The Geometry of Water Veins and Nodes in Polycrystalline Ice

Abstract

AbstractWater in polycrystalline ice at its melting point forms a system of veins at the three-grain junctions. The veins join 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 33.6°, the paper computes the tetrahedral shape. This is a surface-tension problem with initially unknown boundaries. The result shows that the ratio of vein volume to node volume is R = 0.072 l/d, where l is the average length of a vein between two nodes, and d is the vein diameter measured between edges. For example, in a specimen of ice grown from the melt in the laboratory R was 18.