Vol48/04/2005def


583

ANNALS  OF  GEOPHYSICS,  VOL.  48,  N.  4/5,  August/October  2005

Key  words  polymerisation – basicity – oxidation
state – water speciation – Temkin model

1. Introduction

During the last century many models have
been proposed dealing with the thermodynamic
properties of silicate melts (or slags), especial-
ly with the goal of understanding slag-melt par-
titioning of elements for industrial reasons rele-
vant to steelmaking. The heuristic capability of
a model assessing silicate melts energetics be-

comes particularly important when dealing
with the generalised problem of multicompo-
nent, mutliphase equilibria, as shown by the
thermochemical treatments presented in Ghior-
so et al. (1983), Ghiorso and Sack (1994), Pel-
ton (1998), Papale (1999) and Moretti et al.
(2003). To model element solubility and speci-
ation it is necessary to account fully for the
compositional variables of the system. Never-
theless, compositional variables cannot be un-
derstood without a comprehensive model able
to rescale measured concentrations in terms of
component activities, which represent the obvi-
ous control parameters of chemical reactions
taking place in the system. Therefore, the
choice of the model for component activities
represents a crucial step in silicate melt thermo-
dynamics. Here, I will show that ionic models
accounting for the variable degree of polymeri-

Polymerisation, basicity, oxidation state
and their role in ionic modelling 

of silicate melts

Roberto Moretti
Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Napoli, Italy

Abstract
In order to describe and quantify the reactivity of silicate melts, the ionic notation provided by the Temkin for-
malism has been historically accepted, giving rise to the study of melt chemical equilibria in terms of complete-
ly dissociated ionic species. Indeed, ionic modelling of melts works properly as long as the true extension of the
anionic matrix is known. This information may be attained in the framework of the Toop-Samis (1962a,b) mod-
el, through a parameterisation of the acid-base properties of the dissolved oxides. Moreover, by combining the
polymeric model of Toop and Samis with the «group basicity» concept of Duffy and Ingram (1973, 1974a,b,
1976) the bulk optical basicity (Duffy and Ingram, 1971; Duffy, 1992) of molten silicates and glasses can be split
into two distinct contributions, i.e. the basicity of the dissolved basic oxides and the basicity of the polymeric
units. Application to practical cases, such as the assessment of the oxidation state of iron, require bridging of the
energetic gap between the standard state of completely dissociated component (Temkin standard state) and the
standard state of pure melt component at P and T of interest. On this basis it is possible to set up a preliminary
model for iron speciation in both anhydrous and hydrous aluminosilicate melts. In the case of hydrous melts, I
introduce both acidic and basic dissociation of the water component, requiring the combined occurrence of H+

cations, OH− free anions and, to a very minor extent, of T-OH groups. The amphoteric behaviour of water re-
vealed by this study is therefore in line with the earlier prediction of Fraser (1975).

Mailing address: Dr. Roberto Moretti, Istituto Nazio-
nale di Geofisica e Vulcanologia, Osservatorio Vesuviano,
Via Diocleziano 328, 80124 Napoli, Italy; e-mail: moret-
ti@ov.ingv.it



584

Roberto Moretti

sation represent suitable tools to model silicate
melt reactivity.

The earliest theories on the constitution of
silicate slags were developed as a result of min-
eralogical examination of the constituents of
solidified melts and may be classified as molec-
ular models. In 1923, Colclough (quoted in
Gaskell, 2000), perhaps anticipating Bowen
(1928), pointed out that, as the phases occurring
in the solid state are formed by selective crys-
tallisation from the melt, mineralogical exami-
nation cannot provide evidence that the com-
pounds, observed in the solid state, had existed
in the liquid. The concept of thermodynamic
equilibrium was particularly stressed by
Schenck (1945), who recognised that each reac-
tion proceeds up to the achievement of equilib-
rium, independently of the extension of the sys-
tem. In molecular models it is assumed that mo-
lecular complexes are formed in the melt in
proportions dictated by the overall melt stoi-
chiometry. Gaskell (2000) states that a common
feature of molecular models is that «rather than
the constitution of the slag being deduced from
the observed behaviour, a set of arbitrary as-
sumptions was manipulated to reproduce the
observed behaviour. Comparison among the ap-
proaches shows that the degree of success of
any model in giving the required reproduction
is not sensitive to the finer details of the as-
sumed constitution or to the internal thermody-
namic consistency of the model». This recalls
somehow the normative deconvolution adopted
by Ghiorso et al. (1983) in their multicompo-
nent free energy minimization procedure con-
ducted in a regular solution approximation of
the zeroth order. In fact this model does not ac-
count for the true nature of silicate melts and
the choice of components reflects the topology
of the compositional space investigated by the
authors.

Most melts or slags are however «ionic»
rather than «molecular» liquids. The existence of
ions in the liquid state was already demonstrated
in 1923 by Sauerwald and Neuendorff (quoted in
Gaskell, 2000) who successfully electrolysed
iron silicate melts, and in 1924 by Farup et al.
(quoted in Gaskell, 2000) who measured the
conductivity of melts in the systems CaO-SiO2
and CaO-Al2O3-SiO2.

Tamman (1931, quoted in Gaskell, 2000) al-
ready assumed electrolytic dissociation of met-
allurgical slags. A first application of an ionic
theory of slags to the treatment of slag-metal
equilibria was made by Herasymenko (1938)
who assumed that slags were mixtures of Fe2+,
Mn2+, Ca2+, Al3+ and SiO44-.

The need for an ionic model of silicate
melts emerged clearly from the experimental
determinations on viscosity and electrical con-
ductivity. Further electrical conductivity meas-
urements carried out by various authors indi-
cate an essentially ionic unipolar conductivity
(Bockris et al., 1952a,b; Bockris and Mellors,
1956; Waffe and Weill, 1975), where charge
transfer evidently operates by cations, with an-
ions being essentially stationary. Transference
of electronic charges (h- and n-type conductiv-
ity) is observed only in melts enriched in tran-
sition elements, where band conduction and
electron hopping phenomena are favoured. I
will hereon dismiss the neutral molecular ap-
proach and accept that silicate melts, like other
fused salts, are ionic liquids. In an ionic melt,
coulombic forces acting between charges of op-
posite sign lead to a relative short-distance or-
dering of ions, with anions surrounded by
cations and vice versa. The probability of find-
ing a cation replacing an anion in such ordering
is effectively zero and, from a statistical point
of view, the melt can be considered a quasi-lat-
tice, with two distinct sites, usually defined as
«anion matrix» and «cation matrix».

The distinction between these two matrices
was made by Temkin (1945), who considered
that the electrostatic forces characterising ionic
interactions are sufficiently strong to make the
arrangements of ions in the pure fused salts and
in mixture of salts similar to those in the crys-
talline state, implying co-ordination of cations
by anions.

In the Temkin approach to fused salts, the
activity of component AZ in the ideal mixture
of the two fused salts AZ and BY is expressed
by the Temkin equation

(1.1)

A straight application of the Temkin model to
silicate melts is inadequate because the exten-

.a X X
n n n n

nn
,AZ melt A Z

A B Z Y

ZA $=
+ +

=



585

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

sion of the anion matrix varies in a complicated
fashion with composition. This complexity is
reflected by activity-composition relationships
deviating from the ideal Temkin model behav-
iour and may be fully accounted for by polymer
chemistry.

2. The Toop-Samis model

In polymeric models of silicate melts, it is
postulated that, at each composition, for given P-
T values, the melt is characterized by an equilib-
rium distribution of several ionic species of oxy-
gen, metal cations and ionic silicate polymers.

The charge balance of a polymerization re-
action involving SiO44− monomers may be for-
mally described by a homogenous reaction in-
volving three forms of oxygen: singly bonded
O-, doubly bonded O0 (or «bridging oxygen»),
and free oxygen O2− (Fincham and Richardson,
1954)

(2.1)

Polymer chemistry shows that the larger the
various polymers are, the more their reactivity
is independent of the length of polymer chains.
This fact, known as the «principle of equal re-
activity of co-condensing functional groups»,
has been verified in fused polyphosphate sys-
tems, which are analogous, in several respects,
to silicate melts (cf. Fraser, 1977; Ottonello,
1997).

Assuming this principle to be valid, the
equilibrium constant of reaction (2.1) becomes

(2.2)

Terms in parentheses represent the number of
moles in the melt, which can be used in place of
activities since all three species of oxygen spe-
ciate over the same matrix (anion matrix: the
three oxygen types either mix ideally or their
activity coefficients cancel out ).

Toop and Samis (1962 a,b) showed that in a
binary melt MO-SiO2 the total number of bonds
per mole of melt is given by

(2.3)( ) ( ) N2 O O 4 SiO0 2+ =-

( )
( ) ( )

.K
O

O O
.2 1 2

0 2

= -
-

.O O O2 2 2m m m
0 2

, +- -

where NSiO2 are the moles of SiO2 in the MO-
SiO2 melt. The Toop and Samis model assumes
the basic oxide MO to be completely dissociat-
ed. The number of bridging oxygens in the melt
is thus

(2.4)

Mass balance gives the number of moles of free
oxygen per unit mole of melt

(2.5)

where obviously 1−NSiO2 represents the number
of moles of basic oxide in the melt.

Combining the various equations one gets

(2.6)

which reduces to a quadratic equation in (O−)

(2.7)

Given NSiO2, eq. (2.7) may be solved.
Since the number of oxygens which react

according to eq. (2.2) is (O−)/2 per mole of melt,
the free energy of mixing per mole of melt is

(2.8)

The validity of this equation has been proved
many times (see for example Fraser, 1975; Ot-
tonello, 1997; Ottonello et al., 2001). 

3. Polymerisation and acid-base properties

It is evident that the reaction (2.1) between
the three oxygen species represents the character-
istic process of an acid-base reaction in oxide sys-
tems, which was defined by Flood and Förland
(1947) as «the transfer of an oxygen ion from a
state of polarisation to another». This acceptance
is particularly important in silicate melts and
glasses where polymerisation reactions govern-
ing extension and distribution of polymeric units
may be restated as (as already shown) simple

[( ) / ] .lnG RT KO 2 .mixing 2 1=∆ -

( ) ( ) ( ) ( )

( ) .

K N

N N

O 4 1 O 2 2

8 1 0

. iO

iO iO

2
2 1 S

S S

2

2 2

- + + +

+ - =

- -

( )
[ ( )] [ ( )]

K
N N

4 O
4 O 2 2 O

.
iO

2 1 2

SiOS 2 2=
- - -

-

- -

( ) ( )
( )

NO 1
2
O

SiO
2

2
= - --

-

( )
( )

.
N

O
2

4 OSiO0 2=
- -



586

Roberto Moretti

acid-base reactions involving three distinct polar-
isation states of oxygen (see eq. (2.2)).

Although the Lux-Flood formulation for-
mally differs from a Brönsted-Lowry (proton-
based) exchange, the two formulations are mu-
tually consistent (Flood and Förland, 1947)
and, with this proviso, the link between redox
and acid-base exchanges in the Lux-Flood ac-
ceptation is represented by the «normal oxygen
electrode» equilibrium

(3.1)

Thus in aprotic solvents O2− replaces H+. A ba-
sic oxide is the one capable of furnishing oxy-
gen ions and an acidic oxide is one that associ-
ates oxygen ions

(3.2)

It is well established that the Lux-Flood acid-
base property of dissolved oxides markedly af-
fects the extent of polymerisation by producing
or consuming free oxygen ions (O2−). Thus, for
a generic oxide MO (Fraser, 1975, 1977):

(3.3)

(3.4)

with (3.3) and (3.4) showing acidic and basic
behaviours, respectively. Although it is concep-
tually immediate to envisage directly a direct
relationship between polymerisation constant
(K2) and basicity of dissolved oxides in binary
systems (Toop and Samis, 1962,a,b), the exten-
sion to multicomponent melts and glasses is not
immediate. Moreover, in the presence of alter-
valent elements such as Fe, mutual interactions
are established between the normal oxygen
electrode reaction (3.1) and the dissociation
equilibria ((3.3)-(3.4)). These may be addressed
by taking into account both the polymeric na-
ture of the anion matrix, along the guidelines of
the Toop-Samis model, and Fraser’s am-
photheric treatment of dissolved oxides.

In a chemically complex melt or glass, the
capability of transferring fractional electronic
charges from the ligands to the central cation
depends in a complex fashion on the melt or

MO MO O2 2, + -+

MO O MO2 2
2

,+ - -

.Base Acid O2, + -

.
2
1

O 2e O2
2

,+ - -

glass structure, which affects the polarisation
state of the ligand itself. The mean polarisation
state of the various ligands (mainly oxide ions
in natural silicate melts) and their ability to
transfer fractional electronic charges to the cen-
tral cation are nevertheless conveniently repre-
sented by an experimentally observable param-
eter which is an index of the basicity of the
medium: the optical basicity (see Duffy, 1992
for an exhaustive review of the subject). A for-
mal link is thus needed between polymerisation
constant and optical basicity.

4. The «optical basicity» concept

As we have already seen there are strict mu-
tual interconnections between the concepts of
«oxidation state» and «basicity», whenever this
last term is referred to non-protonated systems.
Following Jørgensen (1969) we may define ox-
idation by means of four distinct formalisms:

– Formal oxidation number denoted by
Roman numeral superscripts (including the
non-Roman notations 0, −I, ...) whenever  this
does not imply an accurate description of the
true nature of the complex (i.e. NiII for nickel in
the aqueous complex Ni(H2O)6

2+ or SVI in the
sulphate complex SO4

2−).
– Spectroscopic oxidation states derived

by experimentally observed excited levels, de-
noted by on-line Roman numerals in parenthe-
ses; i.e. Cr(III)O6, Ni(II)Cl6, etc.

– Conditional oxidation states derived
from electronic configuration; i.e. [Ar]3d 5 for
Mn2+, Fe2+, etc.

– Distributed oxidation states adjacent
atoms bonded in the complex share the elec-
trons equally; i.e. C〈0〉 and H〈0〉 in CH4; S〈0〉
and O〈-I〉 in SiO4

4− etc. 
The usual notation with arabic numeral su-

perscripts (i.e. Li+, Mg2+, Cr3+, F-) which we will
hereafter refer to « formal ionic charges» should
be reserved for cases in which «entities and mol-
ecules are sufficiently separated and are either
neutral or carry charges which are a positive or
negative integer multiplied by the protonic
charge» (Jørgensen, 1969). 

In Brönsted’s formalism, redox reactions
are those involving exchange of electrons be-



587

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

tween the reactants and acid-base reactions are
those involving protons. The Brönsted acid-
base function for protonated systems is usually
represented as

(4.1)

The link joining redox and acid-base reactions
is the normal hydrogen electrode reaction

(4.2)

As in non-protonated systems the Brönsted-
Lowry formalism is better replaced by the Lux-
Flood acid-base definition (Flood and Förland,
1947), three sorts of transitions are involved in
acid-base equilibria:

i) Transitions accompanied by an alteration
of the co-ordination number of oxygen, but no
change of distributed oxidation state, for atoms
with a high ionisation energy, such as for exam-
ple in

(4.3)

ii) Transitions which do not involve any
change in co-ordination number, but a change
in distributed oxidation state, for medium ioni-
sation energy atoms, such as in 

(4.4)

iii) Transitions which involve both change
in co-ordination number and in distributed oxi-
dation state, leading to the formation of isolat-
ed cations, such as occurring for low ionisation
energy atoms

(4.5)

In silicate melts we envisage simple acid-base
reactions involving three distinct polarisation
states of oxygen, eq. (2.1), which in a distrib-
uted oxidation state notation may be expressed
as follows:

(4.6)

Although formally different, the Brönsted-
Lowry and the Lux-Flood formulations are mu-

.O I O O2 0 2,- +- -

.CaO Ca O0 2, ++ -2

.O O OSi I Si 0 2 24
4

2, +-
- -

.CO CO O0 03
2 2

2, +
- -

.2e 2H H2,+
- +

.Acid Base H, + +

tually consistent and, if we still accept the
Brönsted definition of redox reactions, then it
may be readily seen that the link joining redox
and acid-base exchanges in the Lux-Flood ac-
ceptation is now represented by the oxygen
electrode equilibrium.

The fact that reaction (3.1) could also re-
semble an equilibrium between a Lewis acid
(i.e. a substance acting as acceptor of a pair of
electrons; O2 in our case) and a Lewis base (i.e.
a substance acting as donor of a pair of elec-
trons; O2− in our case), leading to a stable octet
configuration, further emphasises the necessity of
distinguishing a redox equilibrium, i.e. «a reac-
tion involving free electrons (in the broad sense
of the term) and resulting in a change of formal
oxidation number» from an acid-base equilibri-
um which, in the Brönsted-Lowry formalism is
basically «the transfer of an oxygen ion from a
state of polarisation to another», as already noted.

Although we may conceive formal integer
charges for isolated non-interacting (gaseous)
ions (i.e. Li+, Mg2+, Fe3+, etc.) and (although
much less evidently) for isolated complexes,
this formalism cannot be readily transferred to
the formal oxidation state within a complex
since, in most cases, it is in contrast with both
the quantum-mechanical concept of «electron
density» and with the notion of «fractional ion-
ic character of a bond» (Pauling, 1932, 1960;
Gordy, 1950; Hinze et al., 1963; Phillips, 1970,
see below). Moreover, in a chemically complex
melt or glass the capability of transferring frac-
tional electronic charges from the ligands to the
central cation depends in a complex fashion on
the melt structure, which affects the polarisation
state of the ligand itself. The mean polarisation
state of the various ligands (mainly oxide ions in
natural silicate melts) and their ability to trans-
fer fractional electronic charges to the central
cation are nevertheless conveniently represent-
ed by the «optical basicity» of the medium
(Duffy and Ingram, 1971). The concept of opti-
cal basicity arises primarily from the systematic
study of the orbital expansion (or «nephe-laux-
etic effect») induced by an increased localised
donor pressure on p-block metals. Metal ions
such as TlI (group III), PbII (group IV), BiIII

(group V) (i.e. oxidation number = group num-
ber −2) have an electron pair in the outermost



588

Roberto Moretti

(6s) orbital. When trace concentrations of the
metal are dissolved in melts and glasses, coordi-
nation with the ligand field anions results in for-
mation of Molecular Orbitals (MOs) which in-
crease the electron density of the inner shells.
The consequent shielding of nuclear charges af-
fects the energy involved in the outermost
6s → 6 p transitions which become lower the
more the inner shell electron density is increased.
Lowering of the 6s → 6 p transition energy is ex-
perimentally observed as a dramatic red-ward
shift of the 6s → 6p UV absorption band when the
p-block free ion is immersed in a ligand field.
The spectroscopic shift of the 1S0 → 3P1 absorp-
tion band experienced by Pb when passing from
a free ion (Pb2+) condition to PbII in an O2- ligand
field is for instance 60700 − 29700 = 31000 cm−1

(Duffy and Ingram, 1971, 1974b, 1976). For BiIII

the analogous redward shift is 28.8 kK (1 kK =
1000 cm−1) and is 18.3 kK for TlI.

This phenomenon is quantitatively under-
stood in terms of ligand field theory by analogy
with the behavior of 3d, 4d and 5f transition
ions (Jørgensen, 1962, 1969; and references
therein). In octahedral 3d chromophores for ex-
ample, the energy splitting between anti bond-
ing , MOs and the dxy, dxz, dyz AOs of
the central atom (∆ cov-σ) is linearly affected by
the position of the ligand in the spectrochemi-
cal series (represented by parameter f ) and by a
representative parameter of the central cation
(g), according to the simple relationship (Jør-
gensen, 1969)

(4.7)

The precision achieved by this simple equation
in describing ∆ cov-σ in 3d 3, 3d 6 and 3d 8 chro-
mophores is remarkable (cf. table 5.8 in Jør-
gensen, 1969). However, the energy shift in-
duced by changes in f is not so marked as to al-
low a basicity scale to be proposed on the basis
of eq. (4.7) (cf. table 5.5. in Jørgensen, 1969).

Jørgensen (1962) pointed out that the ex-
pansion of the radial function consequent on
lowering of the effective nuclear charge (Zeff)
results in three distinct nephelauxetic parame-
ters (β ). These are β ll for the interaction be-
tween two electrons in the lower sub-shell, β lu.
for the interaction between an electron in the

f ( ) ( )cov ligand cation=∆ -v g$ .

*
x y2 2Ψ -*z2Ψ

lower and an electron in the upper sub-shell and
β uu for the interaction between two electrons in
the upper sub-shell

(4.8)

(4.9)

(4.10)

Zeff* in the above equations is the effective nu-
clear charge of the free cation; a is related to the
mean radial distance of the orbital from the cen-
tre of nuclear charges and β ll > β lu > β uu. Ac-
cording to Duffy and Ingram (1971) the optical
basicity, Λ, is represented by the ratio h/h*

where h is the Jørgensen’s (1962) function of
the ligand in the polarisation state of interest
and h* is the same function relative to the ligand
in an unpolarised state (i.e. free O2− ions in an
oxide medium)

(4.11)

with ν free = 1S0 → 3P1 absorption band of the free
p-block cation; ν glass = 1S0 → 3P1 absorption band
measured in the glass; ν *= 1S0→ 3P1 absorption
band in a free O2− medium.

As we see in fig. 1, the optical basicity of
simple oxides appears related to the atomistic
properties of the intervening cations, such as
the Pauling and Sanderson’s electronegativities
(χP and χS respectively) or the free ion polariz-
ability (Young et al., 1992).

Although Duffy and Ingram (1974a) sug-
gest a simple linear dependency between the re-
ciprocal of optical basicity Λ (or «basicity mod-
erating parameter» γ ; see later) and Pauling
electronegativity χP (straight line in fig. 1), here
I focus attention on the fact that a strict connec-
tion between optical basicity and bond ionicity
should exist. The true nature of this relationship
(which we depict as a second order polynomial
dependency in the same figure) can be envis-
aged by equating the spectroscopic definition of
fractional ionic character of a bond (Phillips,

h
h

1

1
* * *

free

free glass
= =

-

-
=

-
-

b
b

o o
o o

Λ

a
Z
Z

*uu u
4

eff

eff=b

a a
Z
Z

*lu l u
2 2

eff

eff=b

a
Z
Z

*ll l
4

eff

eff=b



589

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

1970) with Pauling notation

(4.12)

where χO and χM are respectively the Pauling
electronegativity of oxygen and metal and

(4.13)

Ei in eq. (4.13) is the «ionic energy gap» and Eg
is the total energy gap between bonding and an-
ti bonding orbitals (Ec corresponds to Eg for the
non-polar covalent bond in the same row of the
periodic table, with a correction for inter-atom-
ic spacing)

(4.14)

with = plasma frequency for valence elec-
trons; and ε∞ = optical dielectric constant.

The operational relationship between frac-
tional ionic character of the bond in the oxide
and optical basicity is the following:

(4.15)

( . .4 6242 4 6702-= f . .R 0 9517i
1 =Λ - 2)

P'~

( )
E

1
g

P

2
1

'
=

-f
~

3

i cg
2 2

2
1

( ) .E E E= +

( )
expf

E E
E

1
4
1

i
i c

i
2 2

2

O M= +
= - - -| |^ h: D

Based on eqs. (4.12) and (4.15) we get the fol-
lowing approximation:

(4.16)

which suggests an optical basicity of 0.225 for
a purely covalent non polar bond (see also eq.
(4.13)). This value compares favourably with
the value 0.46 ÷ 0.48 indicated by Duffy and
Ingram (1974a) for SiO2 which has a fractional
ionic character around 0.5 (0.516 according to
Pauling, 1960).

The reciprocal of optical basicity («basicity
moderating parameter» γ M, according to Duffy
and Ingram, 1973) represents the tendency of
an oxide forming cation M to reduce the lo-
calised donor properties of oxide ions. It is re-
lated to the optical basicity of the medium by

(4.17)

where ZM = formal oxidation number of cation
M in MO; ZO = formal oxidation number of ox-
ide ion in MO; r M = stoichiometric ratio be-
tween number of cations M and number of total
oxide ions in the medium.

Although γ M reduces to in a simple single ox-
ide medium, it has the property to describe the
additive Jorgensen’s h function in chemically
complex media (with A, B, ... oxide forming
cations) according to (Duffy and Ingram, 1973):

(4.18)

Moreover, based on eqs. (4.16) and (4.17) the op-
tical basicity of the medium may be expressed as

. (4.19)

Direct estimates of the basicity moderating pa-
rameter of the central cation may then be ob-
tained from electronegativies (fig. 1) by appli-

Z r Z r
2 2A
A A

B

B B# # f= + +
c c

Λ

.

h h
Z

Z r
Z

Z r
1 1

1

1
1

*

O A O

B

A A B B# # $

$ f

= - - -

- -

c

c

c

c

m

m

<

F

Z
Z r

M
M M

M M

#
#

=c
Λ O

.
E E

E
4 6 1

1

i c

i
2 2

2
.

-
+

Λ
c m

Fig. 1. Pauling and Sanderson electronegativities
and basicity moderating parameter. The straight line
is the intepolation of Duffy and Ingram (1974),
γ = 1.36 × ( χP − 0.26).



590

Roberto Moretti

cation of the second order polynomials

(4.20)

(4.21)

. ) .0 96=(R.0 1880|+.0 0193|S-.0 7398= S2c 2

.0 97)=(R.0 7404|+.0 6703|- P.0 8969= P2c 2

Equation (4.20), although conceptually less ob-
vious than (4.16), is operationally more accu-
rate and has been adopted by Ottonello et al.
(2001) to evaluate basicity parameters, when-
ever literature values were controversial or
lacking.

Table I summarises the functional relation-
ships among the previously discussed parameters.

Table I. Optical basicity Λ and basicity moderating parameter of the central cation γ according to various
sources. Pauling’s and Sanderson’s electronegativities (Pauling, 1932, 1960; Sanderson, 1967) are also listed. Λ,
γ, χS: adimensional; χP: eV (from Ottonello et al., 2001).

Oxide Λ γ χ P χ S

(1) (2) (3) (4) (5) (6) (6) (7)

H2O 0.40 0.39 2.56 2.50 2.15 3.55
Li2O 1.00 1.00 1.0 0.74
B2O3 0.42 0.42 2.38 2.0 2.84
Na2O 1.15 1.15 1.15 1.15 1.15 0.87 0.87 0.9 0.70
MgO 0.78 0.78 0.78 0.78 0.78 0.78 1.28 1.28 1.2 1.99
Al2O3 0.60 0.60 0.60 0.61 0.59 0.59 1.69 1.67 1.5 2.25
SiO2 0.48 0.46 0.48 0.48 0.48 0.48 2.09 2.09 1.8 2.62
P2O5 0.40 0.40 0.33 0.8 0.40 0.40 2.50 2.50 2.1 3.34
SO3 0.33 0.25 0.33 3.03 3.03 2.5 4.11
K2O 1.40 1.4 1.40 1.40 1.36 0.74 0.71 0.8 0.41
CaO 1.00 1.00 1.00 1.00 1.00 0.99 1.00 1.00 1.0 1.22
TiO2 0.65 0.61 0.61 0.58 1.72 1.54 1.6 1.60
Cr2O3 0.70 0.58 1.72 1.6 1.88
MnO 0.94-1.03 0.98 0.90 0.59 0.59 1.69 1.69 1.5 2.07
FeO 0.86-1.08 1.03 1.00 1.03 0.51 0.48 2.09 1.354 1.8 2.10

Fe2O3 0.73-0.81 0.77 1.21 0.48 0.48 2.09 2.09 1.8 2.10
CoO 0.51 1.96 1.96 1.7 2.10
NiO 0.48 2.09 2.09 1.8 2.10
Cu2O 0.43 2.30 2.30 1.9 2.60
ZnO 0.82-0.98 0.58 1.72 1.72 1.6 2.84
SrO 1.10 1.03 0.97 1.0 1.00
SnO 0.48 2.09 2.09 1.8 3.10
BaO 1.15 1.15 1.15 1.15 1.12 0.89 0.9 0.78
PbO 0.48 2.09 2.09 1.8 3.08

(1) Duffy (1992); (2) Young et al. (1992); (3) Duffy and Ingram (1974a,b); (4) Sosinsky and Sommerville
(1986); (5) Gaskell (1982); (6) Ottonello et al. (2001); eq. (4.19) (note that Λ=γ −1); (7) Ottonello et al. (2001);
obtained by non linear minimization of FeO thermodynamic activity data in multicomponent melts.



591

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

4.1. Group basicity

Since we have established that the experi-
mentally derived concept of optical basicity is re-
lated to atomistic properties and first principles
such as Pauling’s electronegativity and fractional
ionic character of a bond (or «bond order») (see
eqs. (4.12), (4.15) and (4.16)) we may tentatively
extend the concept to formal entities such as the
silica polymers (or «structons» in the sense of
Fraser, 1975, 1977) within binary joins and then
to complex melts. To address the problem we
may still use eq. (4.19) but now the cation to ox-
ide ratio represents the local coordination present
in the structon (Duffy and Ingram, 1976). For in-
stance, for a monomer SiO44− rA = M/O〈−I〉 = 1/4,
for a dimer Si2O7

6− (or Si〈0〉2Ο〈0〉Ο〈−I〉66− in dis-
tributed oxidation state notation) rA = 1/3, and so
on. Group basicities of the most important poly-
mer units present in silicate melts are listed in
table II. We may note that, with the increase of

polymerisation, the group basicity of polymer
chains progressively decreases due to the de-
crease of the ratio O〈−I〉/O〈0〉. We may also note
that the presence of foreign cations (i.e. AlIII,
FeIII) in the polymer units changes the group ba-
sicity in a linear fashion with respect to the group
stoichiometry.

We may now inquire if, based on this new
concept, the basicity of a complex medium such
as a silicate melt or glass may be expected to vary
linearly with composition along a binary join.

For this purpose the three forms of oxygen
present in the melt (i.e. O2−, O〈−I〉 and O〈0〉)
(Toop and Samis, 1962a,b) are related to melt
stoichiometry and to the polymerisation reac-
tion constant K2 by mass balance (eqs. (2.4),
(2.5), (2.7)).

Along the polymerisation path (from
monomers SiO44− to silica), the group basicity
of the polyanion (or structon) matrix, Λ«structons»,
may be expressed as a linear function of the ra-
tio between singly bonded oxygen and total
oxygen within the structons (see also table II)

(4.22)

where , are respectively the group
basicity of the SiO44– monomer and of the SiO2
tectosilicate. The bulk basicity of the medium
results expressed as

(4.23)

where

(4.24)

and ΛΜΟ is the basicity of the oxide in the bina-
ry join MO-SiO2.

By combining eq. (4.23) with the mass bal-
ances (2.4), (2.5) and (2.7) we may evaluate
which part of the bulk basicity of the medium
may be ascribed to the effect of the structon ma-

O O I O O0 2= - + + -^ ^ ]h h g/

+( )1- -Λ Λ

Λ

=

+
2

( ) .

O

O

O

O I

O

O I

O

O I O

0 5

1
0

medium MO MO

SiO SiO

2

4
4

# -

+
-

-
- +

Λ

Λ

-

-

^

^
^

^ ^

h

h
h

h h

/ /

/ /

SiO2ΛSiO44Λ -

Λ+=
O I O

O I
1

0
structons SiO SiO4

4 2

-

-
-

+
Λ Λ -

^ ^

^
^

h h

h
hTable II. Basicities of «structons» along the poly-

merisation path.

Group Group basicity 

SiO44− 0.50000 0.73923
AlO45− 0.37500 0.85227
FeO45− 0.37500 0.80443
Si2O76− 0.57143 0.70198
Al2O711− 0.42857 0.83117
Fe2O711− 0.42857 0.77649
SiAlO77− - 0.76658
SiFeO77− - 0.73924
Si3O108− 0.60000 0.68707
Si4O1310− 0.61538 0.67906
SiO32−; Si2O64−; Si3O96−; 0.66667 0.65231
Si4O128−; Si5O1510−; 1-ring
Si2O52−; Si4O104−; Si6O156−; 0.80000 0.58278
Si8O208−; Si10O2510−; 2-rings
Si3O72−; Si9O216−; Si12O289−; 0.85714 0.55297
3-rings
SiO2 1.00000 0.47847
Al2O3 1.00000 0.60606
Fe2O3 1.00000 0.47847

Z r
2

A A#



592

Roberto Moretti

trix (third and fourth terms on the right in eq.
(4.23)).

In fig. 2 see how the basicity of the structon
matrix is affected by the value of the polymeri-
sation constant, which dictates the structons
contribution to the basicity of the medium.

Moles of quasi-chemical species of oxygen are
also shown for comparison.

Table III lists structural details along the join
CaO-SiO2, calculated adopting K2 . 1 = 0.0017
(Toop and Samis, 1962a) and ΛMO = 1.00 (Duffy
and Ingram, 1974b). We may note that the bulk
optical basicity of the medium is identical to
that obtainable through direct application of eq.
(4.19). However, note also that the bulk basici-
ty of the medium may be entirely ascribed to
the structon matrix over most part of the com-
positional join (for XSiO2 >1/3). The basicity
control operated by the structon matrix is the
more extended the more the dissolved oxide in
the binary MO-SiO2 system is basic (in the
Lux-Flood acceptation of the term) and the
lower the polymerisation constant K2.1.

We have seen that in solving the various mass
balances for different values of the polymerisa-
tion constant, Toop and Samis (1962a,b) showed
that the Fincham and Richardson assumption of a
purely anionic contribution to the Gibbs free en-
ergy of mixing in binaries MO-SiO2 (with MO
completely dissociated basic oxide) holds true.

It must be noted that the Toop-Samis model
accounts for (negative) chemical interactions on-
ly and is not able to reproduce the experimental-
ly observed solvi at high silica content even in
simple systems. This implies additional excess
Gibbs free energy terms of mixing which are not

Fig. 2. Basicity of the medium and of the structon
matrix (ordinate right-axis) calculated along the binary
join CaO-SiO2 assuming ΛCaO = 1 and K2.1= 0.0017
(Toop and Samis, 1962a) and K2.1= 1 (guess value put
for comparison). Abundances of quasi-chemical
species of oxygen (ordinate left-axis) are shown as a
function of the molar fraction of SiO2.

Table III. Basicity of structons and basicity of the medium in the MO-SiO2 binary (MO is CaO). ΛMO=1,
Kp = 0.0017.

NSiO2 O 〈0〉 O 〈−I〉 O
2− Λstructons Λmedium

0.000 0.000 0.000 1.000 0.739 1.000
0.100 0.000 0.399 0.700 0.739 0.905
0.200 0.003 0.795 0.403 0.738 0.826
0.300 0.019 1.162 0.119 0.735 0.759
0.400 0.211 1.178 0.011 0.700 0.702
0.500 0.503 0.993 0.003 0.652 0.652
0.600 0.801 0.797 0.001 0.609 0.609
0.700 1.101 0.599 0.001 0.570 0.571
0.800 1.400 0.400 0.000 0.536 0.536
0.900 1.700 0.200 0.000 0.506 0.506
1.000 2.000 0.000 0.000 0.478 0.478



593

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

accounted by the model itself, as shown by Ot-
tonello (2001). These additional terms (mechan-
ical strain) are much smaller than chemical inter-
action, but are sufficient to open solvi at high sil-
ica content (Ottonello, 2001, 2005; Ottonello
and Moretti, 2004). Nevertheless, the mechani-
cal strain energy contribution is so low that eqs.
(2.1) and (2.8) may be used by Ottonello et al.
(2001) to infer appropriate values of the poly-
merisation constant K2.1 in MO-SiO2 systems
from measured thermodynamic activities or
Gibbs free energy of mixing (fig. 3 and Ottonel-
lo and Moretti, 2004).

A simple T-independent exponential rela-
tionship linking the polymerisation constant K2
and the basicity moderating parameter of the
dissolved cation, based on the estimates of
Toop and Samis (1962a,b), Hess (1971), Reyes
and Gaskell (1983), Masson et al. (1970) on bi-
nary MO-SiO2 melts has been proposed by Ot-
tonello et al. (2001)

(4.25)

M M .
.

( . )
ln K

R
4 662

1 1445
0 997.2 1v v= +

+
=c c+ + 2

(4.26)

Since, according to eq. (4.18), the Jorgensen h
function is a generalised property, accepting
the validity of the above discussed relationship
which links ∆γ and K2.1 in simple systems, the
extent of polymerisation of chemically com-
plex melts and glasses may be readily obtained
by a simple mass balance involving oxide con-
stituents and their specific γ values (Ottonello
et al., 2001)

(4.27)

where and are respectively
atom fraction and basicity moderating parameter
of network modifiers and network formers in
one mole of the multicomponent melt or slag. 

We thus have a formal link between acid-
base properties of the medium (expressed as a
«contrast» between formers and modifier basic-
ities) and polymerisation constants.

This equation represents a high T approxi-
mation, polymerisation constants on single bi-
naries being defined at a unique T for each bi-
nary (see table 1 in Ottonello et al., 2001).
More precise formulations in the multicompo-
nent space are in progress, based on new T-de-
pendent parameterisations of polymerisation in
binary joins (Ottonello and Moretti, 2004).

Let us furnish now more details about the
calculation of the anionic structure of the melt.

To estimate K2.1 for the various binaries,
Hess (1971) adopted Temkin’s model for fused
salts, which ascribes the thermodynamic activi-
ty of the molten oxide to the activity product of
ionic fractions over cationic and anionic ma-
trixes, i.e.

(4.28)

where terms in brackets denote activities and
terms in parentheses number of moles.

M
M

M [ ] [ ]
( ) ( )

a O
cations anions

O
O

2
v 2

v #= =+ -
+ -

/ /

TXT j j+ +h hcM MX iiv vc+ +

exp= # M

X

M.

.

K X4 662

1 1445

. , melt

i

j

T

2 1 i

j

i

j

vv +

- -

c+ +

+ +h h
Tc

a

l

:

E

/

/

MM ( . )

( . ) .

expK

R

4 10 3 8452

0 926

. , SiOO2 1
5

2
v#=

=

c- - +
2

Fig. 3. Linear relationship between logarithm of
the constant of polymerization reaction (2.1) in MO-
SiO2 melts and basicity moderating parameter of the
network modifier Mν+. ∆γ = γ Mν+ −γ Si4+ .



594

Roberto Moretti

Since in a MO-SiO2 melt

(4.29)

and since the number of moles of O2− in the
melt is related to K2.1 and NSiO2 by mass balance
(eqs. (2.4), (2.5) and (2.8)), the evaluation of
aMO rests solely on the estimate of the number
of structons present in the anion matrix

(4.30)

. (4.31)

To evaluate Σstructons, Hess (1971) followed
the method devised by Flory (1953)

(4.32)

where NSi are the moles of silicon in the melt,
is the number of silicon atoms in the struc-

ton of and P〈0〉 is the fraction of silicon bonds
that link to doubly bonded oxygens, i.e.

(4.33)

Being dependent on composition in a com-
plex fashion, eq. (4.32) cannot be easily adapt-
ed to multicomponent melts.

To address the problem quantitatively we
must know the acid-base behavior of each dis-
solved oxide (i.e. the disproportionation between
«network formers» and «network modifiers») in
order to consider the effect of mixing of both
cationic and anionic constituents over the two
sulblattices of interest (the activity of the gener-
ic oxide MO being now the bulk of eq. (4.27)).

To solve the problem Toop and Samis
(1962a,b) proposed a «polymerisation path» of
general validity, based essentially on the vis-
cosity data of Bockris et al. (1955). As shown
by Ottonello (1983), the polymerization path of
the Toop-Samis model may be reconducted to

or

.P
I2 O 0 O

2 O 0
0 =

+ -^ ^

^

h h

h

7 A

or

$=

!

structons

( ) !
( ) !

N
P

P P P1 1

2 2
4 3

x

n

Si

x x

Si

Si

0

0
2

0 0
2

1

$

- -

+o o
o

=

r r
r

^ ^h h
<

<

F

F

/ /

M
( )

( )
a

O structons

O
2

2

=
+-

-

O

7 A/

anions O onsstruct2= +-] g/ /

M( ) cationsv /+ /

the simple form 

(4.34)

where the simple power function

(4.35)

accounts for the mean number of tetrahedrally
coordinated cation per structon, P〈−Ι〉 is the pro-
portion of singly bonded oxygen

(4.36)

and accounts for the presence of charge-bal-
anced tetrahedrally coordinated cations other
than Si (see Ottonello, 1983, for details), i.e.
NT = NSi + NAl + NFeIII.

Equations (4.32) and (4.34) lead to consis-
tent results, in terms of K2.1 when applied to
MO-SiO2 melts. However it has been shown by
Ottonello (1983) that the polymerisation path in
chemically complex immiscible liquid portions
(Watson, 1976; Ryerson and Hess, 1978, 1980)
is better represented by the exponential form

(4.37)

The amount of experimental data is at present-
day large enough to allow a re-estimation of the
above parameters. Through non linear minimi-
sation techniques we obtained 

(4.38)

Such a form allows us to define the extension of
the anion matrix in the Toop-Samis framework
along a unique polymerisation path. 

The generalisations made for complex melts
through eqs. (4.27), (4.28), (4.34), (4.36) and
(4.38), together with eq. (4.17) and the Toop-
Samis equations constitute the polymeric model.

Deconvolution of the investigated systems
into network formers and network modifiers was
carried out by (Ottonello et al., 2001) assuming
amphotheric behaviour for Al2O3 and Fe2O3: i.e.
Al3+ and Fe3+ are considered to have a partly
acidic behaviour. They are network formers if
counterbalanced by basic oxides such as H2O,

( . ) .exp P2 8776 ( )#=o - .1 7165-

. )2 67-( .exp ln P5 I= -o lr

N
P

O 0 O I

O I

T
I =

+ - +

-
-

^ ^

^

h h

h

7 A

P .I
1 95=o --r

N
structons T=

or
/



595

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

Na2O, K2O and CaO, to form complexes of the
type MAl4+, MFe4+or M0.5Al4+, M0.5Fe4+ which
polymerise as SiO44+ does. A completely acidic
behaviour was assigned to P5+ while Ti4+ is treat-
ed as a network modifier, in agreement with new
experimental observations (see later on) and with
findings based on quantum chemistry argumen-
tation applied to glass clusters (Kowada et al.,
1995). A more precise definition of the Lux-
Flood character of the various oxides was later
achieved by Ottonello and Moretti (2004) based
on the conversion of the Pelton and Blander
(1986) quasi-chemical parameterisation of bina-
ry MO-SiO2 interactions to the Hybrid Polymer-
ic Model. The new classification does not sub-
stantially alter the preceding observations. 

On the basis of the above considerations, we
may now address the problem of reactivity of
altervalent oxides (i.e. those oxides which do
disproportionate into different valent states and
have potentially distinct structural roles) on a
thermochemical basis. 

5. Factors controlling the FeII/FeIII ratio 
in silicate melts

Since iron is the main redox buffer in natu-
ral silicate melts, the treatment is specifically
developed for this element. Equilibrium among
dissolved iron in glasses or melts, the anion ma-
trix and the gaseous phase is usually written in
the form (Johnston, 1964; Duffy, 1996)

(5.1)

However, based on what was previously stated,
this form is misleading since it confuses formal
oxidation numbers with formal ionic charges.
Let us assume that we have spectroscopic evi-
dence that ferric iron is only present in polyan-
ionic complexes, and that the octahedral coordi-
nation of Fe2+ observed in melts is the result of
ionic couplings dictated by simple coulomb in-
teractions. We will have in this case the bulk
homogeneous equilibrium

(5.2)

+Fe,e+O+( )Fe III O

O O

2
7

0

7
2
1

( ) ( ) ( )

( ) ( )

melt melt melt

melt melt

4
5 2

2+ +

- +

- -

-

.O4+Fe4,O4+Fe4 ( ) ( ) ( ) ( )melt melt melt gas
3 2 2

2
+ - +

obtained summing up the partial equilibria

(5.3)

(5.4)

(5.5)

(5.6)

and the corresponding heterogeneous reaction

(5.7)

Adopting the usual polymeric notation it may
be easily seen that iron reduction induces de-
polymerisation of the melt structure

(5.8)

(5.9)

Let us now imagine that we have the spectro-
scopic evidence that ferrous iron form in the
melt or glass true octahedral complexes (in the
sense of Pauling, 1960). We could write the fol-
lowing homogeneous equilibria:

(5.10)

(5.11)

(5.12)

6O e ,++

+

( )

( )

Fe III O I

Fe II O O O3 0

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

4
5

6
10 2

,

-

+

- -

- -

O5 e ,++

+

( )

( )

Fe III O I

Fe II O O O
2
5

0
2
1

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

4
5

6
10 2

,

-

+

- -

- -

O4 e ,++

+

( )

( )

Fe III O I

Fe II O O2 0

( ) ( )

( ) ( )

melt melt

melt melt

4
5

6
10

,

-- -

-

+Fe,Si O

2 .O

+

+

( )Fe III O

SiO

2
7

7
2
1

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

4
5

2 7
6 2

4
4+

- - +

-

+Fe,e+Si O

O

+

+

( )Fe III O

SiO

2
7

7
2
1

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

4
5

2 7
6 2

4
4 2+

- - - +

- -

( )Fe III O O Fe

O O

2
7

0

7
4
1

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

4
5 2

2

,+ +

+

- +

-

Fe Fee( ) ( )melt melt
3 2

,++ - +

O O O
2
7

2
7

0 7( ) ( ) ( )melt melt melt
2

,+- -

O O
2
1

e
4
1

( ) ( )melt gas
2

2, +
- -

( )Fe III O Fe O4( ) ( ) ( )melt melt melt4
5 3 2

, +- + -



596

Roberto Moretti

or the corresponding heterogeneous reactions

(5.13)

(5.14)

(5.15)

The above notations emphasise the fact that we
must now produce additional free oxygen ions
O2− by polymerisation steps

(5.16)

(5.17)

The iron reduction may be regarded as an inter-
nally buffered auto catalytic reaction: produc-
tion of free electrons through the normal oxy-
gen electrode favours decomposition of ferric
iron clusters, making iron ions available to re-
duction by free electrons. This is true regardless
of the fact that octahedral iron clusters may be
present as simple ionic couplings (eqs. (5.2) to
(5.4)) or as true complexes (eqs. (5.11) to
(5.17)). In both instances, the whole process is
buffered by the availability of free oxygen in
the melt, which ceases at a critical acidity lim-
it, due to polymeric equilibria.

The fact that nominal O2− may appear either
as reactants or products stresses how mislead-
ing it could be to conceive the Le Chatelier
principle in terms of the simple mass action ef-
fect of oxide ions. As noted by Douglas et al.
(1966) the altervalent equilibria in melts and

.O+O2+ Si( )Fe II O

+ ,

,

( )Fe III O SiO5

4
1

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

4
5

4
4

6
10

7
6

2

- -

- -
2

O+OSi+

+

( )Fe II O

,

,

( )Fe III O SiO5 e

2
5

2
1

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

4
5

4
4

6
10

7
6 2

+- - -

- - -
2

+( )Fe II O,O6+

O+

( )

.

Fe III O I

2
1

0
4
1

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

4
5

6
10

2

-

+

- -

O3+2 -O

O5 ,+

+

( )

( )

Fe III O I

Fe II O O O
2
5

0
4
1

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

4
5

6
10

2,

-

+

-

-

4O ,++

+

( )

( )

Fe III O I O

Fe II O O O

2
1

2 0
1
4

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

4
5 2

6
10

2,

-

+

- -

-

glasses may be generalised as follows:

(5.18)

Equilibria such as those proposed by Johnston
(1964); or Duffy (1996), (eq. (4.38)) and appar-
ently violating the Le Chatelier principle de-
mand . If , such
as in the Holmquist (1966) formulation

(5.19)

there is no paradox, and when 
the equilibrium is written in a simple stoichio-
metric form (i.e. no oxide ions involved)

(5.20)

In the above equations it is assumed that ferric
iron behaves essentially as a network former,
although we know that in chemically complex
melts or glasses the structural behavior of FeIII

is a complex function of both bulk composition
and FeIII concentration. 

This simply means that the above equation,
written for macroscopic melt components, must
be coupled with homogeneous speciation reac-
tions defining the structural state of iron in
melts and glasses (which is a function of bulk
composition and P, T conditions, as shown by
experimental evidence). Mössbauer observa-
tions on quenched melts (Mysen, 1990, and ref-
erences therein) indicate that when FeIII exceeds
FeII (FeIII/ΣFe ≥ 0.3) ferric iron is only present in
tetrahedral clusters; for 0.5 ≥ FeIII/ΣFe ≥ 0.3 both
tetrahedrally and octahedrally coordinated FeIII

is present and for FeIII/ΣFe ≤ 0.5 tetrahedral
clusters are absent. Virgo and Mysen (1985) on
the basis of spectroscopic and magnetic data
suggested that coexistence of FeIII and FeII leads
to formation of units stoichiometrically resem-
bling Fe3O4 and composed of 0.33 tetrahedrally
coordinated FeIII, 0.33 octahedrally coordinated
FeIII and 0.33 octahedrally coordinated FeII (Vir-
go and Mysen, 1985). Experimental data on melt

.FeO O FeO
4
1

.2 1 5,+

( / )b a m 2+=

( )Fe III O I Fe O

O

4 4 6( ) ( ) ( )

( )

melt melt melt

gas

2
2 2

2

,- + +

+

- + -

( / )b a m 22 +( / )b a m 21 +

( ) ( )

( )

R n
m

R n m

a b
m

O
4

O O

2
O

ba 2

2

,+ + +

+ - + -: D



597

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

densities at various T, f O2 conditions seem to
confirm that FeIII is essentially present in tetrahe-
dral coordination, although some discrepancies
in the partial molar volumes of molten Fe2O3
based on various experiments could be ascribed
to the limited presence of a higher coordination
state in some of the investigated materials (see
Bottinga et al., 1983; Dingwell et al., 1988, and
references therein).

The fact that FeIII could partly exist in octa-
hedral coordination with oxygen may be as-
cribed to the partial reaction

(5.21)

The above equilibria show us that the nature of
bonding between central cations and ligands
must be attentively evaluated before reaching
unwarranted conclusions. 

Although the compositional effect differs in
the various investigated systems ( f O2 being
held constant), Duffy (1992, 1996) has shown
that the basicity effect is identical for all binary
systems whenever optical basicity is introduced
for the compositional axis. Duffy (1992) pro-
posed, at T = 1400°C, the following semiloga-
rithmic relationship between the observed re-
dox mass ratio of iron and optical basicity

(5.22)

Although this relationship disregards the effect
of temperature on the extent of the polymerisa-
tion reaction, it is sufficiently accurate to allow
comparative estimates on widely differing sys-
tems.

Nevertheless, this kind of equation cannot
be usefully employed on an empirical basis, not
because of the chosen parametric scale (i.e. op-
tical basicity) but rather because of the adopted
functional form. Figure 4 shows that Duffy’s re-
worked expression (see figure) does not reach a
good accuracy in reproducing the 1400°C data
available from the literature.

Following Fraser (1975, 1977), Ottonello 
et al. (2001) assumed that Fe2O3 behaves as an
amphoteric oxide in the Lux-Flood acid-base

. . .ogl
Fe
Fe

3 2 6 5III
II

= - Λb l

( ) ( )

.

Fe III O O I Fe III O

O O

5

2
5

0
2
1

( ) ( )

( ) ( )

melt melt

melt melt

4
5

6
9

2

,+ - +

+ +

- -

-

acceptation. Its double dissociation in the melt
(or glass) may be reconducted to the following
homogeneous reactions:

(5.23)

(5.24)

For ferrous iron on the other hand only a basic
dissociation is plausible, i.e.

(5.25)

Adopting the Temkin model for ionic salts
(Temkin, 1945) and assuming the Fe(III)O〈−I〉2
clusters to mix ideally over the structon matrix
and the Fe3+, Fe2+ cations to mix ideally over the
cation matrix, after some passages one arrives
at (Ottonello et al., 2001)

(5.26)

which is analogous to eq. (14) in Fraser (1975),

K a

K a K

a K

Fe
Fe 1

anions cations

cations

.
/

.
/

.
/

/
.

III

II

O

O

O

5 20
1 4

5 23
1 2 2

5 24
1 2

1 2
5 25

2

2

2

#

#

=

+-

-

b l

/ /
/

.FeO Fe O( ) ( ) ( )melt melt melt
2 2

, ++ -

.Fe O Fe O2 3( ) ( ) ( )melt melt melt2 3
3 2

, ++ -

( )Fe O O Fe III O I2( ) ( ) ( )melt melt melt2 3
2

2,+ -
-

Fig. 4. Experimental ferrous to ferric iron ratio ver-
sus summation of oxide optical basicities. Data from
various sources, also included in the database of Ot-
tonello et al. (2001), show the need for a more rigor-
ous approach to the functional form based on optical
basicity.



598

Roberto Moretti

although here Σanions replaces, more correctly,
Σstructons, since free anions such as O2−, CO32−,
S2−, SO42− etc., are present in the anionic matrix,
besides polymeric species.

Equation (5.26) implies that, due to dispro-
portionation of trivalent iron between the
cationic and anionic matrixes, we cannot expect
the ratio of rational activity coefficients of
FeO1.5 and FeO (second term on the right) to be
1. In fact the first term on the right side of eq.
(5.26) represents aFeO/aFeO1.5 (see eq. (5.20)),
whereas the second term represents γ FeO1.5/γ FeO.

If we compare eq. (5.26) with the function-
al form (5.22) we would deduce that the inter-
cept term in the equation of Duffy (1992) corre-
sponds to the first term on the right in eq.
(5.26), whilst the slope coefficient embodies the
remaining structural parameters.

Since the polymeric model allows the calcu-
lation of the extension of the structon and the
cation matrixes, Ottonello et al. (2001) conve-
niently solved eq. (5.26) on thermochemical
grounds, based on the plethora of experimental
data concerning ferrous iron solubility and iron
redox ratios in melts (and/or glasses) equilibrat-
ed at known T and f O2 conditions. Neverthe-
less, this was done only for nominally anhy-
drous melts synthesised at 1 bar pressure. On
this basis we can also investigate the depend-
ence of iron oxidation state under hydrous con-
ditions and therefore at higher pressure. It may

be here anticipated that the way iron dispropor-
tionates also depends on water speciation in
melts, as a consequence of the effect that water
carries on polymerisation and then basicity in
terms of free oxygen ions activity.

6. Iron oxidation state in hydrous alumino-
silicate melts: a preliminary model
extension

Water is commonly perceived as the most
basic oxide: its presence in the natural systems
undergoing melting dramatically affects the
solidus temperature and the composition of the
incipient melting liquid. Nevertheless, its basic-
ity (in the Lux-Flood sense of the term) seems
to be over rated, ΛH2O being very close to ΛSiO2
(table I). Therefore, it is of primary interest to
test the model reproducibility at pressure and
investigate how both polymerisation and the
ferric to ferrous iron ratio in melts are affected.
The still few data at present available in litera-
ture also involve the presence of water. Here I
present an exploratory extension of the 1-bar
anhydrous model of Ottonello et al. (2001).

First of all, it is necessary to introduce the
effect of pressure on the equilibrium constants
for reactions (5.20) and ((5.23) to (5.25)). This
is easily done by accounting for volume terms
of both ionic species and macroscopic compo-

Table IV. Molar volumes employed for macroscopic and ionic species involved in reactions (5.20), ((5.23) to
(5.25)), (6.3) and (6.12). For ionic species I also listed the the adopted ionic radius.

Molar Volume @ 298.15 K Ionic radius Reference
298.15 K (cc/mol) (Å)

FeO 9.64 - Lange (1994)
Fe2O3 29.63 - Lange (1994)
Fe2+ 0.90 0.78 Shannon (1976)
Fe3+ 0.51 0.645 Shannon (1976)
O2− 6.92 1.40 Shannon (1976)

FeO2− 75.99 (*) 3.29 (**) Shannon (1976)
OH− 6.92 1.40 Shannon (1976)
OH 6.92 1.40 Shannon (1976)
H+ 0 0 This work

(*) See text for details.
(**) The value here adopted represents the summation of the radius of four-folded ferric iron (0.49 Å) and the
diameter of an oxide ion O2−.



599

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

nents. This procedure is consistent with the
Temkin approach inherent in the Toop-Samis
model, which demands scaling of the activities
of liquid components from the standard state of
pure melt components at P and T of interest to
the standard state of completely dissociated
ionic component.

The equilibrium constant for reaction
(5.20), involving the macroscopic oxides FeO
and FeO1.5 is then recomputed as

(6.1)

where

Molar volumes of melt phases, as well as
isothermal compressibilities and isobaric ther-
mal expansivities have been taken by Lange
(1994).

For reactions (5.23) to (5.25) I still consider
the Lange (1994) data for macroscopic oxides
Fe2O3 and FeO, whereas volume of ionic
species are calculated on the basis of ionic radii
of Shannon (1976) assuming that the ‘effective
molar volume’ of each ionic species equals that
of a mole of spherical molecules each charac-
terised by its appropriate Shannon radius. Note
that for FeO2− species I calculated the molar
volume from that of a sphere of radius

. Since the spherical volume
associated with this radius should represent, at a
first approximation, the ‘effective volume’ of the
FeIIIO45− complex, I subtracted the volume of two
oxide ions O2− in order to obtain the ‘effective
volume’ of the FeO2− compound. This means that
I assume the volume change reaction for the as-
sociation reaction to be
zero.

Values of employed volumes are listed in
table IV.

In our calculation the ionic radius for each
ionic species is fixed for all temperatures (i.e.

FeO 2O FeO2
2

4
5

,+- - -

( / )r r1 2 ( )O Fe IV2 3+- +

( ) .V dP V V dP, ,melt

P

FeO melt FeO melt

P

1 1

.1 5
= -∆ c c c# #

+ln K -

,O gas

= V dPmelt∆

+

ln K
RT

RT
V dP

1

4
1

. ( , ) . ( , )P T T

P

P

5 20 5 20 1

1

1

2

c

c

#

#

thermal expansivity is zero), therefore I recal-
culated the thermal expansivity of macroscopic
oxides at 298.15 K, obtaining that the variation
in the reaction volume change is a constant at
any temperature.

The model is now ready to investigate the
role played by water in the ferric to ferrous iron
ratio of melts. Data in the literature disclose
some controversies about the oxidation state of
iron under hydrous conditions. Following
Moore et al. (1995), water does not affect the
ferric to ferrous iron ratio, which is a record of
other processes having imposed the oxygen fu-
gacity.

According to Baker and Rutherford (1996)
and Gaillard et al. (2001) water does affect the
ferric to ferrous ratio. In some region of the P-
T-f O2 space it may cause either a decrease or an
increase of oxidation. For example water-bear-
ing rhyolitic melts have higher ferric to ferrous
ratio than anhydrous melts of the same compo-
sition (Baker and Rutherford, 1996). The same
occurs in metaluminous melts, but at higher
temperatures (T > 900°C) and around NNO,
whereas in peralkaline melts such an increase is
observed at high T (Baker and Rutherford,
1996). Gaillard et al. (2001) generalise this per-
spective, observing an increase in the ferric to
ferrous ratio of iron in hydrous melts at log f O2 <
< NNO + 1.5 for all studies compositions, meta-
luminous and rhyolitic melts and natural pera-
luminous and peralkaline obsidians. However
they find that above NNO + 1.5 water does no
longer affects the ferric to ferrous iron ratio,
controlled by the anhydrous composition in
agreement with Moore et al. (1995). Finally,
Wilke et al. (2002) investigated tonalitic melts
at 850°C, whose ferric to ferrous iron ratio
showed a marked decrease with respect to the
values computed through the Kress and
Carmichael (1991) and then based on the anhy-
drous composition. Nevertheless, this effect is
mainly ascribed to the inaccurate calibration of
the Kress-Carmichael equation at low T rather
than to the water content of melts.

It is important to remark that Wilke et al.
(2002) and Gaillard et al. (2001) did not ob-
serve any effect of the quench rate on the ferric
to ferrous ratio of investigated melts. This con-
clusion cannot be obviously extended to the re-



600

Roberto Moretti

maining data here discussed, so quench-rate ef-
fects may still represent an important source of
uncertainty.

Moreover, the dependencies of the ferric to
ferrous iron ration on water amount are con-
trasting: Baker and Rutherford (1996) find dif-
ferent explanations about the role of hydroxyl
groups (Baker and Rutherford, 1996), whose
complexity is enriched by the T dependency of
water speciation (between OH− and H2O for all
the authors observing change on the iron oxida-
tion state with the water content).

These experimental results are likely to
show only apparent controversies. I then con-
sidered the database generated by these authors
(119 compositions) in order to expand the mod-
el of Ottonello et al. (2001). It is clear that the
parameterisation of the ferric to ferrous ratio
must consider the «impact» of water on melt
acid-base properties and then polymerisation.
In order to match this goal in the widest avail-
able P-T-X range, I also considered thirty-seven
1 bar compositions (from Fudali, 1965; and
Shibata, 1967) showing some water content (up
to 0.66 wt%) and which were already account-
ed for by Ottonello et al. (2001).

Consistent with the Temkin formalism of
complete dissociation of component oxides and
on the basis of that «common perception»
which requires water to behave as a strong
modifier (being a strong basic oxide in the Lux-
Flood notation), I first considered water as un-
dergoing uniquely a basic dissociation

(6.2)

Let us recall that this kind of dissociation is ac-
companied by other homogeneous reactions in
the melt phase (Fraser, 1975; Ottonello, 1997),
i.e. the association to NBOs’ originating strong
hydrogen bonding, and the polymerisation re-
action (6.4)

(6.3)

(6.4)

The summation of eqs. (6.2), (6.3) and (6.4) gives

(6.5)H O O 2OH2 0 ,+

.O O O22 0 ,+- -

H O OH2 2 2,++ -

.H O H O22
2

, ++ -

which well displays the depolymerising effect
of water and which has been first discussed by
Fraser (1975, 1977).

According to the Temkin notation of com-
plete dissociation, implicit in the Toop-Samis
approach, all the protons were considered to
contribute in defining the basicity of modifiers
(i.e. the basicity of the cationic matrix). The
polymeric constant and then initial (O−) values
were computed assuming only the occurrence
of reaction (6.2), without any concomitant equi-
librium (i.e. eq. (6.3)) leading to bonding with
NBO’s. The latter mechanism was considered
as a subsequent step involving depletion of both
initial O− and H+ to form OH. The following
mass balances must be satisfied:

(6.6)

(6.7)

The equilibrium constant for reaction (6.3) may
be expressed as

(6.8)

With some passages, substitution of eqs. (6.6)
and ((6.7) to (6.8)) gives the following quadrat-
ic equation:

(6.9)

The equation above has two possible roots, but
only the following one provides solutions
falling between initial O− and initial H+, and
then physically meaningful

(6.10)

(O2−), (O0), Σstructons were then recalculated
on the basis of the new O− values. The number
of newly formed OH groups, nOH, was then in-
cluded in the quantity Σanions.

n$n$K4 $-

n
K n K n

K

K n K n

cations

2

cations

/ /

/

/ /

. .

.

. . .

OH

1 2
H
IN 1 2

O
IN

1 2

1 2
H
IN 1 2

O
IN 2

H
IN

O
IN

6 3 6 3

6 3

6 3 6 3 6 3

$ $

$ $

=
+ + +

- + +

+ -

+ - + -_ i

/

/

.

K n K n K n

n K n n

cations

0

/ / /

/

. . .

.

1 2
OH
2 1 2

H
IN 1 2

O
IN

OH
1 2

H
IN

O
IN

6 3 6 3 6 3

6 3

$ $ $ $

$ $ $

- + +

+ =

+ -

+ -

_ i/

.K
n
n

n
cations

/
.

1 2

O

OH

H
6 3 $=

- +

/

.n n nH H
IN

OH= -+ +

n n nO OHO
IN= -- -



601

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

Furthermore, we should also consider that
the theory, based on the Lux-Flood formalism,
gives us an alternative to be evaluated: the am-
photeric behavior of water, i.e. the existence of
an acidic dissociation, as testified by its rela-
tively low value of optical basicity. The follow-
ing reaction:

(6.11)

was first proposed by Fraser (1975). Moreover
the existence of free OH− has recently been re-
ported by Xue and Kanzaky (2003). Reaction
(6.11) is actually that normally invoked in liter-
ature to explain water dissolution in aluminosil-
icate melts. Nevertheless, in the literature it is
not regarded as an acidic dissolution mecha-
nism, neglecting the fact that it leads to melt
polymerisation because of the consumption of
free oxygens.

I then introduced in the model the difference
between reaction (6.11) and reaction (6.2), i.e.

(6.12)

whose equilibrium constant may be written as

(6.13)

This equation simply recognises the existence
of two dissolved species of water in melts, i.e.
OH− and H+, consistently with the Temkin for-
malism and the Lux-Flood notation for oxide
solvents.

I therefore by-pass the problem of determin-
ing the activity of water in melts as well as in
the fluid phase, a problem which would be
posed by solving eqs. (6.2) and (6.11) separate-
ly or by solving their algebraic sum. The system
of equations is simply solved through addition-
al mass balance on water

(6.14)

and the equilibrium constant for water specia-
tion reaction (6.12). Equation (6.10) partitions
the initial water amount, so that K2.1, polymerisation
is no more defined on the total analytical water
content.

n n n2H
IN

OH H O2$+ =+ -

.K
n
n

n n

cations
. TOT

O

OH

H OH
6 12

2
$=

--
-

+ -

/

H O OH2 ,++ - -

H O O OH22
2
,+ - -

Regression on available experimental data
is performed through non-linear minimisation
techniques based on steepest descent and gradi-
ent migration methods (James and Roos, 1977)
on both K6.3

1/2 and K6.12. Equilibrium constants
values and statistics for the extended iron mod-
el are given in table V, whereas reproducibility
may be appreciated in fig. 5. It is worth remark-
ing that the T dependence obtained for equilib-
rium (6.12) shows that this reaction becomes
more important at higher T. On the other hand,
reaction (6.3) is independent of temperature
(the entropic term of the arrhenian dependence

Fig. 5. Reproduciblity (calculated versus experi-
mental) of the extended iron oxidation state model.
Anhydrous and hydrous datasets are distinguished.
The whole database consists of 608 compositions.

Table V. Equilibrium constants for water speciation
mechanisms and model statistics.

logK6.12 1.835 – 1304.65/T
1/2(logK6.3) –1.335
Number of hydrous 120
compositions
Number of all compositions 608
(anhydrous+hydrous)
Mean error (hydrous dataset) 0.277
Standard error 0.357
(hydrous dataset)
Mean error (whole dataset) 0.187
Standard error (whole dataset) 0.264



602

Roberto Moretti

describes the equilibrium constant) and left-
ward shifted.

The effect of pressure was neglected for re-
actions involving water species as the volume
associated with H+ was assumed to be zero, so
that VO2− =VOH− =VOH.

The comparatively low precision of the hy-
drous dataset with respect to the anhydrous one
probably reflects model approximations, similar-
ly to what was described for sulphur speciation in
Moretti and Ottonello (2003a). In particular, a
more general model based on the assessment of
water solubility and speciation should require the
Flood-Grjotheim treatment (Flood and Gr-
jotheim, 1952) opportunely implemented and al-
ready used for sulphur species (Moretti, 2002;
Moretti and Ottonello, 2003b). Moreover, more
accurate data for molar partial volumes are need-
ed, in particular for iron oxides. In principle, we
could improve the precision of our model by re-
fining on volume reactions, but I prefer to em-
ploy independent experimental volume data. A
possible source of error is also related to the T-in-
dependent computation of the polymeric exten-
sion of the anionic matrix: a more general, i.e. T-
dependent (Ottonello and Moretti, 2004, and
work in progress) polymerisation equation would
represent a step forward in the continuos attempt
to ameliorate model results and applications.

Figure 6a,b shows a comparison between: i)
equation (5.26), accounting for water specia-
tion and volume terms; ii) equation (5.26) un-
der the 1 bar approximation and without con-
sidering eqs. (6.3) and (6.12); and iii) the Kress
and Carmichael (1991) empirical model.

It is evident that both eq. (5.26) under the 1
bar approximation and the Kress-Carmichael al-
gorithm do not work well in reproducing the ob-
served FeII/FeIII ratio, which is largely underes-
timated in the first case.

It is important to remark that the fact that we
«identify» three water-derived species in melts
(H+ cations, OH− free anions and, to a very mi-
nor extent, OH groups terminating polymeric
units, which can be then ascribed to T-OH link-
ages) is quite consistent with NMR findings
(Kohn et al., 1989; Schmidt, 2001; Xue and
Kanzaki, 2003). Intuitively, it would seem that
their combination reproduces the water specia-
tion – and solubility – observed in melts, simi-

larly to what was argued by Liu et al. (2002).
Nevertheless these arguments cannot be pushed
further and are purely qualitative: the model
here developed is not aimed at reproducing the
speciation observed via FTIR or NMR since
model computations are based on a particular
standard state (that of completely dissociated
component) which is introduced to describe the
acid-base properties of melts and not the struc-
tural units detected by spectroscopic tools. For
example, the existence of equilibrium (6.2) and
(6.11) (and hence equilibrium (6.12)) implies in-
complete dissociation of the water component

Fig. 6a,b.  Model reproducibility of the hydrous
datasets following different approaches (see text). In
part a) of the figures data from various sources have
been distinguished. H2O-unsaturated data from Bak-
er and Rutherford (1996) were not considered.

a

b



603

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

and therefore the presence of molecular water.
The existence of this species is not ruled out by
the present model, but calculations need not
treat it to solve chemical interactions of interest
whenever the Temkin standard state is applied.

Model generated distributions of (O−), (O0).
(O2−), nOH, nOH−, nH+ are plotted in fig. 7a,b for
the system Na5-4x Alx Si3x (Al/Si =1/3) contain-
ing an arbitrary amount of water (6 wt% in the
whole compositional range) at 900°C. We see
that H+ and OH− are always the predominant
water derived species in melts, whereas OH are
subordinated. In particular, abundances of OH−

anions and H+ cations are inversely related, ob-
taining similar values at both low and high alu-
mina contents. The abundance of T-OH groups
follows the same trend of H+ cations, although
much more smoothed. A slight increase in the
concentration of free oxygen (O2−) is computed
for compositions with alumina content larger
than that of albite (X=1).

Finally, it is worth remarking that the appre-
ciable occurrence of both eqs. (6.2) and (6.11)
suggests a strong similarity with water behav-
iour in aqueous phase.

7. Conclusions and perspectives

The superiority of polymeric models in de-
picting silicte melts and slags reactivity with re-

spect to other conceptual approaches is linked
to the following facts:

i) It is well recognised that «regular mix-
ture» models fail to reproduce the Gibbs free
energy of mixing of silicate melts. Minima in
the Gibbs free energy of mixing are badly allo-
cated and badly conformed in the chemical
space of interest. For heterogeneous equilibria
(solid-liquid or liquid-gas in multicomponent
systems) this problem is almost ineffective
since internal consistency is achieved with ex-
tended databases encompassing model devia-
tions through adjustable interaction parameters.

ii) The arbitrary deconvolution of chemi-
cally complex melts into fictive components is
a path-dependent process eventually complicat-
ed by charge-balance considerations whenever
amphotheric oxides are involved (this applies to
iron and other transitional elements in slags and
natural melts).

iii) Preliminary attempts to parameterise the
bulk polymerisation proved satisfactory in de-
ciphering the complex effect of the bulk Lux-
Flood acidity of the system on the oxidation
state of iron in multicomponent melts and
glasses (Ottonello et al., 2001). The Gibbs free
energy of mixing of simple binaries MO-SiO2
and of ternary systems (CaO-FeO-SiO2) was
successfully simulated (Ottonello, 2001).

iv) Polymeric models carry a minimal set of
structural information which can be employed

a b

Fig. 7a,b.  Relative proportions of oxygens of the Fincham-Richardson (1954) notation (a) plotted against the
compositional parameter in the binary join Na5-4x Alx Si3x O8. Water-derived species dissolved in the same com-
positional range have been plotted in b). Note the comparable amount of OH and OH− for the albitic composi-
tion (x = 1).



604

Roberto Moretti

for the study of partitioning of elements, vis-
cosity and – plausibly – other transport proper-
ties of silicate melts such as thermal and electri-
cal conductivity.

The adopted polymeric parameterisation is
based on three main previous observations:

1) The basicity of a complex aprotic medi-
um such as a silicate melt or glass is conve-
niently represented by the «optical basicity»,
arising from the nephelauxetic effect induced
on p-block metals by the ligand field (Duffy
and Ingram, 1971, 1973, 1974a,b, 1976; Duffy
and Grant, 1975). 

2) Optical basicity is related to atomistic
properties of the dissolved oxide components in
the melts or glass, such as the Pauling and
Sanderson electronegativities (Pauling, 1960;
Sanderson, 1967) and the fractional ionic charac-
ter of the bond (Pauling, 1960; Phillips, 1970). 

3) Bulk optical basicity of molten silicates,
or glasses can be split into two distinct contri-
butions, the basicity of the dissolved basic ox-
ides and the basicity of the polymeric units (or
«structon matrix» in the sense of Fraser,
1975a,b, 1977). While the optical basicity ef-
fect induced by the dissolved oxides varies
widely with the type of oxide component, the
optical basicity effect ascribable to the structon
matrix is virtually unaffected by composition,
at parity of silica content in the system, and is
dominant at high silica contents.

An exploratory application to the modelling
of the oxidation state of iron shows that it is
possible to extend the model of Ottonello et al.
(2001) to hydrous aluminosilicate melts. This
requires the introduction of volume terms for
both ionic species and macroscopic compo-
nents, together with equilibria relevant to water
speciation. These preliminary results are quite
satisfactory and promising, especially consider-
ing that the polymerisation constant employed
represents the high-T approximation (Ottonello
and Moretti, 2004) and that I adopted experi-
mental values for molar volumes, whereas
more accurate partial molar volumes should be
employed. In particular, data are well explained
as long as both basic and acidic dissociations of
water are considered.

A further slight amelioration to model preci-
sion may be introduced by accounting for a sub-

sequent process of association to NBO’s, that
may be seen at first approximation as character-
istic of strongly hydrogen-bonded T-OH groups.
The fact that water also undergoes an acidic dis-
sociation, originating free anions OH−, agrees
with the recent findings of Xue and Kanzaki
(2001, 2003), based on density functional theory,
inferring the existence of NaOH groups in alka-
line silicate glasses and confirms the prediction
of Fraser (Fraser, 1975, 2003; and this issue).

It is worth stressing that the reliability of
calibrated equilibrium constants involving ion-
ic species of water and iron is subjected to i) the
quality and P-T-X extension of the reference
database; and to ii) accurate estimates of reac-
tion volumes of iron species and of reactions in
which they are involved. Moreover, it must be
clear that the present modelling does not have
any straight implication about the geometry of
coordination polyhedra in silicate melts, not re-
quired for the purposes of understanding poly-
merisation and the acid-base behaviour of in-
vestigated species. Therefore, ionic species de-
picted by the model are not necessarily related
to structural units that can be identified by
means of current spectroscopic tools.

In the light of these results, some future ac-
tivity may be here planned, both experimental
and theoretical. Some research lines may be
proposed and followed contemporaneously to
solve accurately, the mixing properties of sili-
cate melts:

i) Experimental – in situ measurement of
optical basicity (nephelaxeutic parameter) at T
and P.

ii) Experimental – XPS measurement of
free oxygen (O2−) in silicate melts coupled to
the Toop-Samis modelling of silicate melts (see
next point).

iii) Theoretical – application of the hybrid
model of Ottonello (2001) to the conformation
of liquidus in multicomponent systems, follow-
ing the guidelines of the Flood and Grjotheim
treatment for the calculation of chemical inter-
actions coupled to strain energy modelling.

iv) Theoretical – by applying quantum-me-
chanical codes to simple binaries and ternaries;
in order to better assess the nature of nephelaux-
etic effect in ligand field-related spectroscopic
observations.



605

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

The first task has the objective of improving
the Toop-Samis model, by translating the T de-
pendence of nephelaxeutic parameters into
polymerisation constants of the type of eq.
(4.27). As required by the second task, this may
also be done through XPS measurements of
oxygen species, which coupled to predictions
of the Fincham-Richardson approach allow a
thorough assessment of polymerisation in melts
(Park and Rhee, 2001). The third task has the
objective of deciphering the contribution given
by the dissociation of every component in
chemical systems of increasing complexity.
First we should reconstruct the binary SiO2-
Al2O3 and then study ternary fields MO-Al2O3-
SiO2. With the introduction of alumina it is im-
portant to investigate the effect of entropic ef-
fects, because of the similitude of acid-base
properties with silica. Navrotsky (1994) point-
ed out that in this binary the Al3+ cation is
forced to occupy the octahedral site. Entropic
terms, arising from a «competitive» effect of
Al2O3 and SiO2 upon the polymerisation are
then expected to come out. Entropic terms
should also be much more evident in the pres-
ence of alkalies in the system, mainly because
of the charge compensation of the tetrahedral
aluminum. The effects of non-random mixing
of some network modifier oxides like Na2O and
K2O must be carefully evaluated. Moreover, a
systematic comparison, while creating the ther-
modynamic database, will allow us to further
refine nephelauxetic parameters and their de-
pendence upon intensive variables, especially
in terms of temperature. Finally, we should also
consider the mechanical strain energy contribu-
tion to the bulk free energy of mixing, since
such a term explains the observed solvi experi-
mentally determined in SiO2 rich ranges of bi-
nary systems. As shown by Ottonello and
Moretti (2004) the plethora of thermodynamic
data emerging from the metallurgical commu-
nity is, to this purpose, of invaluable help.
Some queries may be addressed to experimen-
talists, such as coupling optical basicity meas-
urements with spectroscopic measurements on
the Rydberg’s and electron transfer emission
lines of 3d chromophores. This would allow us
to assess better the differential nephelauxetic
effects and the structural state of complexes.

The fourth research line is devoted to a better
comprehension of model clusters and complex-
es which characterise the speciation state of sil-
icate melts. A feasibility study for the adoption
of parallel computing techniques has to be car-
ried out. Semi-empirical methods, such as
Huckel-MO, have to be ruled out as they need
a large amount of experimental data, the consis-
tency of which is often doubtful.

All the considerations here reported are pre-
liminary to the set-up of an ambitious general
thermochemical simulator able to depict the
evolution of a complex (but essentially aprotic)
system. Given such a general polymeric model,
we can promote on its grounds thorough studies
of water solubility (as well as any other
volatile), through recalculation of equilibrium
constants for both eqs. (6.2) and (6.11).

For our scientific community final applica-
tions will concern the study of the degassing of
active volcanoes, the dynamics of magma flow
and eruption, the interpretation of glass inclusion
and plume composition analyses. Results will be
also valuable for material scientists devoted to
the physical chemistry of oxide systems.

Acknowledgements

I wish to thank Giulio Ottonello for his
helpful comments to a preliminary version of
this paper, and also for his continuous encour-
agement during recent years. The manuscript
benefited of reviews by Don Fraser and Max
Wilke. Mike Carroll is acknowledged for edito-
rial handling. This work was carried out with
the financial support of Regione Campania,
L.R. 5/2002 grant for basic research.

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