞ x2 x1 V ¼ ðx2  x1ÞF In the present work, first principle calculations within GGA ð2Þ is carried out by employing WIEN2 K to investigate the structural parameters of the rock salt type ternary lithium where, G is the Gibbs free energy of the compound. F is the Faraday’s constant. The free energy change associated with metal sulfides Li TiS and Li NbS as positive electrodes 2 3 3 4 the transfer of one mole of lithium between the two for lithium battery. To acquire knowledge about the impact composition limits. The above Eq. (2) provides the average of lithium extraction in the electronic and bonding prop- of the equilibrium potential between the lithium erties of the host compounds, the electronic band structure, compositions x1 and x2. In DFT calculations, Free density of electronic states and valence charge distribution energies can be replaced by the ground state energies are calculated. With a view to have a better insight into the with very little error [50–54]. Therefore, the discharge transport properties due to the impact of Li extraction, the voltage can be determined by computing the total energies electronic conductivity has been calculated and found to of the compounds and their delithiated phases. 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