the lattice constant of the spinel ferrites is strongly correlated to the cationic composition and distribution in Oh and Td sites. Calculation of the lattice constant is possible, see for instance the attached paper and the references mentioned in it.
In soft ferrites, when the crystalline size increases, it can cause a decrease in the lattice constant observed in XRD. This phenomenon is due to the rearrangement of atoms within the crystal structure. It's fascinating how these changes can affect the material's properties!🔬
When it comes to soft ferrites and XRD, the increase in crystalline size can be due to factors like annealing or sintering, while the decrease in lattice constant might be influenced by the substitution of different ions in the crystal structure.
For any type of spinel ferrite the lattice parameter is calculated by :
a=(8/3*(3)1/2)*(rA+ro) + 31/2*(rB+ro), so depending on rA and rB, that are the average cationic radio of occupation atoms on octahedral sites (A), and tetrahedral sites (B). For example in the case of zinc ferrite if the ocupattion in sites A of zinc is 40% and iron 60%, the average radio is rA=0.4*rZn+++0.6rFe+++. Therefore 'a' depends on the cationic distribution on A and B positions. However size crystallite depending of synthesis process and later treatments like milling and annelaing for example.
The increase in the size of the crystallites may be associated with a change in the chemical composition, a defect in the structure, and the method of obtaining the material. One crystallite contains many elementary cells, so its size consists of several lattice parameters and will not necessarily correlate with the cell size. So, for example, when choosing another type of replacement cations or another method of obtaining crystals, the opposite trend may be observed.
In addition, there is another factor affecting the lattice parameter: in nanoscale objects, due to the increasing role of the surface, the compression mechanism is manifested due to surface tension forces.