Distribution of apparent angles on random sections with emphasis on dihedral angle measurements

Abstract

The distribution of apparent solid‐liquid dihedral angles, normally observed on planar sections of partial melting experiments, is examined in terms of a normal distribution of “true” dihedral angles present in any sample. A theory for predicting the distribution of apparent angles observed on a random planar section of a three‐dimensional aggregate with one true dihedral angle is reviewed and comparisons are made between apparent angle distributions obtained from partial melting experiments and various theoretical distributions. The results of these comparisons suggest that the observed distribution of solid‐liquid dihedral angles in partial melting experiments rarely yield a satisfactory match to the theoretical distribution for a single unique dihedral angle. However, good agreement is generally obtained assuming a normal distribution of true dihedral angles about a mean value. The origin of this normal distribution is discussed both in terms of measuring error and crystalline anisotropy with respect to interfacial energies.