Geometric description
Grain boundaries - Theory and experimentation

In a region where two periodic structures interpenetrate, it is logical to envisage the preservation of a certain "geometric" order. Determining this order requires, first of all, specifying the parameters of the transformation linking the two crystals.

From there, we can describe the bicrystal's lattice, which, like the crystal's lattice and its imperfections, can be used to approximate the structure and structural defects of the joint. However, since a joint only exists in the presence of a plane, it is necessary to take into account the position of this plane in the intergranular region to fully describe the "grain boundary" object.

For more details on this description, please refer to the following references