The possible reasons for the cell parameters to change in this way could be due to the presence of the (+2) ion in the A site. This ion is smaller than the (+3) ion, so it would take up less space in the lattice, resulting in a decrease in the a and c parameters. The b parameter would increase because the lattice would be more compressed due to the smaller ion. The monoclinic crystal system is characterized by three unequal axes, with one axis being perpendicular to the other two. The angles between the axes are all different, and the cell is not symmetrical. The cell parameters for a monoclinic crystal are a, b, c, and β (the angle between the a and c axes).

When an A-site cation (+3) is doped with a (+2) cation in a double perovskite, the crystal structure of the material can change, leading to changes in the unit cell parameters. The specific changes in the cell parameters (such as a and c decreasing and b increasing) can depend on the nature of the dopant cation and the host lattice.

One possible reason for the decrease in the cell parameter a and c and increase in b is the difference in ionic radius between the dopant and host cations. If the dopant cation has a smaller ionic radius than the host cation, it will occupy a smaller volume in the lattice. This can lead to a reduction in the distance between neighboring cations along the a and c axis (decreasing a and c), and an increase in the distance between cations along the b axis (increasing b).

Another possible reason could be the change in the bond angles between the cations due to doping. If the dopant cation has a different coordination environment than the host cation, it could lead to a change in the bond angles which in turn can change the length of the lattice vectors.

Additionally, the electronic and electronic structure changes that happens due to doping can also influence the lattice parameters. A more detailed analysis of the electronic structure, for example by DFT calculations, can give more information about the mechanism.