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Journal of Non-Crystalline Solids 354 (2008) 203–207

A molecular dynamics study of the role of the cation in modifyingthe structure of alkali borate glasses

Miguel Angel Gonzalez a,d,*, Claudia Mondelli b,d, Giovanna D’Angelo c,Cristina Crupi c, Mark R. Johnson d

a Instituto de Ciencia de Materiales de Aragon, CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spainb INFM-OGG and CRS-SOFT, Italy

c Dipartimento di Fisica, Universita di Messina, 98166 S. Agata, Messina, Italyd Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, F-38042 Grenoble, France

Available online 24 October 2007

Abstract

The structures of the full series of alkali borate glasses (M2O)x(B2O3)1�x (M = Li, Na, K, Rb and Cs) at two different concentrations,x = 0.14 and x = 0.30, have been investigated by means of molecular dynamics simulations. Additional compositions have also beeninvestigated for the lithium and caesium borate glasses (x = 0.10, 0.20, 0.25, and 0.40). The main experimental trends are well reproducedby the simulations, even if the agreement is not quantitative. Our results indicate that lithium atoms can enter into the matrix of purevitreous B2O3 without inducing large modifications in the B–O network, even at large concentrations. However when the other alkaliions are added to the initial structure, the network opens to accommodate the larger size of the cation. These modifications inducethe appearance of a low-Q shoulder or pre-peak, whose intensity increases with increasing alkali concentration as well as with increasingalkali size.� 2007 Elsevier B.V. All rights reserved.

PACS: 61.43.Bn; 61.43.Fs

Keywords: Molecular dynamics; Alkali borate glass; Long range order

1. Introduction

The addition of alkali oxides to borate glasses mayresult in strong modifications of the structure as comparedto that of pure vitreous B2O3. The extent of such modifica-tions depends on the nature of the alkali introduced in theoriginal matrix as well as on the concentration of the alkalimetal employed. Thus in pure v-B2O3 all the boron atomsform part of triangular borate units BO3 [1] and the addi-tion of the network modifier transforms some of thoseunits into tetrahedral BO4 units. The proportion of BO4

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.08.079

* Corresponding author. Address: Institut Laue Langevin, 6 rue JulesHorowitz, BP 156, F-38042 Grenoble, France. Tel.: +33 4 76207166; fax:+33 4 76483906.

E-mail address: gonzalez@ill.fr (M.Angel Gonzalez).

units increases with increasing alkali content up to about30 mol%, while at larger concentrations non-bridging oxy-gens are formed that depolymerize the borate network [2–4]. Although the extent of the formation of the tetrahedralunits depends on the alkali size, the behavior shown by allthe alkalis is quite similar. However this is not the case inrelation with the intermediate range order on these glasses.Thus the addition of Li2O does not change substantiallythe boron–oxygen network as probed by neutron diffrac-tion experiments, where the boron and oxygen contribu-tions dominate the scattering [5]. But when larger cationsare introduced one observes strong modifications in thefirst sharp diffraction peak (FSDP) associated with changesin the intermediate range order [5–8]. Generally, at lowalkali concentrations one observes the appearance of apre-peak that becomes the FSDP at concentrations above

204 M.Angel Gonzalez et al. / Journal of Non-Crystalline Solids 354 (2008) 203–207

30 mol%. Those changes become more pronounced withincreasing cation size, being particularly evident for thecase of the caesium borate glass [7]. Therefore alkali borateglasses offer the possibility of exploring in detail relevantquestions concerning the structure of glasses and the natureof intermediate range order by investigating the modifica-tions brought about by changes in the alkali concentrationand in the alkali size. Here we investigate some of thesequestions by means of a series of molecular dynamics sim-ulations of the system M2O–B2O3 for the five alkali metalsat several concentrations.

2. Molecular dynamics simulations

The full series of alkali borate glasses (M2O)x(B2O3)1�x

(M = Li, Na, K, Rb and Cs) has been studied at two differ-ent compositions (x = 0.14 and 0.3). Additional composi-tions have also been investigated for the Li and Csborate glasses (x = 0.10, 0.20, 0.25, and 0.40). In all cases,a random initial structure containing between 1260 and1500 atoms depending on the composition was generatedand then those structures were equilibrated and quenchedfrom 6000 to 300 K in several steps for a total simulatedtime of 800 ps. The quench runs were performed underNVT conditions employing Berendsen’s thermostat witha coupling constant of 1 ps. For each composition the vol-ume of the simulation box was chosen in order to repro-duce the experimental density [9–12]. Details about thenumber of atoms, composition and the box lengthemployed in the NVT simulations are given in Table 1.Additionally another set of simulations has been per-formed under the same conditions but a using a quenchrate 10 times faster in order to check for possible effectsdue to the quenching rate. Furthermore for three Li borate

Table 1Composition and side length of the cubic simulation box for each of thesystems studied

System Composition Lbox/A

Li (x = 0.10) Li60B540O840 25.4 (26.0)Li (x = 0.14) Li84B516O816 25.1Li (x = 0.20) Li120B480O780 24.5Li (x = 0.25) Li150B450O750 23.9 (24.3)Li (x = 0.30) Li180B420O720 23.4Li (x = 0.40) Li240B360O660 22.8 (23.3)Na (x = 0.14) Na84B516O816 25.3Na (x = 0.30) Na180B420O720 24.3K (x = 0.14) K84B516O816 25.9K (x = 0.30) K180B420O720 25.6Rb (x = 0.14) Rb84B516O816 26.3Rb (x = 0.30) Rb180B420O720 26.8Cs (x = 0.10) Cs60B540O840 26.5Cs (x = 0.14) Cs84B516O816 26.9Cs (x = 0.20) Cs120B480O780 27.1Cs (x = 0.25) Cs150B450O750 27.0Cs (x = 0.30) Cs180B420O720 27.2Cs (x = 0.40) Cs240B360O660 28.3

Values in parentheses correspond to the size of the box obtained at 300 Kfrom the NPT simulations (see text).

glasses corresponding to concentrations x = 0.10, 0.25, and0.40 we also performed quenches under NPT conditionsusing Berendsen’s thermostat and barostat with couplingconstants of 1 and 5 ps, respectively. The reference pressureemployed in those simulations is 8 kbar, as this is the aver-age value obtained in the NVT simulations at room tem-perature and at the experimental density. While thisrelatively high value of the pressure indicates some deficien-cies in the potential model employed, it allows us to obtainfinal configurations having densities similar to the experi-mental ones and check the possible structural differencesbrought forward when allowing the density to change dur-ing the quench. Interatomic interactions were treated withthe Born–Mayer–Huggins potential using the set of param-eters derived by Verhoef and den Hartog [13]. This forcefield has already been used recently to explore the structureand dynamics of lithium [14] and caesium [15] borateglasses, giving reasonable agreement with experimentaldata. All simulations were performed using the DL_POLYpackage [16] and applying periodic boundary conditionsand the Ewald summation method to deal with the long-range electrostatic interactions. A cut-off radius of 10 Awas used for the Born–Mayer–Huggins potential and forthe real part of the electrostatic interactions. The time-stepemployed was 1 fs and the final structural results were com-puted by averaging over 1024 configurations selected overthe last 50 ps of the room temperature simulation.

3. Results

In borate glasses addition of alkali oxide favors thechange of the coordination number of boron from 3 to 4,giving rise to a partial transformation of some basic trian-gular units into four coordinated tetrahedra. The fractionof tetrahedral units, x4, as a function of the alkali concen-tration, obtained by simulation, is shown in Fig. 1. In thesame figure the stoichiometry theoretical curve x4 = x/(1�x), describing the formation of two BO4 groups foreach oxygen introduced by metallic oxide is also shown.As in previous computer simulations, the values obtainedare smaller than the experimental results obtained fromNMR [17]. They are also too small compared to the valuesestimated from neutron diffraction data on Li, Na, and Kat x = 0.35 [18] or on Li at different concentrations(x = 0.11, 0.2, 0.33) [5]. Nevertheless it should be notedthat the coordination numbers NBO given in Ref. [5] wouldlead to x4 = 0.03 and 0.15 for the lower concentrationsx = 0.11 and 0.2, i.e. closer to the values obtained here,while for x = 0.33 the resulting x4 = 0.48 is again much lar-ger than our simulated result. The present data also agreereasonably well with the values of x4 obtained from neu-tron diffraction for several caesium borates [7]. Even ifthe results obtained here underestimate the values deducedfrom NMR studies, the main trends observed experimen-tally are well reproduced. Thus at x = 0.30 one observesthat x4 tends to decrease with increasing alkali size, asfound from NMR data [17]. Comparing the data for Li

Fig. 1. Fraction of fourfold coordinated boron atoms as a function ofalkali oxide concentration. The solid line shows the theoretical curve,x4 = x/(1�x). The inset shows the fractions obtained for the Li borateglass using three different quenching procedures: NVT quench at 7 K/ps(full squares), NVT quench at 70 K/ps (open triangles), and NPT quenchat 7 K/ps (open circles).

Fig. 2. Neutron-weighted static structure factor for v-B2O3 and the fivealkali borates for the compositions x = 0.14 (top) and x = 0.30 (bottom).

M.Angel Gonzalez et al. / Journal of Non-Crystalline Solids 354 (2008) 203–207 205

and Cs borates one also finds that the latter exhibits a max-imum at a lower alkali oxide concentration, again in rea-sonable agreement with experiment [17]. As comparedwith other MD studies, the fraction of tetrahedral unitsfound by us for the lithium borate is somewhat smallerthan in previous works [13,14], but they are comparableor even larger for the case of the caesium borate. The effectof the quenching rate or of the conditions applied duringthe quenching procedure (NVT vs. NPT) can be gaugedfrom the data shown in the inset of Fig. 1. The two differentquenching rates explored here produce structures contain-ing the same fraction of four coordinated boron atoms.The quench under NPT conditions results in structuresslightly less dense (see Table 1), but the values obtainedfor x4 do not differ significantly from those obtained fromthe NVT quench. Those results indicate that the differencein the fraction of tetrahedral units found in simulationstudies depends more on details of the implementation ofthree-body potentials than on the thermodynamic historyof the samples simulated. The inability of the simulationsto reproduce quantitatively the experimental data is mostlikely due to some inadequacies of the simple force fieldemployed here, as already pointed by the high value ofthe equilibrium pressure at the experimental density. How-ever they reproduce qualitatively well the main trendsobserved, so the structures obtained can be considered asgood models to determine the changes introduced intothe B2O3 matrix by the addition of alkali cations of differ-ent size. These changes are shown in Fig. 2, where the sim-ulated static structure factor S(Q) is compared for the fullseries of alkali cations at the compositions x = 0.14 andx = 0.30. Again there are some differences when comparing

with experimental data, such as the position of the FSDPthat appears shifted to slightly larger Q values than inexperiment [5–8]. Nevertheless the main changes are wellreproduced. Thus for the lithium borate glasses oneobserves that there are not big variations with increasingalkali content, in good agreement with neutron diffractionresults [5]. For the other cations, even at concentrations ofonly 14 mol%, the FSDP develops a low-Q shoulder thatbecomes a pre-peak for the larger cations, Rb and Cs.Again such findings are in good agreement with experimen-tal data for potassium and caesium borates [6,7]. At30 mol% the intensity of such pre-peak increases, becomingcomparable to that of the FSDP in the case of the caesiumborate glass. This trend is even more pronounced in exper-iment, where this peak becomes the most intense one forconcentrations above 20 or 30 mol% [6,7]. The evolutionof the static structure factor with increasing alkali contentis shown for the case of the caesium borate in Fig. 3. By

Fig. 3. Evolution of the static structure factor for (Cs2O)x(B2O3)1�x as afunction of the caesium oxide concentration, x.

206 M.Angel Gonzalez et al. / Journal of Non-Crystalline Solids 354 (2008) 203–207

increasing the Cs content, a clear increase of the pre-peakintensity at the expense of the FSDP one is observed, indi-cating the appearance of a new characteristic distance cor-responding to larger correlation lengths than in pure v-B2O3. The fact that these changes are much more pro-nounced in experiment [7] may be attributed both to theinability of the potential employed here to reproduce in fulldetail the true structure of the real glass and to the extre-mely fast quench rate of the simulations. In order to deter-mine the nature of the changes produced by the addition ofthe alkali we compare in Fig. 4 the partial static structurefactors of (Cs2O)x(B2O3)1�x for x = 0.10 and x = 0.30.Each partial Sab(Q) has been weighted by the term (cacb

babb/Rcacbbabb), where c is the concentration of eachatomic species and b is its coherent scattering length. Thus

Fig. 4. Partial static structure factors for (Cs2O)x(B2O3)1�x at x = 0.10(dotted line) and x = 0.30 (thin solid line).

the curves of Fig. 4 show the real contribution of each par-tial function to the total S(Q). They show clear changes atthe larger Cs concentration in the boron–oxygen networkgiving rise to a strong peak at 1.1 A�1 due to contributionsfrom the B–B, O–O, and in particular the B–O partial staticstructure factors.

In order to explore the changes in the B–O networkbrought about by the addition of the different alkali ionswe have focussed on the variations observed on the voiddistribution when adding larger quantities of two alkaliions of very different size, Li and Cs. A good descriptionof the empty space inside the simulated models can beachieved using the Voronoy–Delaunay approach, whichcan provide a good picture of the void distribution andthe connectivity of holes. Here we have computed the totaldistribution of interstices (including overlapping voids)using the algorithm and software developed by Malavasiet al. [19]. In order to look for differences in the organiza-tion of the B–O matrix only, a set of 100 configurations

Fig. 5. Distribution of overlapping interstice sizes in the B–O matrix forlithium (top) and caesium (bottom) borate glasses at several compositions.

M.Angel Gonzalez et al. / Journal of Non-Crystalline Solids 354 (2008) 203–207 207

obtained from the simulated trajectories was selected andthen the alkali ions removed before performing the Voro-noy–Delaunay analysis. In such way we can determinethe size of the interstices present in the B–O matrix anddetermine how the network rearranges to accommodatethe alkali ions.

The results obtained are shown in Fig. 5, where thestrongly different behavior of Li and Cs borate glasses isclearly evidenced. The inclusion of Li atoms do not modifyappreciably the number density of the skeleton boron–oxy-gen atoms, even at the larger concentrations studied. Fur-thermore the Li ion seems to produce a polarizationeffect that makes the network to contract around it, givingrise to a narrowing of the void size distribution on the rightside. The small changes observed in this case serve toexplain the experimental result that the static structure fac-tor of lithium borate glasses does not differ appreciablyfrom that of v-B2O3 even for large concentrations ofLi2O [5]. The situation is completely different for caesium,where the changes in the distribution function testify of theopening of the network to accommodate the larger cation.The most interesting aspect is that a bimodal distribution isobserved, with the first peak decreasing in intensity whilethe second one increases with increasing Cs content. Theaddition of the later modifies then the network by introduc-ing a longer characteristic correlation length, leading to theappearance of a pre-peak in the static structure factorwhose intensity increases with increasing Cs concentrationsas observed in neutron scattering experiments [7,8].

4. Conclusions

We have investigated the structure of five alkali borateglasses at several alkali concentrations by means of molec-ular dynamics simulations. The comparison of our resultswith NMR and neutron diffraction data shows that themain experimental trends are well reproduced by the simu-lations, even if the agreement is not quantitative. We find

that Li can get into the original B2O3 matrix withoutapparently changing the B–O network. However this isnot the case for the rest of alkali ions. When they are addedto the boron oxide, the network opens slightly to accom-modate the larger cation, giving rise to a shoulder or apre-peak at lower Q-values than the FSDP whose intensityincreases with increasing alkali concentration. This effect isparticularly strong for the Cs borate glass, where the anal-ysis of the void distribution indicates that two characteris-tics correlation lengths exist and are at the origin of thechanges observed in the static structure factor.

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