Thermodynamic Models of

MagmasLecture 13

Silicate MagmasBasic structural unit of silicates (solid & liquid) is the silica tetrahedron

• These are variously joined by shared, or bridging, oxygens, to form various structures in solids and liquids.

• Basic difference between solids and liquids is lack of long-range structure in the latter.

• Liquids structure can be studied by quenching them to glass.

Liquid Structures• Bridging oxygens and joining

tetrahedra results in polymerization of the melt, changing its properties.

• Al3+, Ti, and Fe3+ can promote polymerization and, along with Si, are called network-forming ions.

• Other ions, Ca2+, Mg2+, Fe2+, Na+, K+, and H+ tend to break up this structure and are called network modifiers.

Modeling Silicate Liquids

• Problems are:o Decide on the componentso Determine the nature of the model

• Ghiorso et al. adopt a regular solution model for their MELTS model.

• Determine the interaction parameters from experimental data.

• The resulting program then iteratively computes free energy of the liquid plus free energy of all possible precipitating solids and calculates the equilibrium assemblage based on the principles that o the stable assemblage is the one with the lowest

free energy.o The chemical potentials of components in

coexisting phases are equal.

• Silicate liquids are complex solutions of many components.

• Solids crystallizing from them are generally solutions themselves.

• Generally these solutions cannot be treated as ideal.

• Crystallization (or melting) occurs over a wide range of T (400-500˚C).

MELTS Model• Free energy of the

liquid solution is:

• Activity coefficients calculated as:

• For network modifiers, Ghiroso chose silicate components such as CaSiO3, Mg2SiO4, Na2SiO3, KAlSiO4, etc. because mole fractions of individual oxides tend to be small numbers, reducing influence of interaction parameters.

• Network formers generally just the oxides (e.g., Al2O3).

• Eleven components, plus water treated separately.

pMELTSPredicted and actual pyroxene compositions in lavas.

Predicted and actual SiO2 concentrations in experimental melts of peridotite as a function of melt percent.