The Effect of Wavelength-Dependent Emissivity on the Melting Temperatures of Iron From Shock Wave Measurements

The high-pressure melting curve of iron at the conditions of the outer core is anchored by the shock wave measurements of Bass et. al. 1987. They used spectral radiometric techniques, looking at shocked iron films or foils through a transparent anvil. They assumed that the emissivity of the iron was independent of wavelength. The wavelength dependence of the emissivity of fcc and bcc iron was measured by Taylor, 1952. Both structures have a change in emissivity of 20% over 200nm in the visible, although the absolute magnitude of the emissivity is different. In the measurement of temperature using spectral radiometry, the absolute value of the emissivity does not effect the temperature measurement. In iron the 3d-bands straddle the Fermi Energy in any close packed structure (Boness and Brown, 1990). The electrons at the Fermi Energy can easily be promoted into the empty states of the conduction band, and thus are the basis of the electronic contribution to the heat capacity. It is these same electrons in the 3d-bands that also control the emissivity. With increasing wavelength, more electrons are promoted into the conduction band, which means the emissivity is higher at shorter wavelengths than at longer wavelengths. We reanalyzed the shock wave data of Bass et. al. using the wavelength dependent emissivity. The corrected melting temperature of iron at 243 GPa is 5900 +/-500 K compared to Bass et. al.'s determination of 6700 +/- 400 K. This is just slightly higher then the estimate (based upon the assumption of the heat capacity being equal to 5R) of Brown and McQueen, 1986 of 5000-5700 K, and in good agreement with theoretical calculations of Alfe, 2010. Alfe, D., 2010, Rev. Min. and Geochem., 71, 337-354. Bass, J. D., B. Svendsen, and T. J. Ahrens, 1987, M. H. Manghnani and Y. Syono, Terra Scientific Publishing Co. / American Geophysical Union, Washington, D. C., 393-402. Boness, D. A., and J. M. Brown, 1990, JGR, 95, 21,721-30. Brown, J. M. and R. G. McQueen, 1986, JGR, 91, 7485-94. Taylor, J. E., 1952, Jour. Optical Soc. America, 42, 33-36.