## 4 Results and Discussion
### Component Partitioning  
The Nernst distribution coefficient [44], also called the partition coefficient, in this case represents the affinity of each of the oxide components for the two liquid phases, either a component preferably partitions into Fe-rich or Si-rich liquid. Nernst distribution coefficients are the simplest conventional form of quantitative presentation of element  
Figure 4: Temperature dependence of (**a**) phase fraction of L\({}_{\text{Si}}\)-dispersed amoeboids and composition of (**b**) Fe-rich and (**c**) Si-rich liquids. Dashed curves correspond to analytical measurements from TEM and colors correspond to different components (FeO-red, SiO\({}_{2}\)-green, Al\({}_{2}\)O\({}_{3}\)-blue, CaO-orange, MgO-purple).  
partitioning between phases. In this work, we calculate ratios of the oxide wt% in the LFe phase to that in the LSi phase for the two amoeboid morphologies, so that any values calculated greater than unity would indicate the component partitions into the iron-rich liquid, and values less than one mean that the component prefers the Si-rich liquid. Nernst coefficients (Figure 5) are another representation of the computed compositions of each phase plotted in Figures 3 and 4. The CALPHAD computed coefficients are calculated as a function of temperature, whereas the coefficients calculated from analytically measured data using TEM (dashed lines) are independent of temperature.  
The computed Nernst coefficients for MgO, FeO, and CaO are most sensitive to temperature, offering a constraint for partitioning. For instance, in LFe-dispersed amoeboids, the coefficient computed for FeO broadly approaches agreement with coefficients derived from analytical measurements at \(\sim\)1400 \({}^{\circ}\)C, and MgO is in agreement with analytical measurements around 1500 \({}^{\circ}\)C. The CALPHAD method, which predicted the partitioning of CaO into LFe liquid, disagrees with observed microstructures, where CaO clearly partitions in the silicate-rich liquid phase (true for both LFe-dispersed and LSi-dispersed morphologies). In LFe-dispersed amoeboids, the distribution coefficient is underestimated compared to analytical measurements. Specifically, the dispersed phase (FeO-rich liquid) was calculated to be rather iron-deficient compared to the compositions observed in TEM. Al2O3 content in both liquids are calculated to be near equal, with a slight preference for Si-rich liquid at elevated temperatures in LFe-dispersed amoeboids. Coefficients from analytical measurements clearly indicate a preference of Al2O3 for the Si-rich matrix phase, as their values are greater than unity.  
Distribution coefficients for LSi-dispersed amoeboid compositions show sensitivity to temperature for FeO and MgO, while CaO distribution appears to be less temperature dependent. All three components partition into the iron-rich liquid; however, coefficients derived from analytical measurements of CaO indicate a preference for the Si-rich liquid, contrary to conditions computed under equilibrium. While most of the component partitioning is in qualitative agreement with measurements of chemical analysis, discrepancies still exist. Inconsistent agreement of CALPHAD-computed Nernst coefficients with those that were derived from analytical measurements suggests that either amoeboids reflect non-equilibrium behavior or, if they represent equilibrium behavior, incorporation of alkali behavior (Na and K oxides) is needed to better describe equilibrium formation conditions. Alternatively, amoeboids could form as a result of emulsification of compositionally distinct  
Figure 5: Predicted Nernst distribution coefficients between two liquids vs. those derived by analytical measurements for (**a**) LFe-dispersed and (**b**) LSi-dispersed. Dashed curves correspond to analytical measurements and colors correspond to different components (FeO-red, SiO2-green, Al2O3-blue, CaO-orange, MgO-purple).  
liquids rather than decomposition from a single miscible liquid, but this process was not evaluated for this study.