LETTER TO THE EDITOR

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Journal of Non-Crystalline Solids 343 (2004) 159–162

Letter to the Editor

g-Factor calculations for the species occurring in borate glasses

George Kordas *

Sol-Gel Laboratory for Glass and Ceramics, Institute of Materials Science, NCSR ‘Demokritos’,

Aghia Paraskevi Attikis, 15310 Athens, Greece

Received 7 October 2003

Abstract

The g-factors expected for the various structures reported in borate glasses were calculated to predict the spectra observed in

these glasses. The g-factors were calculated by DFT methods (ADF and G03w). Based on these calculations, the BOHC1 and

BOHC2 were attributed to non-bridging oxygen bonded to threefold coordinated boron attached to a boroxol ring and an unpaired

electron trapped by an orthoborate unit, respectively.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

TheElectron Paramagnetic Resonance (EPR) spectro-

scopy has been used in the borate glasses quite fre-

quently to determine the defects occurring in these

glasses [1–16]. This was done to better understand the

defects induced by the irradiation in fiber optic materials

[13] or nuclear waste glasses [15]. So far, two defects

were identified [1–16], though a large number of otherstates occur in these glasses as it has been shown in a re-

cent study [16]. The g-values of these defects are given in

Table 1.

Although these defects were identified long time ago

[1], their g-values have not been determined theoreti-

cally. Such calculations are important for structural

model development.

In the present study, the g-values of the various struc-tures reported in literature [17] were calculated by the

Density Functional Theory (DFT). Two programs were

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doi:10.1016/j.jnoncrysol.2004.07.015

* Corresponding author. Tel.: +30 1 650 3301; fax: +30 1 654 7690.

E-mail address: gkordas@ims.demokritos.gr

used the one the Gaussian03Windows (G03W) underB3LYP and 6-311G basis [18] and the other the ADF

(Amsterdam Density Function) using TZ2P wave func-

tion [19]. These methods were described elsewhere in lit-

erature and will not be made at this time [18,19].

2. Results

Table 2 gives the g-values for the unpaired electron

trapped by non-bridging oxygen attached to three-fold

coordinated boron. This test was done to determine

how the g-values are affected by the size of the wave

function. This result shows that very little deviation

(D%) was observed among the various basis sets. So,

the 6-311G-basis set was used for the G03W program.

Table 3 gives the g-values of various units reported inthe borate glasses. One can observe a significant varia-

tion of the g-values for the different units.

Some units were also used to calculate the g-values

with the ADF program. Table 4 summarizes the g-val-

ues calculated by using the ADF using TZ2P wave func-

tion. The results can be compared quite well with the

G03W procedure.

Table 4

DFT calculations of the g-factors of different potential paramagnetic states in the borate glasses

Defect-ring-structure g1 g2 g3 giso�OBOH

OH-Centera 2.0023 2.0117 2.0334 2.0158

Boroxol a(BOHC1a) 2.0025 2.0111 2.0269 2.0135HOHOB

OHAO�ABOHOH

a 2.0023 2.0027 2.0032 2.0027

Triboratea 2.0031 2.0061 2.0080 2.0057

a Wave function: TZ2P, XC: LDA VWN, GGA Becke Perdew.

Table 1

Defects occurring in the borate glasses and c-B2O3

Defect Glass g1 g2 g3 giso Reference

BOHC1 <25% 2.0020 2.0103 2.0350 2.0158 [1–16]

BOHC2 >25% 2.0049 2.0092 2.0250 2.0130 [1–16]

BOHC1c c-B2O3 2.0000 2.0107 2.0415 2.0174 [7–12]

BOHC1a a-B2O3 2.0025 2.0118 2.0370 2.0171 [7–12]

Table 2

g-Values of the �OBO2H2 defect calculated by using the B3LYP method and various basis sets. The deviation, D%, from the average value

(giso = 2.0173) is less than 0.05%

Defect Basis g1 g2 g3 giso D%�OBO2H2 6-311 G 2.0116 2.0127 2.0305 2.0183 0.05

6-311+G 2.0115 2.0123 2.0294 2.0177 0.03

6-311++G 2.0115 2.0123 2.0294 2.0177 0.04

EPR-II 2.0107 2.0110 2.0262 2.0160 0.04

EPR-III 2.0112 2.0123 2.0267 2.0167 0.01

Average 2.0173

Table 3

g-Factor calculations for various units using the G03W under B3LYP and 6-311G basis set

Defect g1 g2 g3 giso�BO3Li2(othoborate) (BOHC2) 2.0076 2.0111 2.0115 2.0101

Boroxol (BOHC1a) 2.0046 2.0115 2.0305 2.0155

Pentaborate 2.0095 2.0095 2.0236 2.0142

Pyroborate 2.0053 2.0100 2.0209 2.0121

Diborate 2.0153 2.0135 2.0456 2.0248

BN-nboa 2.0086 2.0113 2.0184 2.0128

Triborate 2.0032 2.0058 2.0073 2.0054HOHOB

OHAO�ABOHOH 1.9926 2.0098 2.0115 2.0047

�OBO2–A–A–A (A@OBOHO) (BOHC1c) 2.0032 2.0137 2.0312 2.0160

a Boron network non-bridging oxygen.

160 G. Kordas / Journal of Non-Crystalline Solids 343 (2004) 159–162

LETTER TO THE EDITOR

3. Discussion

The gi=1, 2, 3-factors describing the paramagnetic state

can be calculated by the equation:

gi¼1;2;3 ¼ ge � 2kX

n 6¼0

h0 j Li j nihn j Li j 0iEn � E0

;

where k is the spin orbit coupling constant and h0jLijniand hnjLij0i are the matrix elements of the angular

momentum operator, Li, between the ground state j0iand the further molecular orbital states, jni, with ener-

gies, En. The energy difference En � E0 can be deter-

mined from the optical spectra of the defects, as it has

been accomplished in the silicate glasses [20]. There are

though very little reports in literature where such calcu-

lations were accomplished.

In the last few years, DFT made possible the calcula-

tion of the g-factors allowing for the first time to deter-

mine the structure of defects in glasses using asbenchmark the most significant information of the

EPR spectra, namely the g-factors. Though, two differ-

ent programs were used (ADF and G03W), the results

G. Kordas / Journal of Non-Crystalline Solids 343 (2004) 159–162 161

LETTER TO THE EDITOR

of these calculations are astonishingly very close to each

other. This claim arises from the evaluation of the

Tables 3 and 4 where few structures were the same to

allow the comparison. Furthermore, the extend of the

basis functions does not affect the g-factors significantly

as one can perceive from Table 2. The basis set 6-311Gwas used in Table 3 because of reasons of the time of the

calculations.

There is significant work concerning the determina-

tion of the structures occurring in the glasses in the bor-

ate glasses as a function of R (molar percentage of the

alkali oxide to the molar percentage of boron oxide).

The structure of a-B2O3 remains as an essential dilemma

in glass spectroscopy. There are rejections [21] or sugges-tions [22] of the B3O6 boroxol rings in the a-B2O3 glass.

EPR spectroscopy has also been employed to address

this issue. In this glass, the BOHC1 dominates the

EPR spectrum. A number of advanced EPR methods

were engaged to determine the structure of the BOHC1

defect up to the third neighbor [7–12]. The spectroscopic

parameters deduced from the simulations and DFT cal-

culations suggested the existence of the boroxol groupsin these glasses. Here, the g-factor for the boroxol group

was calculated by both G03W and ADF methods (Table

3 and 4). The results of these calculations indicate the g-

values of the boroxol group are very close to the exper-

imental g-values of the BOHC1 (Tables 1, 3 and 4). This

comparison suggests the existence of the boroxol groups

in the B2O3 glasses supporting the proof provided by the

FT-EPR spectroscopy [7–12].In the near the beginning [1], the BOHC1 was as-

signed to an unpaired hole trapped by bridging oxygen

between a three-fold and four-fold coordinated boron

ions. This arrangement gives g-values listed in Tables 3

and 4 that are very dissimilar than the g-values deter-

mined for the BOHC1 (Table 1). Therefore, this model

cannot be proposed for the structure of this defect.

In addition to the BOHC1, the BOHC2 has been iso-lated in the borate glass that is exclusively present in the

B2O3 Li2O glass [1–16]. In the region R � 1, the four-

fold coordinated units coexist with three-fold coordi-

nated units [23–30]. Raman spectroscopy suggested the

coexistence between pyroborate and orthoborate units

[31]. Advanced EPR spectroscopy developed a model

for the BOHC2 composed of an orthoborate group in

the proximity of fourfold coordinated boron. The g-value calculation of the orthoborate group presented

in Table 3 fully supports this model.

In between, different ring structures occur the concen-

tration of which was determined by NMR spectroscopy

[23]. Tables 3 and 4 summarize the expected g-factors of

a number of species occurring in the borate glasses. The

expected g-factors of these units are very close to each

other. Thus, the expected EPR signals may overlap.Simple X-Band EPR spectroscopy may not be sufficient

to separate these individual lines. The use of advanced

pulsed EPR techniques becomes of paramount impor-

tance to resolve the different states and to contribute

to the important issues for the borate glasses such as

the boron oxide anomaly. The results of the theoretical

g-factor calculations might be the guide for future EPR

work where the better resolution of the spectra willallow the identification of the different species, which

will be interpreted, based on the g-factor data provided

by this work.

4. Conclusions

The present work presents for the first time in litera-ture data for the expected g-factors of the various struc-

tures occurring in the borate glasses and beyond that the

first g-value calculations for defects in glasses. Consider-

ing the fact that the g-factor for a paramagnetic state is

of most indispensable property for the development of a

structural model, this paper presents a landmark for

EPR spectroscopy in glasses. Two different methods

were engaged (G03W and ADF) leading to beyondbelief similar results. Based on the g-factor results, the

BOHC1 can be described by the boroxol ring structures

while the BOHC2 can be attributed to orthoborate

groups.

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