ABSTRACT
This chapter considers a case where translational symmetry elements are present. It focuses on the notion of space groups which represent all the symmetry elements of the crystal. The appreciation of space groups is essential in the solution of structures, transformations which lead to changes in symmetry, and the properties of crystals. The International Union of Crystallography publishes much more comprehensive space group tables which list the multiplicity of coordinates as a function of symmetry at that coordinate, for all possible scenarios and for all space groups. Crystallography is one of the characteristics that can influence the shape of a precipitate, but its influence is usually overwhelming when the precipitation occurs in the solid state. The structure of cementite clearly is very anisotropic so its properties, such as the elastic moduli, also vary strongly with the direction within the crystal.
