M.Fa´biań ,E.Sva´b ,Th.Proffen ,E.Veress Structurestudyofmulti-componentborosilicateglassesfromhigh-QneutrondiffractionmeasurementandRMCmodeling

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Structure study of multi-component borosilicate glasses from high-Q neutron diﬀraction measurement and RMC modeling

M. Fa´bia´n

^a,*

, E. Sva´b

^a

, Th. Proﬀen

^b

, E. Veress

^c

aResearch Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary

bLos Alamos National Laboratory, Lujan Neutron Scattering Ctr, Los Alamos, NM 87545, USA

cBabesß-Bolyai University, Faculty of Chemistry, 11 Arany Ja´nos Street, RO-3400 Cluj, Romania Received 18 October 2007; received in revised form 24 January 2008

Available online 17 March 2008

Abstract

A neutron diffraction structure study has been performed on multi-component borosilicate glasses with compositions (65x)SiO2xB2O325Na2O5BaO5ZrO2,x= 5–15 mol%. The structure factor has been measured up to a rather high momentum transfer value of 30 A˚¹, which made highr-space resolution available for real space analyses. Reverse Monte Carlo simulation was applied to calculate the partial atomic pair correlation functions, nearest neighbor atomic distances and coordination number distributions. The Si–O network consists of tetrahedral SiO₄units with characteristic first neighbor distances atr_Si–O= 1.60 A˚ andr_Si–Si= 3.0 A˚ . The boron environment contains two well-resolved B–O distances at 1.40 and 1.60 A˚ and both 3- and 4-fold coordinated B atoms are present. A chemically mixed network structure is proposed including^[4]B–O–^[4]Si and^[3]B–O–^[4]Si chain segments. The O–O and Na–O distributions suggest partial segregation of silicon and boron rich regions. The highly effective ability of Zr to stabilize glassy and hydrolytic properties of sodium-borosilicate materials is interpreted by the network-forming role of Zr ions.

PACS: 61.12.Ld; 61.43.Bn; 61.43.Fs; 81.05.Pj

Keywords: Neutron diﬀraction/scattering; Monte Carlo simulations; Borosilicates; Short-range order

1. Introduction

Alkali borosilicate glasses have potential application in the nuclear industry as suitable materials for the immobili- zation of high-activity nuclear waste[1,2]. Structural char- acterization of these glasses is essential for understanding glass durability. We are motivated in the investigation of multi-component sodium borosilicate glasses with the gen- eral composition of (65x)SiO2xB2O325Na2O 5BaO5ZrO2, x= 5–15 mol% with added UO3 or CeO2

(Ce is considered as non-radioactive surrogate for Pu).

Our primary aim is to clarify correlations between structural characteristics and thermal and glass stability. In these glasses SiO2and B2O3are strong network formers,

while the cations modify and/or stabilize the network structure. Among the alkali cations sodium is the most widely used and investigated modifier[3–7]. Ba ions, having large ionic radius, are frequently used[8–10]as modifier, acting as glass and hydrolytic stabilizer. Addition of Zr has also been found very promising for stabilizing the glass, due to its strong charge compensating ability [11]. However, it is still a question of debate whether it acts as a network former or as a modifier[12–15].

Due to the large number of contributing elements and the overlapping distances, it is very difficult to derive ade- quate structural data, like the partial atomic correlation functions, coordination numbers, etc., from diffraction experiments. Recently, we have performed a high momentum transfer (Q) neutron diffraction study on a series of glassy specimens, starting from vitreous B2O3 and SiO2, through a binary sodium silicate glass (70SiO2–30Na2O)

doi:10.1016/j.jnoncrysol.2008.01.024

* Corresponding author. Tel.: +36 1 3922222; fax: +36 1 3959162.

E-mail addresses:fabian@szfki.hu,svab@szfki.hu(M. Fa´bia´n).

www.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 354 (2008) 3299–3307

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and, by systematically adding a new component (Ba, Zr, B), we have reached the 5-component glass. The ﬁrst results of this study have been reported in Ref. [16] with an emphasis on the total distribution functions obtained by direct Fourier transformation of the experimental data.

The detailed structure analysis of the 70SiO2–30Na2O glass was reported in Ref.[17].

Here we focus our interest on the structural analyses of (65x)SiO2xB2O325Na2O5BaO5ZrO2borosilicate glasses as a function of the boron content. The neutron diffraction structure factors have been measured up to Q= 30 A˚¹and subsequently, the experimental data were modeled by using the reverse Monte Carlo (RMC) method [18]. Our aim is to discuss the local- and intermediate range order of the network structure at the level of the partial atomic correlation functions and coordination number distributions.

2. Experimental details and results 2.1. Samples

The compositions of the investigated 5-component sodium borosilicate glassy specimens are (65x)SiO2 xB2O325Na2O5BaO5ZrO2 with x= 5, 10, 15 mol%

(hereafter referred to as B5, B10 and B15).

For sample preparation the conventional melt-quench technique was applied. A high temperature electrical fur- nace was used with a platinum crucible under atmospheric conditions. The raw materials used were all of p.a. grade, SiO2, Na2CO3 supplied by Reactivul (Bucuresti), BaO and ZrO2 by Merck (Darmstadt). B2O3, enriched in

11B-isotope in order to avoid high neutron absorption of natural boron, was obtained from Sigma–Aldrich Co.

(Hungary). The ¹¹B-isotope enrichment was 99.6% as determined by inductively coupled plasma mass spectros- copy (ICP-MS) technique[19]. Borosilicate glass compositions were synthesized by melting at 1400, 1450 and 1500°C the previously homogenized powder mixtures obtained from the properly weighed dry starting components for the B5, B10 and B15 specimens, respectively.

The melted mixture has been kept at the melting temperature for 2 h, during which the melt was periodically homog-

enized by mechanical stirring. Thereafter the melt was cooled to the pouring temperature (1300, 1350 and 1450°C), and kept there for 30 min. Finally the melt was quenched by pouring it on a stainless steel plate.

Prompt Gamma Activation Analysis (PGAA) [20,21]

was applied to verify the elemental composition. The nominal and measured composition data are collected inTable 1.

Powder samples of about 3–4 g each for neutron diﬀrac- tion measurements were prepared by powder milling of the quenched glasses in an agate mill.

2.2. Neutron diﬀraction experiments and structure factors

Neutron diffraction (ND) measurements have been performed in a relatively broad momentum transfer range, Q= 0.4–50 A˚¹, using the ‘PSD’ diffractometer [22] with k0= 1.068 A˚ monochromatic neutrons at the 10 MW research reactor in Budapest and the time-of-flight ‘NPDF’

instrument [23] at the LANSCE pulsed neutron source.

The structure factor,S(Q), was obtained with a good sig- nal-to-noise ratio up to Qmax= 30 A˚¹ [16,17]. In order to make clear the relatively low amplitude oscillations at high-Q-values the interference functions, I(Q) (see Eq. (2) in part 3.1), are displayed inFig. 1.

Table 1

Elemental composition (at.%) of the multi-component matrix glasses, nominal and the measured value by PGAA method Elemental composition (at.%)

Si B Na O Ba Zr

B5 Nominal 19.67 3.28 16.39 57.38 1.64 1.64

PGAA 19.1 (1.8) 3.69 (1.0) 15.37 (1.4) 58.0 (0.5) 1.3 (2.6) 2.19 (2.5)

B10 Nominal 17.46 6.35 15.87 57.14 1.59 1.59

PGAA 19.1 (1.8) 6.59 (1.0) 14.3 (1.5) 58.4 (0.5) 1.3 (2.6) 2.18 (2.4)

B15 Nominal 15.38 9.23 15.38 56.92 1.54 1.54

PGAA 15.24 (1.8) 9.15 (0.9) 13.08 (1.4) 58.5 (0.4) 1.3 (2.5) 2.42 (2.4)

The relative errors (%) are indicated in brackets.

0 10 15 20 25 30

-1 0 1 2

I(Q)

Q [Å^-1] 5

Fig. 1. Neutron diffraction total interference function of the (65x)SiO2xB2O325Na2O5BaO5ZrO2 glasses with different boron concentration. (B5 filled squares; B10 open circles; B15 crosses.)

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The overall character of the neutron diffraction spectra is rather similar for the three specimens, however, slight but significant differences may be observed between the three datasets. The first peak centered at 1.8 A˚¹for the B5 sample slightly splits into two sub-peaks centered at 1.4 A˚¹and 2.0 A˚¹for the B15 sample. The intensity of the main peak at around 5.4 A˚¹ is rather similar for all three samples, while significant differences may be observed between 12 and 23 A˚¹. These differences may be regarded as fingerprints for differences in the short-range ordering, i.e. first neighbor atomic arrangements.

3. Data evaluation procedure 3.1. Applied formalism

For data evaluation we have applied both the traditional direct Fourier transformation method and the reverse Monte Carlo modeling. The following notations and expressions have been used.

The total reduced atomic distribution function, G(r), was calculated from the structure factor, S(Q), (or more correctly from the interference function,I(Q)) by Fourier transformation:

GðrÞ ¼2 p

Z Q_max o

Q½SðQÞ 1MðQÞsinQrdQ; ð1Þ

IðQÞ ¼Q½SðQÞ 1; ð2Þ

whereM(Q) is a modification function, which is applied to reduce artificial oscillations caused by the finite truncation.

We have used the function

MðQÞ ¼sinx

x ; ð3Þ

where x¼_Q^pðQ20Þ

max20 for QP20 A˚¹ and M(Q) = 1 for Q< 20 A˚¹.

The integration limitQmax was selected around 30 A˚¹ whereS(Qmax) = 1 to minimize termination errors.

Relation betweenG(r) and the total atomic pair correlation function,g(r), which characterises the one-dimensional average atomic pair correlations is

GðrÞ ¼4pq₀r½gðrÞ 1; ð4Þ

whereq0is the average number density.

The partial atomic pair correlation functionsgij(r) were calculated by RMC method. The following basic relations were used:

S_ijðQÞ ¼1þ4pq₀ Q

Z rmax 0

r½g_ijðrÞ 1sinQrdr; ð5Þ

SðQÞ ¼X^k

i;j

w_ijS_ijðQÞ; ð6Þ

w_ij ¼ cicjbibj

Pk i;jc_ib_j

h i2; ð7Þ

gðrÞ ¼X^k

i;j

w_ijg_ijðrÞ; ð8Þ

where rmax is the simulation box half edge-length, wij the weighting factor,c_i,c_jthe molar fractions of components, b_i, b_j the coherent neutron scattering amplitudes. In the investigated glasses k= 6, thus k(k+ 1)/2 = 21 diﬀerent atom pairs are present. In the RMC calculation procedure allgij(r) components take part, although their weights are rather diﬀerent, depending on the concentration (seeTable 1) and the scattering amplitude [24] of the actual atoms.

Table 2 illustrates several weighting factors, especially the ones where the weight of the corresponding atom pair is not signiﬁcantly less than 1%.

The coordination number CNij was derived from the RMC conﬁgurations; however, in some special cases we have calculated from the radial distribution function, RDFij(r)

RDFijðrÞ ¼4pr²q₀g_ijðrÞ ð9Þ by integrating the RDF in a coordination shell between radius r1andr2

CNij ¼c_j Z r2

r1

RDFijðrÞdr: ð10Þ

3.2. Details of reverse Monte Carlo modeling

The experimentalS(Q) data have been simulated by the RMC method[18]. The RMC minimizes the squared diﬀer- ence between the experimentalS(Q) and the calculated one from a three-dimensional atomic conﬁguration using Eqs.

(5)–(7). The structure of this computer conﬁguration is modiﬁed by moving the atoms randomly until the calculated S(Q) agrees with the experimental data within the experimental errors. Moves are only accepted if they are in accordance with certain constraints (see below the ones applied in this work).

For the RMC starting model a disordered atomic con- ﬁguration was built up with a simulation box containing

Table 2

Several weighting factors,wij(%) of the multi-component matrix glasses Weighting factors,wij(%)

Si–O B–O O–O Si–Si Si–B B–B Na–O Zr–O Ba–O Si–Na B–Na Na–Na

B5 19.84 6.14 42.19 2.33 1.44 0.22 13.95 3.93 1.64 3.28 1.01 1.15

B10 18.68 10.32 39.95 2.18 2.41 0.66 12.24 3.68 1.58 2.86 1.58 0.93

B15 14.97 14.40 40.26 1.39 2.67 1.28 11.24 4.13 1.63 2.09 2.01 0.78

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5000 atoms andrmax= 20 A˚ (see Eq.(5)). The density was 0.073 ± 0.002 atoms A˚³ for all three samples, as it was calculated from the slope ofG(r) below the ﬁrst main peak using Eqs.(1) and (4)(for more details see[16]).

In the RMC simulation procedure two types of constraints were used restricting in this way the possible atomic movements: the minimum interatomic distances (cut-off distances) were applied for each atom pair and connectivity constraints were applied for the network former Si–O and B–O atom pairs. For Si–O it was reasonable to suppose [16] that the network former units are similar to those reported for sodium silicate glass [17] and references therein, therefore we have forced for Si a 4-fold coordinated first neighbor surrounding by oxygen atoms in the 1.5–1.9 A˚ interval. The value of 1.5 A˚ for the cut- off distance was chosen, not to overlap with the first neighbor B–O distribution at around 1.4 A˚ . To find the correct constraints for B–O was a more tangled procedure.

NMR and Raman studies have reported both 3- and 4-fold coordination for B–O, and a mixed connectivity with Si–O units for multi-component sodium borosilicate glasses of similar compositions as studied here [2,3,5,6,8,25]. However, from these studies no information was derived on the first neighbor B–O distances. Diffrac- tion studies on sodium-diborate glasses have reported first neighbor B–O distance between 1.35 and 1.5 A˚ [26–30]. To be consistent with these data, the B–O first neighbor distribution were forced between 0.8 and 1.5 A˚ range in a first set of RMC runs, not to overlap with the Si–O distribution. These RMC runs, however, could not match the experimental S(Q). To overcome the inconsistency between experimental and calculated S(Q) data, we have allowed for the B–O first neighbor distribution a broader 0.8–1.9 A˚ interval. The applied starting constraints for the cut-off distances of the other atom pairs were based on our recent study on a sample series consisting of systematically increased number of components as described in detail in Ref. [16].

Several RMC runs have been performed by modifying the shortest neighbor distances for the various atom pairs.

The results of each run have been carefully checked to obtain reliable data for eachgij(r) and coordination number distributions. The convergence of the RMC calculation was good and the ﬁnalS(Q) matched very well the experimental structure factor, as it is illustrated in Fig. 2. The actual set of constraints used in the ﬁnal RMC run is collected inTable 3.

An outstanding agreement has been obtained between the total atomic pair correlation function, gtotal(r) calculated by direct Fourier transformation using Eqs. (1) and (4), and that of derived from RMC models using Eq.(8) (seeFig. 3).

Several partial atomic pair correlation functions, gij(r), have been revealed from RMC simulation with a fairly good stability and acceptable statistics, like the gSiO(r), gBO(r), gOO(r), gSiSi(r), gSiB(r), gNaO(r), gBaO(r), gZrO(r) and gSiNa(r). A characteristic set of gij(r) and the corre-

sponding Sij(Q) are displayed for the B15 sample in Figs. 4 and 5, respectively. For the two other compositions most of the gij(r)s look very similar, except gBO(r) and gOO(r) (see Fig. 6). The ﬁrst neighbor atomic distances, as calculated from RMC models, are displayed in Table 4.

Several gij(r) functions obtained for the three borosilicate samples are compared inFig. 6.Fig. 7shows the coordination number distributions obtained by the RMC modeling, while the average coordination numbers are collected inTable 5.

0 10 15 20 25 30

0 1 2 3 4

B5

B10

B15

S(Q)

Q [Å^-1] 5

Fig. 2. Neutron diﬀraction total structure factors of the borosilicate glasses: experimental data (open circles) and RMC simulation (solid line).

(The curves are shifted vertically for clarity.)

Table 3

Constraints applied in the final RMC run: first neighbor coordination number CNij(the corresponding interval is indicated in brackets) and the cut-off distances,rij(A˚ )

Atom pair CNij Cut-oﬀ distance,rij(A˚ )

B5 B10 B15

Si–O 4 (1.45–2.0) 1.45 1.5 1.5

B–O 3 and 4 (0.9–1.9) 1.0 0.8 1.0

Si–Si – 2.86 2.8 2.81

O–O – 2.15 2.15 2.15

Na–O – 2.07 2.05 2.05

Zr–O – 1.95 1.9 1.98

Ba–O – 2.42 2.51 2.45

Na–Na – 2.53 3.01 3.02

Si–B – 2.75 2.44 2.41

Si–Na – 2.48 2.35 2.47

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4. Discussion

For the Si–O distribution we ﬁnd a very characteristic and reproducible peak at 1.60 A˚ for all three samples (see

Fig. 6andTable 4). This is a somewhat shorter value than that inv-SiO2(1.615 A˚ ) or in 70SiO2–30Na2O (1.62 A˚ )[17]

and references therein. Similarly, the Si–Si ﬁrst neighbor distance at 3.0 A˚ (seeTable 4) is slightly shorter than the corresponding value at 3.10 A˚ and 3.05 A˚ in v-SiO2 and in 70SiO₂–30Na₂O, respectively [17]. The coordination number distribution shows that more than 98% of Si atoms are surrounded by four oxygen atoms (note that this was an initial requirement, imposed by a geometrical constraint, see above). The actual average coordination numbers obtained from RMC modeling are 3.95, 3.7 and 3.98 (±0.15) for the B5, B10 and B15 compositions, respectively (seeTable 5). The shorter Si–O and Si–Si distances suggest a somewhat more compact formation of the SiO4tetrahe- dral units in the multi-component borosilicate than that in the binary glass. This observation may be interpreted by the characteristic features of B–O network, which (partly) forms a mixed network with SiO4units, as it will be discussed in the following.

The first neighbor B–O distribution shows two distinct peaks at 1.40 A˚ and 1.60 A˚. The second one agrees with the Si–O distance (seeTable 4), while the first one is close torB–O= 1.36 A˚ which is a characteristic first neighbor B–

O distance in trigonal BO3units forming boroxol ring inv- B2O3 [16,31,32]; this distance also agrees fairly well with the value of 1.39 A˚ reported for alkali diborate glasses [27]. To obtain a deeper insight into the characteristic features of B–O network, a detailed coordination number distribution analysis has been performed. RMC calculations have revealed that more than 90% of the boron atoms

1 2 3 4 5 6

0 4 8 12

B5

B10

B15 gtotal(r)

r [Å]

Fig. 3. The total atomic pair correlation functions of the borosilicate glasses: calculated by direct-Fourier transformation (open circles) and RMC simulation (solid line). (The curves are shifted vertically for clarity.)

1 0 5 10 15 20 25 30 35

40 B15 glass

Si-Na Zr-O Ba-O Na-O B-O B-B Si-B Si-Si O-O Si-O g ij (r)

r [Å ]

8 7 6 5 4 3 2

Fig. 4. The partial pair correlation functions obtained by RMC simulation for the B15 matrix glass (the curves are shifted vertically for clarity).

0 10 15 20 25 30

0 4 8 12 16 20 24 28 32 36

40 B15 glass

Si-Na Zr-O

Ba-O Na-O B-O B-B Si-B Si-Si O-O Si-O Sij (Q)

Q [ Å^-1] 5

Fig. 5. The partial structure factors obtained by RMC simulation for the B15 matrix glass (the curves are shifted vertically for clarity).

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are 3-fold (denoted as^[3]B or BO3) and 4-fold (denoted as

[4]B or BO4) coordinated by oxygen atoms. The average coordination numbers, CNB–O are 3.5, 3.05 and 3.15 (±0.15) for the B5, B10 and B15 compositions, respectively. The fraction of BO3 and BO4 to the total number of B–O neighbors (CNB–O) depends on the boron concentration. With increasing boron content the ratio of BO3

increases, while that of BO4 decreases. Namely, for the B5 sample the actual values are 38% and 57%, for B10

69% and 21%, and for B15 79% and 18%, respectively (seeFig. 8). The missing 5–10% of boron atoms participate in less than 3-fold coordinated units; this is probably within the uncertainties of our RMC calculations.

It is an important demand to ﬁnd the correlation between the population of BO3, BO4units and the average B–O coordination numbers centered at 1.40 and 1.60 A˚ (denoted as CN1(1.40 A˚ ) and CN2(1.60 A˚)), respectively.

CN1 and CN2 were calculated from the B–O radial distribution function using Eqs.(9) and (10) (see alsoFig. 9). It is a reasonable approach to assign BO3with CN1(1.40 A˚ ) and BO4with CN2(1.60 A˚ ), as it is illustrated in Fig. 10.

It is obviously seen, that the number of BO3is greater than CN1, while the number of BO4units is less than CN2 and, the diﬀerence between their actual values increases with increasing boron content. If we suppose that CN1 is formed completely by BO3, even than about 30% of BO3

units contribute to CN2 in addition to BO4in the case of B15 sample. This ﬁnding suggests a structural model in which a certain number of boron atoms form a mixed con- tinuous network with the tetrahedrally coordinated Si–O network, where several diﬀerent mixed ^[3]B–O–^[4]Si and

[4]B–O–^[4]Si linkages are present at rB–O=rSi–O= 1.60 A˚ . Our results are consistent with the NMR and Raman spec-

1 2 3 4 5

0 5 10 15 20

Si-O

gSi-O(r)

r [Å ]

1 2 3 4 5

0 1 2 3 4

Si-Si

gSi-Si(r)

r [ Å]

r [Å ] ^{r [ Å]}

1 2 3 4 5

0 5 10 15

B-O gB-O(r)

1 2 3 4 5

0 1 2 3 4

O-O

gO-O(r)

1 2 3 4 5

0 1 2 3

Na-O

gNa-O(r)

1 2 3 4 5

0 2 4 6

Zr-O gZr-O(r)

6

Fig. 6. Comparison of several partial correlation functions obtained by RMC modeling for the multi-component borosilicate glasses: B5 (square), B10 (open circle), B15 (crosses). ForgNa–O(r) the results for 70SiO2–30Na2O glass[17](triangle) are also indicated (for details see text).

Table 4

Several interatomic distances,rij(A˚ ) obtained from RMC simulation

Atom pairs Interatomic distances,rij(A˚ )

B5, B10, B15 glasses

Si–O 1.60 (±0.005)

B–O 1.40 and 1.60 (±0.01)

O–O 2.30 and 2.60 (±0.05)

Si–Si 3.0 (±0.1)

B–B 2.4–2.6 (±0.1)

Si–B 2.5–3.1 (±0.1)

Na–O 2.10 and 2.65 (±0.1)

Si–Na 2.7–3.2 (±0.1)

Zr–O 2.0 (±0.1)

Ba–O 2.6 (±0.2)

The actual values for the three glasses are the same within limit of error.

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troscopy [4–6,25] and XANES [33] results obtained for sodium borosilicate glasses, indicating 3- and 4-fold coordinated boron atoms forming mixed network with SiO₄ units. Note, however, that these techniques cannot provide any information on the interatomic distances.

The oxygen–oxygen nearest neighbor correlation shows two characteristic peaks at 2.3 and 2.6 A˚ (see gO–O(r) in Fig. 6), and with increasing boron content the peak at the lowerr-value becomes more pronounced. The ﬁrst peak position agrees fairly well with the rO–O(r) = 2.35 A˚ distance characteristic for the boroxol ring network structure inv-B2O3[16,31,32], while the second peak agrees with that

in v-SiO2 (2.63 A˚ ) and in 70SiO2–30Na2O (2.61 A˚ ) [17].

This suggests a mixed phase conﬁguration of boron and silicon rich regions; the latter is a mixed Si–O–B network, as we have discussed above.

The Zr–O distribution function shows a sharp ﬁrst peak at 2.05 A˚ for all three samples (seeFig. 6) in a fairly good agreement with Refs.[12–15], even though the sharp peak in our results is more pronounced with a signiﬁcantly

2 3 4

0 300 600 900

Si-O

CNSi-O(n)

n

1 2 3 4 5 6

0 100 200 300

Na-O

CNNa-O(n)

n

2 3 4

0 200 400

B-O

CNB-O(n)

n

1 2 3 4 5 6 7 8

0 300 600 900

O-O

CNO-O(n)

n

0 1 2 3

0 20 40 60

Zr-O1

CNZr-O1(n)

n

1 2 3 4 5 6

0 20 40 60

Zr-O2

CNZr-O2(n)

n

7

Fig. 7. Coordination number distribution calculated by RMC modeling for the multi-component borosilicate glasses: B5 (black), B10 (crosses), B15 (gray). For the intervals seeTable 5.

Table 5

Coordination numbers, CNijfor the three glassy samples obtained from RMC simulation

Atom pairs Coordination number, CNij

B5 B10 B15

Si–O (1.45–2.0) 3.95 3.7 3.98

B–O (1.0–1.8) 3.5 3.05 3.15

O–O (2.1–3.0) 5.15 5.05 5.15

Na–O (2.0–2.9) 4.2 4.1 4.2

Zr–O1 (1.8–2.3) 1.4 1.2 1.2

Zr–O2 (1.8–2.9) 3.1 2.8 3.1

The actual intervals are indicated in brackets (A˚ ).

5 10 15

30 60

Fraction of BO₄ units

BO4 [%]

Boron concentration, x

Fig. 8. Fraction of BO4 units to the total number of B–O neighbors calculated from RMC modeling.

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diﬀerent coordination number. Refs.[12–15]have reported a 6-fold coordinated Zr–O surrounding while our coordination number analysis has revealed 3-fold coordination in the 1.8–2.9 A˚ interval with two characteristic distances;

at 2.05 A˚ with an average coordination number of 1.2 atoms, and a smaller intensity but characteristic peak at 2.65 A˚ with an average coordination number of about 2 atoms (seeFig. 6andTable 5). The Zr–O weighting factor in the total neutron g(r) is high enough, around 4% (see Table 2), to get correct results from RMC calculations.

We have performed several RMC runs changing the Zr–

O constraints; the obtained results proved to be highly reproducible. The results may be interpreted by a model, where a Zr⁴⁺ ion forms a divalent bond with an oxygen atom (at the short distance), while the other two valences form bridging between two network former units. In this way Zr would act as a network former. The origin of the disagreement between our data and that of others[12–15]

may be due to the diﬀerent composition and/or preparation technique.

The Ba–O distribution shows a broad ﬁrst neighbor peak (seeFig. 4) with a peak position at around 2.6 A˚ , in fairly good agreement with data reported in the literature [34]. The weighting factor ofgBaO(r) is rather small, around 1.6% (see Table 2) and overlaps with O–O distance, thus further analysis of the data was not performed.

The Na–O distribution contains a narrow peak at 2.10 A˚ which is followed by a characteristic broad peak centered at 2.65 A˚ (see Figs. 4 and 6). Comparing g_Na–

O(r) with that of 70SiO2–30Na2O binary glass [17]significant differences may be observed (seeFig. 6). The Na–O first neighbor distance is at 2.30 A˚ in the binary glass, which belongs presumably to the terminal (non-bridging) oxygen neighbors, Na–OT. This distance becomes somewhat shorter in the multi-component glass while the intensity of the peak drastically decreases. The position of the second peak at 2.65 A˚ belongs presumably to the bridging oxygen neighbors (Na–OB), which is somewhat shorter than the corresponding distance in the binary glass (2.70 A˚ ), while the intensity of the peak drastically increases. The average Na–O coordination number is 4(±0.2) as calculated from RMC modeling in the 2–2.9 A˚ interval. These findings reflect a considerable change of the Na surrounding in the multi-component glass in comparison to the binary silica glass. In the latter, Na ions are closely connected to terminal oxygen atoms[17], while in the present glasses the number of bridging oxygen atoms increases in the Na surrounding. This finding may be interpreted by the drastic charge compensating effect Zr ions as it was discussed above. A shoulder on the left side of the broad Na–O peak is observed at 2.30 A˚ , and its intensity slightly increases with increasing boron content, suggesting that Na ions prefer B–O surrounding. We refer here to the results of Ref.[28]: they have reportedrNa–O= 2.30 A˚ for sodium-diborate glass, in good agreement with our findings.

5. Conclusions

A neutron diffraction structure study has been performed on multi-component borosilicate glasses with compositions (65x)SiO2xB2O325Na2O5BaO5ZrO2, x= 5–15 mol%. The structure factor has been measured over a broad momentum transfer range, between 0.4 and 30 A˚¹, which made finer-space resolution possible for real space analyses. The RMC method was successfully applied to calculate a possible three-dimensional atomic configura- tion that is consistent with the measured structure factor.

The partial atomic pair correlation functions, nearest 1

0 10

20 CN2 (1.60 Å)

CN1 (1.40 Å)

B-O

RDFB-O(r)

r [Å]

5 4

3 2

Fig. 9. Radial distribution function for B–O atomic pairs: B5 (square), B10 (open circle), B15 (crosses).

5 10 15

0 1 2 3

CN1(1.40 Å)

BO₃

CNB-O

5 10 15

0 1 2 3

CN2(1.60 Å)

BO₄ CNB-O

Fig. 10. Comparison of the coordination number of BO3 and BO4 units, revealed from RMC modeling, with the average coordination numbers CN1(1.40 A˚ ) and CN2(1.60 A˚) calculated from RDFB–O(r) analysis.

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neighbor atomic distances, coordination number distributions and average coordination number values have been revealed. The Si–O distribution proved to be highly stable with characteristic ﬁrst neighbor distances atrSi–O= 1.60 A˚ andrSi–Si= 3.0 A˚ , the coordination number analyses have revealed the presence of network former tetrahedral SiO4

units (note that this was an initial geometrical constraint in the RMC runs). The boron environment proved to be more complex. The ﬁrst neighbor B–O distance shows two distinct distances at 1.40 and 1.60 A˚ and, both trigonal BO3 and tetrahedral BO4units are present. A chemically mixed network structure is proposed including ^[4]B–

O–^[4]Si and^[3]B–O–^[4]Si chain segments. The highly eﬀective ability of Zr to stabilize glassy and hydrolytic properties of sodium-borosilicate materials[16]is interpreted by the network-forming role of Zr ions.

Acknowledgements

The authors are indebted to Prof L. Pusztai for careful reading of the manuscript and for his useful comments.

The neutron transmission measurements are gratefully acknowledged to Dr. L. K}oszegi, the ICP-MS measurement to Mr Zs. Varga and the PGAA measurements to Dr. Zs. Re´vay are highly acknowledged.

This study was supported by the Hungarian Research Grants OTKA T-042495 and EC HPRI-RII3-CT-2003- 505925. This work has beneﬁted from the use of NPDF at the Lujan Center at Los Alamos Neutron Science Cen- ter, funded by DOE Oﬃce of Basic Energy Sciences. Los Alamos National Laboratory is operated by Los Alamos National Security LLC under DOE Contract DE-AC52- 06NA25396. The upgrade of NPDF has been funded by NSF through Grant DMR 00-76488.

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