American Journal of Condensed Matter Physics

p-ISSN: 2163-1115    e-ISSN: 2163-1123

2020;  10(2): 39-43


Received: Nov. 1, 2020; Accepted: Nov. 22, 2020; Published: Nov. 28, 2020


Study on Conduction Mechanism, Ferrous Ion Concentration, Oxygen Deficiency, and Fermi Energy Determination from a Thermal Variation of Seebeck Coefficient Measurement for Zn0.3Mn0.7+xSixFe2-2xO4 Ferrite Series

Kiran G. Saija1, Pooja Y. Raval2, Nimish H. Vasoya3, Uday N. Trivedi4, Kunal B. Modi5

1Smt. R. P. Bhalodia Mahila College, Upleta, India

2Department of Physics, C. U. Shah University, Wadhwan City, Surendranagar, India

3Department of Balbhavan, Children's University, Sector -20, Gandhinagar, India

4Government Polytechnic, Ahmedabad, India

5Department of Physics, Saurashtra University, Rajkot, India

Correspondence to: Kunal B. Modi, Department of Physics, Saurashtra University, Rajkot, India.


Copyright © 2020 The Author(s). Published by Scientific & Academic Publishing.

This work is licensed under the Creative Commons Attribution International License (CC BY).


The compositional and temperature (T = 300 – 525 K) dependence of Seebeck coefficient measurement has been carried out on microcrystalline ferrite samples of Zn0.3Mn0.7+xSixFe2-2xO4 (x = 0.0, 0.1, 0.2 and 0.3) series. The probable conduction mechanism is the exchange of electrons between Fe3+ and Fe2+ ions on the octahedral interstitial site of the spinel structure. The absolute concentration of ferrous and ferric ions has been deduced that used to determine the actual occupancy of metallic cations, oxygen deficiency, and to describe the compositional variation of dc resistivity. Finally, the Fermi energy values at T = 0 K have been derived.

Keywords: Ferrites,Thermoelectric power study, Conduction mechanism, Fermi energy

Cite this paper: Kiran G. Saija, Pooja Y. Raval, Nimish H. Vasoya, Uday N. Trivedi, Kunal B. Modi, Study on Conduction Mechanism, Ferrous Ion Concentration, Oxygen Deficiency, and Fermi Energy Determination from a Thermal Variation of Seebeck Coefficient Measurement for Zn0.3Mn0.7+xSixFe2-2xO4 Ferrite Series, American Journal of Condensed Matter Physics, Vol. 10 No. 2, 2020, pp. 39-43. doi: 10.5923/j.ajcmp.20201002.02.

1. Introduction

The Seebeck coefficient is also referred to as thermoelectric sensitivity, thermopower, and thermoelectric power. The Hall coefficient and Seebeck coefficient measurements are the most promising characterization techniques to understand responsible mechanisms for electrical conduction in various classes of materials. Regarding low mobility and high resistivity materials, for instance, ferrites, and perovskites, the Hall voltage measurement becomes difficult. The only alternative in such a case is the temperature dependence of Seebeck coefficient measurement. The thermoelectric power measurement is very simple and carrier type (holes or electrons) accountable for the conduction process can be decided without any ambiguity. This is further used to determine many important parameters, charge carrier density, Fermi energy, mobility of charge carrier, oxygen deficiency, activation energy, charge disproportionation, etc., [1-5].
Restricted to thermopower study on spinel structured ferrite series, in recent years (2016 - 2020), very limited research communications are available in literature. Polycrystalline sample of magnesium ferrite (MgFe2 O4) synthesized by spark plasma and solid-state reaction sintering processes [6], non-stoichiometric ferrite system, Mg0.5+xCuxZn0.5Fe1.9O4-δ (x = 0.0 - 0.3) [7], Ni2+ - substituted Mg-Cu-Zn ferrites [8], tetravalent Sn4+ substituted copper ferrite [9] and Li0.5 – 0.5xCuxFe2.5 – 0.5xO4 (x = 0.0 -1.0) series [1] have been investigated for their thermoelectric sensitivity. The thermoelectric properties of composites of carbon nanotubes, multiwalled carbon nanotubes, graphene and Mn0.7Zn0.3Fe2O4 spinel ferrite synthesized by spark plasma sintering process have been studied by Zhang et al. [10-12]. Thermopower study has been carried out on nanoparticles of MnxZn1-xFe2O4 (x = 0.0 – 1.0) [13], NiSmxFe2-xO4 [14], CoxMn0.5-xZn0.5Fe2O4 (x = 0.0, 0.1, 0.3 and 0.5) [15], and Li0.15Ni0.5Sm0.1Fe2.15O4 [16] spinel ferrite systems prepared by co-precipitation technique/citrate –gel auto combustion route.
In recent years, the structural, microstructural, bulk magnetic, electric and dielectric characteristics of ferrite series, Zn0.3Mn0.7+xSixFe2-2xO4 with x = 0.0, 0.1, 0.2 and 0.3, by means of energy dispersive analysis of X-rays (EDAX), X-ray powder diffractometry (XRD), scanning electron microscopy (SEM), bulk magnetization (Hmax = 2.5 kOe, T = 80 K and 300 K ), temperature dependence of low field (0.5 Oe) ac (263 Hz) susceptibility measurement (T = 300 K – 525 K), temperature dependence of dc resistivity measurement (T = 300 K - 773 K), current versus voltage (I - V) characteristics (T = 300 K – 673 K and V = 0 – 400 V), frequency (f = 20 Hz – 1 MHz) and temperature (T = 300 K – 673 K) dependent permeability and dielectric constants measurements have been investigated [17-23].
In this communication, the thermal variation of Seebeck coefficient () measurement carried out on this well-characterized system, Zn0.3Mn0.7+xSixFe2-2xO4 (x = 0.0 – 0.3), has been reported. The values of α have been used to calculate ferrous ion concentration, oxygen deficiency, and Fermi energy.

2. Experimental Details

The technical particulars related to the preparation of four single-phase, microcrystalline compositions of ferrite series, Zn0.3Mn0.7+xSixFe2-2xO4 where x = 0.0, 0.1, 0.2 and 0.3, by high-temperature solid-state reaction method, phase analysis, and structural parameters including cation distribution determination from X-ray diffraction line intensity calculations [20,22] and thermoelectric power measurement are well described in [2-5].

3. Results and Discussion

The values of the thermoelectric power coefficient have been calculated by = V/T, where V is the electric potential difference generated as a result of temperature difference (ΔT) between the hot junction temperature (T) and the cold junction temperature (T´). The values show small variation ( 1.0%) during the heating and cooling cycles of measurement. In Fig. 1, the plots for the system, Zn0.3Mn0.7+xSixFe2-2xO4 (x = 0.0, 0.1, 0.2 and 0.3) are depicted. It is found that for all the compositions is negative throughout the temperature range studied. This suggests that electrons are the majority charge carriers or dominant conduction mechanism is n-type in the series. Earlier, Ivanovskaya et al. [24] have shown that Mn-Zn ferrite materials synthesized without controlled parameters (high-pressure preparation of material in an oxygen atmosphere) possess oxygen vacancies, that turns out to be a partial reduction of ferric ion (Fe3+ ) into ferrous ion (Fe2+ ) in the system. The existence of Fe3+ ions in other valance states (Fe2+ or Fe4+ ) results in interesting changes in the electrical characteristics of ferrites [24-26]. At the octahedral (B-) sites of the spinel structure, the exchange of electron takes place between Fe3+ and Fe2+ by the conduction mechanism: Fe2+ ↔ Fe3+ + e-.
Figure 1. Seebeck coefficient (α) against hot junction temperature plots for Zn0.3Mn0.7+xSixFe2-2xO4 series
When in any system, two types of hopping conduction mechanisms are assumed to be involved, the parameters, the concentration of substituted metallic cation (x), and measurement temperature will decide the dominance of one mechanism over the other mechanism. If the hole exchange mechanism given by Mn3+ ↔ Mn2+ + e+ (p-type conduction) is dominating over the electron exchange mechanism that takes place by Fe2+ Fe3+ + e- in the system under investigation, Zn0.3Mn0.7+xSixFe2-2xO4, the ferrite composition might conduct as a p-type semiconducting material or vice versa.
A careful examination of Fig. 1 shows that the Seebeck coefficient () initially increases rapidly with temperature from T = 300 – 425 K while α increases slowly with a further increase in temperature (T ≥ 425 K) for all the compositions. This observed variation in curves can be explained as follows. In n-type semiconducting material, owing to the loss of electrons, the hot surface becomes positively charged while the cold surface becomes negatively charged due to the diffusion of these liberated electrons. The hopping mechanism, Fe2+ ↔ Fe3+ + e-, turns out to be most probable on increasing temperature that produces electrons. The accumulation of such electrons at the cold surface results in the development of potential difference thus α increases rapidly during T = 300 – 425 K. The observed small variation in with T for T ≥ 425 K is mainly due to the saturation in the generation of electrons and electrons-holes recombination in the system. When valence electrons are given energy equal or greater than the energy band gap, they will be transferred to the conduction band and recombination of an electron-hole occurs. Following the classifications proposed by Bashikiriv et al. [27], the significant variation in with T (Fig. 1) suggests that the ferrite materials under investigation are non-degenerate semiconductors.
The thermoelectric power in the instance of hopping conduction is given by the formula as suggested by Heikes formula [28]:
where k and e are Boltzmann´s constant and electronic charge, respectively, ST is the temperature-independent effective entropy transport by the charge carriers. According to Goodenough et al. [29], the ST/k is commonly insignificant for oxide/ferrite systems. It contributes not more than 10 μV/K and thus neglected in the above expression (1). The ratio of the number of carriers in the states (n) to the number of available states (N), i.e., n/N is denoted by ‘c’. Thus, the above eq. (1) can be rewritten as:
A more generalized formula for the oxide systems in which cation in two different valence states, Mn+ /M(n+1)+, is present has been derived by Doumerc et al. [30] and accordingly:
Here, number of holes (p) per active transport site (N) i.e., the hole concentration (ch) is given by ch = 1-c = p/N. Based on the assumption that ‘N is equal to the total number of ferrous and ferric ions residing at the octahedral environment and ‘n ’ is the number of ferric ions at the B-site, above eq. (3) becomes:
For various types of oxides systems such as spinel ferrites [5,31], magnetite [32], hausmannite [33], and manganite perovskites [3], this has been found suitable for the determination of the relative concentration of ferrous ion to ferric ion on the B-site.
The Seebeck coefficient values registered at T = 373 K have been used to determine the relative concentration of Fe2+/Fe3+, the absolute ferrous ion concentration, and the product of (Fe2+) (Fe3+) ions residing at the octahedral interstitial sites, and the same have been summarized in Table 1. Based on this the actual distribution of cations and oxygen deficiency (δ) for each composition has been determined and shown in Table 2.
Table 1. Seebeck coefficient (α), the cationic concentration at T = 373 K and Fermi energy at T = 0 K for Zn0.3Mn0.7+xSixFe2-2xO4 series
Table 2. Occupancy of cations and oxygen deficiency (δ) for spinel structured ferrite series Zn0.3Mn0.7+xSixFe2-2xO4
It is found that the percentage variation of the Fe2+ -ion concentration and the product of (Fe2+)(Fe3+) ions on the octahedral sites is ~ 91% for a given range of compositions (Table 1). This suggests that the percentage variation in dc resistivity (ρdc) value cannot exceed 91% if these two parameters are responsible for the observed change in ρdc. Recently, it has been found that the percentage variation in ρdc as a function of composition (x) at T = 373 K is ~ 90% [20].
In solids, the energy of the highest filled state in the electronic band structure at T = 0 K is referred to as the Fermi energy, EF(0). An effort has been made to determine EF(0) by extrapolating values of EF(T) to T = 0 K. The region in which electric conduction solely owing to either of the charge carriers (electrons or holes, not both), the and EF are correlated by the relation [34]:
where ‘A’ is a dimensionless constant related to the kinetic energy of the charge carrier. The temperature dependence of EF for A = 0 and A = 2 are shown in Fig. 2 for all the compositions.
Figure 2. Thermal variation of Fermi energy for Zn0.3Mn0.7+xSixFe2-2xO4 series
The extrapolation of these two curves of EF intercepts the y-axis at a specific point (T = 0 K), yield EF(0). The magnitude EF(0) has been taken into consideration as EF(0) cannot be negative [35]. The EF(0) shows small variation with Mn-Si concentration (x) in the series Zn0.3Mn0.7+xSixFe2-2xO4 (Table 1). The observed difference between the activation energy values (E = 0.21 eV to 0.27 eV for x = 0.0 to 0.3 compositions) determined from logρdc against reciprocal of temperature plots [20] and EF(0) (E > EF(0)) may be ascribed to the activation energy analogous to hopping of charge carriers. Consequently, total activation energy is made up of two terms, kinetic energy related to the generation of charge carriers and kinetic energy associated with the hopping of charge carriers between crystallographically equivalent sites.

4. Conclusions

The following intriguing conclusions are drawn based on the compositional and thermal variation of thermoelectric power study on ferrite series, Zn0.3Mn0.7+xSixFe2-2xO4 (x = 0.0 – 0.3).
The ferrites under investigation are non-degenerate semiconducting materials and the exchange of electrons among ferrous (Fe2+) and ferric (Fe3+) ions on the octahedral site is the governing mechanism of electrical conduction. The relative and absolute concentration of ferrous and ferric ions, as well as oxygen deficiency, can be determined from the temperature-dependent thermopower measurement. The Fermi energy shows compositional variation consistent with the variation of Fe2+ - ions in the system.


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