MATHS: Macroscopic, Atomistic, and THermodynamic models of mineralS and meltS

Anticipated Event Location *

Thessaloniki, Greece

Anticipated Event Date/Timing *

9-13 September 2024

Aims and Scope *Please explain the relevance, timeliness and novelty of this event.

We propose to organize a school in September 2024 on the thermodynamic modeling of natural silicate liquids and their equilibria with minerals and fluids, combining two complementary intellectual approaches: macroscopic and atomistic. Few young scientists today are trained in both approaches, and the intent of this course is to bring them together to highlight the strengths and weaknesses of each, the rapid advances being made in both areas, and the ways that convergence of the two approaches can lead to robust predictive understanding of natural phenomena.

The macroscopic part of the school will introduce the fundamental thermodynamics of multicomponent phase equilibria and the ideas behind the design of solution models before outlining the specific details of the MELTS family of models and the associated software packages (Ghiorso and Sack, 1995; Asimow and Ghiorso, 1998; Smith and Asimow, 2005; Gualda and Ghiorso, 2015). The current incarnations of this approach — pMELTS (Ghiorso et al., 2002), rhyoliteMELTS (Gualda et al., 2012), and the H2O-CO2-bearing extension of rhyoliteMELTS (Ghiorso and Gualda, 2015) — enable calculation from subsolidus to superliquidus conditions from ambient pressure up to about 3 GPa in systems from ultramafic to highly felsic with mixed volatiles and a wide range of oxidation states. The lecture will be followed by practical exercises demonstrating and teaching the use of the software, including new capabilities to fully and seamlessly integrate MELTS calculations into MATLAB, Python, and other programming environments, enabling for the first time a range of large-scale calculations and code integration.

The atomistic part of the school will center on the application of first-principles (FP) molecular dynamics (MD) to understand static, dynamic, thermodynamic, and transport properties of multicomponent silicate liquids. In MD the atoms move according to Newtonian dynamics under the action of interatomic forces. In FPMD the ionic forces are computed directly from the electronic structure of the system, which is obtained by solving an approximate form of the Schrödinger equation. We will present different ensembles, statistical analysis of the MD runs, and applications in geophysics. Again, the lecture series will be followed by practical FP and MD tutorials. We introduce the participants to UMD package (Caracas et al., 2021), which is a specialized tool designed for intricate and comprehensive examination of atomistic simulations of fluids. We will exemplify this by obtaining a series of structural, transport and thermodynamic properties of various dry, wet, and carbonated silicate melts.

We will complement the theoretical part with lectures on experimental apparatus and in situ measurements. Finally, we will bring the two approaches together with a final practical exercise in which the heat capacity and the entropy of mixing is evaluated both by application of the MELTS model and from a set of FPMD calculations.

The novelty of the proposed event, which builds upon a very successful recent series of NSF-funded MELTS workshops in the USA and previous workshops sponsored by CECAM, EGU, and ERC in Europe, is to combine and showcase complementary progress in both empirical and ab initio thermodynamic modeling. The two approaches have only recently begun to capture the complex behavior of multicomponent fluid solutions relevant to magmatic phenomena at realistic and experimentally challenging physicochemical conditions of the deep Earth. Consequently, in the last decade, a large part of the geoscientific community focused on their critical role in the evolution of terrestrial planets, from the early age of the solar system, dominated by Giant Impacts and large-scale magma oceans, all the way to the current evolved state of solidified terrestrial planets.

Using MELTS code, the participants will be able to do the following:
1. To model magmatic evolution scenarios as a series of steps in temperature and pressure (Gibbs energy minimization), temperature and volume (Helmholtz energy minimization), enthalpy and pressure (entropy maximization) or entropy and pressure (enthalpy minimization),
2. To apply these scenarios to exploring open- and closed-system magmatic processes such as energy constrained assimilation, adiabatic decompression melting, or post-entrapment crystallization in phenocryst-hosted melt inclusions,
3. To compute equilibrium states in systems constrained to follow oxygen fugacity buffers,
4. To simulate forward, down-temperature, fractional crystallization and to learn what is possible in terms of inverse (up-temperature) fractionation modeling,
5. To compute complete models of the melting regime underlying a mid-ocean ridge,
6. To access all these calculations from within MATLAB or Python in order to enable seamless coupling to geodynamic codes or large-scale modeling efforts.
All workshop participants will leave with the necessary software installed and configured on their own computers and with membership in the users forum for ongoing communication among users and developers of the software.

Using the UMD package the participants will be able to do the following:
1. To extract all relevant results from simulations of ab initio molecular dynamics, and construct UMD (=”Universal Molecular Dynamics”) files,
2. To apply the individual components of the UMD package to analyze these results,
3. To calculate the pair distribution functions, determine the bond length, the size of the coordination sphere, the average coordination numbers,
4. To build the connectivity matrix and from there to obtain the chemical speciation, including the population analysis, the polymerization of the melt, and the lifetimes of the different chemical species,
5. To determine the mean-square displacements, and from there to extract the diffusion coefficients,
6. To compute the self-correlation of the atomic velocities from which to obtain the vibrational spectrum of the fluid and the diffusion coefficients, 
7. To calculate the self-correlation of the stress tensor from which to estimate the viscosity of the fluid.

The invited experimental lectures will illustrate modern methods for determining liquid properties at elevated temperature and pressure in the lab, including
1. In situ measurements in static presses: piston-cylinder apparatus, multi-anvil presses, diamond anvil cells; applications of synchrotron radiation.
2. Shock wave methods for equations of state and phase transition determination.
3. Criteria for attainment of equilibrium in phase relations and uncertainty assessment in transport property measurements.

Caracas, R., Kobsch, A., Solomatova, N. V., Li, Z., Soubiran F. & Hernandez, J.-A., UMD – an open-source python-based package to analyze ab initio molecular dynamics simulations,

Ghiorso, M. S., & Gualda, G. A. (2015). An H2O–CO2 mixed fluid saturation model compatible with rhyolite-MELTS. Contributions to Mineralogy and Petrology, 169(6), 1-30.

Gualda, G. A., & Ghiorso, M. S. (2015). MELTS_Excel: A Microsoft Excel‐based MELTS interface for research and teaching of magma properties and evolution. Geochemistry, Geophysics, Geosystems, 16(1), 315-324. 

Gualda, G. A., Ghiorso, M. S., Lemons, R. V., & Carley, T. L. (2012). Rhyolite-MELTS: a modified calibration of MELTS optimized for silica-rich, fluid-bearing magmatic systems. Journal of Petrology, 53(5), 875-890.

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