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Workshops

Dynamical Properties of Earth and Planetary Materials

October 10, 2011 to October 13, 2011
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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Organisers

  • Razvan Caracas (Ecole Normale Supérieure-Lyon, France)
  • Lars Stixrude (University College London, United Kingdom)
  • Bjoern Winkler (Johann Wolfgang Goethe University, Frankfurt, Germany)

Supports

   CECAM

   Psi-k

Description

The exponential development of powerful algorithms, implementations and computational power over the last decade has seen the application of first-principles calculations in solving critical problems of mineral physics expand at an unprecedented pace. Theoretical mineral spectroscopy, high-pressure thermodynamics, construction of phase diagrams, determination of melts and melting curves go hand in hand today with experimental investigations. The thermodynamic and thermochemical conditions that we are able to successfully reproduce in the computer simulations cover the entire range existent in our planet, our solar system or in other distant worlds. 

This workshop aims at advancing exchanges among theorists using different approaches, as well as between theorists and experimentalists, in order to enhance and broaden the use of first principles calculations in geosciences. In particular we focus on the dynamical properties of crystalline lattices covering vibrational spectroscopy, phonons and phonon band dispersion, elasticity, thermodynamics and phase diagrams, melts, melting curves and glasses as well as non-linear effects. 

Many of the physical properties of an atomic crystalline lattice can be successfully characterized and understood from first-principles within the static approximation at zero temperature. However, the crystal lattice is not just a rigid collection of atoms under symmetry constraints. On the contrary it is in a continuous dynamical state, with atoms vibrating around their respective equilibrium positions. The description of many of the thermo-physical properties, like thermodynamics, phase transitions, infra-red or Raman spectra or non-linear effects require the ability to describe the fluctuations of the nuclei positions with respect to their static equilibrium positions occurring during these vibrations, while the description of other properties, like anharmonicity, melting curves, or the dynamical characterization of melts and glasses, require the ability to describe the movements of the atoms over finite but long periods of time. 

Over the last decades advances in software capabilities, in terms of both algorithms and implementations went hand-in-hand with advances in hardware capabilities and transformed the ab initio methods from simple descriptive means to very accurate and predictive tools for studying a wide range of above-mentioned properties of real materials. Combined with adiabatic perturbation theory, they allow a priori the computation of the derivatives of the energy and related thermodynamic potentials up to any order. At the second order, this approach has been applied to compute linear response functions such as lattice dynamics through phonon frequencies and eigendisplacements, dynamical atomic charges or elastic constants tensors with an accuracy of a few percent. At the third order this approach has been applied to determining non-linear optical properties and Raman tensors. Combined with Newtonian mechanics in the form of ab initio molecular dynamics these computational methods have been successfully applied to study anharmonic properties, melts and glasses and to determine melting curves. 

Therefore even more than in other fields in Earth science the importance of first-principles theory is well recognized and the number of theoretical studies and practitioners is exponentially growing. First-principles theory interacts strongly with advances in experimental high-pressure geophysics. The growth of diamond anvil cell and multianvil high-pressure research has lead to a wealth of new information about the behavior of minerals and rocks under the high pressure and temperature conditions of the deep Earth. Despite rapid progress our knowledge of the properties of high-pressure phases does not compare to that of the low-pressure phases that make up the Earth's crust. Predictions of rheological and transport properties are needed for geodynamical modeling. Melting curves of the important phases and melting relations for candidate rock compositions are still difficult experiments and there is often lack of consensus among experimental results. Only by using theory in conjunction with experiment will progress be made in understanding these fundamentals of Earth materials’ behavior.  Within this line of thought during the last several years, we have witnessed an increasing trend of computational studies of the Earth and planetary materials. If the first studies addressed only relatively “simple” issues like crystal structure, static equation of state or static elastic constants tensor, nowadays more and more studies address complex properties, like phase diagrams described in pressure-temperature-composition space, thermoelasticity, melting curves, transport properties, Raman spectra, etc. 

Thus the computational approach offers today complementarity to experimental mineralogy, petrology and geochemistry, and can increasingly play a predictive role in exploring a wide range of geophysical conditions difficult to reach experimentally. Computational mineralogy helped understanding the perovskite to post-perovskite phase transition in Fe- and Al- bearing MgSiO3 and its implications on the structure of the deep Earth, its seismic and geodynamic properties.  Computational mineralogy allowed the prediction of several new high-pressure and high-temperature phase transitions crystal structures of various minerals under extreme thermodynamic conditions. Advances in computational mineralogy made possible the start of the first repository of computed data for minerals, the WURM project, freely available at http://www.wurm.info.

Today computational mineralogy is well advanced to open widely to the more traditional fields of geosciences, like experimental mineralogy, petrology and geochemistry, seismology and geodynamics, to offer the much-needed complementarity a modern approach to science should have. 

It is the aim of this workshop to bring a considerable brick to this construction.

References

S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, ‘Phonons and related crystal properties from density-functional perturbation theory’, Rev. Mod. Phys. 73, 515-562 (2001).

R. M. Wentzcovitch, B. B. Karki, M. Cococcioni, S. de Gironcoli, ‘Thermoelastic Properties of MgSiO3-Perovskite: Insights on the Nature of the Earth’s Lower Mantle‘, Phys. Rev. Lett. 92, 018501-018503 (2004).

R. Caracas, ‘Dynamical instabilities of ice X’, Phys. Rev. Lett. 101, 085502-085505 (2008).

S. Merkel, A. Kubo, L. Miyagi, S. Speziale, T.S. Duffy, H.K. Mao, H.R. Wenk, ‘Plastic deformation of MgGeO3 post-perovskite at lower mantle pressures’, Science 311, 644-646 (2006).

Ph. Carrez, D. Ferré and P. Cordier, ‘Implications for plastic flow in the deep mantle from modelling dislocations in MgSiO3 minerals’, Nature 446, 68-70 (2007).

W. Sturhahn, J.M. Jackson, ‘Geophysical applications of nuclear resonant scattering’, in Ohtani, E., ed., Advances in High-Pressure Mineralogy: GSA Special Paper 421, 157-174, (2007)

S. Speziale, A. Milner, V.L. Lee, S.M. Clark, M.P. Pasternak, R. Jeanloz, ‘Iron spin transition in Earth’s mantle’, Proc. of the National Acad. of Sciences 102, 17918-17922 (2005).

C. McCammon, I. Kantor, O. Narygina, J. Rouquette, U. Ponkratz, I. Sergueev, M. Mezouar, V. Prakapenka, L. Dubrovinsky, ‘Stable intermediate-spin ferrous iron in lower-mantle perovskite’, Nature Geoscience 1, 684 - 687 (2008).

A. Bengtson, K. Persson, D. Morgan, ‘Ab initio study of the composition dependence of the pressure-induced spin crossover in perovskite (Mg1 – x F x )SiO3’, Earth Plan. Sci. Lett. 265, 535-545 (2008).

J. W. Zwanziger, ‘Computation of Mössbauer isomer shifts from first principles’, J. Phys.: Condens. Matter 21, 195501- 195506 (2009).

J. S. Tse, ‘Ab initio molecular dynamics with density functional theory’, Annual Review of Physical Chemistry, 53, 249-290 (2002).

L. Stixrude, B. B. Karki, ‘Structure and freezing of MgSiO3 liquid in the Earth’s lower mantle’, Science 310, 297–299. (2005).