Journal of Non-Crystalline Solids 352 (2006) 3088–3094 www.elsevier.com/locate/jnoncrysol
Dissolution behavior of ZnO–P2O5 glasses in water H. Takebe
a,*
, Y. Baba b, M. Kuwabara
a
a
b
Department of Engineering Sciences for Electronics and Materials, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan Department of Applied Science for Electronics and Materials, Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan Received 31 October 2005; received in revised form 18 January 2006 Available online 6 June 2006
Abstract Bulk binary ZnO–P2O5 glasses with 50–70 mol% ZnO were immersed in distilled water at 30–90 C for up to 72 h. The immersed samples were characterized by weight loss, the change in solution pH, X-ray diffraction (XRD) analysis, scanning electron microscopy and Raman spectroscopy. Weight loss decreased with ZnO concentration for all immersion temperatures. Dissolution behavior was classified into two types in terms of weight loss and macroscopic appearance. Type I was primarily recognized in 50–60 mol% ZnO glasses. In type I, the weight loss for 72 h was relatively large (>1.0 · 107 kg mm2, >10% of initial sample weight). Raman spectra of the type I glasses indicated that the depolymerization of phosphate glass network occurred during the dissolution process. Crystalline Zn2P2O7 Æ 3H2O was precipitated in the water solution after immersion. Type II dissolution behavior was recognized in the 65 and 70 mol% ZnO glasses except for the 65ZnO–35P2O5 glass immersed at 90 C. In the type II behavior, the weight loss for 72 h was relatively-small (<1.0 · 108 kg mm2, <1% of initial sample weight). The microstructure of the type II glass indicated selective dissolution. The dissolution process of the type II glass is discussed. 2006 Elsevier B.V. All rights reserved. Keywords: Chemical durability; Microstructure; Raman spectroscopy; Phosphates; Medium-range order
1. Introduction Phosphate glasses are of recent interest for applications including low melting sealing glasses, optical glasses for precision molding, and active fiber devices [1–3]. Poor water durability often limits the use of phosphate glasses, however. It is well known that the water durability of phosphate glasses is improved by the addition of trivalent metal oxides such as Al2O3 and Fe2O3 [1,4] Some experiments on water durability have been performed for complex, multicomponent phosphate glasses [1,5]. However, there are few reports on the compositional dependence of water durability for basic binary glasses consisting of P2O5 and a network modifier. The relationship between dissolution
*
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[email protected] (H. Takebe).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.04.002
behavior and glass structure is currently not well understood. The ZnO–P2O5 (ZP) system is a basic one for lead-free low melting sealing glasses and molded optical glasses because of the low glass transition temperatures characteristic of this system (Tg < 500 C) [6]. In this study, binary ZP glasses with various ZnO concentrations were immersed in distilled water at 30–90 C. The correlation of dissolution behavior with phosphate network structure is studied by weight loss, the change in solution pH, X-ray diffraction (XRD) analysis, a scanning electron microscopy (SEM), and Raman spectroscopy. 2. Experimental procedure The batch composition was xZnO–(100x)P2O5 where x = 50–70 mol%. The starting material for x = 50 mol% was 99.99% Zn(PO3)2. Samples for the other compositions
H. Takebe et al. / Journal of Non-Crystalline Solids 352 (2006) 3088–3094
were prepared from mixtures of Zn(PO3)2 and reagent grade ZnO. A similar sample preparation was described in a previous study [7]. The batches with 10 g in weight were melted in silica crucibles at 1250 C for 1 h. The melts with 50–60 mol% ZnO were poured into a graphite mold and annealed near the glass transition temperature for 1 h. The melts with 65 and 70 mol% were poured onto a graphite plate and immediately covered with another graphite plate to form thin glass samples. Each sample was cut into a piece having a dimension of 10 mm · 10 mm · 1 mm and polished surfaces were used for immersion tests. The immersion test was carried out by using the MCC-1 static leaching method [8]. The sample was suspended by a Teflon thread in a Teflon beaker with a Teflon lid and immersed in distilled water with a total volume of 2 · 104 m3 at pH = 6.1–6.8. The glass surface area to solution volume ratio was 0.01 cm1. The sample was held at 30–90 C for up to 72 h. After immersion, the sample was cleaned with acetone and dried for evaluation. The leaching weight per unit area of each sample, weight loss, was calculated from the equation of DW/2S, where DW is the measured weight change in kilograms, S is the single-side surface area in mm2. The dissolution of edge area was ignored. The weight loss measurements were performed once for samples with the larger weight losses of >1.0 · 107 (kg mm2). As for samples with the relatively-smaller values of <1.0 · 108 (kg mm2), the losses were measured two or three times for confirmation. The pH of leaching solution was measured using a pH meter (D-13, HORIBA, Kyoto, Japan). The errors in the pH
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experiments are in the range of 0.02–0.16. The immersed glass samples were characterized by powder XRD (RINT2000, Rigaku, Tokyo, Japan) and grazing incidence XRD (RINT2100, Rigaku, Tokyo, Japan) using Cu Ka radiation. The X-ray incidence angle of the grazing incidence XRD was 1.0. The microstructure was observed by a scanning electron microscope (JSM-6340F, JEOL, Tokyo, Japan). The glass structure was also analyzed by Raman spectroscopy (NSR-2100, JASCO, Tokyo, Japan). 3. Results 3.1. Weight loss Table 1 shows weight loss and solution pH after immersion at 30–90 C for 72 h. The increase of weight loss corresponds to the shift of leaching solution pH from neutral (6.3–6.8) to acidic (2.8–4.5). Fig. 1 shows the macroscopic appearance of the samples: (a) a glass plate before the immersion test, (b) a precipitated product and (c) an immersed glass sample. The appearance after 72 h immersion is divided into two types (Fig. 1(b) and (c)). In type I, the sample had been perfectly dissolved and the white-colored product (Fig. 1(b)) is precipitated from the solution. On the other hand, in type II, the macroscopic plate-shape of the immersed sample is maintained and only the sample surface color changes from transparent to white (Fig. 1(c)). The type I and II behaviors for immersed samples are also shown in Table 1. Fig. 2 shows the relationship between weight loss and ZnO concentration in ZP glass samples immersed for
Table 1 Immersion test results of ZnO–P2O5 glasses Composition (mol%)
Immersed temperature (C)
Weight loss (kg mm2)
50ZnO–50P2O5
30 50 70 90
(±2) (±2) (±2) (±2)
55ZnO–45P2O5
30 50 70 90
60ZnO–40P2O5
pH
Macroscopic appearance (see Fig. 1)
Before
After
P1.5 · 106 P1.5 · 106 P1.5 · 106 P1.5 · 106
6.3 6.7 6.6 6.3
(±0.12) (±0.07) (±0.05) (±0.10)
4.1 3.3 2.9 2.8
(±0.05) (±0.02) (±0.05) (±0.07)
Type Type Type Type
I I I I
(±2) (±2) (±2) (±2)
1.2 · 106 1.1 · 106 1.0 · 106 1.0 · 106
6.3 6.3 6.7 6.8
(±0.10) (±0.10) (±0.05) (±0.08)
4.5 3.1 3.0 3.0
(±0.01) (±0.02) (±0.06) (±0.04)
Type Type Type Type
I I I I
30 50 70 90
(±2) (±2) (±2) (±2)
3.3 · 107 3.2 · 107 3.2 · 107 3.9 · 107
6.5 6.4 6.5 6.2
(±0.11) (±0.05) (±0.07) (±0.10)
4.3 3.2 3.1 3.2
(±0.05) (±0.07) (±0.05) (±0.01)
Type Type Type Type
I I I I
65ZnO–35P2O5
30 50 70 90
(±2) (±2) (±2) (±2)
6.3 · 109 5.1 · 109 3.2 · 109 1.1 · 107
6.5 6.3 6.5 6.6
(±0.07) (±0.04) (±0.16) (±0.05)
6.5 6.1 6.2 3.6
(±0.04) (±0.05) (±0.04) (±0.10)
Type Type Type Type
II II II I
70ZnO–30P2O5
30 50 70 90
(±2) (±2) (±2) (±2)
1.8 · 109 1.1 · 109 1.2 · 109 5.4 · 1010
6.5 6.3 6.7 6.3
(±0.06) (±0.13) (±0.11) (±0.11)
6.8 6.2 6.5 6.4
(±0.08) (±0.10) (±0.04) (±0.03)
Type Type Type Type
II II II II
Samples were immersed for 72 h.
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Fig. 1. Macroscopic appearances of samples: (a) a glass plate before immersion test, (b) a precipitated product and (c) an immersed glass sample.
Type I : 60ZnO-40P2O5 (T=30°C) -6
10
-7
Type I Type II
30°C
-8
50°C
10
-9
70°C 90°C
10
-10
50
55 60 65 ZnO concentration (mol%)
Type II : 65ZnO-35P2O5 (T=70°C)
3
Weight loss (kg ·mm-2 × 10-8)
10
10
4
-5
Weight loss (kg· mm-2 × 10-8)
Weight loss (kg· mm-2)
10
2
1
0.5 0.4 0.3 0.2 0.1 0 0
10 20 Immersion time (h)
30
70
Fig. 2. Relationships between weight loss and ZnO concentration. Samples were immersed in distilled water for 72 h. The dot line shows the boundary between types I and II. The solid lines are guides to the eye. The symbols of type I show values of a measurement. The symbols of type II show average values of two measurements.
72 h. Weight loss decreases with increasing ZnO concentration for all immersed temperatures. The magnitude of weight loss corresponds well to the classification of appearance. The type I glass has larger weight losses of >1.0 · 107 (kg mm2) (>10% of initial sample weight) and the type II glass has relatively-smaller values of <1.0 · 108 (kg mm2) (<1% of initial sample weight). Fig. 3 shows the variations of weight loss with immersion time for two types of representative glasses. Representative conditions of types I and II are the 60ZnO–40P2O5 glass immersed at 30 C and the 65ZnO–35P2O5 glass immersed at 70 C, respectively. Weight loss increases linearly with time in the type I glass. The type II glass also shows a gradual increase until 3 h and then the weight loss increases slightly after 72 h. 3.2. XRD and SEM Fig. 4(a) shows the XRD pattern of white product precipitated in the water solution of the type I glass (see Fig. 1(b)). Fig. 4(b) shows the grazing incidence XRD pattern of the surface of the immersed type II glass (see Fig. 1(c)). The precipitated product in the type I glass is
0 0
10
20
30
40
50
60
70
Immersion time (h) Fig. 3. Variations of weight loss with immersion time for representative ZnO–P2O5 glasses. Inset: weight loss for the type II samples collected at the first stage. The lines are guide to the eye. The symbols of type I show values of a measurement. The symbols of type II show average values of three measurements. The error bars are also shown for type II.
identified as Zn2P2O7 Æ 3H2O. The surface of the type II glass shows X-ray halo. Fig. 5 shows the SEM micrographs of the surface of immersed type II glass samples. SEM micrographs indicate that the selective dissolution occurs at the surface of the type II glasses. 3.3. Raman spectroscopy Fig. 6 shows Raman spectra of as-prepared ZP glasses in the composition range of 50–70 mol% ZnO. Table 2 summarizes Raman band assignments of the asymmetric and symmetric stretching modes of P non-bridging (or terminal) bonds in the Qn structures of the ZP glasses [9]. The notation Qn represents the number n of bridging oxygen per PO4 tetrahedron. The Raman spectra of as-prepared ZP glasses (Fig. 6) qualitatively agree with data in a previous study [6]. The 1206 cm1 Raman band is due to the symmetric stretching mode of Q2 units and the 1138 cm1 Raman band is due to the P–O stretching mode of Q1 chain terminator. The 1046 and 970 cm1 Raman bands are attributed to the symmet-
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(a)
Intensity (a.u.)
Zn2P2O7 ⋅3H2O
Q0 970
Q2 Chain 1206 terminator Q1 1138 1046
Intensity (a.u.)
50ZnO-50P2O5
10
20
30
40
50
60
70
55ZnO-45P2O5
60ZnO-40P2O5
65ZnO-35P2O5
2θ (degrees) (b)
70ZnO-30P2O5
400
600
800
1000
1200
1400
Intensity (a.u.)
Raman shift (cm-1) Fig. 6. Raman spectra of as-prepared ZnO–P2O5 glasses with various ZnO concentrations. The dot lines show the positions of the Raman scattering bands due to Qn species of phosphate units.
10
20
30
40
50
60
70
2θ (degrees) Fig. 4. (a) The XRD pattern of product precipitated in the water solution. The 60ZnO–40P2O5 glass sample was immersed at 30 C for 72 h (type I). (b) The grazing incidence XRD pattern of the surface of the 65ZnO– 35P2O5 glass immersed at 70 C for 72 h (type II).
ric stretching mode of Q1 units and that of Q0 units, respectively. The 50ZnO–50P2O5 glass consists of metaphosphate Q2 tetrahedra, the fraction of Q1 units increases with increasing ZnO concentration. The 70ZnO–30P2O5 glass is mainly composed of Q1 and Q0 units with a small fraction of Q2 tetrahedral units. Figs. 7 and 8 show Raman spectra of the surfaces of 60ZnO–40P2O5 and 65ZnO–35P2O5 glasses immersed in
Fig. 5. SEM micrographs of the surface of the 65ZnO–35P2O5 glasses immersed in distilled water at 70 C (type II). (a) A glass immersed for 1 h. (a’) Idem (a) at high magnification. (b) A glass immersed for 72 h. (b’) Idem (b) at high magnification.
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Table 2 Assignments of Raman scattering bands in ZnO–P2O5 glasses [9] 970 cm
Assignment
1
(PO4)sym stretch (non-bridging oxygen), Q0 species (PO3)sym stretch (non-bridging oxygen), Q1 species P-O stretch, Q1chain terminator (PO2)sym stretch (non-bridging oxygen), Q2 species
1046 cm1 1138 cm1 1206 cm1
Q0 970
0 Intensity (a.u.)
Frequency
Immersion time (h)
Chain terminator 1138 2 Q1 Q 1046 1206
1
3
Immersion time (h) Q0 970
Intensity (a.u.)
0
1115
Q2 Chain 1206 terminator Q1 1138 1046
72
400
3
800
1000
1200
1400
Raman shift (cm-1) Fig. 8. Raman spectra of the surface of 65ZnO–35P2O5 glasses asprepared and immersed in distilled water at 70 C (type II). The dot lines show the positions of the Raman scattering bands due to Qn species of phosphate units.
6
Zn2P2O7 ⋅ 3H2O
400
600
600
glasses (68 and 70 mol% ZnO). The assignment of this peak is considered in the next chapter. 800
1000
1200
1400
4. Discussion
Raman shift (cm-1) Fig. 7. Raman spectra of the surface of 60ZnO–40P2O5 glasses asprepared and immersed in distilled water at 30 C (type I). Raman spectrum of the Zn2P2O7 Æ 3H2O crystalline product precipitated in the water solution after 72 h immersion is also shown for comparison. The dot lines show the positions of the Raman scattering bands due to Qn species of phosphate units.
distilled water at 30 C and 70 C, respectively, as typical examples of the type I and II glasses. In the 60ZnO–40P2O5 glass (type I), the relative intensity of 1206 cm1 Raman band due to the Q2 units decreases and that of 1138 cm1 Raman band due to Q1 chain terminator increases with immersion time (Fig. 7). Raman spectra of crystalline Zn2P2O7 Æ 3H2O, the product formed from the solution of a 60ZnO–40P2O5 glass sample immersed for 72 h, has only the 1046 cm1 Raman band due to the symmetric stretching mode of Q1 units. Raman spectra of the 65ZnO–35P2O5 glass are mainly assigned to the 1046 cm1 Raman band due to Q1 structure and the 1138 cm1 Raman band due to Q1 chain terminator (Fig. 8). The result of Raman spectroscopy indicates that the Qn structure of the type II glass has almost no changes but the 1206 cm1 band due to the symmetric stretching mode of Q2 units may decrease slightly in intensity after immersion for 72 h. Note that a peak newly appears at 1115 cm1 in the type II glass (the arrow in Fig. 8) with the immersion range of 3–72 h. The similar peak was also observed in the immersed other type II
4.1. Compositional dependence of dissolution type Immersion results reveal that the dissolution behavior of ZP glass is classified into the types I and II from weight loss and macroscopic appearance. As shown in Fig. 2, the weight loss is related to ZnO concentration and lower P2O5 concentration exhibits better water durability. PO4 tetrahedral structures of as-prepared ZP glasses have been investigated by 31P magic angle spinning nuclear magnetic resonance (MAS-NMR) and Raman spectroscopy [5,9], X-ray photoelectron spectroscopy [10] and neutron and X-ray diffraction [11]. The metaphosphate Q2 units exist in the as-prepared ZP glass containing 50 mol% ZnO. The fraction of Q1 units increases with increasing ZnO concentration at P50 mol% ZnO and Q1 or Q1 and Q0 units exist mainly at 65 and 70 mol% ZnO. The deconvolution of 31P MAS-NMR spectra for a high ZnO containing glass, the 67ZnO–33P2O5 glass, also showed the existence of Q2 and Q0 phosphate tetrahedra due to a small disproportionation of Q1 into Q2 and Q0 tetrahedra (2Q1 ! Q2 + Q0) [6]. Raman spectra (Fig. 6) at the high-ZnO composition range (65–70 mol% ZnO) also indicated shoulders and bands at 1206 and 970 cm1 suggesting the co-existence of Q2 and Q0 tetrahedral units. These spectra agree with the previous result [5]. As for the dissolution behavior in water, ZP glasses with 50–60 mol% ZnO which contain Q2 tetrahedra as a major component (P 50%) belong to the type I and ZP glasses with 65–
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4.2. Dissolution process The dissolution process of the type I glass is considered. The non-bridging oxygen (NBO) of Q2 tetrahedra assigned to the 1206 cm1 Raman band (Fig. 6) indicates a middle part of the Q2 phosphate chains. The Q1 chain terminator assigned to the 1138 cm1 Raman band indicates the terminal part of the Q2 structure. The result of Raman spectroscopy (Fig. 7) reveals that the fraction of Q2 structure decreases and that of the Q1 chain terminator increases with immersion time. This is an indication that the decrease of the chain length of Q2 structure [5]. That is, when the type I glass is immersed in distilled water, the phosphate chain breaks and dissolves into water. The change of solution pH (Table 1) from neutral to acid supports the following reactions [12,13]
NBO bonds of the Q2 structure have bond strengths of 1.5 vu. Similarly NBO bonds of Q1 tetrahedra have bond strengths of 1.33 vu and NBO bonds of Q0 tetrahedra have bond strengths of 1.25 vu. Based on the bond strength approach, the relationship between the peak wavenumber of the Raman scattering band and the P–O bond strength has been used, as shown in Fig. 9 [6]. From this linear relationship, the observed 1115 cm1 Raman peak has a slightly-larger bond strength than that of Q1 tetrahedra. Fig. 10 shows schematic Q1 structural units with a hydroxyl group and a H2O molecule [15]. The oxygen balance for P may be distributed to the hydroxyl group and/or 1250 1200 Raman frequency (cm-1)
70 mol% ZnO containing Q1 or Q1 and Q0 structure mainly belong to the type II except for the 65ZnO–35P2O5 glass immersed at 90 C.
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Q2
1150
1115 cm-1
1100
Q1 1050 1000
Q0
950 900 1.1
where n and m are integers and represent the number of phosphate units (n > m). Finally the crystalline Zn2P2O7 Æ 3H2O consisting of the Q1 structure only is precipitated in the solution. As for the type II, the result of SEM (Fig. 5) indicates that the fine pits less than one micrometer are formed at the surface of the type II immersed ZP glass. This microstructure suggests the selective dissolution of glass component. For example, the 67ZnO–33P2O5 glass consists of Q1 structure mainly and of the Q0 and Q2 units with a small fraction [5]. Raman spectra of Figs. 6 and 8 also suggest that the existence of Q2 and Q0 tetrahedra with a large fraction of Q1 tetrahedra at 65 mol% and Q2 units may dissolve selectively under the similar mechanism of the type I glasses. According to the selective dissolution, the surface color of the type II glass sample changes from transparent to macroscopically white (Fig. 1(c)). In the dissolution process of the type II glass, the 1115 cm1 Raman peak is newly recognized (Fig. 8). The bond strength based on Pauling’s second rule [14] is considered in a similar manner of Brow et al. [2,9]. The bond strength is given in valence units (vu) and defined as the charge divided by its coordination number. Phosphorus (P) has a bond strength of 5.0 vu and is bonded to two bridging oxygens (BOs) with bond strengths of 1.0 vu. The remaining 3.0 vu for P is divided equally between the two non-bridging oxygen (NBO) bonds. Therefore, the
1.3
1.5
1.7
P-O- bond strength (vu) Fig. 9. Relationship between Raman frequency and oxygen bond strength. The open circle shows the peak frequency of a Raman scattering band observed in the type II ZP glasses. The dot lines are the guides to the eyes.
H
H
O-
P
P O
O
O H
O-
O
O-
O-
O-
O-
P
P O
O O-
O O-
Q1 Fig. 10. Schematic Q1 tetrahedra with a hydroxyl group and a H2O molecule.
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H2O molecule after the microscopic selective dissolution of Q2 phosphate tetrahedra. The bond strength of the oxygen with the hydrogen decreases and the bond strength of the other two NBO increases, and then the 1115 cm1 Raman peak may appear by the balance disproportionation of oxygen ions. The Raman spectrum of dehydrated, a-Zn2P2O7 also indicates the 1114 cm1 Raman band due to the asymmetric stretching motion of Q1 dimers [16]. From the above consideration of Raman spectra, after the selective dissolution, hydroxyl groups and/or H2O molecules may form at the surface of the type II glass consisting mainly of Q1 structure. 5. Conclusions The dissolution behavior of ZnO–P2O5 (ZP) glass was classified into two types from weight loss and macroscopic appearance. The type I is recognized in the immersion test of the ZP glass samples with 50–60 mol% ZnO at 30–90 C and with 65 mol% ZnO at 90 C. The type I glasses dissolve continuously in water and crystalline Zn2P2O7 Æ 3H2O is precipitated in the water solution. The weight loss after 72 h in the type I glasses is relatively large (>1.0 · 107 kg mm2, >10% of initial sample weight). The results of Raman spectroscopy suggest that the chain length of Q2 phosphate tetrahedra decreases with phosphate dissolution. The type II behavior is observed in the tests of ZP glass samples with 65 mol% ZnO at 30–70 C and with 70 mol% ZnO at 30–90 C. After the immersion test, the macroscopic plate-shape of samples is maintained and the only the sample surface color changes from transparent to white. The weight loss for 72 h in the type II glasses is rel-
atively small (<1.0 · 108 kg mm2, <1% of initial sample weight). SEM observation indicates that microscopic selective dissolution occurs during the immersion of the type II glasses. Raman spectroscopy suggests the formation of Q1 tetrahedral units with hydroxyl groups and/or H2O molecules at the surface of the type II glasses. References [1] A.E. Marino, S.R. Arrasmith, L.L. Gregg, S.D. Jacobs, G. Chen, Y. Duc, J. Non-Cryst. Solids 289 (2001) 37. [2] R.K. Brow, J. Am. Ceram. Soc. 76 (1993) 913. [3] N. Peyghambarian, T. Qiu, P. Polynkin, A. Schulzgen, L. Li, V. Temyanko, M. Mansuripur, J.V. Moloney, Opt. Photonics News (2004) 41. [4] X. Yu, D.E. Day, G.J. Long, R.K. Brow, J. Non-Cryst. Solids 215 (1997) 21. [5] R.C. Bunker, G.W. Arnold, J.A. Wilder, J. Non-Cryst. Solids 64 (1984) 291. [6] R.K. Brow, D.R. Tallant, S.T. Myers, C.C. Phifer, J. Non-Cryst. Solids 191 (1995) 45. [7] T. Harada, H. In, H. Takebe, K. Morinaga, J. Am. Ceram. Soc. 87 (2004) 408. [8] Materials Characterization Center. Nuclear Waste Materials Handbook. DOE/TIC-11400, Pacific Northwest Laboratory, Richland, Washington, 1981. [9] R. Brow, J. Non-Cryst. Solids 263&264 (2000) 1. [10] E.C. Onyiriuka, J. Non-Cryst. Solids 163 (1993) 268. [11] U. Hoppe, G. Walter, G. Carl, J. Neuefeind, A.C. Hannon, J. NonCryst. Solids 351 (2005) 1020. [12] H. de Jager, A.M. Heyns, Appl. Spectro. 52 (1998) 808. [13] T.M. Alam, D.P. Lang, Chem. Phys. Lett. 336 (2001) 385. [14] L. Pauling, The Nature of Chemical Bond, 3rd Ed., Cornell University, Ithaca, NY, 1960. [15] R.M. Wenslow, K.T. Mueller, J. Phys. Chem. B 102 (1998) 9033. [16] G.T. Stranford, R.A. Condrate Sr., B.C. Cornilsen, J. Mol. Struct. 73 (1981) 231.