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The Nature of Silicate Melts
Silicate melts are ionic solutions composed of anionic clusters (or polymers)
sharing exchangeable cations.
The anionic clusters are dominated
by tetrahedrally coordinated cations
because of the high field strength
(charge/radius Z/r) of Si, thedominate cation (SiO2 = 35 to 75
wt.%).
MgZ/r = 4.35, Mg-O ionic bond strength = Z/coord no. = 2/6 = 1/3
SiZ/r = 22.22, Si-O ionic bond strength = Z/coord no. = 4/4 = 1
Futhermore, unlike the Mg-O bond the Si-O bond is significantly if not dominantly covalent in character.
-4
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Non-Bridging
Oxygen
Bridging
Oxygen
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Raman Spectra Studies indicate that 4 different
types of anionic clusters dominate most silicate
melts.
Isolated Tetrahedra TO4
2-D Sheets T2O5
1-D Chains TO3
3-D networks TO2
dec
reasing
abunda
nce
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The average NBO/T of a silicate melt is a measure of the population distribution of
anionic clusters existing in the melt, which is a function of its bulk composition.
The average NBO/T ratio represents the summation of many reactions of the type:
M-O-M + T-O-T 2 M-O-T
O=
+ Oo
2 O-
free oxygen bridging oxygen non-bridging oxygens
Equil. constant K = a(O-)2 / a(O=)a(Oo)
There are many such reactions in any silicate melt involving differing metals anddiffering anion tetrahedral clusters. The magnitude of the equilibrium constants (K) for
any given reaction is a function of the relative Z/r of the Metal versus T cations. There is
thus a competition between metal cations in a melt for oxygen ions with which to bond.
Because of the Si-O bond strength and its abundance, Si is one of the strongest players.
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H, K, Na, Ca, Mg, Fe2+, Al, Fe3+, Cr, Ti, Si, P, C, S, O, Cl, F
Base Acid
Increasing field strength Z / r
The more basic a metal oxide, the greater the value of the equilibrium constant,
and thus the lower the number of bridging oxygens and the more depolymerized
the melt.
M-O-M + T-O-T 2 M-O-T
O= + Oo 2 O-
Equil. constant K = a(O-)2 / a(O=)a(Oo)
free oxygen bridging oxygen non-bridging oxygens
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The activity of O= reflects the summation of all such reactions in a given melt and
is taken as a measure of the basicityof a melt.
The ratio of non-bridging oxygens to tetrahedral cations (NBO/T) of a melt is a
measure of its average degree of polymerizations and thus another measure of the
basicity of a melt, whose advantage is that it can be simply calculated from thechemical composition of the melt.
Basicity of a Melt
As in the case of silicate minerals, there is not enough oxygen to coordinate all the Si4+
ions without being sharing with other metal cations. The result is a solution consisting of
negatively charged tetrahedrally-coordinated clusters or polymers that are loosely heldtogether by other metal ions in higher coordinated sites. The addition of oxides that are
more acidic than Si (such as Ti, P, C) have equilibrium constants that are less than 1 and
thus promote the increased polymerization of the melt by robbing Si complexes of O-. The
addition of basic oxides to a melt decreases the polymerization of the melt by providing
addition oxygen to coordinate Si.
NBO = 2 O 4 T = n(NMi)n+
T = No. Network-forming cations
T = SiO2 + KAlO2 + NaAlO2 (CaAl2O4 MgAl2O4 +TiO2 + Ca2(PO4)2)
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Estimated fraction of
major anion complexes in
silicate melts versus the
parameter:
NBO/T
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Bases: H2O, K2O, Na2OAct as bases, giving oxygens to anionic
tetrahedrally coordinated anions,
promoting the conversion of bridging
oxygens to non bridging oxygens and thus
depolymerizing the melt.
The common oxide components of silicate melts can be classified in terms of
their acid/base character:
M-O-M + T-O-T 2 M-O-T
O= + Oo 2 O-free oxygen bridging oxygen non-bridging oxygens
Equil. constant K = a(O-)2 / a(O=)a(Oo) > 1
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Acids: TiO2, P2O5, CO2 Act as acids competing with Si for oxygen toachieve tetrahedral coordination. They promotethe increased polymerization of the melt by
taking non-bridging oxygens from Si anion
clusters to form their own anion clusters, or
substitute for Si in its anion clusters.
The common oxide components of silicate melts can be classified in terms of
their acid/base character:
Ti-O-Ti + T-O-T 2 Ti-O-T
O= + Oo 2 O-free oxygen bridging oxygen non-bridging oxygens
Equil. constant K = a(O-)2 / (a(O=)a(Oo)) < 1
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Amphoteric behaviour reflects solid solution in tetrahedral sites
SiO2constitutes between ~35 and 75% of most terrestrial igneous melts.
Some of the Al3+ and Fe3+ occupy
tetrahedral sites, substituting for Si, if otherelements in higher coordinated sites (such as
Na+ and K+, and even Ca2+) are availablefor local charge balance as the components:
KAlO2, NaAlO2, CaAl2O4
Amphoteric: Al2O3, Fe2O3, Cr2O3Act as an acid in tetrahedral coordination
charge-balanced by K or Na as the components
KAlO2 + NaAlO2. Al2O3 in excess of alkalisacts as a base.
Note the viscosity peak at Na/Al ratio
of 1, corresponding to maximum Al
substitution of Al for Si in tetrahedral
sitesmaximum polymerization.
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Extrapolations of phase equilibria in simple systems
to more complex natural systems.
Korzinskis Rule # 2: a rise in the basicity of a melt shifts the compositions
of eutectics, peritectics, and cotectics towards the acid components.
Qualitative Applications of acid-base model
Korzinskis Rule # 1: a rise in the basicity of a melt enlarges the liquidus volume ofminerals rich in basic oxides at the expense of minerals rich in acidic oxides, and vice
versa.
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Extrapolations of phase equilibria in simple systems
to more complex natural systems.
Korzinskis Rule # 1: a rise in the basicity of a melt enlarges the liquidus volume ofminerals rich in basic oxides at the expense of minerals rich in acidic oxides, and vice
versa.
Effect of P2O5addition
Qualitative Applications of acid-base model
+
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Prediction of Liquid Immiscibility
Qualitative Applications of acid-base model
Mg Ca Ba Na KZ/r 2.5 1.9 1.3 0.9 0.6
The degree of polymerization in Si-rich melts is
high and thus the availability of O= ions to
coordinate other metal cations is low. As
temperature decreases, it becomes increasingly
favourable for acidic components to form their
own immiscible liquids rater than substitute for Si.
In binary systems, the width of the liquid
immiscibility gap is proportional to the field
strength (Z/r) or acidity of the oxide
Acidic Basic
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Prediction of Trace element partitioning between coexisting immiscible
Liquid Immiscibility
Acid trace elements partition
preferentially into the basic immiscible
melt because of the higher activity of
non-bridging oxygens with which to
achieve their preferred coordination
number
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The viscosity of silicate melts is sensitive to composition
Acidic melts are more viscous than
basic melts, with viscosity being
inversely proportional to:
1/~ NBO / T.
Adding a relatively basic component (eg
Na2O) to a silicate melt will decrease the
melts viscosity.
Adding a relatively acidic component (eg.P2O5)to a silicate melt will increase the melts
viscosity.
Log
Viscosity
(poise)
rhyolites
andesites
basalts
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A 2 Lattice Model for Silicate Melts
Assumption: Silicate melts are made of two types of chemical components.
Network Formers (NF) consisting of Si and other high field
strength elements capable of substituting for Si in tetrahedral
anion clusters, or forming their own tetrahedral anion clusters.
Network Modifiers (NM) which compete with the
tetrahedrally coordinated anion clusters for oxygen - those
involved in charge balancing elements in tetrahedral
coordination
Mixing of cations is restricted to either the NF or NM sites, but there is nointerchange of cations between the two.
Activity-composition models for the thermodynamic calculation of phase
equilibria
Quantitative Applications of acid-base model
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MgOliq + 0.5SiO2liq = 0.5(Mg2SiO4)
G = 0.0 = Gproducts = Greactants
GMgO + 0.5GSiO2 =0.5GFo
GoMgOliq + RTln(aMgO
liq) + 0.5G
oSiO2
liq + RTln(aSiO2liq)0.5
= 0.5GoFo + RTln(aFo)0.5
GoT = - RTln ((aFo)0.5 / (aMgO
liq)(aSiO2liq)0.5))
Predicting the composition of minerals in equilibrium with melt
Olivine
Ho - TSo = - RTln ((aFo)0.5 / (aMgO
liq)(aSiO2liq)0.5))
For reactions not involving a volatile phase,Ho andSo are ~ constants for small
changes in temperature and pressure, thus to a first approximation:
a/T + b = - Rln ((aFo)0.5
/ (aMgOliq
)(aSiO2liq
)0.5
))
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This is the equation of a straight line. Once we have activity-composition
models for olivine and silicate melt, the constants a and b can bedetermined by experiment.
a/T + b = - Rln ((aFo)0.5 / (aMgO
liq)(aSiO2liq)0.5)) = - RLnK
Ideal Mixing: If weassume silicate melts are ideal
mixtures, then the activities ofits components are simply
equal to their mole fraction:
aMgOliq = XMgO
aSiO2liq = XSiO2
The activity of forsterite (aFo) in
olivine is generally taken as:
aFo = (XM1Mg)(XM2Mg) = (XMg)2
ba = slope
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2 Lattice Model:
aMgOliq = Mg / NM
aSiO2liq = Si / NF
Ideal Mixing:
aMgOliq = XMgO
aSiO2liq = XSiO2
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Prediction of trace
element partitioning
Quantitative Applications
Ideal mixing
Mixing of network
modifiers
Ideally trace elements are those
elements whose concentration is so
low that they obey Henrys law.
Cisolid / Ciliq = K constant
In practice, many trace element
partition coefficients vary with
the composition of the silicatemelt. Using a two lattice
activity model one can greatly
reduce this dependence
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Oxidation State of Magmas
Korzinski observed long ago that:
Fe3+ / Fe2+ increases with the basicity of a silicate melt.
FeO Fe2+ + O=
Fe2O3 + O= 2 [FeO2]
-1
K1= ([O=] [Fe2+])/ [FeO]
K2 = [FeO2-]2 / [Fe2O3] [O
=]
4[FeO2]- 4Fe2+ + 6O= + O2
K3 = ([Fe2+]4 [O=] fO2 )/ [FeO2
-]4
Base:
Acid:
increasing basicity
Increasing basicity (increasing O=)
favours Fe3+ over Fe2+
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There are now formulations that enable the calculation of viscosity, density, and ratio of
Fe2O3/FeO of silicate melts as the sums of partial molar quantities of their oxidecomponents calculated taking into account whether the components are network
modifiers or network formers at any given temperature, pressure, and fO2.
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The Nature of Silicate Magmas
Melt versus Magma
Most magmas and lavas are actually 2 phase mixtures of silicate liquid and crystals.
Some are three and four phase mixtures with the presence of immiscible sulfide droplets
and vapour bubbles. The situation gets even more complicated when crystals of
different aspect ratios raise the number of mechanical components to 5 or more.
Pillow MarginBaffin Is.
glass
gas
glass
gas
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Viscosities and Densities of Magmas are
affected by the phenocrysts that they
carry.
For ideal crystal spheres:
Einstein-Roscoe equation:
Viscosity of solid - fluid mixtures:
mix = (1 - 3.5 X) - 2.5 oX =volume fraction crystals
For high aspect ratio crystals, such as plagioclase, the
effect is much more significant.
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Natural silicate melts, however, are complex systems with many components and thus melt
over a range of temperatures. Because of the high aspect ratios of plagioclase, basalt
becomes rigid in the range of 30 to 40% solidification. Note how a cube of solid basalt
retains its shape to 70% melting, even as the partial melt drains out of the bottom.
Basalt Cube - % melted
60% 70% 75%
Philpotts & Carroll, 1996
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The compositions of liquids in silicate magmas follow compositional paths constrained by
the liquidus volumes of the phenocrysts they carry. For example, in the binary system Forst.
Qtz. system, the composition of the liquids follow the liquidus curves.
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