The geometry of water veins and nodes in polycrystalline ice

Abstract

Water in polycrystalline ice at its melting point forms a system of veins at the three-grain junctions. The veins joint together at nodes, which are the four-grain junctions. The shape of a node, a tetrahedron with non-spherical faces and open corners, is determined completely by the dihedral angle for water in contact with a grain boundary. Using the observed value for this angle, namely 33.6o, the paper computes the tetrahedral shape. This is a surface-tension problem with initially unknown boundaries. -from Author