Journal of Alloys and Compounds 657 (2016) 608e615
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Microwave absorption properties of LiZn ferrites hollow microspheres doped with La and Mg by self-reactive quenching technology Xudong Cai a, *, Jianjiang Wang a, Baochen Li b, Aihua Wu c, Baocai Xu a, Bing Wang c, Haitao Gao a, Liang Yu a, Ze Li a a b c
Mechanical Engineering College, Advanced Material Institute, Shijiazhuang, 050003, PR China Mechanical Engineering College, Scientific Research Department, Shijiazhuang 050003, PR China Hebei Semiconductor Institute, Shijiazhuang 050051, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 July 2015 Received in revised form 13 October 2015 Accepted 18 October 2015 Available online 21 October 2015
LithiumeZinc ferrite hollow microspheres (LiZn FHMs) doped with La and Mg were synthesized by Fe þ Zn þ Fe2O3 þ O2 þ Li2CO3 reactive system based on self-reactive quenching technology. Influence of La and Mg doping on the surface morphology, phase structure and microwave absorption properties of LiZn FHMs were investigated. The results show that the surface morphology of LiZn FHMs changes little and are still composed of unnoticeable multi-shape crystal grains, whether they are doped or not. The phases are mainly made up of Fe3O4, Fe2O3, Li0.435Zn0.195Fe2.37O4 and Li0.5Fe2.5O4 without doping. The phases remain unchangeable after Mg doping, while LaFeO3 appears in the phase components after La doping. When LiZn ferrites are without doping, their minimum reflectivity at 4 mm is 14 dB at 7.5 GHz, and the effective absorption frequency band less than 10 dB is 6.4e8.6 GHz, with the bandwidth of 2.2 GHz. Compared with that without doping, the minimum reflectivity increases after Mg doping, and the effective absorption frequency band less than 10 dB disappears. After La doping, the minimum reflectivity is 30.2 dB at 6.2 GHz, and the effective absorption frequency band is 4.7e7.7 GHz, with the bandwidth of 3 GHz. It is found from the present investigations that the microwave absorption properties are improved after La doping, and those of LiZn FHMs after Mg doping are reduced. © 2015 Elsevier B.V. All rights reserved.
Keywords: LiZn ferrites Self-reactive quenching technology Microwave absorption properties
1. Introduction Stealth technology is the development and extension of traditional camouflage technology and it plays an important role in military technology. It has been widely used in weapons systems of developed countries, and has been considered as the principal high technology in military field. Meanwhile, effect of stealth technology on the survival and combat of modern weapons has been increasing. These factors have attracted great interest in exploiting microwave-absorbing materials [1,2]. They are mainly composed of traditional absorbing materials including conducting polymers, carbon-based absorbents, ferrites, iron carbonyl, ultra-fine metal powder and new absorbing materials containing chiral materials, intelligent absorbing materials, meta-material absorbing materials, nano-absorbing materials and high-temperature absorbing materials. Good microwave-absorbing material is needed with high
* Corresponding author. Heping West Road 97, Shijiazhuang 050003, PR China. E-mail address:
[email protected] (X. Cai). http://dx.doi.org/10.1016/j.jallcom.2015.10.153 0925-8388/© 2015 Elsevier B.V. All rights reserved.
microwave permeability, high magnetic loss, a favorable form of frequency dependence of permeability, and a proper ratio between the permeability and permittivity [3]. Moreover, the impedance matching between the material and free space is essential for low reflectivity. At present, our measurement frequency bands of microwave absorption are located in 0.5e18 GHz. So 0.5e8 GHz is low frequency and 8e18 GHz is high frequency. And domestic and foreign research funding and human resources are mainly focused on high-frequency absorbing materials (8e18 GHz) currently, and the study has become mature. However, the research of lowfrequency absorbing materials lower than 8 GHz is relatively scarce [3e5]. This actuality not only makes it difficult to meet the military needs of the large wavelength electromagnetic shielding, but also forms great incipient fault in civil application [6]. Due to its cheap and broad sources, simple and stable production technology, high curie temperature, low sensitivity of remanent magnetization stress and great temperature stability, LiZn ferrites are not only good gyromagnetic materials, but also soft magnetic ferrite materials that are widely applied in 0.5e8 GHz [7]. And current research has indicated that doping and substituting
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metal or rare earth ions earth ions in spinel ferrites may modify their electromagnetic properties, which would also lead to modifications in their microwave absorption properties [8]. Chang Sun et al. [9] employed a combination of solegel process with subsequent calcination to prepare LiZn ferrites doped with Ce, and found that the enrichment of CeO2 can strengthen the dielectric attenuation for microwave and improve the low-frequency microwave absorption of LiZn FHMs. Jie Song et al. [10] used solegel combustion method to prepared LiZn ferrites doped with Mg2þ, and showed that appropriate amounts of Mg2þ substitution could adjust microwave electromagnetic parameters magically. However, these LiZn ferrites have their own disadvantages such as narrow absorption frequency band, large density and poor matching thickness, which restrict an extensive use in low-frequency microwave absorbents. Researches also show that hollowness is an effective solution for conquering high weight of absorbents and plays an important role in broadening absorption bands and improving compatibility [11]. Therefore, in the present work, we have focused on the effects of different doped elements (Mg, La) on the morphology, phase structure and microwave absorption properties of LiZn ferrites hollow microspheres (LiZn FHMs), prepared by self-reactive quenching technology based on flame spraying technology, selfpropagating high-temperature synthesis (SHS) technology and quick chilling technology. This thesis is carried out to master an adjusting method of the microwave absorption properties of LiZn FHMs and lay the foundation on the future investigations.
2. Experiments 2.1. Materials and methods Analytical reagent raw materials of Fe powders, Li2CO3 powders, Zn powders, Fe2O3 powders, sucrose (precursor of C, 50 g, in order to obtain agglomerate powders with fine fluidity), epoxy resin (bonding agent, 50 ml, used to bonding reactive units), and Bi2O3 powders (fluxing agent, 2wt. %, used to decrease the sintering temperature and restrain the volatilization of Li2CO3 [12]) were selected. Related information is shown in Table 1. Eq. (1) shows the stoichiometry ratio of main reactive system. According to Literature [13] and [14], the value of k and x are selected as 0.4 and 0.3, respectively. La(NO3)3 is added into the reaction based on Eq. (1) with the mole ratio of 0.1:1, 0.2:1 and 0.3:1, respectively. The same process is used for Mg(NO3)2. The agglomerate powders were prepared as the following processes. Firstly, the raw materials were put into LJM-5L ball mill, and anhydrous ethyl alcohol was taken as the medium sphere to be grinded for 6 h. After that, epoxy resin-alcoholic solution was added into the mill to be stirred for another 2 h. Epoxy resin was used to cooperate with sucrose to enlarge the contact area of the components in the agglomerate powders and to increase the bonding
Table 1 Raw materials and their chemical composition used in the experiments. Material
Particle size/mm
Chemical purity (wt. %)
Fe Li2CO3 ZnO Fe2O3 La(NO3)3 Mg(NO3)2 Epoxy resin(6101) Sucrose Bi2O3
10 15 20 40 35 35 N/A 5 20
Fe 99 Li2CO3 97% ZnO 99 Fe2O3 99.5 La(NO3)3 99.5 Mg(NO3)2 99.5 epoxy resin 99 C12H22O11 99.9 H2O < 0.1 Bi2O3 97.5%
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strength of reactive components. It can be transformed to CO, CO2 and H2O in SHS reaction due to the high temperature. Secondly, the mixtures were dried and carbonized at 150 C in 101-2A horizontal drying cabinet until no smoke released, and then they were comminuted by the FW177 disintegrator. Finally, agglomerate powders with fine fluidity were selected to spray after the sieving process, respectively. Investigations shows that 0.1:1 is the best quantity of La(NO3)3, and when the mole ratio increases to 0.2:1 and 0.3:1, raw materials burn in the carbonization progress due to the strong oxidizability of La(NO3)3. The phenomenon is similar for Mg(NO3)2. So 0.1:1 is selected as the best doping amount in this experiment. Fig. 2 of Literature [15] shows the preparation diagram of LiZn FHMs. As shown in the figure, the agglomerate powders are sprayed into the flame field (about 3500 K) through a CP-D type high-energy flame-spraying gun, and the temperature of the materials increases gradually. When reaching the ignition temperature, the SHS reactions occur promptly, and the temperature of reactive system exceeds the melt point of products. So droplets are generated. Simultaneously, large volume of gases are produced, which results in the droplets with hollow structures. Then the droplets are quenched quickly into the cooling medium (the distilled water). As the gas can not escape from the droplets, LiZn FHMs are obtained immediately after the quenching products are dried and filtered. The reactive equation is showed in Eq. (1). In the experiment, the flame field is used to ignite the SHS reaction. And once the reactions occur, they can be self-sustaining based on the heat released by themselves and the flame field is not required. In addition, the parameters of high-energy flame spraying gun are very important for the products. According to the previous study, it is indicated that the atmosphere (such as O2, N2, Ar, etc) has great effect on LiZn FHMs, and it is found that oxygen provides an oxygen-enriched atmosphere, which are benefical to obtain hollow structures. In addition, the rate of O2 and acetylene (b ¼ VO2 =VC2 H2 ) affects the temperature and oxidizability of flame. In this experiment, the rate is set as 1.4. The quenching distance was set to 500 mm, which guarantee the high balling rates of LiZn FHMs. Moreover, different amounts of sucrose and epoxy resin will generate different amount of gases during the reaction, which will affect both the morphology and the properties of LiZn FHMs. In this experiment, their amounts are 50 g and 50 ml, respectively. 2.2. Characterization of the samples The morphology of the quenching products was detected by scanning electron microscope (SEM, QUANTA FEG-250). The phase composition of the quenching products was studied by X-ray diffraction (XRD, BRUKER D2 PHASER), with Cu K radiation (¼0.15418 nm). Scanning step is 0.02 , and scanning degree is from 10 to 80 . Archimedes Method was used to test the density of LiZn FHMs. 2.3. Measurement of microwave-absorbing behavior for LiZn FHMsparaffin composite The absorbing composite were prepared by molding and curing the mixture of LiZn FHMs and paraffin. Paraffin was used as a polymer matrix due to its good flexibility and wave-transparent property. And it has little effect on investigating the microwave absorption properties of LiZn FHMs-paraffin composite. The mix ratio of LiZn FHMs-to-paraffin was 3:2 by weight. The testing specimens have a toroidal shape with a certain thickness, and the outer and inner diameters are respectively 7.0 mm and 3.0 mm. The ε0 , ε00 , m0 and m00 versus frequency were measured by coaxial
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Fig. 1. SEM photographs of the LiZn FHMs without doping (a, d) and doped with La (b, e) and Mg (c, f).
reflection/transmission method using Vector Network Analyzer (Agilent-N5242A) in 0.5e18 GHz range. The absorbing characteristics can be represented as the reflection loss (R.L.), as shown in Eqs. (2) and (3). Where Zin is the normalized input impedance related to the impedance in free space, εr ¼ ε0 jε00 , mr ¼ m0 jm00 is the complex relative permeability and permittivity of the material, d is the thickness of the absorber, and c and f are the velocity of light and the frequency of microwave in free space, respectively. To represent the perfect absorbing properties, the impedance matching condition is given by Zin ¼ 1. The impedance matching condition is determined by the combination of six parameters ε0 , ε00 , m0 , m00 , f and d. Also, knowing εr and mr, the R.L. value versus frequency can be evaluated by using metlab 8.0 at a specified thickness. 3. Results and discussion 3.1. Effect of La and Mg doping on the micro-structure of LiZn FHMs Fig. 2. XRD patterns of the LiZn FHMs before and after doping.
Fig. 1 shows the micro-structure SEM images of LiZn FHMs
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doped by different elements (La, Mg). Fig. 1(a) represents the SEM image of LiZn FHMs without doping, while Fig. 1(b) and (c) show the SEM images of LiZn FHMs after La and Mg doping, respectively. As shown in Fig. 1, the surface morphology of LiZn FHMs does not change obviously before and after doping, which is in accordance with the conclusions of literature [16]. They are all composed of polygon grains with unobvious crystallization. These structures will enlarge the contacting interfaces between the hollow microspheres and paraffin matrix, and the loss of interfacial polarization is increased. As a result, the microwave absorption properties of LiZn FHMs may be improved [17]. In addition, Fig. 1(d) shows the SEM image of LiZn FHMs before doping with low magnification. Fig. 1(e) and (f) are those after La and Mg doping with low magnification. The three figures demonstrate that most of the quenching products are of hollow structures. This is also verified by the density of the samples. The densities of LiZn FHMs without doping, after La and Mg doping are 1.95 g/cm3, 1.87 g/cm3 and 1.97 g/cm3, respectively. While the density of Li0.435Zn0.195Fe2.37O4 solid powders is 3.26 g/ cm3. The phase identification of the as-prepared doped LiZn FHMs was conducted using XRD patterns. Fig. 2 shows XRD patterns of LiZn FHMs, LiZn FHMs doped with La, and LiZn FHMs doped with Mg. From the figures, it can be concluded that the main phase components are still constituted of Fe3O4 (file no: PDF #65-3107), Fe2O3 (file no: PDF #39-1346), Li0.435Zn0.195Fe2.37O4 (file no: PDF #37-1471) and Li0.5Fe2.5O4 (file no: PDF #49-0266). However, LaFeO3 (file no: PDF# 75-0541) can be seen in the phase components of La-doped LiZn FHMs. No phase containing Mg appears in Mg-doped LiZn FHMs. LaFeO3 is of cubic crystal systems, and the lattice constant can be calculated by Eqs. (4) and (5). Where q is the angle of the position, a is lattice constant, dhkl is interplanar spacing, (h k l) is interplanar indices. According to the interplanar spacing of the strongest diffraction peak of Li0.435Zn0.195Fe2.37O4, it can be calculated that the lattice constant value of Li0.435Zn0.195Fe2.37O4 is 7.9749 Å without doping, while those values after La and Mg doping are 7.9579 Å and 9.9762 Å, respectively. The calculation results indicate that compared with that before doping, the lattice constant of Li0.435Zn0.195Fe2.37O4 changes little after Mg doping, while this after La doping decreases obviously. The changes result from the ionic radius difference of La3þ (1.22 Å), Mg2þ (0.78 Å) and Fe3þ (0.645 Å). Due to their similar radiuses, Mg2þ displaces Fe3þ without changing the crystal structure of Li0.435Zn0.195Fe2.37 O4, which is in accordance with the XRD patterns of the Fig. 2 without the diffraction peak of Mg. When La3þ displaces Fe3þ in the lattice of Li0.435Zn0.195Fe2.37O4, the crystals lattice distortion appears because the radiuse of La3þ is notably bigger than that of Fe3þ. The adjacent lattices are pressed, and the vacancy size of the adjacent lattice is reduced, which prevents La3þ from entering the lattice of Li0.435Zn0.195Fe2.37O4 [18]. Consequently, the doping amount of La3þ has been saturated, and superfluous La3þ appears in the form of LaFeO3 in LiZn FHMs. As Fe3O4 and Li0.5Fe2.5O4 have similar spinel structures with Li0.435Zn0.195Fe2.37O4, it can be concluded that the doping mechanisms mentioned above are similar for Fe3O4 and Li0.5Fe2.5O4. 3.2. Effect of La and Mg doping on electromagnetic parameters of LiZn FHMs Complex permittivity and permeability represent the dielectric and dynamic magnetic properties of materials [19]. The real parts (ε0 and m0 ) of complex permittivity and permeability symbolize the storage and transform capability of electromagnetic energy. The imaginary parts (ε00 and m00 ) represent the loss of electromagnetic energy. The frequency dependence of complex permittivity and permeability for LiZn FHMs before and after doping different
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elements (La, Mg) is shown in Fig. 3. It is indicated that, the real part of permittivity (ε0 ) maintains at about 6.4 without doping, and the imaginary part (ε00 ) of complex permittivity gradually increases from 0.25 to 1.61 with the increasing of frequency. After La doping, ε0 and ε00 all significantly increase. The influence factors of permittivity are complicated, and they are mainly composed of conductance loss, electronic polarization, ionic polarization, orientation polarization of intrinsic dipole, and the interface polarization [20]. After La doping, La3þ is introduced into the lattice of Li0.435Zn0.195Fe2.37O4. On one hand, the cations become more diversified, and they can form multi-dipoles with O2, which enhance the effect of dipole polarization [21]. On the other hand, the introduction of La3þ will effectively promote the transition between Fe2þ and Fe3þ (Fe2þ 4 Fe3þ), and the electron hopping is enhanced. So the conductance losses are increased [22]. In addition, because the radius of La3þ (1.22 Å) is notably bigger than that of Fe3þ (0.645 Å), the lattice constant of Li0.435Zn0.195Fe2.37O4 increases obviously after La doping. The lattice distortion appears, and the physical activity increases obviously. As a result, dielectric losses are increased [23]. The real part of complex permeability (m0 ) changes little, the imaginary part of complex permeability (m00 ) increases in 1e7 GHz. Due to the ions magnetic moment of La3þ, the molecular saturated magnetic moment of Li0.435Zn0.195Fe2.37O4 will be affected and the whole exchange action will also be strengthened. Therefore, magnetic loss attenuation on microwave is strengthened, and the complex permeability is increased [7]. After Mg doping, ε0 changes little, but ε00 decreases. The amplitude of variation is much smaller than those of La doping, and it may be attributed that no lattice distortion appears after Mg2þ entering the crystal. The value of m0 changes little, and the resonance absorption peak m00 at 3 GHz disappears. Mg2þ does not have magnetic property and the relative content of magnetic particles decreases after Mg2þ doping. Therefore, the low-frequency magnetic properties of LiZn FHMs decline after Mg doping. The doping mechanisms of La and Mg on Fe3O4 and Li0.5Fe2.5O4 are similar with Li0.435Zn0.195Fe2.37O4 because of their spinel structures. 3.3. Effect of La and Mg doping on the microwave absorption properties of LiZn FHMs The calculated reflectivity curve of LiZn FHMs before and after doping is shown in Fig. 4. Fig. 4(a) is the reflectivity curve without doping, and Fig. 4(b) and (c) are those after La, Mg doping, respectively. As the figure shows, the best matching thickness of samples without doping is 5 mm. At this thickness, the minimum reflectivity is 14.5 dB at 5.8 GHz, and the effective absorption frequency band less than 10 dB is 4.8e6.8 GHz, with the bandwidth of 2 GHz. After La doping, the best matching thickness is 4 mm. At this thickness, the minimum reflectivity is 30.2 dB at 6.2 GHz, and the effective absorption frequency band is 4.7e7.7 GHz, with the bandwidth of 3 GHz. After Mg doping, the best matching thickness is 7 mm. At this thickness, the minimum reflectivity is 19.9 dB at 3.5 GHz, and the effective absorption frequency band less than 10 dB is 12.6e13.8 GHz, with the bandwidth of 1.2 GHz. It can be concluded that the microwave absorption properties are improved drastically after La doping, but those after Mg doping are reduced. In fact, the absorption peak moves to low frequency with the increasing of thickness, whether doping or not, which is consistent with the conclusion of Literature [24]. This shift could be understood based on the quarter-wave thickness criteria, as is shown in Eq. (6) and Eq. (7) [20]. Here, l0 ¼ c/f is the free-space wavelength of the incident wave, d is the thickness of the absorbing sample, and jmrj and jεrj are the moduli of jmrj and jεrj, respectively. It can be concluded from the equations that the thickness is inversely
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Fig. 3. Permittivity and permeability of LiZn FHMs before and after doping.
proportional to the frequency [11]. In addition, there will be another absorption peak in high frequency band with the thickness increasing furthermore, which is called “double absorption peak”. It can been seen that double absorption peak appears after La doping at 5 mm and Mg at 6 mm, respectively. This may attributed to the follow reasons. On one hand, when the thickness of absorbent coating equals to the odd times of 1/4 wavelength of the electromagnetic waves, the electromagnetic waves reflected from the upper surface and the lower surface superimposes upon each other. Dimensional resonance appears and the energy of electromagnetic waves is strongly absorbed [25]. On the other hand, the wavelength of electromagnetic wave in high frequency band is relatively smaller than that of low frequency band. When the thickness of absorbent coating increases to odd times of the 1/4 wavelength of some electromagnetic wave in high frequency for the second time, an stationary wave absorption appears and electromagnetic wave energy is absorbed. That is to say, when the original absorption peak moves to lower frequency, a new absorption peak appears in higher frequency. Consequently, multiband LiZn FHMs absorbents can be obtained by means of doping and adjusting the sample thickness. In order to meet the requirements of new absorbents “thin, wide, light and strong”, the thickness of the absorbents should not be too large. It can be found that LiZn FHMs generally have good microwave absorption properties at 4 mm thickness before and after doping. Therefore, it is of great significance to investigate the effect of doping on the microwave absorption properties at this thickness. The reflectivity curves of LiZn FHMs at 4 mm before and after doping are shown in Fig. 5. As the figure shows, the minimum reflectivity of LiZn FHMs at 4 mm is 14 dB at 7.5 GHz, and the effective absorption frequency band less than 10 dB is 6.4e8.6 GHz, with the bandwidth of 2.2 GHz. Compared with that
without doping, the minimum reflectivity increases after Mg doping, and the effective absorption frequency band less than 10 dB disappears. After La doping, the minimum reflectivity is 30.2 dB at 6.2 GHz, and the effective absorption frequency band is 4.7e7.7 GHz, with the bandwidth of 3 GHz. In addition, the absorption peak moves to low frequency. Conclusions show that the microwave absorption properties are significantly improved after La doping, but decreased after Mg doping. Consequently, the microwave absorption properties of LiZn FHMs can be effectively controlled by adjusting the doping technology. The obvious improving of the microwave absorption properties after La doping may be ascribed to the follow changes. The magnetocrystalline anisotropy changes after La3þ entering the lattices of LiZn FHMs. In addition, the distribution of ions, the magnetic moment of ions and the exchange of ions also obviously change. So the ferromagnetic resonance frequency varies, resulting in the improving of microwave absorption properties [26]. Specific reasons are as follows. The doping amount of La (0.1 mol) in LiZn FHMs has been saturated, and the excessive of La exists in the form of LaFeO3, as is shown in XRD patterns of Fig. 2. LaFeO3 is a kind of perovskite material, and its Fe3þ is located in the center of the oxygen octahedral structure. Its five degenerate orbitals can be divided into two parts: high energy eg and low energy t2g. The electron configuration 3 e2 . Due to 3d electron configuration of Fe ion, the of Fe3þ is t2g g energy levels of conduction bands are effectively reduced, and 2p orbital energy level of valence band oxygen is stable. So the difference of the charge transferring energy from the valence band to the conduction band decreases [9]. Due to the decreasing of energy gaps, the energy for electronic migration decreases significantly and the electron mobility increases obviously. As a result, dielectric loss increases notably [27,28].
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Fig. 4. Reflectivity curves of LiZn FHMs without doping (a) and doped with La (b) and Mg (c) at different thicknesses.
Magnetic loss is the main absorbing mechanism of LiZn FHMs without doping [9]. After La doping, LaFeO3 is formed and the electronic conductivity of the material increases. In addition, the recombination between LiZn FHMs and LaFeO3 makes the complex permittivity increase greatly. So dielectric loss becomes the main absorbing mechanism of the composite in low frequency, and the electromagnetic waves are absorbed drastically [9]. Mg doping will reduce the whole magnetic properties of LiZn FHMs because Mg2þ does not have magnetic properties. At the same time, the permittivity of LiZn FHMs does not increase, and dielectric loss is not improved. The two factors together result in a decreasing of the microwave absorption properties in the low
frequency. Above all, the microstructure of LiZn FHMs (such as the morphology, phase and crystal structure) can be adjusted by element doping based on self-reactive quenching technology. Meanwhile, the microwave absorption properties in low frequency can be controlled effectively. 4. Conclusions LiZn/La and LiZn/Mg ferrite hollow microspheres were successfully prepared by self-reactive quenching technology. Investigations show that the surface morphology of LiZn FHMs
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Fig. 5. Reflectivity curves of LiZn FHMs before and after doping at 4 mm.
changes little after La and Mg doping. The main phase remains unchangeable after Mg doping, while LaFeO3 appears in the phase components after La doping. Investigations also show that the microwave absorption properties of La-doped samples can be significantly improved by changing the main absorbing mechanism. However, the microwave absorption properties of Mg-doped samples are reduced due to the existence of non-magnetic Mg2þ. Therefore, besides the characteristics of low-cost, simplicity, full use of in situ synthesis, high output and rapid preparation, selfreactive quenching technology can also control the microwave absorption properties of hollow microspheres by adjusting the technology parameters including doping different elements. In other word, self-reactive quenching technology is efficient. Acknowledgments Authors would like to express their sincere appreciation to National Natural Science Fund of China (No. 51172282), Hebei Natural Science Fund of China (E2015506011) and Pre-research of the Weapons Equipment (9140A12040211JB34) for financial support. Tremendous thanks are owed to Baochen Li, Aihua Wu and Guanhui Liang, who provide us with great help in the investigation. Appendices Equations
2kFe þ xZnO þ 0.5(2.50.5x2k)Fe2O3 þ 1.5kO2 þ 0.25(1x) Li2CO3 / Li0.50.5xZnxFe2.50.5xO4 þ 0.25(1x)CO2
ðZ 1Þ R:L:ðdBÞ ¼ 20 log10 in ðZ þ 1Þ
(1)
(2)
in
Zin ¼
" 1=2 # 1=2 mr 2pfd mr tanh j c εr εr
1 h2 þ k2 þ l2 ¼ dhkl a2 a¼
ffi l pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 þ k2 þ l2 2 sin q
(3)
(4)
(5)
. d ¼ l0 4ðjmr jjεr jÞ1=2
(6)
l0 ¼ c=f
(7)
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