Monoclinic crystal system has primitive and base-centered Bravais lattices. Using two-dimensional projections depicted in Figure below (Fig. 2.25), show how a body-centered lattice and a face-centered monoclinic lattice (their unit cells are indicated with the dashed lines) can be reduced to a base-centered lattice. Write the corresponding vectorial relationships between the unit cell vectors of the original body-centered and face-centered lattices and the transformed base-centered lattices. What are the relationships between the unit cell volumes of the original body- and face-centered lattices and the resulting base-centered lattices?

Monoclinic crystal system has primitive and base-centered Bravais lattices. Using two-dimensional projections depicted in Figure below (Fig. 2.25), show how a body-centered lattice and a facecentered monoclinic lattice (their unit cells are indicated with the dashed lines) can be reduced to a base-centered lattice. Write the corresponding vectorial relationships between the unit cell vectors of the original body-centered and face-centered lattices and the transformed base-centered lattices. What are the relationships between the unit cell volumes of the original body-and face-centered lattices and the resulting base-centered lattices? Notes: y is perpendicular to the paper 0 - point at y=0,1, - point at y=1/2,3/2, Fig. 2.25 Body centered (left) and face centered (right) monoclinic lattices projected along the Y-axis with the corresponding unit cells shown using the dashed lines