REDUCED CELLS AND THE INDEXING OF ELECTRON DIFFRACTION PATTERNS

Corresponding to the 14 Bravais lattices there are 44 different types of reduced cells whose base vectors are unique, therefore it is possible to deduce the Bravaislattice type from the scalar products of reduced cell vectors(a·a b·b c·c b·c c·a a·b). If the crystal lattice is already known, the plane reduced cells in the reciprocal space are first calculated from the lattice parameters and then the electron diffraction patterns can be indexed by comparing them with the calculated plane reduced cells. If the crystal lattice is unkown, three diffraction spots are selected from two electron diffraction patterns taken one before and the other after tilting the crystal through an angle ψ, the spots being chosen so that they lie close to the center, corresponding to three reciprocal lattice vectors with low indices. These vectors constitute a primitive cell in reciprocal space which is first transformed to a primitive cell then further to a reduced cell in the crystal space. The lattice type and parameters of the Bravais lattice are then deduced and the indices of diffraction spots fixed. Computer pro-grams of the above indexing procedures have been written in Fortran for the purpose of phase analysis and the direct determination of the Bravais lattice of unknown crystals.