Percolation

Percolative Core Formation

Planet differentiation could proceed through efficient liquid-liquid separation or by percolation of liquid metal in a solid silicate matrix, depending on the size and interior temperature of the planetary bodies. The percolation of liquid metal in the solid silicate matrix is likely a dominant process in the initial differentiation when the temperature is not high enough to melt the entire planetary body. The efficiency of percolation depends on the dihedral angle, determined by the interfacial energies of the solid-solid and solid-liquid interfaces. We can simulate this process in the laboratory by conducting high-pressure and high-temperature experiments on mixture samples of iron alloy and silicate. We have developed a new imaging technique to visualize the distribution of liquid metal in the silicate matrix in three dimension (3D) by combination of focus ion beam (FIB) milling and high-resolution field-emission SEM imaging. The new imaging technique provides precise determination of the dihedral angle and quantitative measure of the volume fraction and connectivity of the liquid phase [Fei, 2013].

Figure 1 shows the 3D reconstruction of Fe-FeS melt (yellow) in olivine matrix (transparent) in the recovered sample. The measured dihedral angle for the Fe-FeS melt in the olivine matrix is 123±1˚, larger than the critical angle (60˚) that divides the non-connected and interconnected networks. The calculated melt percentage is about 4.9 volume percent which is below the minimum percolation threshold. The image clearly shows the metallic melt pockets were trapped at the silicate grain corners because of the large dihedral angle. When we zoom in an individual melt pocket, we can quantitatively determine the true dihedral angle (insert) by using 3D graphic tool or finding the analytical solution between the two intersect interfaces.

Fig. 1. 3D reconstruction of Fe-FeS melt in an olivine matrix. The size of the bounding box is 7x7x3µm. The insert shows an enlargement of an individual melt pocket. There is graphic tool that allows the measure angles in 3D.