ISSN 10613862, International Journal of SelfPropagating HighTemperature Synthesis, 2015, Vol. 24, No. 2, pp. 63–71. © Allerton Press, Inc., 2015.
SolutionCombustion Synthesis and Magnetodielectric Properties of Nanostructured Rare Earth Ferrites A. A. Saukhimova, b, M. A. Hobosyana, G. C. Dannangodaa, N. N. Zhumabekovab, G. A. Almanova, b, S. E. Kumekovb, and K. S. Martirosyana* aDepartment
of Physics and Astronomy, University of Texas at Brownsville, 1 W University Blvd, Brownsville, Texas, 78520 USA bSatpayev Technical University, Almaty, 050013 Kazakhstan email: *
[email protected] Received January 6, 2015
Abstract—Rare earth ferrites exhibit remarkable magnetodielectric properties that are sensitive to the crys tallite size. There is a major challenge to produce these materials in nanoscale due to particles conglomeration during the ferrite nucleation and synthesis. In this paper we report the fabrication of nanostructured particles of rare earth ferrites in the Me–Fe–O system (Me = Y, La, Ce, and Sm) by SolutionCombustion Synthesis (SCS). The yttrium, lanthanum, cerium, samarium and iron nitrates were used as metal precursors and gly cine as a fuel. Thermodynamic calculations of Y(NO3)3–2Fe(NO3)3–nC2H5NO2 systems producing Y3Fe5O12 predicted an adiabatic temperature of 2250 K with generating carbon dioxide, nitrogen and water vapor. The considerable gas evolution helps to produce the synthesized powders friable and loosely agglom erated. Adjusting the glycine/metal nitrates ratio can selectively control the crystallite size and magnetodi electric properties of the ferrites. Increasing the glycine content increased the reaction temperature during the SCS and consequently the particle size. Magnetization of zerofieldcooled (ZFC) and fieldcooled (FC) ferrites in the temperature range of 1.9–300 K showed different patterns when the fraction of glycine was increased. Analysis of ZFC and FC magnetization curves of annealed samples confirmed that nanoparticles exhibit superparamagnetic behavior. The increasing concentration of glycine leads to escalation of blocking temperature. Reduction of dielectric permittivity (εr) toward frequency indicates the relaxation processes in the composites, and the values of εr are shifted upward along the operating temperature. Keywords: solutioncombustion synthesis, rare earth ferrites, magnetodielectric properties DOI: 10.3103/S1061386215020065
The crystallite structure, size, and potential appli cations of rareearth ferrites are strongly influenced by synthesis procedure; therefore a lot of research is aimed both at its processing and application. Rare earth ferrites are often prepared from high tempera ture solidstate reactions of the corresponding simple oxides [3]. However, this process suffers from excessive particle growth, irregular stoichiometry, and forma tion of undesirable phases. Other synthesis routes have also been proposed including chemical precipitation [11], thermal decomposition [12], chemical vapor deposition [13], sonochemical [14, 15] and combus tion synthesis [16, 17].
1. INTRODUCTION One of the main advantages of rare earth ferrites is high electrical resistivity in combination with a suffi ciently high value of magnetic permeability and low power losses, which defines a growing interest for elec tronic applications [1]. Magnetic saturation of ferrites is slightly less compared to the metal magnetic materi als, which allows their use at high frequencies in low induction circuits. Extensive studies indicate the pros pects of such materials for creating magnetic field sen sors, recording and reading devices, and microwave applications [2, 3]. Recent studies also demonstrate that the yttrium ferrite displays electrical and magnetic coupling which shows ferroelectricity near the ferri magnetic transition temperature around 250 K [4]. In addition, LaFeO3 displays significant electrochemical properties making them to be used in advanced tech nologies such as solid oxide fuel cells [5], catalysts [6], chemical sensors [7], photocatalysis [8, 9] and biosen sors [10].
Solutioncombustion synthesis (SCS) is a simple and rapid chemical processing technique suitable for producing a variety of nanosize materials ( 34 wt %, Tad slowly decreases due to oxygen deficiency. Thus, thermody namic calculations confirm the possibility of exother mic reaction in the Y(NO3)3–2Fe(NO3)3–nC2H5NO2 system. 3. EXPERIMENTAL Highpurity metal nitrates (99.9%) and iron(III) nitrate nonahydrate (98%) were used as oxidizers while glycine, CH2NH2CO2H, was used as a fuel to prepare rare earth ferrite nanoparticles via (nitrate– glycine) solutioncombustion synthesis. The chemi cals were purchased from SigmaAldridge and used without further purification. In conventional SCS, both fuel and oxidizer are dissolved in water to form a homogeneous solution. The metal nitrates and glycine were added to 3 mL dis tilled water in a beaker and stirred for one hour. The aqueous solution was then heated on a hotplate to slowly evaporate the water away. During the final stages of evaporation, boiling, frothing, smoldering, flaming, and fumes were observed, resulting in forma tion of nanocrystalline complex oxides. The local com bustion temperature (Tc) was measured by an Stype (Pt–Rh) thermocouple (0.1 mm in diameter) that was inserted in the sample center. Thermocouple readings were recorded and processed by an Omega data acqui sition board connected to a PC. Differential scanning calorimetry (DSC) of the mixtures was used to identify phase transitions and chemical reactions that occurred under an air atmo sphere over the temperature range 20–1000°C (heat ing rate 20°C/min). To increase crystallinity of the pow der and enhance the magnetic properties, the synthe sized ferrites were annealed under air at 1000°C for 1 h. The composition and crystal structure of the prod ucts were determined by Xray diffraction (Siemens D5000 diffractometer) with Cu radiation (1.54056 Å). Scans were taken at room temperature over 5 < 2θ < 80° at 0.05° intervals. Particle morphology and electron microprobe analysis were determined by HighReso lution Transmittal Electronic Microscopy (HRTEM, JEOL JEM2000 CX2). A Coulter SA 3100 BET ana lyzer was used to measure particle size and surface area distributions. Magnetic properties of ferrites were determined by vibrating sample magnetometer by using Physical Property Measurement System (PPMSEverCoolII, Quantum Design, USA). Saturation (Ms), remnant
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FeO(l)
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Adiabatic Temperature, K
Combustion Products, wt %
(b)
10 20 30 40 Glycine Concentration, wt %
0 50
Fig. 1. Adiabatic temperature and equilibrium concentration of condensed and gaseous combustion products as a function of gly cine concentration for Y(NO3)3–2Fe(NO3)3–nC2H5NO2 systems producing YFeO3 (a) and Y3Fe5O12 (b).
magnetization (Mr), and coercivity (Hc) were esti mated from the hysteresis loops obtained at 5 and 300 K under maximum applied magnetic field of ±9 T. Zerofieldcooled (ZFC) and fieldcooled (FC) mag netization curves were measured from 1.9–300 K using 100 Oe magnetic field. Study of the dielectric properties of the ferrites were conducted by precision meter LCR E4980A, over a frequency range of 100 kHz– 2 MHz (accuracy of 0.05%) with changing tempera ture from 300 to 550 K. These experiments were per formed in capacitor shape samples. The electrode material (Ag) was deposited by the screenprinting technique. 3. RESULTS AND DISCUSSION The oxidizer (yttrium and iron nitrates) to fuel (glycine) ratio in the molten solution had a strong impact on the temperature rise, reaction time and par ticle size. Adjusting the ratio of glycine to metal nitrates allowed the combustion temperature to be tuned and controlled. Lower concentrations of glycine
were found to generate lower temperatures that may lead to metastable products with smaller particle size. To conduct safe and controlled combustion reactions, mixtures with less than 10 g of metal nitrates/glycine were used. Liquefied metal nitrates and glycine formed a clear homogeneous solution after mixing. The mix ture boiled, frothed, and then ignited, releasing large amounts of gases and produced brown nanoparticles. The maximum reaction temperature for synthesis of Y3Fe5O12 by using three different concentrations of glycine—n = 3, 6, and 10 wt %—were 257, 279 and 300°C, respectively [24]. These values are lower than the adiabatic temperatures predicted by thermody namic analysis. This indicates that during the combus tion the heat losses were significant. Similar as described in [25] the process may be divided into four different stages, each with different characteristic temperature gradient. The duration of stage (I) of pre heating the precursors is longer (2–5 min) than the other stages. It is characterized by degeneration of the metal nitrates. During the second stage (II) melting of the metal nitrate and glycine occurs. The third stage
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Heat Flow, W/g
–120 773.91°C 304.57°C 0 57.34°C 120.00 J/g 90.31 J/g –1 –110 752.43°C –2 110.61°C 349.77°C 97.09 J/g –100 –3 –4 –90 27.82% –5 29.48% –6 –80 –7 –8 –70 0 400 800 1000 200 600 Exo Up Temperature, °C (b) 0 67.61°C –120 38.66 J/g
–2
113.15°C
330.03°C 56.05 J/g
400.80°C
780.80°C
–110 758.62°C 97.31 J/g
–100
–3 –4
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–5
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–6 –7 0 Exo Up
Weight, %
Heat Flow, W/g
–1
Weight, %
(a)
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600 400 800 Temperature, °C
–70 1000
–120
–2 –4 –6 –8 –10 –12 –14 –16 –18 –20
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811.78°C 29.81 J/g
–100
15.91% 1.992%
200
–110
600 400 800 Temperature, °C
–90
Weight, %
Heat Flow, W/g
(c)
–80 1000
Fig. 2. TG and DTA results for Y(NO3)3–2Fe(NO3)3– nC2H5NO2 systems with n = 3 (a), 6 (b), and 10 wt % (c).
(III) is a combustion stage in which volume combus tion occurs with a temperature rise rate of ΔT/Δt = 20–30°C/s. The duration of this stage was about 3–6 s. After cooling stage (IV), the products were obtained as fine ferrite powders. The TG and DTA curves are shown in Fig. 2. The main weight loss is seen to occur at about 500°C: for n = 3 wt %, 27.82 % (total 29.48%); for n = 6 wt %,
22.23% (total 24.3%), and for n = 10 wt %, 10.73 % (total 15.91%). The observed weight loss was attrib uted to incomplete combustion reactions during the synthesis. Therefore, for the sample with n = 10 wt %, the combustion reaction was observed to be more complete. For the first two samples, the heat curves show two endothermic peaks, the first peak (120 J/g and 39 J/g for n = 3 and 6 wt %, respectively) corre sponding to evaporation of remnant water, and the second one (90 J/g and 56 J/g, respectively) to the final decomposition of remnant nitrates. At 780°C for both samples we observe an exothermic peak without any change in weight curves, which indicates a phase transformation. The phase transformation is irrevers ible, since after cooling the sample and reheating it there is no characteristic exothermic peak. For the third sample with n = 10 wt % we do not observe an endotherm peak demonstrating that the conversion to the product was considerably completed. This indi cates that less moisture and nitrate phases remains after the combustion than for the other two samples. Additionally, a small weight loss is observable prior to phase transformation at 2% for 770°C which is absent in the other samples. We attribute this feature to excess glycine trapped in the powder that eventually reacts with the oxygen in the air. Thus, greater amount of gly cine enhances the decomposition rate of metal nitrates which helps nucleation of the ferrites. The TG/TDA results clearly demonstrate the effectiveness of the selfsustaining combustion for the preparation of yttrium ferrites. Figure 3 shows the diffraction patterns of assyn thesized yttrium ferrite for different n and of those annealed at 1000°C. A broad diffraction peak was found for all samples indicating the amorphous nature of the product. After annealing at 1000°C the diffrac tion patterns exhibit intense reflections thus confirm ing the presence of singlephase Y3Fe5O12 with a gar net structure (standard database JCPDS, 33363). The crystallite size of yttrium ferrites nanoparticles was calculated using the Scherrer equation [22] based on Xray diffraction line broadening: d = Bλ/βcosϕ, (4) where d is the average crystallite size of the phase under investigation, B the Scherrer constant (0.89), λ the wavelength of Xray beam used, β is the full width at half maximum (FWHM) of the diffraction peak, and θ Bragg’s angle. Cristallite sizes were calcu lated to be 24, 47 and 72 nm for powders obtained with n = 3, 6, and 10 wt %, respectively, and annealed at 1000°C. Thus, the crystallite size of yttrium ferrite was larger at elevated glycine concentrations and conse quently higher combustion temperatures. Nitrate/glycine combustion caused considerable gas evolution, mainly carbon dioxide, N2, and H2O vapor, which caused the synthesized powders to become friable and loosely agglomerated. Particle size distribution and the particles surface area were deter
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(b)
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50
0
0 10 20 30 40 50 60 70 80 90100110 2θ, deg
10 20 30 40 50 60 70 80 90100 110 2θ, deg
(c)
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67
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800
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(d)
(e)
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(f)
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200
200 0
0 10 20 30 40 50 60 70 80 90100110 2θ, deg
0 10 20 30 40 50 60 70 80 90100110 2θ, deg
10 20 30 40 50 60 70 80 90100110 2θ, deg
Fig. 3. Diffraction patterns of assynthesized yttrium ferrites: n = 3 (a), 6 (b), and 10 wt % (c) and of those annealed at 1000°C: n = 3 (d), 6 (e), and 10 wt % (f).
mined by using a Coulter SA 3100 Brunauer– Emmett–Teller (BET) analyzer. BET analysis of as synthesized yttrium ferrite particles confirms that for increasing glycine concentration from 3 wt % up to 10 wt % the specific surface area of product decreases monotonically from 42.1 to 18.2 m2/g. Thus, decreas ing the fuel concentration decreases the maximum combustion temperature and increases particles sur face area.
(a)
By using BET measured specific surface area of the powder we can estimate the product average particle size. The specific surface area of a nonporous spherical parti cle is inversely proportional to its diameter (D): D = 6/ρS,
20 nm
(5)
where S is the specific surface area [m2/g] and ρ the theoretical density, [g/m3]. Experiments determined S to be varied from 18.2 to 42.1 m2/g. Assuming that the assynthesized yttrium ferrite particles are spherical with density ρ = 5.17 g/cm3, their size is predicted to be ~27 nm at n = 3 wt % and ~64 nm at n = 10 wt %. The particles morphology of assynthesized yttrium ferrite prepared with 3 wt % gly is shown in Fig. 4. Higher magnification of the products shows that the agglomerates contained ~20 nm particles with smooth surfaces. SCS caused considerable gas evolution gen erating many pores so that the assynthesized powders became homogeneously agglomerated. All combus tion products were friable, and had a spongy porous structure with porosity of up to 80%. Concentration of residual carbon was lower than 1 wt %.
(b)
5 nm
Fig. 4. TEM images of yttrium ferrite powder produced at n = 3 wt %.
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3% ZFC 3% FC 6% ZFC 6% FC 10% ZFC 10% FC
0.06 0.05 M, emu/g
3, 6, and 10 wt %, respectively. The diameter of spher ical particles (D) can be derived from the formula:
0.04
D = (6V/π)1/3.
0.03 0.02 0.01 0 0
50
100
150 T, K
200
250
300
Fig. 5. Zerofieldcooled (ZFC) and fieldcooled (FC) curves for assynthesized yttrium ferrites at n = 3, 6, and 10 wt % (H = 100 Oe).
Magnetic Properties of Yttrium Ferrite The study of the magnetic properties of produced materials was performed by measuring dependence of magnetization (M) on temperature, and on magnetic field strength (H) under 5–300 K. The results of mag netization measurements presented in Fig. 5 show dif ferent patterns of behavior with an increase in n. Dif ference between ZFC and FC curves indicates super paramagnetic behavior of nanoparticles. As it is commonly understood, magnetic moments of super paramagnetic particles are chaotically oriented in a matrix in the absence of magnetic field, and the total magnetic moment of the sample is zero. When cooling in the absence of magnetic field, the particle moments are ‘frozen’ at some certain blocking temperature (Tb), meanwhile their distribution in a matrix remains chaotic, and the total moment is zero as before. Block ing temperature Tb depends on the volume of the par ticles and their anisotropy. If the anisotropy stays the same, Tb depends only on the volume, the bigger the particle volume the higher the blocking temperature. The blocking temperature is directly connected with the size of the particles by the formula: Tb = KV/25kB, (6) where K is the magnetic anisotropy constant, V vol ume of the particle, and kB the Boltzmann constant. The average blocking temperature for the three sam ples is determined to grow in the order: 25, 40, and 70 K for n = 3, 6, and 10 wt %, respectively. Formula (6) can be used to determine average volume of yttrium ferrite nanoparticles under sttudy. The values of magnetic anisotropy constant at different tempera tures were found from the approximation dependence taken from [4]. Simple calculations gave the following estimates for V: 3.55, 5.87, and 10.76 × 10–18 cm3 for n =
(7)
Thus determined D values were found to have a value of 23, 37, and 69 nm for n = 2, 6, and 10 wt %, respectively. Analytical calculations based on experi mental results also confirmed that the samples with n = 3 wt % must have the smallest particle size. The blocking temperature, Tb, above which the particles convert to a ferromagnetic state, is deter mined at the point where the FC and ZFC curves diverge. In case of monosized particles, this will coin cide with a maximum on the ZFC curve. In case of some particle size dispersion, the maximum tempera ture on ZFC curves (Tb) will differ by the temperature (Ti) at which the divergence of FC and ZFC curves occurs. As follws from the ZFC diagrams in Fig. 5a, tem peratures Ti and magnetizations M have the following values: 40 K and 0.03 emu/g; 44 K and 0.017 emu/g; and 170 K and 0.008 emu/g Differences between Tb and Ti may be related to a wide distribution of particles size. An increase in n is seen to affect blocking temperature. As temperature increases, the magnetization of the system increases due to conversion of large particles to an unblocked state. Thus, particles size distribution explains why magnetization of the system increases gradually with increasing temperature in an external magnetic field. Similar magnetic measurements with annealed samples show (Fig. 6a) that the divergence of ZFC and FC curves occurs at the following Ti: values: 290, 275, and 280 K for for n = 2, 6, and 10 wt %, respectively. Figure 6a also shows distinctly different behavior of ZFC curves as a function of temperature. Blocking temperature Tb for n = 3 wt % is 255 K; in case of n = 6 wt %, we have three values of Tb: 70, 140, and 260 K; and in case of n = 10 wt %, two Tb values: 70 and 270 K. As the temperature rises, the magnetization of the sys tem increases due to conversion of large particles to an unblocked state. After reaching Tb, the magnetization begins to relax and declines with increasing tempera ture. Magnetization M as a function of applied magnetic field H for three yttrium ferrite samples after annealing 1000°C for 1 h (Fig. 6b) was measured at 5 and 300 K, i.e. below and above blocking temperatures Tb. The synthesized Y3Fe5O12 exhibit saturation and residual magnetization. The magnetization curves for the three Y3Fe5O12 samples are seen to be distinctly different. The largest saturation and remnant magnetization are observed for n = 3 wt % while the largest coercivity, for n = 10 wt %. At 300 K the magnetization shows a lin ear growth with increasing H, with no signs of satura tion up to 9000 Oe, thus resembling paramagnetics. The Y3Fe5O12 samples At 5 K and H = 9000 Oe, no saturation was achieved. This is indicative of weak fer
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(a)
8
13
LaFerriteBA LaFerriteAA CeFerriteBA CeFerriteAA SaFerriteBA SaFerriteAA
6 12 4 M, emu/g
M, emu/g
11 3% ZFC 3% FC 6% ZFC 6% FC 10% ZFC 10% FC
10 9
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2 0 –2 –4
8
–6 7
–8 0
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–80k–60k–40k–20k 0 20k 40k 60k 80k H, Oe
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3% 5 K 3% 300 K 6% 5 K 6% 300 K 10% 5 K 10% 300 K
–10
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LaFerriteBA LaFerriteAA CeFerriteBA CeFerriteAA SaFerriteBA SaFerriteAA
0.2 M, emu/g
M, emu/g
20
200
(b)
40 30
150 T, K
0 –0.2
–20 –0.4
–30
–4k
–40 –80k –40k 0 40k 80k –60k –20k 20k 60k H, Oe Fig. 6. (a) Zerofieldcooled (ZFC) and fieldcooled (FC) curves for annealed (at 1000°C) yttrium ferrites (H = 100 Oe) and (b) magnetic hysteresis loop of yttrium ferrites with different n (indicated) at 5 and 300 K (after annealing at 1000°C).
romagnetic behavior, as in case of orthoferrite. Large values of the coercive force at 5 K coincide with the rise of magnetic anisotropy, which prevents the align ment of moments along the direction of applied field. For all three samples we observe a decline in the mag netization with increasing n. This can be explained by decline in the growth of some domains through decrease of others and shift of boundaries between them. An increase in n led to an increase in the coer cive force. Hysteresis curves show a rectangular shape, which is typical of soft magnetic materials. Similar magnetic measurements (Fig. 7) were per formed for three assynthesised LaFeO3, CeFeO3, and SmFeO3 ferrites and after their annealing at 1000°C. Compared to yttrium ferrite, the coercive forces
–2k
0 H, Oe
2k
4k
Fig. 7. Magnetic hysteresis loops of La, Ce, and Sm ferrites before (BA) and after annealing (AA) at 1000°C.
decreased significantly, while the saturation magneti zation increased by several orders of mahnitude. Dielectric Behavior The values of dielectric permittivity (εr) were deter mined from the following relationship: C = εrε0(S/d), (8) where C is electrocapacity, εr dielectric permittivity, ε0 dielectric constant, S surface area of the capacitor plates, and d distance between the plates. Figure 8a shows dielectric permittivity εr of Y3Fe5O12 as a function of temperature T and frequency f. Dielectric constant εr is seen to increase with increasing T and decreasing f. This can be rationalized as follows. Temperature increase leads to a decrease in the ferrite viscosity, which facilitates the orientation of the dipoles in applyed alternating voltage and thus enhances the dielectric polarization. Usually the elec
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100 kHz 250 kHz 1.0 kHz 1.5 kHz 2.0 kHz
εr
16 14 12 10 8 300
350
0.30 0.25
450
500
550
100 kHz 250 kHz 1.0 kHz 1.5 kHz 2.0 kHz
0.20 tanδ
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0.15
CONCLUSIONS
0.10 0.05 0
–0.05 300
350
change in dielectric loss tan δ (Fig. 8b). Curves of tan δ exhibit a wavy bevavior with explicit ‘peaks’ at 423 K and 550 K. This is because the Y3Fe5O12 structure admits has two types of losses, dipole and electric ones. The first peak is associated with reaching the maxi mum value of the dielectric loss due to dipole polariza tion at some certain temperature Tk. An increase in temperature and associated decrease in viscosity, as noted above, leads to onset of friction between rotating dipoles. As a result, there is a double effect: the extent of orientation of the dipoles increases, which leads to an increase in tan δ, and the energy loss needs to over come the viscous resistance of the medium when rota tion of the dipoles slows down, which causes a decrease of tan δ. The second peak is caused by increasing loss of conductivity associated with a fur ther increase in temperature. The measured values of tan δ are within the required range for the commercial ferries: 10–3–10–5.
400 450 T, K
500
550
Fig. 8. (a) Dielectric permittivity εr and (b) dielectric loss tan δ of Y3Fe5O12 as a function of temperature T and fre quency f (indicated).
tronic exchange between Fe2+ and Fe3+ in octahedral sites results in local displacement of electrons in the direction of the applied electric field which determines electric polarization behavior of the ferrites. When increasing f, the dipoles do not manage to completely arrange in the direction of the applied field, so the per mittivity (εr) begins to decrease to the values deter mined by electronic polarization, which is observed in all types of insulators and is not associated with energy loss. The obtained results agree with the results [26] of similar studies for Y3Fe5O12: εr = 4–7 at 300 K and f = 100–1000 kHz. This enables us to suggest that the physical processes of polarization of yttrium ferrite garnet bevave similarly all over the specified frequency. The given results are within the required range for commercial ferrites: εr = 8–12 for ferro spinels and 13–13 for ferro garnets [27]. Slight deviations may be caused by the charge heterogeneity due to impurities and polydispersity of nanoparticles resulting from material grinding. Further studies have shown that the changes in εr caused by variation in f and T are accompanied by
Thermodynamic analysis and experimental studies demonstrated the feasibility of direct preparation of nanostructured rare earth ferrite particles by solution combustion synthesis. The enhancement of interac tion between yttrium nitrate pentahydrate and iron (III) nitrate nonahydrate with 10 wt % glycine is con firmed by DSC curves that show a weight decrease from 29.4% at 3 wt % glycine to 15.9% at 10 wt % glycine. The ZFC and FC curves for yttrium ferrite taken before and after annealing at 1000°C show that the sample prepared at 3 wt % glycine has the smallest par ticle size. The difference between temperatures Tb and Ti is associated with a broad particle size distribution. Magnetization curves for Y3Fe5O12 indicate that at 5 K yttrium ferrite exhibits ferromagnetic behavior, while at 300 K it is paramagnetic. Annealing Y3Fe5O12 sam ples results in an obvious change in the domain struc ture illustrated by the rectangular hysteresis loop. The obtained values of εr and tan δ of Y3Fe5O12 are within the interval required for microwave ferrites in industry: εr = 13–15 and tan δ = 10–3–10–5. Reduction in εr with increasing f indicates the relaxation processes due to which the values of εr are shifted upward along the temperature axis. ACKNOWLEDGMENTS This work was supported by the National Science Foundation (grants 1138205 and HRD1242090). REFERENCES 1. Goldman, A., Handbook of Modern Ferromagnetic Materials, New York: Springer, 1999
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INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS
Vol. 24
No. 2
2015