The morphological stability criteria of melts in edge and corner regions in a partially molten system containing several solid phases (three) under textural equilibrium are proposed in terms of dihedral angles. Owing to the variety of edge and corner regions due to combination of the crystalline phases in the multi-solid phase system, melts are morphologically stable in some types of edges and corners, and unstable in others. In order to apply the stability criteria to the partially molten regions in the upper mantle we conducted a partial melting experiment with a peridotite mainly composed of olivine (OL), orthopyroxene (OPX), and clinopyroxene (CPX) crystals at 1300¿ C, 1 GPa and for 300 hours.

Various types of dihedral angles were measured on the run product which contained about 7% melt. The melt versus OL/OL dihedral angle was significantly smaller than other types of melt versus solid/solid dihedral angles. Applying the stability criteria to these experimental results, we predict that in the partially molten peridotite the melts are morphologically stable only in OL-OL-OL edge regions and in OL-OL-OL-OL and OL-OL-OL-OPX corner regions. The connectivity of the melt phase is determined by the melt distribution in the stable edge and corner regions at melt fractions less than 29%. The melt distribution can be modeled by the bond distribution in lattice, that is, bond percolation. The connectivity of the melt phase is estimated as a function of the modal composition and grain size distribution of the matrix and is graphically presented as a connectivity diagram (OL-OPX-CPX modal composition diagram).

The trajectory of modal composition of the solid matrix in the connectivity diagram determines the connectivity history of a rock during progressive partial melting in the upper mantle. Three different cases of connectivity history are discerned depending upon the modal composition before melting and are characterized by the critical melt fractions ϕcm, at which the melt phase suddenly becomes connecting, such as ϕcm=0,0<ϕcm<0.29, and ϕcm=0.29. In a peridotite the modal portion of olivine but also the relative grain size are the most important determinant of the connectivity behavior in the upper mantle.