Influence of the inversion factor on Madelung constants in spinel systems

• Published in: Solid state communications 2021-02, Vol.324, p.114134, Article 114134
• Main Author: Khalaf, Kadhim A.M.
• Format: Article
• Language: English
• Subjects: Configurational entropy; Inversion factor; Madelung constant; Mg-Zn-Ni Spinels; Order parameter
• ISSN: 0038-1098; 1879-2766
• DOI: 10.1016/j.ssc.2020.114134

The influence of the inversion factor on the Madelung constants of the partially inversed spinel systems Mg-Zn-(FeTM)O4 where (TM = Ni and Cr) have been investigated. These results showed that both the ordering parameter, Q and the inversion factor, λ depend on the oxygen positional parameter, u in these spinels. An inverse relation between lattice constants and the inversion factor is well defined in these spinels. From the cation distributions the sample with λ = 2/3, Q = 1 and maximum configurational entropy Sc(≈15.876 J/mol,K) should represents the sample with the complete randomness of the cation distributions in these spinels and can be written as ((MgZn)1/3Fe2/3)[(MgZn)2/3Fe1/3TM3/3]O4. The total Madelung constants Mtot increase as the inversion factor decreases in these spinels. The presence of the Zn2+ (Mg2+) cations enhances the normal (inverse) spin phase arrangements; this might be caused by the strong tendency of the Zn2+ (Mg2+) cations to reside at the tetrahedral (octahedral) sites. The Zn- (Mg-) spinels are largely having the normal (inverse) type structure. Values of the ordering, inversion and randomness parameters moves towards the spinel structure normality as the Zn content (x) increases in the sample. Values of the calculated total Madelung constants, Mtot increase as uavg increases. An inverse relation between the lattice constants and the inversion factor, λ is well defined in these spinels. Madelung Constants for spinels (MCs).•A new suggested method for the prediction of MCs for (FCC) spinels.•Includes normalization of the MCs for the perfect spinels phases versus λ.•The MCs for the tetra-, octa- and anions sublattices can be predicted.•The MCs have been calculated for u= 0.375, 0.380, 0.385 and 0.390.•The relation between λ versus sample contents results in a phase diagram.