Properties of the Earth's deep interior studied using ab initio modelling techniques.

My work relates to the application of ab initio (meaning first-principles quantum mechanical) electronic structure techniques to the thermodynamic and elastic properties of the Earth's inner core. This begins with the application of finite-temperature density functional theory [1] in conjunction with a variety of statistical mechanical techniques to obtain the Helmholtz free energy of a material under any chosen conditions. Knowledge of this quantity allows us to derive all equilibrium thermodynamic and elastic properties.

The work of Gillan, Alfè and co-workers on the properties of the Earth's core is extensively described on their webpages. For a review, see [2]. This work includes a study of the high-p, high-T thermodynamic properties of both solid [3] and liquid Fe [43], the calculation of the high-pressure melting curve [5] and a study of the role of light element impurities in the core [6].

My initial work comprised a study of the effect of a simplifying approximation, known as the particle-in-cell model, on such calculations. This is a statistical mechanical approximation, equivalent to an anharmonic Einstein model of the lattice. I have reported on this work at the 2002 CMMP/CMD joint conference in Brighton of the Institue of Physics and the European Physical Society, and more recently at the 2003 EGS/AGU/EUG joint assembly in Nice. The work has been submitted for publication in Physics of the Earth and Planetary Interiors. A preprint is available below.

Our examination of the PIC model has demonstrated that it cannot be relied upon to give an accurate, quantitative description of the thermodynamics of materials, especially in highly anharmonic regimes. The only elastic constants obtained to date for high-p, high-T Fe, have utilised the PIC model, [7], and show markedly different behaviour in the temperature dependence of the hexagonal c/a ratio. It is therefore now necessary to calculate fully anharmonic, high-T elastic constants using ab initio molecular dynamics. We will also calculate harmonic elastic constants using lattice dynamics. A comparison of these methods will allow an appraisal of harmonic techniques, potentially opening up a much greated region of p-T space to investigation. I am collaborating closely in this work with Lidunka Vočadlo of UCL's Department of Earth Sciences.

[1] Mermin, Phys. Rev., 137: A 1441 (1965); Kohn and Sham, Phys. Rev., 140: A 1133 (1965); Jones and Gunnarsson, Rev. Mod. Phys., 61: 689 (1989)
[2] Alfè, Gillan and Price, Mineral. Mag. 67: 113 (2003)
[3] Alfè, Price and Gillan, Phys. Rev. B, 64: 045123 (2001)
[4] Alfè, Kresse and Gillan, Phys. Rev. B, 61: 132 (2000)
[5] Alfè, Gillan and Price, Nature, 401: 462 (1999)
[6] Alfè, Gillan and Price, Nature, 405: 172 (2000)
[7] Steinle-Neumann et al., Nature, 413: 57 (2001)

Papers and preprints

The particle-in-cell model for ab initio thermodynamics: implications for the elastic anisotropy of the Earth's inner core.
C. M. S. Gannarelli, D. Alfè and M. J. Gillan
Physics of the Earth and Planetary Interiors, 139: 243 (2003)
Available as pdf

The axial ratio of hcp iron at the conditions of the Earth's inner core.
C. M. S. Gannarelli, D. Alfè and M. J. Gillan
Physics of the Earth and Planetary Interiors, 152: 67 (2005)
Available as pdf

Conference talks

Invited talks

ECM22 2004, Budapest
Axial ratio and elastic constants of hcp Fe under Earth's core conditions
C. M. S. Gannarelli, D. Alfè and M. J. Gillan
Abstract Acta Cryst. (2004). A60, s48

Contributed talks

CMD19CMMP 2002, EPS/IOP Conference, Brighton
Ab initio thermodynamics of iron at Earth's core conditions by the 'particle-in-cell' approximation
C. M. S. Gannarelli, D. Alfè and M. J. Gillan
Abstract Europhysics Conference Abstracts 26A: C24.7.3 (2002)

EGS/AGU/EUG Joint Assembly 2003, Nice
Elastic anisotropy in the Earth's inner core - an appraisal of ab initio calculations
C. M. S. Gannarelli, D. Alfè and M. J. Gillan
Abstract Geophysical Research Abstracts, 5: 02632 (2003)

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