Computational Simulation Of Thermodynamic Properties Of Mineral Solid Solutions

Solid solutions are common in natural mineral systems,and their thermodynamic properties,such as their enthalpy and free energy of mixing,are the most fundamental parameters that are required to understand and predict the behavior of solid solutions in geochemical and petrological study.Such processes include composition-temperature phase relations,geothermometer-geobarometer,exsolution and decomposition,partition of elements,order/disorder transition,metallogenic elements impurity,and sequestration of pollution elements in mineral lattice.Traditional techniques for investigating thermodynamic properties of solid solution rely on chemical composition analysis and calorimetry.The errors associated with the experimental data and inevitable dynamic effects in experiment may lead to deviations in isotherms of thermodynamic properties and phase diagram from real systems.The high costs and experimental challenges often encountered in experiments limit the availability of data.The fast development of molecular simulation techniques has led to improved theoretical approaches in the past decades.There are many studies of thermodynamics of solid solutions by employing Monte Carlo simulation and configurational statistics methods.The thermodynamic properties of calcite-smithsonite and rutile-cassiterite solid solutions were firstly investigated by aforementioned methods.Then a modified Bragg-Williams model was developed and applied to calcite-magnesite and diopside-jadeite systems.By combining these case studies with comprehensive analysis,the main conclusions are listed as follows.1.This study shows the cluster phenomenon of Zn2+ in the same cation layer of calcite lattice.By using atomistic simulation and configurational statistics techniques,the thermodynamics of mixing for calcite-smithsonite solid solution have been investigated.The incorporated Zn2+ tends to occur at the sites neighboring to another substituted Zn2+ within the(0001)layer,but the substituted layers are preferentially segregated by calcite layers,and vice versa.The supercells with composition of about Ca0.5Zn0.5CO3 prominently exhibit negative enthalpies and free energies of mixing in various temperatures of reality(e.g.<1000 K),which shows a stable phase with dolomite structure.In the derived phase relation of this solid solution system,the potential incorporation content of Zn into calcite is only 0-1.6 wt%in most geochemistry equilibrium processes,and vice versa.2.The exsolution law of rutile-cassiterite solid solution with different compositions was revealed.The shape of the exsolution phase is from ball,cylinder to slab as the increase of impurity concentration.The thermodynamic of mixing properties of rutile-cassiterite solid solution were explored with Monte Carlo simulations and configurational statistics method based on cluster expansion method.This study shows that the vibrational correction will significantly affect the values of free energy of mixing and subsequently change the shape of phase diagram.The phase relation derived from Monte Carlo simulations agrees well with the available experimental data,under the condition that the free energy is corrected for the effect of the excess vibrational entropy.The direct configurational statistics calculation of the partition function can provide reasonable phase relation only when the configurational entropy is corrected to be consistent with the ideal mixing in the high-temperature limit besides the vibrational correction.It is suggested that a very big supercell combining with Monte Carlo simulation is a much better approach.A quite big miscibility gap was confirmed for rutile-cassiterite solid solution,where the phase separation happens.Based on the thermodynamic properties of rutile-cassiterite solid solution,two new geothermometers are suggested.3.A new model was developed and applied to the studies of order-disorder transition of dolomite and omphacite composition.A modified Bragg-Williams model was developed for the calculation of thermodynamic properties of binary solid solutions.A fictive ternary model was confirmed to be equal with the Bragg-Williams model with a short-range order correction.The Margules parameter can be derived via fitting the excess energies of a series of single-defect structures and/or quasi-random structures to subreguler model.By using an ingenious analysis procedure considering order parameter,temperature and chemical composition,mixing thermodynamic properties of a binary solid solution can be further calculated.The new model was applied to calcite-magnesite and diopside-jadeite solid solutions to verify the practicability.This model can be used to investigate thermodynamic properties of binary solid solution and predict order-disorder transition temperature of the intermediate composition correctly.Only limited number of configurations are required in this strategy,but the calculated thermodynamic properties are comparable to other studies based on large amount of configurations or numerous Monte Carlo simulations.This research disclose phase transition temperatures of dolomite composition and omphacite composition at 1448 ± 25 K and 1148 ± 25 K,respectively.Due to the limited number of the sampled configurations and its mathematical simplicity,the new model could play an important role in extending the thermodynamic database of solid solutions,which is required for a variety of petrological and geochemical calculations.In conclusion,this study applied several simulation models to the study of thermodynamic properties of common mineral solid solutions.It implies the advantage and wide applications of the computational simulation on this research area.More important,the new developed model make the establishment of database of mineral solid solutions related to diagenesis and metallogenesis possible,which will promote the development of petrological and geochemical calculations.