Melting properties by X-ray absorption spectroscopy: common signatures in binary Fe–C, Fe–O, Fe–S and Fe–Si systems

X-ray absorption spectroscopy (XAS) is a widely used technique to probe the local environment around specific atomic species. Applied to samples under extreme pressure and temperature conditions, XAS is sensitive to phase transitions, including melting, and allows gathering insights on compositional variations and electronic changes occurring during such transitions. These characteristics can be exploited for studies of prime interest in geophysics and fundamental high-pressure physics. Here, we investigated the melting curve and the eutectic composition of four geophysically relevant iron binary systems: Fe–C, Fe–O, Fe–S and Fe–Si. Our results show that all these systems present the same spectroscopic signatures upon melting, common to those observed for other pure late 3d transition metals. The presented melting criterion seems to be general for late 3d metals bearing systems. Additionally, we demonstrate the suitability of XAS to extract melt compositional information in situ, such as the evolution of the concentration of light elements with increasing temperature. Diagnostics presented in this work can be applied to studies over an even larger pressure range exploiting the upgraded synchrotron machines, and directly transferred to time-resolved extreme condition studies using dynamic compression (ns) or fast laser heating (ms).

1 Light element content determination with LCA X-ray absorption near edge spectroscopy (XANES) allows to perform an in situ determination of the light element content. In case of co-existence between two phases the linear combination analysis (LCA) allows to evaluate the proportion between the end-members by performing a fit of the data to a linear combination of the normalized end-members XANES reference spectra. As widely discussed in the main text, this analysis was performed for Fe-C and Fe-O systems, producing excellent results. However, critical aspects of this technique applied two our data raised during the analysis, and the assumptions made deserve to be presented and discussed.

-Light elements in solution
In case of a mix of phases, LCA is sensitive to the ratio between constituent phases. With the reference XANES spectra of Fe and FeO it is possible to determine the relative weight of the two phases in an Fe-O system. Assuming that all the oxygen is contained in the FeO phase and knowing that in FeO the oxygen content is 22 wt%, the total oxygen content in Fe-O is proportional to the FeO weight. This assumption, though, is not valid in Fe-C systems, where it is known[1] that the Fe 3 C phase is not the only reservoir of carbon. Up to 2 wt% at ambient pressure of carbon can be trapped in solid iron without forming the Fe 3 C phase. Thus, the total carbon content has to be calculated as the sum of the one contained in the Fe 3 C phase and the one in solution in the iron phase.
The weight of carbon in solution in solid iron has been evaluated in several works at different pressures, as reported in Mashino et al. [1]. In first approximation, an exponential fit of the data well describes the trend of the carbon content as a function of pressure, as shown in Figure 1. The carbon weight found in Fe-C systems with LCA analysis, as reported in Figure 2, was thus added for the different pressures to the carbon weight resulting from the fit.

-Temperature effects
In some cases, after melting the light element content keeps slightly varying. Being unable to determine unquestionably which of those compositions is the eutectic, we averaged all of them defining as the error bar the variance of those points.
Both the quenched spectra and the references slightly vary with pressure. As the effect of pressure is to reduce the volume, XAS oscillations shift to the right. Thus it is important to use reference spectra whose pressure is as close as possible to the one of the spectrum under analysis. In case of doubt, reference spectra at the closest pressures were used and the results are averaged. Again the error bar is defined as the variance of the averaged points.

Results
In Figure 2 are represented in black the raw light element contents as obtained from the LCA analysis. In green are shown the final results, where the carbon in solution in solid iron is taken into account and the fit outputs at the same pressures are averaged. The error bar in the light element content is given by the standard deviation of the fit outputs at the same (or similar) pressure. The x-axis error bar is evaluated as 10% of the pressure value.