A stereoscopic method for dihedral angle measurement

A new method is presented for the measurement of equilibrium dihedral angles in intergranular inclusions, and illustrated with pure copper containing 1 wt% lead. The method is based on the selective dissolution of inclusions visible along a polished metallographic section. Scanning electron microscopy stereo image pairs are then taken and processed so as to enable a three-dimensional digital reconstruction of the inclusion/matrix interface along each inclusion. Spherical caps describing the Cu/Pb interface over non-facetted orientations are then fitted to the measured digital inclusion envelope reconstructions. Knowing the center and radius of these spheres, the true dihedral angle of each specific inclusion can then be deduced with good precision. It is found that the true dihedral angle in the Cu/Pb alloy is not a unique function of temperature, reflecting the (known) anisotropy of high-angle grain boundary energy in copper.