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472216 First-Principles Phase Diagrams: Iron at Earth’s Inner Core Conditions with Full Inclusion of Anharmonic and Finite-Size Effects

*Ab initio*simulation methods (e.g. DFT), provide reliable and rigorous tools that can help predicting iron crystal structure at such conditions. Unfortunately, free energy calculations based on DFT are computationally expensive — especially with the large number of Fe electrons (around 16 electrons) that contribute significantly at such high pressure. Therefore, a wide range of levels of theories have been used to approximate the free energy; e.g., static energy [2], quasiharmonic approximation [3], and self-consistent phonon calculations [4].

In this work [5], we utilize a novel machinery developed by our group (called “harmonically-mapped averaging (HMA)” method [6,7]) to tackle this long standing problem using DFT method as implemented in VASP. The speed up gained by using HMA method to measure thermodynamic properties is at least an order of magnitude faster than “direct” methods. This enabled measuring of the full (harmonic and anharmonic) Gibbs free energy of Iron at several states. In addition, the finite-size effects in free energy were estimated based on a harmonic-based technique described here [8]. Applying these techniques to the three known iron candidate structures (hcp, fcc, and bcc), we were able, to the first time, to build a completely *ab initio*-based phase diagram of iron at Earth’s IC conditions in the thermodynamic limit.

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[2] P. Soderlind, J. Moriarty, and J. Wills, *Phys. Rev. B* **53**, 14063 (1996).

[3] L. Stixrude, *Phys. Rev. Lett.* **108**, 055505 (2012).

[4] W. Luo, B. Johansson, O. Eriksson, S. Arapan, P. Souvatzis, M. I. Katsnelson, and R. Ahuja, *Proc. Natl. Acad. Sci.* **107**,9962 (2010).

[5] S. G. Moustafa, A. J. Schultz, E. Zurek, and D. A. Kofke, *In preparation*, (2016).

[6] S. G. Moustafa, A. J. Schultz, D. A. Kofke, *Phys. Rev. E* 2015, **92**, 043303.

[7] A. J. Schultz, S. G. Moustafa, L. Weisong, S. J. Weinstein, and D. A. Kofke, *J. Chem. Theory Comput.*, 2016, **12** (4), pp 1491-1498.

[8] T. B. Tan, A. J. Schultz, and D. A. Kofke, *J. Chem. Phys.* **133**, 134104 (2010).

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