A set of thermodynamic models suitable for mantle mineral phases, accompanied by a mafic melt model, has been calibrated in the system CaO-MgO-Al<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub> (CMAS) and its subsystems, over the pressure range 0.50 kbar. The models are able to reproduce phase assemblages and reactions observed by experiment. Having a fundamentally thermodynamic form, they can be interpolated reliably between the pressures, temperatures and compositions of the experiments. The models may be used with the phase equilibrium calculation software THERMOCALC, and they incorporate end-members from its internally consistent dataset for greater rigour of calibration. The mafic melt model was the focus of model development. It takes a simple regular solution formulation, in common with many of the solid solution models used in THERMOCALC. However a number of modifications had to be made in order to attain a suitably flexible model melt, since natural mafic liquids cover a very much larger compositional range than any solid solution, and have many more degrees of structural freedom. Faced with these intrinsic problems in melt modelling, the approach taken has been to calibrate the model first in small systems of one, two and three components, combining these to make larger systems. Such an approach leads to a more comprehensive model calibration, exploiting the information available in very simple systems about liquid behaviour. In the CMAS system, model fit is excellent in the pressure range 15-50 kbar. During the fitting process, a case was made for applying a pressure adjustment of -15% to one group of calibration experiments. If this is appropriate, model calculations reproduce the melting reactions well within the experimental error of ±10°C, otherwise, the reactions are calculated at temperatures up to 50°C too high. Calculated phase relations at lower pressure require further attention. Liquid and solid solution compositions are difficult to determine experimentally and probably have large unquantified errors; calculated values typically match those of the calibration experiments to within 20%. The models are able to mimic subtle features of experimental melting relations in CMAS, mostly arising from the interaction of clinopyroxene solid solution with liquid. A preliminary extension of the models was made into the system Na<sub>2</sub>O-CaO-FeO-MgO-Al<sub>2</sub>O<sub>3</sub>-Fe<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub>-Cr<sub>2</sub>O<sub>3</sub> (NCFMASCrO), producing a reasonable fit to experimentally determined oxide trends. A set of sample calculations produced with the CMAS models is presented, demonstrating the modelling of fractional and batch melting and crystallisation. Further calculations take the form of pseudosections: maps of the phase assemblages in <i>P-T </i>space drawn for a single bulk composition, and contoured for phase composition. Pseudosections are powerful means of investigating thermodynamic equilibrium in a rock, since they incorporate the natural constraint of bulk composition – however they cannot produce meaningful calculations without sophisticated and reliable thermodynamic phase models. The propagation of uncertainties in fitted model parameters into pseudosection calculations is explored for the first time using Monte Carlo techniques.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:599659 |
| Date | January 2011 |
| Creators | Green, E. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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