silicate melt 11

7/28/2019 Silicate Melt 11

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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.


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:


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


+


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Prediction of Liquid Immiscibility


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.

silicate melt 11

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