Reverse Monte Carlo study of the 40Li2O–60P2O5 glass

PERGAMON

Solid State Communications 113 (2000) 35–39 www.elsevier.com/locate/ssc

Reverse Monte Carlo study of the 40Li2O–60P2O5 glass R.K. Sistla*, M. Seshasayee Department of Physics, Indian Institute of Technology, Madras 600 036, India Received 20 April 1999; accepted 7 September 1999 by C.N.R. Rao

Abstract Short-range order in the ionically conducting 40Li2O–60P2O5 glass has been studied by the reverse Monte Carlo (RMC) method, using X-ray diffraction data. The initial configuration for RMC was obtained by constant volume molecular dynamics simulation. The glass matrix is made up of a three dimensional network of phosphate chains consisting of PO4 tetrahedra. This is in contrast to the simple chain structure observed in crystalline LiPO3. 60% of the oxygens are non-bridging and 87% of these ˚ . A small fraction of the non-bridging oxygens show double bond character form Li–O bonds at distances shorter than 2.0 A 32 ˚ . Isolated P2 O42 with P–O distances less than 1.52 A 7 and PO4 ions are negligibly small in number. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Disordered systems; C. X-ray diffraction

1. Introduction

2. Experimental

Li2O–P2O5 system forms glass up to 72% of Li2O with a rapid quenching technique. The ionic conductivity (s ) of the glass [1] increases with increasing Li2O up to the glass forming limit. Addition of Li2O modifies the three-dimensional network of P2O5 [2] by creating more non-bridging oxygens (NBOs). Initially the glass transition temperature Tg decreases with the addition of Li2O because of the increase in the number of NBOs. At 20% Li2O, Tg reaches a minimum and increases slowly till 50% Li2O, but still remains lower than that of pure P2O5. This behaviour, namely the increase of Tg with an increase in NBOs is in contrast to what is observed in silicates and is attributed [3] to the restructuring of the glass network. Another study [4] reports a decrease in Tg for Li2O between 50 and 70%. Neutron diffraction results [5] indicate four-fold coordination of oxygen atoms around P and Li atoms, but do not discuss the connectivities of these units, which are necessary for understanding transport properties. We have undertaken a structural study of this system with various compositions to explain the conductivity and the Tg behaviour observed and report here the results for 40Li2O–60P2O5 glass.

2.1. Glass preparation and characterization

* Corresponding author.

xLi2 O–…1 2 x†P2 O5 glass with x ˆ 0:4 was prepared as described by Malugani and Robert [6]. Non-hygroscopic lithium carbonate (Li2CO3) and ammonium dihydrogen orthophosphate (NH4H2PO4) were used as precursors, respectively, for Li2O and P2O5. Appropriate amounts of Li2CO3 and NH4H2PO4 were mixed, ground and heated in a platinum crucible. NH4H2PO4 dissociates at 3008C and gives out ammonia and water. To complete the dissociation of NH4H2PO4, the sample was kept at 3008C for 12 h. Then the sample was heated to 7008C and kept for 1 h to dissociate Li2CO3 to liberate CO2 and then melted at 9008C for 30 min. Bubble free melt was quenched between two preheated (2008C) copper plates to avoid shattering of the glass and annealed at this temperature for few hours and cooled to room temperature to relieve the thermal strains in the sample. The glass was colourless, transparent and hygroscopic. Glassy nature was checked by X-ray diffraction. Density and Tg values measured are 2.35 gm/cc and 2808C, respectively. s at 258C is 2:5 × 10211 S=cm: Reported value for s is 1:9 × 10211 S=cm [1]. Tg values reported are 2348C [1] and 3108C [2]. The small value quoted in Ref. [1] is, according to the authors due to –OH contamination in the sample. As the Tg of our sample is

0038-1098/00/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00437-8

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R.K. Sistla, M. Seshasayee / Solid State Communications 113 (2000) 35–39

Table 1 Potential parameters in MD

Li–Li P–P O–O Li–P Li–O P–O

A (J)

B (nm 21)

D (J nm 6)

1:000 × 10210 0:100 × 10222 0:800 × 10215 0:783 × 10216 0:300 × 10214 0:200 × 10214

125.00 131.58 35.21 128.21 54.95 55.56

0.0 0.0 26.8 × 10 229 0.0 0.0 0.0

lesser than the value quoted in [2], we checked the FT-IR spectra for P–OH stretching mode and found a weak peak at 3448 cm 21. This indicates the presence of P–OH bonds to a small extent. Density value quoted for crystalline LiPO3 is 2.481 gm/cc [7] and no value is available in the literature for glassy LiPO3. 2.2. Molecular dynamics simulation Constant volume molecular dynamics (MD) was done starting at 3000 K and the system was cooled to 300 K in steps of 150 K. The number of atoms in the system was 1080 ˚ . Born–Meyer– and the simulation box length was 23.903 A Huggins potential of the form U…rij † ˆ

Zi Zj e2 D 1 A exp…2Brij † 2 6 rij rij

was used. The initial potential parameters were taken from those reported for Li2SiO3 [8] and modified to produce the correct nearest neighbour bond lengths for P–O, Li–O and O–O as reported for crystalline LiPO3 [7] (Table 1). Newton’s equations were solved by the Verlet algorithm.

The time step used was 1 fs. Electrostatic interactions were calculated using the Ewald summation. The three parameters used in the Ewald summation namely, the real space cut off (rcut), the largest reciprocal space vector (kmax), and ˚ , (6, 6, 6) and the convergence parameter (a ) were 11.95 A ˚ 21, respectively. These values led to the conver4.8 × 10 8 A gence of both the real space sum and the reciprocal space sum. The ionic charges used were 0.799 for Li, 3.4 for P and 21.388 for O. At each temperature, 5000 steps were used to attain equilibrium. Further 10 000 steps were used to collect the pair correlation function (PCF). Figs. 1–4 depict the PCF plots for P–O, P–P, Li–O and Li–Li interactions. The broad peak for Li–Li indicates its mobile nature in the structure. 2.3. X-ray data collection Glass of dimension 30 mm × 20 mm × 2 mm was used to collect the X-ray data. As the sample was hygroscopic, silica gel, calcium carbonate and molecular sieves were kept in the diffractometer sample chamber. Data in the range 1:58 , u , 758 was collected in the fixed count mode. The step size at lower angles was 0.1258, and at higher angles it was increased to 0.258. Fixed counts at higher intensities was 200 000 and at lower intensities reduced to 50 000. Data corrected for background and absorption was normalized using both Krogh-Moe [9] and High angle method [10] to provide the experimental S(Q) vs Q data, where Q ˆ 4p sin u=l: 2.4. Reverse Monte Carlo method The RMC method [11] is a variation of the standard Metropolis Monte Carlo procedure, wherein random

Fig. 1. Pair correlation function (PCF) vs. r for P–O.

R.K. Sistla, M. Seshasayee / Solid State Communications 113 (2000) 35–39

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Fig. 2. Pair correlation function (PCF) vs. r for P–P.

movement of randomly chosen atoms of the system produces a canonical ensemble of atoms. In RMC, the squared difference between experimental and calculated structure function S(Q) is minimized until an equilibrium configuration is obtained. Experimental S(Q) is given by the X-ray data and calculated S(Q) is obtained initially from MD simulated configuration. This configuration from MD was refined using RMC method till a good match with experimentally obtained S(Q) was achieved. The minimum Q value, Qmin used in fitting for RMC is given by 2p=L;

where L is the MD cell size. The structure factors S(Q) obtained from MD analysis and the final RMC generated configuration are shown in Fig. 5 indicating the improvement brought about by RMC refinement. Fig. 6 shows the match between X-ray generated and RMC generated S(Q) functions. The agreement between the two plots is acceptable for X-ray generated data as seen in the other similar published work [12]. The constraints used in RMC were density and distance of closest approach for all pairs of atoms.

Fig. 3. Pair correlation function (PCF) vs. r for Li–O.

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R.K. Sistla, M. Seshasayee / Solid State Communications 113 (2000) 35–39

Fig. 4. Pair correlation function (PCF) vs. r for Li–Li.

The configuration of atoms obtained after the convergence of S(Q) functions was analysed for structural details. Table 2 lists the average number of bonds for all pairs of atoms obtained from the RMC procedure. Sixty-nine percent of Li atoms are four-fold coordinated to oxygens around it. Three- and five-fold coordinations of oxygens occur among the remaining Li atoms in equal proportion. ˚. The average Li–O distance is 2.2 A All the P atoms are four-fold coordinated to oxygens, the

˚ . The average O–P–O average P–O distance being 1.6 A angle in PO4 units is 1098 indicating the tetrahedral nature of PO4 units. Nearly 60% of the oxygens are non-bridging, forming a single O–P bond. As pure P2O5 glass has 25% of oxygens appearing as non-bridging, this increase is attributed to the addition of Li. Majority (87%) of these NBOs ˚ . The form Li–O bonds at distances shorter than 2.0 A remaining NBOs (13%) do not form Li–O bonds and their ˚ . These oxygen atoms defiaverage O–P distance is 1.51 A nitely have a double bond character when compared with the ˚ ) of bridging oxygen atoms average O–P distance (1.61 A with more than one O–P bond. Less than 2% of the bridging ˚ , which is oxygens have one Li neighbour around 2.4 A

Fig. 5. S(Q) generated by MD and RMC refinement.

Fig. 6. Q vs. S(Q) for 40Li2O–60P2O5.

3. Results and discussion

R.K. Sistla, M. Seshasayee / Solid State Communications 113 (2000) 35–39 Table 2 Average number of bonds for all pairs of atoms P–P

O–O

Li–P

Li–O

P–O

O–Li

O–P

2.0

5.4

3.4

4.0

4.0

0.9

1.4

difficult to explain. The rest of the bridging oxygens do not ˚. have any Li neighbour for distances as large as 2.68 A Although 41% of P atoms have two P neighbours at ˚ , 30% of the total have a larger number of P neigh3.23 A bours indicating the three-dimensional nature of the glass network. A quarter of the total number of P atoms have a single P neighbour and almost all of them appear at the ends 32 of the PO4 chains. Isolated ions such as P2 O42 7 ; PO4 and 52 P3 O10 are present to a small fraction of less than 7% of the total number of P atoms. Ions P3 O32 9 with a ring structure are not present and neither are molecules such as P4O10. Although branched chains with larger number of P atoms are present, ions with small-branched structure such as P4 O62 13 do not appear as predicted by earlier workers [13]. 52 Even in ions P2 O42 7 and P3 O10 ; the P–O–P angle is greater than 1408 and not 1348 as reported in Na4P2O7 crystal [14] and NaPO3 glass [15]. The ‘antibranching rule’ [16] in ultraphosphate glasses (P2O5 content . 50%) explain their high hygroscopicity as being due to the presence of branched chains which has high reactivity with H2O. In this glass, 23% of the total P atoms form three P–P linkages, which indicate a high prevalence of branched chains and agree with the above rule. Chains containing PO4 tetrahedra branch and criss-cross in all directions contributing to a three-dimensional network. Pure P2O5 glass has one double bonded oxygen in each PO4 unit. Addition of Li2O has converted a significant number of PyO bonds to P–O–Li bonds and many of the P–O–P bonds to P–O–Li bonds. The mixed coordination around Li of 3, 4 and 5 oxygens leads to branched chains containing PO4 units, instead of the simple chain structure observed in crystalline LiPO3. The increase in Tg around 40% Li2O can be explained by the branching PO4 chains and the cross linking between PO4 and LiOn units as they tend to strengthen the network and the glass. The configuration obtained here agrees with that predicted by Hoppe. According to Hoppe’s model, when N, the number of oxygens around Li far exceeds M, the ratio of the number of non-bridging oxygens to the number of Li atoms, the glass structure becomes stronger by the presence of

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interpenetrating patterns formed by linked PO4 units and less regularly linked LiOn polyhedra with the Li polyhedra coming into closer contact. In our configuration of the glass, the above conditions are fulfilled with 4 and 2.5 being the values for N and M, respectively. The average Li–Li ˚ , which is much shorter than distance observed is 2.16 A ˚ ) indithose observed in the crystalline LiPO3(2.63–3.14 A cating a closer contact amongst the LiOn units. Li being the mobile ion, its increase in concentration increases the conductivity. It is now understood that the increase in NBOs contributes to the enhancement in s . In addition we find that the presence of branched chains does not seem to hinder conduction in this glass.

4. Conclusions The presence of PO4 chains branching in all directions and interpenetrating LiOn polyhedra with NBOs strengthen the network of the glass under consideration, leading to higher values of Tg.

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