We have synthesized a series of Co0.5Cd0.5Fe2-xCexO4 (0.00 ≤ x ≤ 0.1) nanoferrites using sol-gel method. The results showed that Lattice parameter ‘a’ decreases from 8.470 to 8.369 Å by substitution of Fe2+ by Cerium (Ce3+) . However Ce3+ has ionic radii of 1.101 Å and Fe2+ has 0.64 Å of ionic radii. Please explain according to Vegard's rule.
Dear Muhammad,
what you have is a complex spinel phase AB2O4. In your parent compound you have Cd2+ (95pm) and Co2+ (65 pm) and Fe3+ (64 pm not Fe2+ !!). You are partially replacing Fe3+ with Ce3+ (101 pm). It is well known that in case of spinels like Fe3O4 reverse spinels may form in which the divalent cations take B sites instead of A sites, this will affect the lattice parameters.
An simplistic assumption according to Vegard's law is only valid if the structure does not change, it may however well be that partially a reverse spinel is formed in which e.g. Ce3+ takes an A (similar size as Cd2+) site while Co2+ switches to a B site. Moreover depending on heat treatment oxydation states of Co, Fe and Ce may differ from you assumptions.
However, this will be complicated to find out by XRD.
best regards
Frank
Dear Muhammad,
the lattice constant of spinel ferrites is related to the location of the cations in the octahedral (Oh) and tetrahedral (Td) sublattices and their distances with oxygen anions.
There is a simple method to evaluate the lattice constant. This method was proposed by P. Poix (P. Poix, Bull. Soc. Chim. Fr. 2 (1965) 1085e1087). This reference is quite old and perhaps difficult to find. But you will find an example of its application and the formula to calculate the lattice constant in function of the cationic radii in a more recent paper you can access at: https://oatao.univ-toulouse.fr/2317/1/Le_Trong_2317.pdf
or on researchgate .
With best regards.
Philippe.
Dear Muhammad Ayyaz, first of all, make sure it is single-phase, second, the parent structure of Cd0.5Co0.5Fe2O4 is Fd-3m with Wyckoff sequence e d a that caused 56 atoms in the unit cell with 2 types of M-O coordination; octahedral and tetrahedral. Cd-Co-Fe shares the tetrahedral coordination while Fe-Co is octahedral. By charge, balance Cd is most likely to octahedral. The significant differences in radius can cause the octahedral to tilt and or twist. So instead of the lattice increase, it decreases or maybe breaks the symmetry.
If your sample preparation and data collection are excellent, you can compare the raw data, where the corresponding peaks related to Ce will increase or decrease intensity as Ce substitution.
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