- Nano Express
- Open Access
Low temperature-fired Ni-Cu-Zn ferrite nanoparticles through auto-combustion method for multilayer chip inductor applications
© Batoo and Ansari; licensee Springer. 2012
- Received: 27 September 2011
- Accepted: 8 February 2012
- Published: 8 February 2012
Ferrite nanoparticles of basic composition Ni0.7-xZn x Cu0.3Fe2O4 (0.0 ≤ x ≤ 0.2, x = 0.05) were synthesized through auto-combustion method and were characterized for structural properties using X-ray diffraction [XRD], scanning electron microscopy, transmission electron microscopy, and Fourier transform infrared spectroscopy [FT-IR]. XRD analysis of the powder samples sintered at 600°C for 4 h showed the cubic spinel structure for ferrites with a narrow size distribution from 28 to 32 nm. FT-IR showed two absorption bands (v1 and v2) that are attributed to the stretching vibration of tetrahedral and octahedral sites. The effect of Zn doping on the electrical properties was studied using dielectric and impedance spectroscopy at room temperature. The dielectric parameters (ε', ε″, tanδ, and σac) show their maximum value for 10% Zn doping. The dielectric constant and loss tangent decrease with increasing frequency of the applied field. The results are explained in the light of dielectric polarization which is similar to the conduction phenomenon. The complex impedance shows that the conduction process in grown nanoparticles takes place predominantly through grain boundary volume.
PACS: 75.50.Gg; 78.20; 77.22.Gm.
- dielectric constant
- ac conductivity
- impedance spectroscopy.
The study of ferrites has attracted immense attention of the scientific community because of their novel properties and technological applications especially when the size of the particles approaches to nanometer scale. More novel electrical and magnetic behaviors have been observed in comparison with their bulk counterpart [1, 2]. In general, the transport properties of the nanomaterials are predominantly controlled by the grain boundaries than by the grain itself . Due to this reason, the magnetic materials have explored a wide range of applications and thus are replacing conventional materials.
In the last two decades, latest advancement in wireless technology has explored the area of real-time communication. Internet-accessible cell phones and high-speed wireless local area network are the best examples of this technology. The core of these systems is based on a radio frequency [RF] circuit consisting of transmission and receiving circuit blocks required in signal amplification, filtering, and modulation that in turn require hundreds of passive chip components such as capacitors and inductors. Inductors adapted to RF circuits of mobile devices are mostly multilayer chip inductors [MLCIs] and microspiral inductors. MLCIs were developed in the 1980s by thick film printing and co-firing technologies using low temperature-sintered Ni-Cu-Zn ferrite and Ag. Recently, Ni-Cu-Zn ferrites have been developed to meet a demand for miniaturization of electronic components [4, 5]. The ferrite powder needs to be sintered below 950°C in order to co-heat with silver internal electrodes (Tm approximately 962°C) and should have low dielectric constants for MLCI application. Materials with high permeability are also required for reducing the number of layers in MLCIs and for realizing the better miniaturization . Further, ferrite nanoparticles are commercially important for several applications such as in electromagnetic devices operating at radio frequencies where the superparamagnetic [SPM] properties have a strong influence in enhancing their quality of applications [7–9]. Nanoparticles of these materials exhibit interesting phase transitions from SPM state to ferri/ferromagnetic state or vice versa with a variation of temperature depending on their sizes. In this ferrite nanoparticle system, the Cu content of the compositions was kept constant at 30 at.% of the A site (AB2O4 spinel); nonmagnetic Zn2+ ions occupy the tetrahedral A sites, replacing Fe3+ ions, which eventually go to octahedral B sites. Hence, zinc cations magnetically dilute the system by making the A-B exchange interaction relatively weaker. This weaker coupling reduces the anisotropy energy of the system, which facilitates the onset of SPM relaxation in bigger size particles even at room temperature. Many reports are available in the literature on Ni-Cu ferrites where people have reported various properties of the studied ferrite material in bulk as well as in nanoscale form. Chakrabarti et al.  studied the magnetic properties of nanocrystalline Ni0.2Zn0.6Cu0.2Fe2O4 prepared using a chemical route method, and they reported that below 80 K, the nanoparticles exhibit superparamagnetism, and the saturation magnetization increases with increasing particle size. Seong et al.  investigated the structural and electrical properties of Cu-substituted Ni-Zn ferrites, and they have reported that the alternating current [ac] conductivity increases with increasing temperature of the sample and frequency of the applied field. Roy et al.  reported the effect of Mg substitution on electromagnetic properties of (Ni0.25Cu0.20Zn0.55)Fe2O4 ferrite prepared through auto-combustion method, and they found that the permeability and ac resistivity increased while the magnetic loss decreased with the progressive substitution. Jadhav et al.  reported the structural, electrical, and magnetic properties of Ni-Cu-Zn ferrite synthesized by citrate precursor method, and they reported that the dielectric properties (ε' and tanδ) decreases with increasing frequency of the applied field. They further report that the maximum value of the saturation magnetization was found for 20% Cu doping.
However, as per our best search, we have not found any detailed report in the literature on the dielectric and impedance properties of Zn-doped Ni0.7-xCu0.3Fe2O4 ferrite nanoparticles. Therefore, keeping in view the high demand and importance of magnetic ferrite nanoparticles, we report in this paper the effect of Zn doping on the structural, cationic distribution, and conductivity properties of nanocrystalline Ni-Cu-Zn ferrites.
Nanoparticles of Ni0.7-xZn x Cu0.3Fe2O4 (0.0 ≤ x ≤ 0.2, x = 0.05) were prepared by auto-combustion method using 'AR' grade Ni(NO3)2.6H2O, CuCl, Zn(NO3)2.6H2O, and Fe(NO3)2.9H2O as raw materials. The stoichiometric mixtures of the mentioned materials were dissolved in deionized water, and few drops of ethyl alcohol were added to it. The solution was allowed for gel formation on the magnetic stirrer at 65°C with constant stirring. The gel formed was annealed at 200°C for 24 h, followed by grinding for 0.5 h. The dried gel was allowed to burn in a self-propagating combustion manner until the whole gel was completely burnt out to form a fluffy loose powder. The formed powder was heated for 4 h at 600°C to remove any organic material present while maintaining the rate of heating and cooling at 5°C/min and then finally ground for 0.5 h.
X-ray diffraction [XRD] (PANalytical X'Pert Pro, Almelo, The Netherlands) with CuKα (λ = 1.54 Å) was used to study the single-phase nature and nano-phase formation of the pure and doped Ni-Cu-Zn ferrite nanoparticles at room temperature. The microstructural analysis of the samples was carried out by field emission scanning electron microscopy [FESEM] (JSM 7600F, JEOL Ltd., Akishima, Tokyo, Japan) and field emission transmission electron microscopy [FETEM] (Jeol 2010, Tokyo, Japan). The infrared spectra of the powders (as pellets in KBr) were recorded by Fourier transform infrared spectrometry [FT-IR] (PerkinElmer Instruments, Waltham, MA, USA) in the range of 400 to 1,000 cm-1 with a resolution of 1 cm-1.
The samples were pressed into circular disk-shaped pellets, and silver coating was done on the opposite faces to make parallel plate capacitor geometry with ferrite material as the dielectric medium. The dielectric and impedance spectroscopy measurements were performed in the frequency range of 42 Hz to 5 MHz using LCR HI-Tester (HIOKI 3532-50, HIOKI E.E. Corporation, Nagano, Japan).
Here, λ is the wavelength of the CuKα radiation (λ = 1.54060), and β is the full width at half maximum in radians.
Grain size, lattice parameters, and ionic radii data of Ni0.7-xCu0.3Zn x Fe2O4 ferrite nanoparticles
NiFe2O4 and CuFe2O4 [18, 19] are both inverse spinel in structure in which half of the ferric ions preferentially occupy the tetrahedral (A sites) and the other half occupy the octahedral sites (B sites).
On the other hand, Zn ions prefer to occupy the tetrahedral sites .
During the sintering process, oxygen loss occurs, leading a part of Fe3+ ions to transform to Fe2+ for charge compensation .
The data in Table 1 reveals that the values of the theoretical lattice parameter (ath), calculated assuming the suggested cation distribution formula, agree well with those experimentally obtained (aexp).
where Ro is the radius of the oxygen ion (Ro = 1.26 Å), and μ is the oxygen parameter. Here, we have taken the value μ = 0.375 by assuming that the spinel structure is not deformed by Zn2+ doping [22, 23].
X-ray density, apparent density, porosity, and FT-IR spectral data of Ni0.7-xCu0.3Zn x Fe2O4 ferrite nanoparticles
D hkl (nm)
D x (g cm-3)
The apparent density of the specimens is about 94% to 95% of the corresponding X-ray densities. The data in Table 2 show that both densities decrease with increasing Zn content, i.e., the apparent density nearly reflects the same general behavior with the X-ray density.
Furthermore, it is reported that Pinter depends on the grain size . By the study of XRD and transmission electron microscopy [TEM] data of the samples, it is found that as the Zn concentration increases from x = 0.0 up to x = 0.2, there is no major change in the grain size. Therefore, as Zn2+ ion content increases, Pinter remains almost constant. Thus, according to Equation 10, the increase of the total porosity P (in percent) is mainly due to the increase of Pintra with Zn2+ doping [28, 29].
Impedance parameters calculated from the complex impedance plots for various compositions at room temperature
3.9E - 2
4.3E - 3
2.2E - 3
2.5E - 3
9.5E - 3
9.9E - 3
6.7E - 3
6.5E - 3
5.2E - 4
5.1E - 4
The presence of Fe3+ and Fe2+ ions render ferrite materials to be dipolar. Polarization is also affected by factors such as structural homogeneity, stoichiometry, density, grain size, and porosity of the ferrites. The rotational displacement of dipoles results in orientational polarization. In ferrites, rotation of Fe2+ to Fe3+ and vice versa can be visualized as the exchange of electrons between two ions so that the dipoles align themselves with respect to the applied field. The polarization at lower frequencies may result from electron hopping between Fe3+ ⇔Fe2+ ions in the ferrite lattice. The polarization decreases with increasing frequency and reaches a constant value due to the fact that beyond a certain frequency of external field, the electron exchange Fe3+ ⇔ Fe2+ cannot follow the changes in the applied field. Also, the presence of Ni3+/Ni2+ ions, which give rise to p-type carriers, contributes to the net polarization though it is small. The net polarization increases initially and then decreases with increasing frequency .
where B and n are constants which depend both on temperature and composition; n is dimensionless, whereas B has units of electrical conductivity.
In the present study, the conduction mechanism is due to electron hopping between Fe2+⇔Fe3+ ions and hole hopping between Ni2+⇔Ni3+ at two adjacent B sites. The charge exchange frequency increases with increasing frequency of the applied field, but the charge exchange mechanism does not follow the frequency of applied field beyond a certain frequency limit because at high frequencies, the resistivity remains invariant with the frequency, and as a result, the hopping frequency no longer follows the changes of external field beyond a certain frequency limit and thus lags behind .
Composition dependence of dielectric properties
Since dielectric polarization in ferrites is similar to electrical conduction, it is therefore expected that the behavior of ε', ε″, and tanδ is similar to that of σac for x = 0.1.
It is well known that impedance spectroscopy is an important method to study the electrical properties of ferrites since impedance of the grains can be separated from the other impedance sources, such as impedance of electrodes and grain boundaries. One of the important factors, which influence the impedance properties of ferrites, is the nano- or microstructural effect. The complex impedance measurement gives us information about the resistive (real part) and reactive (imaginary part) components in the material. The complex impedance plot known as the Cole-Cole plot can give three semicircles, depending upon the electrical properties of the material. Since the ionic polarization in ferrites is not present, as a result, we have only two semicircles because of the space charge and orientation polarization in the ferrite materials. The first semicircle at low frequency represents the resistance of grain boundary. The second one obtained for high-frequency domain corresponds to the resistance of grain or bulk properties [46, 47].
Nanoparticles of polycrystalline Ni0.7-xCu0.3Fe2Zn x O4 ferrites, with an average crystallite size between 28 and 32 nm, were synthesized through auto-combustion method. The dielectric constant and loss tangent both show a normal behavior with respect to frequency. The dielectric and ac conductivity parameters show their maximum value for 10% Zn-doping composition. The overall resistance has been found solely in grain boundary volume, and the contribution of the grain is not well resolved. As a result, the conduction process predominantly takes place through the grain boundary.
- Subhash C, Srivastava BK, Anjali K: Magnetic behaviour of nano-particles of Ni0.5Co0.5Fe2O4prepared using two different routes. Indian J Pur Appl Phys 2004, 42: 366–367.Google Scholar
- Kittle C: Domain theory and the dependence of the coercive force of fine ferromagnetic powders on particle size. Phys Rev 1948, 73: 810–811. 10.1103/PhysRev.73.810View ArticleGoogle Scholar
- Kale A, Gubbala S, Misara RDK: Magnetic behavior of nanocrystalline nickel ferrite synthesized by the reverse micelle technique. J Magn Magn Mater 2004, 3: 350–358.View ArticleGoogle Scholar
- Kim KY, Kim WS, Ju YD, Jung HJ: Effect of addition of the CuO-Fe2O3system on the electromagnetic wave absorbing properties of sintered ferrite. J Mater Sci 1992, 27: 4741–4745. 10.1007/BF01166015View ArticleGoogle Scholar
- Fujimoto M: Inner stress induced by Cu metal precipitation at grain boundaries in low-temperature-fired Ni-Zn-Cu ferrite. J Am Ceram Soc 1994, 77: 2873–2878. 10.1111/j.1151-2916.1994.tb04517.xView ArticleGoogle Scholar
- Qi XW, Zhou J, Yue Z, Gui ZL, Li LT: Effect of Mn substitution on the magnetic properties of MgCuZn ferrites. J Magn Magn Mater 2002, 251: 316–322. 10.1016/S0304-8853(02)00854-5View ArticleGoogle Scholar
- Nakamura T: Snoek's limit in high-frequency permeability of polycrystalline Ni-Zn, Mg-Zn, and Ni-Zn-Cu spinel ferrites. J Appl Phys 2000, 88: 348–353. 10.1063/1.373666View ArticleGoogle Scholar
- Kim WC, Kim SJ, Lee SW, Kim CS: Growth of ultrafine NiZnCu ferrite and magnetic properties by a sol-gel method. J Magn Magn Mater 2001, 226: 1418–1420.View ArticleGoogle Scholar
- Yue ZX, Zhou J, Wang XH, Gui ZL, Lee LT: Low-temperature sintered Mg-Zn-Cu ferrite prepared by auto-combustion of nitrate-citrate gel. J Mater Sci Lett 2001, 20: 1327–1329. 10.1023/A:1010958719771View ArticleGoogle Scholar
- Chakrabarti PK, Nath BK, Brahma S, Das S, Goswami K, Kumar U, Mukhopadhyay PK, Das D, Ammar M, Mnzaleyrat F: Magnetic and hyperfine properties of nanocrystalline Ni0.2Zn0.6Cu0.2Fe2O4prepared by a chemical route. J Phys Conden Mater 2006, 18: 5253–5267. 10.1088/0953-8984/18/22/023View ArticleGoogle Scholar
- Seong KC, Hassan J, Hashim M, Mohd W, Yusoff DW: Synthesis, microstructure and AC electrical conductivity of copper substituted nickel-zinc ferrites. Sol Stat Sci Tech 2006, 1: 134–140.Google Scholar
- Roy PK, Bera J: Effect of Mg substitution on electromagnetic properties of (Ni0.25Cu0.20Zn0.55)Fe2O4ferrite prepared by auto combustion method. J Magn Magn Mater 2006, 298: 38–42. 10.1016/j.jmmm.2005.03.007View ArticleGoogle Scholar
- Jadhav PA, Devan RS, Kolekar YD, Chougule BK: Structural, electrical and magnetic characterizations of Ni-Cu-Zn ferrite synthesized by citrate precursor method. J Phys Chem Sol 2009, 70: 396–400. 10.1016/j.jpcs.2008.11.019View ArticleGoogle Scholar
- Sattar AA: Physical, magnetic and electrical properties of Ga substituted Mn-ferrites. Egptian J Sol 2004, 27: 99–110.Google Scholar
- Scherrer HE, Kisker H, Kronmuller H, Wurschum R: Magnetic properties of nanocrystalline nickel. Nanostruct Mater 1995, 6: 533–538. 10.1016/0965-9773(95)00114-XView ArticleGoogle Scholar
- Chandra P: Effect of aluminum substitution on electrical conductivity and physical properties of zinc ferrite. J Mater Sci Lett 1987, 6: 651–652. 10.1007/BF01770914View ArticleGoogle Scholar
- Elkony D: Study of dielectric and impedance properties of Mn ferrites. Egypt J Sol 2004, 27: 285–296.Google Scholar
- Gabal MA: Non-isothermal decomposition of NiC2O4-FeC2O4mixture aiming at the production of NiFe2O4. J Phys Chem Sol 2003, 64: 1375–1385. 10.1016/S0022-3697(03)00163-XView ArticleGoogle Scholar
- Rana MU, Islam MU, Abbas T: X-ray diffraction and site preference analysis of Ni-substituted MgFe2O4ferrites. Mater Lett 1999, 41: 52–56. 10.1016/S0167-577X(99)00102-0View ArticleGoogle Scholar
- Ahmed MA, Ateia E, Salah LM, El-Gamal AA: Structural and electrical studies on La3+substituted Ni-Zn ferrites. Mater Chem Phys 2005, 92: 310–321. 10.1016/j.matchemphys.2004.05.049View ArticleGoogle Scholar
- Smith J, Wijin HP: Ferrites. London: Cleaver-hume Press; 1959.Google Scholar
- Batoo KM: Study of dielectric and impedance properties of Mn ferrites. Phys B 2001, 406: 382–387.View ArticleGoogle Scholar
- Gabal MA, Al-Angari YM: Effect of chromium ion substitution on the electromagnetic properties of nickel ferrite. Mater Chem Phys 2009, 118: 153–160. 10.1016/j.matchemphys.2009.07.025View ArticleGoogle Scholar
- Farea AMM, Kumar S, Batoo KM, Yousef A, Lee CG, Alimuddin : Structure and electrical properties of Co0.5Cd x Fe2.5-xO4ferrites. J Alloy Compd 2008, 464: 361–369. 10.1016/j.jallcom.2007.09.126View ArticleGoogle Scholar
- Hemeda OA, Said MZ, Barakat MM: Spectral and transport phenomena in Ni ferrite-substituted Gd2O3. J Magn Magn Mater 2001, 224: 132–142. 10.1016/S0304-8853(00)00578-3View ArticleGoogle Scholar
- Lide DR: Handbook of Chemistry and Physics. New York: CRC Press; 1995.Google Scholar
- Kigery WD, Bowen HK, Uhlmann DR: Introduction of Ceramics. New York: John Wiley and Sons; 1975.Google Scholar
- Rezlescu N, Rezlescu E, Pasnicu C, Craus ML: Effect of rare earth ions on some properties of a nickel-zinc ferrite. J Phys Condens Matter 1994, 6: 5707–5716. 10.1088/0953-8984/6/29/013View ArticleGoogle Scholar
- Kakatkar SV, Kakatkar SS, Patil RS, Maskar PK, Sankapal AM, Suryawanshi SS, Chaudhari ND: X-ray and bulk magnetic properties of aluminium substituted ferrites. J Magn Mater 1996, 159: 361–366. 10.1016/0304-8853(95)00946-9View ArticleGoogle Scholar
- Suryawanshi SS, Deshpand V, Sawant SR: XRD analysis and bulk magnetic properties of Al3+substituted Cu-Cd ferrites. J Mater Chem Phys 1999, 59: 199–203. 10.1016/S0254-0584(99)00046-2View ArticleGoogle Scholar
- Manova E, Kunev B, Paneva D, Mitor I, Petrov L, Estournės C, D'orlėans C, Respringer JL, Kurmoo M: Mechanochemical synthesis and magnetic properties of nano-dimensional cobalt ferrite. Chem Mater Phys 2004, 16: 5689–5696. 10.1021/cm049189uView ArticleGoogle Scholar
- Maxwell JC: A Treatise on Electricity & Magnetism. Oxford: Clarendon Press; 1873.Google Scholar
- Wagner KW: Zur Theorie der Unvolkommenen Dielektrika. Ann Phys 1913, 40: 817–855.View ArticleGoogle Scholar
- Koop's CG: On the dispersion of resistivity and dielectric constant of some semiconductors at audio frequencies. Phys Rev 1951, 83: 121–124. 10.1103/PhysRev.83.121View ArticleGoogle Scholar
- Devan RS, Chougule BK: Effect of composition on coupled electric, magnetic, and dielectric properties of two phase particulate magnetoelectric composite. J Appl Phys 2007, 101: 014109. 10.1063/1.2404773View ArticleGoogle Scholar
- Kharabe RG, Devan RS, Kanamadi CM, Chougle BK: Dielectric properties of mixed Li-Ni-Cd ferrites. Smart Mater Struct 2006, 15: 36. 10.1088/0964-1726/15/2/N02View ArticleGoogle Scholar
- Bellad SS, Chougle BK: Composition and frequency dependent dielectric properties of Li-Mg-Ti ferrites. Mater Chem Phys 2000, 66: 58–63. 10.1016/S0254-0584(00)00273-XView ArticleGoogle Scholar
- Vermaa A, Thakur OP, Prakash C, Goel TC, Mendiratta RG: Temperature dependence of electrical properties of nickel-zinc ferrites processed by the citrate precursor technique. Mater Sci Engg B 2005, 116: 1–6. 10.1016/j.mseb.2004.08.011View ArticleGoogle Scholar
- Pollak M (Ed): Proceedings of the International Conference on the Physics of Semiconductors: 1962 July 16–20: Exeter. London: The Institute of Physics and the Physical Society;Google Scholar
- Abo El Ata AM, El Nimra MK, Attia SM, El Kony D, Al-Hammadi AH: Studies of AC electrical conductivity and initial magnetic permeability of rare-earth-substituted Li-Co ferrites. J Magn Magn Mater 2006, 297: 33–43. 10.1016/j.jmmm.2005.01.085View ArticleGoogle Scholar
- Al-Hiti M: AC electrical conductivity of Ni-Mg ferrites. J Phys D Appl Phys 1996, 29: 501–505. 10.1088/0022-3727/29/3/002View ArticleGoogle Scholar
- Batoo KM, Kumar S, Lee CG, Alimuddin : Finite size effect and influence of temperature on electrical properties of nanocrystalline Ni-Cd ferrites. Curr Appl Phys 2009, 9: 1072–1078. 10.1016/j.cap.2008.12.002View ArticleGoogle Scholar
- Balaji S, Selvan RK, Berchmans LJ, Angappan S, Suramanian K, Augustin CO: Combustion synthesis and characterization of Sn4+substituted nanocrystalline NiFe2O4. Mater Sci Eng B 2005, 119: 119–124. 10.1016/j.mseb.2005.01.021View ArticleGoogle Scholar
- Patankar KK, Mathe VL, Patil AN, Patil SA, Lotke SD, Kolekar YD, Joshi PB: Electrical conduction and magnetoelectric effect in CuFe1.8Cr0.2O4-Ba0.8Pb0.2TiO3composites. J Electroceram 2001, 2: 115–122.View ArticleGoogle Scholar
- Farea AMM, Kumar S, Batoo KM, Yousef A, Alimuddin : Influence of frequency, temperature and composition on electrical properties of polycrystalline Co0.5Cd x Fe2.5-xO4ferrites. Phys B 2008, 403: 684–701. 10.1016/j.physb.2007.09.080View ArticleGoogle Scholar
- Batoo KM, Kumar S, Lee CG, Alimuddin : Influence of Al doping on electrical properties of Ni-Cd nano ferrites. Curr Appl Phys 2009, 9: 826–832. 10.1016/j.cap.2008.08.001View ArticleGoogle Scholar
- Baruwati B, KumarRana R, Sunkara S, Manorma V: Further insights in the conductivity behaviour of nanocrysttaline NiFe2O4. J Appl Phys 2007, 101: 014302. 10.1063/1.2404772View ArticleGoogle Scholar
- Inba H: Impedance measurement of single-crystalline and polycrystalline manganese-zinc ferrites with various non-stoichiometries. J Mater Sci 1997, 32: 1867–1872. 10.1023/A:1018561024682View ArticleGoogle Scholar
- Ponpandian N, Balaya P, Narayanasamy A: Electrical conductivity and dielectric behaviour of nanocrystalline NiFe2O4spinel. J Phys Condens Mater 2002, 14: 3221–3237. 10.1088/0953-8984/14/12/311View ArticleGoogle Scholar
- Bauerie JE: Study of solid electrolyte polarization by a complex admittance method. J Phys Chem Solids 1969, 30: 2657–2670. 10.1016/0022-3697(69)90039-0View ArticleGoogle Scholar
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