@article{Kadatskiy:JPCS:2016, author = {M A Kadatskiy and K V Khishchenko}, journal = {J. Phys.: Conf. Ser.}, month = {nov}, pages = {012005}, publisher = {{IOP} Publishing}, title = {Shock compressibility of iron calculated in the framework of quantum-statistical models with different ionic parts}, volume = {774}, year = {2016}, abstract = {Quantum-statistical calculations of shock compressibility of iron are performed. Electronic part of thermodynamic functions is calculated in the framework of three quantum-statistical approaches: the Thomas-Fermi, the Thomas-Fermi with quantum and exchange corrections and the Hartree-Fock-Slater models. The influence of ionic part of thermodynamic functions is taken into account separately with using three models: the ideal gas, the one-component plasma and the charged hard spheres models. The results of calculations are presented in the pressure range from 1 to 107 GPa for samples with initially densities 7.85, 4.31 and 2.27 g/cm3. Calculated Hugoniots are compared with available experimental data.}, doiurl = {10.1088/1742-6596/774/1/012005}, } @article{Zhang:PRB:2010, author = {Zhang, HL and Lu, Song and Punkkinen, Marko Patrick John and Hu, Q-M and Johansson, B{\"o}rje and Vitos, Levente}, journal = {Phys. Rev. B}, number = {13}, pages = {132409}, publisher = {APS}, title = {Static equation of state of bcc iron}, volume = {82}, year = {2010}, } @article{Basinski:1955, author = {Basinski, Z S and Hume-Rothery, W and Sutton, A L}, journal = {Proc. R. Soc. A}, pages = {459--67}, volume = {229}, year = {1955}, } @article{Redmer:2019, author = {Korell, J A and French, A and Steinle-Neumann, G and Redmer, R}, journal = {Phys. Rev. Lett.}, pages = {086601}, volume = {122}, year = {2019}, } @article{Vocadlo:PEPI:2003, author = {L Vo{\v c}adlo and D Alf{\`e} and M.J Gillan and G.David Price}, journal = {Phys. Earth Planet. Inter.}, note = {Geophysical and Geochemical Evolution of the Deep Earth}, number = {1}, pages = {101--125}, title = {The properties of iron under core conditions from first principles calculations}, volume = {140}, year = {2003}, abstract = {The Earth's core is largely composed of iron (Fe). The phase relations and physical properties of both solid and liquid Fe are therefore of great geophysical importance. As a result, over the past 50 years the properties of Fe have been extensively studied experimentally. However, achieving the extreme pressures (up to 360GPa) and temperatures (∼6000K) found in the core provide a major experimental challenge, and it is not surprising that there are still considerable discrepancies in the results obtained by using different experimental techniques. In the past 15 years quantum mechanical techniques have been applied to predict the properties of Fe. Here we review the progress that has been made in the use of first principles methods in the study of Fe, and focus upon (i) the structure of Fe under core conditions, (ii) the high P melting behaviour of Fe, (iii) the thermodynamic properties of hexagonal close-packed (hcp) Fe, and (iv) the rheological and thermodynamic properties of high P liquid Fe.}, doiurl = {https://doi.org/10.1016/j.pepi.2003.08.001}, issn = {0031-9201}, url = {https://www.sciencedirect.com/science/article/pii/ S0031920103001675}, } @article{Vocadlo:N:2003, author = {Vo{\v c}adlo, Lidunka and Alf{\`e}, Dario and Gillan, M. J. and Wood, I. G. and Brodholt, J. P. and Price, G. David}, journal = {Nature}, number = {6948}, pages = {536--539}, title = {Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core}, volume = {424}, year = {2003}, abstract = {The nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments1 suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations2,3,4 have indicated the possible presence of complex, inner-core layering. Theoretical studies5,6 currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core2,3,4.}, doiurl = {10.1038/nature01829}, isbn = {1476-4687}, url = {https://doi.org/10.1038/nature01829}, } @article{Belonoshko:PR:2009, author = {Belonoshko, Anatoly B. and Rosengren, Anders and Burakovsky, Leonid and Preston, Dean L. and Johansson, B\"orje}, journal = {Phys. Rev. B}, month = {Jun}, number = {22}, pages = {220102}, publisher = {American Physical Society}, title = {Melting of Fe and ${\text{Fe}}_{0.9375}{\text{Si}}_{0.0625}$ at Earth's core pressures studied using ab initio molecular dynamics}, volume = {79}, year = {2009}, doiurl = {10.1103/PhysRevB.79.220102}, url = {https://link.aps.org/doi/10.1103/PhysRevB.79.220102}, } @article{Belonoshko:JPCM:2011, author = {Belonoshko, A B and Arapan, S and Rosengren, A}, journal = {J. Phys.: Condens. Matter}, month = {nov}, number = {48}, pages = {485402}, publisher = {IOP Publishing}, title = {An ab initio molecular dynamics study of iron phases at high pressure and temperature}, volume = {23}, year = {2011}, abstract = {The crystal structure of iron, the major component of the Earth's inner core (IC), is unknown for the IC high pressure (P; 3.3--3.6 Mbar) and temperature (T; 5000--7000 K). There is mounting evidence that the hexagonal close-packed (hcp) phase of iron, stable at the high P of the IC and a low T, might be unstable under the IC conditions due to the impact of high T and impurities. Experiments at the IC P and T are difficult and do not provide a conclusive answer as regards the iron stability at the pressure of the IC and temperatures close to the iron melting curve. Recent theory provides contradictory results regarding the nature of the stable Fe phase. We investigated the possibility of body-centered cubic (bcc) phase stabilization at the P and T in the vicinity of the Fe melting curve by using ab initio molecular dynamics. Thermodynamic calculations, relying on the model of uncorrelated harmonic oscillators, provide nearly identical free energies within the error bars of our calculations. However, direct simulation of iron crystallization demonstrates that liquid iron freezes in the bcc structure at the P of the IC and T = 6000 K. All attempts to grow the hcp phase from the liquid failed. The mechanism of bcc stabilization is explained. This resolves most of the earlier confusion.}, doiurl = {10.1088/0953-8984/23/48/485402}, url = {https://dx.doi.org/10.1088/0953-8984/23/48/485402}, } @article{Barth:1972, author = {U {von Barth} and Hedin, L}, journal = {J. Phys. C: Solid State Phys.}, pages = {1629--42}, volume = {5}, year = {1972}, } @article{Abrikosov:2016, author = {Abrikosov, I A and Ponomareva, A V and Steneteg, P and Barannikova, S A and Alling, B}, journal = {Curr. Opin. Solid State Mater. Sci.}, pages = {85--106}, volume = {20}, year = {2016}, } @article{Kresse:1993, author = {Kresse, G and Hafner, J}, journal = {Phys. Rev. B}, pages = {558--61}, volume = {47}, year = {1993}, } @article{Kresse:1994, author = {Kresse, G and Hafner, J}, journal = {Phys. Rev. B}, pages = {14251--69}, volume = {49}, year = {1993}, } @article{Kresse:1996, author = {Kresse, G and Furthm{\"u}ller, J}, journal = {Phys. Rev. B}, pages = {11169--86}, volume = {54}, year = {1996}, } @article{Kresse:1996-1, author = {Kresse, G and Furthm{\"u}ller, J}, journal = {Comput. Mater. Sci.}, pages = {15--50}, volume = {6}, year = {1996}, } @article{Blochl:1994, author = {Bl{\"o}chl, P E}, journal = {Phys. Rev. B}, pages = {17953--79}, volume = {50}, year = {1994}, } @article{Mermin:1965, author = {Mermin., N D}, journal = {Phys. Rev.}, pages = {A1441--3}, volume = {137}, year = {1965}, } @article{PBE:1996, author = {Perdew, J P and Burke, K and Ernzerhof, M}, journal = {Phys. Rev. Lett.}, pages = {3865}, volume = {77}, year = {1996}, } @article{PBE:1997, author = {Perdew, J P and Burke, K and Ernzerhof, M}, journal = {Phys. Rev. Lett.}, pages = {1396}, volume = {78}, year = {1997}, } @article{Baldereschi:1973, author = {Baldereschi, A}, journal = {Phys. Rev. B}, pages = {5212---5}, volume = {7}, year = {1997}, } @article{Monkhorst:1976, author = {Monkhorst, H J and Pack, J D}, journal = {Phys. Rev. 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B}, month = {Jul}, number = {1}, pages = {014402}, publisher = {American Physical Society}, title = {Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach}, volume = {102}, year = {2020}, doiurl = {10.1103/PhysRevB.102.014402}, url = {https://link.aps.org/doi/10.1103/PhysRevB.102.014402}, } @article{Molibdenum, author = {Minakov, D V and Paramonov, M A and Levashov, P R}, journal = {AIP Adv.}, pages = {125012}, volume = {8}, year = {2018}, } @book{touloukian1975thermal, author = {Touloukian, Y.S.}, publisher = {Springer US}, series = {TPRC data series}, title = {Thermal Expansion: Metallic Elements and Alloys}, year = {1975}, } @article{Kozlovskii:2019, author = {Kozlovskii, {\relax Yu} M and Stankus, S V}, journal = {J. Phys.: Conf. Ser.}, pages = {012181}, volume = {1382}, year = {2019}, }