Date of Award


Degree Name

Master of Science




Ramon Ravelo

Second Advisor

Jorge A. Muñoz


Numerous computational and experimental studies on the crystal structure of metals nearthe melt line, indicate the body-centered cubic (bcc) structure can be favored over other crystal phases at lower temperatures [1]-[4] and even in cases in which other crystal structures are thermodynamically more stable, bcc may nucleate first from the melt, at rapid cooling rates [5]. Iron (Fe) is a polymorph metal, with a bcc ferromagnetic structure at ambient conditions. Even though the phase diagram of Fe is well known at relatively low pressures, there is currently no consensus on the crystal structure of Fe below the melt line at pressures relevant to Earthâ??s inner core conditions and at the inner core boundary (ICB), regions at which the hexagonal-closed-packed structure has been found to be the most stable phase from static [6] and dynamic experiments [7]. Current disagreements between experimental observations and computational calculations can be attributed to the dynamical stability of other structures prior to melting. In this work, the stability of the bcc structure of Fe at pressures in the range of 140-300 GPa is studied by computing the temperature-dependent phonon dispersions of the non-magnetic bcc phase of Fe since at these high pressures the atomic magnetic moments can safely be taken to be zero [8]. The temperature-dependent phonon frequencies are calculated employing quantum molecular dynamics (QMD) and a recently developed lattice-dynamics approach, called Harmonic Ensemble Lattice Dynamics (HELD) [9] that allows the computation of the temperature-dependent interatomic force constants needed to obtain the phonon dispersions. While non-magnetic bcc Fe is known to be unstable at low temperatures, we show that temperature is key in mechanically stabilizing the bcc structure at high pressures and that regular quasi-harmonic lattice dynamics fail to capture the correct phonon dispersions and tetragonal distortions. The phase diagram obtained by means of these lattice dynamics calculations as well as observed trends in the temperature-dependent phonons frequencies will be presented.

[1] S. Alexander and J. McTague. Should all crystals be bcc? Landau theory of solidification and crystal nucleation. Phys. Rev. Lett., 41:702â??705, 1978.[2] E. R. Hernandez, A. Rodriguez-Prieto, A. Bergara, and D. Alfâ??e. First-principles simulations of lithium melting: Stability of the bcc phase close to melting. Phys. Rev.Lett., 104:185701, 2010. [3] Y. Lu, T. Sun, Ping Zhang, P. Zhang, D.-B. Zhang, and R. M. Wentzcovitch. Premelting hcp to bcc transition in beryllium. Phys. Rev. Lett., 118:145702, 2017. [4] Jia-Wei Xian, Jun Yan, Hai-Feng Liu, Tao Sun, Gong-Mu Zhang, Xing-Yu Gao, and Hai-Feng Song. Effect of anharmonicity on the hcp to bcc transition in beryllium at high-pressure and high-temperature conditions. Phys. Rev. B, 99:064102, 2019. [5] Babak Sadigh, Luis Zepeda-Ruiz, and Jonathan L. Belof. Metastable-solid phase diagrams derived from polymorphic solidification kinetics. Proceedings of the National Academy of Sciences, 118(9):e2017809118, 2021. [6] Shigehiko Tateno, Kei Hirose, Yasuo Ohishi, and Yoshiyuki Tatsumi. The structure of iron in Earthâ??s inner core. Science, 330(6002):359â??361, 2010. [7] S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, and G. Morard. Melting of iron at Earth's inner core boundary based on fast x-ray diffraction. Science, 340(6131):464â??466, 2013. [8] Lars Stixrude, R. E. Cohen, and D. J. Singh. Iron at high pressure: Linearizedaugmented-plane-wave computations in the generalized-gradient approximation. Phys. Rev. B, 50:6442â??6445, Sep 1994. [9] Adrian De la Rocha, Vanessa J. Meraz, Armando Garcia, Bethuel O. Khamala, Yu- Hang Tang, Wibe de Jong, and Jorge A. Munoz. Dynamically stable B2 phase of FeV at high pressure and elevated temperature via harmonic ensemble lattice dynamics. Submitted. Phys. Rev. B.




Recieved from ProQuest

File Size

78 p.

File Format


Rights Holder

Valeria Itzel Arteaga Muniz

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Physics Commons