On the principle of duality between direct lattice space and reciprocal lattice space

Unit vectors of a Cartesian base system are used to express both direct and reciprocal lattices of a crystal. The lattice defined by these unit vectors plays a role of transforming the direct lattice to the reciprocal lattice or the reciprocal one to the direct one. It is shown that basic axes of the reciprocal lattice can be expressed in forms of a linear combination of those of the direct lattice or vice versa. A set of parallel planes defined in the reciprocal lattice space is represented by the corresponding direct lattice vector, one of which passing through the origin can be observed as the diffraction pattern by the electron microscope. Explicit expressions are described by which basic axes of the reciprocal lattice and those of the direct lattice can be determined from the diffraction pattern. (auth.)