Two points need be explained are

[A] How does jumpimg ( diffusion) of ions occur?

Yes; there is jumping(diffusion) of ions which can occur in two different ways.

[I]Nanostructured zinc ferrites with different excess iron contents (ZnFe2+zO4, where z = 0.00, 0.05, 0.10 and 0.15) have been synthesized The XRD patterns demonstrated that the samples consist of single phase spinel structure with crystallite sizes of ~25 nm. SEM analysis indicated that the nanosized particles grow together in porous clusters with a size of several microns. The XPS and XMCD analyses revealed that the excess iron ion substitutes Zn2+ in tetrahedral sites and in octahedral sites Fe2+ can be found in addition to Fe3+, WHICH COULD BE CREATED TO RESTORE THE OVERALL CHARGE BALANCE IN THE CRYSTALL LATTICE. Stoichiometric zinc ferrite (ZnFe2+zO4, z = 0.00) exhibited higher photocatalytic activity (40%) than the excess iron sample (ZnFe2+zO4, z = 0.15, i.e. 4%) under visible light irradiation for 3 h. THIS WAS EXPLAINED BY THE FORMATION OF Fe^2 in the octahedral sites of excess iron ZnFe2O4; THESE SPECIES ACT AS RECOMBINATION CENTRES.

REF:

[A Šutka et al 2014 Phys. Scr. 89 044011]

{II}On absorption of radition, there occurs a large Zn{2+}(A)-->Zn{2+}[B] transference that takes place in addition to the well-identified Fe{3+}[B]-->Fe{3+}(A) one, without altering the long-range structural order.

REF:

[Physical Review B . 75(7):073408-073408(.2007)]

[B] How does the dielectric constant change with frequency?

[ Laying stress on last lines written in bold letters]

The dielectric constant is described by a complex real (ε/ ) and imaginary parts(ε//) which describe the storage and loss of energy on each cycle of the applied electric field. The real part is quit high and decreases as the frequency increase. The imaginary part is of less value and may become zero at ver high frequency. It is equal to 9467 for pure and 8870 for 80% wt of ZnFe2O4. The real part( ε/) arises from interfacial and space charge polarization. AT HIGHER FREQUENCIES,THE DIPOLE POLAZIABILITY WILL DECREASE BECAUSE THE FIELD CAN NOT INDUCE THE DIPOLE MOMENT AND THEREBY THE REAL PART OF THE DIELECTRIC CONSTANT DECREASES.

REF:

[ CHIN. PHYS.LETT., Vol.28, No.11(2011)117701]

Dear Sir, Thank you for your clear explanation.

Can you please explain in case of CoFe2O4, NiZnFe2O4

Thanking you in advance

Zinc ferrite (ZnFe,O,) is usually assumed to be a completely normal spine with zinc ions exclusively occupied in the A-sites in bulk material but when prepares in nanosize the same zinc occupies A-site or B-site or substitution else doping can also alter the same. When come to dielectric properties the temperature effect creates Fe2+↔ Fe3+ + e−(electron hopping) But the decrease in dielectric constant at higher frequency is completely due to relaxation process. see this paper file:///C:/Documents%20and%20Settings/Windows%20XP/My%20Documents/Downloads/MCP.pdf

Thks. my friend that this old man’s answers find your favor which keep me amongst young scholars .

[A] ZnNi2O4

This spi n el lies ON THE BOUNDARY BETWEEN NORMAL AND INVERSE SPINEL STRUCTURES { Distorted spinel structure; (I41/amd), which has a slightly off-cubic tetragonal unit cell]. So there is a swift cation inversion, or the preferential swapping of B (Ni ) for a( Zn) which causes diffusion( hopping) even on infinitesimally small change in conditions.

REF:

FILL GOOGLE with ZnNiO4

REACH

p-Type Zinc Oxide Spinels: Application to Transparent ...

arxiv.org/pdf/1312.1728

by M Stoica - ‎2013 - ‎Related articles

Dec 5, 2013 - (2010), ZnNi2O4 is predicted to have a distorted spinel structure (I41/amd), ... radii of A and B; using this method, we confirm that both ZnNi2O4.

CLICK to reach:

p-Type Zinc Oxide Spinels: Application toTransparent Conductors and Spintronics

Maria Stoica and Cynthia S LoDepartment of Energy, Environmental and Chemical Engineering, WashingtonUniversity, 1 Brookings Drive, St. Louis, MO 63130-4899, USAE-mail: [email protected].

Pls. look in the three bottom lines of page-3 and on page-14[ 6.2. Cation Inversion- first two lines]

[B]s regards to CoFe2O4, it is partially inverted[ inversion factor(i=0.8) spinel with Co^2 being predominantly(80%) inoctahedral sites.

[J. Phys. Chem. C 2009, 113, 8606–8615]

As is most common, the hopping between Fe 2+↔Fe 3+ e is most commonly exhibited.