Synthesis of New Complex Ferrite Li0.5MnFe1.5O4, Chemical – Physical and Electrophysical Research

In this article, the sol-gel method was used as a synthesis method, which shows the physico –chemical nature of the synthesis of a new complex material ferrit Li0.5MnFe1.5O4. The synthesized structure and structure were determined by the method of X-ray phase analysis. According to the analysis indicators, it was found that our compound is single-phase, spinel-structured, and syngony - cubic type. The microstructure of the compound and the quantitative composition of the elements contained were analyzed under a scanning electron microscope (SEM). Through a scanning electron microscope, Microsystems were taken from different parts of l Li0.5MnFe1.5O4-type crystallite, the elemental composition of crystals was analyzed, and the general type of surface layer of complex ferrite was shown. As a result, the fact that the compound consists of a single phase, the clarity of its construction was determined by the topography and chemical composition of the compound. As a result, it was found that the newly synthesized complex ferrites correspond to the Formula Li0.5MnFe1.5O4. The particles of the formed compounds have a large size (between 50.0 μm, 20.0 μm and 10.0 μm). Electro physical measurements were carried out on the LCR - 800 unit at intervals of 293-483 K and at frequencies of 1.5 and 10 kHz. The increase in frequency to 10 kHz led to a decrease in the value ε in the range of the studied temperature (293-483 K).

Keywords:

Subject: Chemistry and Materials Science - Materials Science and Technology

1. Introduction

Research in nanotechnology is a fast-growing field at the fore-front of physics and is attracting special interest from the scientific community [1]. Multifunctional materials, in particular, are investigated for their advantageous properties that are combined in one smart compound [2,3]. A broad range of intelli gent materials have been proposed and among them, ferrites have drawn significant attention and are deemed to be promoter hosts due to their extremely prominent features [4,5].

Doped mixed ferrites with impactful features like permeability, magnetic behavior, and magnetic transition at high temperatures are the soft ferrimagnetic compounds, which already mark their presence in the technology field. These materials are significant due to their imprudent magnetization at room environment [6,7].

The extensive use of spinel ferrites is due to their low price, easy fabrication and abundant use in technological and industrial applications [8]. The technological and industrial applications of these magnetic materials is because of their excellent electrical and magnetic properties, which leads to their use in magnetic memory devices, transformers, high frequency applications and electronic devices like cellular phones, video cameras, notebook computers [9].

Many researcher studied the structural, electrical and magnetic properties of various Li based ferrites like Li-Mn [10], Li-Ni [11], Li-Co [12], Li-Mg [13], Li-Cr [14], Li-Zn [15] and Li-Ti [16] prepared by ceramic method. However, Ferrite prepared by a ceramic method involves high calcination temperature synthesis for the completion of solid-state reaction between the constituent oxides or carbonates and the particles are obtained rather bigger and non-uniform in size. These non-uniform particles, on compacting, result in the formation of voids and subsequently the low density ferrites. To overcome these difficulties, the sol-gel method is the preferred method for synthesizing nanoferrit on a volumetric scale by obtaining homogeneous particles and the most convenient method for synthesizing nanoparticles. This is because the simplicity of this method, the low cost precursors, the fact that the annealing process is carried out in a short time, good control of the amount of crystallite and other properties of materials [17].

Nanoscale manganese ferrites exhibit interesting structural and magnetic properties. They have a wide range of applications, from basic research to industrial applications. In this work, the composition of ferrite nanoparticles is studied.

2. Materials and Methods

The sol - gel method was used as an effective way to synthesize a new mixed ferrite of a complex mixed composition. in order to determine the composition of a new complex mixed ferrite obtained by the sol - gel method, an X-ray phase study was carried out, and in order to conduct quantitative and qualitative analysis, an examination under a scanning electron microscope, a study of electrophysical properties (dielectric conductivity and electrical resistance) was carried out.

As a primary raw material, distilled water of the manganese (III) oxide (“chemical pure”) brand, Iron (III) oxide (“chemical pure”) brand and lithium conbanate (“chemical pure”) brand were used. Trihydric alcohol – glycerin and citric acid were used as gel-forming reagents. The raw materials obtained by stoichiometric calculation were weighed on an analytical balance with the highest accuracy of 0.0001 grams, mixed, ground in an agate sieve, placed in an Alund crucible and fired in a muffle furnace at a temperature of 1100ºС.

The resulting dried gel was fired in a muffle oven for 10 hours at a temperature of 600 ºC until a black powder was obtained. Finally, the resulting powder was fired in stages for 7 hours at a temperature of 700-1100 ºC in the air [18].

The pycnometric density of ferrites was determined by the method [19]. Toluene and distilled water were used as indifferent liquids. The density of composite materials was measured 5 times and the average values were calculated.

3. Results

3.1. X-ray Analysis

X-ray analysis was carried out at the Kazakh National Women’s Pedagogical University on the diffractometer Miniflex/600 (Rigaku). Analysis using a sika beam (U=30 KV, J=10 MA, rotation speed 1000 pulses per second, time constant t=5 sec., 2θ with an angle interval between 5 and 900) was carried out on the Miniflex 600 RIGAKU, filtered by a filter.,

During the X-ray observation of the synthesized mixed complex ferrite, it was observed that the amorphous state of the samples decreased, the crystallization process was complete, and the kinetics of the sol-gel reaction was low. In addition, it is proved from the diffractogram shown in Figure 1 below that the samples have changed from the amorphous state to the fully polycrystalline state, and the independent phase has been completely formed.

Below are the results of the Rietveld method of indexing the diffractogram of complex ferrite studied by X-ray analysis.

According to Scherrer’s formula, the average size of crystallites can be written as follows:

d = \frac{K λ}{β \cos θ}

(1)

where

d - average size of crystals;

K - dimensionless particle shape coefficient (Scherrer constant);

λ - is the wavelength of X-ray radiation;

β - half-height reflex width (2θ in radians and units)

θ - diffraction angle (Bragg angle)

A new complex mixed ferrite synthesized by X-ray phase analysis method has unit number Z = 8, Li0,5MnFe1.5O4 is crystallized in cubic wall - centered cell, and space group is Fd ̅3m. Cell parameters a = 8.3677, b = 8.3677, c = 8.3677. The average size of crystallites according to Scherrer’s formula through the X-ray wavelength of ferrite is 40.6 µm, and the correctness of the results of X-ray studies was confirmed by the coincidence of the values of X-ray and pycnometric densities.

3.2. Scanning Electron Microscope

A study was carried out using a scanning electron microscope (SEM) (APPLICATION Note team, Brooker, Germany) to study the spectrum of distribution of the element, quantitative and qualitative analysis, and the percentage content of emenets.

A scanning electron microscope (SEM) is designed to obtain a magnified image of an object by scanning it with an electron beam directed at it and recording the signal generated by the interaction of electrons with a detector. The small diameter of the probe, even at low accelerating voltages and high currents, allows for elemental analysis of samples with dimensions of the analyzed area of several tens of nanometers. The beam current detector is located on the microscope column below the aperture of the objective lens, so that the beam current can be monitored at any time during the analysis.

In order to study the morphology of the surface layer of the new complex mixed ferrite samples synthesized by the sol-gel method, a study was carried out using an electron microscope scanning the microstructures of the electric diffraction image. Electron monographs of the compound taken in an imaging electron microscope are given in Figure 2 a), b), c).

The above images show the results of micrographs taken at magnifications of 10.0μm, 20.0μm and 50.0μm, and also show the general appearance of the complex ferrite surface layer. As a result, the compound consists of one phase, the clarity of its structure was determined by the topography and chemical composition of the compound. Figure 3 shows the spectrum patterns of the newly synthesized mixed complex ferrite Li_0,5MnFe_1.5O₄ and the elemental analysis results of the Li_0,5MnFe_1.5O₄ compound.

Based on the distribution map of elements, on the basis of solving the nature of crystallization, the chemical composition with microstructure and distribution zones of chromium, iron, lithium, and oxygen atoms were studied. As a result of the numerical elemental composition study, it can be concluded that iron, chromium, lithium metals, oxygen, carbon atoms are distributed in the 10.0 μm regions (Figure 2 a). In an imaging electron microscope, it is possible to obtain nanoscale measurements of solids in powder form.

To study the spectrum of distribution of the element, quantitative and qualitative analysis, and the percentage content of emenets, a study was carried out using a scanning electron microscope. The spectrum samples of the synthesized new mixed complex Ferrite and the results of elemental analysis are shown in Figure 3.

3.3. Electrophysical Research

Measurements of electrophysical properties were carried out according to the methods [20,21].

The study of electrophysical properties (dielectric constant and electrical resistance) was carried out by measuring the electrical capacity of samples on a serial device LCR-800 (Taiwan) at an operating frequency of 1 kHz continuously in dry air in a thermostatic mode with a holding time at each fixed temperature.

Plane-parallel samples in the form of disks with a diameter of 10 mm and a thickness of 2-6 mm with a binder additive (1,5 %) were pre-manufactured. The pressing was carried out at a pressure of 20 kg/cm2. The resulting discs were fired in a laboratory furnace “SNOL” at 400 ° C for 6 hours. Then they were carefully double-sided sanded.

The dielectric constant was determined from the electrical capacity of the sample at known values of sample thickness and electrode surface area. The Sawyer-Tower scheme was used to obtain the relationship between the electric induction D and the electric field strength E. Visual observation of the D (E hysteresis loop) was carried out on an oscilloscope C1-83 with a voltage divider consisting of a resistance of 6 MOm and 700 kOm and a reference capacitor of 0.15 mcF. The frequency of the generator is 300 Hz. In all temperature studies, the samples were placed in an oven, the temperature was measured by a chromel-alumel thermocouple connected to a voltmeter B2-34 with an error of 0.1 mV. The rate of temperature change is 5 K/min. The value of the dielectric constant at each temperature was determined by the formula:

ε = \frac{C}{C_{0}}

(2)

where

С_{0} = \frac{ε_{0} \cdot S}{d}

is the capacitance of the capacitor without the test substance (air).

Calculation of the width of the forbidden zone (ΔE) of the substance under investigation is determined by the formula:

Δ E = \frac{2 k T_{1} T_{2}}{0.43 (T_{2} - T_{1})} \lg \frac{R_{1}}{R_{2}},

(3)

where k is the Boltzmann constant equal to 8,6173303·10-5 эВ·К-1, R1 is the resistance at T1, R2 is the resistance at T2.

To ensure the reliability of the data obtained, the dielectric constant of a standard substance, barium titanate BaTiO3, was measured at frequencies equal to 1 kHz, 5 kHz and 10 kHz. Table 1 below shows the results of measurements of the electrophysical characteristics of BaTiO3.

As can be seen from the data in Table 1, the values of dielectric constant at 293 K at frequencies of 1 kHz and 5 kHz are in satisfactory agreement with its recommended value of 1400 ± 250. In addition, the observed changes in the electrical conductivity of BaTiO3 at 383 K at all frequencies (1 kHz, 5 kHz and 10 kHz) are also consistent with its transition from the perovskite cubic phase Pm3m to the tetragonal (polar) ferroelectric phase with space group P4mm [26–28].

It should be noted that despite the reduced values of the dielectric constant of BaTiO3 at a frequency of 10 kHz, and at T equal to 293 K, 303 K, 313 K, all values of ε BaTiO3 at all three frequencies (1 kHz, 5 kHz and 10 kHz) in the range 313-483 K have approximately the same values up to 2150, which indicates that that the frequency change does not particularly affect the temperature dependence of the dielectric constant of BaTiO3 in the range 313-483 K.

Electrophysical measurements of Li_0.5MnFe_1.5O₄ in the range of 293-483 K and frequencies equal to 1, 5 and 10 kHz were carried out at the LCR installation (Table 3, Figure 4)

The data in Tables 3 and Figure 4 show that the value of the dielectric constant (ɛ) reaches a maximum value at 383 K, equal to 1.43·106 (1 kHz). Then they decrease to 6140 at 483 K (frequency 1 kHz). Increasing the frequency to 5 and 10 kHz leads to a decrease in ɛ in the entire temperature range under study (293-483 K).

The study of the temperature dependence of electrical resistance shows the complex nature of conductivity: at ∆T = 293-313 K – semiconductor, at ∆T = 313-333 K – metallic, at 333-393 K – semiconductor, at ∆T = 393-453 K – metallic and at ∆T = 453-483 K – again semiconductor.

a)

Calculation of the width of the forbidden zone (∆E) in the range 293-313 K:

Т, К	lg R
293	5,22
313	5,01

Δ E = \frac{2 \times 0,000086173 \times 293 \times 313}{0,43 (313 - 293)} \lg \frac{5,22}{5,01} = 1,91 э В

b)

Calculation of the width of the forbidden zone (∆E) in the range 333-393 K:

Т, К	lg R
333	5,31
393	3,91

Δ E = \frac{2 \times 0,000086173 \times 333 \times 393}{0,43 (393 - 333)} \lg \frac{5,31}{3,91} = 1,19 э В

c)

Calculation of the width of the forbidden zone (∆E) in the range 453-483 K:

Т, К	lg R
453	5,94
483	5,71

Δ E = \frac{2 \times 0,000086173 \times 453 \times 483}{0,43 (483 - 453)} \lg \frac{5,94}{5,71} = 3,04 э В

The band gap of the material 2 at ∆T = 293-313 K and 333-393 K are equal to 1.91 and 1.19 eV, respectively (narrow-band semiconductor), and at ∆T = 453-483 K is equal to 3.04 eV (wide-band semiconductor).

4. Conclusions

Summing up the results of the study, a new mixed complex ferrite with the composition Li_0.5MnFe_1.5O₄ was synthesized for the first time by the Sol – gel method. In order to determine the composition of the resulting new complex mixed ferrite, an X-ray phase study was carried out, and in order to conduct quantitative and qualitative analysis, an examination under a scanning electron microscope, a study of electrophysical properties (dielectric conductivity and electrical resistance) was carried out.

For the first time, syngony types and parameters of elementary cells of a complex mixed Ferriter synthesized by the method of X-rayophase analysis were determined. Li_0.5MnFe_1.5O₄ (cubic, a=8.3677(9), B= 8.3677(9), C=8.3677(9) Å , Z=8, denX-ray = 4.678 g/cm3, denPycno = 4.675 g/cm3); through the X-ray wavelength of Ferrite, the average size of crystallites according to Scherrer’s formula is 40.6 µm. The results of radiographic research showed that the synthesized compound is polycrystalline. The accuracy of crystallochemical data is evidenced by a satisfactory correspondence of X-ray and pycnometric densities.

Through a scanning electron microscope, Microsystems were taken from different parts of Li_0.5MnFe_1.5O₄ type crystallite, the elemental composition of crystals was analyzed, and the general type of surface layer of complex ferrite was shown. As a result, the fact that the compound consists of a single phase, the clarity of its construction was determined by the topography and chemical composition of the compound. As a result, it was found that the newly synthesized complex ferrites correspond to the formula Li_0.5MnFe_1.5O₄. The particles of the formed compounds have a large size (between 50.0 µm, 20.0 µm and 10.0 µm). The results of the elemental analysis were presented in the form of a table.

Electrophysical measurements of Li_0.5MnFe_1.5O₄ on the LCR - 800 unit were carried out at intervals of 293-483 K and frequencies of 1.5 and 10 kHz.

The fact that 293 K is equal to a relatively high value of 2.69*105 at 1 kHz, the maximum value of 383 K reached 1.43*106. Next, they are reduced to 6140 at 483 K (frequency of 1 kHz). An increase in frequency to 5 and 10 kHz leads to a decrease in the entire test temperature interval (293-483 K).

The study of the dependence of electrical resistance on temperature shows the complex nature of conductivity: t = 293-313 K-semiconductor, t = 313-333 K – Metal, 333-393 K-semiconductor, t = 393-453 K-Metal and T = 453-483 K – semiconductor again.

Supplementary Materials

The following supporting information can be downloaded at the website of this paper posted on Preprints.org.

Funding

Please add: This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare no conflict of interest

References

Hossain, M.D., Jamil, A. T. M. K., Hossain, M. S., Ahmed, S. J., Das, H. N., Rashid, R., Khan, M. N. I. Investigation on structure, thermodynamic and multifunctional properties of Ni–Zn–Co ferrite for Gd3+ substitution. RSC Adv., 2022. 12, 4656. [CrossRef]
Gonçalves, J. M., Silva, M. N., Naik, K. K., Martins, P. R., Rocha, D. P., Nossol, E., Rout, C. S. Multifunctional spinel MnCo₂O₄ based materials for energy storage and conversion: a review on emerging trends, recent developments and future perspectives. J. Mater. Chem.,2021, 9, 3095. [CrossRef]
Yao, C., Ismail, M., Hao, A., Thatikonda, S. K., Huang, W., Qin, N., Bao, D. Annealing atmosphere effect on the resistive switching and magnetic properties of spinel Co3O4 thin films prepared by a sol–gel technique. RSC Adv., 2019, 9, 12615. [CrossRef]
Chandel, M., Moitra, D., Makkar, P., Sinha, H., Hora, H. S., Ghosh, N. N. Synthesis of multifunctional CuFe₂O₄–reduced graphene oxide nanocomposite: an efficient magnetically separable catalyst as well as high performance supercapacitor and first-principles calculations of its electronic structures. RSC Adv., 2018, 8, 27725. [CrossRef]
Li, Z., Wang, Z. L., Wang, Z. In situ tuning of crystallization pathways by electron beam irradiation and heating in amorphous bismuth ferrite films. RSC Adv., 2018, 8, 23522. [CrossRef]
Nilar, L., Fauzi, M.A.N., Sreekantan, S., Othman, R. Physical and electromagnetic properties of nanosized Gd substituted Mg–Mn ferrites by solution combustion method. PhysicaB. 2015 461, 134, . [CrossRef]
XiuBo, X., Wang, B., Wang, Y., Ni, C., Sun, X., Du, W. Spinel structured MFe₂O₄ (M = Fe, Co, Ni, Mn, Zn) and their composites for microwave absorption: A review. Chem. Engg. Journ. 2022, 428 , 131160, . [CrossRef]
Ahmad, I., Farid, M.T. Characterization of cobalt based spinel ferrites with small substitution of gadolinium. World Appl. Sci. J. 2012. 19, 464. [CrossRef]
Fu, Y.P., Lin, C.H., Liu, C.W. Preparation and magnetic properties of Ni_0.25Cu_0.25Zn_0.5 ferrite from microwave-induced combustion. J. Magn. Magn. Mater. 2004. 283, 59. [CrossRef]
Ravinder, D., Balachander, L., Venudhar, Y. C. Electrical conductivity in manganese-substituted lithium ferrites. Mater. Lett. 2001. 49, 267. [CrossRef]
Trivedi, U. N., Jani, K. H., Modi, K. B., Joshi, H. H. Study of cation distribution in lithium doped nickel ferrite. J. Mater. Sci. Lett. 2000. 19, 1271.
Abo El Ata, A. M., Attia, S. M., El Kony, D., Al-Hammadi, A. H. Spectral, initial magnetic permeability and transport studies of Li_0.5−0.5xCo_xFe_2.5−0.5xO₄ spinel ferrite. J. Magn. Magn. Mater. 2005. 295, 28. [CrossRef]
Ravinder, D., Reddy, P. V. B. Thermoelectric power studies of polycrystalline magnesium substituted lithium ferrites. J. Magn. Magn. Mater. 2003. 263, 127. [CrossRef]
Laishram, R., Prakash, C. Magnetic properties of Cr³⁺ substituted Li–Sb ferrites. J. Magn. Magn. Mater. 2006. 305, 35. [CrossRef]
Sattar, A.A., El-Sayed, H.M., Agami, W.R., Ghani, A.A. Magnetic properties and electrical resistivity of Zr⁴⁺ substituted Li-Zn ferrite. Am. J. Appl. Sci. 2007. 4 (2) 89. 16.
Surzhikov, P., Pritulov, A. M., Ivanov, Yu F., Shabardin, R. S., Usmanov, R. U. Electron-Microscopic Study of Morphology and Phase Composition of Lithium-Titanium Ferrites. Russ. Phys. J. 2001. 44 (4) 420.
Mataev, M.М., Madiyarova, A.M., Patrin , G.S., Abduraimova, М.R., Nurbekova, M.A., Tursunova, Zh.I. Synthesis and physico – chemical characteristics of complex ferrite CrNaFe₂O₅. Chem. J. Kaz., 2024, 1(85), 109-118. [CrossRef]
Mataev, M.M., Mustafin, E. S., Kasenov, R. Z., Pudov, A. M., Kaikenov, D. A., Bogzhanova, Zh. K. X ray Diffraction Study of the YbM^IIFe₅O₁₂ (MII = Mg, Ca, Sr) Ferrites. Inorganic Materials, 2014, Vol. 50, No. 6, pp. 622–624. [CrossRef]
Mataev, M. M, Abdraimova, M.R., Saxena, S.X., Nuketaeva, D.Zh., Zheksembieva, B.T. Syntesis and X-Ray analysis of complex ferrites. Key Engineering Materials, -2017,-Vol.744? pp 393-398.
Okazaki, K. Technology of ceramic dielectrics. − M.: Energiya, 1976. – 256 p.
Kasenov, B.K.; Kasenova, S.B.; Sagintaeva, Z.I.; Baisanov, S.; Lu, N.Y.; Nukhuly, A.; Kuanyshbekov, E.E. Heat Capacity and Thermodynamic Functions of Titanium-Manganites of Lanthanum, Lithium and Sodium of LaLi₂TiMnO₆ and LaNa₂TiMnO₆. Molecules 2023, 28, 5194. [CrossRef]
Fesenko, E.G. The perovskite family and ferroelectricity. M.: Atomizdat, 1972.
Venevtsev, Yu.N., Politova, E.D., Ivanov, S.A. Ferroelectric and antisegnetoelectrics of the barium titanate family. Moscow: Chemistry, 1985.
Lines, M., Glass, A. Ferroelectrics and related materials. Moscow: Mir, 1981.

Figure 1. X-ray diffractogram of the complex ferrite Li0,5MnFe1.5O4. Insert: phase ratio diagram.

Figure 2. Image of the new mixed complex ferrite Li_0,5MnFe_1.5O₄ measured with three different micrometer accuracy.

Figure 3. Spectrum samples of the Li_0,5MnFe_1.5O₄ compound. The results of the element analysis are built-in.

Figure 4. Dependence of dielectric constant (a) and electrical resistance (b) on temperature and frequency equal to 1 kHz.

Table 1. Symmetry type and unit cell parameters of Li_0,5MnFe_1.5O_4.

Sample	Li_0,5MnFe_1.5O₄
Space group	$F \bar{d} 3 m$ , cubic side centered
Z Parameter cell (Å) a = b = c = V(A^3) α β γ According to Scherrer’s formula, the average size of crystallites is X-ray density (g/cm3) Pycnometric density (g/cm3)*	8 8.3677(9) 8.3677(9) 8.3677(9) 585.90(11) 90 90 90 40.6 μm 4.678 4.675

Table 2. Dependence of electrical resistance (R), electrical capacity (C) and dielectric constant (ε) on BaTiO₃ temperature.

Т, К	C, nF	R, Oм	ε	lgε	lgR
Measurement frequency at 1 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	0,27278 0,27426 0,27715 0,28125 0,28772 0,29313 0,29916 0,30751 0,31202 0,31702 0,32255 0,32967 0,3423 0,35119 0,36668 0,38018 0,39802 0,4169 0,43147 0,45456	13400 13270 12910 12560 11890 11210 10290 9383 8831 9061 8814 7881 7098 6902 6153 6317 6010 5584 5149 4656	1296 1303 1316 1336 1367 1392 1421 1461 1482 1506 1532 1566 1626 1668 1742 1806 1891 1980 2050 2159	3,11 3,11 3,12 3,13 3,14 3,14 3,15 3,16 3,17 3,18 3,19 3,19 3,21 3,22 3,24 3,26 3,28 3,30 3,31 3,33	4,13 4,12 4,11 4,10 4,08 4,05 4,01 3,97 3,95 3,96 3,95 3,90 3,85 3,84 3,79 3,80 3,78 3,75 3,71 3,67
Measurement frequency at 5 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	0,25678 0,2683 0,2775 0,28638 0,29667 0,30226 0,30787 0,31283 0,31843 0,32148 0,32578 0,32976 0,33303 0,33948 0,35613 0,3713 0,3925 0,41682 0,44245	29630 21650 13080 5236 4301 4733 3296 2966 2805 2529 2669 3172 4434 6377 9644 11520 10430 8021 5978 3799	1220 1274 1318 1360 1389 1409 1436 1462 1486 1513 1527 1547 1566 1582 1613 1692 1764 1864 1980 2102	3,09 3,11 3,12 3,13 3,14 3,15 3,16 3,17 3,17 3,18 3,18 3,19 3,19 3,20 3,21 3,23 3,25 3,27 3,30 3,32	4,47 4,34 4,12 3,72 3,63 3,68 3,52 3,47 3,45 3,40 3,43 3,50 3,65 3,80 3,98 4,06 4,02 3,90 3,78 3,58
Measurement frequency at 10 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	0,11814 0,18494 0,22927 0,25954 0,27501 0,28531 0,29302 0,29988 0,30652 0,31215 0,31667 0,32294 0,32779 0,33406 0,34256 0,35658 0,378 0,39475 0,41687 0,44203	152300 70790 32200 11870 4842 3312 2689 2257 1946 1689 1737 3130 5945 8231 8805 8052 5967 4604 3343 2353	561 878 1089 1233 1306 1355 1392 1424 1456 1483 1504 1534 1557 1587 1627 1694 1796 1875 1980 2100	2,75 2,94 3,04 3,09 3,12 3,13 3,14 3,15 3,16 3,17 3,18 3,19 3,19 3,20 3,21 3,23 3,25 3,27 3,30 3,32	5,18 4,85 4,51 4,07 3,69 3,52 3,43 3,35 3,29 3,23 3,24 3,50 3,77 3,92 3,94 3,91 3,78 3,66 3,52 3,37

Table 3. Dependence of electrical capacity (C), electrical resistance (R) and dielectric constant (ε) of material 2 on temperature and frequency.

Т, К	C, nF	R, Oм	ε	lgε	lgR
Measurement frequency at 1 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	7,7977 10,302 15,68 12,489 8,1684 14,516 86,933 176,65 265,14 378,56 495,27 312,87 11,039 1,8105 0,95809 0,68585 0,70009 0,89737 1,3483 2,1329	165700 135800 101700 131900 203600 121200 32510 19300 14110 10520 8184 10720 85500 379400 649900 843600 874900 796100 666100 511600	22448 29658 45140 35954 23515 41789 250266 508547 763295 1089813 1425802 900702 31779 5212 2758 1974 2015 2583 3882 6140	4,35 4,47 4,65 4,56 4,37 4,62 5,40 5,71 5,88 6,04 6,15 5,95 4,50 3,72 3,44 3,30 3,30 3,41 3,59 3,79	5,22 5,13 5,01 5,12 5,31 5,08 4,51 4,29 4,15 4,02 3,91 4,03 4,93 5,58 5,81 5,93 5,94 5,90 5,82 5,71
Measurement frequency at 5 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	1,3926 1,8886 2,728 1,517 0,9064 2,5719 15,47 31,031 45,909 64,608 82,944 40,501 1,7403 0,28075 0,13233 0,09429 0,09084 0,10483 0,13985 0,19866	140100 115400 89690 128100 184900 93070 29090 17900 13060 9799 7702 11420 79660 293500 455500 533500 555900 536400 477500 401900	4009 5437 7853 4367 2609 7404 44536 89333 132165 185996 238782 116596 5010 808 381 271 262 302 403 572	3,60 3,74 3,90 3,64 3,42 3,87 4,65 4,95 5,12 5,27 5,38 5,07 3,70 2,91 2,58 2,43 2,42 2,48 2,60 2,76	5,15 5,06 4,95 5,11 5,27 4,97 4,46 4,25 4,12 3,99 3,89 4,06 4,90 5,47 5,66 5,73 5,74 5,73 5,68 5,60
Measurement frequency at 10 kHz
293 303 313 323 333 343 353 363 373 383 393 403 413 423 433 443 453 463 473 483	0,62512 0,85581 1,188 0,50394 0,3238 1,2082 7,2162 14,584 21,676 30,192 39,355 14,483 0,64942 0,12128 0,06145 0,04865 0,04694 0,05137 0,06369 0,08415	126300 103700 83510 127500 169200 76460 26640 16680 12440 9304 7426 12940 83960 243700 329700 351900 362500 360400 339200 306100	1800 2464 3420 1451 932 3478 20774 41985 62402 86918 113297 41694 1870 349 177 140 135 148 183 242	3,26 3,39 3,53 3,16 2,97 3,54 4,32 4,62 4,80 4,94 5,05 4,62 3,27 2,54 2,25 2,15 2,13 2,17 2,26 2,38	5,10 5,02 4,92 5,11 5,23 4,88 4,43 4,22 4,09 3,97 3,87 4,11 4,92 5,39 5,52 5,55 5,56 5,56 5,53 5,49

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

MDPI Initiatives

Important Links

Choose an area of interest and we will send you notifications of new preprints at your preferred frequency.

Disclaimer