Journal of Non-Crystalline Solids 303 (2002) 354–371 www.elsevier.com/locate/jnoncrysol
*
Department of Earth and Planetary Sciences, McGill University, 3450 rue Universit ee , Montr ee al, QC, Canada H3A 2A7
Received 17 May 2001; received in revised form 9 January 2002
Abstract
A review of immiscibility data in binary borate and germanate systems was performed in order to compare miscibility gap consolute temperatures with ionic potentials and radii of their associated cations. The trends obtained demonstrate that a selective solution mechanism similar to the one identified for the binary silicate systems is present in the borate and germanate binaries. More importantly, the borate and germanate immiscibility data permitted the identification of a new group of cations depicting an immiscibility behaviour different from the ones identified in binary silicate systems. The new group involves highly polarizable cations possessing a lone pair of electrons. This lone pair of electrons together with oxygen bonded by strong covalent bonds to modifier cations provides efficient shielding to the cations’ nuclei which considerably reduces the coulombic repulsions and produces miscibility gaps with very low consolute temperatures. A new group of cations having an homogenizing effect on melts (i.e. a capacity to make immiscible melts single phase) is thus reported. Experimental and spectroscopic data suggest that miscibility gaps associated with cations having a lone pair of electrons exist in binary silicate systems such as TlO
1 = 2
–SiO
2
, PbO–SiO
2
,
SnO–SiO
2 and Bi
2
O
3
–SiO
2
. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable.
Ó 2002 Elsevier Science B.V. All rights reserved.
PACS: 64.75.
þ g ; 61.43.Fs; 61.20.Gy
1. Introduction
Comparisons of miscibility gap sizes with ionic potentials in binary silicate systems [1] permit the identification of three distinct groups of cations which can unmix at high SiO
2 concentrations. The
*
Corresponding author. Tel.: +1-514 398 7485; fax: +1-514
398 4680.
E-mail address: pierreh@eps.mcgill.ca (P. Hudon).
criteria that distinguish these groups from each other are related to the ionic radius, valence and electronic orbital configurations of the cations.
The first group involves cations capable of acting only as network modifiers; they have an ionic radius in octahedral coordination larger than about
87.2 pm. The second group consists of amphoteric cations, i.e. of cations that exist in both 4- and
5- (or more) fold coordination; they have an ionic radius in 6-fold coordination smaller than 87.2
pm. The last group includes cations with variable crystal field stabilization energies (VCFSE).
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 0 4 5 - 1

P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
Immiscibility data exist at atmospheric pressure for a sufficient number of heterovalent cations in binary borate and germanate systems to verify if the same groups of cations exist in these systems.
However, phase separation in borate and germanate systems may be more complex because the structure of BO
3 = 2 silica at one bar.
and GeO
2 melts is different from
The structure of BO
3 = 2 glass was studied by Xray [2,3] and neutron [4,5] diffraction, infrared [6],
Raman [6–9] and NMR [10–13] spectroscopies. All investigations report that BO
3 = 2 sentially of BO
3 is composed estriangles forming three-membered
(boroxol) rings; however, controversy still surrounds the way that these rings are branched together [5,14]. Moreover, the addition of a modifier oxide to BO
3 = 2 changes some BO
3 triangles to BO
4 tetrahedra which further complicate the structure (see the reviews of Uhlmann and Shaw [15],
Konijnendijk [16], Bril [17], Konijnendijk and
Stevels [18,19], Griscom [20] and Meera and Ramakrishna [21]).
In the case of GeO
2
, the glass structure was investigated by X-ray [22,23] and neutron [23–27] diffraction, infrared [26] and Raman [6,26,28–
32] spectroscopies and by EXAFS [33–35] and
XANES [35] methods. These studies show that
Ge 4 þ , like Si 4 þ , form MO 4
4 tetrahedra but when a modifier oxide is added to GeO
2
, some Ge 4 þ becomes 6-fold coordinated (see [36–40]). For this reason, the structure of a binary germanate glass is not the same as the binary silicate analog.
The present study investigates binary borate and germanate systems and finds that immiscibility is correlated with similar cation properties as in silicate systems plus one additional property of cations.
355 same temperature (see [1]). Preferably, the widths of the miscibility gaps are taken at the monotectic temperature because it is often the only temperature at which the miscibility gap is measured and it is also usually the temperature at which the width is best constrained because the liquidus of the primary crystalline phase field helps fix the composition of the metal oxide-rich liquid. More importantly, monotectic temperatures virtually always lie at the same temperature in silicate systems. This happens because the phase fields that underlie miscibility gaps are most often located next to SiO
2
. At the monotectic temperature, the two liquids are always in equilibrium with the same silica polymorph which ‘buffers’ (i.e. fixes) the temperature of the monotectic.
All the primary phase fields that underlie the miscibility gaps in binary borate and germanate systems are located on the opposite side of the phase diagram, i.e. where a compound or the bounding simple modifier oxide lie. For this reason the monotectic temperature is never the same from system to system, which makes the comparisons of miscibility gap widths impossible. Another temperature needs to be selected in order to make consistent compositional extent comparisons. Unfortunately this is not possible because most borate and germanate miscibility gaps are metastable and no unique temperature embodies all the miscibility gap data available. Consequently, no comparisons of miscibility gap extents were performed and only systems with consolute temperature data were considered. Systems for which immiscibility was detected or partially constrained were not included (see for example, the CaO–BO
3 = 2 and TeO
2
–GeO
2
.
binary of
Carlson [41] and Ohta et al. [42]) except for TeO
2
–
BO
3 = 2
2. The ionic potential approach
The consolute temperatures of binary borate and germanate systems were compared with ionic potentials as in the first part of this paper [1].
Compositional extent correlations with ionic potential were not made for borate and germanate systems, as was done for silicate systems, because miscibility gap widths need to be compared at the
3. Compilation of experimental data
Phase relations of immiscible melts and glasses for metal oxide–boron oxide and –germanium oxide binary systems are summarized in Tables 1 and 2, respectively. The strategy employed to collect the data is the same as the one used for the binary silicate systems (see [1]). Details concerning immiscibility data are given in Appendix A. Data

356 P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
Table 1
Consolute temperatures of immiscible melts and glasses for metal oxide–boron oxide binary systems; see text for explanations
Oxide Coordination number
Ionic radius
(pm)
Ionic potential
(10
2
)
T consolute
( ° C) Reference Notes
1+ cations
CsO
1 = 2
12
6 a
188
167
0.53
0.60
570
– none selected
[45]
[46]
Metastable gap
No gap observed
RbO
1 = 2
12 172 0.58
590
– none selected
[45]
[46]
Metastable gap
No gap observed
TlO
1 = 2
KO
1 = 2
8
6
8
6
159
150
151
138
0.63
0.67
0.66
0.72
Doubtful data
Metastable gap
No gap observed
NaO
LiO
1 = 2
1 = 2
6
5
4
6
4 a a a a
102
100
99
76
59
0.98
1.00
1.01
1.32
1.69
720
590
– none selected
[63]
[45]
[46]
> 500
> 420
615
590
– none selected
[65]
[66]
[67]
[45]
[46] n.d.
n.d.
660
453
557
þ 103
104
[43]
[44]
[45]
[46] selected (average)
Metastable gap
Metastable gap
Metastable gap
Metastable gap
No gap observed
Metastable gap
Metastable gap
Metastable gap
2+ cations
BaO 8
6
142
135
1.41
1.48
Unreliable data
Unreliable data
PbO
SrO
12
8
6 a
4 a
3 a
8
6
149
129
119
98
87.5
b
126
118
1.34
1.55
1.68
2.04
2.29
b
1.59
1.69
> 1500
P 1200
1412
1180
5
1256
1266
1180
5
1221
þ 45
41
12
[47]
[48]
[49]
[50]
[42]
[51]
[52] selected (average)
785
785
785
785
774
779
784.1
789
783
þ 6
9
[53]
[54]
[55]
[56]
[57]
[42]
[58]
[59] selected (average)
1435
1483
1459
þ 24
24
[42]
[51] selected (average)
–

P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
Table 1 ( continued )
Oxide Coordination number
CaO 8
6
MgO 6 a
Ionic radius
(pm)
112
100
72
3 þ cations
BiO
3 = 2
8
6 a
3 a
117
103 n.d.
4+ cations
TeO
2
6
4
97
66 a
Determined by spectroscopy; see Appendix B.
b
Estimated.
Ionic potential
(10
2
)
1.79
2.00
2.78
2.56
2.91
n.d.
4.12
6.06
T
>
> consolute
1698
1865
831
920
1200
( ° C) Reference
[51]
[51]
[42]
[68]
[69]
Notes
357
Colour: yellow–green
Table 2
Consolute temperatures of immiscible melts and glasses for metal oxide–germanium oxide binary systems; see text for explanations
Oxide Coordination Ionic radius
(pm)
Ionic potential
(10 2 )
T consolute
( ° C) Reference Notes
2 þ cations
BaO 8
6
142
135
1.41
1.48
912 [60] Metastable gap
PbO 12
8
6 b
4 b
3 b
149
129
119
98
87.5
a
1.34
1.55
1.68
2.04
2.29
a
580 [60] Metastable gap
–
SrO
CaO
ZnO
8
6
8
6
6
126
118
112
100
74
1.59
1.69
1.79
2.00
2.70
1135
1370
1282
1326
þ 44
44
1400
[60]
[61]
[60] selected (average)
[60]
Metastable gap
3 þ cations
BiO
3 = 2
528 [60] Metastable gap 8
6 b
4 b
3 b
117
103 n.d.
n.d.
2.56
2.91
n.d.
n.d.
4 þ cations
TeO
2
6
4
97
66 a
Estimated.
b
Determined by spectroscopy; see Appendix B.
4.12
6.06
P 1005 n.d.
[70]
[71]
Metastable gap
Metastable gap

358 P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 concerning coordination numbers are given in
Appendix B.
4. Results
Consolute temperatures of miscibility gaps lying in binary borate and germanate systems are compared with ionic potentials in Fig. 1. The consolute temperatures for the binary silicate systems
[1] are plotted for comparison with the amphoterics in octahedral coordination. This coordination was chosen because spectroscopic studies [82] have shown that Mg 2 þ (the only amphoteric cation for which spectroscopic data are reported) is 6-fold coordinated in binary borate systems. Trends describing convex upward curves are observed for the 2 þ cations in both the borate and germanate systems as seen in binary silicate systems. Data for the 1 þ and 3 þ cations in borate systems exist only for lithium and bismuth, respectively; therefore no trends can be seen for these cations. Data for the
1 þ cations do not exist for the germanate systems and for the 3 þ and 4 þ cations only bismuth and tellurium are plotted. The phase equilibria between either borate or germanate and oxides with higher valence cations ( > 4) have not been investigated.
All the 2 þ cations fall on their respective trends for the borate and germanate systems with the exception of lead. Consolute temperatures associated with Pb 2 þ for the borate and germanate systems lie respectively at 660 and 580 ° C below the temperatures predicted from the trends of the 2 þ cations. It can be presumed that the wrong coordination number (6) was selected for Pb 2 þ , but when the range of coordination numbers (from 3 to 12) known for this cation is considered (see the horizontal bars in Fig. 1) lead still falls below the trends of the 2 þ cations. Pb 2 þ falls closely to the trends for the 2 þ cations only when its coordination number is 12 but such a high coordination number was never reported for lead in binary borate and germanate melts and glasses (see [5,83–
88,90–92,95,96]). Despite the fact that there is no trend plotted for the 3 þ and 4 þ cations, the same
‘low consolute temperature anomaly’ appears to affect Bi 3 þ and Te 4 þ because the latter fall at consolute temperatures close to Pb 2 þ in both systems. This is not expected because in binary silicate systems it is observed that the trends for the
3 þ and 4 þ cations fall above the trend associated to the 2 þ cations. The anomalous behaviour of
Pb 2 þ , Bi 3 þ and Te 4 þ is examined below.
Consolute temperatures are compared with ionic radius in Fig. 2. For the germanate systems the maximum observed in the convex upward trend of the 2 þ cations occurs at 74.8 pm. This value is close to the tetrahedral critical radius of
78.8 pm reported earlier [1] for the 2 þ cations in binary silicate systems and is 12.4 pm smaller than the average value of 87.2 pm calculated for the 2 þ and 3 þ cations obtained in the same silicate systems. For the borate binaries the trend observed for the 2 þ cations is less significantly curved.
When fitted with a second-degree polynomial the maximum observed in the trend lies at 55.9 pm.
5. Discussion
5.1. Selective solution mechanism in binary borate and germanate melts and glasses
Phase separation was identified to be the result of coulombic repulsions between poorly shielded cations in the first part of this paper [1]: the higher the ionic potential of a cation, the greater the coulombic repulsions with its neighbours and the larger the size of its immiscibility field. The consolute temperature plots in Figs. 1 and 2 suggest that borate and germanate systems also obey this rule because consolute temperatures increase with an increase of the ionic potential.
However, in silicate systems, the structure of the solvent (SiO
2
) was found to play also a role on phase separation by selecting which cations can fit in pentagonal-like cages and adopt a 4-fold coordination in the melt (or glass) [99]. Cations capable of such a behaviour (e.g. Li þ , Mg 2 þ , Al 3 þ , Ti 4 þ ) are labeled amphoteric, have an ionic radius for an octahedral coordination smaller than about
87.2 pm and are characterized by miscibility gaps smaller than expected for a network modifier with the same ionic potential. In binary borate and germanate systems, a similar selective solution

P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 359
Fig. 1.
Consolute temperatures of M n þ
O n = 2
–BO
3 = 2
M n þ O n = 2
–GeO
2 and melts and glasses plotted against the ionic potential of M. Coordination numbers are based on spectroscopic determinations. Homovalent cations are fitted with a seconddegree polynomial. The small vertical line is not an error bar; it depicts the consolute temperature range which has been reported for Li þ (Table 1). For other data points, these bars are not visible because they are smaller than the symbols. The horizontal bars show the range of ionic potentials taken by
Pb 2 þ if coordination numbers of 3 (III) and 12 (XII) are considered. The consolute temperature trends of the binary silicate melts are plotted for the 1 þ , 2 þ , 3 þ and 4 þ cations for comparison (see [1]); they are labeled 1 þ , 2 þ , 3 þ and 4 þ . Dotted lines are partially constrained.
mechanism appears to exist: in Figs. 1 and 2 the consolute temperatures associated to Mg 2 þ and
Zn 2 þ fall at a lower temperature than expected by the linear trend followed by the other 2 þ cations
(Ba 2 þ , Sr 2 þ and Ca 2 þ ). This makes the trends for the 2 þ cations curve downwards which suggests that some magnesium and zinc must exist in 4-fold coordination in the borate and germanate systems, respectively.
In the borate system, the proportion of Mg 2 þ in
4-fold coordination does not appear to be important because the trend associated to the 2 þ cations is not curved significantly (particularly in Fig. 2).
This is consistent to some extent with the infrared investigation of the MgO–BO
3 = 2 system performed by Kamitsos et al. [82]: the authors failed to observe Mg 2 þ in 4-fold coordination. However, Mg 2 þ is thought to be present in 4-fold coordination in
Fig. 2.
Consolute temperatures of M n þ O n = 2
–BO
3 = 2
M n þ O n = 2
–GeO
2 and melts and glasses plotted against the ionic radius of M. Legend same as Fig. 1.
the melt in small amounts because its presence explains the slow rate of decrease of boroxol ring abundance as the Mg 2 þ content is increased in the binary system [21]. Mg 2 þ was also not detected in ternary magnesium borate systems, but it is proposed to exist in 4-fold coordination in small concentration [100–102] which is consistent with its low content in the binary system. The proportion of cations in 4-fold coordination in borate systems is probably less important than in silicate
(and germanate) systems because the small ionic radius (1 pm in coordination 3; 11 pm in coordination 4) and the high charge (3 þ ) of the boron generates a very large ionic potential (300 in 3-fold coordination; 27.3 in 4-fold coordination). The oxygen are therefore very strongly polarized towards the boron, which restricts their accessibility to other cations (like Mg 2 þ ) capable of polarizing them, making covalent bonds and adopting 4-fold coordination.
In Fig. 2 the maximum observed in the consolute temperature trends separate the cations in two groups: the first one includes cations small enough to be capable of 4-fold coordination (the amphoteric cations) while the second group involves cations too large to assume a coordination of 4 (the

360 P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 network modifiers). For the silicates, the maxima in the consolute temperature trends average
87.2 pm when the amphoterics are considered to be 6-fold coordinated. In the second part of this paper [99], this tetrahedral critical radius was used to suggest the presence of pentagonal-like cages in binary silicate melts because the free aperture in a regular pentagonal face (88.7 pm) is very close to 87.2 pm which permits the selective entry of amphoteric cations capable of 4-fold coordination in the cages. In borate systems such cages
(pentagonal or other) have never been reported.
However, the structure of binary borate melts and glasses is still debated [103] and it appears to be quite complex: many investigators (e.g. [15–21]) reported that B 3 þ has two stable coordination polyhedra (the triangle and the tetrahedra), Yasui et al. [104] observed in two binaries (SrO–BO
3 = 2 and PbO–BO
3 = 2
) the presence of some oxygen in threefold coordination and recently, Wright et al.
[5,14,103] proposed the existence in borate binaries of superstructural units containing large numbers of boroxol groups that include locally independent interpenetrating networks. Therefore, the complexity and the lack of data concerning the definite structure of binary borate melts and glasses cannot rule out the existence of cages that can host 4-fold cations such as Mg 2 þ . If such cages exist in the binary borate systems their sizes are probably smaller than the pentagonal-like cages believed to be present in the binary silicate systems because the maximum (or tetrahedral critical radius) observed in the consolute temperature trend of the borate miscibility gaps associated to the 2 þ cations in Fig. 2 lies only at 55.9 pm.
The consolute temperature trend associated to the 2 þ cations in the binary germanate systems is almost parallel to the trend associated to the
2 þ cations in the silicate binary. Moreover, the tetrahedral critical radius of the germanates lies at
74.8 pm which is close to the value of 78.8 pm reported in [1] for the divalent silicates. A selective solution mechanism comparable to the one proposed for the silicates [99] appears therefore to be present in binary germanate systems. This result is not surprising because Ge 4 þ and Si 4 þ are isovalent and have similar electronic configurations (their valence shell is made of sp 3 orbitals, [105,106]).
However, it is important to note that the structure of binary germanate glasses is slightly different from the binary silicates at atmospheric pressure:
Ge 4 þ is known to have two stable coordination polyhedra (the tetrahedra and the octahedra, see
[36–39]) whereas Si 4 þ has only one (the tetrahedra). This structural difference does not seem to affect the way cations are put in solution with GeO
2 because the consolute temperature trends associated to the 2 þ cations in the germanate and silicate systems are almost parallel to each other (Fig. 2).
In the binary silicate systems, the presence of pentagonal-like cages was proposed to explain the selective solution mechanism that affects the cations with a radius smaller than about 87.2 pm. In the binary germanate systems, the presence of such pentagonal-like cages can only be suggested because, as far as we know, there are no structural data on germanate systems to support this hypothesis.
5.2. Consolute temperature comparisons between borate, germanate and silicate systems
Consolute temperature data are sufficiency numerous for the 2 þ cations in the borate, germanate and silicate systems to define trends in Figs. 1 and
2. This is useful because comparisons between immiscibility fields associated to a same group of homovalent cations (here the 2 þ ) can be made. On each trend shown in Figs. 1 and 2, the positions of the cations with respect to each other are always the same: Ba 2 þ , Sr 2 þ , Ca 2 þ , Mg 2 þ ; i.e. the consolute temperatures associated to these cations increase with the ionic potential. This trend exists because phase separation was identified [1] to be the result of coulombic repulsions between poorly shielded cations: the higher the ionic potential of a cation, the greater the coulombic repulsions with its neighbours and the larger the compositional and thermal extents of its immiscibility field. Borate and germanate systems, like silicate binaries, follow this rule.
On the other hand, the positions of the consolute temperature trends with respect to each other
(i.e. the absolute consolute temperatures) are not determined by the network-modifier cations; they are fixed by the network-former oxides (here

P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
Table 3
Critical consolute temperatures of network formers
Oxide Coordination number
3
Ionic radius (pm)
GeO
SiO
BO
2
2
3 = 2
–
–
1
Ionic potential
(10 2 )
–
–
300
4
Ionic radius (pm)
39
26
11
Ionic potential
ð 10 2 Þ
10.26
15.38
27.27
361
Critical consolute temperature (2 þ cations) (cf. Fig. 1)
( ° C)
1440
2030
1886
BO
3 = 2
, GeO
2 and SiO
2
) that bound the immiscibility field binaries. This is shown in Figs. 1 and 2: the consolute temperature trend associated with the immiscibility fields of the 2 þ cations is higher for binary silicate systems than for borate and germanate binaries, respectively. This result is surprising to some extent because the ionic potential of B 3 þ in 3- and 4-fold coordination is much higher than the ionic potentials of Si 4 þ and Ge 4 þ
(Table 3); consequently, the consolute temperatures of the borate systems should lie at higher temperatures than the silicate and germanate binaries. To understand this it is necessary to consider the factors that control immiscibility in a binary system.
In a borate melt the oxygen are very strongly polarized towards boron because boron has a high ionic potential. This polarization restricts the accessibility of the oxygen to the modifying cations put in solution with BO
3 = 2 and for this reason the cations, which are partly or wholly coordinated by bridging oxygen, remain poorly shielded from each other’s influence. Consequently, substantial coulombic repulsions occur between modifying cations and phase separation takes place. The stronger the polarization of the oxygen towards the network former (here BO
3 = 2
), the smaller the shielding offered by the oxygen to the modifiers cations put in solution and the larger the compositional and thermal extent of the resulting miscibility gap (e.g. GeO
2 and SiO
2
). In Table 3, the ionic potentials of GeO
2
, SiO
2 and BO
3 = 2 compared and it can be seen that BO
3 = 2 are has the largest ionic potential; the consolute temperatures associated to its miscibility gaps should therefore lie above the silicate systems which is not observed.
To explain this apparent contradiction, it is necessary to examine the type of bond B
3 þ makes with oxygen. In BO
3 = 2 melt, the B 3 þ cation coordinates essentially with three oxygen to form BO
3 triangles [2–13]. The high ionic potential of B
3
3 þ
(300; cf. Table 3) allows it to polarize strongly the oxygen and make three covalent bonds. On a
Lewis diagram this is represented by
ð 1 Þ where ‘x’ and ‘o’ represent electrons that come from the boron and the oxygen, respectively.
When a modifier oxide (e.g. CaO) is added to a
BO
3 = 2 melt, some B 3 þ ions that forms the BO triangles are capable of pulling out the oxygen bonded to the modifier cations and make BO tetrahedra [15–21]. Such B 3 þ cations act as electron acceptors (i.e. as Lewis acids) and make coordinate covalent bonds with the oxygen originally bonded to the network-modifier cations:
ð 2 Þ
However, coordinate covalent bonds are weak compared to ordinary covalent bonds [107] and the oxygen associated to them can be relatively easily polarized by modifier cations. The latter are therefore more shielded than initially expected and the repulsions between cations less important; immiscibility field extents are consequently smaller. For the 2 þ cations this additional shielding, provided by the oxygen bonded by coordinate covalent bonds, appears to be sufficiently important to decrease the consolute temperatures of their

362 P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 miscibility gaps below the consolute temperatures associated with the silicate binaries (Figs. 1 and 2).
For the germanate systems, the consolute temperatures are lower than those associated to the borate and silicate binaries because the ionic potential of Ge 4 þ (10.26) is smaller than B 3 þ and Si 4 þ
(Table 3); it is therefore easier for a modifier cation in a GeO
2 melt to polarize the oxygen towards itself, mask its nucleus and reduce the coulombic repulsions that generate immiscibility. This creates small miscibility gaps with low consolute temperatures. Moreover, the germanate binaries possess some Ge 4 þ in 6-fold coordination [36–39] and the oxygen that bound these octahedra are far from the germanium cations and therefore more weakly bonded to them. It is therefore relatively easy for the modifier cations to polarize these oxygen towards themselves, shield their nucleus and reduce coulombic repulsions.
5.3. The ‘anomalous’ Pb 2 þ , Bi 3 þ and Te 4 þ
The consolute temperatures associated with
Pb 2 þ , Bi 3 þ and Te 4 þ are found to lie at much lower temperatures than expected in Figs. 1 and 2. In the study of immiscibility in binary silicate systems [1] the opposite phenomenon was observed: a group of cations was characterized by miscibility gaps larger than expected. These cations had in common their particular electronic configurations (valence shells made of d-orbitals) and their VCFSE.
The miscibility gaps associated with the VCFSE cations were interpreted to be very large because their electrons in the d-orbitals provide a poor screening for the nucleus [108], which results in strong coulombic repulsions between modifier cations and generates very large immiscibility fields with high consolute temperatures.
As for the VCFSE cations, the electronic configuration of Pb 2 þ , Bi 3 þ and Te 4 þ are particular: these cations have a lone pair of electrons. In SnO
(a 2 þ cation with a lone pair of electrons like
Pb 2 þ ) this lone pair is located at the apex of a square pyramid bounded by four oxygen (Fig. 3).
The stability of this configuration is explained by the high polarizing power of Sn 2 þ [109]: the four oxygen are largely polarized towards Sn 2 þ and strong covalent bonds are established which re-
Fig. 3. Bond arrangement between Sn
2 þ
(shaded circles) in a square pyramid. A similar arrangement is adopted by Pb
2 þ
. The two dots represent the lone pair of electrons. From [109].
(black circle) and O
2 sults in the relatively close approach of oxygen to each other in the same plane. In this arrangement the Sn–O bond length is relatively small (it is smaller than a Si–O bond according to Karim and
Holland [109]) which positions the oxygen near
Sn 2 þ fields.
and provides additional shielding of its nucleus. The lone pair of electrons is located on the opposite side of the plane formed by the oxygen and effectively shields the top of the pyramid [109].
The shielding provided by the lone pair of electrons and by the four oxygen consequently permits the efficient masking of the nucleus which considerably reduces the coulombic repulsions between cations and results in small immiscibility
Spectroscopic studies have shown that Pb 2 þ is present as PbO
3 and PbO
4 pyramids in binary germanate [95,96] and borate [83–88,90–92] systems which support the present model. The same observation was made for Bi 3 þ in binary germanate [97,98] and borate [92,93] systems. The model can be therefore applied to Bi 3 þ as well. Immiscibility data for Te 4 þ in the borate and germanate systems (Tables 1 and 2) suggest the presence of low temperature ( > 1200 and P 1000 ° C, respectively) immiscibility domes in these systems which

is also consistent with the model described above.
It is probably also suitable for other cations with a lone pair of electrons such as Tl þ and Sn 2 þ for example. However, immiscibility data collected by
Bouaziz and Touboul [63] for the TlO
1 = 2
–BO
3 = 2 system indicate the presence of a relatively high temperature miscibility gap in this binary. The immiscibility field was observed to be stable and the consolute temperature was fixed at 720 ° C which makes this the only stable miscibility gap associated with a monovalent cation (cf. Table 1 in
[1] and Tables 1 and 2 in this paper). Moreover, this binary is the only one to have its miscibility gap positioned between two intermediate compounds (B
2
Tl
2
O
5 and B
4
Tl
2
O
7
) which casts some doubts on its immiscibility data. Oxidation problems are difficult to avoid with Tl þ [63,110] and the presence of Tl 3 þ can be proposed. This highly charged cation can considerably enlarge the immiscibility field associated to Tl þ which explains some of its particularities.
5.4. Evidence of low temperature miscibility gaps in binary silicate systems
Miscibility gaps belonging to binary silicate systems were investigated in [1]. Unfortunately the limited number of immiscibility data for cations with a lone pair of electrons made the treatment of these impossible. The information obtained on the miscibility gaps associated with a cation containing a lone pair of electrons for the binary borate and germanate systems now make the small number of data existing for the binary silicate systems relevant.
Much evidence suggests that low temperature immiscibility fields associated with cations with a lone pair of electron exist in silicate systems. Vogel
[111] observed metastable phase separation in the
TlO
1 = 2
–SiO
2 binary at an unspecified temperature while Zubareva et al. [110] reported metastable immiscibility between 400 and 600 ° C for this system. In the SnO–SiO
2 system, Karim and
Holland [109] measured the variation of density, molar volume, thermal expansion, refractive index and molar refractivity with SnO content and observed systematic discontinuities in these physical properties at about 70 mol% SiO
2
. The authors
P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 363 attributed this behaviour to a change in Sn–O bonding: at low SnO concentrations the Sn–O bond is mostly ionic and Sn 2 þ behaves like a modifier cation; at SnO contents > 30 mol% Sn–O bond is more covalent and Sn 2 þ behaves more like a network former. The presence of a metastable miscibility gap was not proposed by Karim and
Holland [109], but it is consistent with their explanation and compatible with the discontinuities observed. The glass in which the discontinuities were observed was prepared by quenching the melt from about 1500 ° C and by annealing the glass so obtained for 1 h at only 400 ° C.
Metastable immiscibility in the PbO–SiO
2 system has been observed by Vogel [111] and Oberlies
[112] and predicted by Shaw and Uhlmann [113] from density measurements. Calvert and Shaw
[114] observed immiscibility at 1417 ° C in a binary silicate glass containing 24.6 mol% PbO and Dupree et al. [115] observed the same phenomenon at 1100 ° C in a glass with a PbO content of 48 mol%. These temperatures are respectively 296 and
613 ° C lower than the consolute temperature predicted from the trend for the 2 þ cations in Figs. 1 of
Ref. [1].
Pb
Two coordination numbers were identified for
2 þ in the binary silicate system as for Pb 2 þ and Bi 3 þ in binary borate and germanate systems.
Using various spectroscopic studies, some investigators found that lead predominantly has a coordination of 3 [90,116–118] or 4 [85,119,120], while others [121–124] detected the presence of PbO
4 and PbO
6 units. Moreover, NMR measurements performed by Dupree et al. [115], Kim and Bray
[124] and Worrell and Henshall [125] showed that the Pb 2 þ ion may act as both network former and network modifier in binary silicate glasses.
All of this evidence points towards the existence of low temperature miscibility gaps associated with cations containing a lone pair of electrons in binary silicate systems.
5.5. Phase separation in binary alkali borate systems
Shaw and Uhlmann [45] observed immiscibility in CsO
1 = 2
–, RbO
1 = 2
–, KO
1 = 2
– and NaO
1 = 2
–BO
3 = 2 systems using a transmission electron microscope

364 P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 and fixed the consolute temperatures at 570, 590,
590 and 590 ° C, respectively. Golubkov et al. [46] used the small-angle X-ray scattering technique and observed no changes in the intensity of X-rays scattered by samples heated up to 500 ° C in the same systems. The presence of immiscibility in the NaO
1 = 2
–BO
3 = 2 system was also reported by
Skatulla et al. [65], Eipeltauer and Schaden [66] and Wagstaff and Charles [67] who estimated the consolute temperature at about 615 ° C. Agreement exists only for the LiO
1 = 2
–BO
3 = 2 system, but the consolute temperatures reported are quite different: Shaw and Uhlmann [45] fixed the consolute point at 660 ° C while Golubkovet al. [46] place it at 453 ° C, i.e. 207 ° C lower.
Some information about phase separation in binary alkali borate systems can be extracted from the trends depicted in Figs. 1 and 2. The trends observed for the 2 þ cations in the silicate and germanate systems are parallel to each other in Figs. 1 and 2 and less parallel to the borate one.
However, if the trends associated to the silicate and germanate systems are shifted to coincide with the position of the consolute temperature data point for Li
þ in the borate system, the consolute temperatures for Na þ and K þ in the binary borate systems can be estimated to lie at about 424 and
11 ° C; in other words phase separation appears to be present in the NaO
1 = 2
–BO
3 = 2
BO
3 = 2 and the KO
1 = 2
– systems. It is important to note that the temperature estimates obtained for these binaries are probably wrong but their numerical values gives an idea of the order of magnitude expected for the consolute points of their miscibility gaps. Moreover, phase separation does not appear to be totally absent in the CsO
1 = 2
–BO
3 = 2
BO
3 = 2 and RbO
1 = 2
– systems. The relatively high consolute temperatures reported by Shaw and Uhlmann [45] for the binary alkali borate systems (between 570 and 600 ° C) can be due contamination or poor purity of their samples as Golubkovet al. [46] proposed.
6. Conclusion
A review of immiscibility data in binary borate and germanate systems permitted the identification of a selective solution mechanism similar to the one identified for the binary silicate systems. The selective solution mechanism involves the presence of polygonal cages bounded by bridging and nonbridging oxygen. These cages play a key role in phase separation by selecting which cations can fit in them and adopt a 4-fold coordination. In tetrahedral coordination, a cation is efficiently shielded from the coulombic repulsions exerted by its neighbours which prevent its participation in immiscibility. The complexity and lack of data concerning the structure of binary borate melts do not permit the definition of the shape of the cages expected to host the modifier cations. However, the tetrahedral critical radius measured for the 2 þ cations (55.9 pm) indicate that the size of these cages is smaller than for the silicate binaries. For the germanate binaries, the tetrahedral critical radius measured for the 2 þ cations (74.8 pm) is practically identical to the one observed for the
2 þ cations in the silicate binaries (78.8). Moreover, the consolute temperature trends associated to the
2 þ cations in the binary germanate and silicate systems are virtually parallel to each other which suggest that pentagonal-like cages are probably present in germanate melts.
Ionic potential comparisons between networkformer cations can aid in determining which binary system will have the largest immiscibility fields: the higher the ionic potential of a network former, the stronger the polarization of the oxygen towards it, the smaller the shielding offered by the oxygen to the modifiers cations put in solution with the network former and the larger the compositional and thermal extent of the resulting miscibility gap (e.g. GeO
2 and SiO
2
). However, this simple rule does not apply to all the networkformer cations. In the case of BO
3 = 2 binary melts relatively weak coordinate covalent bonds are created in BO tetrahedra and the oxygen involved in these bonds can be polarized by the modifier cations which give to the latter additional shielding for their nucleus and reduce coulombic repulsions and miscibility gap extents.
A new group of cations depicting an immiscibility behaviour different from the ones observed in binary silicate systems was identified. The new group involves highly polarizable cations pos-

sessing a lone pair of electrons. This lone pair of electrons together with oxygen bonded by strong covalent bonds to modifier cations provides efficient shielding to the cations’ nuclei which considerably reduces the coulombic repulsions and produces miscibility gaps with very low consolute temperatures. Experimental and spectroscopic data suggest that miscibility gaps associated with cations having a lone pair of electrons exist in binary silicate systems such as TlO
1 = 2
–SiO
2
, PbO–
SiO
2
, SnO–SiO
2 and Bi
2
O
3
–SiO
2
. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable.
The similar shapes of the consolute temperature trends obtained for the silicate, borates and germanates binaries permit the prediction of the existence of immiscibility in the NaO
1 = 2
–BO
3 = 2
,
KO
1 = 2
–BO
3 = 2
, RbO
1 = 2
–BO
3 = 2 and CsO
1 = 2
–BO
3 = 2 systems. The consolute temperatures of the miscibility gaps can not be estimated, but they appear to lie below 450 ° C.
Acknowledgements
P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
We thank P.C. Hess for his constructive comments on the first ‘draft’ of this paper. This work benefited the financial support of NSERC and
Reinhardt scholarships, Leroy and McGregor fellowships and a GSA research grant (no. 4957-92) to P.H. and NSERC operating grant (no.
OGP0089662) to D.R.B.
Appendix A.
A.1. Immiscibility data in binary borate systems
A.1.1. LiO
1 = 2
Hummel [43] and Krogh-Moe [44] detected the presence of phase separation in the LiO
1 = 2
–
B
2
O
3 system with the electron microscope but no attempts were made to measure the consolute temperature. Shaw and Uhlmann [45] observed the metastable miscibility gap under the transmission electron microscope and fixed the consolute point at 660 ° C. Golubkovet al. [46] found a much lower consolute temperature, 453 °
365
C, using the smallangle X-ray scattering technique. Data of Shaw and Uhlmann [45] and Golubkovet al. [46] were averaged and the consolute temperature of the miscibility gap was fixed at 557 ° C.
A.1.2. BaO
Levin and McMurdie [47] observed the presence of a stable miscibility gap in the system BaO–B
2
O
3 but were unable to reach the consolute temperature which they estimated to lie above 1500 ° C.
This temperature was considered unreliable because experiments were slowly quenched in air.
Levin and Cleek [48] quickly quenched their samples with a blast of air and determined with the petrographic microscope that the miscibility gap was closing at a temperature located above, but close to, 1200 ° C. Hageman and Oonk [49] quenched their samples in water and measured their compositions under the petrographic microscope using indices of refraction of coexisting glasses.
Data were fitted with an empirical Gibbs energy function and the consolute temperature was calculated to be 1412 ° C. Clemens et al. [50] observed the microstructure of water quenched immiscible liquids with the electron microscope and located the consolute point at 1180 ° C. Ohta et al. [42] fixed the consolute temperature at 1256 ° C using differential thermal analysis. Hageman and Oonk
[51] employed a fast quench microfurnace and using the techniques described in their earlier study
(see [49]), they fixed the consolute point at 1266
° C. The consolute temperature reported earlier by them (1412 ° C) was in their opinion in error and was not used. Crichton and Tomozawa [52] observed in situ phase separation opalescence through a window in their furnace and found that the miscibility gap was closing at 1180 ° C. The consolute temperature of the miscibility gap was fixed at 1221 ° C by averaging the data of Clemens et al. [50], Ohta et al. [42], Hageman and Oonk [51] and Crichton and Tomozawa [52].
A.1.3. PbO
Geller and Bunting [53], Kr oger and Lieck [54],
Liedberg et al. [55] and Zarzycki and Naudin [56] fixed the consolute temperature of the stable miscibility gap present in the PbO–B
2
O
3 at 785 ° C.

366
Geller and Bunting [53] and Liedberg et al. [55] made their determinations by measuring the temperature at which the change from opaque to clear liquid occurred in the upper limit of the gap,
Kr oger and Lieck [54] used a conductometric method and Zarzycki and Naudin [56] used smallangle X-ray scattering and electron microscope techniques. Simmons [57] examined the opacity of glass beads attached to the junction of a thermocouple to fix the consolute temperature at 774 ° C.
Differential thermal analysis was used by Ohta et al.
[42] and the critical temperature was found to lie at
779 ° C. Podlesny et al. [58] measured maximum clouding and minimum clearing temperatures of immiscible liquids and fixed the consolute point at
784.1
° C. Inoue et al. [59] continuously monitored the physical changes in a series of liquids with a video camera as they were cooled down through the immiscibility field and found a consolute temperature of 789 ° C. The consolute temperature of the miscibility gap was obtained by averaging the critical temperatures cited above which gave the value of 783 ° C.
A.1.4. SrO
The consolute temperature of the stable miscibility gap present in the system SrO–B
2
O
3 was determined to be 1435 ° C by Ohta et al. [42] using differential thermal analysis. Hageman and Oonk
[51] employed a fast quench microfurnace and using techniques described in their study of the
BaO–B
2
O
3 system, they fixed the consolute point at 1483 ° C. Data were averaged and the temperature of 1459 ° C was used for the consolute point of the miscibility gap.
A.1.5. CaO, MgO
P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
A.2. Immiscibility data in binary germanate systems
Hageman and Oonk [51] fixed the consolute temperatures of the stable miscibility gaps present in the CaO– and MgO–BO
3 = 2 systems at 1698 and 1865 ° C, respectively. The techniques were the same as used by them for the system BaO–
BO
3 = 2
.
A.1.6. BiO
3 = 2
Ohta et al. [42] used differential thermal analysis to fix the critical temperature of the BiO
3 = 2 stable miscibility gap at 831 ° C.
–BO
3 = 2
A.2.1. BaO, PbO, SrO, CaO, ZnO, BiO
Tabata et al. [60] used differential thermal analysis to locate the consolute points of the miscibility gap present in the BaO–, PbO–, SrO–,
ZnO– and BiO
3 = 2
–GeO
2
A.3. Ambiguous systems systems at 912, 580, 1135,
1400 and 528 ° C, respectively. Shirvinskaya et al.
[61] (see also [62]) determined that the stable immiscibility field present in the CaO–GeO
2 system was closing at approximately 1370 ° C. Tabata et al.
[60] studied the same miscibility gap and fixed the consolute point at 1282 ° C. Both temperatures were averaged and the consolute temperature was fixed at 1326 ° C.
A.3.1. CsO
1 = 2
–, RbO
1 = 2
NaO
1 = 2
–BO
3 = 2
3 = 2
–, TlO
1 = 2
–, KO
1 = 2
–,
The borate-rich portions of the binary systems
CsO
1 = 2
–, RbO
1 = 2
– and KO
1 = 2
–B
2
O
3 were investigated by Shaw and Uhlmann [45]. No visible opalescence was observed in quenched samples and attempts to detect changes in surface etching behaviour were also unsuccessful. However phase separation was observed under the transmission electron microscope and consolute temperatures were respectively fixed at 570, 590 and 590 ° C for the CsO
1 = 2
–, RbO
1 = 2
– and KO
1 = 2
–B
2
O
3 miscibility gaps. Golubkovet al. [46] used the smallangle X-ray scattering technique to study the same binary systems and observed no changes in the intensity of X-rays scattered by samples heated up to 500 ° C. The authors concluded that phase separation did not occur in these systems. Because the measurements of Shaw and Uhlmann [45] were irreconcilable with the conclusion of Golubkov et al. [46], no data were selected for these systems.
Bouaziz and Touboul [63] investigated the system TlO
1 = 2
–B
2
O
3 and reported the presence of a stable miscibility gap with a monotectic temperature of about 536 ° C and a consolute point of 720
° C. It is notable that this is the only system, among the 62 binaries that were surveyed for this study
(see Section 3), to have its immiscibility field positioned between two intermediate compounds
(B
2
Tl
2
O
5 and B
4
Tl
2
O
7
). Moreover, Tl þ is appar-

P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 ently the only monovalent cation to possess a stable miscibility gap in binary borate (and silicate) systems. Bouaziz and Touboul [63] mentioned that precautions were taken to avoid oxidation of their samples but the phase B
2
Tl
2
O
5
, located next to the immiscibility field, was reported to be slightly gray coloured which suggests that some of the thallium was oxidized to the 3 þ state. Cations with ionic radii and valences similar to Tl 3 þ (see the trivalent rare-earth-borate monotectic miscibility gap widths determined by Levin [64]) are known to have stable immiscibility fields. The presence of some Tl 3 þ could explain some of the particularities of the miscibility gap present in the TlO
1 = 2
–B
2
O
3 system. For this reason, the data of Bouaziz and Touboul [63] were considered doubtful and its consolute temperature was not selected. The particular behaviour of Tl þ is examined in Section 5.
Phase separation was observed with the electron microscope in the NaO
1 = 2
–BO
3 = 2 system at 500 ° C by Skatulla et al. [65] and at 420 ° C by Eipeltauer and Schaden [66] but no consolute temperatures were reported. Wagstaff and Charles [67] measured electrical conductivities of NaO
1 = 2
–B
2
O
3 melts during cooling and found a discontinuity which they attributed to the presence of a metastable immiscibility dome with a consolute temperature of about 615 ° C. Shaw and Uhlmann [45] used the transmission electron microscope and located the consolute point of the miscibility gap at 590 ° C.
Golubkovet al. [46] performed small-angle X-ray scattering measurements and did not observe changes in their intensities up to 500 ° C which lead them to conclude that phase separation did not occur. Due to the discrepancies between the data reported by the authors cited above, no consolute temperature was selected for the NaO
1 = 2
–B
2
O
3 binary system.
A.3.2. TeO
2
, –BO
3 = 2
, –GeO
2
Stable immiscibility was observed in the TeO
2
–
BO
3 = 2 system at 920 ° C and below by Dimitriev and Kashchieva [68]; the glasses were yellowishgreen in colour. B urger et al. [69] constrained the miscibility gap boundaries between 600 and 1200
° C. The consolute point was not determined but the limbs of the immiscibility field suggest that the gap closes a few 100 ° C above 1200 ° C (i.e. at about 1500 ° C).
In the TeO
2
–GeO
2 binary, metastable phase separation was observed at 1005 ° C and below by
Dimitrievet al. [70]. The consolute temperature was not fixed but the opacity observed in the quenched samples suggest that the miscibility gap closes near 1000 ° C. Osaka et al. [71] reported phase separation in the same system; unfortunately they did not specify the temperatures at which their samples were melted.
Appendix B.
367
B.1. Coordination numbers of modifier cations in binary borate melts and glasses
B.1.1. 1 þ cations (Cs, Tl, Na, Li)
Iwadate et al. [72] investigated the structure of two CsO
1 = 2
–BO
3 = 2 glasses containing 10 and 20 mol% CsO
1 = 2 by X-ray diffraction and Raman spectroscopy. In both glasses, the Cs þ ion was found to be surrounded by 6 oxygen that defined a distorted octahedron.
The coordination states of Tl þ in binary borate glasses have not been determined, but NMR data collected by Baugher and Bray [73] and Nachtrieb and Momii [74] indicated the presence of at least two types of Tl–O bonds in binary thallium borate glasses. The first one is ionic and predominates in glasses with low TlO
2 contents; the second type is covalent and predominates in thallium-rich glasses.
Greaves [75] used the EXAFS method to study the sodium environment in NaO
1 = 2
–2BO
3 = 2
His analysis showed that the Na þ glass.
ion was 6-fold coordinated. Paschina et al. [76] performed X-ray diffraction measurements on two NaO
1 = 2
–BO
3 = 2 glasses containing 9 and 23 mol% NaO
1 = 2
. According to them, about 5 to 5.5 oxygen surround the sodium ion in these glasses. Medda et al. [77, 78] investigated the structure of NaO
1 = 2
–2BO
3 = 2
NaO
1 = 2
–3BO
3 = 2 and glasses by X-ray diffraction. Oxygen coordination numbers of about 4 and 5 were attributed to the sodium ion in the di- and triborate glasses, respectively. Swenson et al. [79] applied neutron diffraction to examine the structure of

368
NaO
1 = 2
–2BO
3 = 2
P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371 glass. Their study suggested that the sodium ion was surrounded by 6 oxygen. On the basis of the above results, coordination numbers of 4, 5 and 6 were attributed to the Na þ ion in binary borate glass; the coordination 6 was selected.
Kolesova [80] used infrared spectroscopy to investigate the structure of a series of binary lithium borate glasses with a LiO
1 = 2 content varying between 18 and 60 mol%. In all glasses, the lithium ion was found to be coordinated by 4 oxygen.
Kamitsos et al. [81] found the same coordination number (4) in a series of glasses with a LiO
1 = 2 content varying between 20 and 65 mol% using
Raman spectroscopy. Swenson et al. [79] performed neutron-diffraction measurements on three
LiO
1 = 2
–BO
3 = 2 glasses with LiO
1 = 2 contents of 12.5,
25 and 50 mol%. The coordination state of the Li þ ion was also estimated to be about 4.
B.1.2. 2 þ cations (Mg, Pb)
Kamitsos et al. [82] investigated the structure of
MgO–BO
3 = 2 glasses containing between 29 and
37.5 mol% MgO by infrared spectroscopy. Their results suggested that the magnesium ion was
6-fold coordinated.
Bray et al. [83] and Leventhal and Bray [84] performed NMR measurements on a series of
PbO–BO
3 = 2 glasses and concluded that lead behaves as a network former and forms a PbO
4 square pyramid (with Pb at the apex). The same
PbO
4 unit was also observed by Raman and infrared spectra of binary lead borate glasses by
Zahra et al. [85] and Witke et al. [86–88]. However, infrared data collected earlier by Tarte and Pottier
[89] indicated the existence of two types of Pb–O bonds in PbO–BO
3 = 2 glasses. The first type of bond was covalent and associated with a networkforming behaviour. The second type was ionic and associated with a network modifying behaviour.
Hosono et al. [90] investigated binary lead borate glasses containing between 40 and 87 mol% BO
3 = 2 by electron spin resonance spectroscopy and found that the Pb–O bond was ionic at low PbO concentrations and mostly covalent at high PbO concentrations. The ionic bond was associated with a coordination number close to 6 and the covalent one to a coordination number of 3 (i.e. to a trigonal pyramid). Yoko et al. [91] performed NMR measurements on a 67PbO–33BO
3 = 2 that despite the fact that PbO
4 glass and showed and PbO
3 pymamids are present in this glass, two or three extra oxygen with long Pb–O bonds can be linked to the pyramidal lead to form a highly distorted PbO
6 octahedra. Wright et al. [5] investigated 14PbO–
86BO
3 = 2
, 33PbO–67BO
3 = 2 and 60PbO–40BO
3 = 2 glasses by neutron diffraction and reported the presence of PbO
3 or PbO
4 pyramids. Recently,
Terashima et al. [92] collected Raman spectra on binary borate glasses with BO
3 = 2 contents of 40 to
86.7 mol% and reached the same conclusions as
Hosono et al. [90] and Yoko et al. [91]. Consequently, from the studies invoked above, one can conclude that the lead exists in 3- (and/or 4-) and 6fold coordination in binary lead borate glasses; the coordination 6 was selected.
B.1.3. 3
Bishay and Maghrabi [93] reported the presence of BiO
BiO
3 = 2
3
þ cations (Bi) trigonal pyramids (i.e. 3-fold coordination) in the infrared spectra of binary bismuth borate glasses with BiO
3 = 2 with BiO
3 = 2 contents ranging between 25 and 65 mol%. Mochida and Takahashi [94] investigated the structure of BiO
3 = 2
–BO
3 = 2
BiO
3 = 2 glasses with contents varying between 25 to 85 mol% using infrared spectroscopy. At high BiO
3 = 2 the Bi 3 þ content ion was found to act as a network former with a coordination number lower than 6. At low content it was found to behave as a network modifier with a coordination number higher than 6.
Terashima et al. [92] studied bismuth borate glasses content extending between 46.2 and
78.8 mol% BiO
3 = 2 by Raman spectroscopy and found that the coordination number of the Bi 3 þ ion was 5 or 6. From the works cited above, it appears therefore that the bismuth ion is both 3- and 6- (or
5)-fold coordinated in binary borate glasses; the coordination 6 was selected.
B.2. Coordination numbers of modifier cations in binary germanate melts and glasses
B.2.1. 2 þ cations (Pb)
Yamamoto et al. [95] investigated a series of lead germanate glasses (0–50 mol% PbO) with the

EXAFS method and proposed that a large fraction of the Pb 2 þ ions act as network formers and a small fraction as network modifiers. The coordination state of Pb 2 þ ions that behave as network modifiers was not specified but the networkforming lead was associated with PbO
3 and PbO
4 pyramids pyramids. The presence of PbO
4 pyramids was also reported in the neutron scattering spectra of binary germanate glasses containing 20,
33 and 40 mol% PbO by Umesaki et al. [96] who attributed a coordination number of 6 to the Pb 2 þ ion in these glasses. On the basis of these observations, lead can be 3-, 4- and 6-fold coordinated in binary germanate glasses; a coordination of 6 was selected.
B.2.2. 3+ cations (Bi)
P. Hudon, D.R. Baker / Journal of Non-Crystalline Solids 303 (2002) 354–371
Takeda et al. [97] investigated the structure of
92BiO
3 = 2
–8GeO
2
43GeO
2 melts using a high-temperature energy dispersive X-ray diffraction method. At low GeO
2 contents the bismuth ion was found to be coordinated by about 3 to 4 oxygen. At high GeO
2 tents coordination numbers of 4.7 and 5.6 were measured which led the authors to suggest the presence of distorted octahedral BiO
6 melts. Omote and Waseda [98] applied the EXAFS technique to three binary bismuth germanate glasses containing 18, 33 and 50 mol% BiO
3 = 2
. The measured spectra were best fit using two distances for the first-neighbour Bi–O pair. The first shell contained about 2.5 oxygen and the second one about 1.5, which suggest that the Bi ion is surrounded by about 4 oxygen. From the results reported above it appears that the bismuth ion occupies two coordination environments in binary germanate glasses. One is 3- and/or 4-fold coordinated and the other, 6-fold coordinated; the latter value was selected.
References
, 67BiO
3 = 2
–33GeO
2 and 57BiO
3 = 2
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