- Email: [email protected]
First principle study of 0.75AgI:0.25AgCl: A density functional approach
Chemical Physics Letters 661 (2016) 157–160
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
First principle study of 0.75AgI:0.25AgCl: A density functional approach B. Keshav Rao ⇑, Mohan L. Verma Department of Applied Physics, FET, SSGI, Shri Shankaracharya Technical Campus, Junwani, Bhilai, Chhattisgarh 490020, India
a r t i c l e
i n f o
Article history: Received 25 July 2016 In final form 26 August 2016 Available online 27 August 2016 Keywords: Density functional theory SIESTA PDOS DOS
a b s t r a c t The first principles calculations based on norm-conserving pseudo potentials and density functional theory are performed for zincblende structured new host 0.75AgI:0.25AgCl. For comparison point of view zincblende structured b-AgI is considered. The structural analysis provides the higher cationic concentration in new host. Density of state analysis explains a weak p-d hybridization in b-AgI and strong in new host. There is decrease in forbidden energy band gap by 0.05 eV and hence large ionic concentration and conductivity is found in new host. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction
2. Methodology
Superionic solids give exceptionally high ionic conductivity 10 1–10 4 S/cm at room temperature, it is comparable to that of liquid/aqueous electrolytes; hence, they are potentially used to develop solid-state electrochemical devices [1,2]. Amongst known superionic materials, fast Ag+-ion conducting solids are often attracted special attentions due to their relatively higher room temperature conductivity (10 1–10 2 S/cm) as well as ease of material handling during synthesis [3,4]. A variety of Ag+ ion superionic solids and composite phases have been synthesized [5–9]. AgI is known for its characteristic structural phase transition 147 °C at which it exhibits a conductivity jump of 103–104 orders of magnitude during the transition from a low conducting b-phase (zinc blende/wurtzite) to the superionic a-phase (cubic) [10–12]. An alternative host salt instead of AgI which is called a quenched/annealed mixed system/solid solution (0.75AgI:0.25A gCl) is synthesized [13], it exhibits not only improved ion transport characteristics akin to AgI, but also resulted into several new Ag+ ion superionic solids in glassy/amorphous 2-phase composite and polycrystalline electrolytes with superior ionic properties [14,15]. In present work the first principle calculations based on density functional theory are performed to investigate the structural and electronic properties of zinc-blende structured new host b0.75AgI:0.25AgCl and b-AgI.
Density functional theory (DFT) is used commonly in recent years [16]; since it is computationally less intensive than other methods with similar accuracy. All calculations are performed by using the SIESTA (Spanish Initiative for Electronic Simulations with Thousand of Atoms) code [17,18], where a numerical atomic basis approximation is implemented which is rather fast and appropriate for electronic structure calculations of large systems [19,20]. The main feature of this code is to use of flexible basis sets composed of linear combinations of numerical atomic orbitals, which can be generated by solving the Kohn–Sham equation of atomic pseudo potentials [21]. The equilibrium positions of the atoms are obtained by the forces on each atom smaller than 0.01 eV/Å. Norm-conserving pseudo potentials are used [22] with the following electronic configuration of the elements: Ag: [Kr] 4d10 5s1, I: [Kr] 4d10 5s2 5p5 and Cl: [Ne] 3s2 3p5, where the core configurations are shown in parenthesis. A generalized gradient approximation (GGA) is used in the scheme of Perdew–Burke–Eruzerhof (PBE) to describe the exchange and correlation potential, since GGA is found relatively more efficient to predict the energy gap than the local-density approximation (LDA) [17].
⇑ Corresponding author. E-mail addresses: [email protected] (B.K. Rao), [email protected] (M.L. Verma). http://dx.doi.org/10.1016/j.cplett.2016.08.069 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.
3. Results and discussion The structural optimization is performed mainly by mesh cutoff, k-points and simulation box size (i.e. the lattice constant) optimizations. Mesh-cutoff corresponds to fineness of the real-space grid; its convergence test is performed in the range of 50 to 500 Ry for both b-AgI and b-new host. On the basis of lowest and stable energy, the calculated mesh-cutoff of both systems are
158
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Fig. 1. Equilibrium configurations of zincblende: (a) b-AgI and (b) b-New host 0.75AgI:0.25AgCl.
150 Ry and 200 Ry, respectively. In the next step of geometry optimization, K-points are optimized in the range of 2–12 and with lowest energy value, these are 4 & 5, respectively. By the optimized values of mesh-cutoff and k-points; the cell size is optimized in the range of 6.0–12.0 Å. According to minimum energy, obtained optimized values are 9.0 Å & 8.5 Å, respectively. Fig. 1a and b represent the equilibrium structures of zincblende b-AgI and b-New host 0.75AgI:0.25AgCl. We find that there is dispersion in the structure of b-new host, the number of free cations are increased after replacement of one iodide atom
40
(a)
by chlorine atom. It justifies the experimental results, where the ionic concentration of b-new host is 10 times higher than bAgI [13]. In charge density analysis, it is found that there is an ionic bond between silver and iodide atoms, which is not shown here, there is large charge density around the iodine atom compared to the silver atom. After dispersion of chlorine atom, due to having larger electro negativity, higher charge density is observed around chlorine atom.
40
Ag I
PDOS (States/eV)
PDOS (States/eV)
30 25 20 15
30 25 20 15
10
10
5
5 -4
-2
0
2
Ag (4d) Ag (5p) Ag (5s)
35
35
0 -6
(b)
0 -6
4
-4
6
2
4
E-Ef (eV)
(c)
I (5p) I (5s)
40
(d)
AgI
35
DOS (States/eV)
5
PDOS (States/eV)
0
-2
E-Ef (eV)
4 3 2
30 25 20 15 10
1 0
-6
5
-4
-2 E-Ef (eV)
0
2
0 -6
-4
-2
0
E-Ef (eV) Fig. 2. (a), (b), (c) are PDOS and (d) is DOS of b-AgI.
2
4
159
B.K. Rao, M.L. Verma / Chemical Physics Letters 661 (2016) 157–160
40
40
(a)
Ag I Cl
(b)
Ag (4d) Ag (5p) Ag (5s)
35
30
PDOS (States/eV)
PDOS (States/eV)
35
25 20 15
30 25 20 15
10
10
5
5 0
0 -6
-4
0
-2
2
-6
4
-4
0
-2
2
4
E-Ef (eV)
E-Ef (eV) 4
6
(c)
(d)
I (5p) I (5s)
Cl (3p) Cl (3s)
5
PDOS (States/eV)
PDOS (States/eV)
3 4 3 2
2
1 1 0 -6
-4
0
-2
2
0 -6
4
-4
2
4
E-Ef (eV)
(e)
40
0
-2
E-Ef (eV)
NH
DOS (States/eV)
35 30 25 20 15 10 5 0 -6
-4
0
-2
2
4
E-Ef (eV) Fig. 3. (a), (b), (c), (d) are PDOS and (e) is DOS of b-new host.
Since, a silver ion Ag+ is a strong acid; and a chloride ion (Cl ) is a strong base than iodide ion (I ), and due to hard/soft acid base (HSAB) principle, a strong acid silver atoms are attracted strongly towards a strong base [23,24]. Hence, there is hopping motion of silver ions via anions which causes the cationic motion, it is larger in new host, i.e. there is decrease in the activation energy of cations [25]. The projected density states (PDOS) of silver and iodide atoms of b-AgI are presented in Fig. 2a; the contribution made by electrons of silver atom in valence and conduction band is larger than iodide atom. In silver atom contribution made by 4d orbital
electrons are larger in the lower valence band, high peak is at 3.5 eV, contribution of 5s electrons is larger near Fermi level (0 eV) and in the conduction band beyond to 0.5 eV, it is shown in Fig. 2b. There is small contribution of 5p orbital electrons of the iodide atom in the valence band; high peak is at 2.1 eV, it is shown in Fig. 2c. Density of states (DOS) analysis presents the p-d hybridization between d-states of Ag+ and p-states of I , it verifies the results [26,27], the width of band is of the order of 4 eV, it is shown in Fig. 2d. The highest occupied molecular orbital (HOMO) is at around 0.3 eV and the lowest un-occupied molecular orbital
160
B.K. Rao, M.L. Verma / Chemical Physics Letters 661 (2016) 157–160
(LUMO) is at around 0.35 eV, the valence band is continues from 5.6 eV to 1.8 eV and there are three intermediate valence bands also observed in between 1.8 eV and 0 eV. There is a continuous conduction band after LUMO, the forbidden energy gap is around 0.65 eV. In b-new host, PDOS of elements is shown in Fig. 3a, there is a slight shift in peaks of 4d-states of Ag+ and 5p-states of I towards Fermi level, shown in Fig. 3b and c. There is a peak of 3p-states of Cl at 2.2 eV, given in Fig. 3d. There is also a p-d hybridization in new host, here a whole band is shifted towards Fermi level with broader width, it is of the order of 4.5 eV, shown in Fig. 3e. Before Fermi level; there is a thin valence band followed by a broader valence band, HOMO is around 0.3 eV and the LUMO is around 0.3 eV, a lower valence band is obtained from 0.8 eV to 5.5 eV, the conduction band is obtained after LUMO. The forbidden energy gap is around 0.6 eV. In b-new host, there is a broader valence band near Fermi level and the forbidden energy is reduced by 0.05 eV than b-AgI, hence silver atoms get easily converted into cations by breaking a band with halides, therefore the cationic concentration is large in bnew host than b-AgI [13]. Since there is strong p-d hybridization in b-new host and weak p-d hybridization in b-AgI [26,27], hence mobility of cations is reduced in some extent but overall ionic conductivity is increased in b-new host [25]. 4. Conclusions The structural analysis explains the dispersion in b-new host and large cationic concentration due to breaking of bond between Ag & I. Projected density of states analysis exhibits a weak p-d hybridization in b-AgI and a strong hybridization in new host, as a result of that a forbidden energy gap is reduced by 0.05 eV in b-new host which causes the higher ionic concentration and higher ionic conductivity than b-AgI. Acknowledgements We gratefully acknowledge the kind support of the management of Shri Shankaracharya Group of Institutions (SSTC). Helpful
discussions with Prof. Ravindra Pandey (Michigan Technological University, USA) and Dr. Rodrigo Garcia Amorim (Universidade Federal Fluminense-UFF, Brazil) are acknowledged. References [1] S. Chandra, Superionic Solids: Principles and Applications, North Holland, Amsterdam, 1981. [2] A.L. Laskar, S. Chandra, Superionic Solids and Solid Electrolytes-Recent Trends, Academic Press, New York, 1989. [3] R.C. Agrawal, M.L. Verma, R.K. Gupta, Indian J. Pure & Appl. Phys. 37 (1999) 334. [4] R.C. Agrawal, M.L. Verma, R.K. Gupta, S. Thaker, Solid State Ionics 136 (2000) 473. [5] B.K. Rao, M.L. Verma, J. Chem. Phys. (2016), http://dx.doi.org/10.1016/j. chemphys. [6] M.L. Verma, H.D. Sahu, J. Ionics 21 (2015) 3223. [7] M.L. Verma, M.M. Sundaram, N.K. Singh, Electrochem. Acta 137 (2014) 497. [8] B.K. Rao, M.L. Verma, J. Ionics (2014), http://dx.doi.org/10.1007/s11581-0141344-4. [9] M.L. Verma, B.K. Rao, J. Ionics 20 (2014) 697. [10] C. Tubandt, E. Lorenz, J. Phys. Chem. 513 (1914) 87. [11] M.L. Verma, R.C. Agrawal, M. Mukherjee, J. Rad. Eff. Defects Solids 61 (2006) 225. [12] M.L. Verma, B.K. Rao, J. Ionics 17 (2011) 323. [13] R.C. Agrawal, R.K. Gupta, R. Kumar, A. Kumar, J. Mater. Sci. 29 (1994) 3673. [14] R.C. Agrawal, Chandra Angesh, Alok Bhatt, Y.K. Mahipal, J. Phys. D: Appl. Phys. 40 (2007) 4714. [15] R.C. Agrawal, Angesh Chandra, Alok Bhatt, Y.K. Mahipal, Eur. Phys. J. Appl. Phys. 43 (2008) 209. [16] R.M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004. [17] E. Artacho, J.M. Cela, J.D. Gale, A. Garcia, J. Junquera, R.M. Martin, P. Ordejon, D. S. Portal, J.M. Soler, SIESTA 3.1, 2011. [18] http://www.uam.es/siesta. [19] P. Ordejo´n, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) R10441. [20] J.M. Soler, E. Artacho, J.D. Gale, A. Garcı´a, J. Junquera, P. Ordejo´n, D. Sa´nchezPortal, J. Phys. C: Condens. Matter 14 (2002) 2745. [21] R.Q. Zhang, Q.Z. Zhang, M.W. Zhao, Theor. Chem. Acc. 112 (2004) 158. [22] N. Trouillier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [23] F.M. Gray, Solid Polymer Electrolytes: Fundamentals and Technological Applications. Scotland, UK, 1991. [24] F.M. Gray, Polymer Electrolytes, The Royal Society of Chemistry, Cambridge, 1997. [25] M.L. Verma, Thesis Pt. Ravishankar Shukla Univ. Raipur, 2000. [26] S. Ono, M. Kobayashi, H. Iyetomi, T. Tomoyose, Solid State Ionics 139 (2001) 249. [27] M. Kobayashi, S. Ono, T. Kohda, H. Iyetomi, S. Kashida, T. Tomoyose, Solid State Ionics 154 (2002) 209.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
First principle study of 0.75AgI:0.25AgCl: A density functional approach B. Keshav Rao ⇑, Mohan L. Verma Department of Applied Physics, FET, SSGI, Shri Shankaracharya Technical Campus, Junwani, Bhilai, Chhattisgarh 490020, India
a r t i c l e
i n f o
Article history: Received 25 July 2016 In final form 26 August 2016 Available online 27 August 2016 Keywords: Density functional theory SIESTA PDOS DOS
a b s t r a c t The first principles calculations based on norm-conserving pseudo potentials and density functional theory are performed for zincblende structured new host 0.75AgI:0.25AgCl. For comparison point of view zincblende structured b-AgI is considered. The structural analysis provides the higher cationic concentration in new host. Density of state analysis explains a weak p-d hybridization in b-AgI and strong in new host. There is decrease in forbidden energy band gap by 0.05 eV and hence large ionic concentration and conductivity is found in new host. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction
2. Methodology
Superionic solids give exceptionally high ionic conductivity 10 1–10 4 S/cm at room temperature, it is comparable to that of liquid/aqueous electrolytes; hence, they are potentially used to develop solid-state electrochemical devices [1,2]. Amongst known superionic materials, fast Ag+-ion conducting solids are often attracted special attentions due to their relatively higher room temperature conductivity (10 1–10 2 S/cm) as well as ease of material handling during synthesis [3,4]. A variety of Ag+ ion superionic solids and composite phases have been synthesized [5–9]. AgI is known for its characteristic structural phase transition 147 °C at which it exhibits a conductivity jump of 103–104 orders of magnitude during the transition from a low conducting b-phase (zinc blende/wurtzite) to the superionic a-phase (cubic) [10–12]. An alternative host salt instead of AgI which is called a quenched/annealed mixed system/solid solution (0.75AgI:0.25A gCl) is synthesized [13], it exhibits not only improved ion transport characteristics akin to AgI, but also resulted into several new Ag+ ion superionic solids in glassy/amorphous 2-phase composite and polycrystalline electrolytes with superior ionic properties [14,15]. In present work the first principle calculations based on density functional theory are performed to investigate the structural and electronic properties of zinc-blende structured new host b0.75AgI:0.25AgCl and b-AgI.
Density functional theory (DFT) is used commonly in recent years [16]; since it is computationally less intensive than other methods with similar accuracy. All calculations are performed by using the SIESTA (Spanish Initiative for Electronic Simulations with Thousand of Atoms) code [17,18], where a numerical atomic basis approximation is implemented which is rather fast and appropriate for electronic structure calculations of large systems [19,20]. The main feature of this code is to use of flexible basis sets composed of linear combinations of numerical atomic orbitals, which can be generated by solving the Kohn–Sham equation of atomic pseudo potentials [21]. The equilibrium positions of the atoms are obtained by the forces on each atom smaller than 0.01 eV/Å. Norm-conserving pseudo potentials are used [22] with the following electronic configuration of the elements: Ag: [Kr] 4d10 5s1, I: [Kr] 4d10 5s2 5p5 and Cl: [Ne] 3s2 3p5, where the core configurations are shown in parenthesis. A generalized gradient approximation (GGA) is used in the scheme of Perdew–Burke–Eruzerhof (PBE) to describe the exchange and correlation potential, since GGA is found relatively more efficient to predict the energy gap than the local-density approximation (LDA) [17].
⇑ Corresponding author. E-mail addresses: [email protected] (B.K. Rao), [email protected] (M.L. Verma). http://dx.doi.org/10.1016/j.cplett.2016.08.069 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.
3. Results and discussion The structural optimization is performed mainly by mesh cutoff, k-points and simulation box size (i.e. the lattice constant) optimizations. Mesh-cutoff corresponds to fineness of the real-space grid; its convergence test is performed in the range of 50 to 500 Ry for both b-AgI and b-new host. On the basis of lowest and stable energy, the calculated mesh-cutoff of both systems are
158
B.K. Rao, M.L. Verma / Chemical Physics Letters 661 (2016) 157–160
Fig. 1. Equilibrium configurations of zincblende: (a) b-AgI and (b) b-New host 0.75AgI:0.25AgCl.
150 Ry and 200 Ry, respectively. In the next step of geometry optimization, K-points are optimized in the range of 2–12 and with lowest energy value, these are 4 & 5, respectively. By the optimized values of mesh-cutoff and k-points; the cell size is optimized in the range of 6.0–12.0 Å. According to minimum energy, obtained optimized values are 9.0 Å & 8.5 Å, respectively. Fig. 1a and b represent the equilibrium structures of zincblende b-AgI and b-New host 0.75AgI:0.25AgCl. We find that there is dispersion in the structure of b-new host, the number of free cations are increased after replacement of one iodide atom
40
(a)
by chlorine atom. It justifies the experimental results, where the ionic concentration of b-new host is 10 times higher than bAgI [13]. In charge density analysis, it is found that there is an ionic bond between silver and iodide atoms, which is not shown here, there is large charge density around the iodine atom compared to the silver atom. After dispersion of chlorine atom, due to having larger electro negativity, higher charge density is observed around chlorine atom.
40
Ag I
PDOS (States/eV)
PDOS (States/eV)
30 25 20 15
30 25 20 15
10
10
5
5 -4
-2
0
2
Ag (4d) Ag (5p) Ag (5s)
35
35
0 -6
(b)
0 -6
4
-4
6
2
4
E-Ef (eV)
(c)
I (5p) I (5s)
40
(d)
AgI
35
DOS (States/eV)
5
PDOS (States/eV)
0
-2
E-Ef (eV)
4 3 2
30 25 20 15 10
1 0
-6
5
-4
-2 E-Ef (eV)
0
2
0 -6
-4
-2
0
E-Ef (eV) Fig. 2. (a), (b), (c) are PDOS and (d) is DOS of b-AgI.
2
4
159
B.K. Rao, M.L. Verma / Chemical Physics Letters 661 (2016) 157–160
40
40
(a)
Ag I Cl
(b)
Ag (4d) Ag (5p) Ag (5s)
35
30
PDOS (States/eV)
PDOS (States/eV)
35
25 20 15
30 25 20 15
10
10
5
5 0
0 -6
-4
0
-2
2
-6
4
-4
0
-2
2
4
E-Ef (eV)
E-Ef (eV) 4
6
(c)
(d)
I (5p) I (5s)
Cl (3p) Cl (3s)
5
PDOS (States/eV)
PDOS (States/eV)
3 4 3 2
2
1 1 0 -6
-4
0
-2
2
0 -6
4
-4
2
4
E-Ef (eV)
(e)
40
0
-2
E-Ef (eV)
NH
DOS (States/eV)
35 30 25 20 15 10 5 0 -6
-4
0
-2
2
4
E-Ef (eV) Fig. 3. (a), (b), (c), (d) are PDOS and (e) is DOS of b-new host.
Since, a silver ion Ag+ is a strong acid; and a chloride ion (Cl ) is a strong base than iodide ion (I ), and due to hard/soft acid base (HSAB) principle, a strong acid silver atoms are attracted strongly towards a strong base [23,24]. Hence, there is hopping motion of silver ions via anions which causes the cationic motion, it is larger in new host, i.e. there is decrease in the activation energy of cations [25]. The projected density states (PDOS) of silver and iodide atoms of b-AgI are presented in Fig. 2a; the contribution made by electrons of silver atom in valence and conduction band is larger than iodide atom. In silver atom contribution made by 4d orbital
electrons are larger in the lower valence band, high peak is at 3.5 eV, contribution of 5s electrons is larger near Fermi level (0 eV) and in the conduction band beyond to 0.5 eV, it is shown in Fig. 2b. There is small contribution of 5p orbital electrons of the iodide atom in the valence band; high peak is at 2.1 eV, it is shown in Fig. 2c. Density of states (DOS) analysis presents the p-d hybridization between d-states of Ag+ and p-states of I , it verifies the results [26,27], the width of band is of the order of 4 eV, it is shown in Fig. 2d. The highest occupied molecular orbital (HOMO) is at around 0.3 eV and the lowest un-occupied molecular orbital
160
B.K. Rao, M.L. Verma / Chemical Physics Letters 661 (2016) 157–160
(LUMO) is at around 0.35 eV, the valence band is continues from 5.6 eV to 1.8 eV and there are three intermediate valence bands also observed in between 1.8 eV and 0 eV. There is a continuous conduction band after LUMO, the forbidden energy gap is around 0.65 eV. In b-new host, PDOS of elements is shown in Fig. 3a, there is a slight shift in peaks of 4d-states of Ag+ and 5p-states of I towards Fermi level, shown in Fig. 3b and c. There is a peak of 3p-states of Cl at 2.2 eV, given in Fig. 3d. There is also a p-d hybridization in new host, here a whole band is shifted towards Fermi level with broader width, it is of the order of 4.5 eV, shown in Fig. 3e. Before Fermi level; there is a thin valence band followed by a broader valence band, HOMO is around 0.3 eV and the LUMO is around 0.3 eV, a lower valence band is obtained from 0.8 eV to 5.5 eV, the conduction band is obtained after LUMO. The forbidden energy gap is around 0.6 eV. In b-new host, there is a broader valence band near Fermi level and the forbidden energy is reduced by 0.05 eV than b-AgI, hence silver atoms get easily converted into cations by breaking a band with halides, therefore the cationic concentration is large in bnew host than b-AgI [13]. Since there is strong p-d hybridization in b-new host and weak p-d hybridization in b-AgI [26,27], hence mobility of cations is reduced in some extent but overall ionic conductivity is increased in b-new host [25]. 4. Conclusions The structural analysis explains the dispersion in b-new host and large cationic concentration due to breaking of bond between Ag & I. Projected density of states analysis exhibits a weak p-d hybridization in b-AgI and a strong hybridization in new host, as a result of that a forbidden energy gap is reduced by 0.05 eV in b-new host which causes the higher ionic concentration and higher ionic conductivity than b-AgI. Acknowledgements We gratefully acknowledge the kind support of the management of Shri Shankaracharya Group of Institutions (SSTC). Helpful
discussions with Prof. Ravindra Pandey (Michigan Technological University, USA) and Dr. Rodrigo Garcia Amorim (Universidade Federal Fluminense-UFF, Brazil) are acknowledged. References [1] S. Chandra, Superionic Solids: Principles and Applications, North Holland, Amsterdam, 1981. [2] A.L. Laskar, S. Chandra, Superionic Solids and Solid Electrolytes-Recent Trends, Academic Press, New York, 1989. [3] R.C. Agrawal, M.L. Verma, R.K. Gupta, Indian J. Pure & Appl. Phys. 37 (1999) 334. [4] R.C. Agrawal, M.L. Verma, R.K. Gupta, S. Thaker, Solid State Ionics 136 (2000) 473. [5] B.K. Rao, M.L. Verma, J. Chem. Phys. (2016), http://dx.doi.org/10.1016/j. chemphys. [6] M.L. Verma, H.D. Sahu, J. Ionics 21 (2015) 3223. [7] M.L. Verma, M.M. Sundaram, N.K. Singh, Electrochem. Acta 137 (2014) 497. [8] B.K. Rao, M.L. Verma, J. Ionics (2014), http://dx.doi.org/10.1007/s11581-0141344-4. [9] M.L. Verma, B.K. Rao, J. Ionics 20 (2014) 697. [10] C. Tubandt, E. Lorenz, J. Phys. Chem. 513 (1914) 87. [11] M.L. Verma, R.C. Agrawal, M. Mukherjee, J. Rad. Eff. Defects Solids 61 (2006) 225. [12] M.L. Verma, B.K. Rao, J. Ionics 17 (2011) 323. [13] R.C. Agrawal, R.K. Gupta, R. Kumar, A. Kumar, J. Mater. Sci. 29 (1994) 3673. [14] R.C. Agrawal, Chandra Angesh, Alok Bhatt, Y.K. Mahipal, J. Phys. D: Appl. Phys. 40 (2007) 4714. [15] R.C. Agrawal, Angesh Chandra, Alok Bhatt, Y.K. Mahipal, Eur. Phys. J. Appl. Phys. 43 (2008) 209. [16] R.M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004. [17] E. Artacho, J.M. Cela, J.D. Gale, A. Garcia, J. Junquera, R.M. Martin, P. Ordejon, D. S. Portal, J.M. Soler, SIESTA 3.1, 2011. [18] http://www.uam.es/siesta. [19] P. Ordejo´n, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) R10441. [20] J.M. Soler, E. Artacho, J.D. Gale, A. Garcı´a, J. Junquera, P. Ordejo´n, D. Sa´nchezPortal, J. Phys. C: Condens. Matter 14 (2002) 2745. [21] R.Q. Zhang, Q.Z. Zhang, M.W. Zhao, Theor. Chem. Acc. 112 (2004) 158. [22] N. Trouillier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [23] F.M. Gray, Solid Polymer Electrolytes: Fundamentals and Technological Applications. Scotland, UK, 1991. [24] F.M. Gray, Polymer Electrolytes, The Royal Society of Chemistry, Cambridge, 1997. [25] M.L. Verma, Thesis Pt. Ravishankar Shukla Univ. Raipur, 2000. [26] S. Ono, M. Kobayashi, H. Iyetomi, T. Tomoyose, Solid State Ionics 139 (2001) 249. [27] M. Kobayashi, S. Ono, T. Kohda, H. Iyetomi, S. Kashida, T. Tomoyose, Solid State Ionics 154 (2002) 209.