High temperature properties of transition metals

The elastic constants of iron have been studied experimentally and theoretically at low temperature and high pressure (Mao et al. 1998 Soderlind et al. 1996 Steinle-Neumann et al. 1999 Stixrude and Cohen 1995), but there has not yet been a first principles calculation of the full elastic constant tensor at inner core conditions (see Nye 1985 for a review of elastic constants). Laio et al. (2000) developed a clever hybrid method that combines first principles total energy and force calculations for a limited number of time steps with a semi-empirical potential fit to the first principles results. These authors investigated a number of properties with their ab initio method including 

In order to investigate the full elastic constant tensor of iron at inner core conditions, Steinle-Neumann et al. (2001) combined first principles GGA density functional theory with the particle in a cell method. The crystallographic structure of iron was assumed to be hexagonal close-packed (hep). Experiments show that this is the low temperature high pressure phase of iron from 10 GPa, to at least 300 GPa, the highest pressures so far explored in static experiments (Mao et al. 1990). Experiments also show that hep is the liquidus phase to at least 100 GPa (Shen et al. 1998). There is theoretical evidence that hep is the stable phase of iron at the conditions of the Earth s inner core (Vocadlo et al. 1999). Experimental observations of other structures at high pressures and temperatures (Andrault et al. 1997 Saxena et al. 1995) have been controversial (Boehler 2000) the proposed structures are closely related to hep. 

Because the axial ratio c/a of hep iron is observed experimentally to vary significantly with pressure and temperature, we were careful to determine the minimum energy structure of this phase at all conditions. The results (Fig. 9) show that the axial ratio of hep iron at conditions comparable to those in the inner core (-1.7) is significantly greater than that found at low temperatures in experiment and theory (-1.6) (Jepheoat et al. 1986 Mao et al. 1990 Stixrude et al. 1994). Our results are consistent with experiments at lower pressures (Funamori et al. 1996 Huang et al. 1987), and earlier theoretical work that also found that c/a increases with temperature (Wasserman et al. 1996b). 

As the inner core is nearly isothermal (Stixrude et al. 1997), the comparison of the elastic properties of iron with those of the inner core determined seismologically provides a way to estimate the temperature in the earth s deep interior. This approach is 

It is now possible to explore the high temperature properties of Earth materials from first principles. The combination of efficient first principles methods for computing the total energy, interatomic forces, and stresses, with a variety of statistical mechanical methods including molecular dynamics, Monte Carlo, and approximate treatments such as the cell model promises rapid progress. With continued advances in computational power, and in the development of new theoretical methods, one foresees significant progress in three areas. 

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GIN2] Gingerich, K. A., High-temperature properties of transition metal phosphides and related refractory materials, Pennsylvania State Univ., ReportNYO-2541-1, (1964). Cited on page 201. 

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