**3.1. X-ray diffraction analysis**

**Figure 3** shows the XRD patterns of the foil ferrite samples analyzed here and labeled as FF-1, FF-2, and FF-3. These samples are polycrystalline with spinel oxide structure. Several peaks appear, which correspond to the (111), (022), (113), (004), (224), (115), (044), (026), and (335) crystallographic planes of the magnetite phase (Fe3 O4 ).

Frequently, structural defects in Mn-Zn ferrites are classified as grain boundaries, where there is a face-centered cubic lattice of oxygen ions with a unit cell consisting of eight functional units [19, 20]. Such configurations indicate the presence of clusters which are interpreted in terms of complex defects consisting of Fe ions in an interstitial tetrahedral site with two adjacent octahedral Fe vacancies, which suggest that the foil ferrites are nonstoichiometric oxides in composition. Thus, in foil ferrite samples, their chemical formula can be written as *Mnx Zny Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup> , where the Mn cations occupy the tetrahedral sites and the Zn cations occupy the octahedral sites, while x and y will be defined as composition parameters [21].

In the case of the foil ferrite irradiated by CoKα radiation, the Debye-Scherrer relation becomes

**Figure 3.** XRD patterns of three different foil ferrite samples, where XRD patterns of MnO and ZnO are included as

peak with respect to the substrate, ∆*θ* as the difference between incident angle for measured (113) plane and the (113) plane corresponding at the magnetite, and ϕ is the angle with respect to the

−1

, where D is the mean crystallite size, *N* ≈ *c*/*r* is the interatomic spacing with

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0

tan*<sup>ϕ</sup>*, where Δd/d is the average strain along the (113) reflection

the unstrained atomic plane spacing [23]. **Table 1** gives the structure parameters

ion, and θ is the reflection angle to the (113)

mixed with MnO and ZnO on lattice strain,

)/*d* with d as the actual atomic plane

, where t is the minimum thickness for carrier

*D* = *N* [(*FWHM*) cos*θ*]−<sup>1</sup>

spacing and *d*

0

it can be well studied by using \_\_\_ <sup>∆</sup>*<sup>d</sup>*

c = 8.494 Å for magnetite, r = 0.64 Å as the radius of *Fe*+3

conduction in the absence of scattering events and ϵ2*<sup>θ</sup>* <sup>=</sup> (*<sup>d</sup>* <sup>−</sup> *<sup>d</sup>*

*<sup>d</sup>* <sup>=</sup> \_\_\_\_\_ <sup>∆</sup>*<sup>θ</sup>*

orientation, while the Scherrer relation *<sup>t</sup>* <sup>=</sup> *<sup>λ</sup>* [ϵ2*<sup>θ</sup>* cos*θ*]

reference for analysis of the strain and chemical composition.

attained from XRD patterns in foil ferrite samples.

To know the effect of the complex composition of *Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup>

The relative number of planes oriented in a certain direction can be related to the area under the XRD peak, as well as the peak height which will represent that reflection; here XRD is used to determine the orientation corresponding to the significant plane in the foil ferrite structure, being it the c-axis orientation as the area under the (113) reflection peak. The effect of powder preparation and sintering cycle on the crystal size and thickness in ceramic process technologies for Mn-Zn ferrites is associated with the full width at half maximum (FWHM) and elastic strain (ϵ2*<sup>θ</sup>* ) [22]. Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green… http://dx.doi.org/10.5772/intechopen.72418 195

finding of the Mn-Zn ferrites, predicting theoretically their uncommon properties is a possibility in foil ferrite analysis; then studying structure and conduction properties makes it possible

This section discusses structure and conduction properties in foil ferrites. It then reviews general capabilities of x-ray diffraction (XRD) and electrical characterization techniques for the study of foil ferrites and behavior with emphasis on knowledge of their properties. The interrelation of structure and conduction properties as a function on their magnetic ordering is the

Usually, copper source with CuKα radiation (λ = 0.154 nm) is employed in x-ray diffraction studies; however, features of Mn-Zn ferrites at higher wavelengths are indistinguishable. Thereby, a PANalytical x-ray diffractometer with CoKα radiation (λ = 0.179 nm) is used here to obtain XRD patterns in foil ferrite samples. Cobalt source allows higher diffraction angles and peak spreads. Current-voltage measurements are performed by using a digital storage oscilloscope (Tektronix, TDS1012C) at room temperature. A function generator (Matrix, MFG-8250A) is used to produce a linear-ramp signal at low frequency (f = 100 Hz) with voltage scanned from −10 V to 10 V to ensure that the magnetic saturation in the samples does not

**Figure 3** shows the XRD patterns of the foil ferrite samples analyzed here and labeled as FF-1, FF-2, and FF-3. These samples are polycrystalline with spinel oxide structure. Several peaks appear, which correspond to the (111), (022), (113), (004), (224), (115), (044), (026), and (335)

Frequently, structural defects in Mn-Zn ferrites are classified as grain boundaries, where there is a face-centered cubic lattice of oxygen ions with a unit cell consisting of eight functional units [19, 20]. Such configurations indicate the presence of clusters which are interpreted in terms of complex defects consisting of Fe ions in an interstitial tetrahedral site with two adjacent octahedral Fe vacancies, which suggest that the foil ferrites are nonstoichiometric oxides in composi-

Mn cations occupy the tetrahedral sites and the Zn cations occupy the octahedral sites, while x

The relative number of planes oriented in a certain direction can be related to the area under the XRD peak, as well as the peak height which will represent that reflection; here XRD is used to determine the orientation corresponding to the significant plane in the foil ferrite structure, being it the c-axis orientation as the area under the (113) reflection peak. The effect of powder preparation and sintering cycle on the crystal size and thickness in ceramic process technologies for Mn-Zn ferrites is associated with the full width at half maximum (FWHM) and elastic strain (ϵ2*<sup>θ</sup>*

tion. Thus, in foil ferrite samples, their chemical formula can be written as *Mnx Zny Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup>

).

, where the

) [22].

**3. Structure and conduction properties in foil ferrites**

to estimate their physical behavior.

194 Iron Ores and Iron Oxide Materials

key issue in green electronic device design.

occur.

**3.1. X-ray diffraction analysis**

crystallographic planes of the magnetite phase (Fe3 O4

and y will be defined as composition parameters [21].

**Figure 3.** XRD patterns of three different foil ferrite samples, where XRD patterns of MnO and ZnO are included as reference for analysis of the strain and chemical composition.

In the case of the foil ferrite irradiated by CoKα radiation, the Debye-Scherrer relation becomes *D* = *N* [(*FWHM*) cos*θ*]−<sup>1</sup> , where D is the mean crystallite size, *N* ≈ *c*/*r* is the interatomic spacing with c = 8.494 Å for magnetite, r = 0.64 Å as the radius of *Fe*+3 ion, and θ is the reflection angle to the (113) orientation, while the Scherrer relation *<sup>t</sup>* <sup>=</sup> *<sup>λ</sup>* [ϵ2*<sup>θ</sup>* cos*θ*] −1 , where t is the minimum thickness for carrier conduction in the absence of scattering events and ϵ2*<sup>θ</sup>* <sup>=</sup> (*<sup>d</sup>* <sup>−</sup> *<sup>d</sup>* 0 )/*d* with d as the actual atomic plane spacing and *d* 0 the unstrained atomic plane spacing [23]. **Table 1** gives the structure parameters attained from XRD patterns in foil ferrite samples.

To know the effect of the complex composition of *Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup> mixed with MnO and ZnO on lattice strain, it can be well studied by using \_\_\_ <sup>∆</sup>*<sup>d</sup> <sup>d</sup>* <sup>=</sup> \_\_\_\_\_ <sup>∆</sup>*<sup>θ</sup>* tan*<sup>ϕ</sup>*, where Δd/d is the average strain along the (113) reflection peak with respect to the substrate, ∆*θ* as the difference between incident angle for measured (113) plane and the (113) plane corresponding at the magnetite, and ϕ is the angle with respect to the


**Table 1.** Structure parameters in foil ferrites.

substrate planes [24]. As the Mn-Zn ferrite is a powder composition with *Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup> as their main constituent, a foil ferrite can be approximately seem as a structure MnO/*Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup> /ZnO where diffusion processes occur; then, for strain analysis the equivalent substrate planes will be both MnO and ZnO as reference XRD patterns (see **Figure 3**) [1]. **Table 2** provides the average strain estimated from XRD patterns in foil ferrite samples.

#### **3.2. Electrical analysis**

**Figures 4** and **5** explain the measuring strategy to know electrical performance in foil ferrite samples labeled as FF-1, FF-2, and FF-3. Two conditions are performed, both longitudinal and transverse bias as shown in **Figures 4(a)** and **5(a)**, respectively. Current-voltage (I-V) curves are displayed in **Figure 4(b)** at longitudinal bias and at transverse bias in **Figure 5(b)**. Two aluminum electrodes of circular geometry with cross section area of 3.14 *mm*<sup>2</sup> are placed on each foil ferrite sample to inject and collect voltage signals. A resistor of 1 kΩ is used to measure the output voltage and thus calculate the current flow by Ohm's law. Ohmic behavior is observed in I-V curves for voltage bias from −2 to 2 V, while at higher voltages, I-V curves indicate that current and voltage follow a power-law relationship *I* = *α V<sup>n</sup>* with n = 1.5. Such power-law dependence is characteristic of space-charge-limited conduction (SCLC) [25]. Analysis in I-V curves by using a SCLC model is the experimental method used here with current-voltage dependence proportional to *<sup>α</sup>* <sup>=</sup> \_\_9 <sup>8</sup> *<sup>ε</sup>*<sup>0</sup> *<sup>ε</sup><sup>r</sup> <sup>S</sup> <sup>L</sup>*<sup>−</sup><sup>3</sup> , where *ε*<sup>0</sup> *<sup>ε</sup><sup>r</sup>* is the dielectric constant, *μ* is the carrier mobility, L is the spacing between electrodes, and S is the crosssectional area.

**Figure 4.** (a) Schematic diagram of the foil ferrites in cross-sectional view connected in the test circuit. (b) Current-

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**Figure 5.** (a) Schematic diagram of the foil ferrites in cross-sectional view connected in the test circuit. (b) Current-

voltage (I-V) curves of the three different foil ferrite samples, which are transversally biased.

voltage (I-V) curves of the three different foil ferrite samples, which are longitudinally biased.


**Table 2.** Average strain in foil ferrites associated with ZnO and MnO.

Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green… http://dx.doi.org/10.5772/intechopen.72418 197

substrate planes [24]. As the Mn-Zn ferrite is a powder composition with *Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup>

**Sample 2***θ* **FWHM** ϵ**2***<sup>θ</sup>* **D (nm) t (nm)** FF-1 40.88° 0.19 1.22 × 10<sup>−</sup><sup>4</sup> 13.34 1565.86 FF-2 40.93° 0.19 1.07 × 10<sup>−</sup><sup>3</sup> 13.35 178.55 FF-3 40.93° 0.19 1.07 × 10<sup>−</sup><sup>3</sup> 13.35 178.55

processes occur; then, for strain analysis the equivalent substrate planes will be both MnO and ZnO as reference XRD patterns (see **Figure 3**) [1]. **Table 2** provides the average strain estimated

**Figures 4** and **5** explain the measuring strategy to know electrical performance in foil ferrite samples labeled as FF-1, FF-2, and FF-3. Two conditions are performed, both longitudinal and transverse bias as shown in **Figures 4(a)** and **5(a)**, respectively. Current-voltage (I-V) curves are displayed in **Figure 4(b)** at longitudinal bias and at transverse bias in **Figure 5(b)**.

on each foil ferrite sample to inject and collect voltage signals. A resistor of 1 kΩ is used to measure the output voltage and thus calculate the current flow by Ohm's law. Ohmic behavior is observed in I-V curves for voltage bias from −2 to 2 V, while at higher voltages, I-V

Such power-law dependence is characteristic of space-charge-limited conduction (SCLC) [25]. Analysis in I-V curves by using a SCLC model is the experimental method used here

constant, *μ* is the carrier mobility, L is the spacing between electrodes, and S is the cross-

<sup>∆</sup>*<sup>θ</sup>* (

40.89° −5 × 10<sup>−</sup><sup>3</sup> −0.016

40.89° 44 × 10<sup>−</sup><sup>3</sup> 0.14

40.89° 44 × 10<sup>−</sup><sup>3</sup> 0.14

<sup>8</sup> *<sup>ε</sup>*<sup>0</sup> *<sup>ε</sup><sup>r</sup> <sup>S</sup> <sup>L</sup>*<sup>−</sup><sup>3</sup>

**\_\_\_**

−0.008

0.072

0.072

, where *ε*<sup>0</sup> *<sup>ε</sup><sup>r</sup>*

<sup>∆</sup>*dd* )*ZnO* (

**\_\_\_** ∆*d <sup>d</sup>* )*MnO*

−0.013

0.11

0.11

Two aluminum electrodes of circular geometry with cross section area of 3.14 *mm*<sup>2</sup>

curves indicate that current and voltage follow a power-law relationship *I* = *α V<sup>n</sup>*

with current-voltage dependence proportional to *<sup>α</sup>* <sup>=</sup> \_\_9

**2***ϕ* **(MnO)**

**Table 2.** Average strain in foil ferrites associated with ZnO and MnO.

stituent, a foil ferrite can be approximately seem as a structure MnO/*Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup>

from XRD patterns in foil ferrite samples.

**Table 1.** Structure parameters in foil ferrites.

**3.2. Electrical analysis**

196 Iron Ores and Iron Oxide Materials

sectional area.

**Sample 2***ϕ*

FF-1 34.42°

FF-2 34.42°

FF-3 34.42°

**(ZnO)**

62.86°

62.86°

62.86°

as their main con-

are placed

with n = 1.5.

is the dielectric

/ZnO where diffusion

**Figure 4.** (a) Schematic diagram of the foil ferrites in cross-sectional view connected in the test circuit. (b) Currentvoltage (I-V) curves of the three different foil ferrite samples, which are longitudinally biased.

**Figure 5.** (a) Schematic diagram of the foil ferrites in cross-sectional view connected in the test circuit. (b) Currentvoltage (I-V) curves of the three different foil ferrite samples, which are transversally biased.

To obtain conduction parameters in foil ferrite samples, the parameter *α* was initially calculated from I-V curves. Then, by tracing slopes on I-V curves, the critical voltage, *VC* <sup>=</sup> <sup>10</sup>*en <sup>L</sup>*<sup>2</sup> (*ε*<sup>0</sup> *εr*) −1 , and trap-filled limit voltage, *VTFL* <sup>=</sup> <sup>6</sup>*<sup>e</sup> Nt L*2 (*ε*<sup>0</sup> *εr*) −1 , are found as in earlier methodologies, where both carrier concentration, *n*, and trap concentration, *Nt* , has been well estimated [26, 27]. Also, adiabatic activation energy, ∆*G*<sup>∗</sup> , should be responsible for the diffusion processes (displacement reactions) during sintering cycle in processing technology of Mn-Zn bulk ferrites in contrast to the overall activation energy under SCLC. Theoretical studies have reported ∆*G*<sup>∗</sup> with value of 0.5 eV for pure hematite (*Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup> ) smaller than the activation energy of about 1 eV at *T* > 800° C for conductivity [28]; then as reference ∆*G*<sup>∗</sup> can be estimated as a function of *VC* for this analysis.

Thus, ∆*G*<sup>∗</sup> <sup>=</sup> 0.5 *VC* will be used to evaluate conduction properties in foil ferrite samples as a function of the mobility *μ*~*exp*(<sup>−</sup> ∆*G*<sup>∗</sup> \_\_\_\_\_ *kT* ), where k is the Boltzmann constant and T is equivalent at the processing temperature during sintering cycle. Finally, knowing *α* and *μ* parameters, *ε*<sup>0</sup> *<sup>ε</sup><sup>r</sup>* was estimated for both longitudinal and transverse bias. **Table 3** summarizes the conduction parameters at longitudinal bias where L = 2 mm, W = 1 mm (physical width of each foil ferrite under test), and *S* = *t* × *W* with *t* as the thickness previously estimated by XRD analysis in Section 3.1, while the conduction parameters at transverse bias are registered in **Table 4**, where L = 1 mm and *S* = 3.14 × 10<sup>−</sup><sup>2</sup> cm<sup>2</sup> is the cross section area of the aluminum electrodes.

**4. Foil ferrite as functional green device**

**Table 4.** Conduction parameters at transverse bias.

**4.1. Mixer circuit**

signals at low-power excitation [30].

(Matrix, MFG-8250A) was used to produce the input voltage signals.

**Sample** *α VC* **(***V***)** ∆*G*<sup>∗</sup> **(***eV***)** *VTFL* **(***V***)** *μ* **(***cm***<sup>2</sup>** *V***<sup>−</sup><sup>1</sup>** *s* **<sup>−</sup><sup>1</sup>**

FF-1 0.92 × 10<sup>−</sup><sup>4</sup> 1.12 0.56 2.32 5.49 × 10<sup>−</sup><sup>3</sup> 4.74 × 10<sup>−</sup><sup>4</sup> FF-2 1.82 × 10<sup>−</sup><sup>5</sup> 1.28 0.64 2.42 2.97 × 10<sup>−</sup><sup>3</sup> 1.73 × 10<sup>−</sup><sup>4</sup> FF-3 0.48 × 10<sup>−</sup><sup>5</sup> 1.12 0.56 2.56 5.49 × 10<sup>−</sup><sup>3</sup> 2.47 × 10<sup>−</sup><sup>5</sup>

Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green…

This section discusses the possibility of the functional green devices built by foil ferrite samples. Electrical performance under both longitudinal and transverse bias conditions has confirmed nonlinear behavior which obeys at the conduction properties through orderly small grained structure being it equivalent to the magnetic-electrical conduct of a self-inductor with hysteresis when it is connected as shown in **Figure 6**. Current-voltage (I-V) curves are obtained by using a digital storage oscilloscope (Tektronix, TDS1012C) at room temperature. A function generator

To connect the input signal and collect the output signal in the applications shown here, two

placed on each foil ferrite; also, a resistor has been used to measuring of the output signals.

Modulation is the process of converting information one wants to obtain into one or more properties of a sinusoidal signal called the carrier. This information can be analogic signal, such as a varying voltage or current, or a digital signal, which consists of sequence of bits, i.e., 0 and 1 values. In general several modulation schemes can be represented by using mixer

To disclose the performance of a foil ferrite as mixer circuit to modulation process, a basic schematic diagram of **Figure 7** has been built. A full-rectified signal with amplitude of 15 V was applied on first outer node at operating frequency of 120 Hz. In the middle node, a sinusoidal signal with amplitude of ±7.5 V at operating frequency of 500 Hz was applied. The full-rectified signal was obtained by a variable self-transformer of alternating voltage from 0 to 150 V. A resistor of 1 kΩ is connected in the second outer node to monitoring of mixing signal (see **Figure 7**). It is observed that the mixing signal follows the shape of the full-rectified signal when it is larger than the sinusoidal signal, producing an output signal with amplitude of ±3.5 V. Otherwise, when the amplitude of the sinusoidal signal is greater with respect to the full-rectified signal, mixing process is negligible, because there are strong anisotropy differences among longitudinal and transverse paths on foil ferrite samples related to its structural disorder. Therefore, a foil ferrite will operate in the electronic signal processors integrated by mixer circuits to drive control systems as a function of complex

circuits. The main type of modulator recently employed is the quadrature mixer [29].

have been

**)** *ε***<sup>0</sup>** *ε<sup>r</sup>* **(***F cm***<sup>−</sup>1)**

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199

aluminum electrodes of circular geometry with cross section area of 0.1 × 0.1 cm2

Chemical formula *Mnx Zny Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup> allows explaining structure and conduction properties in foil ferrites where magnetite *Fe*<sup>3</sup> *<sup>O</sup>*<sup>4</sup> is equivalent to *Fe* <sup>∙</sup> *Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup> with *Fe*+3 ion substituted by *Mn*+2 in the tetrahedral sites and *Zn*+2 in the octahedral sites. As radius of *Fe*+3 is smaller than that of *Zn*+2 and greater than that of *Mn*+2 , structural disorder will occur; therefore, exchange interactions via the oxygen ions will define magnetic properties as a function of the distance and angle of the Mn─O─Zn bonds; also, SCLC will depend on different conduction mechanisms related to the exponential distribution of defects (grain boundaries) [13, 27]. From results attained here, it is confirmed that the sample FF-1 exhibits lower ϵ2*<sup>θ</sup>* than FF-2 and FF-3 samples. Chemical composition approximately proportional to the average strain (*x*~( \_\_\_ ∆*d <sup>d</sup>* )*MnO* and *y*~( \_\_\_ <sup>∆</sup>*dd* )*Zno* ) in samples FF-2 and FF-3 resulted to be positive associated to tensile stress while negative in sample FF-1 related to compressive stress. In the samples, *x* and *y* are connected by the coupling type dominant in the Mn-O-Zn bonds, where tensile stress dominated by longer distance and angle of 180° is *antiferromagnetically coupled*, while compressive stress is *ferromagnetically coupled* at shorter distance with angle of 90° . The *VC* and *VTFL* voltages from **Tables 3** and **4** were extracted to evaluate the charge concentration (carrier distribution), resulting *n* in the range from 1020 to 1022 cm<sup>−</sup><sup>3</sup> at the surface while *Nt* in the range from 1015 to 1017 cm<sup>−</sup><sup>3</sup> at the bulk of each sample, which reveals that major differences of *ε*<sup>0</sup> *ε<sup>r</sup>* and magnetic ordering are correlating to the charge concentration differences of foil ferrites.


**Table 3.** Conduction parameters at longitudinal bias.


**Table 4.** Conduction parameters at transverse bias.
