next up previous
Next: Heat Flow at Up: Mineral physics of iron Previous: Specific Heatand

Thermal Expansivity, , for the Core

Braginsky and Roberts [1995] calculated from their results on and using , obtaining and . Their results for , , , and form a thermodynamically self-consistent set.

The value of can also be estimated by new theories and experiments independent of the Braginsky and Roberts approach that have arisen in the last four years. The value of at 300 K for fcc solid iron has been measured up to 40 GPa by Boehler et al. [1990], whose data fall on a straight line in versus space. This correlation shows that the law [ Anderson, 1967] holds over the pressure range measured, and that . For a high compression such as found in the core, the above equation needs to be modified, since is a function of (but not ) [ Anderson et al., 1992; Chopelas and Boehler, 1992]. This dependence requires a parameter, , that is independent of T but varies linearly with volume [ Anderson and Isaak, 1993]. The Anderson-Isaak equation for at high compression is

where . Anderson et al. [1992] found that the isotherms of this equation converge at high T, so there is no temperature effect on at high compression.

Assuming that for liquid iron is the same as found for fcc solid iron, taking , which seems to be universally true for silicates, and using for liquid iron at ambient conditions [ Wood, 1993], I find . This is close to at the ICB used by Braginsky and Roberts . From the discussion above, I find , which is somewhat close to the value of used by Braginsky and Roberts [1995], . For comparison, Ahrens and Duffy [1993] reported that from shock wave measurements for solid hcp Fe, and will be a little less for . Stacey [1994] estimated that at mid core is , which agrees well with the Braginsky and Roberts values. Jeanloz and Wenk [1988] estimated for the inner core.



next up previous
Next: Heat Flow at Up: Mineral physics of iron Previous: Specific Heatand



U.S. National Report to IUGG, 1991-1994
Rev. Geophys. Vol. 33 Suppl., © 1995 American Geophysical Union